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+The Project Gutenberg EBook of A Budget of Paradoxes, Volume I (of II), by 
+Augustus De Morgan
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: A Budget of Paradoxes, Volume I (of II)
+
+Author: Augustus De Morgan
+
+Editor: David Eugene Smith
+
+Release Date: October 20, 2007 [EBook #23100]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK A BUDGET OF PARADOXES ***
+
+
+
+
+Produced by David Starner, Keith Edkins and the Online
+Distributed Proofreading Team at http://www.pgdp.net
+
+
+
+
+
+Transcriber's note: A few typographical errors have been corrected: they
+are listed at the end of the text.
+
+       *       *       *       *       *
+
+
+BY AUGUSTUS DE MORGAN
+
+A BUDGET OF
+PARADOXES
+
+REPRINTED WITH THE AUTHOR'S ADDITIONS FROM THE ATHENAEUM
+
+
+
+SECOND EDITION EDITED BY DAVID EUGENE SMITH
+
+WITH A NEW INTRODUCTION BY ERNEST NAGEL
+
+PROFESSOR OF PHILOSOPHY, COLUMBIA UNIVERSITY
+
+UNABRIDGED EDITION--TWO VOLUMES BOUND AS ONE
+
+
+
+Volume I
+
+
+
+DOVER PUBLICATIONS, INC., NEW YORK
+
+       *       *       *       *       *
+
+
+PREFACE TO THE FIRST EDITION.
+
+(1872)
+
+It is not without hesitation that I have taken upon myself the editorship
+of a work left avowedly imperfect by the author, and, from its
+miscellaneous and discursive character, difficult of completion with due
+regard to editorial limitations by a less able hand.
+
+Had the author lived to carry out his purpose he would have looked through
+his Budget again, amplifying and probably rearranging some of its contents.
+He had collected materials for further illustration of Paradox of the kind
+treated of in this book; and he meant to write a second part, in which the
+contradictions and inconsistencies of orthodox learning would have been
+subjected to the same scrutiny and castigation as heterodox ignorance had
+already received.
+
+It will be seen that the present volume contains more than the _Athenæum_
+Budget. Some of the additions formed a Supplement to the original articles.
+These supplementary paragraphs were, by the author, placed after those to
+which they respectively referred, being distinguished from the rest of the
+text by brackets. I have omitted these brackets as useless, except where
+they were needed to indicate subsequent writing.
+
+Another and a larger portion of the work consists of discussion of matters
+of contemporary interest, for the Budget was in some degree a receptacle
+for the author's thoughts on any literary, scientific, or social question.
+Having grown thus gradually to its present size, the book as it was left
+was not quite in a fit condition for publication, but the alterations which
+have been made are slight and few, being in most cases verbal, and such as
+the sense absolutely required, or transpositions of sentences to secure
+coherence with the rest, in places where the author, in his more recent
+insertion of them, had overlooked the connection in which they stood. In no
+case has the meaning been in any degree modified or interfered with.
+
+One rather large omission must be mentioned here. It is an account of the
+quarrel between Sir James South and Mr. Troughton on the mounting, etc. of
+the equatorial telescope at Campden Hill. At some future time when the
+affair has passed entirely out of the memory of living Astronomers, the
+appreciative sketch, which is omitted in this edition of the Budget, will
+be an interesting piece of history and study of character.[1]
+
+A very small portion of Mr. James Smith's circle-squaring has been left
+out, with a still smaller portion of Mr. De Morgan's answers to that
+Cyclometrical Paradoxer.
+
+In more than one place repetitions, which would have disappeared under the
+author's revision, have been allowed to remain, because they could not have
+been taken away without leaving a hiatus, not easy to fill up without
+damage to the author's meaning.
+
+I give these explanations in obedience to the rules laid down for the
+guidance of editors at page 15.[2] If any apology for the fragmentary
+character of the book be thought necessary, it may be found in the author's
+own words at page 281 of the second volume.[3]
+
+The publication of the Budget could not have been delayed without lessening
+the interest attaching to the writer's thoughts upon questions of our own
+day. I trust that, incomplete as the work is compared with what it might
+have been, I shall not be held mistaken in giving it to the world. Rather
+let me hope that it will be welcomed as an old friend returning under great
+disadvantages, but bringing a pleasant remembrance of the amusement which
+its weekly appearance in the _Athenæum_ gave to both writer and reader.
+
+The Paradoxes are dealt with in chronological order. This will be a guide
+to the reader, and with the alphabetical Index of Names, etc., will, I
+trust, obviate all difficulty of reference.
+
+SOPHIA DE MORGAN.
+
+    6 MERTON ROAD, PRIMROSE HILL.
+
+       *       *       *       *       *
+
+
+PREFACE TO THE SECOND EDITION.
+
+If Mrs. De Morgan felt called upon to confess her hesitation at taking upon
+herself the labor of editing these Paradoxes, much more should one who was
+born two generations later, who lives in another land and who was reared
+amid different influences, confess to the same feeling when undertaking to
+revise this curious medley. But when we consider the nature of the work,
+the fact that its present rarity deprives so many readers of the enjoyment
+of its delicious satire, and the further fact that allusions that were
+commonplace a half century ago are now forgotten, it is evident that some
+one should take up the work and perform it _con amore_.
+
+Having long been an admirer of De Morgan, having continued his work in the
+bibliography of early arithmetics, and having worked in his library among
+the books of which he was so fond, it is possible that the present editor,
+whatever may be his other shortcomings, may undertake the labor with as
+much of sympathy as any one who is in a position to perform it. With this
+thought in mind, two definite rules were laid down at the beginning of the
+task: (1) That no alteration in the text should be made, save in slightly
+modernizing spelling and punctuation and in the case of manifest
+typographical errors; (2) That whenever a note appeared it should show at
+once its authorship, to the end that the material of the original edition
+might appear intact.
+
+In considering, however, the unbroken sequence of items that form the
+Budget, it seems clear that readers would be greatly aided if the various
+leading topics were separated in some convenient manner. After considerable
+thought it was decided to insert brief captions from time to time that
+might aid the eye in selecting the larger subjects of the text. In some
+parts of the work these could easily be taken from the original folio
+heads, but usually they had to be written anew. While, therefore, the
+present editor accepts the responsibility for the captions of the various
+subdivisions, he has endeavored to insert them in harmony with the original
+text.
+
+As to the footnotes, the first edition had only a few, some due to De
+Morgan himself and others to Mrs. De Morgan. In the present edition those
+due to the former are signed A. De M., and those due to Mrs. De Morgan
+appear with her initials, S. E. De M. For all other footnotes the present
+editor is responsible. In preparing them the effort has been made to
+elucidate the text by supplying such information as the casual reader might
+wish as he passes over the pages. Hundreds of names are referred to in the
+text that were more or less known in England half a century ago, but are
+now forgotten there and were never familiar elsewhere. Many books that were
+then current have now passed out of memory, and much that agitated England
+in De Morgan's prime seems now like ancient history. Even with respect to
+well-known names, a little information as to dates and publications will
+often be welcome, although the editor recognizes that it will quite as
+often be superfluous. In order, therefore, to derive the pleasure that
+should come from reading the Budget, the reader should have easy access to
+the information that the notes are intended to supply. That they furnish
+too much here and too little there is to be expected. They are a human
+product, and if they fail to serve their purpose in all respects it is
+hoped that this failure will not seriously interfere with the reader's
+pleasure.
+
+In general the present editor has refrained from expressing any opinions
+that would strike a discordant note in the reading of the text as De Morgan
+left it. The temptation is great to add to the discussion at various
+points, but it is a temptation to be resisted. To furnish such information
+as shall make the reading more pleasant, rather than to attempt to improve
+upon one of the most delicious bits of satire of the nineteenth century,
+has been the editor's wish. It would have been an agreeable task to review
+the history of circle squaring, of the trisection problem, and of the
+duplication of the cube. This, however, would be to go too far afield. For
+the benefit of those who wish to investigate the subject the editor can
+only refer to such works and articles as the following: F. Rudio,
+_Archimedes, Huygens, Lambert, Legendre,--mit einer Uebersicht über die
+Geschichte des Problemes von der Quadratur des Zirkels_, Leipsic, 1892;
+Thomas Muir, "Circle," in the eleventh edition of the _Encyclopædia
+Britannica_; the various histories of mathematics; and to his own article
+on "The Incommensurability of [pi]" in Prof. J. W. A. Young's _Monographs
+on Topics of Modern Mathematics_, New York, 1911.
+
+The editor wishes to express his appreciation and thanks to Dr. Paul Carus,
+editor of _The Monist_ and _The Open Court_ for the opportunity of
+undertaking this work; to James Earl Russell, LL.D., Dean of Teachers
+College, Columbia University, for his encouragement in its prosecution; to
+Miss Caroline Eustis Seely for her intelligent and painstaking assistance
+in securing material for the notes; and to Miss Lydia G. Robinson and Miss
+Anna A. Kugler for their aid and helpful suggestions in connection with the
+proof-sheets. Without the generous help of all five this work would have
+been impossible.
+
+DAVID EUGENE SMITH.
+
+    TEACHERS COLLEGE, COLUMBIA UNIVERSITY.
+
+       *       *       *       *       *
+
+
+A BUDGET OF PARADOXES
+
+{1}
+
+INTRODUCTORY.
+
+If I had before me a fly and an elephant, having never seen more than one
+such magnitude of either kind; and if the fly were to endeavor to persuade
+me that he was larger than the elephant, I might by possibility be placed
+in a difficulty. The apparently little creature might use such arguments
+about the effect of distance, and might appeal to such laws of sight and
+hearing as I, if unlearned in those things, might be unable wholly to
+reject. But if there were a thousand flies, all buzzing, to appearance,
+about the great creature; and, to a fly, declaring, each one for himself,
+that he was bigger than the quadruped; and all giving different and
+frequently contradictory reasons; and each one despising and opposing the
+reasons of the others--I should feel quite at my ease. I should certainly
+say, My little friends, the case of each one of you is destroyed by the
+rest. I intend to show flies in the swarm, with a few larger animals, for
+reasons to be given.
+
+In every age of the world there has been an established system, which has
+been opposed from time to time by isolated and dissentient reformers. The
+established system has sometimes fallen, slowly and gradually: it has
+either been upset by the rising influence of some one man, or it has been
+sapped by gradual change of opinion in the many.
+
+I have insisted on the isolated character of the dissentients, as an
+element of the _a priori_ probabilities of the case. Show me a schism,
+especially a growing schism, and it is another thing. The homeopathists,
+for instance, shall be, if any one so think, as wrong as St. John Long; but
+an {2} organized opposition, supported by the efforts of many acting in
+concert, appealing to common arguments and experience, with perpetual
+succession and a common seal, as the Queen says in the charter, is, be the
+merit of the schism what it may, a thing wholly different from the case of
+the isolated opponent in the mode of opposition to it which reason points
+out.
+
+During the last two centuries and a half, physical knowledge has been
+gradually made to rest upon a basis which it had not before. It has become
+_mathematical_. The question now is, not whether this or that hypothesis is
+better or worse to the pure thought, but whether it accords with observed
+phenomena in those consequences which can be shown necessarily to follow
+from it, if it be true. Even in those sciences which are not yet under the
+dominion of mathematics, and perhaps never will be, a working copy of the
+mathematical process has been made. This is not known to the followers of
+those sciences who are not themselves mathematicians and who very often
+exalt their horns against the mathematics in consequence. They might as
+well be squaring the circle, for any sense they show in this particular.
+
+A great many individuals, ever since the rise of the mathematical method,
+have, each for himself, attacked its direct and indirect consequences. I
+shall not here stop to point out how the very accuracy of exact science
+gives better aim than the preceding state of things could give. I shall
+call each of these persons a _paradoxer_, and his system a _paradox_. I use
+the word in the old sense: a paradox is something which is apart from
+general opinion, either in subject-matter, method, or conclusion.
+
+Many of the things brought forward would now be called _crotchets_, which
+is the nearest word we have to old _paradox_. But there is this difference,
+that by calling a thing a _crotchet_ we mean to speak lightly of it; which
+was not the necessary sense of _paradox_. Thus in the sixteenth century
+many spoke of the earth's motion as the _paradox of {3} Copernicus_, who
+held the ingenuity of that theory in very high esteem, and some, I think,
+who even inclined towards it. In the seventeenth century, the depravation
+of meaning took place, in England at least. Phillips says _paradox_ is "a
+thing which seemeth strange"--here is the old meaning: after a colon he
+proceeds--"and absurd, and is contrary to common opinion," which is an
+addition due to his own time.
+
+Some of my readers are hardly inclined to think that the word _paradox_
+could once have had no disparagement in its meaning; still less that
+persons could have applied it to themselves. I chance to have met with a
+case in point against them. It is Spinoza's _Philosophia Scripturæ
+Interpres, Exercitatio Paradoxa_, printed anonymously at Eleutheropolis, in
+1666. This place was one of several cities in the clouds, to which the
+cuckoos resorted who were driven away by the other birds; that is, a
+feigned place of printing, adopted by those who would have caught it if
+orthodoxy could have caught them. Thus, in 1656, the works of Socinus could
+only be printed at Irenopolis. The author deserves his self-imposed title,
+as in the following:[4]
+
+"Quanto sane satius fuisset illam [Trinitatem] pro mysterio non habuisse,
+et Philosophiæ ope, antequam quod esset statuerent, secundum veræ logices
+præcepta quid esset cum Cl. Kleckermanno investigasse; tanto fervore ac
+labore in profundissimas speluncas et obscurissimos metaphysicarum
+speculationum atque fictionum recessus se recipere ut ab adversariorum
+telis sententiam suam in tuto collocarent. {4} Profecto magnus ille vir ...
+dogma illud, quamvis apud theologos eo nomine non multum gratiæ iniverit,
+ita ex immotis Philosophiæ fundamentis explicat ac demonstrat, ut paucis
+tantum immutatis, atque additis, nihil amplius animus veritate sincere
+deditus desiderare possit."
+
+This is properly paradox, though also heterodox. It supposes, contrary to
+all opinion, orthodox and heterodox, that philosophy can, with slight
+changes, explain the Athanasian doctrine so as to be at least compatible
+with orthodoxy. The author would stand almost alone, if not quite; and this
+is what he meant. I have met with the counter-paradox. I have heard it
+maintained that the doctrine as it stands, in all its mystery is _a priori_
+more likely than any other to have been Revelation, if such a thing were to
+be; and that it might almost have been predicted.
+
+After looking into books of paradoxes for more than thirty years, and
+holding conversation with many persons who have written them, and many who
+might have done so, there is one point on which my mind is fully made up.
+The manner in which a paradoxer will show himself, as to sense or nonsense,
+will not depend upon what he maintains, but upon whether he has or has not
+made a sufficient knowledge of what has been done by others, _especially as
+to the mode of doing it_, a preliminary to inventing knowledge for himself.
+That a little knowledge is a dangerous thing is one of the most fallacious
+of proverbs. A person of small knowledge is in danger of trying to make his
+_little_ do the work of _more_; but a person without any is in more danger
+of making his _no_ knowledge do the work of _some_. Take the speculations
+on the tides as an instance. Persons with nothing but a little geometry
+have certainly exposed themselves in their modes of objecting to results
+which require the higher mathematics to be known before an independent
+opinion can be formed on sufficient grounds. But persons with no geometry
+at all have done the same thing much more completely. {5}
+
+There is a line to be drawn which is constantly put aside in the arguments
+held by paradoxers in favor of their right to instruct the world. Most
+persons must, or at least will, like the lady in Cadogan Place,[5] form and
+express an immense variety of opinions on an immense variety of subjects;
+and all persons must be their own guides in many things. So far all is
+well. But there are many who, in carrying the expression of their own
+opinions beyond the usual tone of private conversation, whether they go no
+further than attempts at oral proselytism, or whether they commit
+themselves to the press, do not reflect that they have ceased to stand upon
+the ground on which their process is defensible. Aspiring to lead _others_,
+they have never given themselves the fair chance of being first led by
+_other_ others into something better than they can start for themselves;
+and that they should first do this is what both those classes of others
+have a fair right to expect. New knowledge, when to any purpose, must come
+by contemplation of old knowledge in every matter which concerns thought;
+mechanical contrivance sometimes, not very often, escapes this rule. All
+the men who are now called discoverers, in every matter ruled by thought,
+have been men versed in the minds of their predecessors, and learned in
+what had been before them. There is not one exception. I do not say that
+every man has made direct acquaintance with the whole of his mental
+ancestry; many have, as I may say, only known their grandfathers by the
+report of their fathers. But even on this point it is remarkable how many
+of the greatest names in all departments of knowledge have been real
+antiquaries in their several subjects.
+
+I may cite, among those who have wrought strongly upon opinion or practice
+in science, Aristotle, Plato, Ptolemy, Euclid, Archimedes, Roger Bacon,
+Copernicus, Francis Bacon, Ramus, Tycho Brahé, Galileo, Napier, Descartes,
+Leibnitz, Newton, Locke. I take none but names known out of their {6}
+fields of work; and all were learned as well as sagacious. I have chosen my
+instances: if any one will undertake to show a person of little or no
+knowledge who has established himself in a great matter of pure thought,
+let him bring forward his man, and we shall see.
+
+This is the true way of putting off those who plague others with their
+great discoveries. The first demand made should be--Mr. Moses, before I
+allow you to lead me over the Red Sea, I must have you show that you are
+learned in all the wisdom of the Egyptians upon your own subject. The plea
+that it is unlikely that this or that unknown person should succeed where
+Newton, etc. have failed, or should show Newton, etc. to be wrong, is
+utterly null and void. It was worthily versified by Sylvanus Morgan (the
+great herald who in his _Sphere of Gentry_ gave coat armor to "Gentleman
+Jesus," as he said), who sang of Copernicus as follows (1652):
+
+ "If Tellus winged be,
+  The earth a motion round;
+  Then much deceived are they
+  Who nere before it found.
+  Solomon was the wisest,
+  His wit nere this attained;
+  Cease, then, Copernicus,
+  Thy hypothesis is vain."
+
+Newton, etc. were once unknown; but they made themselves known by what they
+knew, and then brought forward what they could do; which I see is as good
+verse as that of Herald Sylvanus. The demand for previous knowledge
+disposes of twenty-nine cases out of thirty, and the thirtieth is worth
+listening to.
+
+I have not set down Copernicus, Galileo, etc. among the paradoxers, merely
+because everybody knows them; if my list were quite complete, they would
+have been in it. But the reader will find Gilbert, the great precursor of
+sound magnetical theory; and several others on whom no censure can be cast,
+though some of their paradoxes are inadmissible, {7} some unprovoked, and
+some capital jokes, true or false: the author of _Vestiges of Creation_ is
+an instance. I expect that my old correspondent, General Perronet Thompson,
+will admit that his geometry is part and parcel of my plan; and also that,
+if that plan embraced politics, he would claim a place for his _Catechism
+on the Corn Laws_, a work at one time paradoxical, but which had more to do
+with the abolition of the bread-tax than Sir Robert Peel.
+
+My intention in publishing this Budget in the _Athenæum_ is _to enable
+those who have been puzzled by one or two discoverers to see how they look
+in a lump_. The only question is, has the selection been fairly made? To
+this my answer is, that no selection at all has been made. The books are,
+without exception, those which I have in my own library; and I have taken
+_all_--I mean all of the kind: Heaven forbid that I should be supposed to
+have no other books! But I may have been a collector, influenced in choice
+by bias? I answer that I never have collected books of this sort--that is,
+I have never searched for them, never made up my mind to look out for this
+book or that. I have bought what happened to come in my way at show or
+auction; I have retained what came in as part of the _undescribed_ portion
+of miscellaneous auction lots; I have received a few from friends who found
+them among what they called their rubbish; and I have preserved books sent
+to me for review. In not a few instances the books have been bound up with
+others, unmentioned at the back; and for years I knew no more I had them
+than I knew I had Lord Macclesfield's speech on moving the change of Style,
+which, after I had searched shops, etc. for it in vain, I found had been
+reposing on my own shelves for many years, at the end of a summary of
+Leibnitz's philosophy. Consequently, I may positively affirm that the
+following list is formed by accident and circumstance alone, and that it
+truly represents the casualties of about a third of a century. For
+instance, the large proportion of works {8} on the quadrature of the circle
+is not my doing: it is the natural share of this subject in the actual run
+of events.
+
+[I keep to my plan of inserting only such books as I possessed in 1863,
+except by casual notice in aid of my remarks. I have found several books on
+my shelves which ought to have been inserted. These have their titles set
+out at the commencement of their articles, in leading paragraphs; the
+casuals are without this formality.[6]]
+
+Before proceeding to open the Budget, I say something on my personal
+knowledge of the class of discoverers who square the circle, upset Newton,
+etc. I suspect I know more of the English class than any man in Britain. I
+never kept any reckoning; but I know that one year with another--and less
+of late years than in earlier time--I have talked to more than five in each
+year, giving more than a hundred and fifty specimens. Of this I am sure,
+that it is my own fault if they have not been a thousand. Nobody knows how
+they swarm, except those to whom they naturally resort. They are in all
+ranks and occupations, of all ages and characters. They are very earnest
+people, and their purpose is _bona fide_ the dissemination of their
+paradoxes. A great many--the mass, indeed--are illiterate, and a great many
+waste their means, and are in or approaching penury. But I must say that
+never, in any one instance, has the quadrature of the circle, or the like,
+been made a pretext for begging; even to be asked to purchase a book is of
+the very rarest occurrence--it has happened, and that is all.
+
+These discoverers despise one another: if there were the concert among them
+which there is among foreign mendicants, a man who admitted one to a
+conference would be plagued to death. I once gave something to a very
+genteel French applicant, who overtook me in the street, at my own door,
+saying he had picked up my handkerchief: whether he picked it up in my
+pocket for an introduction, I know not. {9} But that day week came another
+Frenchman to my house, and that day fortnight a French lady; both failed,
+and I had no more trouble. The same thing happened with Poles. It is not so
+with circle-squarers, etc.: they know nothing of each other. Some will read
+this list, and will say I am right enough, generally speaking, but that
+there _is_ an exception, if I could but see it.
+
+I do not mean, by my confession of the manner in which I have sinned
+against the twenty-four hours, to hold myself out as accessible to personal
+explanation of new plans. Quite the contrary: I consider myself as having
+made my report, and being discharged from further attendance on the
+subject. I will not, from henceforward, talk to any squarer of the circle,
+trisector of the angle, duplicator of the cube, constructor of perpetual
+motion, subverter of gravitation, stagnator of the earth, builder of the
+universe, etc. I will receive any writings or books which require no
+answer, and read them when I please: I will certainly preserve them--this
+list may be enlarged at some future time.
+
+There are three subjects which I have hardly anything upon; astrology,
+mechanism, and the infallible way of winning at play. I have never cared to
+preserve astrology. The mechanists make models, and not books. The
+infallible winners--though I have seen a few--think their secret too
+valuable, and prefer _mutare quadrata rotundis_--to turn dice into coin--at
+the gaming-house: verily they have their reward.
+
+I shall now select, to the mystic number seven, instances of my personal
+knowledge of those who think they have discovered, in illustration of as
+many misconceptions.
+
+1. _Attempt by help of the old philosophy, the discoverer not being in
+possession of modern knowledge._ A poor schoolmaster, in rags, introduced
+himself to a scientific friend with whom I was talking, and announced that
+he had found out the composition of the sun. "How was that done?"--"By
+consideration of the four elements."--"What are {10} they?"--"Of course,
+fire, air, earth, and water."--"Did you not know that air, earth, and
+water, have long been known to be no elements at all, but
+compounds?"--"What do you mean, sir? Who ever heard of such a thing?"
+
+2. _The notion that difficulties are enigmas, to be overcome in a moment by
+a lucky thought._ A nobleman of very high rank, now long dead, read an
+article by me on the quadrature, in an early number of the _Penny
+Magazine_. He had, I suppose, school recollections of geometry. He put
+pencil to paper, drew a circle, and constructed what seemed likely to
+answer, and, indeed, was--as he said--certain, if only this bit were equal
+to that; which of course it was not. He forwarded his diagram to the
+Secretary of the Diffusion Society, to be handed to the author of the
+article, in case the difficulty should happen to be therein overcome.
+
+3. _Discovery at all hazards, to get on in the world._ Thirty years ago, an
+officer of rank, just come from foreign service, and trying for a
+decoration from the Crown, found that his claims were of doubtful amount,
+and was told by a friend that so and so, who had got the order, had the
+additional claim of scientific distinction. Now this officer, while abroad,
+had bethought himself one day, that there really could be no difficulty in
+finding the circumference of a circle: if a circle were rolled upon a
+straight line until the undermost point came undermost again, there would
+be the straight line equal to the circle. He came to me, saying that he did
+not feel equal to the statement of his claim in this respect, but that if
+some clever fellow would put the thing in a proper light, he thought his
+affair might be managed. I was clever enough to put the thing in a proper
+light to himself, to this extent at least, that, though perhaps they were
+wrong, the advisers of the Crown would never put the letters K.C.B. to such
+a circle as his.
+
+4. _The notion that mathematicians cannot find the circle for common
+purposes._ A working man measured the altitude of a cylinder accurately,
+and--I think the process of {11} Archimedes was one of his
+proceedings--found its bulk. He then calculated the ratio of the
+circumference to the diameter, and found it answered very well on other
+modes of trial. His result was about 3.14. He came to London, and somebody
+sent him to me. Like many others of his pursuit, he seemed to have turned
+the whole force of his mind upon one of his points, on which alone he would
+be open to refutation. He had read some of Kater's experiments, and had got
+the Act of 1825 on weights and measures. Say what I would, he had for a
+long time but one answer--"Sir! I go upon Captain Kater and the Act of
+Parliament." But I fixed him at last. I happened to have on the table a
+proof-sheet of the _Astronomical Memoirs_, in which were a large number of
+observed places of the planets compared with prediction, and asked him
+whether it could be possible that persons who did not know the circle
+better than he had found it could make the calculations, of which I gave
+him a notion, so accurately? He was perfectly astonished, and took the
+titles of some books which he said he would read.
+
+5. _Application for the reward from abroad._ Many years ago, about
+twenty-eight, I think, a Jesuit came from South America, with a quadrature,
+and a cutting from a newspaper announcing that a reward was ready for the
+discovery in England. On this evidence he came over. After satisfying him
+that nothing had ever been offered here, I discussed his quadrature, which
+was of no use. I succeeded better when I told him of Richard White, also a
+Jesuit, and author of a quadrature published before 1648, under the name of
+_Chrysæspis_, of which I can give no account, having never seen it. This
+White (_Albius_) is the only quadrator who was ever convinced of his error.
+My Jesuit was struck by the instance, and promised to read more
+geometry--he was no Clavius--before he published his book. He relapsed,
+however, for I saw his book advertised in a few days. I may say, as
+sufficient proof of my being no collector, that I had not the curiosity to
+buy his book; and my friend the {12} Jesuit did not send me a copy, which
+he ought to have done, after the hour I had given him.
+
+6. _Application for the reward at home._ An agricultural laborer squared
+the circle, and brought the proceeds to London. He left his papers with me,
+one of which was the copy of a letter to the Lord Chancellor, desiring his
+Lordship to hand over forthwith 100,000 pounds, the amount of the alleged
+offer of reward. He did not go quite so far as M. de Vausenville, who, I
+think in 1778, brought an action against the Academy of Sciences to recover
+a reward to which he held himself entitled. I returned the papers, with a
+note, stating that he had not the knowledge requisite to see in what the
+problem consisted. I got for answer a letter in which I was told that a
+person who could not see that he had done the thing should "change his
+business, and appropriate his time and attention to a Sunday-school, to
+learn what he could, and keep the _litle_ children from _durting_ their
+_close_." I also received a letter from a friend of the quadrator,
+informing me that I knew his friend had succeeded, and had been heard to
+say so. These letters were printed--without the names of the writers--for
+the amusement of the readers of _Notes and Queries_, First Series, xii. 57,
+and they will appear again in the sequel.
+
+[There are many who have such a deep respect for any attempt at thought
+that they are shocked at ridicule even of those who have made themselves
+conspicuous by pretending to lead the world in matters which they have not
+studied. Among my anonyms is a gentleman who is angry at my treatment of
+the "poor but thoughtful" man who is described in my introduction as
+recommending me to go to a Sunday-school because I informed him that he did
+not know in what the difficulty of quadrature consisted. My impugner quite
+forgets that this man's "thoughtfulness" chiefly consisted in his demanding
+a hundred thousand pounds from the Lord Chancellor for his discovery; and I
+may add, that his greatest stretch of invention was finding out that "the
+clergy" {13} were the means of his modest request being unnoticed. I
+mention this letter because it affords occasion to note a very common
+error, namely, that men unread in their subjects have, by natural wisdom,
+been great benefactors of mankind. My critic says, "Shakspeare, whom the
+Pro^r (_sic_) may admit to be a wisish man, though an object of contempt as
+to learning ..." Shakespeare an object of contempt as to learning! Though
+not myself a thoroughgoing Shakespearean--and adopting the first half of
+the opinion given by George III, "What! is there not sad stuff? only one
+must not say so"--I am strongly of opinion that he throws out the masonic
+signs of learning in almost every scene, to all who know what they are. And
+this over and above every kind of direct evidence. First, foremost, and
+enough, the evidence of Ben Jonson that he had "little Latin and less
+Greek"; then Shakespeare had as much Greek as Jonson would call _some_,
+even when he was depreciating. To have any Greek at all was in those days
+exceptional. In Shakespeare's youth St. Paul's and Merchant Taylor's
+schools were to have masters learned in good and clean Latin literature,
+_and also in Greek if such may be gotten_. When Jonson spoke as above, he
+intended to put Shakespeare low among the learned, but not out of their
+pale; and he spoke as a rival dramatist, who was proud of his own learned
+sock; and it may be a subject of inquiry how much Latin _he_ would call
+_little_. If Shakespeare's learning on certain points be very much less
+visible than Jonson's, it is partly because Shakespeare's writings hold it
+in chemical combination, Jonson's in mechanical aggregation.]
+
+7. An elderly man came to me to show me how the universe was created. There
+was one molecule, which by vibration became--Heaven knows how!--the Sun.
+Further vibration produced Mercury, and so on. I suspect the nebular
+hypothesis had got into the poor man's head by reading, in some singular
+mixture with what it found there. Some modifications of vibration gave
+heat, electricity, etc. I {14} listened until my informant ceased to
+vibrate--which is always the shortest way--and then said, "Our knowledge of
+elastic fluids is imperfect." "Sir!" said he, "I see you perceive the truth
+of what I have said, and I will reward your attention by telling you what I
+seldom disclose, never, except to those who can receive my theory--the
+little molecule whose vibrations have given rise to our solar system is the
+Logos of St. John's Gospel!" He went away to Dr. Lardner, who would not go
+into the solar system at all--the first molecule settled the question. So
+hard upon poor discoverers are men of science who are not antiquaries in
+their subject! On leaving, he said, "Sir, Mr. De Morgan received me in a
+very different way! he heard me attentively, and I left him perfectly
+satisfied of the truth of my system." I have had much reason to think that
+many discoverers, of all classes, believe they have convinced every one who
+is not peremptory to the verge of incivility.
+
+My list is given in chronological order. My readers will understand that my
+general expressions, where slighting or contemptuous, refer to the
+ignorant, who teach before they have learned. In every instance, those of
+whom I am able to speak with respect, whether as right or wrong, have
+sought knowledge in the subject they were to handle before they completed
+their speculations. I shall further illustrate this at the conclusion of my
+list.
+
+Before I begin the list, I give prominence to the following letter,
+addressed by me to the _Correspondent_ of October 28, 1865. Some of my
+paradoxers attribute to me articles in this or that journal; and others may
+think--I know some do think--they know me as the writer of reviews of some
+of the very books noticed here. The following remarks will explain the way
+in which they may be right, and in which they may be wrong. {15}
+
+       *       *       *       *       *
+
+THE EDITORIAL SYSTEM.
+
+"Sir,--I have reason to think that many persons have a very inaccurate
+notion of the _Editorial System_. What I call by this name has grown up in
+the last _centenary_--a word I may use to signify the hundred years now
+ending, and to avoid the ambiguity of _century_. It cannot conveniently be
+explained by editors themselves, and _edited_ journals generally do not
+like to say much about it. In _your_ paper perhaps, in which editorial
+duties differ somewhat from those of ordinary journals, the common system
+may be freely spoken of.
+
+"When a reviewed author, as very often happens, writes to the editor of the
+reviewing journal to complain of what has been said of him, he
+frequently--even more often than not--complains of 'your reviewer.' He
+sometimes presumes that 'you' have, 'through inadvertence' in this
+instance, 'allowed some incompetent person to lower the character of your
+usually accurate pages.' Sometimes he talks of 'your scribe,' and, in
+extreme cases, even of 'your hack.' All this shows perfect ignorance of the
+journal system, except where it is done under the notion of letting the
+editor down easy. But the editor never accepts the mercy.
+
+"All that is in a journal, except what is marked as from a correspondent,
+either by the editor himself or by the correspondent's real or fictitious
+signature, is published entirely on editorial responsibility, as much as if
+the editor had written it himself. The editor, therefore, may claim, and
+does claim and exercise, unlimited right of omission, addition, and
+alteration. This is so well understood that the editor performs his last
+function on the last revise without the 'contributor' knowing what is done.
+The word _contributor_ is the proper one; it implies that he furnishes
+materials without stating what he furnishes or how much of it is accepted,
+or whether he be the only contributor. All this applies both to political
+and literary journals. No editor acknowledges {16} the right of a
+contributor to withdraw an article, if he should find alterations in the
+proof sent to him for correction which would make him wish that the article
+should not appear. If the _demand_ for suppression were made--I say nothing
+about what might be granted to _request_--the answer would be, 'It is not
+your article, but mine; I have all the responsibility; if it should contain
+a libel, I could not give you up, even at your own desire. You have
+furnished me with materials, on the known and common understanding that I
+was to use them at my discretion, and you have no right to impede my
+operations by making the appearance of the article depend on your
+approbation of my use of your materials.'
+
+"There is something to be said for this system, and something against it--I
+mean simply on its own merits. But the all-conquering argument in its favor
+is, that the only practicable alternative is the modern French plan of no
+articles without the signature of the writers. I need not discuss this
+plan; there is no collective party in favor of it. Some may think it is not
+the only alternative; they have not produced any intermediate proposal in
+which any dozen of persons have concurred. Many will say, Is not all this,
+though perfectly correct, well known to be matter of form? Is it not
+practically the course of events that an engaged contributor writes the
+article, and sends it to the editor, who admits it as
+written--substantially, at least? And is it not often very well known, by
+style and in other ways, who it was wrote the article? This system is
+matter of form just as much as loaded pistols are matter of form so long as
+the wearer is not assailed; but matter of form takes the form of matter in
+the pulling of a trigger, so soon as the need arises. Editors and
+contributors who can work together find each other out by elective
+affinity, so that the common run of events settles down into most articles
+appearing much as they are written. And there are two safety-valves; that
+is, when judicious persons come together. In the first place, the editor
+himself, when he has selected his contributor, feels that {17} the
+contributor is likely to know his business better than an editor can teach
+him; in fact, it is on that principle that the selection is made. But he
+feels that he is more competent than the writer to judge questions of
+strength and of tone, especially when the general purpose of the journal is
+considered, of which the editor is the judge without appeal. An editor who
+meddles with substantive matter is likely to be wrong, even when he knows
+the subject; but one who prunes what he deems excess, is likely to be
+right, even when he does not know the subject. In the second place, a
+contributor knows that he is supplying an editor, and learns, without
+suppressing truth or suggesting falsehood, to make the tone of his
+communications suit the periodical in which they are to appear. Hence it
+very often arises that a reviewed author, who thinks he knows the name of
+his reviewer, and proclaims it with expressions of dissatisfaction, is only
+wrong in supposing that his critic has given all his mind. It has happened
+to myself more than once, to be announced as the author of articles which I
+could not have signed, because they did not go far enough to warrant my
+affixing my name to them as to a sufficient expression of my own opinion.
+
+"There are two other ways in which a reviewed author may be wrong about his
+critic. An editor frequently makes slight insertions or omissions--I mean
+slight in quantity of type--as he goes over the last proof; this he does in
+a comparative hurry, and it may chance that he does not know the full sting
+of his little alteration. The very bit which the writer of the book most
+complains of may not have been seen by the person who is called the writer
+of the article until after the appearance of the journal; nay, if he be one
+of those--few, I daresay--who do not read their own articles, may never
+have been seen by him at all. Possibly, the insertion or omission would not
+have been made if the editor could have had one minute's conversation with
+his contributor. Sometimes it actually contradicts something which is {18}
+allowed to remain in another part of the article; and sometimes, especially
+in the case of omission, it renders other parts of the article
+unintelligible. These are disadvantages of the system, and a judicious
+editor is not very free with his _unus et alter pannus_. Next, readers in
+general, when they see the pages of a journal with the articles so nicely
+fitting, and so many ending with the page or column, have very little
+notion of the cutting and carving which goes to the process. At the very
+last moment arises the necessity of some trimming of this kind; and the
+editor, who would gladly call the writer to counsel if he could, is obliged
+to strike out ten or twelve lines. He must do his best, but it may chance
+that the omission selected would take from the writer the power of owning
+the article. A few years ago, an able opponent of mine wrote to a journal
+some criticisms upon an article which he expressly attributed to me. I
+replied as if I were the writer, which, in a sense, I was. But if any one
+had required of me an unmodified 'Yes' or 'No' to the question whether I
+wrote the article, I must, of two falsehoods, have chosen 'No': for certain
+omissions, dictated by the necessities of space and time, would have
+amounted, had my signature been affixed, to a silent surrender of points
+which, in my own character, I must have strongly insisted on, unless I had
+chosen to admit certain inferences against what I had previously published
+in my own name. I may here add that the forms of journalism obliged me in
+this case to remind my opponent that it could not be permitted to me, _in
+that journal_, either to acknowledge or deny the authorship of the
+articles. The cautions derived from the above remarks are particularly
+wanted with reference to the editorial comments upon letters of complaint.
+There is often no time to send these letters to the contributor, and even
+when this can be done, an editor is--and very properly--never of so
+editorial a mind as when he is revising the comments of a contributor upon
+an assailant of the article. He is then in a better position as to
+information, and a more {19} critical position as to responsibility. Of
+course, an editor never meddles, except under notice, with the letter of a
+correspondent, whether of a complainant, of a casual informant, or of a
+contributor who sees reason to become a correspondent. Omissions must
+sometimes be made when a grievance is too highly spiced. It did once happen
+to me that a waggish editor made an insertion without notice in a letter
+signed by me with some fiction, which insertion contained the name of a
+friend of mine, with a satire which I did not believe, and should not have
+written if I had. To my strong rebuke, he replied--'I know it was very
+wrong; but human nature could not resist.' But this was the only occasion
+on which such a thing ever happened to me.
+
+"I daresay what I have written may give some of your readers to understand
+some of the _pericula et commoda_ of modern journalism. I have known men of
+deep learning and science as ignorant of the prevailing system as any
+uneducated reader of a newspaper in a country town. I may perhaps induce
+some writers not to be too sure about this, that, or the other person. They
+may detect their reviewer, and they may be safe in attributing to him the
+general matter and tone of the article. But about one and another point,
+especially if it be a short and stinging point, they may very easily chance
+to be wrong. It has happened to myself, and within a few weeks to
+publication, to be wrong in two ways in reading a past article--to
+attribute to editorial insertion what was really my own, and to attribute
+to myself what was really editorial insertion."
+
+
+
+What is a man to do who is asked whether he wrote an article? He may, of
+course, refuse to answer; which is regarded as an admission. He may say, as
+Swift did to Serjeant Bettesworth, "Sir, when I was a young man, a friend
+of mine advised me, whenever I was asked whether I had written a certain
+paper, to deny it; and I accordingly tell that I did _not_ write it." He
+may say, as I often do, {20} when charged with having invented a joke,
+story, or epigram, "I want all the credit I can get, and therefore I always
+acknowledge all that is attributed to me, truly or not; the story, etc.
+_is_ mine." But for serious earnest, in the matter of imputed criticism,
+the answer may be, "The article was of my material, but the editor has not
+let it stand as I gave it; I cannot own it as a whole." He may then refuse
+to be particular as to the amount of the editor's interference. Of this
+there are two extreme cases. The editor may have expunged nothing but a
+qualifying adverb. Or he may have done as follows. We all remember the
+account of Adam which satirizes woman, but eulogizes her if every second
+and third line be transposed. As in:
+
+ "Adam could find no solid peace
+    When Eve was given him for a mate,
+  Till he beheld a woman's face,
+    Adam was in a happy state."
+
+If this had been the article, and a gallant editor had made the
+transpositions, the author could not with truth acknowledge. If the
+alteration were only an omitted adverb, or a few things of the sort, the
+author could not with truth deny. In all that comes between, every man must
+be his own casuist. I stared, when I was a boy, to hear grave persons
+approve of Sir Walter Scott's downright denial that he was the author of
+Waverley, in answer to the Prince Regent's downright question. If I
+remember rightly, Samuel Johnson would have approved of the same course.
+
+It is known that, whatever the law gives, it also gives all that is
+necessary to full possession; thus a man whose land is environed by land of
+others has a right of way over the land of these others. By analogy, it is
+argued that when a man has a right to his secret, he has a right to all
+that is necessary to keep it, and that is not unlawful. If, then, he can
+only keep his secret by denial, he has a right to denial. This I admit to
+be an answer against all men except the denier himself; if conscience and
+self-respect will allow {21} it, no one can impeach it. But the question
+cannot be solved on a case. That question is, A lie, is it _malum in se_,
+without reference to meaning and circumstances? This is a question with two
+sides to it. Cases may be invented in which a lie is the only way of
+preventing a murder, or in which a lie may otherwise save a life. In these
+cases it is difficult to acquit, and almost impossible to blame; discretion
+introduced, the line becomes very hard to draw.
+
+I know but one work which has precisely--as at first appears--the character
+and object of my Budget. It is the _Review of the Works of the Royal
+Society of London_, by Sir John Hill, M.D. (1751 and 1780, 4to.). This man
+offended many: the Royal Society, by his work, the medical profession, by
+inventing and selling extra-pharmacopoeian doses; Garrick, by resenting the
+rejection of a play. So Garrick wrote:
+
+ "For physic and farces his equal there scarce is;
+  His farces are physic; his physic a farce is."
+
+I have fired at the Royal Society and at the medical profession, but I have
+given a wide berth to the drama and its wits; so there is no epigram out
+against me, as yet. He was very able and very eccentric. Dr. Thomson
+(_Hist. Roy. Soc._) says he has no humor, but Dr. Thomson was a man who
+never would have discovered humor.
+
+Mr. Weld (_Hist. Roy. Soc._) backs Dr. Thomson, but with a remarkable
+addition. Having followed his predecessor in observing that the
+_Transactions_ in Martin Folkes's time have an unusual proportion of
+trifling and puerile papers, he says that Hill's book is a poor attempt at
+humor, and glaringly exhibits the feelings of a disappointed man. It is
+probable, he adds, that the points told with some effect on the Society;
+for shortly after its publication the _Transactions_ possess a much higher
+scientific value.
+
+I copy an account which I gave elsewhere.
+
+When the Royal Society was founded, the Fellows set {22} to work to prove
+all things, that they might hold fast that which was good. They bent
+themselves to the question whether sprats were young herrings. They made a
+circle of the powder of a unicorn's horn, and set a spider in the middle of
+it; "but it immediately ran out." They tried several times, and the spider
+"once made some stay in the powder." They inquired into Kenelm Digby's
+sympathetic powder. "Magnetic cures being discoursed of, Sir Gilbert Talbot
+promised to communicate what he knew of sympathetical cures; and those
+members who had any of the powder of sympathy, were desired to bring some
+of it at the next meeting."
+
+June 21, 1661, certain gentlemen were appointed "curators of the proposal
+of tormenting a man with the sympathetic powder"; I cannot find any record
+of the result. And so they went on until the time of Sir John Hill's
+satire, in 1751. This once well-known work is, in my judgment, the greatest
+compliment the Royal Society ever received. It brought forward a number of
+what are now feeble and childish researches in the Philosophical
+Transactions. It showed that the inquirers had actually been inquiring; and
+that they did not pronounce decision about "natural _knowledge_" by help of
+"_natural_ knowledge." But for this, Hill would neither have known what to
+assail, nor how. Matters are now entirely changed. The scientific bodies
+are far too well established to risk themselves. _Ibit qui zonam perdidit:_
+
+    "Let him take castles who has ne'er a groat."
+
+These great institutions are now without any collective purpose, except
+that of promoting individual energy; they print for their contributors, and
+guard themselves by a general declaration that they will not be answerable
+for the things they print. Of course they will not put forward anything for
+everybody; but a writer of a certain reputation, or matter of a certain
+look of plausibility and safety, {23} will find admission. This is as it
+should be; the pasturer of flocks and herds and the hunters of wild beasts
+are two very different bodies, with very different policies. The scientific
+academies are what a spiritualist might call "publishing mediums," and
+_their_ spirits fall occasionally into writing which looks as if minds in
+the higher state were not always impervious to nonsense.
+
+The following joke is attributed to Sir John Hill. I cannot honestly say I
+believe it; but it shows that his contemporaries did not believe he had no
+humor. Good stories are always in some sort of keeping with the characters
+on which they are fastened. Sir John Hill contrived a communication to the
+Royal Society from Portsmouth, to the effect that a sailor had broken his
+leg in a fall from the mast-head; that bandages and a plentiful application
+of tarwater had made him, in three days, able to use his leg as well as
+ever. While this communication was under grave discussion--it must be
+remembered that many then thought tarwater had extraordinary remedial
+properties--the joker contrived that a second letter should be delivered,
+which stated that the writer had forgotten, in his previous communication,
+to mention that the leg was a wooden leg! Horace Walpole told this story, I
+suppose for the first time; he is good authority for the fact of
+circulation, but for nothing more.
+
+Sir John Hill's book is droll and cutting satire. Dr. Maty, (Sec. Royal
+Society) wrote thus of it in the _Journal Britannique_ (Feb. 1751), of
+which he was editor:
+
+"Il est fâcheux que cet ingénieux Naturaliste, qui nous a déjà donné et qui
+nous prépare encore des ouvrages plus utiles, emploie à cette odieuse tâche
+une plume qu'il trempe dans le fiel et dans l'absinthe. Il est vrai que
+plusieurs de ses remarques sont fondées, et qu'à l'erreur qu'il indique, il
+joint en même tems la correction. Mais il n'est pas toujours équitable, et
+ne manque jamais d'insulter. Que peut {24} après tout prouver son livre, si
+ce n'est que la quarante-cinquième partie d'un très-ample et très-utile
+Recueil n'est pas exempte d'erreurs? Devoit-il confondre avec des Ecrivains
+superficiels, dont la Liberté du Corps ne permet pas de restreindre la
+fertilité, cette foule de savans du Premier ordre, dont les Ecrits ont orné
+et ornent encore les Transactions? A-t-il oublié qu'on y a vu fréquemment
+les noms des Boyle, des Newton, des Halley, des De Moivres, des Hans
+Sloane, etc.? Et qu'on y trouve encore ceux des Ward, des Bradley, des
+Graham, des Ellicot, des Watson, et d'un Auteur que Mr. Hill préfère à tous
+les autres, je veux dire de Mr. Hill lui-même?"[7]
+
+This was the only answer; but it was no answer at all. Hill's object was to
+expose the absurdities; he therefore collected the absurdities. I feel sure
+that Hill was a benefactor of the Royal Society; and much more than he
+would have been if he had softened their errors and enhanced their praises.
+No reviewer will object to me that I have omitted Young, Laplace, etc. But
+then my book has a true title. Hill should not have called his a review of
+the "Works."
+
+It was charged against Sir John Hill that he had tried to become a Fellow
+of the Royal Society and had failed. This he denied, and challenged the
+production of the certificate which a candidate always sends in, and which
+is preserved. {25} But perhaps he could not get so far as a
+certificate--that is, could not find any one to recommend him; he was a
+likely man to be in such a predicament. As I have myself run foul of the
+Society on some little points, I conceive it possible that I may fall under
+a like suspicion. Whether I could have been a Fellow, I cannot know; as the
+gentleman said who was asked if he could play the violin, I never tried. I
+have always had a high opinion of the Society upon its whole history. A
+person used to historical inquiry learns to look at wholes; the
+Universities of Oxford and Cambridge, the College of Physicians, etc. are
+taken in all their duration. But those who are not historians--I mean not
+possessed of the habit of history--hold a mass of opinions about current
+things which lead them into all kinds of confusion when they try to look
+back. Not to give an instance which will offend any set of existing
+men--this merely because I can do without it--let us take the country at
+large. Magna Charta for ever! glorious safeguard of our liberties! _Nullus
+liber homo capiatur aut imprisonetur ... aut aliquo modo destruatur, nisi
+per judicium parium_ ....[8] _Liber homo: frank home_; a capital thing for
+him--but how about the _villeins_? Oh, there are none _now_! But there
+were. Who cares for villains, or barbarians, or helots? And so England, and
+Athens, and Sparta, were free States; all the freemen in them were free.
+Long after Magna Charta, villains were sold with their "chattels and
+offspring," named in that order. Long after Magna Charta, it was law that
+"Le Seigniour poit rob, naufrer, et chastiser son villein a son volunt,
+salve que il ne poit luy maim."[9]
+
+The Royal Society was founded as a co-operative body, and co-operation was
+its purpose. The early charters, etc. do not contain a trace of the
+intention to create a _scientific distinction_, a kind of Legion of Honor.
+It is clear that the {26} qualification was ability and willingness to do
+good work for the promotion of natural knowledge, no matter in how many
+persons, nor of what position in society. Charles II gave a smart rebuke
+for exclusiveness, as elsewhere mentioned. In time arose, almost of course,
+the idea of distinction attaching to the title; and when I first began to
+know the Society, it was in this state. Gentlemen of good social position
+were freely elected if they were really educated men; but the moment a
+claimant was announced as resting on his science, there was a disposition
+to inquire whether he was scientific enough. The maxim of the poet was
+adopted; and the Fellows were practically divided into _Drink-deeps_ and
+_Taste-nots_.
+
+I was, in early life, much repelled by the tone taken by the Fellows of the
+Society with respect to their very mixed body. A man high in science--some
+thirty-seven years ago (about 1830)--gave me some encouragement, as he
+thought. "We shall have you a Fellow of the Royal Society in time," said
+he. Umph! thought I: for I had that day heard of some recent elections, the
+united science of which would not have demonstrated I. 1, nor explained the
+action of a pump. Truly an elevation to look up at! It came, further, to my
+knowledge that the Royal Society--if I might judge by the claims made by
+very influential Fellows--considered itself as entitled to the best of
+everything: second-best being left for the newer bodies. A secretary, in
+returning thanks for the Royal at an anniversary of the Astronomical, gave
+rather a lecture to the company on the positive duty of all present to send
+the very best to the old body, and the absolute right of the old body to
+expect it. An old friend of mine, on a similar occasion, stated as a fact
+that the thing was always done, as well as that it ought to be done.
+
+Of late years this pretension has been made by a President of the Society.
+In 1855, Lord Rosse presented a confidential memorandum to the Council on
+the expediency of enlarging their number. He says, "In a Council so small
+it {27} is impossible to secure a satisfactory representation of the
+leading scientific Societies, and it is scarcely to be expected that, under
+such circumstances, they will continue to publish inferior papers while
+they send the best to our _Transactions_."
+
+And, again, with all the Societies represented on the Council, "even if
+every Science had its Society, and if they published everything,
+withholding their best papers [i.e., from the Royal Society], which they
+would not be likely to do, still there would remain to the Royal Society
+...." Lord Rosse seems to imagine that the minor Societies themselves
+transfer their best papers to the Royal Society; that if, for instance, the
+Astronomical Society were to receive from A.B. a paper of unusual merit,
+the Society would transfer it to the Royal Society. This is quite wrong:
+any preference of the Royal to another Society is the work of the
+contributor himself. But it shows how well hafted is the Royal Society's
+claim, that a President should acquire the notion that it is acknowledged
+and acted upon by the other Societies, in their joint and corporate
+capacities. To the pretension thus made I never could give any sympathy.
+When I first heard Mr. Christie, Sec. R. S., set it forth at the
+anniversary dinner of the Astronomical Society, I remembered the Baron in
+Walter Scott:
+
+ "Of Gilbert the Galliard a heriot he sought,
+  Saying, Give thy best steed as a vassal ought."
+
+And I remembered the answer:
+
+ "Lord and Earl though thou be, I trow
+  I can rein Buck's-foot better than thou."
+
+Fully conceding that the Royal Society is entitled to preeminent rank and
+all the respect due to age and services, I could not, nor can I now, see
+any more obligation in a contributor to send his best to that Society than
+he can make out to be due to himself. This pretension, in my mind, was
+hooked on, by my historical mode of viewing things already mentioned, to my
+knowledge of the fact that the Royal {28} Society--the chief fault,
+perhaps, lying with its President, Sir Joseph Banks--had sternly set itself
+against the formation of other societies; the Geological and Astronomical,
+for instance, though it must be added that the chief rebels came out of the
+Society itself. And so a certain not very defined dislike was generated in
+my mind--an anti-aristocratic affair--to the body which seemed to me a
+little too uplifted. This would, I daresay, have worn off; but a more
+formidable objection arose. My views of physical science gradually arranged
+themselves into a form which would have rendered F.R.S., as attached to my
+name, a false representation symbol. The Royal Society is the great
+fortress of general physics: and in the philosophy of our day, as to
+general physics, there is something which makes the banner of the R.S. one
+under which I cannot march. Everybody who saw the three letters after my
+name would infer certain things as to my mode of thought which would not be
+true inference. It would take much space to explain this in full. I may
+hereafter, perhaps, write a budget of collected results of the _a priori
+philosophy_, the nibbling at the small end of omniscience, and the effect
+it has had on common life, from the family parlor to the jury-box, from the
+girls'-school to the vestry-meeting. There are in the Society those who
+would, were there no others, prevent my criticism, be its conclusions true
+or false, from having any basis; but they are in the minority.
+
+There is no objection to be made to the principles of philosophy in vogue
+at the Society, when they are stated as principles; but there is an
+omniscience in daily practice which the principles repudiate. In like
+manner, the most retaliatory Christians have a perfect form of round words
+about behavior to those who injure them; none of them are as candid as a
+little boy I knew, who, to his mother's admonition, You should love your
+enemies, answered--Catch me at it!
+
+Years ago, a change took place which would alone have {29} put a sufficient
+difficulty in the way. The co-operative body got tired of getting funds
+from and lending name to persons who had little or no science, and wanted
+F.R.S. to be in every case a Fellow Really Scientific. Accordingly, the
+number of yearly elections was limited to fifteen recommended by the
+Council, unless the general body should choose to elect more; which it does
+not do. The election is now a competitive examination: it is no longer--Are
+you able and willing to promote natural knowledge; it is--Are you one of
+the upper fifteen of those who make such claim. In the list of
+candidates--a list rapidly growing in number--each year shows from thirty
+to forty of those whom Newton and Boyle would have gladly welcomed as
+fellow-laborers. And though the rejected of one year may be the accepted of
+the next--or of the next but one, or but two, if self-respect will permit
+the candidate to hang on--yet the time is clearly coming when many of those
+who ought to be welcomed will be excluded for life, or else shelved at
+last, when past work, with a scientific peerage. Coupled with this attempt
+to create a kind of order of knighthood is an absurdity so glaring that it
+should always be kept before the general eye. This distinction, this mark
+set by science upon successful investigation, is of necessity a
+class-distinction. Rowan Hamilton, one of the greatest names of our day in
+mathematical science, never could attach F.R.S. to his name--_he could not
+afford it_. There is a condition precedent--Four Red Sovereigns. It is four
+pounds a year, or--to those who have contributed to the Transactions--forty
+pounds down. This is as it should be: the Society must be supported. But it
+is not as it should be that a kind of title of honor should be forged, that
+a body should take upon itself to confer distinctions _for science_, when
+it is in the background--and kept there when the distinction is
+trumpeted--that the wearer is a man who can spare four pounds a year. I am
+well aware that in England a person who is not gifted either by nature or
+art, with this amount of money power, {30} is, with the mass, a very
+second-rate sort of Newton, whatever he may be in the field of
+investigation. Even men of science, so called, have this feeling. I know
+that the _scientific advisers_ of the Admiralty, who, years ago, received
+100 pounds a year each for his trouble, were sneered at by a wealthy
+pretender as "fellows to whom a hundred a year is an object." Dr. Thomas
+Young was one of them. To a bookish man--I mean a man who can manage to
+collect books--there is no tax. To myself, for example, 40 pounds worth of
+books deducted from my shelves, and the life-use of the Society's splendid
+library instead, would have been a capital exchange. But there may be, and
+are, men who want books, and cannot pay the Society's price. The Council
+would be very liberal in allowing books to be consulted. I have no doubt
+that if a known investigator were to call and ask to look at certain books,
+the Assistant-Secretary would forthwith seat him with the books before him,
+absence of F.R.S. not in any wise withstanding. But this is not like having
+the right to consult any book on any day, and to take it away, if farther
+wanted.
+
+So much for the Royal Society as concerns myself. I must add that there is
+not a spark of party feeling against those who wilfully remain outside. The
+better minds of course know better; and the smaller _savants_ look
+complacently on the idea of an outer world which makes _élite_ of them. I
+have done such a thing as serve on a committee of the Society, and report
+on a paper: they had the sense to ask, and I had the sense to see that none
+of my opinions were compromised by compliance. And I will be of any use
+which does not involve the status of _homo trium literarum_; as I have
+elsewhere explained, I would gladly be _Fautor Realis Scientiæ_, but I
+would not be taken for _Falsæ Rationis Sacerdos_.
+
+Nothing worse will ever happen to me than the smile which individuals
+bestow on a man who does not _groove_. Wisdom, like religion, belongs to
+majorities; who can {31} wonder that it should be so thought, when it is so
+clearly pictured in the New Testament from one end to the other?
+
+The counterpart of _paradox_, the isolated opinion of one or of few, is the
+general opinion held by all the rest; and the counterpart of false and
+absurd paradox is what is called the "vulgar error," the _pseudodox_. There
+is one great work on this last subject, the _Pseudodoxia Epidemica_ of Sir
+Thomas Browne, the famous author of the _Religio Medici_; it usually goes
+by the name of Browne "On Vulgar Errors" (1st ed. 1646; 6th, 1672). A
+careful analysis of this work would show that vulgar errors are frequently
+opposed by scientific errors; but good sense is always good sense, and
+Browne's book has a vast quantity of it.
+
+As an example of bad philosophy brought against bad observation. The
+Amphisbæna serpent was supposed to have two heads, one at each end; partly
+from its shape, partly because it runs backwards as well as forwards. On
+this Sir Thomas Browne makes the following remarks:
+
+"And were there any such species or natural kind of animal, it would be
+hard to make good those six positions of body which, according to the three
+dimensions, are ascribed unto every Animal; that is, _infra_, _supra_,
+_ante_, _retro_, _dextrosum_, _sinistrosum_: for if (as it is determined)
+that be the anterior and upper part wherein the senses are placed, and that
+the posterior and lower part which is opposite thereunto, there is no
+inferior or former part in this Animal; for the senses, being placed at
+both extreams, doth make both ends anterior, which is impossible; the terms
+being Relative, which mutually subsist, and are not without each other. And
+therefore this duplicity was ill contrived to place one head at both
+extreams, and had been more tolerable to have settled three or four at one.
+And therefore also Poets have been more reasonable than Philosophers, and
+_Geryon_ or _Cerberus_ less monstrous than _Amphisbæna_." {32}
+
+There may be paradox upon paradox: and there is a good instance in the
+eighth century in the case of Virgil, an Irishman, Bishop of Salzburg and
+afterwards Saint, and his quarrels with Boniface, an Englishman, Archbishop
+of Mentz, also afterwards Saint. All we know about the matter is, that
+there exists a letter of 748 from Pope Zachary, citing Virgil--then, it
+seems, at most a simple priest, though the Pope was not sure even of
+that--to Rome to answer the charge of maintaining that there is another
+world (_mundus_) under our earth (_terra_), with another sun and another
+moon. Nothing more is known: the letter contains threats in the event of
+the charge being true; and there history drops the matter. Since Virgil was
+afterwards a Bishop and a Saint, we may fairly conclude that he died in the
+full flower of his orthodox reputation. It has been supposed--and it seems
+probable--that Virgil maintained that the earth is peopled all the way
+round, so that under some spots there are antipodes; that his
+contemporaries, with very dim ideas about the roundness of the earth, and
+most of them with none at all, interpreted him as putting another earth
+under ours--turned the other way, probably, like the second piece of
+bread-and-butter in a sandwich, with a sun and moon of its own. In the
+eighth century this would infallibly have led to an underground Gospel, an
+underground Pope, and an underground Avignon for him to live in. When, in
+later times, the idea of inhabitants for the planets was started, it was
+immediately asked whether they had sinned, whether Jesus Christ died for
+_them_, whether their wine and their water could be lawfully used in the
+sacraments, etc.
+
+On so small a basis as the above has been constructed a companion case to
+the persecution of Galileo. On one side the positive assertion, with
+indignant comment, that Virgil was deposed for antipodal heresy, on the
+other, serious attempts at justification, palliation, or mystification.
+Some writers say that Virgil was found guilty; others that he gave
+satisfactory explanation, and became very good friends with {33} Boniface:
+for all which see Bayle. Some have maintained that the antipodist was a
+different person from the canonized bishop: there is a second Virgil, made
+to order. When your shoes pinch, and will not stretch, always throw them
+away and get another pair: the same with your facts. Baronius was not up to
+the plan of a substitute: his commentator Pagi (probably writing about
+1690) argues for it in a manner which I think Baronius would not have
+approved. This Virgil was perhaps a slippery fellow. The Pope says he hears
+that Virgil pretended licence from him to claim one of some new bishoprics:
+this he declares is totally false. It is part of the argument that such a
+man as this could not have been created a Bishop and a Saint: on this point
+there will be opinions and opinions.[10]
+
+Lactantius, four centuries before, had laughed at the antipodes in a manner
+which seems to be ridicule thrown on the idea of the earth's roundness.
+Ptolemy, without reference to the antipodes, describes the extent of the
+inhabited part of the globe in a way which shows that he could have had no
+objection to men turned opposite ways. Probably, in the eighth century, the
+roundness of the earth was matter of thought only to astronomers. It should
+always be remembered, especially by those who affirm persecution of a true
+opinion, that but for our knowing from Lactantius that the antipodal notion
+had been matter of assertion and denial among theologians, we could never
+have had any great confidence in Virgil really having maintained the simple
+theory of the existence of antipodes. And even now we are not entitled to
+affirm it as having historical proof: the evidence {34} goes to Virgil
+having been charged with very absurd notions, which it seems more likely
+than not were the absurd constructions which ignorant contemporaries put
+upon sensible opinions of his.
+
+One curious part of this discussion is that neither side has allowed Pope
+Zachary to produce evidence to character. He shall have been an Urban, say
+the astronomers; an Urban he ought to have been, say the theologians. What
+sort of man was Zachary? He was eminently sensible and conciliatory; he
+contrived to make northern barbarians hear reason in a way which puts him
+high among that section of the early popes who had the knack of managing
+uneducated swordsmen. He kept the peace in Italy to an extent which
+historians mention with admiration. Even Bale, that Maharajah of
+pope-haters, allows himself to quote in favor of Zachary, that "multa
+Papalem dignitatem decentia, eademque præclara (scilicet) opera
+confecit."[11] And this, though so willing to find fault that, speaking of
+Zachary putting a little geographical description of the earth on the
+portico of the Lateran Church, he insinuates that it was intended to affirm
+that the Pope was lord of the whole. Nor can he say how long Zachary held
+the see, except by announcing his death in 752, "cum decem annis
+pestilentiæ sedi præfuisset."[12]
+
+There was another quarrel between Virgil and Boniface which is an
+illustration. An ignorant priest had baptized "in nomine Patri_a_, et
+Fili_a_ et Spiritu_a_ Sancta." Boniface declared the rite null and void:
+Virgil maintained the contrary; and Zachary decided in favor of Virgil, on
+the ground that the absurd form was only ignorance of Latin, and not
+heresy. It is hard to believe that this man deposed a priest for asserting
+the whole globe to be inhabited. To me the little information that we have
+seems {35} to indicate--but not with certainty--that Virgil maintained the
+antipodes: that his ignorant contemporaries travestied his theory into that
+of an underground cosmos; that the Pope cited him to Rome to explain his
+system, which, as reported, looked like what all would then have affirmed
+to be heresy; that he gave satisfactory explanations, and was dismissed
+with honor. It may be that the educated Greek monk, Zachary, knew his
+Ptolemy well enough to guess what the asserted heretic would say; we have
+seen that he seems to have patronized geography. The _description_ of the
+earth, according to historians, was a _map_; this Pope may have been more
+ready than another to prick up his ears at any rumor of geographical
+heresy, from hope of information. And Virgil, who may have entered the
+sacred presence as frightened as Jacquard, when Napoleon I sent for him and
+said, with a stern voice and threatening gesture, "You are the man who can
+tie a knot in a stretched string," may have departed as well pleased as
+Jacquard with the riband and pension which the interview was worth to him.
+
+A word more about Baronius. If he had been pope, as he would have been but
+for the opposition of the Spaniards, and if he had lived ten years longer
+than he did, and if Clavius, who would have been his astronomical adviser,
+had lived five years longer than he did, it is probable, nay almost
+certain, that the great exhibition, the proceeding against Galileo, would
+not have furnished a joke against theology in all time to come. For
+Baronius was sensible and witty enough to say that in the Scriptures the
+Holy Spirit intended to teach how to go to Heaven, not how Heaven goes; and
+Clavius, in his last years, confessed that the whole system of the heavens
+had broken down, and must be mended.
+
+The manner in which the Galileo case, a reality, and the Virgil case, a
+fiction, have been hawked against the Roman see are enough to show that the
+Pope and his adherents have not cared much about physical philosophy. In
+truth, orthodoxy has always had other fish to fry. Physics, which {36} in
+modern times has almost usurped the name _philosophy_, in England at least,
+has felt a little disposed to clothe herself with all the honors of
+persecution which belong to the real owner of the name. But the bishops,
+etc. of the Middle Ages knew that the contest between nominalism and
+realism, for instance, had a hundred times more bearing upon orthodoxy than
+anything in astronomy, etc. A wrong notion about _substance_ might play the
+mischief with _transubstantiation_.
+
+The question of the earth's motion was the single point in which orthodoxy
+came into real contact with science. Many students of physics were
+suspected of magic, many of atheism: but, stupid as the mistake may have
+been, it was _bona fide_ the magic or the atheism, not the physics, which
+was assailed. In the astronomical case it was the very doctrine, as a
+doctrine, independently of consequences, which was the _corpus delicti_:
+and this because it contradicted the Bible. And so it did; for the
+stability of the earth is as clearly assumed from one end of the Old
+Testament to the other as the solidity of iron. Those who take the Bible to
+be _totidem verbis_ dictated by the God of Truth can refuse to believe it;
+and they make strange reasons. They undertake, _a priori_, to settle Divine
+intentions. The Holy Spirit did not _mean_ to teach natural philosophy:
+this they know beforehand; or else they infer it from finding that the
+earth does move, and the Bible says it does not. Of course, ignorance
+apart, every word is truth, or the writer did not mean truth. But this puts
+the whole book on its trial: for we never can find out what the writer
+meant, until we otherwise find out what is true. Those who like may, of
+course, declare for an inspiration over which they are to be viceroys; but
+common sense will either accept verbal meaning or deny verbal inspiration.
+
+       *       *       *       *       *
+
+
+{37}
+
+A BUDGET OF PARADOXES.
+
+VOLUME I.
+
+THE STORY OF BURIDAN'S ASS.
+
+    Questiones Morales, folio, 1489 [Paris]. By T. Buridan.
+
+This is the title from the Hartwell Catalogue of Law Books. I suppose it is
+what is elsewhere called the "Commentary on the Ethics of Aristotle,"
+printed in 1489.[13] Buridan[14] (died about 1358) is the creator of the
+famous ass which, as _Burdin's_[15] ass, was current in Burgundy, perhaps
+is, as a vulgar proverb. Spinoza[16] says it was a jenny ass, and that a
+man would not have been so foolish; but whether the compliment is paid to
+human or to masculine character does not appear--perhaps to both in one.
+The story _told_ about the famous paradox is very curious. The Queen of
+France, Joanna or Jeanne, was in the habit of sewing her lovers up in
+sacks, and throwing them into the Seine; not for blabbing, but that they
+might not blab--certainly the safer plan. Buridan was exempted, and, in
+gratitude, invented the sophism. What it has to do with the matter {38} has
+never been explained. Assuredly _qui facit per alium facit per se_ will
+convict Buridan of prating. The argument is as follows, and is seldom told
+in full. Buridan was for free-will--that is, will which determines conduct,
+let motives be ever so evenly balanced. An ass is _equally_ pressed by
+hunger and by thirst; a bundle of hay is on one side, a pail of water on
+the other. Surely, you will say, he will not be ass enough to die for want
+of food or drink; he will then make a choice--that is, will choose between
+alternatives of equal force. The problem became famous in the schools; some
+allowed the poor donkey to die of indecision; some denied the possibility
+of the balance, which was no answer at all.
+
+
+
+MICHAEL SCOTT'S DEVILS.
+
+The following question is more difficult, and involves free-will to all who
+answer--"Which you please." If the northern hemisphere were land, and all
+the southern hemisphere water, ought we to call the northern hemisphere an
+island, or the southern hemisphere a lake? Both the questions would be good
+exercises for paradoxers who must be kept employed, like Michael
+Scott's[17] devils. The wizard {39} knew nothing about squaring the circle,
+etc., so he set them to make ropes out of sea sand, which puzzled them.
+Stupid devils; much of our glass is sea sand, and it makes beautiful
+thread. Had Michael set them to square the circle or to find a perpetual
+motion, he would have done his work much better. But all this is
+conjecture: who knows that I have not hit on the very plan he adopted?
+Perhaps the whole race of paradoxers on hopeless subjects are Michael's
+subordinates, condemned to transmigration after transmigration, until their
+task is done.
+
+The above was not a bad guess. A little after the time when the famous
+Pascal papers[18] were produced, I came into possession of a correspondence
+which, but for these papers, I should have held too incredible to be put
+before the world. But when one sheep leaps the ditch, another will follow:
+so I gave the following account in the _Athenæum_ of October 5, 1867:
+
+"The recorded story is that Michael Scott, being bound by contract to
+produce perpetual employment for a number of young demons, was worried out
+of his life in inventing jobs for them, until at last he set them to make
+ropes out of sea sand, which they never could do. We have obtained a very
+curious correspondence between the wizard Michael and his demon-slaves; but
+we do not feel at liberty to say how it came into our hands. We much regret
+that we did not receive it in time for the British Association. It appears
+that the story, true as far as it goes, was never finished. The demons
+easily conquered the rope difficulty, by the simple process of making the
+sand into glass, and spinning the glass into thread, which they twisted.
+Michael, thoroughly disconcerted, hit upon the plan of setting some to {40}
+square the circle, others to find the perpetual motion, etc. He commanded
+each of them to transmigrate from one human body into another, until their
+tasks were done. This explains the whole succession of cyclometers, and all
+the heroes of the Budget. Some of this correspondence is very recent; it is
+much blotted, and we are not quite sure of its meaning: it is full of
+figurative allusions to driving something illegible down a steep into the
+sea. It looks like a humble petition to be allowed some diversion in the
+intervals of transmigration; and the answer is--
+
+  Rumpat et serpens iter institutum,[19]
+
+--a line of Horace, which the demons interpret as a direction to come
+athwart the proceedings of the Institute by a sly trick. Until we saw this,
+we were suspicious of M. Libri,[20] the unvarying blunders of the
+correspondence look like knowledge. To be always out of the road requires a
+map: genuine ignorance occasionally lapses into truth. We thought it
+possible M. Libri might have played the trick to show how easily the French
+are deceived; but with our present information, our minds are at rest on
+the subject. We see M. Chasles does not like to avow the real source of
+information: he will not confess himself a spiritualist."
+
+
+
+PHILO OF GADARA.
+
+Philo of Gadara[21] is asserted by Montucla,[22] on the {41} authority of
+Eutocius,[23] the commentator on Archimedes, to have squared the circle
+within the _ten-thousandth_ part of a unit, that is, to _four_ places of
+decimals. A modern classical dictionary represents it as done by Philo to
+_ten thousand_ places of decimals. Lacroix comments on Montucla to the
+effect that _myriad_ (in Greek _ten thousand_) is here used as we use it,
+vaguely, for an immense number. On looking into Eutocius, I find that not
+one definite word is said about the extent to which Philo carried the
+matter. I give a translation of the passage:
+
+"We ought to know that Apollonius Pergæus, in his Ocytocium [this work is
+lost], demonstrated the same by other numbers, and came nearer, which seems
+more accurate, but has nothing to do with Archimedes; for, as before said,
+he aimed only at going near enough for the wants of life. Neither is Porus
+of Nicæa fair when he takes Archimedes to task for not giving a line
+accurately equal to the circumference. He says in his Cerii that his
+teacher, Philo of Gadara, had given a more accurate approximation ([Greek:
+eis akribesterous arithmous agagein]) than that of Archimedes, or than 7 to
+22. But all these [the rest as well as Philo] miss the intention. They
+multiply and divide by _tens of thousands_, which no one can easily do,
+unless he be versed in the logistics [fractional computation] of Magnus
+[now unknown]."
+
+Montucla, or his source, ought not to have made this mistake. He had been
+at the Greek to correct Philo _Gadetanus_, as he had often been called, and
+he had brought away {42} and quoted [Greek: apo Gadarôn]. Had he read two
+sentences further, he would have found the mistake.
+
+We here detect a person quite unnoticed hitherto by the moderns, Magnus the
+arithmetician. The phrase is ironical; it is as if we should say, "To do
+this a man must be deep in Cocker."[24] Accordingly, Magnus, Baveme,[25]
+and Cocker, are three personifications of arithmetic; and there may be
+more.
+
+
+
+ON SQUARING THE CIRCLE.
+
+Aristotle, treating of the category of relation, denies that the quadrature
+has been found, but appears to assume that it can be done. Boethius,[26] in
+his comment on the passage, says that it has been done since Aristotle, but
+that the demonstration is too long for him to give. Those who have no
+notion of the quadrature question may look at the _English Cyclopædia_,
+art. "Quadrature of the Circle."
+
+    Tetragonismus. Id est circuli quadratura per Campanum, Archimedem
+    Syracusanum, atque Boetium mathematicæ perspicacissimos adinventa.--At
+    the end, Impressum Venetiis per Ioan. Bapti. Sessa. Anno ab
+    incarnatione Domini, 1503. Die 28 Augusti.
+
+{43}
+
+This book has never been noticed in the history of the subject, and I
+cannot find any mention of it. The quadrature of Campanus[27] takes the
+ratio of Archimedes,[28] 7 to 22 to be absolutely correct; the account
+given of Archimedes is not a translation of his book; and that of Boetius
+has more than is in Boet_h_ius. This book must stand, with the next, as the
+earliest in print on the subject, until further showing: Murhard[29] and
+Kastner[30] have nothing so early. It is edited by Lucas Gauricus,[31] who
+has given a short preface. Luca Gaurico, Bishop of Civita Ducale, an
+astrologer of astrologers, published this work at about thirty years of
+age, and lived to eighty-two. His works are collected in folios, but I do
+not know whether they contain this production. The poor fellow could never
+tell his own fortune, because his father neglected to note the hour and
+minute of his birth. But if there had been anything in astrology, he could
+have worked back, as Adams[32] and Leverrier[33] did when they caught {44}
+Neptune: at sixty he could have examined every minute of his day of birth,
+by the events of his life, and so would have found the right minute. He
+could then have gone on, by rules of prophecy. Gauricus was the
+mathematical teacher of Joseph Scaliger,[34] who did him no credit, as we
+shall see.
+
+
+
+BOVILLUS ON THE QUADRATURE PROBLEM.
+
+    In hoc opere contenta Epitome.... Liber de quadratura Circuli....
+    Paris, 1503, folio.
+
+The quadrator is Charles Bovillus,[35] who adopted the views of Cardinal
+Cusa,[36] presently mentioned. Montucla is hard on his compatriot, who, he
+says, was only saved from the laughter of geometers by his obscurity.
+Persons must guard against most historians of mathematics in one point:
+they frequently attribute to _his own_ age the obscurity which a writer has
+in _their own_ time. This tract was printed by Henry Stephens,[37] at the
+instigation of Faber Stapulensis,[38] {45} and is recorded by Dechales,[39]
+etc. It was also introduced into the _Margarita Philosophica_ of 1815,[40]
+in the same appendix with the new perspective from Viator. This is not
+extreme obscurity, by any means. The quadrature deserved it; but that is
+another point.
+
+It is stated by Montucla that Bovillus makes [pi] = [root]10. But Montucla
+cites a work of 1507, _Introductorium Geometricum_, which I have never
+seen.[41] He finds in it an account which Bovillus gives of the quadrature
+of the peasant laborer, and describes it as agreeing with his own. But the
+description makes [pi] = 3-1/8, which it thus appears Bovillus could not
+distinguish from [root]10. It seems also that this 3-1/8, about which we
+shall see so much in the sequel, takes its rise in the thoughtful head of a
+poor laborer. It does him great honor, being so near the truth, and he
+having no means of instruction. In our day, when an ignorant person chooses
+to bring his fancy forward in opposition to demonstration which he will not
+study, he is deservedly laughed at.
+
+{46}
+
+
+
+THE STORY OF LACOMME'S ATTEMPT AT QUADRATURE.
+
+Mr. James Smith,[42] of Liverpool--hereinafter notorified--attributes the
+first announcement of 3-1/8 to M. Joseph Lacomme, a French well-sinker, of
+whom he gives the following account:
+
+"In the year 1836, at which time Lacomme could neither read nor write, he
+had constructed a circular reservoir and wished to know the quantity of
+stone that would be required to pave the bottom, and for this purpose
+called on a professor of mathematics. On putting his question and giving
+the diameter, he was surprised at getting the following answer from the
+Professor: _'Qu'il lui était impossible de le lui dire au juste, attendu
+que personne n'avait encore pu trouver d'une manière exacte le rapport de
+la circonférence au diametre.'_[43] From this he was led to attempt the
+solution of the problem. His first process was purely mechanical, and he
+was so far convinced he had made the discovery that he took to educating
+himself, and became an expert arithmetician, and then found that
+arithmetical results agreed with his mechanical experiments. He appears to
+have eked out a bare existence for many years by teaching arithmetic, all
+the time struggling to get a hearing from some of the learned societies,
+but without success. In the year 1855 he found his way to Paris, where, as
+if by accident, he made the acquaintance of a young gentleman, son of M.
+Winter, a commissioner of police, and taught him his peculiar methods of
+calculation. The young man was so enchanted that he strongly recommended
+Lacomme to his father, and {47} subsequently through M. Winter he obtained
+an introduction to the President of the Society of Arts and Sciences of
+Paris. A committee of the society was appointed to examine and report upon
+his discovery, and the society at its _séance_ of March 17, 1856, awarded a
+silver medal of the first class to M. Joseph Lacomme for his discovery of
+the true ratio of diameter to circumference in a circle. He subsequently
+received three other medals from other societies. While writing this I have
+his likeness before me, with his medals on his breast, which stands as a
+frontispiece to a short biography of this extraordinary man, for which I am
+indebted to the gentleman who did me the honor to publish a French
+translation of the pamphlet I distributed at the meeting of the British
+Association for the Advancement of Science, at Oxford, in
+1860."--_Correspondent_, May 3, 1866.
+
+My inquiries show that the story of the medals is not incredible. There are
+at Paris little private societies which have not so much claim to be
+exponents of scientific opinion as our own Mechanics' Institutes. Some of
+them were intended to give a false lustre: as the "Institut Historique,"
+the members of which are "Membre de l'Institut Historique." That M. Lacomme
+should have got four medals from societies of this class is very possible:
+that he should have received one from any society at Paris which has the
+least claim to give one is as yet simply incredible.
+
+
+
+NICOLAUS OF CUSA'S ATTEMPT.
+
+    Nicolai de Cusa Opera Omnia. Venice, 1514. 3 vols. folio.
+
+The real title is "Hæc accurata recognitio trium voluminum operum clariss.
+P. Nicolai Cusæ ... proxime sequens pagina monstrat."[44] Cardinal Cusa,
+who died in 1464, is one of the earliest modern attempters. His quadrature
+is found in the second volume, and is now quite unreadable.
+
+{48} In these early days every quadrator found a geometrical opponent, who
+finished him. Regimontanus[45] did this office for the Cardinal.
+
+
+
+HENRY CORNELIUS AGRIPPA.
+
+    De Occulta Philosophia libri III. By Henry Cornelius Agrippa. Lyons,
+    1550, 8vo.
+
+    De incertitudine et vanitate scientiarum. By the same. Cologne, 1531,
+    8vo.
+
+The first editions of these works were of 1530, as well as I can make out;
+but the first was in progress in 1510.[46] In the second work Agrippa
+repents of having wasted time on the magic of the first; but all those who
+actually deal with demons are destined to eternal fire with Jamnes and
+Mambres and Simon Magus. This means, as is the fact, that his occult
+philosophy did not actually enter upon _black_ magic, but confined itself
+to the power of the stars, of numbers, etc. The fourth book, which appeared
+after the death of Agrippa, and really concerns dealing with evil spirits,
+is undoubtedly spurious. It is very difficult to make out what Agrippa
+really believed on the subject. I have introduced his books as the most
+marked specimens of treatises on magic, a paradox of our day, though not
+far from orthodoxy in his; and here I should have ended my notice, if I had
+not casually found something more interesting to the reader of our day.
+
+{49}
+
+
+
+WHICH LEADS TO WALTER SCOTT.
+
+Walter Scott, it is well known, was curious on all matters connected with
+magic, and has used them very widely. But it is hardly known how much pains
+he has taken to be correct, and to give the real thing. The most decided
+detail of a magical process which is found in his writings is that of
+Dousterswivel in _The Antiquary_; and it is obvious, by his accuracy of
+process, that he does not intend the adept for a mere impostor, but for one
+who had a lurking belief in the efficacy of his own processes, coupled with
+intent to make a fraudulent use of them. The materials for the process are
+taken from Agrippa. I first quote Mr. Dousterswivel:
+
+"... I take a silver plate when she [the moon] is in her fifteenth mansion,
+which mansion is in de head of _Libra_, and I engrave upon one side de
+worts _Schedbarschemoth Scharta_ch_an_ [_ch_ should be _t_]--dat is, de
+Intelligence of de Intelligence of de moon--and I make his picture like a
+flying serpent with a turkey-cock's head--vary well--Then upon this side I
+make de table of de moon, which is a square of nine, multiplied into
+itself, with eighty-one numbers [nine] on every side and diameter nine...."
+
+In the _De Occulta Philosophia_, p. 290, we find that the fifteenth mansion
+of the moon _incipit capite Libræ_, and is good _pro extrahendis
+thesauris_, the object being to discover hidden treasure. In p. 246, we
+learn that a _silver_ plate must be used with the moon. In p. 248, we have
+the words which denote the Intelligence, etc. But, owing to the falling of
+a number into a wrong line, or the misplacement of a line, one or
+other--which takes place in all the editions I have examined--Scott has,
+sad to say, got hold of the wrong words; he has written down the _demon of
+the demons_ of the moon. Instead of the gibberish above, it should have
+been _Malcha betarsisim hed beruah schenhakim_. In p. 253, we have the
+magic square of the moon, with eighty-one numbers, and the symbol for the
+Intelligence, which Scott likens to a flying {50} serpent with a
+turkey-cock's head. He was obliged to say something; but I will stake my
+character--and so save a woodcut--on the scratches being more like a pair
+of legs, one shorter than the other, without a body, jumping over a
+six-barred gate placed side uppermost. Those who thought that Scott forged
+his own nonsense, will henceforth stand corrected. As to the spirit
+Peolphan, etc., no doubt Scott got it from the authors he elsewhere
+mentions, Nicolaus Remigius[47] and Petrus Thyracus; but this last word
+should be Thyræus.
+
+The tendency of Scott's mind towards prophecy is very marked, and it is
+always fulfilled. Hyder, in his disguise, calls out to Tippoo: "Cursed is
+the prince who barters justice for lust; he shall die in the gate by the
+sword of the stranger." Tippoo was killed in a gateway at Seringapatam.[48]
+
+
+
+FINAEUS ON CIRCLE SQUARING.
+
+    Orontii Finaei ... Quadratura Circuli. Paris, 1544, 4to.
+
+Orontius[49] squared the circle out of all comprehension; but he was killed
+by a feather from his own wing. His {51} former pupil, John Buteo,[50] the
+same who--I believe for the first time--calculated the question of Noah's
+ark, as to its power to hold all the animals and stores, unsquared him
+completely. Orontius was the author of very many works, and died in 1555.
+Among the laudatory verses which, as was usual, precede this work, there is
+one of a rare character: a congratulatory ode to the wife of the author.
+The French now call this writer Oronce Finée; but there is much difficulty
+about delatinization. Is this more correct than Oronce Fine, which the
+translator of De Thou uses? Or than Horonce Phine, which older writers
+give? I cannot understand why M. de Viette[51] should be called Viète,
+because his Latin name is Vieta. It is difficult to restore Buteo; for not
+only now is _butor_ a blockhead as well as a bird, but we really cannot
+know what kind of bird Buteo stood for. We may be sure that Madame Fine was
+Denise Blanche; for Dionysia Candida can mean nothing else. Let her shade
+rejoice in the fame which Hubertus Sussannæus has given her.
+
+I ought to add that the quadrature of Orontius, and solutions of all the
+other difficulties, were first published in _De Rebus Mathematicis Hactenus
+Desideratis_,[52] of which I have not the date.
+
+
+
+{52}
+
+DUCHESNE, AND A DISQUISITION ON ETYMOLOGY.
+
+    Nicolai Raymari Ursi Dithmarsi Fundamentum Astronomicum, id est, nova
+    doctrina sinuum et triangulorum.... Strasburg, 1588, 4to.[53]
+
+People choose the name of this astronomer for themselves: I take _Ursus_,
+because he _was_ a bear. This book gave the quadrature of Simon
+Duchesne,[54] or à Quercu, which excited Peter Metius,[55] as presently
+noticed. It also gave that unintelligible reference to Justus Byrgius which
+has been used in the discussion about the invention of logarithms.[56]
+
+The real name of Duchesne is Van der Eycke. I have met with a tract in
+Dutch, _Letterkundige Aanteekeningen_, upon Van Eycke, Van Ceulen,[57]
+etc., by J. J. Dodt van Flensburg,[58] which I make out to be since 1841 in
+date. I should {53} much like a translation of this tract to be printed,
+say in the _Phil. Mag._ Dutch would be clear English if it were properly
+spelt. For example, _learn-master_ would be seen at once to be _teacher_;
+but they will spell it _leermeester_. _Of these_ they write as _van deze_;
+_widow_ they make _weduwe_. All this is plain to me, who never saw a Dutch
+dictionary in my life; but many of their misspellings are quite
+unconquerable.
+
+
+
+FALCO'S RARE TRACT.
+
+    Jacobus Falco Valentinus, miles Ordinis Montesiani, hanc circuli
+    quadraturam invenit. Antwerp, 1589, 4to.[59]
+
+The attempt is more than commonly worthless; but as Montucla and others
+have referred to the verses at the end, and as the tract is of the rarest,
+I will quote them:
+
+      _Circulus loquitur._
+  Vocabar ante circulus
+  Eramque curvus undique
+  Ut alta solis orbita
+  Et arcus ille nubium.
+  Eram figura nobilis
+  Carensque sola origine
+  Carensque sola termino.
+  Modo indecora prodeo
+  Novisque foedor angulis.
+  Nec hoc peregit Archytas[60]
+  Neque Icari pater neque
+  Tuus, Iapete, filius.
+  Quis ergo casus aut Deus
+  Meam quadravit aream?
+
+      _Respondet auctor._
+  Ad alta Turiæ ostia
+  Lacumque limpidissimum
+  Sita est beata civitas
+  {54}
+  Parum Saguntus abfuit
+  Abestque Sucro plusculum.
+  Hic est poeta quispiam
+  Libenter astra consulens
+  Sibique semper arrogans
+  Negata doctioribus,
+  Senex ubique cogitans
+  Sui frequenter immemor
+  Nec explicare circinum
+  Nec exarare lineas
+  Sciens ut ipse prædicat.
+  Hic ergo bellus artifex
+  Tuam quadravit aream.[61]
+
+Falco's verses are pretty, if the U-mysteries be correct; but of these
+things I have forgotten--what I knew. [One mistake has been pointed out to
+me: it is Arch[=y]tas].
+
+As a specimen of the way in which history is written, I copy the account
+which Montucla--who is accurate when he writes about what he has
+seen--gives of these verses. He gives the date 1587; he places the verses
+at the beginning instead of the end; he says the circle thanks its
+quadrator affectionately; and he says the good and modest chevalier gives
+all the glory to the patron saint of his order. All of little consequence,
+as it happens; but writing at second-hand makes as complete mistakes about
+more important matters.
+
+{55}
+
+
+
+BUNGUS ON THE MYSTERY OF NUMBER.
+
+    Petri Bungi Bergomatis Numerorum mysteria. Bergomi [Bergamo], 1591,
+    4to. Second Edition.
+
+The first edition is said to be of 1585;[62] the third, Paris, 1618. Bungus
+is not for my purpose on his own score, but those who gave the numbers
+their mysterious characters: he is but a collector. He quotes or uses 402
+authors, as we are informed by his list; this just beats Warburton,[63]
+whom some eulogist or satirist, I forget which, holds up as having used 400
+authors in some one work. Bungus goes through 1, 2, 3, etc., and gives the
+account of everything remarkable in which each number occurs; his accounts
+not being always mysterious. The numbers which have nothing to say for
+themselves are omitted: thus there is a gap between 50 and 60. In treating
+666, Bungus, a good Catholic, could not compliment the Pope with it, but he
+fixes it on Martin Luther with a little forcing. If from A to I represent
+1-10, from K to S 10-90, and from T to Z 100-500, we see:
+
+   M   A   R   T   I   N     L   U   T   E   R   A
+  30   1  80  100  9  40    20  200 100  5  80   1
+
+which gives 666. Again, in Hebrew, _Lulter_ does the same:
+
+  [Hebrew:   R    T    L    W   L]
+            200  400  30    6  30
+
+And thus two can play at any game. The second is better than the first: to
+Latinize the surname and not the Christian {56} name is very unscholarlike.
+The last number mentioned is a thousand millions; all greater numbers are
+dismissed in half a page. Then follows an accurate distinction between
+_number_ and _multitude_--a thing much wanted both in arithmetic and logic.
+
+
+
+WHICH LEADS TO A STORY ABOUT THE ROYAL SOCIETY.
+
+What may be the use of such a book as this? The last occasion on which it
+was used was the following. Fifteen or sixteen years ago the Royal Society
+determined to restrict the number of yearly admissions to fifteen men of
+science, and noblemen _ad libitum_; the men of science being selected and
+recommended by the Council, with a power, since practically surrendered, to
+the Society to elect more. This plan appears to me to be directly against
+the spirit of their charter, the true intent of which is, that all who are
+fit should be allowed to promote natural knowledge in association, from and
+after the time at which they are both fit and willing. It is also working
+more absurdly from year to year; the tariff of fifteen per annum will soon
+amount to the practical exclusion of many who would be very useful. This
+begins to be felt already, I suspect. But, as appears above, the body of
+the Society has the remedy in its own hands. When the alteration was
+discussed by the Council, my friend the late Mr. Galloway,[64] then one of
+the body, opposed it strongly, and inquired particularly into the reason
+why _fifteen_, of all numbers, was the one to be selected. Was it because
+fifteen is seven and eight, typifying the Old Testament Sabbath, and the
+New Testament day of the resurrection following? Was it because Paul strove
+fifteen days against Peter, proving that he was a doctor both of the Old
+and New Testament? Was it because the prophet Hosea bought a lady {57} for
+fifteen pieces of silver? Was it because, according to Micah, seven
+shepherds and eight chiefs should waste the Assyrians? Was it because
+Ecclesiastes commands equal reverence to be given to both Testaments--such
+was the interpretation--in the words "Give a portion to seven, and also to
+eight"? Was it because the waters of the Deluge rose fifteen cubits above
+the mountains?--or because they lasted fifteen decades of days? Was it
+because Ezekiel's temple had fifteen steps? Was it because Jacob's ladder
+has been supposed to have had fifteen steps? Was it because fifteen years
+were added to the life of Hezekiah? Was it because the feast of unleavened
+bread was on the fifteenth day of the month? Was it because the scene of
+the Ascension was fifteen stadia from Jerusalem? Was it because the
+stone-masons and porters employed in Solomon's temple amounted to fifteen
+myriads? etc. The Council were amused and astounded by the volley of
+fifteens which was fired at them; they knowing nothing about Bungus, of
+which Mr. Galloway--who did not, as the French say, indicate his
+sources--possessed the copy now before me. In giving this anecdote I give a
+specimen of the book, which is exceedingly rare. Should another edition
+ever appear, which is not very probable, he would be but a bungling Bungus
+who should forget the _fifteen_ of the Royal Society.
+
+
+
+AND ALSO TO A QUESTION OF EVIDENCE.
+
+[I make a remark on the different colors which the same person gives to one
+story, according to the bias under which he tells it. My friend Galloway
+told me how he had quizzed the Council of the Royal Society, to my great
+amusement. Whenever I am struck by the words of any one, I carry away a
+vivid recollection of position, gestures, tones, etc. I do not know whether
+this be common or uncommon. I never recall this joke without seeing before
+me my friend, leaning against his bookcase, with Bungus open in his hand,
+and a certain half-depreciatory tone which he often used {58} when speaking
+of himself. Long after his death, an F.R.S. who was present at the
+discussion, told me the story. I did not say I had heard it, but I watched
+him, with Galloway at the bookcase before me. I wanted to see whether the
+two would agree as to the fact of an enormous budget of fifteens having
+been fired at the Council, and they did agree perfectly. But when the
+paragraph of the Budget appeared in the _Athenæum_, my friend, who seemed
+rather to object to the _showing-up_, assured me that the thing was grossly
+exaggerated; there was indeed a fifteen or two, but nothing like the number
+I had given. I had, however, taken sharp note of the previous narration.
+
+
+
+AND TO ANOTHER QUESTION OF EVIDENCE.
+
+I will give another instance. An Indian officer gave me an account of an
+elephant, as follows. A detachment was on the march, and one of the
+gun-carriages got a wheel off the track, so that it was also off the
+ground, and hanging over a precipice. If the bullocks had moved a step,
+carriages, bullocks, and all must have been precipitated. No one knew what
+could be done until some one proposed to bring up an elephant, and let him
+manage it his own way. The elephant took a moment's survey of the fix, put
+his trunk under the axle of the free wheel, and waited. The surrounders,
+who saw what he meant, moved the bullocks gently forward, the elephant
+followed, supporting the axle, until there was ground under the wheel, when
+he let it quietly down. From all I had heard of the elephant, this was not
+too much to believe. But when, years afterwards, I reminded my friend of
+his story, he assured me that I had misunderstood him, that the elephant
+was _directed_ to put his trunk under the wheel, and saw in a moment why.
+This is reasonable sagacity, and very likely the correct account; but I am
+quite sure that, in the fit of elephant-worship under which the story was
+first told, it was told as I have first stated it.] {59}
+
+
+
+GIORDANO BRUNO AND HIS PARADOXES.
+
+    [Jordani Bruni Nolani de Monade, Numero et Figura ... item de
+    Innumerabilibus, Immenso, et Infigurabili ... Frankfort, 1591, 8vo.[65]
+
+I cannot imagine how I came to omit a writer whom I have known so many
+years, unless the following story will explain it. The officer reproved the
+boatswain for perpetual swearing; the boatswain answered that he heard the
+officers swear. "Only in an emergency," said the officer. "That's just it,"
+replied the other; "a boatswain's life is a life of 'mergency." Giordano
+Bruno was all paradox; and my mind was not alive to his paradoxes, just as
+my ears might have become dead to the boatswain's oaths. He was, as has
+been said, a vorticist before Descartes,[66] an optimist before Leibnitz, a
+Copernican before Galileo. It would be easy to collect a hundred strange
+opinions of his. He was born about 1550, and was roasted alive at Rome,
+February 17, 1600, for the maintenance and defence of the holy Church, and
+the rights and liberties of the same. These last words are from the writ of
+our own good James I, under which Leggatt[67] was roasted at Smithfield, in
+March 1612; and if I had a copy of the instrument under which Wightman[68]
+was roasted at Lichfield, a month afterwards, I daresay I should {60} find
+something quite as edifying. I extract an account which I gave of Bruno in
+the _Comp. Alm._ for 1855:
+
+"He was first a Dominican priest, then a Calvinist; and was roasted alive
+at Rome, in 1600, for as many heresies of opinion, religious and
+philosophical, as ever lit one fire. Some defenders of the papal cause have
+at least worded their accusations so to be understood as imputing to him
+villainous actions. But it is positively certain that his death was due to
+opinions alone, and that retractation, even after sentence, would have
+saved him. There exists a remarkable letter, written from Rome on the very
+day of the murder, by Scioppius[69] (the celebrated scholar, a waspish
+convert from Lutheranism, known by his hatred to Protestants and Jesuits)
+to Rittershusius,[70] a well-known Lutheran writer on civil and canon law,
+whose works are in the index of prohibited books. This letter has been
+reprinted by Libri (vol. iv. p. 407). The writer informs his friend (whom
+he wished to convince that even a Lutheran would have burnt Bruno) that all
+Rome would tell him that Bruno died for Lutheranism; but this is because
+the Italians do not know the difference between one heresy and another, in
+which simplicity (says the writer) may God preserve them. That is to say,
+they knew the difference between a live heretic and a roasted one by actual
+inspection, but had no idea of the difference between a Lutheran and a
+Calvinist. The countrymen of Boccaccio would have smiled at the idea which
+the German scholar entertained of them. They said Bruno was burnt for
+Lutheranism, a name under which they classed all Protestants: and they are
+better witnesses than Schopp, or Scioppius. He then proceeds to describe to
+his Protestant friend (to whom he would certainly not have omitted any act
+which both their churches would have condemned) the mass of opinions with
+which Bruno was charged; as that there {61} are innumerable worlds, that
+souls migrate, that Moses was a magician, that the Scriptures are a dream,
+that only the Hebrews descended from Adam and Eve, that the devils would be
+saved, that Christ was a magician and deservedly put to death, etc. In
+fact, says he, Bruno has advanced all that was ever brought forward by all
+heathen philosophers, and by all heretics, ancient and modern. A time for
+retractation was given, both before sentence and after, which should be
+noted, as well for the wretched palliation which it may afford, as for the
+additional proof it gives that opinions, and opinions only, brought him to
+the stake. In this medley of charges the Scriptures are a dream, while
+Adam, Eve, devils, and salvation are truths, and the Saviour a deceiver. We
+have examined no work of Bruno except the _De Monade_, etc., mentioned in
+the text. A strong though strange _theism_ runs through the whole, and
+Moses, Christ, the Fathers, etc., are cited in a manner which excites no
+remark either way. Among the versions of the cause of Bruno's death is
+_atheism_: but this word was very often used to denote rejection of
+revelation, not merely in the common course of dispute, but by such
+writers, for instance, as Brucker[71] and Morhof.[72] Thus Morhof says of
+the _De Monade, etc._, that it exhibits no manifest signs of atheism. What
+he means by the word is clear enough, when he thus speaks of a work which
+acknowledges God in hundreds of places, and rejects opinions as blasphemous
+in several. The work of Bruno in which his astronomical opinions are
+contained is _De Monade, etc._ (Frankfort, 1591, 8vo). He is the most
+thorough-going Copernican possible, and throws out almost every opinion,
+true or false, which has ever been discussed by astronomers, from the
+theory of innumerable inhabited worlds and systems to that {62} of the
+planetary nature of comets. Libri (vol. iv)[73] has reprinted the most
+striking part of his expressions of Copernican opinion."
+
+
+
+THIS LEADS TO THE CHURCH QUESTION.
+
+The Satanic doctrine that a church may employ force in aid of its dogma is
+supposed to be obsolete in England, except as an individual paradox; but
+this is difficult to settle. Opinions are much divided as to what the Roman
+Church would do in England, if she could: any one who doubts that she
+claims the right does not deserve an answer. When the hopes of the
+Tractarian section of the High Church were in bloom, before the most
+conspicuous intellects among them had _transgressed_ their ministry, that
+they might go to their own place, I had the curiosity to see how far it
+could be ascertained whether they held the only doctrine which makes me the
+personal enemy of a sect. I found in one of their tracts the assumption of
+a right to persecute, modified by an asserted conviction that force was not
+efficient. I cannot now say that this tract was one of the celebrated
+ninety; and on looking at the collection I find it so poorly furnished with
+contents, etc., that nothing but searching through three thick volumes
+would decide. In these volumes I find, augmenting as we go on, declarations
+about the character and power of "the Church" which have a suspicious
+appearance. The suspicion is increased by that curious piece of sophistry,
+No. 87, on religious reserve. The queer paradoxes of that tract leave us in
+doubt as to everything but this, that the church(man) is not bound to give
+his whole counsel in all things, and not bound to say what the things are
+in which he does not give it. It is likely enough that some of the "rights
+and liberties" are but scantily described. There is now no fear; but the
+time was when, if not fear, there might be a looking for of fear to come;
+nobody could then be so {63} sure as we now are that the lion was only
+asleep. There was every appearance of a harder fight at hand than was
+really found needful.
+
+Among other exquisite quirks of interpretation in the No. 87 above
+mentioned is the following. God himself employs reserve; he is said to be
+decked with light as with a garment (the old or prayer-book version of
+Psalm civ. 2). To an ordinary apprehension this would be a strong image of
+display, manifestation, revelation; but there is something more. "Does not
+a garment veil in some measure that which it clothes? Is not that very
+light concealment?"
+
+This No. 87, admitted into a series, fixes upon the managers of the series,
+who permitted its introduction, a strong presumption of that underhand
+intent with which they were charged. At the same time it is honorable to
+our liberty that this series could be published: though its promoters were
+greatly shocked when the Essayists and Bishop Colenso[74] took a swing on
+the other side. When No. 90 was under discussion, Dr. Maitland,[75] the
+librarian at Lambeth, asked Archbishop Howley[76] a question about No. 89.
+"I did not so much as know there _was_ a No. 89," was the answer. I am
+almost sure I have seen this in print, and quite sure that Dr. Maitland
+told it to me. It is creditable that there was so much freedom; but No. 90
+was _too bad_, and was stopped.
+
+The Tractarian mania has now (October 1866) settled down into a chronic
+vestment disease, complicated with fits of transubstantiation, which has
+taken the name of {64} _Ritualism_. The common sense of our national
+character will not put up with a continuance of this grotesque folly;
+millinery in all its branches will at last be advertised only over the
+proper shops. I am told that the Ritualists give short and practical
+sermons; if so, they may do good in the end. The English Establishment has
+always contained those who want an excitement; the New Testament, in its
+plain meaning, can do little for them. Since the Revolution, Jacobitism,
+Wesleyanism, Evangelicism, Puseyism,[77] and Ritualism, have come on in
+turn, and have furnished hot water for those who could not wash without it.
+If the Ritualists should succeed in substituting short and practical
+teaching for the high-spiced lectures of the doctrinalists, they will be
+remembered with praise. John the Baptist would perhaps not have brought all
+Jerusalem out into the wilderness by his plain and good sermons: it was the
+camel's hair and the locusts which got him a congregation, and which,
+perhaps, added force to his precepts. When at school I heard a dialogue,
+between an usher and the man who cleaned the shoes, about Mr. ----, a
+minister, a very corporate body with due area of waistcoat. "He is a man of
+great erudition," said the first. "Ah, yes sir," said Joe; "any one can see
+that who looks at that silk waistcoat."]
+
+
+
+OF THOMAS GEPHYRANDER SALICETUS.
+
+[When I said at the outset that I had only taken books from my own store, I
+should have added that I did not make any search for information given as
+_part_ of a work. Had I looked _through_ all my books, I might have made
+some curious additions. For instance, in Schott's _Magia Naturalis_[78]
+{65} (vol. iii. pp. 756-778) is an account of the quadrature of
+Gephyra_u_der, as he is misprinted in Montucla. He was Thomas Gephyrander
+Salicetus; and he published two editions, in 1608 and 1609.[79] I never
+even heard of a copy of either. His work is of the extreme of absurdity: he
+makes a distinction between geometrical and arithmetical fractions, and
+evolves theorems from it. More curious than his quadrature is his name;
+what are we to make of it? If a German, he is probably a German form of
+_Bridgeman_. and Salicetus refers him to _Weiden_. But _Thomas_ was hardly
+a German Christian name of his time; of 526 German philosophers,
+physicians, lawyers, and theologians who were biographed by Melchior
+Adam,[80] only two are of this name. Of these one is Thomas Erastus,[81]
+the physician whose theological writings against the Church as a separate
+power have given the name of Erastians to those who follow his doctrine,
+whether they have heard of him or not. Erastus is little known;
+accordingly, some have supposed that he must be Erastus, the friend of St.
+Paul and Timothy (Acts xix. 22; 2 Tim. iv. 20; Rom. xvi. 23), but what this
+gentleman did to earn the character is not hinted at. Few words would have
+done: Gaius (Rom. xvi. 23) has an immortality which many more noted men
+have missed, given by John Bunyan, out of seven words of St. Paul. I was
+once told that the Erastians got their name from _Blastus_, and I could not
+solve _bl = er_: at last I remembered that Blastus was a _chamberlain_[82]
+as well as Erastus; hence the association which {66} caused the mistake.
+The real heresiarch was a physician who died in 1583; his heresy was
+promulgated in a work, published immediately after his death by his widow,
+_De Excommunicatione Ecclesiastica_. He denied the power of excommunication
+on the principle above stated; and was answered by Besa.[83] The work was
+translated by Dr. R. Lee[84] (Edinb. 1844, 8vo). The other is Thomas
+Grynæus,[85] a theologian, nephew of Simon, who first printed Euclid in
+Greek; of him Adam says that of works he published none, of learned sons
+four. If Gephyrander were a Frenchman, his name is not so easily guessed
+at; but he must have been of La Saussaye. The account given by Schott is
+taken from a certain Father Philip Colbinus, who wrote against him.
+
+In some manuscripts lately given to the Royal Society, David Gregory,[86]
+who seems to have seen Gephyrander's work, calls him Salicetus
+_Westphalus_, which is probably on the title-page. But the only Weiden I
+can find is in Bavaria. Murhard has both editions in his Catalogue, but had
+plainly never seen the books: he gives the author as Thomas Gep. Hyandrus,
+Salicettus Westphalus. Murhard is a very old referee of mine; but who the
+_non nominandus_ was to see Montucla's _Gephyrander_ in Murhard's _Gep.
+Hyandrus_, both writers being usually accurate?]
+
+
+
+NAPIER ON REVELATIONS.
+
+    A plain discoverie of the whole Revelation of St. John ... whereunto
+    are annexed certain oracles of Sibylla.... Set Foorth by John Napeir L.
+    of Marchiston. London, 1611, 4to.[87]
+
+{67}
+
+The first edition was Edinburgh, 1593,[88] 4to. Napier[89] always believed
+that his great mission was to upset the Pope, and that logarithms, and such
+things, were merely episodes and relaxations. It is a pity that so many
+books have been written about this matter, while Napier, as good as any, is
+forgotten and unread. He is one of the first who gave us the six thousand
+years. "There is a sentence of the house of Elias reserved in all ages,
+bearing these words: The world shall stand six thousand years, and then it
+shall be consumed by fire: two thousand yeares voide or without lawe, two
+thousand yeares under the law, and two thousand yeares shall be the daies
+of the Messias...."
+
+I give Napier's parting salute: it is a killing dilemma:
+
+"In summar conclusion, if thou o _Rome_ aledges thyselfe reformed, and to
+beleeue true Christianisme, then beleeue Saint _John_ the Disciple, whome
+Christ loued, publikely here in this Reuelation proclaiming thy wracke, but
+if thou remain Ethnick in thy priuate thoghts, beleeuing[90] the old
+Oracles of the _Sibyls_ reuerently keeped somtime in thy _Capitol_: then
+doth here this _Sibyll_ proclame also thy wracke. Repent therefore alwayes,
+in this thy latter breath, as thou louest thine Eternall salvation.
+_Amen_."
+
+--Strange that Napier should not have seen that this appeal could not
+succeed, unless the prophecies of the Apocalypse were no true prophecies at
+all.
+
+{68}
+
+
+
+OF GILBERT'S DE MAGNETE.
+
+    De Magnete magneticisque corporibus, et de magno magnete tellure. By
+    William Gilbert. London, 1600, folio.--There is a second edition; and a
+    third, according to Watt.[91]
+
+Of the great work on the magnet there is no need to speak, though it was a
+paradox in its day. The posthumous work of Gilbert, "De Mundo nostro
+sublunari philosophia nova" (Amsterdam, 1651, 4to)[92] is, as the title
+indicates, confined to the physics of the globe and its atmosphere. It has
+never excited attention: I should hope it would be examined with our
+present lights.
+
+
+
+OF GIOVANNI BATISTA PORTA.
+
+    Elementorum Curvilineorium Libri tres. By John Baptista Porta. Rome,
+    1610, 4to.[93]
+
+This is a ridiculous attempt, which defies description, except that it is
+all about lunules. Porta was a voluminous writer. His printer announces
+fourteen works printed, and four to come, besides thirteen plays printed,
+and eleven waiting. His name is, and will be, current in treatises on
+physics for more reasons than one.
+
+{69}
+
+
+
+CATALDI ON THE QUADRATURE.
+
+    Trattato della quadratura del cerchio. Di Pietro Antonio Cataldi.
+    Bologna, 1612, folio.[94]
+
+Rheticus,[95] Vieta, and Cataldi are the three untiring computers of
+Germany, France, and Italy; Napier in Scotland, and Briggs[96] in England,
+come just after them. This work claims a place as beginning with the
+quadrature of Pellegrino Borello[97] of Reggio, who will have the circle to
+be exactly 3 diameters and 69/484 of a diameter. Cataldi, taking Van
+Ceulen's approximation, works hard at the finding of integers which nearly
+represent the ratio. He had not then the _continued fraction_, a mode of
+representation which he gave the next year in his work on the square root.
+He has but twenty of Van Ceulen's thirty places, which he takes from
+Clavius[98]: and any one might be puzzled to know whence the Italians got
+the result; Van Ceulen, in 1612, not having been translated from Dutch. But
+Clavius names his comrade Gruenberger, and attributes the approximation to
+them {70} jointly; "Lud. a Collen et Chr. Gruenbergerus[99] invenerunt,"
+which he had no right to do, unless, to his private knowledge, Gruenberger
+had verified Van Ceulen. And Gruenberger only handed over twenty of the
+places. But here is one instance, out of many, of the polyglot character of
+the Jesuit body, and its advantages in literature.
+
+
+
+OF LANSBERGIUS.
+
+    Philippi Lausbergii Cyclometriæ Novæ Libri Duo. Middleburg, 1616,
+    4to.[100]
+
+This is one of the legitimate quadratures, on which I shall here only
+remark that by candlelight it is quadrature under difficulties, for all the
+diagrams are in red ink.
+
+
+
+A TEXT LEADING TO REMARKS ON PRESTER JOHN.
+
+    Recherches Curieuses des Mesures du Monde. By S. C. de V. Paris, 1626,
+    8vo (pp. 48).[101]
+
+It is written by some Count for his son; and if all the French nobility
+would have given their sons the same kind of instruction about rank, the
+old French aristocracy would have been as prosperous at this moment as the
+English peerage and squireage. I sent the tract to Capt. Speke,[102]
+shortly after his arrival in England, thinking he might like {71} to see
+the old names of the Ethiopian provinces. But I first made a copy of all
+that relates to Prester John,[103] himself a paradox. The tract contains,
+_inter alia_, an account of the four empires; of the great Turk, the great
+Tartar, the great Sophy, and the great Prester John. This word _great_
+(_grand_), which was long used in the phrase "the great Turk," is a generic
+adjunct to an emperor. Of the Tartars it is said that "c'est vne nation
+prophane et barbaresque, sale et vilaine, qui mangent la chair demie cruë,
+qui boiuent du laict de jument, et qui n'vsent de nappes et seruiettes que
+pour essuyer leurs bouches et leurs mains."[104] Many persons have heard of
+Prester John, and have a very indistinct idea of him. I give all that is
+said about him, since the recent discussions about the Nile may give an
+interest to the old notions of geography.
+
+"Le grand Prestre Jean qui est le quatriesme en rang, est Empereur
+d'Ethiopie, et des Abyssins, et se vante d'estre issu de la race de Dauid,
+comme estant descendu de la Royne de Saba, Royne d'Ethiopie, laquelle
+estant venuë en Hierusalem pour voir la sagesse de Salomon, enuiron l'an du
+monde 2952, s'en retourna grosse d'vn fils qu'ils nomment Moylech, duquel
+ils disent estre descendus en ligne directe. Et ainsi il se glorifie
+d'estre le plus ancien Monarque de la terre, disant que son Empire a duré
+plus de trois mil ans, ce que nul autre Empire ne peut dire. Aussi met-il
+en ses tiltres ce qui s'ensuit: Nous, N. Souuerain en mes Royaumes,
+vniquement aymé de Dieu, colomne de la foy, sorty de la race de Inda, etc.
+Les limites de cet Empire touchent à la mer Rouge, et aux montagnes d'Azuma
+vers {72} l'Orient, et du costé de l'Occident, il est borné du fleuue du
+Nil, qui le separe de la Nubie, vers le Septentrion il a l'Ægypte, et au
+Midy les Royaumes de Congo, et de Mozambique, sa longueur contenant
+quarante degré, qui font mille vingt cinq lieuës, et ce depuis Congo ou
+Mozambique qui sont au Midy, iusqu'en Ægypte qui est au Septentrion, et sa
+largeur contenant depuis le Nil qui est à l'Occident, iusqu'aux montagnes
+d'Azuma, qui sont à l'Orient, sept cens vingt cinq lieues, qui font vingt
+neuf degrez. Cét empire a sous soy trente grandes Prouinces, sçavoir,
+Medra, Gaga, Alchy, Cedalon, Mantro, Finazam, Barnaquez, Ambiam, Fungy,
+Angoté, Cigremaon, Gorga, Cafatez, Zastanla, Zeth, Barly, Belangana, Tygra,
+Gorgany, Barganaza, d'Ancut, Dargaly, Ambiacatina, Caracogly, Amara, Maon
+(_sic_), Guegiera, Bally, Dobora et Macheda. Toutes ces Prouinces cy dessus
+sont situées iustement sous la ligne equinoxiale, entres les Tropiques de
+Capricorne, et de Cancer. Mais elles s'approchent de nostre Tropique, de
+deux cens cinquante lieuës plus qu'elles ne font de l'autre Tropique. Ce
+mot de Prestre Jean signifie grand Seigneur, et n'est pas Prestre comme
+plusieurs pense, il a esté tousiours Chrestien, mais souuent Schismatique:
+maintenant il est Catholique, et reconnaist le Pape pour Souuerain Pontife.
+I'ay veu quelqu'vn des ses Euesques, estant en Hierusalem, auec lequel i'ay
+conferé souuent par le moyen de nostre trucheman: il estoit d'vn port graue
+et serieux, succiur (_sic_) en son parler, mais subtil à merueilles en tout
+ce qu'il disoit. Il prenoit grand plaisir au recit que je luy faisais de
+nos belles ceremonies, et de la grauité de nos Prelats en leurs habits
+Pontificaux, et autres choses que je laisse pour dire, que l'Ethiopien est
+ioyoux et gaillard, ne ressemblant en rien a la saleté du Tartare, ny à
+l'affreux regard du miserable Arabe, mais ils sont fins et cauteleux, et ne
+se fient en personne, soupçonneux à merueilles, et fort devotieux, ils ne
+sont du tout noirs comme l'on croit, i'entens parler de ceux qui ne sont
+pas sous la ligne Equinoxiale, ny trop proches {73} d'icelle, car ceux qui
+sont dessous sont les Mores que nous voyons."[105]
+
+It will be observed that the author speaks of his conversation with an
+Ethiopian bishop, about that bishop's sovereign. Something must have passed
+between the two which satisfied the writer that the bishop acknowledged his
+own sovereign under some title answering to Prester John.
+
+{74}
+
+
+
+CONCERNING A TRACT BY FIENUS.
+
+    De Cometa anni 1618 dissertationes Thomæ Fieni[106] et Liberti
+    Fromondi[107] ... Equidem Thomæ Fieni epistolica quæstio, An verum sit
+    Coelum moveri et Terram quiescere? London, 1670, 8vo.
+
+This tract of Fienus against the motion of the earth is a reprint of one
+published in 1619.[108] I have given an account of it as a good summary of
+arguments of the time, in the _Companion to the Almanac_ for 1836.
+
+{75}
+
+
+
+ON SNELL'S WORK.
+
+    Willebrordi Snellii. R. F. Cyclometricus. Leyden, 1621, 4to.
+
+This is a celebrated work on the approximative quadrature, which, having
+the suspicious word _cyclometricus_, must be noticed here for
+distinction.[109]
+
+
+
+ON BACON'S NOVUM ORGANUM.
+
+1620. In this year, Francis Bacon[110] published his _Novum Organum_,[111]
+which was long held in England--but not until the last century--to be the
+work which taught Newton and all his successors how to philosophize. That
+Newton never mentions Bacon, nor alludes in any way to his works, passed
+for nothing. Here and there a paradoxer ventured not to find all this
+teaching in Bacon, but he was pronounced blind. In our day it begins to be
+seen that, great as Bacon was, and great as his book really is, he is not
+the philosophical father of modern discovery.
+
+But old prepossession will find reason for anything. A learned friend of
+mine wrote to me that he had discovered proof that Newton owned Bacon for
+his master: the proof was that Newton, in some of his earlier writings,
+used the {76} phrase _experimentum crucis_, which is Bacon's. Newton may
+have read some of Bacon, though no proof of it appears. I have a dim idea
+that I once saw the two words attributed to the alchemists: if so, there is
+another explanation; for Newton was deeply read in the alchemists.
+
+I subjoin a review which I wrote of the splendid edition of Bacon by
+Spedding,[112] Ellis,[113] and Heath.[114] All the opinions therein
+expressed had been formed by me long before: most of the materials were
+collected for another purpose.
+
+
+
+    The Works of Francis Bacon. Edited by James Spedding, R. Leslie Ellis,
+    and Douglas D. Heath. 5 vols.[115]
+
+No knowledge of nature without experiment and observation: so said
+Aristotle, so said Bacon, so acted Copernicus, Tycho Brahé,[116] Gilbert,
+Kepler, Galileo, Harvey, etc., before Bacon wrote.[117] No derived
+knowledge _until_ experiment and observation are concluded: so said Bacon,
+and no one else. We do not mean to say that he laid down his principle in
+these words, or that he carried it to the utmost extreme: we mean that
+Bacon's ruling idea was the {77} collection of enormous masses of facts,
+and then digested processes of arrangement and elimination, so artistically
+contrived, that a man of common intelligence, without any unusual sagacity,
+should be able to announce the truth sought for. Let Bacon speak for
+himself, in his editor's English:
+
+"But the course I propose for the discovery of sciences is such as leaves
+but little to the acuteness and strength of wits, but places all wits and
+understandings nearly on a level. For, as in the drawing of a straight line
+or a perfect circle, much depends on the steadiness and practice of the
+hand, if it be done by aim of hand only, but if with the aid of rule or
+compass little or nothing, so it is exactly with my plan.... For my way of
+discovering sciences goes far to level men's wits, and leaves but little to
+individual excellence; because it performs everything by the surest rules
+and demonstrations."
+
+To show that we do not strain Bacon's meaning, we add what is said by
+Hooke,[118] whom we have already mentioned as his professed disciple, and,
+we believe, his only disciple of the day of Newton. We must, however,
+remind the reader that Hooke was very little of a mathematician, and spoke
+of algebra from his own idea of what others had told him:
+
+"The intellect is not to be suffered to act without its helps, but is
+continually to be assisted by some method or engine, which shall be as a
+guide to regulate its actions, so as that it shall not be able to act
+amiss. Of this engine, no man except the incomparable Verulam hath had any
+thoughts and he indeed hath promoted it to a very good pitch; but there is
+yet somewhat more to be added, which he seemed to want time to complete. By
+this, as by that {78} art of algebra in geometry, 'twill be very easy to
+proceed in any natural inquiry, regularly and certainly.... For as 'tis
+very hard for the most acute wit to find out any difficult problem in
+geometry without the help of algebra ... and altogether as easy for the
+meanest capacity acting by that method to complete and perfect it, so will
+it be in the inquiry after natural knowledge."
+
+Bacon did not live to mature the whole of this plan. Are we really to
+believe that if he had completed the _Instauratio_ we who write this--and
+who feel ourselves growing bigger as we write it--should have been on a
+level with Newton in physical discovery? Bacon asks this belief of us, and
+does not get it. But it may be said, Your business is with what he _did_
+leave, and with its consequences. Be it so. Mr. Ellis says: "That his
+method is impracticable cannot, I think, be denied, if we reflect not only
+that it never has produced any result, but also that the process by which
+scientific truths have been established cannot be so presented as even to
+appear to be in accordance with it." That this is very true is well known
+to all who have studied the history of discovery: those who deny it are
+bound to establish either that some great discovery has been made by
+Bacon's method--we mean by the part peculiar to Bacon--or, better still, to
+show that some new discovery can be made, by actually making it. No general
+talk about _induction_: no reliance upon the mere fact that certain
+experiments or observations have been made; let us see where _Bacon's
+induction_ has been actually used or can be used. Mere induction,
+_enumeratio simplex_, is spoken of by himself with contempt, as utterly
+incompetent. For Bacon knew well that a thousand instances may be
+contradicted by the thousand and first: so that no enumeration of
+instances, however large, is "sure demonstration," so long any are left.
+
+The immortal Harvey, who was _inventing_--we use the word in its old
+sense--the circulation of the blood, while {79} Bacon was in the full flow
+of thought upon his system, may be trusted to say whether, when the system
+appeared, he found any likeness in it to his own processes, or what would
+have been any help to him, if he had waited for the _Novum Organum_. He
+said of Bacon, "He writes philosophy like a Lord Chancellor." This has been
+generally supposed to be only a sneer at the _sutor ultra crepidam_; but we
+cannot help suspecting that there was more intended by it. To us, Bacon is
+eminently the philosopher of _error prevented_, not of _progress
+facilitated_. When we throw off the idea of being _led right_, and betake
+ourselves to that of being _kept from going wrong_, we read his writings
+with a sense of their usefulness, his genius, and their probable effect
+upon purely experimental science, which we can be conscious of upon no
+other supposition. It amuses us to have to add that the part of Aristotle's
+logic of which he saw the value was the book on _refutation of fallacies_.
+Now is this not the notion of things to which the bias of a practised
+lawyer might lead him? In the case which is before the Court, generally
+speaking, truth lurks somewhere about the facts, and the elimination of all
+error will show it in the residuum. The two senses of the word _law_ come
+in so as to look almost like a play upon words. The judge can apply the law
+so soon as the facts are settled: the physical philosopher has to deduce
+the law from the facts. Wait, says the judge, until the facts are
+determined: did the prisoner take the goods with felonious intent? did the
+defendant give what amounts to a warranty? or the like. Wait, says Bacon,
+until all the facts, or all the obtainable facts, are brought in: apply my
+rules of separation to the facts, and the result shall come out as easily
+as by ruler and compasses. We think it possible that Harvey might allude to
+the legal character of Bacon's notions: we can hardly conceive so acute a
+man, after seeing what manner of writer Bacon was, meaning only that he was
+a lawyer and had better stick to his business. We do ourselves believe that
+Bacon's philosophy {80} more resembles the action of mind of a common-law
+judge--not a Chancellor--than that of the physical inquirers who have been
+supposed to follow in his steps. It seems to us that Bacon's argument is,
+there can be nothing of law but what must be either perceptible, or
+mechanically deducible, when all the results of law, as exhibited in
+phenomena, are before us. Now the truth is, that the physical philosopher
+has frequently to conceive law which never was in his previous thought--to
+educe the unknown, not to choose among the known. Physical discovery would
+be very easy work if the inquirer could lay down his this, his that, and
+his t'other, and say, "Now, one of these it must be; let us proceed to try
+which." Often has he done this, and failed; often has the truth turned out
+to be neither this, that, nor t'other. Bacon seems to us to think that the
+philosopher is a judge who has to choose, upon ascertained facts, which of
+known statutes is to rule the decision: he appears to us more like a person
+who is to write the statute-book, with no guide except the cases and
+decisions presented in all their confusion and all their conflict.
+
+Let us take the well-known first aphorism of the _Novum Organum_:
+
+"Man being the servant and interpreter of nature, can do and understand so
+much, and so much only, as he has observed in fact or in thought of the
+course of nature: beyond this he neither knows anything nor can do
+anything."
+
+This aphorism is placed by Sir John Herschel[119] at the head of his
+_Discourse on the Study of Natural Philosophy_: a book containing notions
+of discovery far beyond any of which Bacon ever dreamed; and this because
+it was written {81} after discovery, instead of before. Sir John Herschel,
+in his version, has avoided the translation of _re vel mente observaverit_,
+and gives us only "by his observation of the order of nature." In making
+this the opening of an excellent sermon, he has imitated the theologians,
+who often employ the whole time of the discourse in stuffing matter into
+the text, instead of drawing matter out of it. By _observation_ he
+(Herschel) means the whole course of discovery, observation, hypothesis,
+deduction, comparison, etc. The type of the Baconian philosopher as it
+stood in his mind, had been derived from a noble example, his own father,
+William Herschel,[120] an inquirer whose processes would have been held by
+Bacon to have been vague, insufficient, compounded of chance work and
+sagacity, and too meagre of facts to deserve the name of induction. In
+another work, his treatise on Astronomy,[121] Sir John Herschel, after
+noting that a popular account can only place the reader on the threshold,
+proceeds to speak as follows of all the higher departments of science. The
+italics are his own:
+
+"Admission to its sanctuary, and to the privileges and feelings of a
+votary, is only to be gained by one means--_sound and sufficient knowledge
+of mathematics, the great instrument of all exact inquiry, without which no
+man can ever make such advances in this or any other of the higher
+departments of science as can entitle him to form an independent opinion on
+any subject of discussion within their range_."
+
+How is this? Man can know no more than he gets from observation, and yet
+mathematics is the great instrument of all exact inquiry. Are the results
+of mathematical deduction results of observation? We think it likely that
+{82} Sir John Herschel would reply that Bacon, in coupling together
+_observare re_ and _observare mente_, has done what some wags said Newton
+afterwards did in his study-door--cut a large hole of exit for the large
+cat, and a little hole for the little cat.[122] But Bacon did no such
+thing: he never included any deduction under observation. To mathematics he
+had a dislike. He averred that logic and mathematics should be the
+handmaids, not the mistresses, of philosophy. He meant that they should
+play a subordinate and subsequent part in the dressing of the vast mass of
+facts by which discovery was to be rendered equally accessible to Newton
+and to us. Bacon himself was very ignorant of all that had been done by
+mathematics; and, strange to say, he especially objected to astronomy being
+handed over to the mathematicians. Leverrier and Adams, calculating an
+unknown planet into visible existence by enormous heaps of algebra, furnish
+the last comment of note on this specimen of the goodness of Bacon's views.
+The following account of his knowledge of what had been done in his own day
+or before it, is Mr. Spedding's collection of casual remarks in Mr. Ellis's
+several prefaces:
+
+"Though he paid great attention to astronomy, discussed carefully the
+methods in which it ought to be studied, constructed for the satisfaction
+of his own mind an elaborate theory of the heavens, and listened eagerly
+for the news from the stars brought by Galileo's telescope, he appears to
+have been utterly ignorant of the discoveries which had just been made by
+Kepler's calculations. Though he complained in 1623 of the want of
+compendious methods for facilitating arithmetical computations, especially
+with regard to the doctrine of Series, and fully recognized the importance
+of them as an aid to physical inquiries--he does not say a word about
+Napier's Logarithms, which had been published only nine years before and
+reprinted more than once in the {83} interval. He complained that no
+considerable advance had made in geometry beyond Euclid, without taking any
+notice of what had been done by Archimedes and Apollonius. He saw the
+importance of determining accurately the specific gravity of different
+substances, and himself attempted to form a table of them by a rude process
+of his own, without knowing of the more scientific though still imperfect
+methods previously employed by Archimedes, Ghetaldus,[123] and Porta. He
+speaks of the [Greek: heurêka] of Archimedes in a manner which implies that
+he did not clearly apprehend either the nature of the problem to be solved
+or the principles upon which the solution depended. In reviewing the
+progress of mechanics, he makes no mention of Archimedes himself, or of
+Stevinus,[124] Galileo, Guldinus,[125] or Ghetaldus. He makes no allusion
+to the theory of equilibrium. He observes that a ball of one pound weight
+will fall nearly as fast through the air as a ball of two, without alluding
+to the theory of the acceleration of falling bodies, which had been made
+known by Galileo more than thirty years before. He proposes an inquiry with
+regard to the lever--namely, whether in a balance with arms of different
+length but equal weight the distance from the fulcrum has any effect upon
+the inclination,--though the theory of the lever was as well understood in
+his own time as it is now. In making an experiment {84} of his own to
+ascertain the cause of the motion of a windmill, he overlooks an obvious
+circumstance which makes the experiment inconclusive, and an equally
+obvious variation of the same experiment which would have shown him that
+his theory was false. He speaks of the poles of the earth as fixed, in a
+manner which seems to imply that he was not acquainted with the precession
+of the equinoxes; and in another place, of the north pole being above and
+the south pole below, as a reason why in our hemisphere the north winds
+predominate over the south."
+
+Much of this was known before, but such a summary of Bacon's want of
+knowledge of the science of his own time was never yet collected in one
+place. We may add, that Bacon seems to have been as ignorant of
+Wright's[126] memorable addition to the resources of navigation as of
+Napier's addition to the means of calculation. Mathematics was beginning to
+be the great instrument of exact inquiry: Bacon threw the science aside,
+from ignorance, just at the time when his enormous sagacity, applied to
+knowledge, would have made him see the part it was to play. If Newton had
+taken Bacon for his master, not he, but somebody else, would have been
+Newton.[127]
+
+
+
+ON METEOROLOGICAL OBSERVATORIES.
+
+There is an attempt at induction going on, which has yielded little or no
+fruit, the observations made in the meteorological observatories. This
+attempt is carried on in a manner which would have caused Bacon to dance
+for joy; for he lived in times when Chancellors did dance. {85} Russia,
+says M. Biot,[128] is covered by an army of meteorographs, with generals,
+high officers, subalterns, and privates with fixed and defined duties of
+observation. Other countries have also their systematic observations. And
+what has come of it? Nothing, says M. Biot, and nothing will ever come of
+it; the veteran mathematician and experimental philosopher declares, as
+does Mr. Ellis, that no single branch of science has ever been fruitfully
+explored in this way. There is no _special object_, he says. Any one would
+suppose that M. Biot's opinion, given to the French Government upon the
+proposal to construct meteorological observatories in Algeria (_Comptes
+Rendus_, vol. xli, Dec. 31, 1855), was written to support the mythical
+Bacon, modern physics, against the real Bacon of the _Novum Organum_. There
+is no _special object_. In these words lies the difference between the two
+methods.
+
+
+
+[In the report to the Greenwich Board of Visitors for 1867 Mr. Airy,[129]
+speaking of the increase of meteorological observatories, remarks, "Whether
+the effect of this movement will be that millions of useless observations
+will be added to the millions that already exist, or whether something may
+be expected to result which will lead to a meteorological theory, I cannot
+hazard a conjecture." This _is_ a conjecture, and a very obvious one: if
+Mr. Airy would have given 2-3/4d. for the chance of a meteorological theory
+formed by masses of observations, he would never have said what I have
+quoted.]
+
+
+
+BASIS OF MODERN DISCOVERY.
+
+Modern discoveries have not been made by large collections of facts, with
+subsequent discussion, separation, and {86} resulting deduction of a truth
+thus rendered perceptible. A few facts have suggested an _hypothesis_,
+which means a _supposition_, proper to explain them. The necessary results
+of this supposition are worked out, and then, and not till then, other
+facts are examined to see if these ulterior results are found in nature.
+The trial of the hypothesis is the _special object_: prior to which,
+hypothesis must have been started, not by rule, but by that sagacity of
+which no description can be given, precisely because the very owners of it
+do not act under laws perceptible to themselves.[130] The inventor of
+hypothesis, if pressed to explain his method, must answer as did Zerah
+Colburn,[131] when asked for his mode of instantaneous calculation. When
+the poor boy had been bothered for some time in this manner, he cried out
+in a huff, "God put it into my head, and I can't put it into yours."[132]
+{87} Wrong hypotheses, rightly worked from, have produced more useful
+results than unguided observation. But this is not the Baconian plan.
+Charles the Second, when informed of the state of navigation, founded a
+Baconian observatory at Greenwich, to observe, observe, observe away at the
+moon, until her motions were known sufficiently well to render her useful
+in guiding the seaman. And no doubt Flamsteed's[133] observations, twenty
+or thirty of them at least, were of signal use. But how? A somewhat
+fanciful thinker, one Kepler, had hit upon the approximate orbits of the
+planets by trying one hypothesis after another: he found the _ellipse_,
+which the Platonists, well despised of Bacon, and who would have despised
+him as heartily if they had known him, had investigated and put ready to
+hand nearly 2000 years before.[134] The sun in the focus, the motions of
+the planet more and more rapid as they approach the sun, led Kepler--and
+Bacon would have reproved him for his rashness--to imagine that a force
+residing in the sun might move the planets, a force inversely as the
+distance. Bouillaud,[135] upon a fanciful analogy, rejected the inverse
+distance, {88} and, rejecting the force altogether, declared that if such a
+thing there were, it would be as the inverse _square_ of the distance.
+Newton, ready prepared with the mathematics of the subject, tried the fall
+of the moon towards the earth, away from her tangent, and found that, as
+compared with the fall of a stone, the law of the inverse square did hold
+for the moon. He deduced the ellipse, he proceeded to deduce the effect of
+the disturbance of the sun upon the moon, upon the assumed theory of
+_universal_ gravitation. He found result after result of his theory in
+conformity with observed fact: and, by aid of Flamsteed's observations,
+which amended what mathematicians call his _constants_, he constructed his
+lunar theory. Had it not been for Newton, the whole dynasty of Greenwich
+astronomers, from Flamsteed of happy memory, to Airy whom Heaven
+preserve,[136] might have worked away at nightly observation and daily
+reduction, without any remarkable result: looking forward, as to a
+millennium, to the time when any man of moderate intelligence was to see
+the whole explanation. What are large collections of facts for? To make
+theories _from_, says Bacon: to try ready-made theories _by_, says the
+history of discovery: it's all the same, says the idolater: nonsense, say
+we!
+
+Time and space run short: how odd it is that of the three leading ideas of
+mechanics, time, space, and matter, the first two should always fail a
+reviewer before the third. We might dwell upon many points, especially if
+we attempted a more descriptive account of the valuable edition before us.
+No one need imagine that the editors, by their uncompromising attack upon
+the notion of Bacon's influence common even among mathematicians and
+experimental philosophers, have lowered the glory of the great man whom it
+was, many will think, their business to defend through thick and thin. They
+have given a clearer notion of his {89} excellencies, and a better idea of
+the power of his mind, than ever we saw given before. Such a correction as
+theirs must have come, and soon, for as Hallam says--after noting that the
+_Novum Organum_ was _never published separately in England_, Bacon has
+probably been more read in the last thirty years--now forty--than in the
+two hundred years which preceded. He will now be more read than ever he
+was. The history of the intellectual world is the history of the worship of
+one idol after another. No sooner is it clear that a Hercules has appeared
+among men, than all that imagination can conceive of strength is attributed
+to him, and his labors are recorded in the heavens. The time arrives when,
+as in the case of Aristotle, a new deity is found, and the old one is
+consigned to shame and reproach. A reaction may afterwards take place, and
+this is now happening in the case of the Greek philosopher. The end of the
+process is, that the opposing deities take their places, side by side, in a
+Pantheon dedicated not to gods, but to heroes.
+
+
+
+THE REAL VALUE OF BACON'S WORKS.
+
+Passing over the success of Bacon's own endeavors to improve the details of
+physical science, which was next to nothing, and of his method as a whole,
+which has never been practised, we might say much of the good influence of
+his writings. Sound wisdom, set in sparkling wit, must instruct and amuse
+to the end of time: and, as against error, we repeat that Bacon is soundly
+wise, so far as he goes. There is hardly a form of human error within his
+scope which he did not detect, expose, and attach to a satirical metaphor
+which never ceases to sting. He is largely indebted to a very extensive
+reading; but the thoughts of others fall into his text with such a
+close-fitting compactness that he can make even the words of the Sacred
+Writers pass for his own. A saying of the prophet Daniel, rather a
+hackneyed quotation in our day, _Multi pertransibunt, et augebitur
+scientia_, stands in the title-page of the first edition {90} of Montucla's
+_History of Mathematics_ as a quotation from Bacon--and it is not the only
+place in which this mistake occurs. When the truth of the matter, as to
+Bacon's system, is fully recognized, we have little fear that there will be
+a reaction against the man. First, because Bacon will always live to speak
+for himself, for he will not cease to be read: secondly, because those who
+seek the truth will find it in the best edition of his works, and will be
+most ably led to know what Bacon was, in the very books which first showed
+at large what he _was not_.
+
+
+
+THE CONGREGATION OF THE INDEX, ON COPERNICUS.
+
+In this year (1620) appeared the corrections under which the Congregation
+of the Index--i.e., the Committee of Cardinals which superintended the
+_Index_ of forbidden books--proposed to allow the work of Copernicus to be
+read. I insert these conditions in full, because they are often alluded to,
+and I know of no source of reference accessible to a twentieth part of
+those who take interest in the question.
+
+By a decree of the Congregation of the Index, dated March 5, 1616, the work
+of Copernicus, and another of Didacus Astunica,[137] are suspended _donec
+corrigantur_, as teaching:
+
+"Falsam illam doctrinam Pythagoricam, divinæ que Scripturæ omnino
+adversantem, de mobilitate Terræ et immobilitate Solis."[138]
+
+But a work of the Carmelite Foscarini[139] is:
+
+{91}
+
+"Omnino prohibendum atque damnandum," because "ostendere conatur præfatam
+doctrinam ... consonam esse veritati et non adversari Sacræ
+Scripturæ."[140]
+
+Works which teach the false doctrine of the earth's motion are to be
+corrected; those which declare the doctrine conformable to Scripture are to
+be utterly prohibited.
+
+In a "Monitum ad Nicolai Copernici lectorem, ejusque emendatio, permissio,
+et correctio," dated 1620 without the month or day, permission is given to
+reprint the work of Copernicus with certain alterations; and, by
+implication, to read existing copies after correction in writing. In the
+preamble the author is called _nobilis astrologus_; not a compliment to his
+birth, which was humble, but to his fame. The suspension was because:
+
+"Sacræ Scripturæ, ejusque veræ et Catholicæ interpretationi repugnantia
+(quod in homine Christiano minime tolerandum) non _per hypothesin_
+tractare, sed _ut verissima_ adstruere non dubitat!"[141]
+
+And the corrections relate:
+
+"Locis in quibus non _ex hypothesi_, sed _asserendo_ de situ et motu Terræ
+disputat."[142]
+
+That is, the earth's motion may be an hypothesis for elucidation of the
+heavenly motions, but must not be asserted as a fact.
+
+
+
+(In Pref. circa finem.) "_Copernicus._ Si fortasse erunt [Greek:
+mataiologoi], qui cum omnium Mathematum ignari sint, tamen de illis
+judicium sibi summunt, propter aliquem locum scripturæ, male ad suum
+propositum detortum, ausi fuerint meum {92} hoc institutum reprehendere ac
+insectari: illos nihil moror adeo ut etiam illorum judicium tanquam
+temerarium contemnam. Non enim obscurum est Lactantium, celebrem alioqui
+scriptorem, sed Mathematicum parum, admodum pueriliter de forma terræ
+loqui, cum deridet eos, qui terram globi formam habere prodiderunt. Itaque
+non debet mirum videri studiosis, si qui tales nos etiam videbunt.
+Mathemata Mathematicis scribuntur, quibus et hi nostri labores, si me non
+fallit opinio, videbuntur etiam Reipub. ecclesiasticæ conducere aliquid....
+_Emend._ Ibi _si fortasse_ dele omnia, usque ad verbum _hi nostri labores_
+et sic accommoda--_Coeterum hi nostri labores_."[143]
+
+All the allusion to Lactantius, who laughed at the notion of the earth
+being round, which was afterwards found true, is to be struck out.
+
+
+
+(Cap. 5. lib. i. p. 3) "_Copernicus._ Si tamen attentius rem consideremus,
+videbitur hæc quæstio nondum absoluta, et ideireo minime contemnenda.
+_Emend._ Si tamen attentius rem consideremus, nihil refert an Terram in
+medio Mundi, an extra Medium existere, quoad solvendas coelestium motuum
+apparentias existimemus."[144]
+
+{93}
+
+We must not say the question is not yet settled, but only that it may be
+settled either way, so far as mere explanation of the celestial motions is
+concerned.
+
+
+
+(Cap. 8. lib. i.) "Totum hoc caput potest expungi, quia ex professo tractat
+de veritate motus Terræ, dum solvit veterum rationes probantes ejus
+quietem. Cum tamen problematice videatur loqui; ut studiosis satisfiat,
+seriesque et ordo libri integer maneat; emendetur ut infra."[145]
+
+A chapter which seems to assert the motion should perhaps be expunged; but
+it may perhaps be problematical; and, not to break up the book, must be
+amended as below.
+
+
+
+(p. 6.) "_Copernicus._ Cur ergo hesitamus adhuc, mobilitatem illi formæ suæ
+a natura congruentem concedere, magisquam quod totus labatur mundus, cujus
+finis ignoratur, scirique nequit, neque fateamur ipsius cotidianæ
+revolutionis in coelo apparentiam esse, et in terra veritatem? Et hæc
+perinde se habere, ac si diceret Virgilianus Æneas: Provehimur portu ...
+_Emend._ Cur ergo non possum mobilitatem illi formæ suæ concedere, magisque
+quod totus labatur mundus, cujus finis ignoratur scirique nequit, et quæ
+apparent in coelo, perinde se habere ac si ..."[146]
+
+{94}
+
+"Why should we hesitate to allow the earth's motion," must be altered into
+"I cannot concede the earth's motion."
+
+
+
+(p. 7.) "_Copernicus._ Addo etiam, quod satis absurdum videretur,
+continenti sive locanti motum adscribi, et non potius contento et locato,
+quod est terra. _Emend._ Addo etiam difficilius non esse contento et
+locato, quod est Terra, motum adscribere, quam continenti."[147]
+
+We must not say it is absurd to refuse motion to the _contained_ and
+_located_, and to give it to the containing and locating; say that neither
+is more difficult than the other.
+
+
+
+(p. 7.) "_Copernicus._ Vides ergo quod ex his omnibus probabilior sit
+mobilitas Terræ, quam ejus quies, præsertim in cotidiana revolutione,
+tanquam terræ maxime propria. _Emend._ _Vides_ ... delendus est usque ad
+finem capitis."[148]
+
+Strike out the whole of the chapter from this to the end; it says that the
+motion of the earth is the most probable hypothesis.
+
+
+
+(Cap. 9. lib. i. p. 7.) "_Copernicus._ Cum igitur nihil prohibeat
+mobilitatem Terræ, videndum nunc arbitror, an etiam plures illi motus
+conveniant, ut possit una errantium syderum existimari. _Emend._ Cum igitur
+Terram moveri assumpserim, videndum nunc arbitror, an etiam illi plures
+possint convenire motus."[149]
+
+{95}
+
+We must not say that nothing prohibits the motion of the earth, only that
+having _assumed_ it, we may inquire whether our explanations require
+several motions.
+
+
+
+(Cap. 10. lib. i. p. 9.) "_Copernicus._ Non pudet nos fateri ... hoc potius
+in mobilitate terræ verificari. _Emend._ Non pudet nos assumere ... hoc
+consequenter in mobilitate verificari."[150]
+
+(Cap. 10. lib. i. p. 10.) "_Copernicus._ Tanta nimirum est divina hæc. Opt.
+Max. fabrica. _Emend._ Dele illa verba postrema."[151]
+
+(Cap. ii. lib. i.[152]) "_Copernicus._ De triplici motu telluris
+demonstratio. _Emend._ De hypothesi triplicis motus Terræ, ejusque
+demonstratione."[153]
+
+(Cap. 10. lib. iv. p. 122.[154]) "_Copernicus._ De magnitudine horum trium
+siderum, Solis, Lunæ, et Terræ. _Emend._ Dele verba _horum trium siderum_,
+quia terra non est sidus, ut facit eam Copernicus."[155]
+
+We must not say we are not ashamed to _acknowledge_; _assume_ is the word.
+We must not call this assumption a _Divine work_. A chapter must not be
+headed _demonstration_, but _hypothesis_. The earth must not be called a
+_star_; the word implies motion.
+
+It will be seen that it does not take much to reduce Copernicus to pure
+hypothesis. No personal injury being done to the author--who indeed had
+been 17 years out of {96} reach--the treatment of his book is now an
+excellent joke. It is obvious that the Cardinals of the Index were a little
+ashamed of their position, and made a mere excuse of a few corrections.
+Their mode of dealing with chap. 8, this _problematice videtur loqui, ut
+studiosis satisfiat_,[156] is an excuse to avoid corrections. But they
+struck out the stinging allusion to Lactantius[157] in the preface, little
+thinking, honest men, for they really believed what they said--that the
+light of Lactantius would grow dark before the brightness of their own.
+
+
+
+THE CONVOCATION AT OXFORD EQUALLY AT FAULT.
+
+1622. I make no reference to the case of Galileo, except this. I have
+pointed out (_Penny Cycl. Suppl._ "Galileo"; _Engl. Cycl._ "Motion of the
+Earth") that it is clear the absurdity was the act of the _Italian_
+Inquisition--for the private and personal pleasure of the Pope, who _knew_
+that the course he took would not commit him as _Pope_--and not of the body
+which calls itself the _Church_. Let the dirty proceeding have its right
+name. The Jesuit Riccioli,[158] the stoutest and most learned
+Anti-Copernican in Europe, and the Puritan Wilkins, a strong Copernican and
+Pope-hater, are equally positive that the Roman _Church_ never pronounced
+any decision: and this in the time immediately following the ridiculous
+proceeding of the Inquisition. In like manner a decision of the Convocation
+of Oxford is not a law of the _English_ Church; which is fortunate, for
+that Convocation, in 1622, came to a decision quite as absurd, and a great
+deal {97} more wicked than the declaration against the motion of the earth.
+The second was a foolish mistake; the first was a disgusting surrender of
+right feeling. The story is told without disapprobation by Anthony Wood,
+who never exaggerated anything against the university of which he is
+writing eulogistic history.
+
+In 1622, one William Knight[159] put forward in a sermon preached before
+the University certain theses which, looking at the state of the times, may
+have been improper and possibly of seditious intent. One of them was that
+the bishop might excommunicate the civil magistrate: this proposition the
+clerical body could not approve, and designated it by the term
+_erronea_,[160] the mildest going. But Knight also declared as follows:
+
+"Subditis mere privatis, si Tyrannus tanquam latro aut stuprator in ipsos
+faciat impetum, et ipsi nec potestatem ordinariam implorare, nec alia
+ratione effugere periculum possint, in presenti periculo se et suos contra
+tyrannum, sicut contra privatum grassatorem, defendere licet."[161]
+
+That is, a man may defend his purse or a woman her honor, against the
+personal attack of a king, as against that of a private person, if no other
+means of safety can be found. The Convocation sent Knight to prison,
+declared the proposition _"falsa_, periculosa, et _impia_," and enacted
+that all applicants for degrees should subscribe this censure, and make
+oath that they would neither hold, teach, nor defend Knight's opinions.
+
+The thesis, in the form given, was unnecessary and improper. Though strong
+opinions of the king's rights were advanced at the time, yet no one
+ventured to say that, {98} ministers and advisers apart, the king might
+_personally_ break the law; and we know that the first and only attempt
+which his successor made brought on the crisis which cost him his throne
+and his head. But the declaration that the proposition was _false_ far
+exceeds in all that is disreputable the decision of the Inquisition against
+the earth's motion. We do not mention this little matter in England. Knight
+was a Puritan, and Neal[162] gives a short account of his sermon. From
+comparison with Wood,[163] I judge that the theses, as given, were not
+Knight's words, but the digest which it was customary to make in criminal
+proceedings against opinion. This heightens the joke, for it appears that
+the qualifiers of the Convocation took pains to present their condemnation
+of Knight in the terms which would most unequivocally make their censure
+condemn themselves. This proceeding took place in the interval between the
+two proceedings against Galileo: it is left undetermined whether we must
+say pot-kettle-pot or kettle-pot-kettle.
+
+
+
+    Liberti Fromondi.... Ant-Aristarchus, sive orbis terræ immobilis.
+    Antwerp, 1631, 8vo.[164]
+
+This book contains the evidence of an ardent opponent of Galileo to the
+fact, that Roman Catholics of the day did not consider the decree of the
+_Index_ or of the _Inquisition_ as a declaration of their _Church_. Fromond
+would have been glad to say as much, and tries to come near it, but
+confesses he must abstain. See _Penny Cyclop. Suppl._ "Galileo," and _Eng.
+Cycl._ "Motion of the Earth." The author of a celebrated article in the
+_Dublin Review_, in defence of the {99} Church of Rome, seeing that
+Drinkwater Bethune[165] makes use of the authority of Fromondus, but for
+another purpose, sneers at him for bringing up a "musty old Professor." If
+he had known Fromondus, and used him he would have helped his own case,
+which is very meagre for want of knowledge.[166]
+
+
+
+    Advis à Monseigneur l'eminentissime Cardinal Duc de Richelieu, sur la
+    Proposition faicte par le Sieur Morin pour l'invention des longitudes.
+    Paris, 1634, 8vo.[167]
+
+This is the Official Report of the Commissioners appointed by the Cardinal,
+of whom Pascal is the one now best known, to consider Morin's plan. See the
+full account in Delambre, _Hist. Astr. Mod._ ii. 236, etc.
+
+
+
+THE METIUS APPROXIMATION.
+
+    Arithmetica et Geometria practica. By Adrian Metius. Leyden, 1640,
+    4to.[168]
+
+This book contains the celebrated approximation _guessed at_ by his father,
+Peter Metius,[169] namely that the diameter is {100} to the circumference
+as 113 to 355. The error is at the rate of about a foot in 2,000 miles.
+Peter Metius, having his attention called to the subject by the false
+quadrature of Duchesne, found that the ratio lay between 333/106 and
+377/120. He then took the liberty of taking the mean of both numerators and
+denominators, giving 355/113. He had no right to presume that this mean was
+better than either of the extremes; nor does it appear positively that he
+did so. He published nothing; but his son Adrian,[170] when Van Ceulen's
+work showed how near his father's result came to the truth, first made it
+known in the work above. (See _Eng. Cyclop._, art. "Quadrature.")
+
+
+
+ON INHABITABLE PLANETS.
+
+    A discourse concerning a new world and another planet, in two books.
+    London, 1640, 8vo.[171]
+
+    Cosmotheoros: or conjectures concerning the planetary worlds and their
+    inhabitants. Written in Latin, by Christianus Huyghens. This
+    translation was first published in 1698. Glasgow, 1757, 8vo. [The
+    original is also of 1698.][172]
+
+The first work is by Bishop Wilkins, being the third edition, [first in
+1638] of the first book, "That the Moon may be a Planet"; and the first
+edition of the second work, {101} "That the Earth may be a Planet." [See
+more under the reprint of 1802.] Whether other planets be inhabited or not,
+that is, crowded with organisations some of them having consciousness, is
+not for me to decide; but I should be much surprised if, on going to one of
+them, I should find it otherwise. The whole dispute tacitly assumes that,
+if the stars and planets be inhabited, it must be by things of which we can
+form some idea. But for aught we know, what number of such bodies there
+are, so many organisms may there be, of which we have no way of thinking
+nor of speaking. This is seldom remembered. In like manner it is usually
+forgotten that the _matter_ of other planets may be of different chemistry
+from ours. There may be no oxygen and hydrogen in Jupiter, which may have
+_gens_ of its own.[173] But this must not be said: it would limit the
+omniscience of the _a priori_ school of physical inquirers, the larger half
+of the whole, and would be very _unphilosophical_. Nine-tenths of my best
+paradoxers come out from among this larger half, because they are just a
+little more than of it at their entrance.
+
+There was a discussion on the subject some years ago, which began with
+
+    The plurality of worlds: an Essay. London, 1853, 8vo. [By Dr. Wm.
+    Whewell, Master of Trinity College, Cambridge]. A dialogue on the
+    plurality of worlds, being a supplement to the Essay on that subject.
+    [First found in the second edition, 1854; removed to the end in
+    subsequent editions, and separate copies issued.][174]
+
+A work of skeptical character, insisting on analogies which prohibit the
+positive conclusion that the planets, stars, etc., are what we should call
+_inhabited_ worlds. It produced {102} several works and a large amount of
+controversy in reviews. The last predecessor of whom I know was
+
+    Plurality of Worlds.... By Alexander Maxwell. Second Edition. London,
+    1820, 8vo.
+
+This work is directed against the plurality by an author who does not admit
+modern astronomy. It was occasioned by Dr. Chalmers's[175] celebrated
+discourses on religion in connection with astronomy. The notes contain many
+citations on the gravity controversy, from authors now very little read:
+and this is its present value. I find no mention of Maxwell, not even in
+Watt.[176] He communicated with mankind without the medium of a publisher;
+and, from Vieta till now, this method has always been favorable to loss of
+books.
+
+A correspondent informs me that Alex. Maxwell, who wrote on the plurality
+of worlds, in 1820, was a law-bookseller and publisher (probably his own
+publisher) in Bell Yard. He had peculiar notions, which he was fond of
+discussing with his customers. He was a bit of a Swedenborgian.
+
+
+
+INHABITED PLANETS IN FICTION.
+
+There is a class of hypothetical creations which do not belong to my
+subject, because they are _acknowledged_ to be fictions, as those of
+Lucian,[177] Rabelais,[178] Swift, Francis {103} Godwin,[179] Voltaire,
+etc. All who have more positive notions as to either the composition or
+organization of other worlds, than the reasonable conclusion that our
+Architect must be quite able to construct millions of other buildings on
+millions of other plans, ought to rank with the writers just mentioned, in
+all but self-knowledge. Of every one of their systems I say, as the Irish
+Bishop said of Gulliver's book,--I don't believe half of it. Huyghens had
+been preceded by Fontenelle,[180] who attracted more attention. Huyghens is
+very fanciful and very positive; but he gives a true account of his method.
+"But since there's no hopes of a Mercury to carry us such a journey, we
+shall e'en be contented with what's in our power: we shall suppose
+ourselves there...." And yet he says, "We have proved that they live in
+societies, have hands and feet...." Kircher[181] had gone to the stars
+before him, but would not find any life in them, either animal or
+vegetable.
+
+The question of the inhabitants of a particular planet is one which has
+truth on one side or the other: either there are some inhabitants, or there
+are none. Fortunately, it is of no consequence which is true. But there are
+many cases where the balance is equally one of truth and falsehood, in
+which the choice is a matter of importance. My work selects, for the most
+part, sins against demonstration: but the world is full of questions of
+fact or opinion, in which a struggling minority will become a majority, or
+else will {104} be gradually annihilated: and each of the cases subdivides
+into results of good, and results of evil. What is to be done?
+
+ "Periculosum est credere et non credere;
+  Hippolitus obiit quia novercæ creditum est;
+  Cassandræ quia non creditum ruit Ilium:
+  Ergo exploranda est veritas multum prius
+  Quam stulta prove judicet sententia."[182]
+
+
+
+    Nova Demonstratio immobilitatis terræ petita ex virtute magnetica. By
+    Jacobus Grandamicus. Flexiae (La Flèche), 1645, 4to.[183]
+
+No magnetic body can move about its poles: the earth is a magnetic body,
+therefore, etc. The iron and its magnetism are typical of two natures in
+one person; so it is said, "Si exaltatus fuero à terra, omnia traham ad me
+ipsum."[184]
+
+
+
+A VENETIAN BUDGET OF PARADOXES.
+
+    Le glorie degli incogniti, o vero gli huomini illustri dell' accademia
+    de' signori incogniti di Venetia. Venice, 1647, 4to.
+
+This work is somewhat like a part of my own: it is a budget of Venetian
+nobodies who wished to be somebodies; but paradox is not the only means
+employed. It is of a serio-comic character, gives genuine portraits in
+copperplate, and grave lists of works; but satirical accounts. The
+astrologer Andrew Argoli[185] is there, and his son; both of whom, with
+some of the others, have place in modern works {105} on biography. Argoli's
+discovery that logarithms facilitate easy processes, but increase the labor
+of difficult ones, is worth recording.
+
+
+
+    Controversiæ de vera circuli mensura ... inter ... C. S. Longomontanum
+    et Jo. Pellium.[186] Amsterdam, 1647, 4to.
+
+Longomontanus,[187] a Danish astronomer of merit, squared the circle in
+1644: he found out that the diameter 43 gives the square root of 18252 for
+the circumference; which gives 3.14185... for the ratio. Pell answered him,
+and being a kind of circulating medium, managed to engage in the
+controversy names known and unknown, as Roberval, Hobbes, Carcavi, Lord
+Charles Cavendish, Pallieur, Mersenne, Tassius, Baron Wolzogen, Descartes,
+Cavalieri and Golius.[188] Among them, of course, Longomontanus was made
+{106} mincemeat: but he is said to have insisted on the discovery of his
+epitaph.[189]
+
+{107}
+
+
+
+THE CIRCULATING MEDIA OF MATHEMATICS.
+
+The great circulating mediums, who wrote to everybody, heard from
+everybody, and sent extracts to everybody else, have been Father Mersenne,
+John Collins, and the late Professor Schumacher: all "late" no doubt, but
+only the last recent enough to be so styled. If M.C.S. should ever again
+stand for "Member of the Corresponding Society," it should raise an
+acrostic thought of the three. There is an allusion to Mersenne's
+occupation in Hobbes's reply to him. He wanted to give Hobbes, who was very
+ill at Paris, the Roman Eucharist: but Hobbes said, "I have settled all
+that long ago; when did you hear from Gassendi?" We are reminded of
+William's answer to Burnet. John Collins disseminated Newton, among others.
+Schumacher ought to have been called the postmaster-general of astronomy,
+as Collins was called the attorney-general of mathematics.[190]
+
+{108}
+
+
+
+THE SYMPATHETIC POWDER.
+
+    A late discourse ... by Sir Kenelme Digby.... Rendered into English by
+    R. White. London, 1658, 12mo.
+
+On this work see _Notes and Queries_, 2d series, vii. 231, 299, 445, viii.
+190. It contains the celebrated sympathetic powder. I am still in much
+doubt as to the connection of Digby with this tract.[191] Without entering
+on the subject here, I observe that in Birch's _History of the Royal
+Society_,[192] to which both Digby and White belonged, Digby, though he
+brought many things before the Society, never mentioned the powder, which
+is connected only with the names of Evelyn[193] and Sir Gilbert
+Talbot.[194] The sympathetic powder was that which cured by anointing the
+weapon with its salve instead of the wound. I have long been convinced that
+it was efficacious. The directions were to keep the {109} wound clean and
+cool, and to take care of diet, rubbing the salve on the knife or
+sword.[195] If we remember the dreadful notions upon drugs which prevailed,
+both as to quantity and quality, we shall readily see that any way of _not_
+dressing the wound would have been useful. If the physicians had taken the
+hint, had been careful of diet etc., and had poured the little barrels of
+medicine down the throat of a practicable doll, _they_ would have had their
+magical cures as well as the surgeons.[196] Matters are much improved now;
+the quantity of medicine given, even by orthodox physicians, would have
+been called infinitesimal by their professional ancestors. Accordingly, the
+College of Physicians has a right to abandon its motto, which is _Ars
+longa, vita brevis_, meaning _Practice is long, so life is short_.
+
+
+
+HOBBES AS A MATHEMATICIAN.
+
+    Examinatio et emendatio Mathematicæ Hodiernæ. By Thomas Hobbes. London,
+    1666, 4to.
+
+In six dialogues: the sixth contains a quadrature of the circle.[197] But
+there is another edition of this work, without place or date on the
+title-page, in which the quadrature is omitted. This seems to be connected
+with the publication {110} of another quadrature, without date, but about
+1670, as may be judged from its professing to answer a tract of Wallis,
+printed in 1669.[198] The title is "Quadratura circuli, cubatio sphæræ,
+duplicatio cubi," 4to.[199] Hobbes, who began in 1655, was very wrong in
+his quadrature; but, though not a Gregory St. Vincent,[200] he was not the
+ignoramus in geometry that he is sometimes supposed. His writings,
+erroneous as they are in many things, contain acute remarks on points of
+principle. He is wronged by being coupled with Joseph Scaliger, as the two
+great instances of men of letters who have come into geometry to help the
+mathematicians out of their difficulty. I have never seen Scaliger's
+quadrature,[201] except in the answers of Adrianus Romanus,[202] Vieta and
+Clavius, and in the extracts of Kastner.[203] Scaliger had no right to such
+strong opponents: Erasmus or Bentley might just as well have tried the
+problem, and either would have done much better in any twenty minutes of
+his life.[204]
+
+
+
+AN ESTIMATE OF SCALIGER.
+
+Scaliger inspired some mathematicians with great respect for his
+geometrical knowledge. Vieta, the first man of his time, who answered him,
+had such regard for his opponent {111} as made him conceal Scaliger's name.
+Not that he is very respectful in his manner of proceeding: the following
+dry quiz on his opponent's logic must have been very cutting, being true.
+"In grammaticis, dare navibus Austros, et dare naves Austris, sunt æque
+significantia. Sed in Geometricis, aliud est adsumpsisse circulum BCD non
+esse majorem triginta sex segmentis BCDF, aliud circulo BCD non esse majora
+triginta sex segmenta BCDF. Illa adsumptiuncula vera est, hæc falsa."[205]
+Isaac Casaubon,[206] in one of his letters to De Thou,[207] relates that,
+he and another paying a visit to Vieta, the conversation fell upon
+Scaliger, of whom the host said that he believed Scaliger was the only man
+who perfectly understood mathematical writers, especially the Greek ones:
+and that he thought more of Scaliger when wrong than of many others when
+right; "pluris se Scaligerum vel errantem facere quam multos [Greek:
+katorthountas]."[208] This must have been before Scaliger's quadrature
+(1594). There is an old story of some one saying, "Mallem cum Scaligero
+errare, quam cum Clavio recte sapere."[209] This I cannot help suspecting
+to have been a version of Vieta's speech with Clavius satirically inserted,
+on account of the great hostility which Vieta showed towards Clavius in the
+latter years of his life.
+
+Montucla could not have read with care either Scaliger's quadrature or
+Clavius's refutation. He gives the first a wrong date: he assures the world
+that there is no question about Scaliger's quadrature being wrong, in the
+eyes of geometers at least: and he states that Clavius mortified him {112}
+extremely by showing that it made the circle less than its inscribed
+dodecagon, which is, of course, equivalent to asserting that a straight
+line is not always the shortest distance between two points. Did _Clavius_
+show this? No, it was Scaliger himself who showed it, boasted of it, and
+declared it to be a "noble paradox" that a theorem false in geometry is
+true in arithmetic; a thing, he says with great triumph, not noticed by
+Archimedes himself! He says in so many words that the periphery of the
+dodecagon is greater than that of the circle; and that the more sides there
+are to the inscribed figure, the more does it exceed the circle in which it
+is. And here _are_ the words, on the independent testimonies of Clavius and
+Kastner:
+
+"Ambitus dodecagoni circulo inscribendi plus potest quam circuli ambitus.
+Et quanto deinceps plurium laterum fuerit polygonum circulo inscribendum,
+tanto plus poterit ambitus polygoni quam ambitus circuli."[210]
+
+There is much resemblance between Joseph Scaliger and William
+Hamilton,[211] in a certain impetuousity of character, and inaptitude to
+think of quantity. Scaliger maintained that the arc of a circle is less
+than its chord in arithmetic, though greater in geometry; Hamilton arrived
+at two quantities which are identical, but the greater the one the less the
+other. But, on the whole, I liken Hamilton rather to Julius than to Joseph.
+On this last hero of literature I repeat Thomas Edwards,[212] who says that
+a man is unlearned who, be his other knowledge what it may, does not {113}
+understand the subject he writes about. And now one of many instances in
+which literature gives to literature character in science. Anthony
+Teissier,[213] the learned annotator of De Thou's biographies, says of
+Finæus, "Il se vanta sans raison avoir trouvé la quadrature du cercle; la
+gloire de cette admirable découverte était réservée à Joseph Scalinger,
+comme l'a écrit Scévole de St. Marthe."[214]
+
+
+
+JOHN GRAUNT AS A PARADOXER.
+
+    Natural and Political Observations ... upon the Bills of Mortality. By
+    John Graunt, citizen of London. London, 1662, 4to.[215]
+
+This is a celebrated book, the first great work upon mortality. But the
+author, going _ultra crepidam_, has attributed to the motion of the moon in
+her orbit all the tremors which she gets from a shaky telescope.[216] But
+there is another paradox about this book: the above absurd opinion is
+attributed to that excellent mechanist, Sir William Petty, who passed his
+days among the astronomers. Graunt did not write his own book! Anthony
+Wood[217] hints that Petty "assisted, or put into a way" his old
+benefactor: no doubt the two friends talked the matter over many a time.
+Burnet and Pepys[218] state that Petty wrote the book. It is enough for me
+that {114} Graunt, whose honesty was never impeached, uses the plainest
+incidental professions of authorship throughout; that he was elected into
+the Royal Society because he was the author; that Petty refers to him as
+author in scores of places, and published an edition, as editor, after
+Graunt's death, with Graunt's name of course. The note on Graunt in the
+_Biographia Britannica_ may be consulted; it seems to me decisive. Mr.
+C. B. Hodge, an able actuary, has done the best that can be done on the
+other side in the _Assurance Magazine_, viii. 234. If I may say what is in
+my mind, without imputation of disrespect, I suspect some actuaries have a
+bias: they would rather have Petty the greater for their Coryphæus than
+Graunt the less.[219]
+
+Pepys is an ordinary gossip: but Burnet's account has an animus which is of
+a worse kind. He talks of "one Graunt, a Papist, under whose name Sir
+William Petty[220] published his observations on the bills of mortality."
+He then gives the cock without a bull story of Graunt being a trustee of
+the New River Company, and shutting up the cocks and carrying off their
+keys, just before the fire of London, by which a supply of water was
+delayed.[221] It was one of the first objections made to Burnet's work,
+that Graunt was _not_ a trustee at the time; and Maitland, the historian of
+London, ascertained from the books of the Company that he was not admitted
+until twenty-three days after the breaking out of the fire. Graunt's first
+admission {115} to the Company took place on the very day on which a
+committee was appointed to inquire into the cause of the fire. So much for
+Burnet. I incline to the view that Graunt's setting London on fire strongly
+corroborates his having written on the bills of mortality: every practical
+man takes stock before he commences a grand operation in business.
+
+
+
+MANKIND A GULLIBLE LOT.
+
+    De Cometis: or a discourse of the natures and effects of Comets, as
+    they are philosophically, historically, and astrologically considered.
+    With a brief (yet full) account of the III late Comets, or blazing
+    stars, visible to all Europe. And what (in a natural way of judicature)
+    they portend. Together with some observations on the nativity of the
+    Grand Seignior. By John Gadbury, [Greek: Philomathêmatikos]. London,
+    1665, 4to.
+
+Gadbury, though his name descends only in astrology, was a well-informed
+astronomer.[222] D'Israeli[223] sets down Gadbury, Lilly, Wharton, Booker,
+etc., as rank rogues: I think him quite wrong. The easy belief in roguery
+and intentional imposture which prevails in educated society is, to my
+mind, a greater presumption against the honesty of mankind than all the
+roguery and imposture itself. Putting aside mere swindling for the sake of
+gain, and looking at speculation and paradox, I find very little reason to
+suspect wilful deceit.[224] My opinion of mankind is founded upon the {116}
+mournful fact that, so far as I can see, they find within themselves the
+means of believing in a thousand times as much as there is to believe in,
+judging by experience. I do not say anything against Isaac D'Israeli for
+talking his time. We are all in the team, and we all go the road, but we do
+not all draw.
+
+
+
+A FORERUNNER OF A WRITTEN ESPERANTO.
+
+    An essay towards a real character and a philosophical language. By John
+    Wilkins [Dean of Ripon, afterwards Bishop of Chester].[225] London,
+    1668, folio.
+
+This work is celebrated, but little known. Its object gives it a right to a
+place among paradoxes. It proposes a language--if that be the proper
+name--in which _things_ and their relations shall be denoted by signs, not
+_words_: so that any person, whatever may be his mother tongue, may read it
+in his own words. This is an obvious possibility, and, I am afraid, an
+obvious impracticability. One man may construct such a system--Bishop
+Wilkins has done it--but where is the man who will learn it? The second
+tongue makes a language, as the second blow makes a fray. There has been
+very little curiosity about his performance, the work is scarce; and I do
+not know where to refer the reader for any account of its details, except,
+to the partial reprint of Wilkins presently mentioned under 1802, in which
+there is an unsatisfactory abstract. There is nothing in the _Biographia
+Britannica_, except discussion of Anthony Wood's statement that the hint
+was derived from Dalgarno's book, {117} _De Signis_, 1661.[226] Hamilton
+(_Discussions_, Art. 5, "Dalgarno") does not say a word on this point,
+beyond quoting Wood; and Hamilton, though he did now and then write about
+his countrymen with a rough-nibbed pen, knew perfectly well how to protect
+their priorities.
+
+
+
+GREGOIRE DE ST. VINCENT.
+
+    Problema Austriacum. Plus ultra Quadratura Circuli. Auctore P. Gregorio
+    a Sancto Vincentio Soc. Jesu., Antwerp, 1647, folio.--Opus Geometricum
+    posthumum ad Mesolabium. By the same. Gandavi [Ghent], 1668,
+    folio.[227]
+
+The first book has more than 1200 pages, on all kinds of geometry. Gregory
+St. Vincent is the greatest of circle-squarers, and his investigations led
+him into many truths: he found the property of the area of the
+hyperbola[228] which led to Napier's logarithms being called _hyperbolic_.
+Montucla says of him, with sly truth, that no one has ever squared the
+circle with so much genius, or, excepting his principal object, with so
+much success.[229] His reputation, and the many merits of his work, led to
+a sharp controversy on his quadrature, which ended in its complete exposure
+by Huyghens and others. He had a small school of followers, who defended
+him in print.
+
+{118}
+
+
+
+RENE DE SLUSE.
+
+    Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liège], 1668,
+    4to.[230]
+
+The Mesolabum is the solution of the problem of finding two mean
+proportionals, which Euclid's geometry does not attain. Slusius is a true
+geometer, and uses the ellipse, etc.: but he is sometimes ranked with the
+trisecters, for which reason I place him here, with this explanation.
+
+The finding of two mean proportionals is the preliminary to the famous old
+problem of the duplication of the cube, proposed by Apollo (not Apollonius)
+himself. D'Israeli speaks of the "six follies of science,"--the quadrature,
+the duplication, the perpetual motion, the philosopher's stone, magic, and
+astrology. He might as well have added the trisection, to make the mystic
+number seven: but had he done so, he would still have been very lenient;
+only seven follies in all science, from mathematics to chemistry! Science
+might have said to such a judge--as convicts used to say who got seven
+years, expecting it for life, "Thank you, my Lord, and may you sit there
+till they are over,"--may the Curiosities of Literature outlive the Follies
+of Science!
+
+
+
+JAMES GREGORY.
+
+1668. In this year James Gregory, in his _Vera Circuli et Hyperbolæ
+Quadratura_,[231] held himself to have proved that {119} the _geometrical_
+quadrature of the circle is impossible. Few mathematicians read this very
+abstruse speculation, and opinion is somewhat divided. The regular
+circle-squarers attempt the _arithmetical_ quadrature, which has long been
+proved to be impossible. Very few attempt the geometrical quadrature. One
+of the last is Malacarne, an Italian, who published his _Solution
+Géométrique_, at Paris, in 1825. His method would make the circumference
+less than three times the diameter.
+
+
+
+BEAULIEU'S QUADRATURE.
+
+    La Géométrie Françoise, ou la Pratique aisée.... La quadracture du
+    cercle. Par le Sieur de Beaulieu, Ingénieur, Géographe du Roi ...
+    Paris, 1676, 8vo. [not Pontault de Beaulieu, the celebrated
+    topographer; he died in 1674].[232]
+
+If this book had been a fair specimen, I might have pointed to it in
+connection with contemporary English works, and made a scornful comparison.
+But it is not a fair specimen. Beaulieu was attached to the Royal
+Household, and throughout the century it may be suspected that the
+household forced a royal road to geometry. Fifty years before, Beaugrand,
+the king's secretary, made a fool of himself, and [so?] contrived to pass
+for a geometer. He had interest enough to get Desargues, the most powerful
+geometer of his time,[233] the teacher and friend of Pascal, prohibited
+from {120} lecturing. See some letters on the History of Perspective, which
+I wrote in the _Athenæum_, in October and November, 1861. Montucla, who
+does not seem to know the true secret of Beaugrand's greatness, describes
+him as "un certain M. de Beaugrand, mathématicien, fort mal traité par
+Descartes, et à ce qu'il paroit avec justice."[234]
+
+Beaulieu's quadrature amounts to a geometrical construction[235] which
+gives [pi] = [root]10. His depth may be ascertained from the following
+extracts. First on Copernicus:
+
+"Copernic, Allemand, ne s'est pas moins rendu illustre par ses doctes
+écrits; et nous pourrions dire de luy, qu'il seroit le seul et unique en la
+force de ses Problèmes, si sa trop grande présomption ne l'avoit porté à
+avancer en cette Science une proposition aussi absurde, qu'elle est contre
+la Foy et raison, en faisant la circonférence d'un Cercle fixe, immobile,
+et le centre mobile, sur lequel principe Géométrique, il a avancé en son
+Traitté Astrologique le Soleil fixe, et la Terre mobile."[236]
+
+I digress here to point out that though our quadrators, etc., very often,
+and our historians sometimes, assert that men of the character of
+Copernicus, etc., were treated with contempt and abuse until their day of
+ascendancy came, nothing can be more incorrect. From Tycho Brahé[237] to
+Beaulieu, there is but one expression of admiration for the genius of
+Copernicus. There is an exception, which, I {121} believe, has been quite
+misunderstood. Maurolycus,[238] in his _De Sphæra_, written many years
+before its posthumous publication in 1575, and which it is not certain he
+would have published, speaking of the safety with which various authors may
+be read after his cautions, says, "Toleratur et Nicolaus Copernicus qui
+Solem fixum et Terram _in girum circumverti_ posuit: et scutica potius, aut
+flagello, quam reprehensione dignus est."[239] Maurolycus was a mild and
+somewhat contemptuous satirist, when expressing disapproval: as we should
+now say, he pooh-poohed his opponents; but, unless the above be an
+instance, he was never savage nor impetuous. I am fully satisfied that the
+meaning of the sentence is, that Copernicus, who turned the earth like a
+boy's top, ought rather to have a whip given him wherewith to keep up his
+plaything than a serious refutation. To speak of _tolerating_ a person _as
+being_ more worthy of a flogging than an argument, is almost a
+contradiction.
+
+I will now extract Beaulieu's treatise on algebra, entire.
+
+"L'Algebre est la science curieuse des Sçavans et specialement d'un General
+d'Armée ou Capitaine, pour promptement ranger une Armée en bataille, et
+nombre de Mousquetaires et Piquiers qui composent les bataillons d'icelle,
+outre les figures de l'Arithmetique. Cette science a 5 figures
+particulieres en cette sorte. P signifie _plus_ au commerce, et à l'Armée
+_Piquiers_. M signifie _moins_, et _Mousquetaire_ en l'Art des bataillons.
+[It is quite true that P and M were used for _plus_ and _minus_ in a great
+many old works.] R signifie _racine_ en la mesure du Cube, et en l'Armée
+_rang_. Q signifie _quaré_ en l'un et l'autre usage. C signifie _cube_ en
+la mesure, et _Cavallerie_ en la composition des bataillons et escadrons.
+Quant à l'operation de cette science, c'est {122} d'additionner un _plus_
+d'avec _plus_, la somme sera _plus_, et _moins_ d'avec _plus_, on soustrait
+le moindre du _plus_, et la reste est la somme requise ou nombre trouvé. Je
+dis seulement cecy en passant pour ceux qui n'en sçavent rien du
+tout."[240]
+
+This is the algebra of the Royal Household, seventy-three years after the
+death of Vieta. Quære, is it possible that the fame of Vieta, who himself
+held very high stations in the household all his life, could have given
+people the notion that when such an officer chose to declare himself an
+algebraist, he must be one indeed? This would explain Beaugrand, Beaulieu,
+and all the _beaux_. Beaugrand--not only secretary to the king, but
+"mathematician" to the Duke of Orleans--I wonder what his "fool" could have
+been like, if indeed he kept the offices separate,--would have been in my
+list if I had possessed his _Geostatique_, published about 1638.[241] He
+makes bodies diminish in weight as they approach the earth, because the
+effect of a weight on a lever is less as it approaches the fulcrum.
+
+{123}
+
+
+
+SIR MATTHEW HALE.
+
+    Remarks upon two late ingenious discourses.... By Dr. Henry More.[242]
+    London, 1676, 8vo.
+
+In 1673 and 1675, Matthew Hale,[243] then Chief Justice, published two
+tracts, an "Essay touching Gravitation," and "Difficiles Nugæ" on the
+Torricellian experiment. Here are the answers by the learned and voluminous
+Henry More. The whole would be useful to any one engaged in research about
+ante-Newtonian notions of gravitation.
+
+
+
+    Observations touching the principles of natural motions; and especially
+    touching rarefaction and condensation.... By the author of _Difficiles
+    Nugæ_. London, 1677, 8vo.
+
+This is another tract of Chief Justice Hale, published the year after his
+death. The reader will remember that _motion_, in old philosophy, meant any
+change from state to state: what we now describe as _motion_ was _local
+motion_. This is a very philosophical book, about _flux_ and _materia
+prima_, _virtus activa_ and _essentialis_, and other fundamentals. I think
+Stephen Hales, the author of the "Vegetable Statics," has the writings of
+the Chief Justice sometimes attributed to him, which is very puny justice
+indeed.[244] Matthew Hale died in 1676, and from his devotion to science it
+probably arose that his famous _Pleas of the Crown_[245] and other law
+works did not appear until after his death. One of his {124} contemporaries
+was the astronomer Thomas Street, whose _Caroline Tables_[246] were several
+times printed: another contemporary was his brother judge, Sir Thomas
+Street.[247] But of the astronomer absolutely nothing is known: it is very
+unlikely that he and the judge were the same person, but there is not a bit
+of positive evidence either for or against, so far as can be ascertained.
+Halley[248]--no less a person--published two editions of the _Caroline
+Tables_, no doubt after the death of the author: strange indeed that
+neither Halley nor any one else should leave evidence that Street was born
+or died.
+
+Matthew Hale gave rise to an instance of the lengths a lawyer will go when
+before a jury who cannot detect him. Sir Samuel Shepherd,[249] the Attorney
+General, in opening Hone's[250] first trial, calls him "one who was the
+most learned man that ever adorned the Bench, the most even man that ever
+blessed domestic life, the _most eminent man that ever advanced the
+progress of science_, and one of the [very moderate] best and most purely
+religious men that ever lived."
+
+{125}
+
+
+
+ON THE DISCOVERY OF ANTIMONY.
+
+    Basil Valentine his triumphant Chariot of Antimony, with annotations of
+    Theodore Kirkringius, M.D. With the true book of the learned Synesius,
+    a Greek abbot, taken out of the Emperour's library, concerning the
+    Philosopher's Stone. London, 1678, 8vo.[251]
+
+There are said to be three Hamburg editions of the collected works of
+Valentine, who discovered the common antimony, and is said to have given
+the name _antimoine_, in a curious way. Finding that the pigs of his
+convent throve upon it, he gave it to his brethren, who died of it.[252]
+The impulse given to chemistry by R. Boyle[253] seems to have brought out a
+vast number of translations, as in the following tract:
+
+
+
+ON ALCHEMY.
+
+    _Collectanea Chymica_: A collection of ten several treatises in
+    chymistry, concerning the liquor Alkehest, the Mercury of Philosophers,
+    and other curiosities worthy the perusal. Written by Eir.
+    Philaletha,[254] Anonymus, J. B. Van-Helmont,[255] Dr. Fr. {126}
+    Antonie,[256] Bernhard Earl of Trevisan,[257] Sir Geo. Ripley,[258]
+    Rog. Bacon,[259] Geo. Starkie,[260] Sir Hugh Platt,[261] and the Tomb
+    of Semiramis. See more in the contents. London, 1684, 8vo.
+
+In the advertisements at the ends of these tracts there are upwards of a
+hundred English tracts, nearly all of the period, and most of them
+translations. Alchemy looks up since the chemists have found perfectly
+different substances composed of the same elements and proportions. It is
+true the chemists cannot yet _transmute_; but they may in time: they poke
+about most assiduously. It seems, then, that the conviction that alchemy
+_must_ be impossible was a delusion: but we do not mention it.
+
+{127}
+
+The astrologers and the alchemists caught it in company in the following,
+of which I have an unreferenced note.
+
+"Mendacem et futilem hominem nominare qui volunt, calendariographum dicunt;
+at qui sceleratum simul ac impostorem, chimicum.[262]
+
+ "Crede ratem ventis corpus ne crede chimistis;
+      Est quævis chimica tutior aura fide."[263]
+
+Among the smaller paradoxes of the day is that of the _Times_ newspaper,
+which always spells it _chymistry_: but so, I believe, do Johnson, Walker,
+and others. The Arabic work is very likely formed from the Greek: but it
+may be connected either with [Greek: chêmeia] or with [Greek: chumeia].
+
+
+
+    Lettre d'un gentil-homme de province à une dame de qualité, sur le
+    sujet de la Comète. Paris, 1681, 4to.
+
+An opponent of astrology, whom I strongly suspect to have been one of the
+members of the Academy of Sciences under the name of a country
+gentleman,[264] writes very good sense on the tremors excited by comets.
+
+
+
+    The Petitioning-Comet: or a brief Chronology of all the famous Comets
+    and their events, that have happened from the birth of Christ to this
+    very day. Together with a modest enquiry into this present comet,
+    London, 1681, 4to.
+
+A satirical tract against the cometic prophecy:
+
+"This present comet (it's true) is of a menacing aspect, but if the _new
+parliament_ (for whose convention so many good men pray) continue long to
+sit, I fear not but the star will lose its virulence and malignancy, or at
+least its portent be averted from this our nation; which being the humble
+request to God of all good men, makes me thus entitle it, a
+Petitioning-Comet."
+
+{128}
+
+The following anecdote is new to me:
+
+"Queen Elizabeth (1558) being then at Richmond, and being disswaded from
+looking on a comet which did then appear, made answer, _jacta est alea_,
+the dice are thrown; thereby intimating that the pre-order'd providence of
+God was above the influence of any star or comet."
+
+The argument was worth nothing: for the comet might have been _on the dice_
+with the event; the astrologers said no more, at least the more rational
+ones, who were about half of the whole.
+
+
+
+    An astrological and theological discourse upon this present great
+    conjunction (the like whereof hath not (likely) been in some ages)
+    ushered in by a great comet. London, 1682, 4to. By C. N.[265]
+
+The author foretells the approaching "sabbatical jubilee," but will not fix
+the date: he recounts the failures of his predecessors.
+
+
+
+    A judgment of the comet which became first generally visible to us in
+    Dublin, December 13, about 15 minutes before 5 in the evening, A.D.
+    1680. By a person of quality. Dublin, 1682, 4to.
+
+The author argues against cometic astrology with great ability.
+
+
+
+    A prophecy on the conjunction of Saturn and Jupiter in this present
+    year 1682. With some prophetical predictions of what is likely to ensue
+    therefrom in the year 1684. By John Case, Student in physic and
+    astrology.[266] London, 1682, 4to.
+
+{129}
+
+According to this writer, great conjunctions of Jupiter and Saturn occur
+"in the fiery trigon," about once in 800 years. Of these there are to be
+seven: six happened in the several times of Enoch, Noah, Moses, Solomon,
+Christ, Charlemagne. The seventh, which is to happen at "the lamb's
+marriage with the bride," seems to be that of 1682; but this is only
+vaguely hinted.
+
+
+
+    De Quadrature van de Circkel. By Jacob Marcelis. Amsterdam, 1698, 4to.
+
+    Ampliatie en demonstratie wegens de Quadrature ... By Jacob Marcelis.
+    Amsterdam, 1699, 4to.
+
+    Eenvoudig vertoog briev-wys geschrevem am J. Marcelis ... Amsterdam,
+    1702, 4to.
+
+    De sleutel en openinge van de quadrature ... Amsterdam, 1704, 4to.
+
+Who shall contradict Jacob Marcelis?[267] He says the circumference
+contains the diameter exactly times
+
+    1008449087377541679894282184894
+  3 --------------------------------
+    6997183637540819440035239271702
+
+But he does not come very near, as the young arithmetician will find.
+
+
+
+MATHEMATICAL THEOLOGY.
+
+    Theologiæ Christianæ Principia Mathematica. Auctore Johanne Craig.[268]
+    London, 1699, 4to.
+
+This is a celebrated speculation, and has been reprinted abroad, and
+seriously answered. Craig is known in the early history of fluxions, and
+was a good mathematician. {130} He professed to calculate, on the
+hypothesis that the suspicions against historical evidence increase with
+the square of the time, how long it will take the evidence of Christianity
+to die out. He finds, by formulæ, that had it been oral only, it would have
+gone out A.D. 800; but, by aid of the written evidence, it will last till
+A.D. 3150. At this period he places the second coming, which is deferred
+until the extinction of evidence, on the authority of the question "When
+the Son of Man cometh, shall he find faith on the earth?" It is a pity that
+Craig's theory was not adopted: it would have spared a hundred treatises on
+the end of the world, founded on no better knowledge than his, and many of
+them falsified by the event. The most recent (October, 1863) is a tract in
+proof of Louis Napoleon being Antichrist, the Beast, the eighth Head, etc.;
+and the present dispensation is to close soon after 1864.
+
+In order rightly to judge Craig, who added speculations on the variations
+of pleasure and pain treated as functions of time, it is necessary to
+remember that in Newton's day the idea of force, as a quantity to be
+measured, and as following a law of variation, was very new: so likewise
+was that of probability, or belief, as an object of measurement.[269] The
+success of the _Principia_ of Newton put it into many heads to speculate
+about applying notions of quantity to other things not then brought under
+measurement. Craig imitated Newton's title, and evidently thought he was
+making a step in advance: but it is not every one who can plough with
+Samson's heifer.
+
+It is likely enough that Craig took a hint, directly or indirectly, from
+Mohammedan writers, who make a reply to the argument that the Koran has not
+the evidence derived {131} from miracles. They say that, as evidence of
+Christian miracles is daily becoming weaker, a time must at last arrive
+when it will fail of affording assurance that they were miracles at all:
+whence would arise the necessity of another prophet and other miracles.
+Lee,[270] the Cambridge Orientalist, from whom the above words are taken,
+almost certainly never heard of Craig or his theory.
+
+
+
+THE ARISTOCRAT AS A SCIENTIST.
+
+    Copernicans of all sorts convicted ... to which is added a Treatise of
+    the Magnet. By the Hon. Edw. Howard, of Berks. London, 1705, 8vo.
+
+Not all the blood of all the Howards will gain respect for a writer who
+maintains that eclipses admit no possible explanation under the Copernican
+hypothesis, and who asks how a man can "go 200 yards to any place if the
+moving superficies of the earth does carry it from him?" Horace Walpole, at
+the beginning of his _Royal and Noble Authors_, has mottoed his book with
+the Cardinal's address to Ariosto, "Dove diavolo, Messer Ludovico, avete
+pigliato tante coglionerie?"[271] Walter Scott says you could hardly pick
+out, on any principle of selection--except badness itself, he means of
+course--the same number of plebeian authors whose works are so bad. But his
+implied satire on aristocratic writing forgets two points. First, during a
+large period of our history, when persons of rank condescended to write,
+they veiled themselves under "a person of honor," "a person of quality,"
+and the like, when not wholly undescribed. Not one of these has Walpole
+got; he omits, {132} for instance, Lord Brounker's[272] translation of
+Descartes on Music. Secondly, Walpole only takes the heads of houses: this
+cuts both ways; he equally eliminates the Hon. Robert Boyle and the
+precious Edward Howard. The last writer is hardly out of the time in which
+aristocracy suppressed its names; the avowal was then usually meant to make
+the author's greatness useful to the book. In our day, literary peers and
+honorables are very favorably known, and contain an eminent class.[273]
+They rough it like others, and if such a specimen as Edw. Howard were now
+to appear, he would be greeted with
+
+ "Hereditary noodle! knowest thou not
+  Who would be wise, himself must make him so?"
+
+
+
+THE LONGITUDE PROBLEM.
+
+    A new and easy method to find the longitude at land or sea. London,
+    1710, 4to.
+
+This tract is a little earlier than the great epoch of such publications
+(1714), and professes to find the longitude by the observed altitudes of
+the moon and two stars.[274] {133}
+
+
+
+    A new method for discovering the longitude both at sea and land, humbly
+    proposed to the consideration of the public.[275] By Wm. Whiston[276]
+    and Humphry Ditton.[277] London, 1714, 8vo.
+
+This is the celebrated tract, written by the two Arian heretics. Swift,
+whose orthodoxy was as undoubted as his meekness, wrote upon it the
+epigram--if, indeed, that be epigram of which the point is pious
+wish--which has been so often recited for the purity of its style, a purity
+which transcends modern printing. Perhaps some readers may think that Swift
+cared little for Whiston and Ditton, except as a chance hearing of their
+plan pointed them out as good marks. But it was not so: the clique had
+their eye on the guilty pair before the publication of the tract. The
+preface is dated July 7; and ten days afterwards Arbuthnot[278] writes as
+follows to Swift:
+
+"Whiston has at last published his project of the longitude; the most
+ridiculous thing that ever was thought on. But a pox on him! he has spoiled
+one of my papers of Scriblerus, which was a proposition for the longitude
+not very unlike his, to this purpose; that since there was no pole for east
+and west, that all the princes of Europe should join and build two
+prodigious poles, upon high mountains, {134} with a vast lighthouse to
+serve for a polestar. I was thinking of a calculation of the time, charges,
+and dimensions. Now you must understand his project is by lighthouses, and
+explosion of bombs at a certain hour."
+
+The plan was certainly impracticable; but Whiston and Ditton might have
+retorted that they were nearer to the longitude than their satirist to the
+kingdom of heaven, or even to a bishopric. Arbuthnot, I think, here and
+elsewhere, reveals himself as the calculator who kept Swift right in his
+proportions in the matter of the Lilliputians, Brobdingnagians, etc. Swift
+was very ignorant about things connected with number. He writes to Stella
+that he has discovered that leap-year comes every four years, and that all
+his life he had thought it came every three years. Did he begin with the
+mistake of Cæsar's priests? Whether or no, when I find the person who did
+not understand leap-year inventing satellites of Mars in correct accordance
+with Kepler's third law, I feel sure he must have had help.
+
+
+
+THE AURORA BOREALIS.
+
+    An essay concerning the late apparition in the heavens on the 6th of
+    March. Proving by mathematical, logical, and moral arguments, that it
+    cou'd not have been produced meerly by the ordinary course of nature,
+    but must of necessity be a prodigy. Humbly offered to the consideration
+    of the Royal Society. London, 1716, 8vo.
+
+The prodigy, as described, was what we should call a very decided and
+unusual aurora borealis. The inference was, that men's sins were bringing
+on the end of the world. The author thinks that if one of the old
+"threatening prophets" were then alive, he would give "something like the
+following." I quote a few sentences of the notion which the author had of
+the way in which Ezekiel, for instance, would have addressed his Maker in
+the reign of George the First:
+
+"Begin! Begin! O Sovereign, for once, with an {135} effectual clap of
+thunder.... O Deity! either thunder to us no more, or when you thunder, do
+it home, and strike with vengeance to the mark.... 'Tis not enough to raise
+a storm, unless you follow it with a blow, and the thunder without the
+bolt, signifies just nothing at all.... Are then your lightnings of so
+short a sight, that they don't know how to hit, unless a mountain stands
+like a barrier in their way? Or perhaps so many eyes open in the firmament
+make you lose your aim when you shoot the arrow? Is it this? No! but, my
+dear Lord, it is your custom never to take hold of your arms till you have
+first bound round your majestic countenance with gathered mists and
+clouds."
+
+
+
+    The principles of the Philosophy of the Expansive and Contractive
+    Forces ... By Robert Greene,[279] M.A., Fellow of Clare Hall.
+    Cambridge, 1727, folio.
+
+Sanderson[280] writes to Jones,[281] "The gentleman has been reputed mad
+for these two years last past, but never gave the world such ample
+testimony of it before." This was said of a former work of Greene's, on
+solid geometry, published in 1712, in which he gives a quadrature.[282] He
+gives the same or another, I do not know which, in the present work, in
+which the circle is 3-1/5 diameters. This volume is of 981 good folio
+pages, and treats of all things, mental and material. The author is not at
+all mad, only wrong on {136} many points. It is the weakness of the
+orthodox follower of any received system to impute insanity to the solitary
+dissentient: which is voted (in due time) a very wrong opinion about
+Copernicus, Columbus, or Galileo, but quite right about Robert Greene. If
+misconceptions, acted on by too much self-opinion, be sufficient evidence
+of madness, it would be a curious inquiry what is the least per-centage of
+the reigning school which has been insane at any one time. Greene is one of
+the sources for Newton being led to think of gravitation by the fall of an
+apple: his authority is the gossip of Martin Folkes.[283] Probably Folkes
+had it from Newton's niece, Mrs. Conduitt, whom Voltaire acknowledges as
+_his authority_.[284] It is in the draft found among Conduitt's papers of
+memoranda to be sent to Fontenelle. But Fontenelle, though a great retailer
+of anecdote, does not mention it in his _éloge_ of Newton; whence it may be
+suspected that it was left out in the copy forwarded to France. D'Israeli
+has got an improvement on the story: the apple "struck him a smart blow on
+the head": no doubt taking him just on the organ of causality. He was
+"surprised at the force of the stroke" from so small an apple: but then the
+apple had a mission; Homer would have said {137} it was Minerva in the form
+of an apple. "This led him to consider the accelerating motion of falling
+bodies," which Galileo had settled long before: "from whence he deduced the
+principle of gravity," which many had considered before him, but no one had
+_deduced anything from it_. I cannot imagine whence D'Israeli got the rap
+on the head, I mean got it for Newton: this is very unlike his usual
+accounts of things. The story is pleasant and possible: its only defect is
+that various writings, well known to Newton, a very _learned_
+mathematician, had given more suggestion than a whole sack of apples could
+have done, if they had tumbled on that mighty head all at once. And
+Pemberton, speaking from Newton himself, says nothing more than that the
+idea of the moon being retained by the same force which causes the fall of
+bodies struck him for the first time while meditating in a garden. One
+particular tree at Woolsthorpe has been selected as the gallows of the
+appleshaped goddess: it died in 1820, and Mr. Turnor[285] kept the wood;
+but Sir D. Brewster[286] brought away a bit of root in 1814, and must have
+had it on his conscience for 43 years that he may have killed the tree.
+Kepler's suggestion of gravitation with the inverse distance, and
+Bouillaud's proposed substitution of the inverse square of the distance,
+are things which Newton knew better than his modern readers. I discovered
+two anagrams on his name, which are quite conclusive; the notion of
+gravitation was _not new_; but Newton _went on_. Some wandering spirit,
+probably whose business it was to resent any liberty taken with Newton's
+name, put into the head of a friend of mine _eighty-one_ anagrams on my own
+pair, some of which hit harder than any apple.
+
+{138}
+
+
+
+DE MORGAN ANAGRAMS.
+
+This friend, whom I must not name, has since made it up to about 800
+anagrams on my name, of which I have seen about 650. Two of them I have
+joined in the title-page: the reader may find the sense. A few of the
+others are personal remarks.
+
+ "Great gun! do us a sum!"
+
+is a sneer at my pursuits: but,
+
+ "Go! great sum! [Integral]a u^{n} du"
+
+is more dignified.
+
+ "Sunt agro! gaudemus,"[287]
+
+is happy as applied to one of whom it may be said:
+
+ "Ne'er out of town; 'tis such a horrid life;
+   But duly sends his family and wife."
+
+ "Adsum, nugator, suge!"[288]
+
+is addressed to a student who continues talking after the lecture has
+commenced: oh! the rascal!
+
+ "Graduatus sum! nego"[289]
+
+applies to one who declined to subscribe for an M.A. degree.
+
+ "Usage mounts guard"
+
+symbolizes a person of very fixed habits.
+
+ "Gus! Gus! a mature don!
+    August man! sure, god!
+  And Gus must argue, O!
+    Snug as mud to argue,
+  Must argue on gauds.
+    A mad rogue stung us.
+  Gag a numerous stud
+    Go! turn us! damage us!
+  Tug us! O drag us! Amen.
+    Grudge us! moan at us!
+  {139}
+  Daunt us! gag us more!
+    Dog-ear us, man! gut us!
+  D---- us! a rogue tugs!"
+
+are addressed to me by the circle-squarers; and,
+
+ "O! Gus! tug a mean surd!"
+
+is smart upon my preference of an incommensurable value of [pi] to 3-1/5,
+or some such simple substitute. While,
+
+ "Gus! Gus! at 'em a' round!"
+
+ought to be the backing of the scientific world to the author of the
+_Budget of Paradoxes_.
+
+The whole collection commenced existence in the head of a powerful
+mathematician during some sleepless nights. Seeing how large a number was
+practicable, he amused himself by inventing a digested plan of finding
+more.
+
+Is there any one whose name cannot be twisted into either praise or satire?
+I have had given to me,
+
+ "Thomas Babington Macaulay
+   Mouths big: a Cantab anomaly."
+
+
+
+NEWTON'S DE MUNDI SYSTEMATE LIBER.
+
+    A treatise of the system of the world. By Sir Isaac Newton. Translated
+    into English. London, 1728, 8vo.
+
+I think I have a right to one little paradox of my own: I greatly doubt
+that Newton wrote this book. Castiglione,[290] in his _Newtoni
+Opuscula_,[291] gives it in the Latin which appeared in 1731,[292] not for
+the first time; he says _Angli omnes Newtono tribuunt_.[293] It appeared
+just after Newton's death, without the name of any editor, or any allusion
+to Newton's {140} recent departure, purporting to be that popular treatise
+which Newton, at the beginning of the third book of the _Principia_, says
+he wrote, intending it to be the third book. It is very possible that some
+observant turnpenny might construct such a treatise as this from the third
+book, that it might be ready for publication the moment Newton could not
+disown it. It has been treated with singular silence: the name of the
+editor has never been given. Rigaud[294] mentions it without a word: I
+cannot find it in Brewster's _Newton_, nor in the _Biographia Britannica_.
+There is no copy in the Catalogue of the Royal Society's Library, either in
+English or Latin, except in Castiglione. I am open to correction; but I
+think nothing from Newton's acknowledged works will prove--as laid down in
+the suspected work--that he took Numa's temple of Vesta, with a central
+fire, to be intended to symbolize the sun as the center of our system, in
+the Copernican sense.[295]
+
+Mr. Edleston[296] gives an account of the _lectures_ "de motu corporum,"
+and gives the corresponding pages of the _Latin_ "De Systemate Mundi" of
+1731. But no one mentions the _English_ of 1728. This English seems to
+agree with the Latin; but there is a mystery about it. The preface says,
+"That this work as here published is genuine will so clearly appear by the
+intrinsic marks it bears, that it will be but losing words and the reader's
+time to take pains in giving him any other satisfaction." Surely fewer
+words would have been lost if the prefator had said at once that the work
+was from the manuscript preserved at Cambridge. Perhaps it was a mangled
+copy clandestinely taken and interpreted. {141}
+
+
+
+A BACONIAN CONTROVERSY.
+
+    Lord Bacon not the author of "The Christian Paradoxes," being a reprint
+    of "Memorials of Godliness and Christianity," by Herbert Palmer,
+    B.D.[297] With Introduction, Memoir, and Notes, by the Rev. Alexander
+    B. Grosart,[298] Kenross. (Private circulation, 1864).
+
+I insert the above in this place on account of a slight connection with the
+last. Bacon's Paradoxes,--so attributed--were first published as his in
+some asserted "Remains," 1648.[299] They were admitted into his works in
+1730, and remain there to this day. The title is "The Character of a
+believing Christian, set forth in paradoxes and seeming contradictions."
+The following is a specimen:
+
+"He believes three to be one and one to be three; a father not to be older
+than his son; a son to be equal with his father; and one proceeding from
+both to be equal with both: he believes three persons in one nature, and
+two natures in one person.... He believes the God of all grace to have been
+angry with one that never offended Him; and that God that hates sin to be
+reconciled to himself though sinning continually, and never making or being
+able to make Him any satisfaction. He believes a most just God to have
+punished a most just person, and to have justified himself, though a most
+ungodly sinner. He believes himself freely pardoned, and yet a sufficient
+satisfaction was made for him."
+
+Who can doubt that if Bacon had written this it must have been wrong? Many
+writers, especially on the {142} Continent, have taken him as sneering at
+(Athanasian) Christianity right and left. Many Englishmen have taken him to
+be quite in earnest, and to have produced a body of edifying doctrine. More
+than a century ago the Paradoxes were published as a penny tract; and,
+again, at the same price, in the _Penny Sunday Reader_, vol. vi, No. 148, a
+few passages were omitted, as _too strong_. But all did not agree: in my
+copy of Peter Shaw's [300] edition (vol. ii, p. 283) the Paradoxes have
+been cut out by the binder, who has left the backs of the leaves. I never
+had the curiosity to see whether other copies of the edition have been
+served in the same way. The Religious Tract Society republished them
+recently in _Selections from the Writings of Lord Bacon_, (no date; bad
+plan; about 1863, I suppose). No omissions were made, so far as I find.
+
+I never believed that Bacon wrote this paper; it has neither his _sparkle_
+nor his idiom. I stated my doubts even before I heard that Mr. Spedding,
+one of Bacon's editors, was of the same mind. (_Athenæum_, July 16, 1864).
+I was little moved by the wide consent of orthodox men: for I knew how
+Bacon, Milton, Newton, Locke, etc., were always claimed as orthodox until
+almost the present day. Of this there is a remarkable instance.
+
+
+
+LOCKE AND SOCINIANISM.
+
+Among the books which in my younger day were in some orthodox publication
+lists--I think in the list of the Christian Knowledge Society, but I am not
+sure--was Locke's [301] "Reasonableness of Christianity." It seems to have
+come down from the eighteenth century, when the battle was belief in Christ
+against unbelief, _simpliciter_, as the {143} logicians say. Now, if ever
+there was a Socinian[302] book in the world, it is this work of Locke.
+"These two," says Locke, "faith and repentance, i.e., believing Jesus to be
+the Messiah, and a good life, are the indispensable conditions of the new
+covenant, to be performed by all those who would obtain eternal life." All
+the book is amplification of this doctrine. Locke, in this and many other
+things, followed Hobbes, whose doctrine, in the Leviathan, is _fidem,
+quanta ad salutem necessaria est, contineri in hoc articulo, Jesus est
+Christus_.[303] For this Hobbes was called an atheist, which {144} many
+still believe him to have been: some of his contemporaries called him,
+rightly, a Socinian. Locke was known for a Socinian as soon as his work
+appeared: Dr. John Edwards,[304] his assailant, says he is "Socinianized
+all over." Locke, in his reply, says "there is not one word of Socinianism
+in it:" and he was right: the positive Socinian doctrine has _not one word
+of Socinianism in it_; Socinianism consists in omissions. Locke and Hobbes
+did not dare _deny_ the Trinity: for such a thing Hobbes might have been
+roasted, and Locke might have been strangled. Accordingly, the well-known
+way of teaching Unitarian doctrine was the collection of the asserted
+essentials of Christianity, without naming the Trinity, etc. This is the
+plan Newton followed, in the papers which have at last been published.[305]
+
+So I, for one, thought little about the general tendency of orthodox
+writers to claim Bacon by means of the Paradoxes. I knew that, in his
+"Confession of Faith"[306] he is a Trinitarian of a heterodox stamp. His
+second Person takes human nature before he took flesh, not for redemption,
+but as a condition precedent of creation. "God is so holy, pure, and
+jealous, that it is impossible for him to be pleased in any creature,
+though the work of his own hands.... [Gen. i. 10, 12, 18, 21, 25, 31,
+freely rendered]. But--purposing to become a Creator, and to communicate to
+his creatures, he ordained in his eternal counsel that one person of the
+Godhead should be united to one nature, and to one particular of his
+creatures; that so, in the person of the Mediator, the true ladder might be
+fixed, whereby God might {145} descend to his creatures and his creatures
+might ascend to God...."
+
+This is republished by the Religious Tract Society, and seems to suit their
+theology, for they confess to having omitted some things of which they
+disapprove.
+
+In 1864, Mr. Grosart published his discovery that the Paradoxes are by
+Herbert Palmer; that they were first published surreptitiously, and
+immediately afterwards by himself, both in 1645; that the "Remains" of
+Bacon did not appear until 1648; that from 1645 to 1708, thirteen editions
+of the "Memorials" were published, all containing the Paradoxes. In spite
+of this, the Paradoxes were introduced into Bacon's works in 1730, where
+they have remained.
+
+Herbert Palmer was of good descent, and educated as a Puritan. He was an
+accomplished man, one of the few of his day who could speak French as well
+as English. He went into the Church, and was beneficed by Laud,[307] in
+spite of his puritanism; he sat in the Assembly of Divines, and was finally
+President of Queens' College, Cambridge, in which post he died, August 13,
+1647, in the 46th year of his age.
+
+Mr. Grosart says, speaking of Bacon's "Remains," "All who have had occasion
+to examine our early literature are aware that it was a common trick to
+issue imperfect, false, and unauthorized writings under any recently
+deceased name that might be expected to take. The Puritans, down to John
+Bunyan, were perpetually expostulating and protesting against such
+procedure." I have met with instances of all this; but I did not know that
+there was so much of it: a good collection would be very useful. The work
+of 1728, attributed to Newton, is likely enough to be one of the class.
+
+{146}
+
+
+
+    Demonstration de l'immobilitez de la Terre.... Par M. de la
+    Jonchere,[308] Ingénieur Français. Londres, 1728, 8vo.
+
+A synopsis which is of a line of argument belonging to the beginning of the
+preceding century.
+
+
+
+TWO FORGOTTEN CIRCLE SQUARERS.
+
+    The Circle squared; together with the Ellipsis and several reflections
+    on it. The finding two geometrical mean proportionals, or doubling the
+    cube geometrically. By Richard Locke[309].... London, no date, probably
+    about 1730, 8vo.
+
+According to Mr. Locke, the circumference is three diameters, three-fourths
+the difference of the diameter and the side of the inscribed equilateral
+triangle, and three-fourths the difference between seven-eighths of the
+diameter and the side of the same triangle. This gives, he says, 3.18897.
+There is an addition to this tract, being an appendix to a book on the
+longitude.
+
+
+
+    The Circle squar'd. By Thos. Baxter, Crathorn, Cleaveland, Yorkshire.
+    London, 1732, 8vo.
+
+Here [pi] = 3.0625. No proof is offered.[310]
+
+
+
+    The longitude discovered by the Eclipses, Occultations, and
+    Conjunctions of Jupiter's planets. By William Whiston. London, 1738.
+
+This tract has, in some copies, the celebrated preface containing the
+account of Newton's appearance before the Parliamentary Committee on the
+longitude question, in 1714 {147} (Brewster, ii. 257-266). This "historical
+preface," is an insertion and is dated April 28, 1741, with four additional
+pages dated August 10, 1741. The short "preface" is by the publisher, John
+Whiston,[311] the author's son.
+
+
+
+THE STEAMSHIP SUGGESTED.
+
+    A description and draught of a new-invented machine for carrying
+    vessels or ships out of, or into any harbour, port, or river, against
+    wind and tide, or in a calm. For which, His Majesty has granted letters
+    patent, for the sole benefit of the author, for the space of fourteen
+    years. By Jonathan Hulls.[312] London: printed for the author, 1737.
+    Price sixpence (folding plate and pp. 48, beginning from title).
+
+(I ought to have entered this tract in its place. It is so rare that its
+existence was once doubted. It is the earliest description of steam-power
+applied to navigation. The plate shows a barge, with smoking funnel, and
+paddles at the stem, towing a ship of war. The engine, as described, is
+Newcomen's.[313]
+
+In 1855, John Sheepshanks,[314] so well known as a friend of Art and a
+public donor, reprinted this tract, in fac-simile, from his own copy;
+twenty-seven copies of the original 12mo size, and twelve on old paper,
+small 4to. I have an original copy, wanting the plate, and with "Price
+sixpence" carefully erased, to the honor of the book.[315]
+
+{148}
+
+It is not known whether Hulls actually constructed a boat.[316] In all
+probability his tract suggested to Symington, as Symington[317] did to
+Fulton.)
+
+
+
+THE NEWTONIANS ATTACKED.
+
+    Le vrai système de physique générale de M. Isaac Newton exposé et
+    analysé en parallèle avec celui de Descartes. By Louis Castel[318]
+    [Jesuit and F.R.S.] Paris, 1743, 4to.
+
+This is an elaborate correction of Newton's followers, and of Newton
+himself, who it seems did not give his own views with perfect fidelity.
+Father Castel, for instance, assures us that Newton placed the sun _at
+rest_ in the center of the system. Newton left the sun to arrange that
+matter with the planets and the rest of the universe. In this volume of 500
+pages there is right and wrong, both clever.
+
+
+
+    A dissertation on the Æther of Sir Isaac Newton. By Bryan
+    Robinson,[319] M.D. Dublin, 1743, 8vo.[320]
+
+{149}
+
+A mathematical work professing to prove that the assumed ether causes
+gravitation.
+
+
+
+MATHEMATICAL THEOLOGY.
+
+    Mathematical principles of theology, or the existence of God
+    geometrically demonstrated. By Richard Jack, teacher of Mathematics.
+    London, 1747, 8vo.[321]
+
+Propositions arranged after the manner of Euclid, with beings represented
+by circles and squares. But these circles and squares are logical symbols,
+not geometrical ones. I brought this book forward to the Royal Commission
+on the British Museum as an instance of the absurdity of attempting a
+_classed_ catalogue from the _titles_ of books. The title of this book
+sends it either to theology or geometry: when, in fact, it is a logical
+vagary. Some of the houses which Jack built were destroyed by the fortune
+of war in 1745, at Edinburgh: who will say the rebels did no good whatever?
+I suspect that Jack copied the ideas of J.B. Morinus, "Quod Deus sit,"
+Paris, 1636,[322] 4to, containing an attempt of the same kind, but not
+stultified with diagrams.
+
+
+
+TWO MODEL INDORSEMENTS.
+
+    Dissertation, découverte, et démonstrations de la quadrature
+    mathématique du cercle. Par M. de Fauré, géomètre. [_s. l._, probably
+    Geneva] 1747, 8vo.
+
+    Analyse de la Quadrature du Cercle. Par M. de Fauré, Gentilhomme
+    Suisse. Hague, 1749,[323] 4to.
+
+According to this octavo geometer and quarto gentleman, a diameter of 81
+gives a circumference of 256. There is an amusing circumstance about the
+quarto which has been overlooked, if indeed the book has ever been {150}
+examined. John Bernoulli (the one of the day)[324] and Koenig[325] have
+both given an attestation: my mathematical readers may stare as they
+please, such is the fact. But, on examination, there will be reason to
+think the two sly Swiss played their countryman the same trick as the
+medical man played Miss Pickle, in the novel of that name. The lady only
+wanted to get his authority against sousing her little nephew, and said,
+"Pray, doctor, is it not both dangerous and cruel to be the means of
+letting a poor tender infant perish by sousing it in water as cold as
+ice?"--"Downright murder, I affirm," said the doctor; and certified
+accordingly. De Fauré had built a tremendous scaffolding of equations,
+quite out of place, and feeling cock-sure that his solutions, if correct,
+would square the circle, applied to Bernoulli and Koenig--who after his
+tract of two years before, must have known what he was at--for their
+approbation of the solutions. And he got it, as follows, well guarded:
+
+    "Suivant les suppositions posées dans ce Mémoire, il est si évident que
+    t doit être = 34, y = 1, et z = 1, que cela n'a besoin ni de preuve ni
+    d'autorité pour être reconnu par tout le monde.[326]
+
+    "à Basle le 7e Mai 1749. JEAN BERNOULLI."
+
+    "Je souscris au jugement de Mr. Bernoulli, en conséquence de ces
+    suppositions.[327]
+
+    "à la Haye le 21 Juin 1749. S. KOENIG."
+
+On which de Fauré remarks with triumph--as I have no doubt it was intended
+he should do--"il conste clairement par ma présente Analyse et
+Démonstration, qu'ils y ont déja {151} reconnu et approuvé parfaitement que
+la quadrature du cercle est mathématiquement démontrée."[328] It should
+seem that it is easier to square the circle than to get round a
+mathematician.
+
+
+
+    An attempt to demonstrate that all the Phenomena in Nature may be
+    explained by two simple active principles, Attraction and Repulsion,
+    wherein the attraction of Cohesion, Gravity and Magnetism are shown to
+    be one the same. By Gowin Knight. London, 1748, 4to.
+
+Dr. Knight[329] was Mr. Panizzi's[330] archetype, the first Principal
+Librarian of the British Museum. He was celebrated for his magnetical
+experiments. This work was long neglected; but is now recognized as of
+remarkable resemblance to modern speculations.
+
+
+
+THOMAS WRIGHT OF DURHAM.
+
+    An original theory or Hypothesis of the Universe. By Thomas Wright[331]
+    of Durham. London, 4to, 1750.
+
+Wright is a speculator whose thoughts are now part of our current
+astronomy. He took that view--or most of it--of the milky way which
+afterwards suggested itself to William Herschel. I have given an account of
+him and his work in the _Philosophical Magazine_ for April, 1848.
+
+Wright was mathematical instrument maker to the King, {152} and kept a shop
+in Fleet Street. Is the celebrated business of Troughton & Simms, also in
+Fleet Street, a lineal descendant of that of Wright? It is likely enough,
+more likely that that--as I find him reported to have affirmed--Prester
+John was the descendant of Solomon and the Queen of Sheba. Having settled
+it thus, it struck me that I might apply to Mr. Simms, and he informs me
+that it is as I thought, the line of descent being Wright, Cole, John
+Troughton, Edward Troughton,[332] Troughton & Simms.[333]
+
+
+
+BISHOP HORNE ON NEWTON.
+
+    The theology and philosophy in Cicero's _Somnium Scipionis_ explained.
+    Or, a brief attempt to demonstrate, that the Newtonian system is
+    perfectly agreeable to the notions of the wisest ancients: and that
+    mathematical principles are the only sure ones. [By Bishop Horne,[334]
+    at the age of nineteen.] London, 1751, 8vo.
+
+This tract, which was not printed in the collected works, and is now
+excessively rare, is mentioned in _Notes and Queries_, 1st S., v, 490, 573;
+2d S., ix, 15. The boyish satire on Newton is amusing. Speaking of old
+Benjamin Martin,[335] he goes on as follows:
+
+{153}
+
+"But the most elegant account of the matter [attraction] is by that
+hominiform animal, Mr. Benjamin Martin, who having attended Dr.
+Desaguliers'[336] fine, raree, gallanty shew for some years [Desaguliers
+was one of the first who gave public experimental lectures, before the
+saucy boy was born] in the capacity of a turnspit, has, it seems, taken it
+into his head to set up for a philosopher."
+
+Thus is preserved the fact, unknown to his biographers, that Benj. Martin
+was an assistant to Desaguliers in his lectures. Hutton[337] says of him,
+that "he was well skilled in the whole circle of the mathematical and
+philosophical sciences, and wrote useful books on every one of them": this
+is quite true; and even at this day he is read by twenty where Horne is
+read by one; see the stalls, _passim_. All that I say of him, indeed my
+knowledge of the tract, is due to this contemptuous mention of a more
+durable man than himself. My assistant secretary at the Astronomical
+Society, the late Mr. Epps,[338] bought the copy at a stall because his eye
+was caught by the notice of "Old Ben Martin," of whom he was a great
+reader. Old Ben could not be a Fellow of the Royal Society, because he kept
+a shop: even though the shop sold nothing but philosophical instruments.
+Thomas Wright, similarly situated as to shop and goods, never was a Fellow.
+The Society of our day has greatly degenerated: those of the old time would
+be pleased, no doubt, that the glories of their day {154} should be
+commemorated. In the early days of the Society, there was a similar
+difficulty about Graunt, the author of the celebrated work on mortality.
+But their royal patron, "who never said a foolish thing," sent them a sharp
+message, and charged them if they found any more such tradesmen, they
+should "elect them without more ado."
+
+Horne's first pamphlet was published when he was but twenty-one years old.
+Two years afterwards, being then a Fellow of his college, and having seen
+more of the world, he seems to have felt that his manner was a little too
+pert. He endeavored, it is said, to suppress his first tract: and copies
+are certainly of extreme rarity. He published the following as his maturer
+view:
+
+    A fair, candid, and impartial state of the case between Sir Isaac
+    Newton and Mr. Hutchinson.[339] In which is shown how far a system of
+    physics is capable of mathematical demonstration; how far Sir Isaac's,
+    as such a system, has that demonstration; and consequently, what regard
+    Mr. Hutchinson's claim may deserve to have paid to it. By George Horne,
+    M.A. Oxford, 1753, 8vo.
+
+It must be remembered that the successors of Newton were very apt to
+declare that Newton had demonstrated attraction as a _physical_ cause: he
+had taken reasonable pains to show that he did not pretend to this. If any
+one had said to Newton, I hold that every particle of matter is a
+responsible being of vast intellect, ordered by the Creator to move as it
+would do if every other particle attracted it, and gifted with power to
+make its way in true accordance with that law, as easily as a lady picks
+her way across the street; what have you to say against it?--Newton must
+have replied, Sir! if you really undertake to maintain this as
+_demonstrable_, your soul had better borrow a little power {155} from the
+particles of which your body is made: if you merely ask me to refute it, I
+tell you that I neither can nor need do it; for whether attraction comes in
+this way or in any other, _it comes_, and that is all I have to do with it.
+
+The reader should remember that the word attraction, as used by Newton and
+the best of his followers, only meant a _drawing towards_, without any
+implication as to the cause. Thus whether they said that matter attracts
+matter, or that young lady attracts young gentleman, they were using one
+word in one sense. Newton found that the law of the first is the inverse
+square of the distance: I am not aware that the law of the second has been
+discovered; if there be any chance, we shall see it at the year 1856 in
+this list.
+
+In this point young Horne made a hit. He justly censures those who fixed
+upon Newton a more positive knowledge of what attraction is than he
+pretended to have. "He has owned over and over he did not know what he
+meant by it--it might be this, or it might be that, or it might be
+anything, or it might be nothing." With the exception of the _nothing_
+clause, this is true, though Newton might have answered Horne by "Thou hast
+said it."
+
+(I thought everybody knew the meaning of "Thou hast said it": but I was
+mistaken. In three of the evangelists [Greek: Su legeis] is the answer to
+"Art thou a king?" The force of this answer, as always understood, is "That
+is your way of putting it." The Puritans, who lived in Bible phrases, so
+understood it: and Walter Scott, who caught all peculiarities of language
+with great effect, makes a marked instance, "Were you armed?--I was not--I
+went in my calling, as a preacher of God's word, to encourage them that
+drew the sword in His cause. In other words, to aid and abet the rebels,
+said the Duke. _Thou hast spoken it_, replied the prisoner.")
+
+Again, Horne quotes Rowning[340] as follows:
+
+{156}
+
+"Mr. Rowning, pt. 2, p. 5 in a note, has a very pretty conceit upon this
+same subject of attraction, about every particle of a fluid being
+intrenched in three spheres of attraction and repulsion, one within
+another, 'the innermost of which (he says) is a sphere of repulsion, which
+keeps them from approaching into contact; the next, a sphere of attraction,
+diffused around this of repulsion, by which the particles are disposed to
+run together into drops; and the outermost of all, a sphere of repulsion,
+whereby they repel each other, when removed out of the attraction.' So that
+between the _urgings_, and _solicitations_, of one and t'other, a poor
+unhappy particle must ever be at his wit's end, not knowing which way to
+turn, or whom to obey first."
+
+Rowning has here started the notion which Boscovich[341] afterwards
+developed.
+
+I may add to what precedes that it cannot be settled that, as Granger[342]
+says, Desaguliers was the first who gave experimental lectures in London.
+William Whiston gave some, and Francis Hauksbee[343] made the experiments.
+The prospectus, as we should now call it, is extant, a quarto tract of
+plates and descriptions, without date. Whiston, in his life, {157} gives
+1714 as the first date of publication, and therefore, no doubt, of the
+lectures. Desaguliers removed to London soon after 1712, and commenced his
+lectures soon after that. It will be rather a nice point to settle which
+lectured first; probabilities seem to go in favor of Whiston.
+
+
+
+FALLACIES IN A THEORY OF ANNUITIES.
+
+    An Essay to ascertain the value of leases, and annuities for years and
+    lives. By W[eyman] L[ee]. London, 1737, 8vo.
+
+    A valuation of Annuities and Leases certain, for a single life. By
+    Weyman Lee, Esq. of the Inner Temple. London, 1751, 8vo. Third edition,
+    1773.
+
+Every branch of exact science has its paradoxer. The world at large cannot
+tell with certainty who is right in such questions as squaring the circle,
+etc. Mr. Weyman Lee[344] was the assailant of what all who had studied
+called demonstration in the question of annuities. He can be exposed to the
+world: for his error arose out of his not being able to see that the whole
+is the sum of all its parts.
+
+By an annuity, say of £100, now bought, is meant that the buyer is to have
+for his money £100 in a year, if he be then alive, £100 at the end of two
+years, if then alive, and so on. It is clear that he would buy a life
+annuity if he should buy the first £100 in one office, the second in
+another, and so on. All the difference between buying the whole from one
+office and buying all the separate contingent payments at different
+offices, is immaterial to calculation. Mr. Lee would have agreed with the
+rest of the world about the payments to be made to the several different
+offices, in consideration of their several contracts: but he differed from
+every one else about the sum to be paid to _one_ office. He contended that
+the way to value an annuity is to find out the term of years which the
+individual has an even chance of surviving, and to charge for the life
+annuity the value of an annuity certain for that term.
+
+{158}
+
+It is very common to say that Lee took the average life, or expectation, as
+it is wrongly called, for his term: and this I have done myself, taking the
+common story. Having exposed the absurdity of this second supposition,
+taking it for Lee's, in my _Formal Logic_,[345] I will now do the same with
+the first.
+
+A mathematical truth is true in its extreme cases. Lee's principle is that
+an annuity on a life is the annuity made certain for the term within which
+it is an even chance the life drops. If, then, of a thousand persons, 500
+be sure to die within a year, and the other 500 be immortal, Lee's price of
+an annuity to any one of these persons is the present value of one payment:
+for one year is the term which each one has an even chance of surviving and
+not surviving. But the true value is obviously half that of a perpetual
+annuity: so that at 5 percent Lee's rule would give less than the tenth of
+the true value. It must be said for the poor circle-squarers, that they
+never err so much as this.
+
+Lee would have said, if alive, that I have put an _extreme case_: but any
+_universal_ truth is true in its extreme cases. It is not fair to bring
+forward an extreme case against a person who is speaking as of usual
+occurrences: but it is quite fair when, as frequently happens, the proposer
+insists upon a perfectly general acceptance of his assertion. And yet many
+who go the whole hog protest against being tickled with the tail. Counsel
+in court are good instances: they are paradoxers by trade. June 13, 1849,
+at Hertford, there was an action about a ship, insured against a _total_
+loss: some planks were saved, and the underwriters refused to pay. Mr. Z.
+(for deft.) "There can be no degrees of totality; and some timbers were
+saved."--L. C. B. "Then if the vessel were burned to the water's edge, and
+some rope saved in the boat, there would be no total loss."--Mr. Z. "This
+is putting a very extreme case."--L. C. B. "The argument {159} would go
+that length." What would _Judge_ Z.--as he now is--say to the extreme case
+beginning somewhere between six planks and a bit of rope?
+
+
+
+MONTUCLA'S WORK ON THE QUADRATURE.
+
+    Histoire des recherches sur la quadrature du cercle ... avec une
+    addition concernant les problèmes de la duplication du cube et de la
+    trisection de l'angle. Paris, 1754, 12mo. [By Montucla.]
+
+This is _the_ history of the subject.[346] It was a little episode to the
+great history of mathematics by Montucla, of which the first edition
+appeared in 1758. There was much addition at the end of the fourth volume
+of the second edition; this is clearly by Montucla, though the bulk of the
+volume is put together, with help from Montucla's papers, by Lalande.[347]
+There is also a second edition of the history of the quadrature, Paris,
+1831, 8vo, edited, I think, by Lacroix; of which it is the great fault that
+it makes hardly any use of the additional matter just mentioned.
+
+Montucla is an admirable historian when he is writing from his own direct
+knowledge: it is a sad pity that he did not tell us when he was depending
+on others. We are not to trust a quarter of his book, and we must read many
+other books to know which quarter. The fault is common enough, but
+Montucla's good three-quarters is so good that the fault is greater in him
+than in most others: I mean the fault of not acknowledging; for an
+historian cannot read everything. But it must be said that mankind give
+little encouragement to candor on this point. Hallam, in his {160} _History
+of Literature_, states with his own usual instinct of honesty every case in
+which he depends upon others: Montucla does not. And what is the
+consequence?--Montucla is trusted, and believed in, and cried up in the
+bulk; while the smallest talker can lament that Hallam should be so unequal
+and apt to depend on others, without remembering to mention that Hallam
+himself gives the information. As to a universal history of any great
+subject being written entirely upon primary knowledge, it is a thing of
+which the possibility is not yet proved by an example. Delambre attempted
+it with astronomy, and was removed by death before it was finished,[348] to
+say nothing of the gaps he left.
+
+Montucla was nothing of a bibliographer, and his descriptions of books in
+the first edition were insufficient. The Abbé Rive[349] fell foul of him,
+and as the phrase is, gave it him. Montucla took it with great good humor,
+tried to mend, and, in his second edition, wished his critic had lived to
+see the _vernis de bibliographe_ which he had given himself.
+
+I have seen Montucla set down as an _esprit fort_, more than once: wrongly,
+I think. When he mentions Barrow's[350] address to the Almighty, he adds,
+"On voit, au reste, par là, que Barrow étoit un pauvre philosophe; car il
+croyait en l'immortalité de l'âme, et en une Divinité autre que la nature
+{161} universelle."[351] This is irony, not an expression of opinion. In
+the book of mathematical recreations which Montucla constructed upon that
+of Ozanam,[352] and Ozanam upon that of Van Etten,[353] now best known in
+England by Hutton's similar treatment of Montucla, there is an amusing
+chapter on the quadrators. Montucla refers to his own anonymous book of
+1754 as a curious book published by Jombert.[354] He seems to have been a
+little ashamed of writing about circle-squarers: what a slap on the face
+for an unborn Budgeteer!
+
+Montucla says, speaking of France, that he finds three notions prevalent
+among the cyclometers: (1) that there is a large reward offered for
+success; (2) that the longitude problem depends on that success; (3) that
+the solution is the great end and object of geometry. The same three {162}
+notions are equally prevalent among the same class in England. No reward
+has ever been offered by the government of either country. The longitude
+problem in no way depends upon perfect solution; existing approximations
+are sufficient to a point of accuracy far beyond what can be wanted.[355]
+And geometry, content with what exists, has long passed on to other
+matters. Sometimes a cyclometer persuades a skipper who has made land in
+the wrong place that the astronomers are in fault, for using a wrong
+measure of the circle; and the skipper thinks it a very comfortable
+solution! And this is the utmost that the problem ever has to do with
+longitude.
+
+
+
+ANTINEWTONIANISMUS.
+
+    Antinewtonianismus.[356] By Cælestino Cominale,[357] M.D. Naples, 1754
+    and 1756, 2 vols. 4to.
+
+The first volume upsets the theory of light; the second vacuum, vis
+inertiæ, gravitation, and attraction. I confess I never attempted these big
+Latin volumes, numbering 450 closely-printed quarto pages. The man who
+slays Newton in a pamphlet is the man for me. But I will lend them to
+anybody who will give security, himself in £500, and two sureties in £250
+each, that he will read them through, and give a full abstract; and I will
+not exact security for their return. I have never seen any mention of this
+book: it has a printer, but not a publisher, as happens with so many
+unrecorded books.
+
+{163}
+
+
+
+OFFICIAL BLOW TO CIRCLE SQUARERS.
+
+1755. The French Academy of Sciences came to the determination not to
+examine any more quadratures or kindred problems. This was the consequence,
+no doubt, of the publication of Montucla's book: the time was well chosen;
+for that book was a full justification of the resolution. The Royal Society
+followed the same course, I believe, a few years afterwards. When our Board
+of Longitude was in existence, most of its time was consumed in listening
+to schemes, many of which included the quadrature of the circle. It is
+certain that many quadrators have imagined the longitude problem to be
+connected with theirs: and no doubt the notion of a reward offered by
+Government for a true quadrature is a result of the reward offered for the
+longitude. Let it also be noted that this longitude reward was not a
+premium upon excogitation of a mysterious difficulty. The legislature was
+made to know that the rational hopes of the problem were centered in the
+improvement of the lunar tables and the improvement of chronometers. To
+these objects alone, and by name, the offer was directed: several persons
+gained rewards for both; and the offer was finally repealed.
+
+
+
+AN INTERESTING HOAX.
+
+    Fundamentalis Figura Geometrica, primas tantum lineas circuli
+    quadraturæ possibilitatis ostendens. By Niels Erichsen (Nicolaus
+    Ericius), shipbuilder, of Copenhagen. Copenhagen, 1755, 12mo.
+
+This was a gift from my oldest friend who was not a relative, Dr. Samuel
+Maitland of the "Dark Ages."[358] He found it among his books, and could
+not imagine how he came by it: I could have told him. He once collected
+interpretations of the Apocalypse: and auction lots of such {164} books
+often contain quadratures. The wonder is he never found more than one.
+
+The quadrature is not worth notice. Erichsen is the only squarer I have met
+with who has distinctly asserted the particulars of that reward which has
+been so frequently thought to have been offered in England. He says that in
+1747 the Royal Society on the 2d of June, offered to give a large reward
+for the quadrature of the circle and a true explanation of magnetism, in
+addition to £30,000 previously promised for the same. I need hardly say
+that the Royal Society had not £30,000 at that time, and would not, if it
+had had such a sum, have spent it on the circle, nor on magnetic theory;
+nor would it have coupled the two things. On this book, see _Notes and
+Queries_, 1st S., xii, 306. Perhaps Erichsen meant that the £30,000 had
+been promised by the Government, and the addition by the Royal Society.
+
+October 8, 1866. I receive a letter from a cyclometer who understands that
+a reward is offered to any one who will square the circle, and that all
+competitors are to send their plans to me. The hoaxers have not yet failed
+out of the land.
+
+
+
+TWO JESUIT CONTRIBUTIONS.
+
+    Theoria Philosophiæ Naturalis redacta ad unicam legem virium in natura
+    existentium. Editio _Veneta_ prima. By Roger Joseph Boscovich. Venice,
+    1763, 4to.
+
+The first edition is said to be of Vienna, 1758.[359] This is a celebrated
+work on the molecular theory of matter, grounded on the hypothesis of
+spheres of alternate attraction and repulsion. Boscovich was a Jesuit of
+varied pursuit. During his measurement of a degree of the meridian, while
+on horseback or waiting for his observations, he composed a Latin poem of
+about five thousand verses on eclipses, {165} with notes, which he
+dedicated to the Royal Society: _De Solis et Lunæ defectibus_,[360] London,
+Millar and Dodsley, 1760, 4to.
+
+
+
+    Traité de paix entre Des Cartes et Newton, _précédé_ des vies
+    littéraires de ces deux chefs de la physique moderne.... By Aimé Henri
+    Paulian.[361] Avignon, 1763, 12mo.
+
+I have had these books for many years without feeling the least desire to
+see how a lettered Jesuit would atone Descartes and Newton. On looking at
+my two volumes, I find that one contains nothing but the literary life of
+Descartes; the other nothing but the literary life of Newton. The preface
+indicates more: and Watt mentions _three_ volumes.[362] I dare say the
+first two contain all that is valuable. On looking more attentively at the
+two volumes, I find them both readable and instructive; the account of
+Newton is far above that of Voltaire, but not so popular. But he should not
+have said that Newton's family came from Newton in Ireland. Sir Rowland
+Hill gives fourteen _Newtons_ in Ireland;[363] twice the number of the
+cities that contended for the birth of Homer may now contend for the origin
+of Newton, on the word of Father Paulian.
+
+
+
+    Philosophical Essays, in three parts. By R. Lovett, Lay Clerk of the
+    Cathedral Church of Worcester. Worcester, 1766, 8vo.
+
+    The Electrical Philosopher: containing a new system of physics {166}
+    founded upon the principle of an universal Plenum of elementary
+    fire.... By R. Lovett, Worcester, 1774, 8vo.
+
+Mr. Lovett[364] was one of those ether philosophers who bring in elastic
+fluid as an explanation by imposition of words, without deducing any one
+phenomenon from what we know of it. And yet he says that attraction has
+received no support from geometry; though geometry, applied to a particular
+law of attraction, had shown how to predict the motions of the bodies of
+the solar system. He, and many of his stamp, have not the least idea of the
+confirmation of a theory by accordance of deduced results with observation
+posterior to the theory.
+
+
+
+BAILLY'S EXAGGERATED VIEW OF ASTRONOMY.
+
+    Lettres sur l'Atlantide de Platon, et sur l'ancien Histoire de l'Asie,
+    pour servir de suite aux lettres sur l'origine des Sciences, adressées
+    à M. de Voltaire, par M. Bailly.[365] London and Paris, 1779, 8vo.
+
+I might enter here all Bailly's histories of astronomy.[366] The paradox
+which runs through them all more or less, is the doctrine that astronomy is
+of immense antiquity, coming from some forgotten source, probably the
+drowned island of Plato, peopled by a race whom Bailly makes, as has {167}
+been said, to teach us everything except their existence and their name.
+These books, the first scientific histories which belong to readable
+literature, made a great impression by power of style: Delambre created a
+strong reaction, of injurious amount, in favor of history founded on
+contemporary documents, which early astronomy cannot furnish. These letters
+are addressed to Voltaire, and continue the discussion. There is one letter
+of Voltaire, being the fourth, dated Feb. 27, 1777, and signed "le vieux
+malade de Ferney, V. puer centum annorum."[367] Then begin Bailly's
+letters, from January 16 to May 12, 1778. From some ambiguous expressions
+in the Preface, it would seem that these are fictitious letters, supposed
+to be addressed to Voltaire at their dates. Voltaire went to Paris February
+10, 1778, and died there May 30. Nearly all this interval was his closing
+scene, and it is very unlikely that Bailly would have troubled him with
+these letters.[368]
+
+
+
+    An inquiry into the cause of motion, or a general theory of physics. By
+    S. Miller. London, 1781, 4to
+
+Newton all wrong: matter consists of two kinds of particles, one inert, the
+other elastic and capable of expanding themselves _ad infinitum_.
+
+
+
+SAINT-MARTIN ON ERRORS AND TRUTH.
+
+    Des Erreurs et de la Vérité, ou les hommes rappelés au principe
+    universel de la science; ouvrage dans lequel, en faisant remarquer aux
+    observateurs l'incertitude de leurs recherches, et leurs méprises
+    continuelles, on leur indique la route qu'ils auroient dû suivre, pour
+    acquérir l'évidence physique sur l'origine du bien et du mal, sur
+    l'homme, sur la nature matérielle, et la nature sacrée; sur la base des
+    gouvernements {168} politiques, sur l'autorité des souverains, sur la
+    justice civile et criminelle, sur les sciences, les langues, et les
+    arts. Par un Ph.... Inc.... A Edimbourg. 1782.[369] Two vols. 8vo.
+
+This is the famous work of Louis Claude de Saint-Martin[370] (1743-1803),
+for whose other works, vagaries included, the reader must look elsewhere:
+among other things, he was a translator of Jacob Behmen.[371] The title
+promises much, and the writer has smart thoughts now and then; but the
+whole is the wearisome omniscience of the author's day and country, which
+no reader of our time can tolerate. Not that we dislike omniscience; but we
+have it of our own country, both home-made and imported; and fashions vary.
+But surely there can be but one omniscience? Must a man have but one wife?
+Nay, may not a man have a new wife while the old one is living? There was a
+famous instrumental professor forty years ago, who presented a friend to
+Madame ----. The friend started, and looked surprised; for, not many weeks
+before, he had been presented to another lady, with the same title, at
+Paris. The musician observed his surprise, and quietly said, "Celle-ci est
+Madame ---- de Londres." In like manner we have a London omniscience now
+current, which would make any one start who only knew the old French
+article.
+
+The book was printed at Lyons, but it was a trick of French authors to
+pretend to be afraid of prosecution: it {169} made a book look wicked-like
+to have a feigned place of printing, and stimulated readers. A Government
+which had undergone Voltaire would never have drawn its sword upon quiet
+Saint-Martin. To make himself look still worse, he was only ph[ilosophe]
+Inc...., which is generally read _Inconnu_[372] but sometimes _Incrédule_;
+[373] most likely the ambiguity was intended. There is an awful paradox
+about the book, which explains, in part, its leaden sameness. It is all
+about _l'homme_, _l'homme_, _l'homme_,[374] except as much as treats of
+_les hommes_, _les hommes_, _les hommes_;[375] but not one single man is
+mentioned by name in its 500 pages. It reminds one of
+
+ "Water, water everywhere,
+  And not a drop to drink."
+
+Not one opinion of any other man is referred to, in the way of agreement or
+of opposition. Not even a town is mentioned: there is nothing which brings
+a capital letter into the middle of a sentence, except, by the rarest
+accident, such a personification as _Justice_. A likely book to want an
+_Edimbourg_ godfather!
+
+Saint-Martin is great in mathematics. The number _four_ essentially belongs
+to straight lines, and _nine_ to curves. The object of a straight line is
+to perpetuate _ad infinitum_ the production of a point from which it
+emanates. A circle [circle] bounds the production of all its radii, tends
+to destroy them, and is in some sort their enemy. How is it possible that
+things so distinct should not be distinguished in their _number_ as well as
+in their action? If this important observation had been made earlier,
+immense trouble would have been saved to the mathematicians, who would have
+been prevented from searching for a common measure to lines which have
+nothing in common. But, though all straight lines have the number _four_,
+it must not be supposed that they are all equal, for a line is the result
+of its law and {170} its number; but though both are the same for all lines
+of a sort, they act differently, as to force, energy, and duration, in
+different individuals; which explains all differences of length, etc. I
+congratulate the reader who understands this; and I do not pity the one who
+does not.
+
+Saint-Martin and his works are now as completely forgotten as if they had
+never been born, except so far as this, that some one may take up one of
+the works as of heretical character, and lay it down in disappointment,
+with the reflection that it is as dull as orthodoxy. For a person who was
+once in some vogue, it would be difficult to pick out a more fossil writer,
+from Aa to Zypoeus, except,--though it is unusual for (,--) to represent an
+interval of more than a year--his unknown opponent. This opponent, in the
+very year of the _Des Erreurs_ ... published a book in two parts with the
+same fictitious place of printing;
+
+    Tableau Naturel des Rapports qui existent entre Dieu, l'Homme, et
+    l'Univers. A Edimbourg, 1782, 8vo.[376]
+
+There is a motto from the _Des Erreurs_ itself, "Expliquer les choses par
+l'homme, et non l'homme par les choses. _Des Erreurs et de la Vérité_, par
+un PH.... INC...., p. 9."[377] This work is set down in various catalogues
+and biographies as written by the PH.... INC.... himself. But it is not
+usual for a writer to publish two works in the same year, one of which
+takes a motto from the other. And the second work is profuse in capitals
+and italics, and uses Hebrew learning: its style differs much from the
+first work. The first work sets out from man, and has nothing to do with
+God: the second is religious and raps the knuckles of the first as follows:
+"Si nous voulons nous préserver de toutes {171} les illusions, et surtout
+des amorces de l'orgueil par lesquelles l'homme est si souvent séduit, ne
+prenons jamais les hommes, mais toujours _Dieu_ pour notre terme de
+comparaison."[378] The first uses _four_ and _nine_ in various ways, of
+which I have quoted one: the second says, "Et ici se trouve déjà une
+explication des nombres _quatre_ et _neuf_, qui ont peu embarrassé dans
+l'ouvrage déjà cité. L'homme s'est égaré en allant de _quatre_ à
+_neuf_...."[379] The work cited is the _Erreurs_, etc., and the citation is
+in the motto, which is the text of the opposition sermon.
+
+
+
+A FORERUNNER OF THE METRIC SYSTEM.
+
+    Method to discover the difference of the earth's diameters; proving its
+    true ratio to be not less variable than as 45 is to 46, and shortest in
+    its pole's axis 174 miles.... likewise a method for fixing an universal
+    standard for weights and measures. By Thomas Williams.[380] London,
+    1788, 8vo.
+
+Mr. Williams was a paradoxer in his day, and proposed what was, no doubt,
+laughed at by some. He proposed the sort of plan which the
+French--independently of course--carried into effect a few years after. He
+would have the 52d degree of latitude divided into 100,000 parts and each
+part a geographical yard. The geographical ton was to be the cube of a
+geographical yard filled with sea-water taken some leagues from land. All
+multiples and sub-divisions were to be decimal.
+
+I was beginning to look up those who had made similar proposals, when a
+learned article on the proposal of a {172} metrical system came under my
+eye in the _Times_ of Sept. 15, 1863. The author cites Mouton,[381] who
+would have the minute of a degree divided into 10,000 _virgulæ_; James
+Cassini,[382] whose foot was to be six thousandths of a minute; and
+Paucton,[383] whose foot was the 400,000th of a degree. I have verified the
+first and third statements; surely the second ought to be the
+_six-thousandth_.
+
+
+
+    An inquiry into the Copernican system ... wherein it is proved, in the
+    clearest manner, that the earth has only her diurnal motion ... with an
+    attempt to point out the only true way whereby mankind can receive any
+    real benefit from the study of the heavenly bodies. By John
+    Cunningham.[384] London, 1789, 8vo.
+
+The "true way" appears to be the treatment of heaven and earth as
+emblematical of the Trinity.
+
+
+
+    Cosmology. An inquiry into the cause of what is called gravitation or
+    attraction, in which the motions of the heavenly bodies, and the
+    preservation and operations of all nature, are deduced from an
+    universal principle of efflux and reflux. By T. Vivian,[385] vicar of
+    Cornwood, Devon. Bath, 1792, 12mo.
+
+{173}
+
+Attraction, an influx of matter to the sun; centrifugal force, the solar
+rays; cohesion, the pressure of the atmosphere. The confusion about
+centrifugal _force_, so called, as demanding an external agent, is very
+common.
+
+
+
+THOMAS PAINE'S RIGHTS OF MAN.
+
+    The rights of MAN, being an answer to Mr. Burke's attack on the French
+    Revolution.[386] By Thomas Paine.[387] In two parts. 1791-1792. 8vo.
+    (Various editions.)[388]
+
+    A vindication of the rights of WOMAN, with strictures on political and
+    moral subjects. By Mary Wollstonecraft.[389] 1792. 8vo.
+
+    A sketch of the rights of BOYS and GIRLS. By Launcelot Light, of
+    Westminster School; and Lætitia Lookabout, of Queen's Square,
+    Bloomsbury. [By the Rev. Samuel Parr,[390] LL.D.] 1792. 8vo. (pp.64).
+
+When did we three meet before? The first work has sunk into oblivion: had
+it merited its title, it might have {174} lived. It is what the French call
+a _pièce de circonstance_; it belongs in time to the French Revolution, and
+in matter to Burke's opinion of that movement. Those who only know its name
+think it was really an attempt to write a philosophical treatise on what we
+now call socialism. Silly government prosecutions gave it what it never
+could have got for itself.
+
+Mary Wollstonecraft seldom has her name spelled right. I suppose the O! O!
+character she got made her W_oo_lstonecraft. Watt gives double insinuation,
+for his cross-reference sends us to G_oo_dwin.[391] No doubt the title of
+the book was an act of discipleship to Paine's _Rights of Man_; but this
+title is very badly chosen. The book was marred by it, especially when the
+authoress and her husband assumed the right of dispensing with legal
+sanction until the approach of offspring brought them to a sense of their
+child's interest.[392] Not a hint of such a claim is found in the book,
+which is mostly about female education. The right claimed for woman is to
+have the education of a rational human being, and not to be considered as
+nothing but woman throughout youthful training. The maxims of Mary
+Wollstonecraft are now, though not derived from her, largely followed in
+the education of girls, especially in home education: just as many of the
+political principles of Tom Paine, again not derived from him, are the
+guides of our actual legislation. I remember, forty years ago, an old lady
+used to declare that she disliked girls from the age of sixteen to
+five-and-twenty. "They are full," said she, "of _femalities_." She spoke of
+their behavior to women as well as to men. She {175} would have been
+shocked to know that she was a follower of Mary Wollstonecraft, and had
+packed half her book into one sentence.
+
+The third work is a satirical attack on Mary Wollstonecraft and Tom Paine.
+The details of the attack would convince any one that neither has anything
+which would now excite reprobation. It is utterly unworthy of Dr. Parr, and
+has quite disappeared from lists of his works, if it were ever there. That
+it was written by him I take to be evident, as follows. Nichols,[393] who
+could not fail to know, says (_Anecd._, vol. ix, p. 120): "This is a
+playful essay by a first-rate scholar, who is elsewhere noticed in this
+volume, but whose name I shall not bring forward on so trifling an
+occasion." Who the scholar was is made obvious by Master Launcelot being
+made to talk of Bellendenus.[394] Further, the same boy is made to say,
+"Let Dr. Parr lay his hand upon his heart, if his conscience will let him,
+and ask himself how many thousands of wagon-loads of this article [birch]
+he has cruelly misapplied." How could this apply to Parr, with his handful
+of private pupils,[395] and no reputation for severity? Any one except
+himself would have called on the head-master of Westminster or Eton. I
+doubt whether the name of Parr could be connected with the rod by anything
+in print, except the above and an anecdote of his pupil, Tom Sheridan.[396]
+The Doctor had dressed for a dinner visit, and {176} was ready a quarter of
+an hour too soon to set off. "Tom," said he, "I think I had better whip you
+now; you are sure to do something while I am out."--"I wish you would,
+sir!" said the boy; "it would be a letter of licence for the whole
+evening." The Doctor saw the force of the retort: my two tutelaries will
+see it by this time. They paid in advance; and I have given liberal
+interpretation to the order.
+
+The following story of Dr. Parr was told me and others, about 1829, by the
+late Leonard Horner,[397] who knew him intimately. Parr was staying in a
+house full of company, I think in the north of England. Some gentlemen from
+America were among the guests, and after dinner they disputed some of
+Parr's assertions or arguments. So the Doctor broke out with "Do you know
+what country you come from? You come from the place to which we used to
+send our thieves!" This made the host angry, and he gave Parr such a severe
+rebuke as sent him from the room in ill-humor. The rest walked on the lawn,
+amusing the Americans with sketches of the Doctor. There was a dark cloud
+overhead, and from that cloud presently came a voice which called _Tham_
+(Parr-lisp for _Sam_). The company were astonished for a moment, but
+thought the Doctor was calling his servant in the house, and that the
+apparent direction was an illusion arising out of inattention. But
+presently the sound was repeated, certainly from the cloud,
+
+    "And nearer, clearer, deadlier than before."
+
+There was now a little alarm: where could the Doctor have got to? They ran
+to his bedroom, and there they discovered a sufficient rather than
+satisfactory explanation. The Doctor had taken his pipe into his bedroom,
+and had seated himself, in sulky mood, upon the higher bar of a large and
+deep old-fashioned grate with a high mantelshelf. Here he had {177} tumbled
+backwards, and doubled himself up between the bars and the back of the
+grate. He was fixed tight, and when he called for help, he could only throw
+his voice up the chimney. The echo from the cloud was the warning which
+brought his friends to the rescue.
+
+
+
+ATTACKS ON RELIGIOUS CUSTOMS.
+
+Days of political paradox were coming, at which we now stare. Cobbett[398]
+said, about 1830, in earnest, that in the country every man who did not
+take off his hat to the clergyman was suspected, and ran a fair chance of
+having something brought against him. I heard this assertion canvassed,
+when it was made, in a party of elderly persons. The Radicals backed it,
+the old Tories rather denied it, but in a way which satisfied me they ought
+to have denied it less if they could not deny it more. But it must be said
+that the Governments stopped far short of what their partisans would have
+had them do. All who know Robert Robinson's[399] very quiet assault on
+church-made festivals in his _History and Mystery of Good Friday_
+(1777)[400] will hear or remember with surprise that the _British Critic_
+pronounced it a direct, unprovoked, and malicious libel on the most {178}
+sacred institutions of the national Church. It was reprinted again and
+again: in 1811 it was in a cheap form at 6s. 6d. a hundred. When the
+Jacobin day came, the State was really in a fright: people thought twice
+before they published what would now be quite disregarded. I examined a
+quantity of letters addressed to George Dyer[401] (Charles Lamb's G.D.) and
+what between the autographs of Thelwall, Hardy, Horne Tooke, and all the
+rebels,[402] put together a packet which produced five guineas, or
+thereabouts, for the widow. Among them were the following verses, sent by
+the author--who would not put his name, even in a private letter, for fear
+of accidents--for consultation whether they could safely be sent to an
+editor: and they were _not_ sent. The occasion was the public thanksgiving
+at St. Paul's for the naval victories, December 19, 1797.
+
+ "God bless me! what a thing!
+  Have you heard that the King
+    Goes to St. Paul's?
+  {179}
+  Good Lord! and when he's there,
+  He'll roll his eyes in prayer,
+  To make poor Johnny stare
+    At this fine thing.
+
+ "No doubt the plan is wise
+  To blind poor Johnny's eyes
+    By this grand show;
+  For should he once suppose
+  That he's led by the nose,
+  Down the whole fabric goes,
+    Church, lords, and king.
+
+ "As he shouts Duncan's[403] praise,
+  Mind how supplies they'll raise
+    In wondrous haste.
+  For while upon the sea
+  We gain one victory,
+  John still a dupe will be
+    And taxes pay.
+
+ "Till from his little store
+  Three-fourths or even more
+    Goes to the Crown.
+  Ah, John! you little think
+  How fast we downward sink
+  And touch the fatal brink
+    At which we're slaves."
+
+I would have indicted the author for not making his thirds and sevenths
+rhyme. As to the rhythm, it is not much better than what the French sang in
+the Calais theater when the Duke of Clarence[404] took over Louis XVIII in
+1814.
+
+ "God save noble Clarence,
+  Who brings our king to France;
+    God save Clarence!
+  He maintains the glory
+  Of the British navy,
+    etc., etc."
+
+{180} Perhaps had this been published, the Government would have assailed
+it as a libel on the church service. They got into the way of defending
+themselves by making libels on the Church, of what were libels, if on
+anything, on the rulers of the State; until the celebrated trials of Hone
+settled the point for ever, and established that juries will not convict
+for one offence, even though it have been committed, when they know the
+prosecution is directed at another offence and another intent.
+
+
+
+HONE'S FAMOUS TRIALS.
+
+The results of Hone's trials (William Hone, 1779-1842) are among the
+important constitutional victories of our century. He published parodies on
+the Creeds, the Lord's Prayer, the Catechism, etc., with intent to bring
+the Ministry into contempt: everybody knew that was his _purpose_. The
+Government indicted him for impious, profane, blasphemous intent, but not
+for seditious intent. They hoped to wear him out by proceeding day by day.
+December 18, 1817, they hid themselves under the Lord's Prayer, the Creed,
+and the Commandments; December 19, under the Litany; December 20, under the
+Athanasian Creed, an odd place for shelter when they could not find it in
+the previous places. Hone defended himself for six, seven, and eight hours
+on the several days: and the jury acquitted him in 15, 105, and 20 minutes.
+In the second trial the offense was laid both as profanity and as sedition,
+which seems to have made the jury hesitate. And they probably came to think
+that the second count was false pretence: but the length of their
+deliberation is a satisfactory addition to the value of the whole. In the
+first trial the Attorney-General (Shepherd) had the impudence to say that
+the libel had nothing of a political tendency about it, but was _avowedly_
+set off against the religion and worship of the Church of England. The
+whole {181} is political in every sentence; neither more nor less political
+than the following, which is part of the parody on the Catechism: "What is
+thy duty towards the Minister? My duty towards the Minister is, to trust
+him as much as I can; to honor him with all my words, with all my bows,
+with all my scrapes, and with all my cringes; to flatter him; to give him
+thanks; to give up my whole soul to him; to idolize his name, and obey his
+word, and serve him blindly all the days of his political life." And the
+parody on the Creed begins, "I believe in George, the Regent almighty,
+maker of new streets and Knights of the Bath." This is what the
+Attorney-General said had nothing of a political tendency about it. But
+this was _on the first trial_: Hone was not known. The first day's trial
+was under Justice Abbott (afterwards C. J. Tenterden).[405] It was
+perfectly understood, when Chief Justice Ellenborough[406] appeared in
+Court on the second day, that he was very angry at the first result, and
+put his junior aside to try his own rougher dealing. But Hone tamed the
+lion. An eye-witness told me that when he implored of Hone not to detail
+his own father Bishop Law's[407] views on the Athanasian Creed, which
+humble petition Hone kindly granted, he held by the desk for support. And
+the same when--which is not reported--the Attorney-General appealed to the
+Court for protection against a {182} stinging attack which Hone made on the
+Bar: he _held on_, and said, "Mr. Attorney, what _can_ I do!" I was a boy
+of twelve years old, but so strong was the feeling of exultation at the
+verdicts that boys at school were not prohibited from seeing the parodies,
+which would have been held at any other time quite unfit to meet their
+eyes. I was not able to comprehend all about the Lord Chief Justice until I
+read and heard again in after years. In the meantime, Joe Miller had given
+me the story of the leopard which was sent home on board a ship of war, and
+was in two days made as docile as a cat by the sailors.[408] "You have got
+that fellow well under," said an officer. "Lord bless your Honor!" said
+Jack, "if the Emperor of Marocky would send us a cock rhinoceros, we'd
+bring him to his bearings in no time!" When I came to the subject again, it
+pleased me to entertain the question whether, if the Emperor had sent a
+cock rhinoceros to preside on the third day in the King's Bench, Hone would
+have mastered _him_: I forget how I settled it. There grew up a story that
+Hone caused Lord Ellenborough's death, but this could not have been true.
+Lord Ellenborough resigned his seat in a few months, and died just a year
+after the trials; but sixty-eight years may have had more to do with it
+than his defeat.
+
+A large subscription was raised for Hone, headed by the Duke of
+Bedford[409] for £105. Many of the leading anti-ministerialists joined: but
+there were many of the other side who avowed their disapprobation of the
+false pretense. Many could not venture their names. In the list I find:
+{183} A member of the House of Lords, an enemy to persecution, and
+especially to religious persecution employed for political purposes--No
+parodist, but an enemy to persecution--A juryman on the third day's
+trial--Ellen Borough--My name would ruin me--Oh! minions of Pitt--Oil for
+the Hone--The Ghosts of Jeffries[410] and Sir William Roy [Ghosts of
+Jeffries in abundance]--A conscientious Jury and a conscientious Attorney,
+£1 6s. 8d.--To Mr. Hone, for defending in his own person the freedom of the
+press, attacked for a political object, under the old pretense of
+supporting Religion--A cut at corruption--An Earldom for myself and a
+translation for my brother--One who disapproves of parodies, but abhors
+persecution--From a schoolboy who wishes Mr. Hone to have a very grand
+subscription--"For delicacy's sake forbear," and "Felix trembled"--"I will
+go myself to-morrow"--Judge Jeffries' works rebound in calf by Law--Keep us
+from Law, and from the Shepherd's paw--I must not give you my name, but God
+bless you!--As much like Judge Jeffries as the present times will
+permit--May Jeffries' fame and Jeffries' fate on every modern Jeffries
+wait--No parodist, but an admirer of the man who has proved the fallacy of
+the Lawyer's Law, that when a man is his own advocate he has a fool for his
+client--A Mussulman who thinks it would not be an impious libel to parody
+the Koran--May the suspenders of the Habeas Corpus Act be speedily
+suspended--Three times twelve for thrice-tried Hone, who cleared the cases
+himself alone, and won three heats by twelve to one, £1 16s.--A
+conscientious attorney, £1 6s. 8d.--Rev. T. B. Morris, rector of
+Shelfanger, who disapproves of the parodies, but abhors the making an
+affected zeal for religion the pretext for political persecution--A Lawyer
+opposed in principle to {184} Law--For the Hone that set the razor that
+shaved the rats--Rev. Dr. Samuel Parr, who most seriously disapproves of
+all parodies upon the hallowed language of Scripture and the contents of
+the Prayer-book, but acquits Mr. Hone of intentional impiety, admires his
+talents and fortitude, and applauds the good sense and integrity of his
+juries--Religion without hypocrisy, and Law without impartiality--O Law! O
+Law! O Law!
+
+These are specimens of a great many allusive mottoes. The subscription was
+very large, and would have bought a handsome annuity, but Hone employed it
+in the bookselling trade, and did not thrive. His _Everyday Book_[411] and
+his _Apocryphal New Testament_,[412] are useful books. On an annuity he
+would have thriven as an antiquarian writer and collector. It is well that
+the attack upon the right to ridicule Ministers roused a dormant power
+which was equal to the occasion. Hone declared, on his honor, that he had
+never addressed a meeting in his life, nor spoken a word before more than
+twelve persons. Had he--which however could not then be done--employed
+counsel and had a _guilty defense_ made for him, he would very likely have
+been convicted, and the work would have been left to be done by another. No
+question that the parodies disgusted all who reverenced Christianity, and
+who could not separate the serious and the ludicrous, and prevent their
+existence in combination.
+
+My extracts, etc., are from the nineteenth, seventeenth, and sixteenth
+editions of the three trials, which seem to have been contemporaneous (all
+in 1818) as they are made up into one book, with additional title over all,
+and the motto "Thrice the brindled cat hath mew'd." They are published by
+Hone himself, who I should have said was a publisher {185} as well as was
+to be. And though the trials only ended Dec. 20, 1817, the preface attached
+to this common title is dated Jan. 23, 1818.[413]
+
+The spirit which was roused against the false dealing of the Government,
+i.e., the pretense of prosecuting for impiety when all the world knew the
+real offense was, if anything, sedition--was not got up at the moment:
+there had been previous exhibitions of it. For example, in the spring of
+1818 Mr. Russell, a little printer in Birmingham, was indicted for
+publishing the Political Litany[414] on which Hone was afterwards tried. He
+took his witnesses to the summer Warwick assizes, and was told that the
+indictment had been removed by certiorari into the King's Bench. He had
+notice of trial for the spring assizes at Warwick: he took his witnesses
+there, and the trial was postponed by the Crown. He then had notice for the
+summer assizes at Warwick; and so on. The policy seems to have been to wear
+out the obnoxious parties, either by delays or by heaping on trials. The
+Government was odious, and knew it could _not_ get verdicts against
+ridicule, and _could_ get verdicts against impiety. No difficulty was found
+in convicting the sellers of Paine's works, and the like. When Hone was
+held to bail it was seen that a crisis was at hand. All parties in politics
+furnished him with parodies in proof of religious persons having made
+instruments of them. The parodies by Addison and Luther were contributed by
+a Tory lawyer, who was afterwards a judge.
+
+Hone had published, in 1817, tracts of purely political ridicule: _Official
+Account of the Noble Lord's Bite,_[415] _Trial of the Dog for Biting the
+Noble Lord_, etc. These were not touched. After the trials, it is manifest
+that Hone was {186} to be unassailed, do what he might. _The Political
+House that Jack built_, in 1819; _The Man in the Moon_, 1820; _The Queen's
+Matrimonial Ladder_, _Non mi ricordo_, _The R--l Fowls_, 1820; _The
+Political Showman at Home_, with plates by G. Cruickshank,[416] 1821 [he
+did all the plates]; _The Spirit of Despotism_, 1821--would have been
+legitimate marks for prosecution in previous years. The biting caricature
+of several of these works are remembered to this day. _The Spirit of
+Despotism_ was a tract of 1795, of which a few copies had been privately
+circulated with great secrecy. Hone reprinted it, and prefixed the
+following address to "Robert Stewart, _alias_ Lord Castlereagh"[417]: "It
+appears to me that if, unhappily, your counsels are allowed much longer to
+prevail in the Brunswick Cabinet, they will bring on a crisis, in which the
+king may be dethroned or the people enslaved. Experience has shown that the
+people will not be enslaved--the alternative is the affair of your
+employers." Hone might say this without notice.
+
+In 1819 Mr. Murray[418] published Lord Byron's _Don Juan_,[419] and Hone
+followed it with _Don John, or Don Juan Unmasked_, a little account of what
+the publisher to the Admiralty was allowed to issue without prosecution.
+The parody on the Commandments was a case very much in point: and Hone
+makes a stinging allusion to the use of the "_unutterable Name_, with a
+profane levity unsurpassed by {187} any other two lines in the English
+language." The lines are
+
+ "'Tis strange--the Hebrew noun which means 'I am,'
+  The English always use to govern d----n."
+
+Hone ends with: "Lord Byron's dedication of 'Don Juan' to Lord Castlereagh
+was suppressed by Mr. Murray from delicacy to Ministers. Q. Why did not Mr.
+Murray suppress Lord Byron's _parody_ on the Ten Commandments? _A._ Because
+it contains nothing in ridicule of Ministers, and therefore nothing that
+_they_ could suppose would lead to the displeasure of Almighty God."
+
+The little matters on which I have dwelt will never appear in history from
+their political importance, except in a few words of result. As a mode of
+thought, silly evasions of all kinds belong to such a work as the present.
+Ignorance, which seats itself in the chair of knowledge, is a mother of
+revolutions in politics, and of unread pamphlets in circle-squaring. From
+1815 to 1830 the question of revolution or no revolution lurked in all our
+English discussions. The high classes must govern; the high classes shall
+not govern; and thereupon issue was to be joined. In 1828-33 the question
+came to issue; and it was, Revolution with or without civil war; choose.
+The choice was wisely made; and the Reform Bill started a new system so
+well dovetailed into the old that the joinings are hardly visible. And now,
+in 1867, the thing is repeated with a marked subsidence of symptoms; and
+the party which has taken the place of the extinct Tories is carrying
+through Parliament a wider extension of the franchise than their opponents
+would have ventured. Napoleon used to say that a decided nose was a sign of
+power: on which it has been remarked that he had good reason to say so
+before the play was done. And so had our country; it was saved from a
+religious war, and from a civil war, by the power of that nose over its
+colleagues. {188}
+
+
+
+THOMAS TAYLOR, THE PLATONIST.
+
+    The Commentaries of Proclus.[420] Translated by Thomas Taylor.[421]
+    London, 1792, 2 vols. 4to.[422]
+
+The reputation of "the Platonist" begins to grow, and will continue to
+grow. The most authentic account is in the _Penny Cyclopædia_, written by
+one of the few persons who knew him well, and one of the fewer who possess
+all his works. At page lvi of the Introduction is Taylor's notion of the
+way to find the circumference. It is not geometrical, for it proceeds on
+the motion of a point: the words "on account of the simplicity of the
+impulsive motion, such a line must be either straight or circular" will
+suffice to show how Platonic it is. Taylor certainly professed a kind of
+heathenism. D'lsraeli said, "Mr. T. Taylor, the Platonic philosopher and
+the modern Plethon,[423] consonant to that philosophy, professes
+polytheism." Taylor printed this in large type, in a page by itself after
+the dedication, without any disavowal. I have seen the following, Greek and
+translation both, in his handwriting: "[Greek: Pas agathos hêi agathos
+ethnikos; kai pas christianos hêi christianos kakos.] Every good man, so
+far as he is a good man, is a heathen; and every Christian, so far as he is
+a Christian, is a bad man." Whether Taylor had in his head the Christian of
+the New Testament, or whether he drew from those members of the "religious
+world" who make manifest the religious flesh and the religious devil, {189}
+cannot be decided by us, and perhaps was not known to himself. If a
+heathen, he was a virtuous one.
+
+
+
+A NEW ERA IN FICTION.
+
+(1795.) This is the date of a very remarkable paradox. The religious
+world--to use a name claimed by a doctrinal sect--had long set its face
+against amusing literature, and all works of imagination. Bunyan, Milton,
+and a few others were irresistible; but a long face was pulled at every
+attempt to produce something readable for poor people and _poor children_.
+In 1795, a benevolent association began to circulate the works of a lady
+who had been herself a dramatist, and had nourished a pleasant vein of
+satire in the society of Garrick and his friends; all which is carefully
+suppressed in some biographies. Hannah More's[424] _Cheap Repository
+Tracts_,[425] which were bought by millions of copies, destroyed the
+vicious publications with which the hawkers deluged the country, by the
+simple process of furnishing the hawkers with something more saleable.
+
+_Dramatic fiction_, in which the _characters_ are drawn by themselves, was,
+at the middle of the last century, the monopoly of writers who required
+indecorum, such as Fielding and Smollett. All, or nearly all, which could
+be permitted to the young, was dry narrative, written by people who could
+not make their personages _talk character_; they all spoke {190} alike. The
+author of the _Rambler_[426] is ridiculed, because his young ladies talk
+Johnsonese; but the satirists forget that all the presentable novel-writers
+were equally incompetent; even the author of _Zeluco_ (1789)[427] is the
+strongest possible case in point.
+
+Dr. Moore,[428] the father of the hero of Corunna,[429] with good narrative
+power, some sly humor, and much observation of character, would have been,
+in our day, a writer of the _Peacock_[430] family. Nevertheless, to one who
+is accustomed to our style of things, it is comic to read the dialogue of a
+jealous husband, a suspected wife, a faithless maid-servant, a tool of a
+nurse, a wrong-headed pomposity of a priest, and a sensible physician, all
+talking Dr. Moore through their masks. Certainly an Irish soldier does say
+"by Jasus," and a cockney footman "this here" and "that there"; and this
+and the like is all the painting of characters which is effected out of the
+mouths of the bearers by a narrator of great power. I suspect that some
+novelists repressed their power under a rule that a narrative should
+narrate, and that the dramatic should be confined to the drama.
+
+I make no exception in favor of Miss Burney;[431] though she was the
+forerunner of a new era. Suppose a country {191} in which dress is always
+of one color; suppose an importer who brings in cargoes of blue stuff, red
+stuff, green stuff, etc., and exhibits dresses of these several colors,
+that person is the similitude of Miss Burney. It would be a delightful
+change from a universal dull brown, to see one person all red, another all
+blue, etc.; but the real inventor of pleasant dress would be the one who
+could mix his colors and keep down the bright and gaudy. Miss Burney's
+introduction was so charming, by contrast, that she nailed such men as
+Johnson, Burke, Garrick, etc., to her books. But when a person who has read
+them with keen pleasure in boyhood, as I did, comes back to them after a
+long period, during which he has made acquaintance with the great novelists
+of our century, three-quarters of the pleasure is replaced by wonder that
+he had not seen he was at a puppet-show, not at a drama. Take some
+_labeled_ characters out of our humorists, let them be put together into
+one piece, to speak only as labeled: let there be a Dominie with nothing
+but "Prodigious!" a Dick Swiveller with nothing but adapted quotations; a
+Dr. Folliott with nothing but sneers at Lord Brougham;[432] and the whole
+will pack up into one of Miss Burney's novels.
+
+Maria Edgeworth,[433] Sydney Owenson (Lady Morgan),[434] Jane Austen,[435]
+Walter Scott,[436] etc., are all of our century; as {192} are, I believe,
+all the Minerva Press novels, as they were called, which show some of the
+power in question. Perhaps dramatic talent found its best encouragement in
+the drama itself. But I cannot ascertain that any such power was directed
+at the multitude, whether educated or uneducated, with natural mixture of
+character, under the restraints of decorum, until the use of it by two
+religious writers of the school called "evangelical," Hannah More and
+Rowland Hill.[437] The _Village Dialogues_, though not equal to the
+_Repository Tracts_, are in many parts an approach, and perhaps a copy;
+there is frequently humorous satire, in that most effective form,
+self-display. They were published in 1800, and, partly at least, by the
+Religious Tract Society, the lineal successor of the _Repository_
+association, though knowing nothing about its predecessor. I think it right
+to add that Rowland Hill here mentioned is not the regenerator of the Post
+Office.[438] Some do not distinguish accurately; I have heard of more than
+one who took me to have had a logical controversy with a diplomatist who
+died some years before I was born.
+
+
+
+THE RELIGIOUS TRACT SOCIETY.
+
+A few years ago, an attempt was made by myself and others to collect some
+information about the _Cheap Repository_ (see _Notes and Queries_, 3d
+Series, vi. 241, 290, 353; _Christian Observer_, Dec. 1864, pp. 944-49). It
+appeared that after the Religious Tract Society had existed more than fifty
+years, a friend presented it with a copy of the original prospectus of the
+_Repository_, a thing the existence of which was not known. In this
+prospectus it is announced that from the plan "will be carefully excluded
+whatever is enthusiastic, absurd, or superstitious." The "evangelical"
+{193} party had, from the foundation of the Religious Tract Society,
+regretted that the _Repository Tracts_ "did not contain a fuller statement
+of the great evangelical principles"; while in the prospectus it is also
+stated that "no cause of any particular party is intended to be served by
+it, but general Christianity will be promoted upon practical principles."
+This explains what has often been noticed, that the tracts contain a mild
+form of "evangelical" doctrine, free from that more fervid dogmatism which
+appears in the _Village Dialogues_; and such as H. More's friend, Bishop
+Porteus[439]--a great promoter of the scheme--might approve. The Religious
+Tract Society (in 1863) republished some of H. More's tracts, with
+alterations, additions, and omissions _ad libitum_. This is an improper way
+of dealing with the works of the dead; especially when the reprints are of
+popular works. A small type addition to the preface contains: "Some
+alterations and abridgements have been made to adapt them to the present
+times and the aim of the Religious Tract Society." I think every publicity
+ought to be given to the existence of such a practice; and I reprint what I
+said on the subject in _Notes and Queries_.
+
+Alterations in works which the Society republishes are a necessary part of
+their plan, though such notes as they should judge to be corrective would
+be the best way of proceeding. But the fact of alteration should be very
+distinctly announced on the title of the work itself, not left to a little
+bit of small type at the end of the preface, in the place where trade
+advertisements, or directions to the binder, are often found. And the
+places in which alteration has been made should be pointed out, either by
+marks of omission, when omission is the alteration, or by putting the
+altered sentences in brackets, when change has been made. May any one alter
+the works of the dead at his own discretion? {194} We all know that readers
+in general will take each sentence to be that of the author whose name is
+on the title; so that a correcting republisher _makes use of his author's
+name to teach his own variation_. The tortuous logic of "the trade," which
+is content when "the world" is satisfied, is not easily answered, any more
+than an eel is easily caught; but the Religious Tract Society may be
+_convinced_ [in the old sense] in a sentence. On which course would they
+feel most safe in giving their account to the God of truth? "In your own
+conscience, now?"
+
+I have tracked out a good many of the variations made by the Religious
+Tract Society in the recently published volume of _Repository Tracts_. Most
+of them are doctrinal insertions or amplifications, to the matter of which
+Hannah More would not have objected--all that can be brought against them
+is the want of notice. But I have found two which the respect I have for
+the Religious Tract Society, in spite of much difference on various points,
+must not prevent my designating as paltry. In the story of Mary Wood, a
+kind-hearted clergyman converses with the poor girl who has ruined herself
+by lying. In the original, he "assisted her in the great work of
+repentance;" in the reprint it is to be shown in some detail how he did
+this. He is to begin by pointing out that "the heart is deceitful above all
+things and desperately wicked." Now the clergyman's name is _Heartwell_: so
+to prevent his name from contradicting his doctrine, he is actually cut
+down to _Harwell_. Hannah Moore meant this good man for one of those
+described in Acts xv. 8, 9, and his name was appropriate.
+
+Again, Mr. Flatterwell, in persuasion of Parley the porter to let him into
+the castle, declares that the worst he will do is to "play an innocent game
+of cards just to keep you awake, or sing a cheerful song with the maids."
+Oh fie! Miss Hannah More! and you a single lady too, and a contemporary of
+the virtuous Bowdler![440] Though Flatterwell be an {195} allegory of the
+devil, this is really too indecorous, even for him. Out with the three last
+words! and out it is.
+
+The Society cuts a poor figure before a literary tribunal. Nothing was
+wanted except an admission that the remarks made by me were unanswerable,
+and this was immediately furnished by the Secretary (_N. and Q._, 3d S.,
+vi. 290). In a reply of which six parts out of seven are a very amplified
+statement that the Society did not intend to reprint _all_ Hannah More's
+tracts, the remaining seventh is as follows:
+
+"I am not careful [perhaps this should be _careful not_] to notice
+Professor De Morgan's objections to the changes in 'Mary Wood' or 'Parley
+the Porter,' but would merely reiterate that the tracts were neither
+designed nor announced to be 'reprints' of the originals [design is only
+known to the designers; as to announcement, the title is ''Tis all for the
+best, The Shepherd of Salisbury Plain, and other narratives by Hannah
+More']; and much less [this must be _careful not_; further removed from
+answer than _not careful_] can I occupy your space by a treatise on the
+Professor's question: 'May any one alter the works of the dead at his own
+discretion?'"
+
+To which I say: Thanks for help!
+
+I predict that Hannah More's _Cheap Repository Tracts_ will somewhat
+resemble the _Pilgrim's Progress_ in their fate. Written for the cottage,
+and long remaining in their original position, they will become classical
+works of their kind. Most assuredly this will happen if my assertion cannot
+be upset, namely, that they contain the first specimens of fiction
+addressed to the world at large, and widely circulated, in which
+dramatic--as distinguished from puppet--power is shown, and without
+indecorum.
+
+{196}
+
+According to some statements I have seen, but which I have not verified,
+other publishing bodies, such as the Christian Knowledge Society, have
+taken the same liberty with the names of the dead as the Religious Tract
+Society. If it be so, the impropriety is the work of the smaller spirits
+who have not been sufficiently overlooked. There must be an overwhelming
+majority in the higher councils to feel that, whenever _altered_ works are
+published, _the fact of alteration should be made as prominent as the name
+of the author_. Everything short of this is suppression of truth, and will
+ultimately destroy the credit of the Society. Equally necessary is it that
+the alterations should be noted. When it comes to be known that the author
+before him is altered, he knows not where nor how nor by whom, the lowest
+reader will lose his interest.
+
+
+
+A TRIBUTE TO WILLIAM FREND.
+
+    The principles of Algebra. By William Frend.[441] London, 1796, 8vo.
+    Second Part, 1799.
+
+This Algebra, says Dr. Peacock,[442] shows "great distrust {197} of the
+results of algebraical science which were in existence at the time when it
+was written." Truly it does; for, as Dr. Peacock had shown by full
+citation, it makes war of extermination upon all that distinguishes algebra
+from arithmetic. Robert Simson[443] and Baron Maseres[444] were Mr. Frend's
+predecessors in this opinion.
+
+The genuine respect which I entertained for my father-in-law did not
+prevent my canvassing with perfect freedom his anti-algebraical and
+anti-Newtonian opinions, in a long obituary memoir read at the Astronomical
+Society in February 1842, which was written by me. It was copied into the
+_Athenæum_ of March 19. It must be said that if the manner in which algebra
+_was_ presented to the learner had been true algebra, he would have been
+right: and if he had confined himself to protesting against the imposition
+of attraction as a fundamental part of the existence of matter, he would
+have been in unity with a great many, including Newton himself. I wish he
+had preferred amendment to rejection when he was a college tutor: he wrote
+and spoke English with a clearness which is seldom equaled.
+
+His anti-Newtonian discussions are confined to the preliminary chapters of
+his _Evening Amusements_,[445] a series of astronomical lessons in nineteen
+volumes, following the moon through a period of the golden numbers.
+
+There is a mistake about him which can never be destroyed. It is constantly
+said that, at his celebrated trial in 1792, for sedition and opposition to
+the Liturgy, etc., he was _expelled_ from the University. He was
+_banished_. People cannot see the difference; but it made all the
+difference to {198} Mr. Frend. He held his fellowship and its profits till
+his marriage in 1808, and was a member of the University and of its Senate
+till his death in 1841, as any Cambridge Calendar up to 1841 will show.
+That they would have expelled him if they could, is perfectly true; and
+there is a funny story--also perfectly true--about their first proceedings
+being under a statute which would have given the power, had it not been
+discovered during the proceedings that the statute did not exist. It had
+come so near to existence as to be entered into the Vice-Chancellor's book
+for his signature, which it wanted, as was not seen till Mr. Frend exposed
+it: in fact, the statute had never actually passed.
+
+There is an absurd mistake in Gunning's[446] _Reminiscences of Cambridge_.
+In quoting a passage of Mr. Frend's pamphlet, which was very obnoxious to
+the existing Government, it is printed that the poor market-women
+complained that they were to be _scotched_ a quarter of their wages by
+taxation; and attention is called to the word by its being three times
+printed in italics. In the pamphlet it is "sconced"; that very common old
+word for fined or mulcted.
+
+Lord Lyndhurst,[447] who has [1863] just passed away under a load of years
+and honors, was Mr. Frend's private pupil at Cambridge. At the time of the
+celebrated trial, he and two others amused themselves, and vented the
+feeling which was very strong among the undergraduates, by chalking the
+walls of Cambridge with "Frend for ever!" While thus engaged in what, using
+the term legally, we are probably to call his first publication, he and his
+friends were surprised by the proctors. Flight and chase followed of
+course: Copley and one of the others, Serjeant Rough,[448] escaped: the
+{199} third, whose name I forget, but who afterwards, I have been told was
+a bishop,[449] being lame, was captured and impositioned. Looking at the
+Cambridge Calendar to verify the fact that Copley was an undergraduate at
+the time, I find that there are but two other men in the list of honors of
+his year whose names are now widely remembered. And they were both
+celebrated schoolmasters; Butler[450] of Harrow, and Tate[451] of Richmond.
+
+But Mr. Frend had another noted pupil. I once had a conversation with a
+very remarkable man, who was generally called "Place,[452] the tailor," but
+who was politician, political economist, etc., etc. He sat in the room
+above his shop--he was then a thriving master tailor at Charing
+Cross--surrounded by books enough for nine, to shame a proverb. The blue
+books alone, cut up into strips, would have measured Great Britain for
+oh-no-we-never-mention-'ems, the Highlands included. I cannot find a
+biography of this worthy and able man. I happened to mention William Frend,
+and he said, "Ah! my old master, as I always call him. Many and many a
+time, and year after year, did he come in every {200} now and then to give
+me instruction, while I was sitting on the board, working for my living,
+you know."
+
+Place, who really was a sound economist, is joined with Cobbett, because
+they were together at one time, and because he was, in 1800, etc., a great
+Radical. But for Cobbett he had a great contempt. He told me the following
+story. He and others were advising with Cobbett about the defense he was to
+make on a trial for seditious libel which was coming on. Said Place, "You
+must put in the letters you have received from Ministers, members of the
+Commons from the Speaker downwards, etc., about your Register, and their
+wish to have subjects noted. You must then ask the jury whether a person so
+addressed must be considered as a common sower of sedition, etc. You will
+be acquitted; nay, if your intention should get about, very likely they
+will manage to stop proceedings." Cobbett was too much disturbed to listen;
+he walked about the room ejaculating "D---- the prison!" and the like. He
+had not the sense to follow the advice, and was convicted.
+
+Cobbett, to go on with the chain, was a political acrobat, ready for any
+kind of posture. A friend of mine gave me several times an account of a
+mission to him. A Tory member--those who know the old Tory world may look
+for his initials in initials of two consecutive words of "Pay his money
+with interest"--who was, of course, a political opponent, thought Cobbett
+had been hardly used, and determined to subscribe handsomely towards the
+expenses he was incurring as a candidate. My friend was commissioned to
+hand over the money--a bag of sovereigns, that notes might not be traced.
+He went into Cobbett's committee-room, told the patriot his errand, and put
+the money on the table. "And to whom, sir, am I indebted?" said Cobbett.
+"The donor," was the answer, "is Mr. Andrew Theophilus Smith," or some such
+unlikely pair of baptismals. "Ah!" said Cobbett, "I have known Mr. A. T. S.
+a long time! he was always a true friend of his country!" {201}
+
+To return to Place. He is a noted instance of the advantage of our jury
+system, which never asks a man's politics, etc. The late King of Hanover,
+when Duke of Cumberland, being unpopular, was brought under unjust
+suspicions by the suicide of his valet: he must have seduced the wife and
+murdered the husband. The charges were as absurd as those brought against
+the Englishman in the Frenchman's attempt at satirical verses upon him:
+
+ "The Englishman is a very bad man;
+  He drink the beer and he steal the can:
+  He kiss the wife and he beat the man;
+  And the Englishman is a very G---- d----."
+
+The charges were revived in a much later day, and the defense might have
+given some trouble. But Place, who had been the foreman at the inquest,
+came forward, and settled the question in a few lines. Every one knew that
+the old Radical was quite free of all disposition to suppress truth from
+wish to curry favor with royalty.
+
+John Speed,[453] the author of the _English History_,[454] (1632) which
+Bishop Nicolson[455] calls the best chronicle extant, was a man, like
+Place, of no education, but what he gave himself. The bishop says he would
+have done better if he had a better training: but what, he adds, could have
+been expected from a tailor! This Speed was, as well as Place. But he was
+{202} released from manual labor by Sir Fulk Grevil,[456] who enabled him
+to study.
+
+
+
+A STORY ON SIMSON.
+
+I have elsewhere noticed that those who oppose the mysteries of algebra do
+not ridicule them; this I want the cyclometers to do. Of the three who
+wrote against the great point, the negative quantity, and the uses of 0
+which are connected with it, only one could fire a squib. That Robert
+Simson[457] should do such a thing will be judged impossible by all who
+admit tradition. I do not vouch for the following; I give it as a proof of
+the impression which prevailed about him:
+
+He used to sit at his open window on the ground floor, as deep in geometry
+as a Robert Simson ought to be. Here he would be accosted by beggars, to
+whom he generally gave a trifle, he roused himself to hear a few words of
+the story, made his donation, and instantly dropped down into his depths.
+Some wags one day stopped a mendicant who was on his way to the window with
+"Now, my man, do as we tell you, and you will get something from that
+gentleman, and a shilling from us besides. You will go and say you are in
+distress, he will ask you who you are, and you will say you are Robert
+Simson, son of John Simson of Kirktonhill." The man did as he was told;
+Simson quietly gave him a coin, and dropped off. The wags watched a little,
+and saw him rouse himself again, and exclaim "Robert Simson, son of John
+Simson of Kirktonhill! why, that is myself. That man must be an impostor."
+Lord Brougham tells the same story, with some difference of details.
+
+{203}
+
+
+
+BARON MASERES.
+
+Baron Maseres[458] was, as a writer, dry; those who knew his writings will
+feel that he seldom could have taken in a joke or issued a pun. Maseres was
+the fourth wrangler of 1752, and first Chancellor's medallist (or highest
+in classics); his second was Porteus[459] (afterward Bishop of London).
+Waring[460] came five years after him: he could not get Maseres through the
+second page of his first book on algebra; a negative quantity stood like a
+lion in the way. In 1758 he published his _Dissertation on the Use of the
+Negative Sign_,[461] 4to. There are some who care little about + and -, who
+would give it house-room for the sake of the four words "Printed by Samuel
+Richardson."
+
+Maseres speaks as follows: "A single quantity can never be marked with
+either of those signs, or considered as either affirmative or negative; for
+if any single quantity, as b, is marked either with the sign + or with the
+sign - without assigning some other quantity, as a, to which it is to be
+added, or from which it is to be subtracted, the mark will have no meaning
+or signification: thus if it be said that the square of -5, or the product
+of -5 into -5, is equal to +25, such an assertion must either signify no
+more than that 5 times 5 is equal to 25 without any regard to the signs, or
+it must be mere nonsense and unintelligible jargon. I speak according to
+the foregoing definition, by which the affirmativeness or negativeness of
+any quantity implies a relation to another quantity of the same kind to
+which it {204} is added, or from which it is subtracted; for it may perhaps
+be very clear and intelligible to those who have formed to themselves some
+other idea of affirmative and negative quantities different from that above
+defined."
+
+Nothing can be more correct, or more identically logical: +5 and -5,
+standing alone, are jargon if +5 and -5 are to be understood as without
+reference to another quantity. But those who have "formed to themselves
+some other idea" see meaning enough. The great difficulty of the opponents
+of algebra lay in want of power or will to see extension of terms. Maseres
+is right when he implies that extension, accompanied by its refusal, makes
+jargon. One of my paradoxers was present at a meeting of the Royal Society
+(in 1864, I think) and asked permission to make some remarks upon a paper.
+He rambled into other things, and, naming me, said that I had written a
+book in which two sides of a triangle are pronounced _equal_ to the
+third.[462] So they are, in the sense in which the word is used in complete
+algebra; in which A + B = C makes A, B, C, three sides of a triangle, and
+declares that going over A and B, one after the other, is equivalent, in
+change of place, to going over C at once. My critic, who might, if he
+pleased, have objected to extension, insisted upon reading me in unextended
+meaning.
+
+On the other hand, it must be said that those who wrote on the other idea
+wrote very obscurely about it and justified Des Cartes (_De Methodo_)[463]
+when he said: "Algebram vero, ut solet doceri, animadverti certis regulis
+et numerandi formulis ita esse contentam, ut videatur potius ars quædam
+confusa, cujus usu ingenium quodam modo turbatur et obscuratur, quam
+scientia qua excolatur et perspicacius {205} reddatur."[464] Maseres wrote
+this sentence on the title of his own work, now before me; he would have
+made it his motto if he had found it earlier.
+
+There is, I believe, in Cobbett's _Annual Register_,[465] an account of an
+interview between Maseres and Cobbett when in prison.
+
+The conversation of Maseres was lively, and full of serious anecdote: but
+only one attempt at humorous satire is recorded of him; it is an
+instructive one. He was born in 1731 (Dec. 15), and his father was a
+refugee. French was the language of the house, with the pronunciation of
+the time of Louis XIV. He lived until 1824 (May 19), and saw the race of
+refugees who were driven out by the first Revolution. Their pronunciation
+differed greatly from his own; and he used to amuse himself by mimicking
+them. Those who heard him and them had the two schools of pronunciation
+before them at once; a thing which seldom happens. It might even yet be
+worth while to examine the Canadian pronunciation.
+
+Maseres went as Attorney-General to Quebec; and was appointed Cursitor
+Baron of our Exchequer in 1773. There is a curious story about his mission
+to Canada, which I have heard as good tradition, but have never seen in
+print. The reader shall have it as cheap as I; and I confess I rather
+believe it. Maseres was inveterately honest; he could not, at the bar, bear
+to see his own client victorious, when he knew his cause was a bad one. On
+a certain occasion he was in a cause which he knew would go against him if
+a certain case were quoted. Neither the judge nor the opposite counsel
+seemed to remember this case, and Maseres could not help dropping an
+allusion which brought it out. {206} His business as a barrister fell off,
+of course. Some time after, Mr. Pitt (Chatham) wanted a lawyer to send to
+Canada on a private mission, and wanted a _very honest man_. Some one
+mentioned Maseres, and told the above story: Pitt saw that he had got the
+man he wanted. The mission was satisfactorily performed, and Maseres
+remained as Attorney-General.
+
+The _Doctrine of Life Annuities_[466] (4to, 726 pages, 1783) is a strange
+paradox. Its size, the heavy dissertations on the national debt, and the
+depth of algebra supposed known, put it out of the question as an
+elementary work, and it is unfitted for the higher student by its elaborate
+attempt at elementary character, shown in its rejection of forms derived
+from chances in favor of _the average_, and its exhibition of the separate
+values of the years of an annuity, as arithmetical illustrations. It is a
+climax of unsaleability, unreadability, and inutility. For intrinsic
+nullity of interest, and dilution of little matter with much ink, I can
+compare this book to nothing but that of Claude de St. Martin, elsewhere
+mentioned, or the lectures _On the Nature and Properties of Logarithms_, by
+James Little,[467] Dublin, 1830, 8vo. (254 heavy pages of many words and
+few symbols), a wonderful weight of weariness.
+
+The stock of this work on annuities, very little diminished, was given by
+the author to William Frend, who paid warehouse room for it until about
+1835, when he consulted me as to its disposal. As no publisher could be
+found who would take it as a gift, for any purpose of sale, it was
+consigned, all but a few copies, to a buyer of waste paper.
+
+Baron Maseres's republications are well known: the _Scriptores
+Logarithmici_[468] is a set of valuable reprints, mixed {207} with much
+which might better have entered into another collection. It is not so well
+known that there is a volume of optical reprints, _Scriptores Optici_,
+London, 1823, 4to, edited for the veteran of ninety-two by Mr. Babbage[469]
+at twenty-nine. This excellent volume contains James Gregory, Des Cartes,
+Halley, Barrow, and the optical writings of Huyghens, the _Principia_ of
+the undulatory theory. It also contains, by the sort of whim in which such
+men as Maseres, myself, and some others are apt to indulge, a reprint of
+"The great new Art of weighing Vanity,"[470] by M. Patrick Mathers,
+Arch-Bedel to the University of St. Andrews, Glasgow, 1672. Professor
+Sinclair,[471] of Glasgow, a good man at clearing mines of the water which
+they did not want, and furnishing cities with water which they did want,
+seems to have written absurdly about hydrostatics, and to have attacked a
+certain Sanders,[472] M.A. So Sanders, assisted by James Gregory, published
+a heavy bit of jocosity about him. This story of the authorship rested on a
+note made in his {208} copy by Robert Gray, M.D.; but it has since been
+fully confirmed by a letter of James Gregory to Collins, in the
+Macclesfield Correspondence. "There is one Master Sinclair, who did write
+the _Ars Magna et Nova_,[473] a pitiful ignorant fellow, who hath lately
+written horrid nonsense in the hydrostatics, and hath abused a master in
+the University, one Mr. Sanders, in print. This Mr. Sanders ... is resolved
+to cause the Bedel of the University to write against him.... We resolve to
+make excellent sport with him."
+
+On this I make two remarks: First, I have learned from experience that old
+notes, made in books by their possessors, are statements of high authority:
+they are almost always confirmed. I do not receive them without hesitation;
+but I believe that of all the statements about books which rest on one
+authority, there is a larger percentage of truth in the written word than
+in the printed word. Secondly, I mourn to think that when the New Zealander
+picks up his old copy of this book, and reads it by the associations of his
+own day, he may, in spite of the many assurances I have received that my
+_Athenæum Budget_ was amusing, feel me to be as heavy as I feel James
+Gregory and Sanders. But he will see that I knew what was coming, which
+Gregory did not.
+
+
+
+MR. FREND'S BURLESQUE.
+
+It was left for Mr. Frend to prove that an impugner of algebra could
+attempt ridicule. He was, in 1803, editor of a periodical _The Gentleman's
+Monthly Miscellany_, which lasted a few months.[474] To this, among other
+things, he contributed the following, in burlesque of the use made of 0, to
+which he objected.[475] The imitation of Rabelais, a writer {209} in whom
+he delighted, is good: to those who have never dipped, it may give such a
+notion as they would not easily get elsewhere. The point of the satire is
+not so good. But in truth it is not easy to make pungent scoffs upon what
+is common sense to all mankind. Who can laugh with effect at six times
+nothing is nothing, as false or unintelligible? In an article intended for
+that undistinguishing know-0 the "general reader," there would have been no
+force of satire, if _division_ by 0 had been separated from multiplication
+by the same.
+
+I have followed the above by another squib, by the same author, on the
+English language. The satire is covertly aimed at theological phraseology;
+and any one who watches this subject will see that it is a very just
+observation that the Greek words are not boiled enough.
+
+PANTAGRUEL'S DECISION _of the_ QUESTION _about_ NOTHING.
+
+"Pantagruel determined to have a snug afternoon with Epistemon and Panurge.
+Dinner was ordered to be set in a small parlor, and a particular batch of
+Hermitage with some choice Burgundy to be drawn from a remote corner of the
+cellar upon the occasion. By way of lunch, about an hour before dinner,
+Pantagruel was composing his stomach with German sausages, reindeer's
+tongues, oysters, brawn, and half a dozen different sorts of English beer
+just come into fashion, when a most thundering knocking was heard at the
+great gate, and from the noise they expected it to announce the arrival at
+least of the First Consul, or king Gargantua. Panurge was sent to
+reconnoiter, and after a quarter of an hour's absence, returned with the
+news that the University of Pontemaca was waiting his highness's leisure in
+the great hall, to propound a question which {210} had turned the brains of
+thirty-nine students, and had flung twenty-seven more into a high fever.
+With all my heart, says Pantagruel, and swallowed down three quarts of
+Burton ale; but remember, it wants but an hour of dinner time, and the
+question must be asked in as few words as possible; for I cannot deprive
+myself of the pleasure I expected to enjoy in the company of my good
+friends for a set of mad-headed masters. I wish brother John was here to
+settle these matters with the black gentry.
+
+"Having said or rather growled this, he proceeded to the hall of ceremony,
+and mounted his throne; Epistemon and Panurge standing on each side, but
+two steps below him. Then advanced to the throne the three beadles of the
+University of Pontemaca with their silver staves on their shoulders, and
+velvet caps on their heads, and they were followed by three times three
+doctors, and thrice three times three masters of art; for everything was
+done in Pontemaca by the number three, and on this account the address was
+written on parchment, one foot in breadth, and thrice three times thrice
+three feet in length. The beadles struck the ground with their heads and
+their staves three times in approaching the throne; the doctors struck the
+ground with their heads thrice three times, and the masters did the same
+thrice each time, beating the ground with their heads thrice three times.
+This was the accustomed form of approaching the throne, time out of mind,
+and it was said to be emblematic of the usual prostration of science to the
+throne of greatness.
+
+"The mathematical professor, after having spit, and hawked, and cleared his
+throat, and blown his nose on a handkerchief lent to him, for he had
+forgotten to bring his own, began to read the address. In this he was
+assisted by three masters of arts, one of whom, with a silver pen, pointed
+out the stops; the second with a small stick rapped his knuckles when he
+was to raise or lower his voice; and a third pulled his hair behind when he
+was to look Pantagruel in the face. Pantagruel began to chafe like a lion:
+{211} he turned first on one side, then on the other: he listened and
+groaned, and groaned and listened, and was in the utmost cogitabundity of
+cogitation. His countenance began to brighten, when, at the end of an hour,
+the reader stammered out these words:
+
+"'It has therefore been most clearly proved that as all matter may be
+divided into parts infinitely smaller than the infinitely smallest part of
+the infinitesimal of nothing, so nothing has all the properties of
+something, and may become, by just and lawful right, susceptible of
+addition, subtraction, multiplication, division, squaring, and cubing: that
+it is to all intents and purposes as good as anything that has been, is, or
+can be taught in the nine universities of the land, and to deprive it of
+its rights is a most cruel innovation and usurpation, tending to destroy
+all just subordination in the world, making all universities superfluous,
+leveling vice-chancellors, doctors, and proctors, masters, bachelors, and
+scholars, to the mean and contemptible state of butchers and
+tallow-chandlers, bricklayers and chimney-sweepers, who, if it were not for
+these learned mysteries, might think that they knew as much as their
+betters. Every one then, who has the good of science at heart, must pray
+for the interference of his highness to put a stop to all the disputes
+about nothing, and by his decision to convince all gainsayers that the
+science of nothing is taught in the best manner in the universities, to the
+great edification and improvement of all the youth in the land.'
+
+"Here Pantagruel whispered in the ear of Panurge, who nodded to Epistemon,
+and they two left the assembly, and did not return for an hour, till the
+orator had finished his task. The three beadles had thrice struck the
+ground with their heads and staves, the doctors had finished their
+compliments, and the masters were making their twenty-seven prostrations.
+Epistemon and Panurge went up to Pantagruel, whom they found fast asleep
+and snoring; nor could he be roused but by as many tugs as there had been
+{212} bowings from the corps of learning. At last he opened his eyes, gave
+a good stretch, made half a dozen yawns, and called for a stoup of wine. I
+thank you, my masters, says he; so sound a nap I have not had since I came
+from the island of Priestfolly. Have you dined, my masters? They answered
+the question by as many bows as at entrance; but his highness left them to
+the care of Panurge, and retired to the little parlor with Epistemon, where
+they burst into a fit of laughter, declaring that this learned Baragouin
+about nothing was just as intelligible as the lawyer's Galimathias. Panurge
+conducted the learned body into a large saloon, and each in his way hearing
+a clattering of plates and glasses, congratulated himself on his
+approaching good cheer. There they were left by Panurge, who took his chair
+by Pantagruel just as the soup was removed, but he made up for the want of
+that part of his dinner by a pint of champagne. The learning of the
+university had whetted their appetites; what they each ate it is needless
+to recite; good wine, good stories, and hearty laughs went round, and three
+hours elapsed before one soul of them recollected the hungry students of
+Pontemaca.
+
+"Epistemon reminded them of the business in hand, and orders were given for
+a fresh dozen of hermitage to be put upon table, and the royal attendants
+to get ready. As soon as the dozen bottles were emptied, Pantagruel rose
+from table, the royal trumpets sounded, and he was accompanied by the great
+officers of his court into the large dining hall, where was a table with
+forty-two covers. Pantagruel sat at the head, Epistemon at the bottom, and
+Panurge in the middle, opposite an immense silver tureen, which would hold
+fifty gallons of soup. The wise men of Pontemaca then took their seats
+according to seniority. Every countenance glistened with delight; the music
+struck up; the dishes were uncovered. Panurge had enough to do to handle
+the immense silver ladle: Pantagruel and Epistemon had no time for eating,
+they were fully employed in carving. The bill {213} of fare announced the
+names of a hundred different dishes. From Panurge's ladle came into the
+soup plate as much as he took every time out of the tureen; and as it was
+the rule of the court that every one should appear to eat, as long as he
+sat at table, there was the clattering of nine and thirty spoons against
+the silver soup-plates for a quarter of an hour. They were then removed,
+and knives and forks were in motion for half an hour. Glasses were
+continually handed round in the mean time, and then everything was removed,
+except the great tureen of soup. The second course was now served up, in
+dispatching which half an hour was consumed; and at the conclusion the wise
+men of Pontemaca had just as much in their stomachs as Pantagruel in his
+head from their address: for nothing was cooked up for them in every
+possible shape that Panurge could devise.
+
+"Wine-glasses, large decanters, fruit dishes, and plates were now set on.
+Pantagruel and Epistemon alternately gave bumper toasts: the University of
+Pontemaca, the eye of the world, the mother of taste and good sense and
+universal learning, the patroness of utility, and the second only to
+Pantagruel in wisdom and virtue (for these were her titles), was drank
+standing with thrice three times three, and huzzas and clattering of
+glasses; but to such wine the wise men of Pontemaca had not been
+accustomed; and though Pantagruel did not suffer one to rise from table
+till the eighty-first glass had been emptied, not even the weakest headed
+master of arts felt his head in the least indisposed. The decanters indeed
+were often removed, but they were brought back replenished, filled always
+with nothing.
+
+"Silence was now proclaimed, and in a trice Panurge leaped into the large
+silver tureen. Thence he made his bows to Pantagruel and the whole company,
+and commenced an oration of signs, which lasted an hour and a half, and in
+which he went over all the matter contained in the Pontemaca address; and
+though the wise men looked very serious during the whole time, Pantagruel
+himself and his whole {214} court could not help indulging in repeated
+bursts of laughter. It was universally acknowledged that he excelled
+himself, and that the arguments by which he beat the English masters of
+arts at Paris were nothing to the exquisite selection of attitudes which he
+this day assumed. The greatest shouts of applause were excited when he was
+running thrice round the tureen on its rim, with his left hand holding his
+nose, and the other exercising itself nine and thirty times on his back. In
+this attitude he concluded with his back to the professor of mathematics;
+and at the instant he gave his last flap, by a sudden jump, and turning
+heels over head in the air, he presented himself face to face to the
+professor, and standing on his left leg, with his left hand holding his
+nose, he presented to him, in a white satin bag, Pantagruel's royal decree.
+Then advancing his right leg, he fixed it on the professor's head, and
+after three turns, in which he clapped his sides with both hands thrice
+three times, down he leaped, and Pantagruel, Epistemon, and himself took
+their leaves of the wise men of Pontemaca.
+
+"The wise men now retired, and by royal orders were accompanied by a guard,
+and according to the etiquette of the court, no one having a royal order
+could stop at any public house till it was delivered. The procession
+arrived at Pontemaca at nine o'clock the next morning, and the sound of
+bells from every church and college announced their arrival. The
+congregation was assembled; the royal decree was saluted in the same manner
+as if his highness had been there in person; and after the proper
+ceremonies had been performed, the satin bag was opened exactly at twelve
+o'clock. A finely emblazoned roll was drawn forth, and the public orator
+read to the gaping assembly the following words:
+
+"'They who can make something out of nothing shall have nothing to eat at
+the court of--PANTAGRUEL.'" {215}
+
+ORIGIN _of the_ ENGLISH LANGUAGE, _related by a_ SWEDE.
+
+"Some months ago in a party in Holland, consisting of natives of various
+countries, the merit of their respective languages became a topic of
+conversation. A Swede, who had been a great traveler, and could converse in
+most of the modern languages of Europe, laughed very heartily at an
+Englishman, who had ventured to speak in praise of the tongue of his dear
+country. I never had any trouble, says he, in learning English. To my very
+great surprise, the moment I sat foot on shore at Gravesend, I found out,
+that I could understand, with very little trouble, every word that was
+said. It was a mere jargon, made up of German, French, and Italian, with
+now and then a word from the Spanish, Latin or Greek. I had only to bring
+my mouth to their mode of speaking, which was done with ease in less than a
+week, and I was everywhere taken for a true-born Englishman; a privilege by
+the way of no small importance in a country, where each man, God knows why,
+thinks his foggy island superior to any other part of the world: and though
+his door is never free from some dun or other coming for a tax, and if he
+steps out of it he is sure to be knocked down or to have his pocket picked,
+yet he has the insolence to think every foreigner a miserable slave, and
+his country the seat of everything wretched. They may talk of liberty as
+they please, but Spain or Turkey for my money: barring the bowstring and
+the inquisition, they are the most comfortable countries under heaven, and
+you need not be afraid of either, if you do not talk of religion and
+politics. I do not see much difference too in this respect in England, for
+when I was there, one of their most eminent men for learning was put in
+prison for a couple of years, and got his death for translating one of
+Æsop's fables into English, which every child in Spain and Turkey is
+taught, as soon as he comes out of his leading strings. Here all the
+company unanimously cried out against the Swede, that it was {216}
+impossible: for in England, the land of liberty, the only thing its worst
+enemies could say against it, was, that they paid for their liberty a much
+greater price than it was worth.--Every man there had a fair trial
+according to laws, which everybody could understand; and the judges were
+cool, patient, discerning men, who never took the part of the crown against
+the prisoner, but gave him every assistance possible for his defense.
+
+"The Swede was borne down, but not convinced; and he seemed determined to
+spit out all his venom. Well, says he, at any rate you will not deny that
+the English have not got a language of their own, and that they came by it
+in a very odd way. Of this at least I am certain, for the whole history was
+related to me by a witch in Lapland, whilst I was bargaining for a wind.
+Here the company were all in unison again for the story.
+
+"In ancient times, said the old hag, the English occupied a spot in
+Tartary, where they lived sulkily by themselves, unknowing and unknown. By
+a great convulsion that took place in China, the inhabitants of that and
+the adjoining parts of Tartary were driven from their seats, and after
+various wanderings took up their abode in Germany. During this time nobody
+could understand the English, for they did not talk, but hissed like so
+many snakes. The poor people felt uneasy under this circumstance, and in
+one of their parliaments, or rather hissing meetings, it was determined to
+seek a remedy: and an embassy was sent to some of our sisterhood then
+living on Mount Hecla. They were put to a nonplus, and summoned the Devil
+to their relief. To him the English presented their petitions, and
+explained their sad case; and he, upon certain conditions, promised to
+befriend them, and to give them a language. The poor Devil was little aware
+of what he had promised; but he is, as all the world knows, a man of too
+much honor to break his word. Up and down the world then he went in quest
+of this new language: visited all the universities, and all {217} the
+schools, and all the courts of law, and all the play-houses, and all the
+prisons; never was poor devil so fagged. It would have made your heart
+bleed to see him. Thrice did he go round the earth in every parallel of
+latitude; and at last, wearied and jaded out, back came he to Hecla in
+despair, and would have thrown himself into the volcano, if he had been
+made of combustible materials. Luckily at that time our sisters were
+engaged in settling the balance of Europe; and whilst they were looking
+over projects, and counter-projects, and ultimatums, and post ultimatums,
+the poor Devil, unable to assist them was groaning in a corner and
+ruminating over his sad condition.
+
+"On a sudden, a hellish joy overspread his countenance; up he jumped, and,
+like Archimedes of old, ran like a madman amongst the throng, turning over
+tables, and papers, and witches, roaring out for a full hour together
+nothing else but 'tis found, 'tis found! Away were sent the sisterhood in
+every direction, some to traverse all the corners of the earth, and others
+to prepare a larger caldron than had ever yet been set upon Hecla. The
+affairs of Europe were at a stand: its balance was thrown aside; prime
+ministers and ambassadors were everywhere in the utmost confusion; and, by
+the way, they have never been able to find the balance since that time, and
+all the fine speeches upon the subject, with which your newspapers are
+every now and then filled, are all mere hocus-pocus and rhodomontade.
+However, the caldron was soon set on, and the air was darkened by witches
+riding on broomsticks, bringing a couple of folios under each arm, and
+across each shoulder. I remember the time exactly: it was just as the
+council of Nice had broken up, so that they got books and papers there dog
+cheap; but it was a bad thing for the poor English, as these were the worst
+materials that entered into the caldron. Besides, as the Devil wanted some
+amusement, and had not seen an account of the transactions of this famous
+council, he had all the books brought from it laid before him, and split
+his sides almost {218} with laughing, whilst he was reading the speeches
+and decrees of so many of his old friends and acquaintances. All this while
+the witches were depositing their loads in the great caldron. There were
+books from the Dalai Lama, and from China: there were books from the
+Hindoos, and tallies from the Caffres: there were paintings from Mexico,
+and rocks of hieroglyphics from Egypt: the last country supplied besides
+the swathings of two thousand mummies, and four-fifths of the famed library
+of Alexandria. Bubble! bubble! toil and trouble! never was a day of more
+labor and anxiety; and if our good master had but flung in the Greek books
+at the proper time, they would have made a complete job of it. He was a
+little too impatient: as the caldron frothed up, he skimmed it off with a
+great ladle, and filled some thousands of our wind-bags with the froth,
+which the English with great joy carried back to their own country. These
+bags were sent to every district: the chiefs first took their fill, and
+then the common people; hence they now speak a language which no foreigner
+can understand, unless he has learned half a dozen other languages; and the
+poor people, not one in ten, understand a third part of what is said to
+them. The hissing, however, they have not entirely got rid of, and every
+seven years, when the Devil, according to agreement, pays them a visit,
+they entertain him at their common halls and county meetings with their
+original language.
+
+"The good-natured old hag told me several other circumstances, relative to
+this curious transaction, which, as there is an Englishman in company, it
+will be prudent to pass over in silence: but I cannot help mentioning one
+thing which she told me as a very great secret. You know, says she to me,
+that the English have more religions among them than any other nation in
+Europe, and that there is more teaching and sermonizing with them than in
+any other country. The fact is this; it matters not who gets up to teach
+them, the hard words of the Greek were not sufficiently {219} boiled, and
+whenever they get into a sentence, the poor people's brains are turned, and
+they know no more what the preacher is talking about, than if he harangued
+them in Arabic. Take my word for it if you please; but if not, when you get
+to England, desire the bettermost sort of people that you are acquainted
+with to read to you an act of parliament, which of course is written in the
+clearest and plainest style in which anything can be written, and you will
+find that not one in ten will be able to make tolerable sense of it. The
+language would have been an excellent language, if it had not been for the
+council of Nice, and the words had been well boiled.
+
+"Here the company burst out into a fit of laughter. The Englishman got up
+and shook hands with the Swede: _si non è vero_, said he, _è ben
+trovato_.[476] But, however I may laugh at it here, I would not advise you
+to tell this story on the other side of the water. So here's a bumper to
+Old England for ever, and God save the king."
+
+
+
+ON YOUTHFUL PRODIGIES.
+
+The accounts given of extraordinary children and adolescents frequently
+defy credence.[477] I will give two well-attested instances.
+
+The celebrated mathematician Alexis Claude Clairault (now Clairaut)[478]
+was certainly born in May, 1713. His treatise on curves of double curvature
+(printed in 1731)[479] received {220} the approbation of the Academy of
+Sciences, August 23, 1729. Fontenelle, in his certificate of this, calls
+the author sixteen years of age, and does not strive to exaggerate the
+wonder, as he might have done, by reminding his readers that this work, of
+original and sustained mathematical investigation, must have been coming
+from the pen at the ages of fourteen and fifteen. The truth was, as
+attested by De Molières,[480] Clairaut had given public proofs of his power
+at twelve years old. His age being thus publicly certified, all doubt is
+removed: say he had been--though great wonder would still have been
+left--twenty-one instead of sixteen, his appearance, and the remembrances
+of his friends, schoolfellows, etc., would have made it utterly hopeless to
+knock off five years of that age while he was on view in Paris as a young
+lion. De Molières, who examined the work officially for the _Garde des
+Sceaux_, is transported beyond the bounds of official gravity, and says
+that it "ne mérite pas seulement d'être imprimé, mais d'être admiré comme
+un prodige d'imagination, de conception, et de capacité."[481]
+
+That Blaise Pascal was born in June, 1623, is perfectly well established
+and uncontested.[482] That he wrote his conic sections at the age of
+sixteen might be difficult to establish, though tolerably well attested, if
+it were not for {221} one circumstance, for the book was not published. The
+celebrated theorem, "Pascal's hexagram,"[483] makes all the rest come very
+easy. Now Curabelle,[484] in a work published in 1644, sneers at
+Desargues,[485] whom he quotes, for having, in 1642, deferred a discussion
+until "cette grande proposition nommée le Pascale verra le jour."[486] That
+is, by the time Pascal was nineteen, the _hexagram_ was circulating under a
+name derived from the author. The common story about Pascal, given by his
+sister,[487] is an absurdity which no doubt has prejudiced many against
+tales of early proficiency. He is made, when quite a boy, to invent
+geometry _in the order of Euclid's propositions_: as if that order were
+natural sequence of investigation. The hexagram at ten years old would be a
+hundred times less unlikely.
+
+The instances named are painfully astonishing: I give one which has fallen
+out of sight, because it will preserve an imperfect biography. John
+Wilson[488] is Wilson of that {222} Ilk, that is, of "Wilson's Theorem." It
+is this: if _p_ be a prime number, the product of all the numbers up to
+_p_-1, increased by 1, is divisible without remainder by _p_. All
+mathematicians know this as Wilson's theorem, but few know who Wilson was.
+He was born August 6, 1741, at the Howe in Applethwaite, and he was heir to
+a small estate at Troutbeck in Westmoreland. He was sent to Peterhouse, at
+Cambridge, and while an undergraduate was considered stronger in algebra
+than any one in the University, except Professor Waring, one of the most
+powerful algebraists of the century.[489] He was the senior wrangler of
+1761, and was then for some time a private tutor. When Paley,[490] then in
+his third year, determined to make a push for the senior wranglership,
+which he got, Wilson was recommended to him as a tutor. Both were ardent in
+their work, except that sometimes Paley, when he came for his lesson, would
+find "Gone a fishing" written on his tutor's outer door: which was insult
+added to injury, for Paley was very fond of fishing. Wilson soon left
+Cambridge, and went to the bar. He practised on the northern circuit with
+great success; and, one day, while passing his vacation on his little
+property at Troutbeck, he received information, to his great surprise, that
+Lord Thurlow,[491] with whom he had {223} no acquaintance, had recommended
+him to be a Judge of the Court of Common Pleas. He died, Oct. 18, 1793,
+with a very high reputation as a lawyer and a Judge. These facts are partly
+from Meadley's _Life of Paley_,[492] no doubt from Paley himself, partly
+from the _Gentleman's Magazine_, and from an epitaph written by Bishop
+Watson.[493] Wilson did not publish anything: the theorem by which he has
+cut his name in the theory of numbers was communicated to Waring, by whom
+it was published. He married, in 1788, a daughter of Serjeant Adair,[494]
+and left issue. _Had a family_, many will say: but a man and his wife are a
+family, even without children. An actuary may be allowed to be accurate in
+this matter, of which I was reminded by what an actuary wrote of another
+actuary. William Morgan,[495] in the life of his uncle Dr. Richard
+Price,[496] says that the Doctor and his {224} wife were "never blessed
+with an addition to their family." I never met with such accuracy
+elsewhere. Of William Morgan I add that my surname and pursuits have
+sometimes, to my credit be it said, made a confusion between him and me.
+Dates are nothing to the mistaken; the last three years of Morgan's life
+were the first three years of my actuary-life (1830-33). The mistake was to
+my advantage as well as to my credit. I owe to it the acquaintance of one
+of the noblest of the human race, I mean Elizabeth Fry,[497] who came to me
+for advice about a philanthropic design, which involved life questions,
+under a general impression that some Morgan had attended to such
+things.[498]
+
+{225}
+
+
+
+NEWTON AGAIN OVERTHROWN.
+
+    A treatise on the sublime science of heliography, satisfactorily
+    demonstrating our great orb of light, the sun, to be absolutely no
+    other than a body of ice! Overturning all the received systems of the
+    universe hitherto extant; proving the celebrated and indefatigable Sir
+    Isaac Newton, in his theory of the solar system, to be as far distant
+    from the truth, as many of the heathen authors of Greece and Rome. By
+    Charles Palmer,[499] Gent. London, 1798, 8vo.
+
+Mr. Palmer burned some tobacco with a burning glass, saw that a lens of ice
+would do as well, and then says:
+
+"If we admit that the sun could be removed, and a terrestrial body of ice
+placed in its stead, it would produce the same effect. The sun is a
+crystaline body receiving the radiance of God, and operates on this earth
+in a similar manner as the light of the sun does when applied to a convex
+mirror or glass."
+
+Nov. 10, 1801. The Rev. Thomas Cormouls,[500] minister of Tettenhall,
+addressed a letter to Sir Wm. Herschel, from which I extract the following:
+
+"Here it may be asked, then, how came the doctrines of Newton to solve all
+astronomic Phenomina, and all problems concerning the same, both _a parte
+ante_ and _a parte post_.[501] It is answered that he certainly wrought the
+principles he made use of into strickt analogy with the real Phenomina of
+the heavens, and that the rules and results arizing from them {226} agree
+with them and resolve accurately all questions concerning them. Though they
+are not fact and true, or nature, but analogous to it, in the manner of the
+artificial numbers of logarithms, sines, &c. A very important question
+arises here, Did Newton mean to impose upon the world? By no means: he
+received and used the doctrines reddy formed; he did a little extend and
+contract his principles when wanted, and commit a few oversights of
+consequences. But when he was very much advanced in life, he suspected the
+fundamental nullity of them: but I have from a certain anecdote strong
+ground to believe that he knew it before his decease and intended to have
+retracted his error. But, however, somebody did deceive, if not wilfully,
+negligently at least. That was a man to whom the world has great
+obligations too. It was no less a philosopher than Galileo."
+
+That Newton wanted to retract before his death, is a notion not uncommon
+among paradoxers. Nevertheless, there is no retraction in the third edition
+of the _Principia_, published when Newton was eighty-four years old! The
+moral of the above is, that a gentleman who prefers instructing William
+Herschel to learning how to spell, may find a proper niche in a proper
+place, for warning to others. It seems that gravitation is not truth, but
+only the logarithm of it.
+
+
+
+BISHOPS AS PARADOXERS.
+
+    The mathematical and philosophical works of the Right Rev. John
+    Wilkins[502].... In two volumes. London, 1802, 8vo.
+
+This work, or at least part of the edition--all for aught I know--is
+printed on wood; that is, on paper made from wood-pulp. It has a rough
+surface; and when held before a candle is of very unequal transparency.
+There is in it a reprint of the works on the earth and moon. The discourse
+on the possibility of going to the moon, in this and the edition of 1640,
+is incorporated: but from the account in the {227} life prefixed, and a
+mention by D'Israeli, I should suppose that it had originally a separate
+title-page, and some circulation as a separate tract. Wilkins treats this
+subject half seriously, half jocosely; he has evidently not quite made up
+his mind. He is clear that "arts are not yet come to their solstice," and
+that posterity will bring hidden things to light. As to the difficulty of
+carrying food, he thinks, scoffing Puritan that he is, the Papists may be
+trained to fast the voyage, or may find the bread of their Eucharist "serve
+well enough for their _viaticum_."[503] He also puts the case that the
+story of Domingo Gonsales may be realized, namely, that wild geese find
+their way to the moon. It will be remembered--to use the usual substitute
+for, It has been forgotten--that the posthumous work of Bishop Francis
+Godwin[504] of Llandaff was published in 1638, the very year of Wilkins's
+first edition, in time for him to mention it at the end. Godwin makes
+Domingo Gonsales get to the moon in a chariot drawn by wild geese, and, as
+old books would say, discourses fully on that head. It is not a little
+amusing that Wilkins should have been seriously accused of plagiarizing
+Godwin, Wilkins writing in earnest, or nearly so, and Godwin writing
+fiction. It may serve to show philosophers how very near pure speculation
+comes to fable. From the sublime to the ridiculous is but a step: which is
+the sublime, and which the ridiculous, every one must settle for himself.
+With me, good fiction is the sublime, and bad speculation the ridiculous.
+The number of bishops in my list is small. I might, had I possessed the
+book, have opened the list of quadrators with an Archbishop of Canterbury,
+or at least with a divine who was not wholly not archbishop. Thomas
+Bradwardine[505] (Bragvardinus, Bragadinus) was elected in {228} 1348; the
+Pope put in another, who died unconsecrated; and Bradwardine was again
+elected in 1349, and lived five weeks longer, dying, I suppose, unconfirmed
+and unconsecrated.[506] Leland says he held the see a year, _unus tantum
+annulus_,[507] which seems to be a confusion: the whole business, from the
+first election, took about a year. He squared the circle, and his
+performance was printed at Paris in 1494. I have never seen it, nor any
+work of the author, except a tract on proportion.
+
+As Bradwardine's works are very scarce indeed, I give two titles from one
+of the Libri catalogues.
+
+    "ARITHMETIC. BRAUARDINI (Thomæ) Arithmetica speculativa revisa et
+    correcta a Petro Sanchez Ciruelo Aragonesi, black letter, _elegant
+    woodcut title-page_, VERY RARE, _folio. Parisiis, per Thomam Anguelast
+    (pro Olivier Senant), s. a. circa 1510_.[508]
+
+"This book, by Thomas Bradwardine, Archbishop of Canterbury must be
+exceedingly scarce as it has escaped the notice of Professor De Morgan,
+who, in his _Arithmetical Books_, speaks of a treatise of the same author
+on proportions,[509] printed at Vienna in 1515, but does not mention the
+present work.
+
+{229}
+
+    "Bradwardine (Archbp. T.). Brauardini (Thomæ) Geometria speculativa,
+    com Tractato de Quadratura Circuli bene revisa a Petro Sanchez Ciruelo,
+    SCARCE, _folio. Parisiis, J. Petit_, 1511.[510]
+
+"In this work we find the _polygones étoilés_,[511] see Chasles (_Aperçu_,
+pp. 480, 487, 521, 523, &c.) on the merit of the discoveries of this
+English mathematician, who was Archbishop of Canterbury in the XIVth
+Century (_tempore_ Edward III. A.D. 1349); and who applied geometry to
+theology. M. Chasles says that the present work of Bradwardine contains
+'Une théorie nouvelle qui doit faire honneur au XIVe Siècle.'"[512]
+
+The titles do not make it quite sure that Bradwardine is the quadrator; it
+may be Peter Sanchez after all.[513]
+
+
+
+THE QUESTION OF PARALLELS.
+
+    Nouvelle théorie des parallèles. Par Adolphe Kircher[514] [so signed at
+    the end of the appendix]. Paris, 1803, 8vo.
+
+An alleged emendation of Legendre.[515] The author refers {230} to attempts
+by Hoffman,[516] 1801, by Hauff,[517] 1799, and to a work of Karsten,[518]
+or at least a theory of Karsten, contained in "Tentamen novæ parallelarum
+theoriæ notione situs fundatæ; auctore G. C. Schwal,[519] Stuttgardæ, 1801,
+en 8 volumes." Surely this is a misprint; _eight_ volumes on the theory of
+parallels? If there be such a work, I trust I and it may never meet, though
+ever so far produced.
+
+{231}
+
+
+
+    Soluzione ... della quadratura del Circolo. By Gaetano Rossi.[520]
+    London, 1804, 8vo.
+
+The three remarkable points of this book are, that the household of the
+Prince of Wales took ten copies, Signora Grassini[521] sixteen, and that
+the circumference is 3-1/5 diameters. That is, the appetite of Grassini for
+quadrature exceeded that of the whole household (_loggia_) of the Prince of
+Wales in the ratio in which the semi-circumference exceeds the diameter.
+And these are the first two in the list of subscribers. Did the author see
+this theorem?
+
+
+
+A PATRIOTIC PARADOX.
+
+    Britain independent of commerce; or proofs, deduced from an
+    investigation into the true cause of the wealth of nations, that our
+    riches, prosperity, and power are derived from sources inherent in
+    ourselves, and would not be affected, even though our commerce were
+    annihilated. By Wm. Spence.[522] 4th edition, 1808, 8vo.
+
+A patriotic paradox, being in alleviation of the Commerce panic which the
+measures of Napoleon I.--who _felt_ our Commerce, while Mr. Spence only
+_saw_ it--had awakened. In this very month (August, 1866), the Pres. Brit.
+Assoc. has applied a similar salve to the coal panic; it is fit that
+science, which rubbed the sore, should find a plaster. We ought to have an
+iron panic and a timber panic; and {232} a solemn embassy to the Americans,
+to beg them not to whittle, would be desirable. There was a gold panic
+beginning, before the new fields were discovered. For myself, I am the
+unknown and unpitied victim of a chronic gutta-percha panic: I never could
+get on without it; to me, gutta percha and Rowland Hill are the great
+discoveries of our day; and not unconnected either, gutta percha being to
+the submarine post what Rowland Hill is to the superterrene. I should be
+sorry to lose cow-choke--I gave up trying to spell it many years ago--but
+if gutta percha go, I go too. I think, that perhaps when, five hundred
+years hence, the people say to the Brit. Assoc. (if it then exist) "Pray
+gentlemen, is it not time for the coal to be exhausted?" they will be
+answered out of Molière (who will certainly then exist): "_Cela était
+autrefois ainsi, mais nous avons changé tout cela._"[523] A great many
+people think that if the coal be used up, it will be announced some
+unexpected morning by all the yards being shut up and written notice
+outside, "Coal all gone!" just like the "Please, ma'am, there ain't no more
+sugar," with which the maid servant damps her mistress just at
+breakfast-time. But these persons should be informed that there is every
+reason to think that there will be time, as the city gentleman said, to
+_venienti_ the _occurrite morbo_.[524]
+
+
+
+SOME SCIENTIFIC PARADOXES.
+
+    An appeal to the republic of letters in behalf of injured science, from
+    the opinions and proceedings of some modern authors of elements of
+    geometry. By George Douglas.[525] Edinburgh, 1810, 8vo.
+
+Mr. Douglas was the author of a very good set of {233} mathematical tables,
+and of other works. He criticizes Simson,[526] Playfair,[527] and
+others,--sometimes, I think, very justly. There is a curious phrase which
+occurs more than once. When he wants to say that something or other was
+done before Simson or another was born, he says "before he existed, at
+least as an author." He seems to reserve the possibility of Simson's
+_pre-existence_, but at the same time to assume that he never wrote
+anything in his previous state. Tell me that Simson pre-existed in any
+other way than as editor of some pre-existent Euclid? Tell Apella![528]
+
+1810. In this year Jean Wood, Professor of Mathematics in the University of
+Virginia (Richmond),[529] addressed a printed circular to "Dr. Herschel,
+Astronomer, Greenwich Observatory." No mistake was more common than the
+natural one of imagining that the _Private Astronomer_ of the king was the
+_Astronomer Royal_. The letter was on the {234} difference of velocities of
+the two sides of the earth, arising from the composition of the rotation
+and the orbital motion. The _paradox_ is a fair one, and deserving of
+investigation; but, perhaps it would not be easy to deduce from it tides,
+trade-winds, aerolithes, &c., as Mr. Wood thought he had done in a work
+from which he gives an extract, and which he describes as published. The
+composition of rotations, &c., is not for the world at large: the paradox
+of the non-rotation of the moon about her axis is an instance. How many
+persons know that when a wheel rolls on the ground, the lowest point is
+moving upwards, the highest point forwards, and the intermediate points in
+all degrees of betwixt and between? This is too short an explanation, with
+some good difficulties.
+
+
+
+    The Elements of Geometry. In 2 vols. [By the Rev. J. Dobson,[530] B.D.]
+    Cambridge, 1815. 4to.
+
+Of this unpunctuating paradoxer I shall give an account in his own way: he
+would not stop for any one; why should I stop for him? It is worth while to
+try how unpunctuated sentences will read.
+
+The reverend J Dobson BD late fellow of saint Johns college Cambridge was
+rector of Brandesburton in Yorkshire he was seventh wrangler in 1798 and
+died in 1847 he was of that sort of eccentricity which permits account of
+his private life if we may not rather say that in such cases private life
+becomes public there is a tradition that he was called Death Dobson on
+account of his head and aspect of countenance being not very unlike the
+ordinary pictures of a human skull his mode of life is reported to have
+been very singular whenever he visited Cambridge he was never known to go
+twice to the same inn he never would sleep at the rectory with another
+person in the house some ancient charwoman used to attend to the house but
+never slept in it he has been known in the time of coach travelling to have
+{235} deferred his return to Yorkshire on account of his disinclination to
+travel with a lady in the coach he continued his mathematical studies until
+his death and till his executors sold the type all his tracts to the number
+of five were kept in type at the university press none of these tracts had
+any stops except full stops at the end of paragraphs only neither had they
+capitals except one at the beginning of a paragraph so that a full stop was
+generally followed by some white as there is not a single proper name in
+the whole of the book I have I am not able to say whether he would have
+used capitals before proper names I have inserted them as usual for which I
+hope his spirit will forgive me if I be wrong he also published the
+elements of geometry in two volumes quarto Cambridge 1815 this book had
+also no stops except when a comma was wanted between letters as in the
+straight lines AB, BC I should also say that though the title is
+unpunctuated in the author's part it seems the publishers would not stand
+it in their imprint this imprint is punctuated as usual and Deighton and
+Sons to prove the completeness of their allegiance have managed that comma
+semicolon and period shall all appear in it why could they not have
+contrived interrogation and exclamation this is a good precedent to
+establish the separate right of the publisher over the imprint it is said
+that only twenty of the tracts were printed and very few indeed of the book
+on geometry it is doubtful whether any were sold there is a copy of the
+geometry in the university library at Cambridge and I have one myself the
+matter of the geometry differs entirely from Euclid and is so fearfully
+prolix that I am sure no mortal except the author ever read it the man went
+on without stops and without stop save for a period at the end of a
+paragraph this is the unpunctuated account of the unpunctuating geometer
+_suum cuique tribuito_[531] Mrs Thrale[532] would have been amused {236} at
+a Dobson who managed to come to a full stop without either of the three
+warnings.
+
+I do not find any difficulty in reading Dobson's geometry; and I have read
+more of it to try reading without stops than I should have done had it been
+printed in the usual way. Those who dip into the middle of my paragraph may
+be surprised for a moment to see "on account of his disinclination to
+travel with a lady in the coach he continued his mathematical studies until
+his death and [further, of course] until his executors sold the type." But
+a person reading straight through would hardly take it so. I should add
+that, in order to give a fair trial, I did not compose as I wrote, but
+copied the words of the correspondent who gave me the facts, so far as they
+went.
+
+
+
+A RELIGIOUS PARADOX.
+
+    _Philosophia Sacra, or the principles of natural Philosophy. Extracted
+    from Divine Revelation._ By the Rev. Samuel Pike.[533] Edited by the
+    Rev. Samuel Kittle.[534] Edinburgh, 1815, 8vo.
+
+This is a work of modified Hutchinsonianism, which I have seen cited by
+several. Though rather dark on the subject, it seems not to contradict the
+motion of the earth, or the doctrine of gravitation. Mr. Kittle gives a
+list of some Hutchinsonians,--as Bishop Horne;[535] Dr. Stukeley;[536] the
+Rev. {237} W. Jones,[537] author of _Physiological Disquisitions_; Mr.
+Spearman,[538] author of _Letters on the Septuagint_ and editor of
+Hutchinson; Mr. Barker,[539] author of _Reflexions on Learning_; Dr.
+Catcott,[540] author of a work on the creation, &c.; Dr. Robertson,[541]
+author of a _Treatise on the Hebrew Language_; _Dr. Holloway_,[542] author
+of _Originals, Physical and Theological_; Dr. Walter Hodges,[543] author of
+a work on _Elohim_; Lord President Forbes (_ob._ 1747).[544]
+
+The Rev. William Jones, above mentioned (1726-1800), the friend and
+biographer of Bishop Horne and his stout {238} defender, is best known as
+William Jones of Nayland, who (1757)[545] published the _Catholic Doctrine
+of the Trinity_; he was also strong for the Hutchinsonian physical trinity
+of fire, light, and spirit. This well-known work was generally recommended,
+as the defence of the orthodox system, to those who could not go into the
+learning of the subject. There is now a work more suited to our time: _The
+Rock of Ages_, by the Rev. E. H. Bickersteth,[546] now published by the
+Religious Tract Society, without date, answered by the Rev. Dr.
+Sadler,[547] in a work (1859) entitled _Gloria Patri_, in which, says Mr.
+Bickersteth, "the author has not even attempted to grapple with my main
+propositions." I have read largely on the controversy, and I think I know
+what this means. Moreover, when I see the note "There are two other
+passages to which Unitarians sometimes refer, but the deduction they draw
+from them is, in each case, refuted by the context"--I think I see why the
+two texts are not named. Nevertheless, the author is a little more disposed
+to yield to criticism than his foregoers; he does not insist on texts and
+readings which the greatest editors have rejected. And he writes with
+courtesy, both direct and oblique, towards his antagonists; which, on his
+side of this subject, is like letting in fresh air. So that I suspect the
+two books will together make a tolerably good introduction to the subject
+for those who cannot go deep. Mr. Bickersteth's book is well arranged and
+indexed, which is a point of superiority to Jones of Nayland. There is a
+point which I should gravely recommend to writers on the orthodox side. The
+Unitarians in {239} England have frequently contended that the method of
+proving the divinity of Jesus Christ from the New Testament would equally
+prove the divinity of Moses. I have not fallen in the way of any orthodox
+answers specially directed at the repeated tracts written by Unitarians in
+proof of their assertion. If there be any, they should be more known; if
+there be none, some should be written. Which ever side may be right, the
+treatment of this point would be indeed coming to close quarters. The
+heterodox assertion was first supported, it is said, by John Bidle or
+Biddle (1615-1662) of Magdalen College, Oxford, the earliest of the English
+Unitarian writers, previously known by a translation of part of Virgil and
+part of Juvenal.[548] But I cannot find that he wrote on it.[549] It is the
+subject of "[Greek: haireseôn anastasis], or a new way of deciding old
+controversies. By Basanistes. Third edition, enlarged," London, 1815,
+8vo.[550] It is the appendix to the amusing, "Six more letters to Granville
+Sharp, Esq., ... By Gregory Blunt, Esq." London, 8vo., 1803.[551] This much
+I can confidently say, that the study of these tracts would prevent
+orthodox writers from some curious slips, which are slips obvious to all
+sides of opinion. The lower defenders of orthodoxy frequently vex the
+spirits of the higher ones.
+
+Since writing the above I have procured Dr. Sadler's answer. I thought I
+knew what the challenger meant when he said the respondent had not grappled
+with his main {240} propositions. I should say that he is clung on to from
+beginning to end. But perhaps Mr. B. has his own meaning of logical terms,
+such as "proposition": he certainly has his own meaning of "cumulative." He
+says his evidence is cumulative; not a catena, the strength of which is in
+its weakest part, but distinct and independent lines, each of which
+corroborates the other. This is the very opposite of _cumulative_: it is
+_distributive_. When different arguments are each necessary to a
+conclusion, the evidence is _cumulative_; when any one will do, even though
+they strengthen each other, it is _distributive_. The word "cumulative" is
+a synonym of the law word "constructive"; a whole which will do made out of
+parts which separately will not. Lord Strafford [552] opens his defence
+with the use of both words: "They have invented a kind of _accumulated_ or
+_constructive_ evidence; by which many actions, either totally innocent in
+themselves, or criminal in a much inferior degree, shall, when united,
+_amount_ to treason." The conclusion is, that Mr. B. is a Cambridge man;
+the Oxford men do not confuse the elementary terms of logic. O dear old
+Cambridge! when the New Zealander comes let him find among the relics of
+your later sons some proof of attention to the elementary laws of thought.
+A little-go of logic, please!
+
+Mr. B., though apparently not a Hutchinsonian, has a nibble at a physical
+Trinity. "If, as we gaze on the sun shining in the firmament, we see any
+faint adumbration of the doctrine of the Trinity in the fontal orb, the
+light ever generated, and the heat proceeding from the sun and its
+beams--threefold and yet one, the sun, its light, and its {241} heat,--that
+luminous globe, and the radiance ever flowing from it, are both evident to
+the eye; but the vital warmth is felt, not seen, and is only manifested in
+the life it transfuses through creation. The proof of its real existence is
+self-demonstrating."
+
+We shall see how Revilo[553] illustrates orthodoxy by mathematics. It was
+my duty to have found one of the many illustrations from physics; but
+perhaps I should have forgotten it if this instance had not come in my way.
+It is very bad physics. The sun, apart from its light, evident to the eye!
+Heat more self-demonstrating than light, because _felt_! Heat only
+manifested by the life it diffuses! Light implied not necessary to life!
+But the theology is worse than Sabellianism[554]. To adumbrate--i.e., make
+a picture of--the orthodox doctrine, the sun must be heavenly body, the
+light heavenly body, the heat heavenly body; and yet, not three heavenly
+bodies, but one heavenly body. The truth is, that this illustration and
+many others most strikingly illustrate the Trinity of fundamental doctrine
+held by the Unitarians, in all its differences from the Trinity of persons
+held by the Orthodox. Be right which may, the right or wrong of the
+Unitarians shines out in the comparison. Dr. Sadler confirms me--by which I
+mean that I wrote the above before I saw what he says--in the following
+words: "The sun is one object with two _properties_, and these properties
+have a parallel not in the second and third persons of the Trinity, but in
+the attributes of Deity."
+
+The letting light alone, as self-evident, and making heat
+self-demonstrating, because felt--i.e., perceptible now and then--has the
+character of the Irishman's astronomy:
+
+{242}
+
+ "Long life to the moon, for a dear noble cratur,
+  Which serves us for lamplight all night in the dark,
+  While the sun only shines in the day, which by natur,
+  Wants no light at all, as ye all may remark."
+
+
+
+SIR RICHARD PHILLIPS.
+
+_Sir Richard Phillips_[555] (born 1768) was conspicuous in 1793, when he
+was sentenced to a year's imprisonment[556] for selling Paine's _Rights of
+Man_; and again when, in 1807[557], he was knighted as Sheriff of London.
+As a bookseller, he was able to enforce his opinions in more ways than
+others. For instance, in James Mitchell's[558] _Dictionary of the
+Mathematical and Physical Sciences_, 1823, 12mo, which, though he was not
+technically a publisher, was printed for him--a book I should recommend to
+the collector of works of reference--there is a temperate description of
+his doctrines, which one may almost swear was one of his conditions
+previous to undertaking the work. Phillips himself was not only an
+anti-Newtonian, but carried to a fearful excess the notion that statesmen
+and Newtonians were in league to deceive the world. He saw this plot in
+Mrs. Airy's[559] pension, and in Mrs. Somerville's[560]. In 1836, he {243}
+did me the honor to attempt my conversion. In his first letter he says:
+
+"Sir Richard Phillips has an inveterate abhorrence of all the pretended
+wisdom of philosophy derived from the monks and doctors of the middle ages,
+and not less of those of higher name who merely sought to make the monkish
+philosophy more plausible, or so to disguise it as to mystify the mob of
+small thinkers."
+
+So little did his writings show any knowledge of antiquity, that I strongly
+suspect, if required to name one of the monkish doctors, he would have
+answered--Aristotle. These schoolmen, and the "philosophical trinity of
+gravitating force, projectile force, and void space," were the bogies of
+his life.
+
+I think he began to publish speculations in the _Monthly Magazine_ (of
+which he was editor) in July 1817: these he republished separately in 1818.
+In the Preface, perhaps judging the feelings of others by his own, he says
+that he "fully expects to be vilified, reviled, and anathematized, for many
+years to come." Poor man! he was let alone. He appeals with confidence to
+the "impartial decision of posterity"; but posterity does not appoint a
+hearing for one per cent. of the appeals which are made; and it is much to
+be feared that an article in such a work of reference as this will furnish
+nearly all her materials fifty years hence. The following, addressed to M.
+Arago,[561] in 1835, will give posterity as good a notion as she will
+probably need:
+
+"Even the present year has afforded EVER-MEMORABLE examples, paralleled
+only by that of the Romish Conclave which persecuted Galileo. Policy has
+adopted that maxim of Machiavel which teaches that it is _more prudent_ to
+_reward_ {244} partisans than to _persecute_ opponents. Hence, a bigotted
+party had influence enough with the late short-lived administration [I
+think he is wrong as to the administration] of Wellington, Peel, &c., to
+confer munificent royal pensions on three writers whose sole distinction
+was their advocacy of the Newtonian philosophy. A Cambridge professor last
+year published an elaborate volume in illustration of _Gravitation_, and on
+him has been conferred a pension of 300l. per annum. A lady has written a
+light popular view of the Newtonian Dogmas, and she has been complimented
+by a pension of 200l. per annum. And another writer, who has recently
+published a volume to prove that the only true philosophy is that of Moses,
+has been endowed with a pension of 200l. per annum. Neither of them were
+needy persons, and the political and ecclesiastical bearing of the whole
+was indicated by another pension of 300l. bestowed on a political writer,
+the advocate of all abuses and prejudices. Whether the conduct of the
+Romish Conclave was more base for visiting with legal penalties the
+promulgation of the doctrines that the Earth turns on its axis and revolves
+around the Sun; or that of the British Court, for its craft in conferring
+pensions on the opponents of the plain corollary, that all the motions of
+the Earth are 'part and parcel' of these great motions, and those again and
+all like them consecutive displays of still greater motions in equality of
+action and reaction, is A QUESTION which must be reserved for the casuists
+of other generations.... I cannot expect that on a sudden you and your
+friends will come to my conclusion, that the present philosophy of the
+Schools and Universities of Europe, based on faith in witchcraft, magic,
+&c., is a system of execrable nonsense, _by which quacks live on the faith
+of fools_; but I desire a free and fair examination of my Aphorisms, and if
+a few are admitted to be true, merely as courteous concessions to
+arithmetic, my purpose will be effected, for men will thus be led to think;
+and if they think, then the fabric {245} of false assumptions, and
+degrading superstitions will soon tumble in ruins."
+
+This for posterity. For the present time I ground the fame of Sir R.
+Phillips on his having squared the circle without knowing it, or intending
+to do it. In the _Protest_ presently noted he discovered that "the force
+taken as 1 is equal to the sum of all its fractions ... thus 1 = 1/4 + 1/9
++ 1/16 + 1/25, &c., carried to infinity." This the mathematician instantly
+sees is equivalent to the theorem that the circumference of any circle is
+double of the diagonal of the cube on its diameter.[562]
+
+I have examined the following works of Sir R. Phillips, and heard of many
+others:
+
+    Essays on the proximate mechanical causes of the general phenomena of
+    the Universe, 1818, 12mo.[563]
+
+    Protest against the prevailing principles of natural philosophy, with
+    the development of a common sense system (no date, 8vo, pp. 16).[564]
+
+    Four dialogues between an Oxford Tutor and a disciple of the
+    common-sense philosophy, relative to the proximate causes of material
+    phenomena. 8vo, 1824.
+
+    A century of original aphorisms on the proximate causes of the
+    phenomena of nature, 1835, 12mo.
+
+Sir Richard Phillips had four valuable qualities; honesty, zeal, ability,
+and courage. He applied them all to teaching {246} matters about which he
+knew nothing; and gained himself an uncomfortable life and a ridiculous
+memory.
+
+
+
+    Astronomy made plain; or only way the true perpendicular distance of
+    the Sun, Moon, or Stars, from this earth, can be obtained. By Wm.
+    Wood.[565] Chatham, 1819, 12mo.
+
+If this theory be true, it will follow, of course, that this earth is the
+only one God made, and that it does not whirl round the sun, but _vice
+versa_, the sun round it.
+
+
+
+WHATELY'S FAMOUS PARADOX.
+
+    Historic doubts relative to Napoleon Buonaparte. London, 1819, 8vo.
+
+This tract has since been acknowledged by Archbishop Whately[566] and
+reprinted. It is certainly a paradox: but differs from most of those in my
+list as being a joke, and a satire upon the reasoning of those who cannot
+receive narrative, no matter what the evidence, which is to them utterly
+improbable _a priori_. But had it been serious earnest, it would not have
+been so absurd as many of those which I have brought forward. The next on
+the list is not a joke.
+
+The idea of the satire is not new. Dr. King,[567] in the dispute on the
+genuineness of Phalaris, proved with humor that Bentley did not write his
+own dissertation. An attempt has lately been made, for the honor of Moses,
+to prove, {247} without humor, that Bishop Colenso did not write his own
+book. This is intolerable: anybody who tries to use such a weapon without
+banter, plenty and good, and of form suited to the subject, should get the
+drubbing which the poor man got in the Oriental tale for striking the
+dervishes with the wrong hand.
+
+The excellent and distinguished author of this tract has ceased to live. I
+call him the Paley of our day: with more learning and more purpose than his
+predecessor; but perhaps they might have changed places if they had changed
+centuries. The clever satire above named is not the only work which he
+published without his name. The following was attributed to him, I believe
+rightly: "Considerations on the Law of Libel, as relating to Publications
+on the subject of Religion, by John Search." London, 1833, 8vo. This tract
+excited little attention: for those who should have answered, could not.
+Moreover, it wanted a prosecution to call attention to it: the fear of
+calling such attention may have prevented prosecutions. Those who have read
+it will have seen why.
+
+The theological review elsewhere mentioned attributes the pamphlet of John
+Search on blasphemous libel to Lord Brougham. This is quite absurd: the
+writer states points of law on credence where the judge must have spoken
+with authority. Besides which, a hundred points of style are decisive
+between the two. I think any one who knows Whately's writing will soon
+arrive at my conclusion. Lord Brougham himself informs me that he has no
+knowledge whatever of the pamphlet.
+
+It is stated in _Notes and Queries_ (3 S. xi. 511) that Search was answered
+by the Bishop of Ferns[568] as S. N., with {248} a rejoinder by Blanco
+White.[569] These circumstances increase the probability that Whately was
+written against and for.
+
+
+
+    VOLTAIRE A CHRISTIAN.
+
+    Voltaire Chrétien; preuves tirées de ses ouvrages. Paris, 1820, 12mo.
+
+If Voltaire have not succeeded in proving himself a strong theist and a
+strong anti-revelationist, who is to succeed in proving himself one thing
+or the other in any matter whatsoever? By occasional confusion between
+theism and Christianity; by taking advantage of the formal phrases of
+adhesion to the Roman Church, which very often occur, and are often the
+happiest bits of irony in an ironical production; by citations of his
+morality, which is decidedly Christian, though often attributed to
+Brahmins; and so on--the author makes a fair case for his paradox, in the
+eyes of those who know no more than he tells them. If he had said that
+Voltaire was a better Christian than himself knew of, towards all mankind
+except men of letters, I for one should have agreed with him.
+
+_Christian!_ the word has degenerated into a synonym of _man_, in what are
+called Christian countries. So we have the parrot who "swore for all the
+world like a Christian," and the two dogs who "hated each other just like
+Christians." When the Irish duellist of the last century, whose name may be
+spared in consideration of its historic fame {249} and the worthy people
+who bear it, was (June 12, 1786) about to take the consequence of his last
+brutal murder, the rope broke, and the criminal got up, and exclaimed, "By
+---- Mr. Sheriff, you ought to be ashamed of yourself! this rope is not
+strong enough to hang a dog, far less a Christian!" But such things as this
+are far from the worst depravations. As to a word so defiled by usage, it
+is well to know that there is a way of escape from it, without renouncing
+the New Testament. I suppose any one may assume for himself what I have
+sometimes heard contended for, that no New Testament word is to be used in
+religion in any sense except that of the New Testament. This granted, the
+question is settled. The word _Christian_, which occurs three times, is
+never recognized as anything but a term of contempt from those without the
+pale to those within. Thus, Herod Agrippa, who was deep in Jewish
+literature, and a correspondent of Josephus, says to Paul (Acts xxvi. 28),
+"Almost thou persuadest me to be (what I and other followers of the state
+religion despise under the name) a Christian." Again (Acts xi. 26), "The
+disciples (as they called _themselves_) were called (by the surrounding
+heathens) Christians first in Antioch." Thirdly (1 Peter iv. 16), "Let none
+of you suffer as a _murderer_.... But if as a _Christian_ (as the heathen
+call it by whom the suffering comes), let him not be ashamed." That is to
+say, no _disciple_ ever called _himself_ a Christian, or applied the name,
+as from himself, to another disciple, from one end of the New Testament to
+the other; and no disciple need apply that name to himself in our day, if
+he dislike the associations with which the conduct of Christians has
+clothed it.
+
+
+
+WRONSKI ON THE LONGITUDE PROBLEM.
+
+    Address of M. Hoene Wronski to the British Board of Longitude, upon the
+    actual state of the mathematics, their reform, {250} and upon the new
+    celestial mechanics, giving the definitive solution of the problem of
+    longitude.[570] London, 1820, 8vo.
+
+M. Wronski[571] was the author of seven quartos on mathematics, showing
+very great power of generalization. He was also deep in the transcendental
+philosophy,[572] and had the Absolute at his fingers' ends. All this
+knowledge was rendered useless by a persuasion that he had greatly advanced
+beyond the whole world, with many hints that the Absolute would not be
+forthcoming, unless prepaid. He was a man of the widest extremes. At one
+time he desired people to see all possible mathematics in
+
+  F_x_ = A_{0}[Omega]_{0} + A_{1}[Omega]_{1} + A_{2}[Omega]_{2} +
+      A_{3}[Omega]_{3} + &c.
+
+which he did not explain, though there is meaning to it in the quartos. At
+another time he was proposing the general solution of the[573] fifth degree
+by help of 625 independent equations of one form and 125 of another. The
+first separate memoir from any Transactions that I ever possessed was given
+to me when at Cambridge; the refutation (1819) of this asserted solution,
+presented to the Academy of Lisbon by Evangelista Torriano. I cannot say I
+read it. The tract above is an attack on modern mathematicians in general,
+and on the Board of Longitude, and Dr. Young.[574]
+
+{251}
+
+
+
+DR. MILNER'S PARADOXES.
+
+1820. In this year died Dr. Isaac Milner,[575] President of Queens'
+College, Cambridge, one of the class of rational paradoxers. Under this
+name I include all who, in private life, and in matters which concern
+themselves, take their own course, and suit their own notions, no matter
+what other people may think of them. These men will put things to uses they
+were never intended for, to the great distress and disgust of their
+gregarious friends. I am one of the class, and I could write a little book
+of cases in which I have incurred absolute reproach for not "doing as other
+people do." I will name two of my atrocities: I took one of those
+butter-dishes which have for a top a dome with holes in it, which is turned
+inward, out of reach of accident, when not in use. Turning the dome
+inwards, I filled the dish with water, and put a sponge in the dome: the
+holes let it fill with water, and I had a penwiper, always moist, and worth
+its price five times over. "Why! what do you mean? It was made to hold
+butter. You are always at some queer thing or other!" I bought a leaden
+comb, intended to dye the hair, it being supposed that the application of
+lead will have this effect. I did not try: but I divided the comb into two,
+separated the part of closed prongs from the other; and thus I had two
+ruling machines. The lead marks paper, and by drawing the end of one of the
+machines along a ruler, I could rule twenty lines at a time, quite fit to
+write on. I thought I should have killed a friend to whom I explained it:
+he could not for the life of him understand how leaden _lines_ on paper
+would dye the hair.
+
+But Dr. Milner went beyond me. He wanted a seat suited to his shape, and he
+defied opinion to a fearful point. {252} He spread a thick block of putty
+over a wooden chair and sat in it until it had taken a ceroplast copy of
+the proper seat. This he gave to a carpenter to be imitated in wood. One of
+the few now living who knew him--my friend, General Perronet
+Thompson[576]--answers for the wood, which was shown him by Milner himself;
+but he does not vouch for the material being putty, which was in the story
+told me at Cambridge; William Frend[577] also remembered it. Perhaps the
+Doctor took off his great seal in green wax, like the Crown; but some soft
+material he certainly adopted; and very comfortable he found the wooden
+copy.
+
+[Illustration]
+
+The same gentleman vouches for Milner's lamp: but this had visible
+_science_ in it; the vulgar see no science in the construction of the
+chair. A hollow semi-cylinder, but not with a circular curve, revolved on
+pivots. The curve was calculated on the law that, whatever quantity of oil
+might be in the lamp, the position of equilibrium just brought the oil up
+to the edge of the cylinder, at which a bit of wick was placed. As the wick
+exhausted the oil, the cylinder slowly revolved about the pivots so as to
+keep the oil always touching the wick.
+
+Great discoveries are always laughed at; but it is very often not the laugh
+of incredulity; it is a mode of distorting the sense of inferiority into a
+sense of superiority, or a mimicry of superiority interposed between the
+laugher and his feeling of inferiority. Two persons in conversation {253}
+agreed that it was often a nuisance not to be able to lay hands on a bit of
+paper to mark the place in a book, every bit of paper on the table was sure
+to contain something not to be spared. I very quietly said that I always
+had a stock of bookmarkers ready cut, with a proper place for them: my
+readers owe many of my anecdotes to this absurd practice. My two
+colloquials burst into a fit of laughter; about what? Incredulity was out
+of the question; and there could be nothing foolish in my taking measures
+to avoid what they knew was an inconvenience. I was in this matter
+obviously their superior, and so they laughed at me. Much more candid was
+the Royal Duke of the last century, who was noted for slow ideas. "The rain
+comes into my mouth," said he, while riding. "Had not your Royal Highness
+better shut your mouth?" said the equerry. The Prince did so, and ought, by
+rule, to have laughed heartily at his adviser; instead of this, he said
+quietly, "It doesn't come in now."
+
+
+
+HERBART'S MATHEMATICAL PSYCHOLOGY.
+
+    De Attentionis mensura causisque primariis. By J. F. Herbart.[578]
+    Koenigsberg, 1822, 4to.
+
+{254}
+
+This celebrated philosopher maintained that mathematics ought to be applied
+to psychology, in a separate tract, published also in 1822: the one above
+seems, therefore, to be his challenge on the subject. It is on _attention_,
+and I think it will hardly support Herbart's thesis. As a specimen of his
+formula, let _t_ be the time elapsed since the consideration began, [beta]
+the whole perceptive intensity of the individual, [phi] the whole of his
+mental force, and _z_ the force given to a notion by attention during the
+time _t_. Then,
+
+z = [phi] (1 - [epsilon]^{-[beta]t})
+
+Now for a test. There is a _jactura_, _v_, the meaning of which I do not
+comprehend. If there be anything in it, my mathematical readers ought to
+interpret it from the formula
+
+_v_ = [pi][phi][beta]/(1 - [beta])[epsilon]^{-[beta]t} + C[epsilon]^{-t}
+
+and to this task I leave them, wishing them better luck than mine. The time
+may come when other manifestations of mind, besides _belief_, shall be
+submitted to calculation: at that time, should it arrive, a final decision
+may be passed upon Herbart.
+
+
+
+ON THE WHIZGIG.
+
+    The theory of the Whizgig considered; in as much as it mechanically
+    exemplifies the three working properties of nature; which are now set
+    forth under the guise of this toy, for children of all ages. London,
+    1822, 12mo (pp. 24, B. McMillan, Bow Street, Covent Garden).
+
+The toy called the _whizgig_ will be remembered by many. The writer is a
+follower of Jacob Behmen,[579] William Law,[580] {255} Richard Clarke,[581]
+and Eugenius Philalethes.[582] Jacob Behmen first announced the three
+working properties of nature, which Newton stole, as described in the
+_Gentleman's Magazine_, July, 1782, p. 329. These laws are illustrated in
+the whizgig. There is the harsh astringent, attractive compression; the
+bitter compunction, repulsive expansion; and the stinging anguish, duplex
+motion. The author hints that he has written other works, to which he gives
+no clue. I have heard that Behmen was pillaged by Newton, and
+Swedenborg[583] by Laplace,[584] and Pythagoras by Copernicus,[585] and
+Epicurus by Dalton,[586] &c. I do not think this mention will revive
+Behmen; but it may the whizgig, a very pretty toy, and philosophical
+withal, for few of those who used it could explain it.
+
+{256}
+
+
+
+SOME MYTHOLOGICAL PARADOXES.
+
+    A Grammar of infinite forms; or the mathematical elements of ancient
+    philosophy and mythology. By Wm. Howison.[587] Edinburgh, 1823, 8vo.
+
+A curius combination of geometry and mythology. Perseus, for instance, is
+treated under the head, "the evolution of diminishing hyperbolic branches."
+
+
+
+    The Mythological Astronomy of the Ancients; part the second: or the key
+    of Urania, the words of which will unlock all the mysteries of
+    antiquity. Norwich, 1823, 12mo.
+
+    A Companion to the Mythological Astronomy, &c., containing remarks on
+    recent publications.... Norwich, 1824, 12mo.
+
+    A new Theory of the Earth and of planetary motion; in which it is
+    demonstrated that the Sun is vicegerent of his own system. Norwich,
+    1825, 12mo.
+
+    The analyzation of the writings of the Jews, so far as they are found
+    to have any connection with the sublime science of astronomy. [This is
+    pp. 97-180 of some other work, being all I have seen.]
+
+These works are all by Sampson Arnold Mackey,[588] for whom see _Notes and
+Queries_, 1st S. viii. 468, 565, ix. 89, 179. Had it not been for actual
+quotations given by one correspondent only (1st S. viii. 565), that journal
+would have handed him down as a man of some real learning. An extraordinary
+man he certainly was: it is not one illiterate shoemaker in a thousand who
+could work upon such a singular mass of Sanskrit and Greek words, without
+showing {257} evidence of being able to read a line in any language but his
+own, or to spell that correctly. He was an uneducated Godfrey Higgins.[589]
+A few extracts will put this in a strong light: one for history of science,
+one for astronomy, and one for philology:
+
+"Sir Isaac Newton was of opinion that 'the atmosphere of the earth was the
+sensory of God; by which he was enabled to see quite round the earth:'
+which proves that Sir Isaac had no idea that God could see through the
+earth.
+
+"Sir Richard [Phillips] has given the most rational explanation of the
+cause of the earth's elliptical orbit that I have ever seen in print. It is
+because the earth presents its watery hemisphere to the sun at one time and
+that of solid land the other; but why has he made his Oxonian astonished at
+the coincidence? It is what I taught in my attic twelve years before.
+
+"Again, admitting that the Eloim were powerful and intelligent beings that
+managed these things, we would accuse _them_ of being the authors of all
+the sufferings of Chrisna. And as they and the constellation of Leo were
+below the horizon, and consequently cut off from the end of the zodiac,
+there were but eleven constellations of the zodiac to be seen; the three at
+the end were wanted, but those three would be accused of bringing Chrisna
+into the troubles which at last ended in his death. All this would be
+expressed in the Eastern language by saying that Chrisna was persecuted by
+those Judoth Ishcarioth!!!!! [the five notes of exclamation are the
+author's]. But the astronomy of those distant ages, when the sun was at the
+south pole in winter, would leave five of those Decans cut off from our
+view, in the latitude of twenty-eight degrees; hence Chrisna died of {258}
+wounds from five Decans, but the whole five may be included in Judoth
+Ishcarioth! for the phrase means 'the men that are wanted at the extreme
+parts.' Ishcarioth is a compound of _ish_, a man, and _carat_ wanted or
+taken away, and oth the plural termination, more ancient than _im_...."
+
+I might show at length how Michael is the sun, and the D'-ev-'l in French
+Di-ob-al, also 'L-evi-ath-an--the evi being the radical part both of
+d_evi_l and l_evi_athan--is the Nile, which the sun dried up for Moses to
+pass: a battle celebrated by Jude. Also how _Moses_, the same name as
+_Muses_, is from _mesha_, drawn out of the water, "and hence we called our
+land which is saved from the water by the name of _marsh_." But it will be
+of more use to collect the character of S. A. M. from such correspondents
+of _Notes and Queries_ as have written after superficial examination. Great
+astronomical and philological attainments, much ability and learning; had
+evidently read and studied deeply; remarkable for the originality of his
+views upon the very abstruse subject of mythological astronomy, in which he
+exhibited great sagacity. Certainly his views were _original_; but their
+sagacity, if it be allowable to copy his own mode of etymologizing, is of
+an _ori-gin-ale_ cast, resembling that of a person who puts to his mouth
+liquors both distilled and fermented.
+
+
+
+A KANTESIAN JEWELER.
+
+    Principles of the Kantesian, or transcendental philosophy. By Thomas
+    Wirgman.[590] London, 1824, 8vo.
+
+Mr. Wirgman's mind was somewhat attuned to psychology; but he was cracky
+and vagarious. He had been a fashionable jeweler in St. James's Street, no
+doubt the son or grandson of Wirgman at "the well-known toy-shop in {259}
+St. James's Street," where Sam Johnson smartened himself with silver
+buckles. (Boswell, _æt._ 69). He would not have the ridiculous large ones
+in fashion; and he would give no more than a guinea a pair; such, says
+Boswell, in Italics, were the _principles_ of the business: and I think
+this may be the first place in which the philosophical word was brought
+down from heaven to mix with men. However this may be, _my_ Wirgman sold
+snuff-boxes, among other things, and fifty years ago a fashionable
+snuff-boxer would be under inducement, if not positively obliged, to have a
+stock with very objectionable pictures. So it happened that Wirgman--by
+reason of a trifle too much candor--came under the notice of the
+_Suppression_ Society, and ran considerable risk. Mr. Brougham was his
+counsel; and managed to get him acquitted. Years and years after this, when
+Mr. Brougham was deep in the formation of the London University (now
+University College), Mr. Wirgman called on him. "What now?" said Mr. B.
+with his most sarcastic look--a very perfect thing of its kind--"you're in
+a scrape again, I suppose!" "No! indeed!" said W., "my present object is to
+ask your interest for the chair of Moral Philosophy in the new University!"
+He had taken up Kant!
+
+Mr. Wirgman, an itinerant paradoxer, called on me in 1831: he came to
+convert me. "I assure you," said he, "I am nothing but an old brute of a
+jeweler;" and his eye and manner were of the extreme of jocosity, as good
+in their way, as the satire of his former counsel. I mention him as one of
+that class who go away quite satisfied that they have wrought conviction.
+"Now," said he, "I'll make it clear to you! Suppose a number of gold-fishes
+in a glass bowl,--you understand? Well! I come with my cigar and go puff,
+puff, puff, over the bowl, until there is a little cloud of smoke: now,
+tell me, what will the gold-fishes say to that?" "I should imagine," said
+I, "That they would not know what to make of it." "By Jove! you're a
+Kantian;" said he, and with this and the like, he left me, vowing that
+{260} it was delightful to talk to so intelligent a person. The greatest
+compliment Wirgman ever received was from James Mill, who used to say he
+did not _understand_ Kant. That such a man as Mill should think this worth
+saying is a feather in the cap of the jocose jeweler.
+
+Some of my readers will stare at my supposing that Boswell may have been
+the first down-bringer of the word _principles_ into common life; the best
+answer will be a prior instance of the word as true vernacular; it has
+never happened to me to notice one. Many words have very common uses which
+are not old. Take the following from Nichols (_Anecd._ ix. 263): "Lord
+Thurlow presents his best respects to Mr. and Mrs. Thicknesse, and assures
+them that he knows of no cause to complain of any part of Mr. Thicknesse's
+carriage; least of all the circumstance of sending the head to Ormond
+Street." Surely Mr. T. had lent Lord T. a satisfactory carriage with a
+movable head, and the above is a polite answer to inquiries. Not a bit of
+it! _carriage_ is here _conduct_, and the _head_ is a _bust_. The vehicles
+of the rich, at the time, were coaches, chariots, chaises, etc., never
+carriages, which were rather _carts_. Gibbon has the word for
+baggage-wagons. In Jane Austen's novels the word carriage is established.
+
+
+
+WALSH'S DELUSIONS.
+
+_John Walsh_,[591] of Cork (1786-1847). This discoverer has had the honor
+of a biography from Professor Boole, who, at my request, collected
+information about him on the scene of his labors. It is in the
+_Philosophical Magazine_ for November, 1851, and will, I hope, be
+transferred to some biographical collection where it may find a larger
+class of readers. It is the best biography of a single hero of the kind
+that I know. Mr. Walsh introduced himself to me, {261} as he did to many
+others, in the anterowlandian days of the Post-office; his unpaid letters
+were double, treble, &c. They contained his pamphlets, and cost their
+weight in silver: all have the name of the author, and all are in octavo or
+in quarto letter-form: most are in four pages, and all dated from Cork. I
+have the following by me:
+
+    The Geometric Base, 1825.--The theory of plane angles. 1827.--Three
+    Letters to Dr. Francis Sadleir. 1838.--The invention of polar geometry.
+    By Irelandus. 1839.--The theory of partial functions. Letter to Lord
+    Brougham. 1839.--On the invention of polar geometry. 1839.--Letter to
+    the Editor of the Edinburgh Review. 1840.--Irish Manufacture. A new
+    method of tangents. 1841.--The normal diameter in curves. 1843.--Letter
+    to Sir R. Peel. 1845.--[Hints that Government should compel the
+    introduction of Walsh's Geometry into Universities.]--Solution of
+    Equations of the higher orders. 1845.
+
+Besides these, there is a _Metalogia_, and I know not how many others.
+
+Mr. Boole,[592] who has taken the moral and social features of Walsh's
+delusions from the commiserating point of view, which makes ridicule out of
+place, has been obliged to treat Walsh as Scott's Alan Fairford treated his
+client Peter Peebles; namely, keep the scarecrow out of court while the
+case was argued. My plan requires me to bring him in: and when he comes in
+at the door, pity and sympathy fly out at the window. Let the reader
+remember that he was not an ignoramus in mathematics: he might have won his
+spurs if he could have first served as an esquire. Though so illiterate
+that even in Ireland he never picked up anything more Latin than
+_Irelandus_, he was a very pretty mathematician spoiled in the making by
+intense self-opinion.
+
+This is part of a private letter to me at the back of a page of print: I
+had never addressed a word to him:
+
+{262}
+
+"There are no limits in mathematics, and those that assert there are, are
+infinite ruffians, ignorant, lying blackguards. There is no differential
+calculus, no Taylor's theorem, no calculus of variations, &c. in
+mathematics. There is no quackery whatever in mathematics; no % equal to
+anything. What sheer ignorant blackguardism that!
+
+"In mechanics the parallelogram of forces is quackery, and is dangerous;
+for nothing is at rest, or in uniform, or in rectilinear motion, in the
+universe. Variable motion is an essential property of matter. Laplace's
+demonstration of the parallelogram of forces is a begging of the question;
+and the attempts of them all to show that the difference of twenty minutes
+between the sidereal and actual revolution of the earth round the sun
+arises from the tugging of the Sun and Moon at the pot-belly of the earth,
+without being sure even that the earth has a pot-belly at all, is perfect
+quackery. The said difference arising from and demonstrating the revolution
+of the Sun itself round some distant center."
+
+In the letter to Lord Brougham we read as follows:
+
+"I ask the Royal Society of London, I ask the Saxon crew of that crazy
+hulk, where is the dogma of their philosophic god now?... When the Royal
+Society of London, and the Academy of Sciences of Paris, shall have read
+this memorandum, how will they appear? Like two cur dogs in the paws of the
+noblest beast of the forest.... Just as this note was going to press, a
+volume lately published by you was put into my hands, wherein you attempt
+to defend the fluxions and _Principia_ of Newton. Man! what are you about?
+You come forward now with your special pleading, and fraught with national
+prejudice, to defend, like the philosopher Grassi,[593] the persecutor of
+Galileo, principles {263} and reasoning which, unless you are actually
+insane, or an ignorant quack in mathematics, you know are mathematically
+false. What a moral lesson this for the students of the University of
+London from its head! Man! demonstrate corollary 3, in this note, by the
+lying dogma of Newton, or turn your thoughts to something you understand.
+
+"WALSH IRELANDUS."
+
+Mr. Walsh--honor to his memory--once had the consideration to save me
+postage by addressing a pamphlet under cover to a Member of Parliament,
+with an explanatory letter. In that letter he gives a candid opinion of
+himself:
+
+(1838.) "Mr. Walsh takes leave to send the enclosed corrected copy to Mr.
+Hutton as one of the Council of the University of London, and to save
+postage for the Professor of Mathematics there. He will find in it geometry
+more deep and subtle, and at the same time more simple and elegant, than it
+was ever contemplated human genius could invent."
+
+He then proceeds to set forth that a certain "tomfoolery lemma," with its
+"tomfoolery" superstructure, "never had existence outside the shallow
+brains of its inventor," Euclid. He then proceeds thus:
+
+"The same spirit that animated those philosophers who sent Galileo to the
+Inquisition animates all the philosophers of the present day without
+exception. If anything can free them from the yoke of error, it is the
+[Walsh] problem of double tangence. But free them it will, how deeply
+soever they may be sunk into mental slavery--and God knows that is deeply
+enough; and they bear it with an admirable grace; for none bear slavery
+with a better grace than tyrants. The lads must adopt my theory.... It will
+be a sad reverse for all our great professors to be compelled to become
+schoolboys in their gray years. But the sore scratch is to be compelled, as
+they had before been compelled one thousand years ago, to have recourse to
+Ireland for instruction." {264}
+
+The following "Impromptu" is no doubt by Walsh himself: he was more of a
+poet than of an astronomer:
+
+   "Through ages unfriended,
+    With sophistry blended,
+  Deep science in Chaos had slept;
+    Its limits were fettered,
+    Its voters unlettered,
+  Its students in movements but crept.
+    Till, despite of great foes,
+    Great WALSH first arose,
+  And with logical might did unravel
+    Those mazes of knowledge,
+    Ne'er known in a college,
+  Though sought for with unceasing travail.
+    With cheers we now hail him,
+    May success never fail him,
+  In Polar Geometrical mining;
+    Till his foes be as tamed
+    As his works are far-famed
+  For true philosophic refining."
+
+Walsh's system is, that all mathematics and physics are wrong: there is
+hardly one proposition in Euclid which is demonstrated. His example ought
+to warn all who rely on their own evidence to their own success. He was
+not, properly speaking, insane; he only spoke his mind more freely than
+many others of his class. The poor fellow died in the Cork union, during
+the famine. He had lived a happy life, contemplating his own perfections,
+like Brahma on the lotus-leaf.[594]
+
+{265}
+
+
+
+GROWTH OF FREEDOM OF OPINION.
+
+The year 1825 brings me to about the middle of my _Athenæum_ list: that is,
+so far as mere number of names mentioned is concerned. Freedom of opinion,
+beyond a doubt, is gaining ground, for good or for evil, according to what
+the speaker happens to think: admission of authority is no longer made in
+the old way. If we take soul-cure and body-cure, divinity and medicine, it
+is manifest that a change has come over us. Time was when it was enough
+that dose or dogma should be certified by "Il a été ordonné, Monsieur, il a
+été ordonné,"[595] as the apothecary said when he wanted to operate upon
+poor de Porceaugnac. Very much changed: but whether for good or for evil
+does not now matter; the question is, whether contempt of _demonstration_
+such as our paradoxers show has augmented with the rejection of _dogmatic
+authority_. It ought to be just the other way: for the worship of reason is
+the system on which, if we trust them, the deniers of guidance ground their
+plan of life. The following attempt at an experiment on this point is the
+best which I can make; and, so far as I know, the first that ever was made.
+
+Say that my list of paradoxers divides in 1825: this of itself proves
+nothing, because so many of the earlier books are lost, or not likely to be
+come at. It would be a fearful rate of increase which would make the number
+of paradoxes since 1825 equal to the whole number before that date. Let us
+turn now to another collection of mine, arithmetical books, of which I have
+published a list. The two collections are similarly circumstanced as to new
+and old books; the paradoxes had no care given to the collection of either;
+the arithmetical books equal care to both. The list of arithmetical books,
+published in 1847, divides at 1735; the paradoxes, up to 1863, divide at
+1825. If we take the process which is most against the distinction, and
+allow every year {266} from 1847 to 1863 to add a year to 1735, we should
+say that the arithmetical writers divide at 1751. This rough process may
+serve, with sufficient certainty, to show that the proportion of paradoxes
+to books of sober demonstration is on the increase; and probably, quite as
+much as the proportion of heterodoxes to books of orthodox adherence. So
+that divinity and medicine may say to geometry, Don't _you_ sneer: if
+rationalism, homoeopathy, and their congeners are on the rise among us,
+your enemies are increasing quite as fast. But geometry replies--Dear
+friends, content yourselves with the rational inference that the rise of
+heterodoxy within your pales is not conclusive against you, taken alone;
+for it rises at the same time within mine. Store within your garners the
+precious argument that you are not proved wrong by increase of dissent;
+because there is increase of dissent against exact science. But do not
+therefore _even_ yourselves to me: remember that you, Dame Divinity, have
+inflicted every kind of penalty, from the stake to the stocks, in aid of
+your reasoning; remember that you, Mother Medicine, have not many years ago
+applied to Parliament for increase of forcible hindrance of
+antipharmacopoeal drenches, pills, and powders. Who ever heard of my asking
+the legislature to fine blundering circle-squarers? Remember that the D in
+dogma is the D in decay; but the D in demonstration is the D in durability.
+
+
+
+THE STATUS OF MEDICINE.
+
+I have known a medical man--a young one--who was seriously of the opinion
+that the country ought to be divided into medical parishes, with a
+practitioner appointed to each, and a penalty for calling in any but the
+incumbent curer. How should people know how to choose? The hair-dressers
+once petitioned Parliament for an act to compel people to wear wigs. My own
+opinion is of the opposite extreme, as in the following letter (_Examiner_,
+April 5, 1856); which, to my surprise, I saw reprinted in a medical
+journal, as a {267} plan not absolutely to be rejected. I am perfectly
+satisfied that it would greatly promote true medical orthodoxy, the
+predominance of well educated thinkers, and the development of their
+desirable differences.
+
+
+
+"SIR. The Medical Bill and the medical question generally is one on which
+experience would teach, if people would be taught.
+
+"The great soul question took three hundred years to settle: the little
+body question might be settled in thirty years, if the decisions in the
+former question were studied.
+
+"Time was when the State believed, as honestly as ever it believed
+anything, that it _might_, _could_, and _should_ find out the true doctrine
+for the poor ignorant community; to which, like a worthy honest state, it
+added _would_. Accordingly, by the assistance of the Church, which
+undertook the physic, the surgery, and the pharmacy of sound doctrine all
+by itself, it sent forth its legally qualified teachers into every parish,
+and woe to the man who called in any other. They burnt that man, they
+whipped him, they imprisoned him, they did everything but what was
+Christian to him, all for his soul's health and the amendment of his
+excesses.
+
+"But men would not submit. To the argument that the State was a father to
+the ignorant, they replied that it was at best the ignorant father of an
+ignorant son, and that a blind man could find his way into a ditch without
+another blind man to help him. And when the State said--But here we have
+the Church, which knows all about it, the ignorant community declared that
+it had a right to judge that question, and that it would judge it. It also
+said that the Church was never one thing long, and that it progressed, on
+the whole, rather more slowly than the ignorant community.
+
+"The end of it was, in this country, that every one who chose taught all
+who chose to let him teach, on condition only of an open and true
+registration. The State was {268} allowed to patronize one particular
+Church, so that no one need trouble himself to choose a pastor from the
+mere necessity of choosing. But every church is allowed its colleges, its
+studies, its diplomas; and every man is allowed his choice. There is no
+proof that our souls are worse off than in the sixteenth century; and,
+judging by fruits, there is much reason to hope they are better off.
+
+"Now the little body question is a perfect parallel to the great soul
+question in all its circumstances. The only things in which the parallel
+fails are the following: Every one who believes in a future state sees that
+the soul question is incomparably more important than the body question,
+and every one can try the body question by experiment to a larger extent
+than the soul question. The proverb, which always has a spark of truth at
+the bottom, says that every man of forty is either a fool or a physician;
+but did even the proverb maker ever dare to say that every man is at any
+age either a fool or a fit teacher of religion?
+
+"Common sense points out the following settlement of the medical question:
+and to this it will come sooner or later.
+
+"Let every man who chooses--subject to one common law of manslaughter for
+all the _crass_ cases--doctor the bodies of all who choose to trust him,
+and recover payment according to agreement in the courts of law. Provided
+always that every person practising should be registered at a moderate fee
+in a register to be republished every six months.
+
+"Let the register give the name, address, and asserted qualification of
+each candidate--as licentiate, or doctor, or what not, of this or that
+college, hall, university, &c., home or foreign. Let it be competent to any
+man to describe himself as qualified by study in public schools without a
+diploma, or by private study, or even by intuition or divine inspiration,
+if he please. But whatever he holds his qualification to be, that let him
+declare. Let all qualification {269} which of its own nature admits of
+proof be proved, as by the diploma or certificate, &c., leaving things
+which cannot be proved, as asserted private study, intuition, inspiration,
+&c., to work their own way.
+
+"Let it be highly penal to assert to the patient any qualification which is
+not in the register, and let the register be sold very cheap. Let the
+registrar give each registered practitioner a copy of the register in his
+own case; let any patient have the power to demand a sight of this copy;
+and let no money for attendance be recoverable in any case in which there
+has been false representation.
+
+"Let any party in any suit have a right to produce what medical testimony
+he pleases. Let the medical witness produce his register, and let his
+evidence be for the jury, as is that of an engineer or a practitioner of
+any art which is not attested by diplomas.
+
+"Let any man who practises without venturing to put his name on the
+register be liable to fine and imprisonment.
+
+"The consequence would be that, as now, anybody who pleases might practise;
+for the medical world is well aware that there is no power of preventing
+what they call quacks from practising. But very different from what is now,
+every man who practises would be obliged to tell the whole world what his
+claim is, and would run a great risk if he dared to tell his patient in
+private anything different from what he had told the whole world.
+
+"The consequence would be that a real education in anatomy, physiology,
+chemistry, surgery, and what is known of the thing called medicine, would
+acquire more importance than it now has.
+
+"It is curious to see how completely the medical man of the nineteenth
+century squares with the priest of the sixteenth century. The clergy of all
+sects are now better divines and better men than they ever were. They have
+lost Bacon's reproach that they took a smaller measure of things than any
+other educated men; and the physicians are now {270} in this particular the
+rearguard of the learned world; though it may be true that the rear in our
+day is further on in the march than the van of Bacon's day. Nor will they
+ever recover the lost position until medicine is as free as religion.
+
+"To this it must come. To this the public, which will decide for itself,
+has determined it shall come. To this the public has, in fact, brought it,
+but on a plan which it is not desirable to make permanent. We will be as
+free to take care of our bodies as of our souls and of our goods. This is
+the profession of all who sign as I do, and the practice of most of those
+who would not like the name
+
+"HETEROPATH."
+
+
+
+    The motion of the Sun in the Ecliptic, proved to be uniform in a
+    circular orbit ... with preliminary observations on the fallacy of the
+    Solar System. By Bartholomew Prescott,[596] 1825, 8vo.
+
+The author had published, in 1803, a _Defence of the Divine System_, which
+I never saw; also, _On the inverted scheme of Copernicus_. The above work
+is clever in its satire.
+
+
+
+THE CHRISTIAN EVIDENCE SOCIETY.
+
+    Manifesto of the Christian Evidence Society, established Nov. 12, 1824.
+    Twenty-four plain questions to honest men.
+
+These are two broadsides of August and November, 1826, signed by Robert
+Taylor,[597] A.B., Orator of the Christian Evidence Society. This gentleman
+was a clergyman, {271} and was convicted of blasphemy in 1827, for which he
+suffered imprisonment, and got the name of the _Devil's Chaplain_. The
+following are quotations:
+
+"For the book of Revelation, there was no original Greek at all, but
+_Erasmus_ wrote it himself in Switzerland, in the year 1516. Bishop
+Marsh,[598] vol. i. p. 320."--"Is not God the author of your reason? Can he
+then be the author of anything which is contrary to your reason? If reason
+be a sufficient guide, why should God give you any other? if it be not a
+sufficient guide, why has he given you _that_?"
+
+I remember a votary of the Society being asked to substitute for _reason_
+"the right leg," and for _guide_ "support," and to answer the two last
+questions: he said there must be a quibble, but he did not see what. It is
+pleasant to reflect that the _argumentum à carcere_[599] is obsolete. One
+great defect of it was that it did not go far enough: there should have
+been laws against subscriptions for blasphemers, against dealing at their
+shops, and against rich widows marrying them.
+
+Had I taken in theology, I must have entered books against Christianity. I
+mention the above, and Paine's _Age of Reason_, simply because they are the
+only English modern works that ever came in my way without my asking for
+them. The three parts of the _Age of Reason_ were published in Paris 1793,
+Paris 1795, and New York 1807. Carlile's[600] edition is of London, 1818,
+8vo. It must be republished when the time comes, to show what stuff
+governments and clergy were afraid of at the beginning of this century. I
+should never have seen the book, if it {272} had not been prohibited: a
+bookseller put it under my nose with a fearful look round him; and I could
+do no less, in common curiosity, than buy a work which had been so
+complimented by church and state. And when I had read it, I said in my mind
+to church and state,--Confound you! you have taken me in worse than any
+reviewer I ever met with. I forget what I gave for the book, but I ought to
+have been able to claim compensation somewhere.
+
+
+
+THE CABBALA.
+
+    Cabbala Algebraica. Auctore Gul. Lud. Christmann.[601] Stuttgard, 1827,
+    4to.
+
+Eighty closely printed pages of an attempt to solve equations of every
+degree, which has a process called by the author _cabbala_. An anonymous
+correspondent spells _cabbala_ as follows, [Greek: chabball], and makes 666
+out of its letters. This gentleman has sent me since my Budget commenced, a
+little heap of satirical communications, each having a 666 or two; for
+instance, alluding to my remarks on the spelling of _chemistry_, he finds
+the fated number in [Greek: chimeia]. With these are challenges to explain
+them, and hints about the end of the world. All these letters have
+different fantastic seals; one of them with the legend "keep your
+temper,"--another bearing "bank token five pence." The only signature is a
+triangle with a little circle in it, which I interpret to mean that the
+writer confesses himself to be the round man stuck in the three-cornered
+hole, to be explained as in Sydney Smith's joke.
+
+{273}
+
+There is a kind of Cabbala Alphabetica which the investigators of the
+numerals in words would do well to take up: it is the formation of
+sentences which contain all the letters of the alphabet, and each only
+once. No one has done it with _v_ and _j_ treated as consonants; but you
+and I can do it. Dr. Whewell[602] and I amused ourselves, some years ago,
+with attempts. He could not make sense, though he joined words: he gave me
+
+  Phiz, styx, wrong, buck, flame, quid.
+
+I gave him the following, which he agreed was "admirable sense": I
+certainly think the words would never have come together except in this
+way:
+
+  I, quartz pyx, who fling muck beds.
+
+I long thought that no human being could say this under any circumstances.
+At last I happened to be reading a religious writer--as he thought
+himself--who threw aspersions on his opponents thick and threefold. Heyday!
+came into my head, this fellow flings muck beds; he must be a quartz pyx.
+And then I remembered that a pyx is a sacred vessel, and quartz is a hard
+stone, as hard as the heart of a religious foe-curser. So that the line is
+the motto of the ferocious sectarian, who turns his religious vessels into
+mudholders, for the benefit of those who will not see what he sees.
+
+I can find no circumstances for the following, which I received from
+another:
+
+  Fritz! quick! land! hew gypsum box.
+
+From other quarters I have the following:
+
+  Dumpy quiz! whirl back fogs next.
+
+This might be said in time of haze to the queer little figure in the Dutch
+weather-toy, which comes out or goes in with the change in the atmosphere.
+Again,
+
+{274}
+
+  Export my fund!  Quiz black whigs.
+
+This Squire Western might have said, who was always afraid of the whigs
+sending the sinking-fund over to Hanover. But the following is the best: it
+is good advice to a young man, very well expressed under the circumstances:
+
+  Get nymph; quiz sad brow; fix luck.
+
+Which in more sober English would be, Marry; be cheerful; watch your
+business. There is more edification, more religion in this than in all the
+666-interpretations put together.
+
+Such things would make excellent writing copies, for they secure attention
+to every letter; _v_ and _j_ might be placed at the end.
+
+
+
+ON GODFREY HIGGINS.
+
+    The Celtic Druids. By Godfrey Higgins,[603] Esq. of Skellow Grange,
+    near Doncaster. London, 1827, 4to.
+
+    Anacalypsis, or an attempt to draw aside the veil of the Saitic Isis:
+    or an inquiry into the origin of languages, nations, and religions. By
+    Godfrey Higgins, &c..., London, 1836, 2 vols. 4to.
+
+The first work had an additional preface and a new index in 1829. Possibly,
+in future time, will be found bound up with copies of the second work two
+sheets which Mr. Higgins circulated among his friends in 1831: the first a
+"Recapitulation," the second "Book vi. ch. 1."
+
+The system of these works is that--
+
+"The Buddhists of Upper India (of whom the Phenician Canaanite,
+Melchizedek, was a priest), who built the Pyramids, Stonehenge, Carnac, &c.
+will be shown to have founded all the ancient mythologies of the world,
+which, however varied and corrupted in recent times, were originally one,
+and that one founded on principles sublime, beautiful, and true."
+
+{275}
+
+These works contain an immense quantity of learning, very honestly put
+together. I presume the enormous number of facts, and the goodness of the
+index, to be the reasons why the _Anacalypsis_ found a permanent place in
+the _old_ reading-room of the British Museum, even before the change which
+greatly increased the number of books left free to the reader in that room.
+
+Mr. Higgins, whom I knew well in the last six years of his life, and
+respected as a good, learned, and (in his own way) _pious_ man, was
+thoroughly and completely the man of a system. He had that sort of mental
+connection with his theory that made his statements of his authorities
+trustworthy: for, besides perfect integrity, he had no bias towards
+alteration of facts: he saw his system in the way the fact was presented to
+him by his authority, be that what it might.
+
+He was very sure of a fact which he got from any of his authorities:
+nothing could shake him. Imagine a conversation between him and an Indian
+officer who had paid long attention to Hindoo antiquities and their
+remains: a third person was present, _ego qui scribo_. _G. H._ "You know
+that in the temples of I-forget-who the Ceres is always sculptured
+precisely as in Greece." _Col._ ----, "I really do not remember it, and I
+have seen most of these temples." _G. H._ "It is so, I assure you,
+especially at I-forget-where." _Col._ ----, "Well, I am sure! I was
+encamped for six weeks at the gate of that very temple, and, except a
+little shooting, had nothing to do but to examine its details, which I did,
+day after day, and I found nothing of the kind." It was of no use at all.
+
+Godfrey Higgins began life by exposing and conquering, at the expense of
+two years of his studies, some shocking abuses which existed in the York
+Lunatic Asylum. This was a proceeding which called much attention to the
+treatment of the insane, and produced much good effect. He was very
+resolute and energetic. The magistracy of his {276} time had such scruples
+about using the severity of law to people of such station as well-to-do
+farmers, &c.: they would allow a great deal of resistance, and endeavor to
+mollify the rebels into obedience. A young farmer flatly refused to pay
+under an order of affiliation made upon him by Godfrey Higgins. He was duly
+warned; and persisted: he shortly found himself in gaol. He went there sure
+to conquer the Justice, and the first thing he did was to demand to see his
+lawyer. He was told, to his horror, that as soon as he had been cropped and
+prison-dressed, he might see as many lawyers as he pleased, to be looked
+at, laughed at, and advised that there was but one way out of the scrape.
+Higgins was, in his speculations, a regular counterpart of Bailly; but the
+celebrated Mayor of Paris had not his nerve. It was impossible to say, if
+their characters had been changed, whether the unfortunate crisis in which
+Bailly was not equal to the occasion would have led to very different
+results if Higgins had been in his place: but assuredly constitutional
+liberty would have had one chance more. There are two works of his by which
+he was known, apart from his paradoxes. First, _An apology for the life and
+character of the celebrated prophet of Arabia, called Mohamed, or the
+Illustrious_. London, 8vo. 1829. The reader will look at this writing of
+our English Buddhist with suspicious eye, but he will not be able to avoid
+confessing that the Arabian prophet has some reparation to demand at the
+hands of Christians. Next, _Horæ Sabaticæ; or an attempt to correct certain
+superstitions and vulgar errors respecting the Sabbath_. Second edition,
+with a large appendix. London, 12mo. 1833. This book was very heterodox at
+the time, but it has furnished material for some of the clergy of our day.
+
+I never could quite make out whether Godfrey Higgins took that system which
+he traced to the Buddhists to have a Divine origin, or to be the result of
+good men's meditations. Himself a strong theist, and believer in a future
+{277} state, one would suppose that he would refer a _universal_ religion,
+spread in different forms over the whole earth from one source, directly to
+the universal Parent. And this I suspect he did, whether he knew it or not.
+The external evidence is balanced. In his preface he says:
+
+"I cannot help smiling when I consider that the priests have objected to
+admit my former book, _The Celtic Druids_, into libraries, because it was
+antichristian; and it has been attacked by Deists, because it was
+superfluously religious. The learned Deist, the Rev. R. Taylor [already
+mentioned], has designated me as the _religious_ Mr. Higgins."
+
+The time will come when some profound historian of literature will make
+himself much clearer on the point than I am.
+
+
+
+ON POPE'S DIPPING NEEDLE.
+
+    The triumphal Chariot of Friction: or a familiar elucidation of the
+    origin of magnetic attraction, &c. &c. By William Pope.[604] London,
+    1829, 4to.
+
+Part of this work is on a dipping-needle of the author's construction. It
+must have been under the impression that a book of naval magnetism was
+proposed, that a great many officers, the Royal Naval Club, etc. lent their
+names to the subscription list. How must they have been surprised to find,
+right opposite to the list of subscribers, the plate presenting "the three
+emphatic letters, J. A. O." And how much more when they saw it set forth
+that if a square be inscribed in a circle, a circle within that, then a
+square again, &c., it is impossible to have more than fourteen circles, let
+the first circle be as large as you please. From this the seven attributes
+of God are unfolded; and further, that all matter was _moral_, until
+Lucifer _churned_ it into _physical_ "as far as the third circle in Deity":
+this Lucifer, called Leviathan in Job, being thus the moving cause of {278}
+chaos. I shall say no more, except that the friction of the air is the
+cause of magnetism.
+
+
+
+    Remarks on the Architecture, Sculpture, and Zodiac of Palmyra; with a
+    Key to the Inscriptions. By B. Prescot.[605] London, 1830, 8vo.
+
+Mr. Prescot gives the signs of the zodiac a Hebrew origin.
+
+
+
+THE JACOTOT METHOD.
+
+    Epitomé de mathématiques. Par F. Jacotot,[606] Avocat. 3ième edition,
+    Paris, 1830, 8vo. (pp. 18).
+
+    Méthode Jacotot. Choix de propositions mathématiques. Par P. Y.
+    Séprés.[607] 2nde édition. Paris, 1830, 8vo. (pp. 82).
+
+Of Jacotot's method, which had some vogue in Paris, the principle was _Tout
+est dans tout_,[608] and the process _Apprendre quelque chose, et à y
+rapporter tout le reste_.[609] The first tract has a proposition in conic
+sections and its preliminaries: the second has twenty exercises, of which
+the first is finding the greatest common measure of two numbers, and the
+last is the motion of a point on a surface, acted on by given forces. This
+is topped up with the problem of sound in a tube, and a slice of Laplace's
+theory of the tides. All to be studied until known by heart, and all the
+rest will come, or at least join on easily when it comes. There is much
+truth in the assertion that new knowledge {279} hooks on easily to a little
+of the old, thoroughly mastered. The day is coming when it will be found
+out that crammed erudition, got up for examinations, does not cast out any
+hooks for more.
+
+
+
+    Lettre à MM. les Membres de l'Académie Royale des Sciences, contenant
+    un développement de la réfutation du système de la gravitation
+    universelle, qui leur a été présentée le 30 août, 1830. Par Félix
+    Passot.[610] Paris, 1830, 8vo.
+
+Works of this sort are less common in France than in England. In France
+there is only the Academy of Sciences to go to: in England there is a
+reading public out of the Royal Society, &c.
+
+
+
+A DISCOURSE ON PROBABILITY.
+
+About 1830 was published, in the _Library of Useful Knowledge_, the tract
+on _Probability_, the joint work of the late Sir John Lubbock[611] and Mr.
+Drinkwater (Bethune).[612] It is one of the best elementary openings of the
+subject. A binder put my name on the outside (the work was anonymous) and
+the consequence was that nothing could drive out of people's heads that it
+was written by me. I do not know how many denials I have made, from a
+passage in one of my own works to a letter in the _Times_: and I am not
+sure that I have succeeded in establishing the truth, even now. I
+accordingly note the fact once more. But as a book has no right here unless
+it contain a paradox--or thing counter to general opinion or practice--I
+will produce two small ones. Sir John Lubbock, with whom lay the executive
+arrangement, had a strong objection to the last word in "Theory of
+Probabilities," he maintained that the singular _probability_, should be
+used; and I hold him quite right.
+
+{280}
+
+The second case was this: My friend Sir J. L., with a large cluster of
+intellectual qualities, and another of social qualities, had one point of
+character which I will not call bad and cannot call good; he never used a
+slang expression. To such a length did he carry his dislike, that he could
+not bear _head_ and _tail_, even in a work on games of chance: so he used
+_obverse_ and _reverse_. I stared when I first saw this: but, to my
+delight, I found that the force of circumstances beat him at last. He was
+obliged to take an example from the race-course, and the name of one of the
+horses was _Bessy Bedlam_! And he did not put her down as _Elizabeth
+Bethlehem_, but forced himself to follow the jockeys.
+
+
+
+    [Almanach Romain sur la Loterie Royale de France, ou les Etrennes
+    nécessaires aux Actionnaires et Receveurs de la dite Loterie. Par M.
+    Menut de St.-Mesmin. Paris, 1830. 12mo.
+
+This book contains all the drawings of the French lottery (two or three,
+each month) from 1758 to 1830. It is intended for those who thought they
+could predict the future drawings from the past: and various sets of
+_sympathetic_ numbers are given to help them. The principle is, that
+anything which has not happened for a long time must be soon to come. At
+_rouge et noir_, for example, when the red has won five times running,
+sagacious gamblers stake on the black, for they think the turn which must
+come at last is nearer than it was. So it is: but observation would have
+shown that if a large number of those cases had been registered which show
+a run of five for the red, the next game would just as often have made the
+run into six as have turned in favor of the black. But the gambling
+reasoner is incorrigible: if he would but take to squaring the circle, what
+a load of misery would be saved. A writer of 1823, who appeared to be
+thoroughly acquainted with the gambling of Paris and London, says that the
+gamesters by {281} profession are haunted by a secret foreboding of their
+future destruction, and seem as if they said to the banker at the table, as
+the gladiators said to the emperor, _Morituri te salutant_.[613]
+
+In the French lottery, five numbers out of ninety were drawn at a time. Any
+person, in any part of the country, might stake any sum upon any event he
+pleased, as that 27 should be drawn; that 42 and 81 should be drawn; that
+42 and 81 should be drawn, and 42 first; and so on up to a _quine
+déterminé_, if he chose, which is betting on five given numbers in a given
+order. Thus, in July, 1821, one of the drawings was
+
+  8   46   16   64   13.
+
+A gambler had actually predicted the five numbers (but not their order),
+and won 131,350 francs on a trifling stake. M. Menut seems to insinuate
+that the hint what numbers to choose was given at his own office. Another
+won 20,852 francs on the quaterne, 8, 16, 46, 64, in this very drawing.
+These gains, of course, were widely advertised: of the multitudes who lost
+nothing was said. The enormous number of those who played is proved to all
+who have studied chances arithmetically by the numbers of simple quaternes
+which were gained: in 1822, fourteen; in 1823, six; in 1824, sixteen; in
+1825, nine, &c.
+
+The paradoxes of what is called chance, or hazard, might themselves make a
+small volume. All the world understands that there is a long run, a general
+average; but great part of the world is surprised that this general average
+should be computed and predicted. There are many remarkable cases of
+verification; and one of them relates to the quadrature of the circle. I
+give some account of this and another. Throw a penny time after time until
+_head_ arrives, which it will do before long: let this be called a _set_.
+Accordingly, H is the smallest set, TH the next smallest, then TTH, &c. For
+abbreviation, let a set in which seven _tails_ {282} occur before _head_
+turns up be T^{7}H. In an immense number of trials of sets, about half will
+be H; about a quarter TH; about an eighth, T^{2}H. Buffon[614] tried 2,048
+sets; and several have followed him. It will tend to illustrate the
+principle if I give all the results; namely, that many trials will with
+moral certainty show an approach--and the greater the greater the number of
+trials--to that average which sober reasoning predicts. In the first column
+is the most likely number of the theory: the next column gives Buffon's
+result; the three next are results obtained from trial by correspondents of
+mine. In each case the number of trials is 2,048.
+
+  H         1,024    1,061    1,048    1,017    1,039
+  TH          512      494      507      547      480
+  T^{2}H      256      232      248      235      267
+  T^{3}H      128      137       99      118      126
+  T^{4}H       64       56       71       72       67
+  T^{5}H       32       29       38       32       33
+  T^{6}H       16       25       17       10       19
+  T^{7}H        8        8        9        9       10
+  T^{8}H        4        6        5        3        3
+  T^{9}H        2                 3        2        4
+  T^{10}H       1                 1        1
+  T^{11}H                         0        1
+  T^{12}H                         0        0
+  T^{13}H       1                 1        0
+  T^{14}H                         0        0
+  T^{15}H                         1        1
+  &c.                             0        0
+            -----    -----    -----    -----    -----
+            2,048    2,048    2,048    2,048    2,048
+
+{283}
+
+In very many trials, then, we may depend upon something like the predicted
+average. Conversely, from many trials we may form a guess at what the
+average will be. Thus, in Buffon's experiment the 2,048 first throws of the
+sets gave _head_ in 1,061 cases: we have a right to infer that in the long
+run something like 1,061 out of 2,048 is the proportion of heads, even
+before we know the reasons for the equality of chance, which tell us that
+1,024 out of 2,048 is the real truth. I now come to the way in which such
+considerations have led to a mode in which mere pitch-and-toss has given a
+more accurate approach to the quadrature of the circle than has been
+reached by some of my paradoxers. What would my friend[615] in No. 14 have
+said to this? The method is as follows: Suppose a planked floor of the
+usual kind, with thin visible seams between the planks. Let there be a thin
+straight rod, or wire, not so long as the breadth of the plank. This rod,
+being tossed up at hazard, will either fall quite clear of the seams, or
+will lay across one seam. Now Buffon, and after him Laplace, proved the
+following: That in the long run the fraction of the whole number of trials
+in which a seam is intersected will be the fraction which twice the length
+of the rod is of the circumference of the circle having the breadth of a
+plank for its diameter. In 1855 Mr. _Ambrose_ Smith, of Aberdeen, made
+3,204 trials with a rod three-fifths of the distance between the planks:
+there were 1,213 clear intersections, and 11 contacts on which it was
+difficult to decide. Divide these contacts equally, and we have 1,218½ to
+3,204 for the ratio of 6 to 5[pi], presuming that the greatness of the
+number of trials gives something near to the final average, or result in
+the long run: this gives [pi] = 3.1553. If all the 11 contacts had been
+treated as intersections, the result would have been {284} [pi] = 3.1412,
+exceedingly near. A pupil of mine made 600 trials with a rod of the length
+between the seams, and got [pi] = 3.137.
+
+This method will hardly be believed until it has been repeated so often
+that "there never could have been any doubt about it."
+
+The first experiment strongly illustrates a truth of the theory, well
+confirmed by practice: whatever can happen will happen if we make trials
+enough. Who would undertake to throw tail eight times running?
+Nevertheless, in the 8,192 sets tail 8 times running occurred 17 times; 9
+times running, 9 times; 10 times running, twice; 11 times and 13 times,
+each once; and 15 times twice.]
+
+
+
+ON CURIOSITIES OF [pi].
+
+1830. The celebrated interminable fraction 3.14159..., which the
+mathematician calls [pi], is the ratio of the circumference to the
+diameter. But it is thousands of things besides. It is constantly turning
+up in mathematics: and if arithmetic and algebra had been studied without
+geometry, [pi] must have come in somehow, though at what stage or under
+what name must have depended upon the casualties of algebraical invention.
+This will readily be seen when it is stated that [pi] is nothing but four
+times the series
+
+  1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...
+
+_ad infinitum_.[616] It would be wonderful if so simple a series {285} had
+but one kind of occurrence. As it is, our trigonometry being founded on the
+circle, [pi] first appears as the ratio stated. If, for instance, a deep
+study of probable fluctuation from average had preceded, [pi] might have
+emerged as a number perfectly indispensable in such problems as: What is
+the chance of the number of aces lying between a million + x and a million
+- x, when six million of throws are made with a die? I have not gone into
+any detail of all those cases in which the paradoxer finds out, by his
+unassisted acumen, that results of mathematical investigation _cannot be_:
+in fact, this discovery is only an accompaniment, though a necessary one,
+of his paradoxical statement of that which _must be_. Logicians are
+beginning to see that the notion of _horse_ is inseparably connected with
+that of _non-horse_: that the first without the second would be no notion
+at all. And it is clear that the positive affirmation of that which
+contradicts mathematical demonstration cannot but be accompanied by a
+declaration, mostly overtly made, that demonstration is false. If the
+mathematician were interested in punishing this indiscretion, he could make
+his denier ridiculous by inventing asserted results which would completely
+take him in.
+
+More than thirty years ago I had a friend, now long gone, who was a
+mathematician, but not of the higher branches: he was, _inter alia_,
+thoroughly up in all that relates to mortality, life assurance, &c. One
+day, explaining to him how it should be ascertained what the chance is of
+the survivors of a large number of persons now alive lying between given
+limits of number at the end of a certain time, I came, of course upon the
+introduction of [pi], which I could only describe as the ratio of the
+circumference of a circle to its diameter. "Oh, my dear friend! that must
+be a delusion; what can the circle have to do with the numbers alive at the
+end of a given time?"--"I cannot demonstrate it to you; but it is
+demonstrated."--"Oh! stuff! I think you can prove anything with your
+differential calculus: figment, {286} depend upon it." I said no more; but,
+a few days afterwards, I went to him and very gravely told him that I had
+discovered the law of human mortality in the Carlisle Table, of which he
+thought very highly. I told him that the law was involved in this
+circumstance. Take the table of expectation of life, choose any age, take
+its expectation and make the nearest integer a new age, do the same with
+that, and so on; begin at what age you like, you are sure to end at the
+place where the age past is equal, or most nearly equal, to the expectation
+to come. "You don't mean that this always happens?"--"Try it." He did try,
+again and again; and found it as I said. "This is, indeed, a curious thing;
+this _is_ a discovery." I might have sent him about trumpeting the law of
+life: but I contented myself with informing him that the same thing would
+happen with any table whatsoever in which the first column goes up and the
+second goes down; and that if a proficient in the higher mathematics chose
+to palm a figment upon him, he could do without the circle: _à corsaire,
+corsaire et demi_,[617] the French proverb says. "Oh!" it was remarked, "I
+see, this was Milne!"[618] It was _not_ Milne: I remember well showing the
+formula to him some time afterwards. He raised no difficulty about [pi]; he
+knew the forms of Laplace's results, and he was much interested. Besides,
+Milne never said stuff! and figment! And he would not have been taken in:
+he would have quietly tried it with the Northampton and all the other
+tables, and would have got at the truth.
+
+{287}
+
+
+
+EUCLID WITHOUT AXIOMS.
+
+    The first book of Euclid's Elements. With alterations and familiar
+    notes. Being an attempt to get rid of axioms altogether; and to
+    establish the theory of parallel lines, without the introduction of any
+    principle not common to other parts of the elements. By a member of the
+    University of Cambridge. Third edition. In usum serenissimæ filiolæ.
+    London, 1830.
+
+The author was Lieut. Col. (now General) Perronet Thompson,[619] the author
+of the "Catechism on the Corn Laws." I reviewed the fourth edition--which
+had the name of "Geometry without Axioms," 1833--in the quarterly _Journal
+of Education_ for January, 1834. Col. Thompson, who then was a contributor
+to--if not editor of--the _Westminster Review_, replied in an article the
+authorship of which could not be mistaken.
+
+Some more attempts upon the problem, by the same author, will be found in
+the sequel. They are all of acute and legitimate speculation; but they do
+not conquer the difficulty in the manner demanded by the conditions of the
+problem. The paradox of parallels does not contribute much to my pages: its
+cases are to be found for the most part in geometrical systems, or in notes
+to them. Most of them consist in the proposal of additional postulates;
+some are attempts to do without any new postulate. Gen. Perronet Thompson,
+whose paradoxes are always constructed on much study of previous writers,
+has collected in the work above named, a budget of attempts, the heads of
+which are in the _Penny_ and _English Cyclopædias_, at "Parallels." He has
+given thirty instances, selected from what he had found.[620]
+
+{288}
+
+Lagrange,[621] in one of the later years of his life, imagined that he had
+overcome the difficulty. He went so far as to write a paper, which he took
+with him to the Institute, and began to read it. But in the first paragraph
+something struck him which he had not observed: he muttered _Il faut que
+j'y songe encore_,[622] and put the paper in his pocket.
+
+
+
+THE LUNAR CAUSTIC JOKE.
+
+The following paragraph appeared in the _Morning Post_, May 4, 1831:
+
+"We understand that although, owing to circumstances with which the public
+are not concerned, Mr. Goulburn[623] declined becoming a candidate for
+University honors, that his scientific attainments are far from
+inconsiderable. He is well known to be the author of an essay in the
+Philosophical Transactions on the accurate rectification of a circular arc,
+and of an investigation of the equation of a lunar caustic--a problem
+likely to become of great use in nautical astronomy."
+
+{289}
+
+This hoax--which would probably have succeeded with any journal--was palmed
+upon the _Morning Post_, which supported Mr. Goulburn, by some Cambridge
+wags who supported Mr. Lubbock, the other candidate for the University of
+Cambridge. Putting on the usual concealment, I may say that I always
+suspected Dr-nkw-t-r B-th-n-[624] of having a share in the matter. The
+skill of the hoax lies in avoiding the words "quadrature of the circle,"
+which all know, and speaking of "the accurate rectification of a circular
+arc," which all do not know for its synonyme. The _Morning Post_ next day
+gave a reproof to hoaxers in general, without referring to any particular
+case. It must be added, that although there are _caustics_ in mathematics,
+there is no _lunar_ caustic.
+
+So far as Mr. Goulburn was concerned, the above was poetic justice. He was
+the minister who, in old time, told a deputation from the Astronomical
+Society that the Government "did not care twopence for all the science in
+the country." There may be some still alive who remember this: I heard it
+from more than one of those who were present, and are now gone. Matters are
+much changed. I was thirty years in office at the Astronomical Society;
+and, to my certain knowledge, every Government of that period, Whig and
+Tory, showed itself ready to help with influence when wanted, and with
+money whenever there was an answer for the House of Commons. The following
+correction subsequently appeared. Referring to the hoax about Mr. Goulburn,
+Messrs. C. H. and Thompson Cooper[625] have corrected an error, by stating
+that the election which gave rise to the hoax was that in which Messrs.
+Goulburn {290} and Yates Peel[626] defeated Lord Palmerston[627] and Mr.
+Cavendish.[628] They add that Mr. Gunning, the well-known Esquire Bedell of
+the University, attributed the hoax to the late Rev. R. Sheepshanks, to
+whom, they state, are also attributed certain clever fictitious
+biographies--of public men, as I understand it--which were palmed upon the
+editor of the _Cambridge Chronicle_, who never suspected their genuineness
+to the day of his death. Being in most confidential intercourse with Mr.
+Sheepshanks,[629] both at the time and all the rest of his life
+(twenty-five years), and never heard him allude to any such things--which
+were not in his line, though he had satirical power of quite another {291}
+kind--I feel satisfied he had nothing to do with them. I may add that
+others, his nearest friends, and also members of his family, never heard
+him allude to these hoaxes as their author, and disbelieve his authorship
+as much as I do myself. I say this not as imputing any blame to the true
+author, such hoaxes being fair election jokes in all time, but merely to
+put the saddle off the wrong horse, and to give one more instance of the
+insecurity of imputed authorship. Had Mr. Sheepshanks ever told me that he
+had perpetrated the hoax, I should have had no hesitation in giving it to
+him. I consider all clever election squibs, free from bitterness and
+personal imputation, as giving the multitude good channels for the vent of
+feelings which but for them would certainly find bad ones.
+
+[But I now suspect that Mr. Babbage[630] had some hand in the hoax. He
+gives it in his "Passages, &c." and is evidently writing from memory, for
+he gives the wrong year. But he has given the paragraph, though not
+accurately, yet with such a recollection of the points as brings suspicion
+of the authorship upon him, perhaps in conjunction with D. B.[631] Both
+were on Cavendish's committee. Mr. Babbage adds, that "late one evening a
+cab drove up in hot haste to the office of the _Morning Post_, delivered
+the copy as coming from Mr. Goulburn's committee, and at the same time
+ordered fifty extra copies of the _Post_ to be sent next morning to their
+committee-room." I think the man--the only one I ever heard of--who knew
+all about the cab and the extra copies must have known more.]
+
+
+
+ON M. DEMONVILLE.
+
+_Demonville._--A Frenchman's Christian name is his own secret, unless there
+be two of the surname. M. Demonville is a very good instance of the
+difference between a {292} French and English discoverer. In England there
+is a public to listen to discoveries in mathematical subjects made without
+mathematics: a public which will hear, and wonder, and think it possible
+that the pretensions of the discoverer have some foundation. The unnoticed
+man may possibly be right: and the old country-town reputation which I once
+heard of, attaching to a man who "had written a book about the signs of the
+zodiac which all the philosophers in London could not answer," is fame as
+far as it goes. Accordingly, we have plenty of discoverers who, even in
+astronomy, pronounce the learned in error because of mathematics. In
+France, beyond the sphere of influence of the Academy of Sciences, there is
+no one to cast a thought upon the matter: all who take the least interest
+repose entire faith in the Institute. Hence the French discoverer turns all
+his thoughts to the Institute, and looks for his only hearing in that
+quarter. He therefore throws no slur upon the means of knowledge, but would
+say, with M. Demonville: "A l'égard de M. Poisson,[632] j'envie loyalement
+la millième partie de ses connaissances mathématiques, pour prouver mon
+systême d'astronomie aux plus incrédules."[633] This system is that the
+only bodies of our system are the earth, the sun, and the moon; all the
+others being illusions, caused by reflection of the sun and moon from the
+ice of the polar regions. In mathematics, addition and subtraction are for
+men; multiplication and division, which are in truth creation and
+destruction, are prerogatives of deity. But _nothing_ multiplied by
+_nothing_ is _one_. M. Demonville obtained an introduction to William the
+Fourth, who desired the opinion of the Royal Society upon his system: the
+{293} answer was very brief. The King was quite right; so was the Society:
+the fault lay with those who advised His Majesty on a matter they knew
+nothing about. The writings of M. Demonville in my possession are as
+follows.[634] The dates--which were only on covers torn off in
+binding--were about 1831-34:
+
+_Petit cours d'astronomie_[635] followed by _Sur l'unité
+mathématique._--_Principes de la physique de la création implicitement
+admis dans la notice sur le tonnerre par M. Arago._--_Question de longitude
+sur mer._[636]--_Vrai système du monde_[637] (pp. 92). Same title, four
+pages, small type. Same title, four pages, addressed to the British
+Association. Same title, four pages, addressed to M. Mathieu. Same title,
+four pages, on M. Bouvard's report.--_Résumé de la physique de la création;
+troisième partie du vrai système du monde._[638]
+
+
+
+PARSEY'S PARADOX.
+
+    The quadrature of the circle discovered, by Arthur Parsey,[639] author
+    of the 'art of miniature painting.' Submitted to the consideration of
+    the Royal Society, on whose protection the author humbly throws
+    himself. London, 1832, 8vo.
+
+Mr. Parsey was an artist, who also made himself conspicuous by a new view
+of perspective. Seeing that the sides of a tower, for instance, would
+appear to meet in a point if the tower were high enough, he thought that
+these sides ought to slope to one another in the picture. On this {294}
+theory he published a small work, of which I have not the title, with a
+Grecian temple in the frontispiece, stated, if I remember rightly, to be
+the first picture which had ever been drawn in true perspective. Of course
+the building looked very Egyptian, with its sloping sides. The answer to
+his notion is easy enough. What is called the picture is not the picture
+from which the mind takes its perception; that picture is on the retina.
+The _intermediate_ picture, as it may be called--the human artist's
+work--is itself seen perspectively. If the tower were so high that the
+sides, though parallel, appeared to meet in a point, the picture must also
+be so high that the _picture-sides_, though parallel, would appear to meet
+in a point. I never saw this answer given, though I have seen and heard the
+remarks of artists on Mr. Parsey's work. I am inclined to think it is
+commonly supposed that the artist's picture is the representation which
+comes before the mind: this is not true; we might as well say the same of
+the object itself. In July 1831, reading an article on squaring the circle,
+and finding that there was a difficulty, he set to work, got a light denied
+to all mathematicians in--some would say through--a crack, and advertised
+in the _Times_ that he had done the trick. He then prepared this work, in
+which, those who read it will see how, he showed that 3.14159... should be
+3.0625. He might have found out his error by _stepping_ a draughtsman's
+circle with the compasses.
+
+Perspective has not had many paradoxes. The only other one I remember is
+that of a writer on perspective, whose name I forget, and whose four pages
+I do not possess. He circulated remarks on my notes on the subject,
+published in the _Athenæum_, in which he denies that the stereographic
+projection is a case of perspective, the reason being that the whole
+hemisphere makes too large a picture for the eye conveniently to grasp at
+once. That is to say, it is no perspective because there is too much
+perspective. {295}
+
+
+
+ON A COUPLE OF GEOMETRIES.
+
+    Principles of Geometry familiarly illustrated. By the Rev. W.
+    Ritchie,[640] LL.D. London, 1833, 12mo.
+
+    A new Exposition of the system of Euclid's Elements, being an attempt
+    to establish his work on a different basis. By Alfred Day,[641] LL.D.
+    London, 1839, 12mo.
+
+These works belong to a small class which have the peculiarity of insisting
+that in the general propositions of geometry a proposition gives its
+converse: that "Every B is A" follows from "Every A is B." Dr. Ritchie
+says, "If it be proved that the equality of two of the angles of a triangle
+depends _essentially_ upon the equality of the opposite sides, it follows
+that the equality of opposite sides depends _essentially_ on the equality
+of the angles." Dr. Day puts it as follows:
+
+"That the converses of Euclid, so called, where no particular limitation is
+specified or implied in the leading proposition, more than in the converse,
+must be necessarily true; for as by the nature of the reasoning the leading
+proposition must be universally true, should the converse be not so, it
+cannot be so universally, but has at least all the exceptions conveyed in
+the leading proposition, and the case is therefore unadapted to geometric
+reasoning; or, what is the same thing, by the very nature of geometric
+reasoning, the particular exceptions to the extended converse must be
+identical with some one or other of the cases under the universal
+affirmative proposition with which we set forth, which is absurd."
+
+{296}
+
+On this I cannot help transferring to my reader the words of the Pacha when
+he orders the bastinado,--May it do you good! A rational study of logic is
+much wanted to show many mathematicians, of all degrees of proficiency,
+that there is nothing in the _reasoning_ of mathematics which differs from
+other reasoning. Dr. Day repeated his argument in _A Treatise on
+Proportion_, London, 1840, 8vo. Dr. Ritchie was a very clear-headed man. He
+published, in 1818, a work on arithmetic, with rational explanations. This
+was too early for such an improvement, and nearly the whole of his
+excellent work was sold as waste paper. His elementary introduction to the
+Differential Calculus was drawn up while he was learning the subject late
+in life. Books of this sort are often very effective on points of
+difficulty.
+
+
+
+NEWTON AGAIN OBLITERATED.
+
+    Letter to the Royal Astronomical Society in refutation of Mistaken
+    Notions held in common, by the Society, and by all the Newtonian
+    philosophers. By Capt. Forman,[642] R.N. Shepton-Mallet, 1833, 8vo.
+
+Capt. Forman wrote against the whole system of gravitation, and got no
+notice. He then wrote to Lord Brougham, Sir J. Herschel, and others I
+suppose, desiring them to procure notice of his books in the reviews: this
+not being acceded to, he wrote (in print) to Lord John Russell[643] to
+complain of their "dishonest" conduct. He then sent a manuscript letter to
+the Astronomical Society, inviting controversy: he was answered by a
+recommendation to study {297} dynamics. The above pamphlet was the
+consequence, in which, calling the Council of the Society "craven dunghill
+cocks," he set them right about their doctrines. From all I can learn, the
+life of a worthy man and a creditable officer was completely embittered by
+his want of power to see that no person is bound in reason to enter into
+controversy with every one who chooses to invite him to the field. This
+mistake is not peculiar to philosophers, whether of orthodoxy or paradoxy;
+a majority of educated persons imply, by their modes of proceeding, that no
+one has a right to any opinion which he is not prepared to defend against
+all comers.
+
+
+
+    David and Goliath, or an attempt to prove that the Newtonian system of
+    Astronomy is directly opposed to the Scriptures. By Wm. Lauder,[644]
+    Sen., Mere, Wilts. Mere, 1833, 12mo.
+
+Newton is Goliath; Mr. Lauder is David. David took five pebbles; Mr. Lauder
+takes five arguments. He expects opposition; for Paul and Jesus both met
+with it.
+
+Mr. Lauder, in his comparison, seems to put himself in the divinely
+inspired class. This would not be a fair inference in every case; but we
+know not what to think when we remember that a tolerable number of
+cyclometers have attributed their knowledge to direct revelation. The works
+of this class are very scarce; I can only mention one or two from
+Montucla.[645] Alphonso Cano de Molina,[646] in the last century, upset all
+Euclid, and squared the circle upon the ruins; he found a follower, Janson,
+who translated him from Spanish into Latin. He declared that he believed in
+Euclid, until God, who humbles the proud, taught him better. One Paul Yvon,
+called from his estate de la Leu, a merchant at Rochelle, supported by his
+book-keeper, M. Pujos, and a {298} Scotchman, John Dunbar, solved the
+problem by divine grace, in a manner which was to convert all Jews,
+Infidels, etc. There seem to have been editions of his work in 1619 and
+1628, and a controversial "Examen" in 1630, by Robert Sara. There was a
+noted discussion, in which Mydorge,[647] Hardy,[648] and others took part
+against de la Leu. I cannot find this name either in Lipenius[649] or
+Murhard,[650] and I should not have known the dates if it had not been for
+one of the keenest bibliographers of any time, my friend Prince Balthasar
+Boncompagni,[651] who is trying to find copies of the works, and has
+managed to find copies of the titles. In 1750, Henry Sullamar, an
+Englishman, squared the circle by the number of the Beast: he published a
+pamphlet every two or three years; but I cannot find any mention of him in
+English works.[652] In France, in 1753, M. de Causans,[653] of the Guards,
+cut a circular piece of turf, squared it, and {299} deduced original sin
+and the Trinity. He found out that the circle was equal to the square in
+which it is inscribed; and he offered a reward for detection of any error,
+and actually deposited 10,000 francs as earnest of 300,000. But the courts
+would not allow any one to recover.
+
+
+
+SIR JOHN HERSCHEL.
+
+1834. In this year Sir John Herschel[654] set up his telescope at
+Feldhausen, Cape of Good Hope. He did much for astronomy, but not much for
+the _Budget of Paradoxes_. He gives me, however, the following story. He
+showed a resident a remarkable blood-red star, and some little time after
+he heard of a sermon preached in those parts in which it was asserted that
+the statements of the Bible must be true, for that Sir J. H. had seen in
+his telescope "the very place where wicked people go."
+
+But red is not always the color. Sir J. Herschel has in his possession a
+letter written to his father, Sir W. H.,[655] dated April 3, 1787, and
+signed "Eliza Cumyns," begging to know if any of the stars be _indigo_ in
+color, "because, if there be, I think it may be deemed a strong conjectural
+illustration of the expression, so often used by our Saviour in the Holy
+Gospels, that 'the disobedient shall be cast into outer darkness'; for as
+the Almighty Being can doubtless confine any of his creatures, whether
+corporeal or spiritual, to what part of his creation He pleases, if
+therefore any of the stars (which are beyond all doubt so many suns to
+other systems) be of so dark a color as that above mentioned, they may be
+calculated to give the most insufferable heat to those dolorous systems
+dependent upon them (and to reprobate spirits placed there), without one
+ray of cheerful light; and may therefore be the scenes of future
+punishments." This letter is addressed to Dr. Heirschel at Slow. Some have
+placed the infernal regions inside the earth, but {300} others have filled
+this internal cavity--for cavity they will have--with refulgent light, and
+made it the abode of the blessed. It is difficult to build without knowing
+the number to be provided for. A friend of mine heard the following (part)
+dialogue between two strong Scotch Calvinists: "Noo! hoo manny d'ye thank
+there are of the alact on the arth at this moment?--Eh! mabbee a
+doozen--Hoot! mon! nae so mony as thot!"
+
+
+
+THE NAUTICAL ALMANAC.
+
+1834. From 1769 to 1834 the _Nautical Almanac_ was published on a plan
+which gradually fell behind what was wanted. In 1834 the new series began,
+under a new superintendent (Lieut. W. S. Stratford).[656] There had been a
+long scientific controversy, which would not be generally intelligible. To
+set some of the points before the reader, I reprint a cutting which I have
+by me. It is from the Nautical _Magazine_, but I did hear that some had an
+idea that it was in the Nautical _Almanac_ itself. It certainly was not,
+and I feel satisfied the Lords of the Admiralty would not have permitted
+the insertion; they are never in advance of their age. The Almanac for 1834
+was published in July 1833.
+
+    THE NEW NAUTICAL ALMANAC--Extract from the 'Primum Mobile,' and 'Milky
+    Way Gazette.' Communicated by AEROLITH.
+
+A meeting of the different bodies composing the Solar System was this day
+held at the Dragon's Tail, for the purpose of taking into consideration the
+alterations and amendments introduced into the New Nautical Almanac. The
+honorable luminaries had been individually summoned {301} by fast-sailing
+comets, and there was a remarkably full attendance. Among the visitors we
+_observed_ several nebulæ, and almost all the stars whose proper motions
+would admit of their being present.
+
+The SUN was unanimously called to the focus. The small planets took the
+oaths, and their places, after a short discussion, in which it was decided
+that the places should be those of the Almanac itself, with leave reserved
+to move for corrections.
+
+Petitions were presented from [alpha] and [delta] Ursæ Minoris, complaining
+of being put on daily duty, and praying for an increase of salary.--Laid on
+the plane of the ecliptic.
+
+The trustees of the eccentricity[657] and inclination funds reported a
+balance of .00001 in the former, and a deficit of 0".009 in the latter.
+This announcement caused considerable surprise, and a committee was moved
+for, to ascertain which of the bodies had more or less than his share.
+After some discussion, in which the small planets offered to consent to a
+reduction, if necessary, the motion was carried.
+
+The FOCAL BODY then rose to address the meeting. He remarked that the
+subject on which they were assembled was one of great importance to the
+routes and revolutions of the heavenly bodies. For himself, though a
+private arrangement between two of his honourable neighbours (here he
+looked hard at the Earth and Venus) had prevented his hitherto paying that
+close attention to the predictions of the Nautical Almanac which he
+declared he always had wished to do; yet he felt consoled by knowing that
+the conductors of that work had every disposition to take his peculiar
+circumstances into consideration. He declared that he had never passed the
+wires of a transit without deeply feeling his inability to adapt himself to
+the present state of his theory; a feeling which he was afraid had
+sometimes caused a slight tremor in his limb. Before {302} he sat down, he
+expressed a hope that honourable luminaries would refrain as much as
+possible from eclipsing each other, or causing mutual perturbations.
+Indeed, he should be very sorry to see any interruption of the harmony of
+the spheres. (Applause.)
+
+The several articles of the New Nautical Almanac were then read over
+without any comment; only we observed that Saturn shook his ring at every
+novelty, and Jupiter gave his belt a hitch, and winked at the satellites at
+page 21 of each month.
+
+The MOON rose to propose a resolution. No one, he said, would be surprised
+at his bringing this matter forward in the way he did, when it was
+considered in how complete and satisfactory a manner his motions were now
+represented. He must own he had trembled when the Lords of the Admiralty
+dissolved the Board of Longitude, but his tranquillity was more than
+reestablished by the adoption of the new system. He did not know but that
+any little assistance he could give in Nautical Astronomy was becoming of
+less and less value every day, owing to the improvement of chronometers.
+But there was one thing, of which nothing could deprive him--he meant the
+regulation of the tides. And, perhaps, when his attention was not occupied
+by more than the latter, he should be able to introduce a little more
+regularity into the phenomena. (Here the honourable luminary gave a sort of
+modest libration, which convulsed the meeting with laughter.) They might
+laugh at his natural infirmity if they pleased, but he could assure them it
+arose only from the necessity he was under, when young, of watching the
+motions of his worthy primary. He then moved a resolution highly laudatory
+of the alterations which appeared in the New Nautical Almanac.
+
+The EARTH rose, to second the motion. His honourable satellite had fully
+expressed his opinions on the subject. He joined his honourable friend in
+the focus in wishing to pay every attention to the Nautical Almanac, but,
+{303} really, when so important an alteration had taken place in his
+magnetic pole[658] (hear) and there might, for aught he knew, be a
+successful attempt to reach his pole of rotation, he thought he could not
+answer for the preservation of the precession in its present state. (Here
+the hon. luminary, scratching his side, exclaimed, as he sat down, "More
+steamboats--confound 'em!")
+
+An honourable satellite (whose name we could not learn) proposed that the
+resolution should be immediately despatched, corrected for refraction, when
+he was called to order by the Focal Body, who reminded him that it was
+contrary to the moving orders of the system to take cognizance of what
+passed inside the atmosphere of any planet.
+
+SATURN and PALLAS rose together. (Cries of "New member!" and the former
+gave way.) The latter, in a long and eloquent speech, praised the
+liberality with which he and his colleagues had at length been relieved
+from astronomical disqualifications. He thought that it was contrary to the
+spirit of the laws of gravitation to exclude any planet from office on
+account of the eccentricity or inclination of his orbit. Honourable
+luminaries need not talk of the want of convergency of his series. What had
+they to do with any private arrangements between him and the general
+equations of the system? (Murmurs from the opposition.) So long as he
+obeyed the laws of motion, to which he had that day taken a solemn oath, he
+would ask, were old planets, which were now so well known that nobody
+trusted them, to....
+
+The FOCAL BODY said he was sorry to break the continuity of the
+proceedings, but he thought that remarks upon character, with a negative
+sign, would introduce {304} differences of too high an order. The
+honourable luminary must eliminate the expression which he had brought out,
+in finite terms, and use smaller inequalities in future. (Hear, hear.)
+
+PALLAS explained, that he was far from meaning to reflect upon the orbital
+character of any planet present. He only meant to protest against being
+judged by any laws but those of gravitation, and the differential calculus:
+he thought it most unjust that astronomers should prevent the small planets
+from being observed, and then reproach them with the imperfections of the
+tables, which were the result of their own narrow-minded policy. (Cheers.)
+
+SATURN thought that, as an old planet, he had not been treated with due
+respect. (Hear, from his satellites.) He had long foretold the wreck of the
+system from the friends of innovation. Why, he might ask, were his
+satellites to be excluded, when small planets, trumpery comets, which could
+not keep their mean distances (cries of oh! oh!), double stars, with
+graphical approximations, and such obscure riff-raff of the heavens (great
+uproar) found room enough. So help him Arithmetic, nothing could come of
+it, but a stoppage of all revolution. His hon. friend in the focus might
+smile, for he would be a gainer by such an event; but as for him (Saturn),
+he had something to lose, and hon. luminaries well knew that, whatever they
+might think _under_ an atmosphere, _above_ it continual revolution was the
+only way of preventing perpetual anarchy. As to the hon. luminary who had
+risen before him, he was not surprised at his remarks, for he had
+invariably observed that he and his colleagues allowed themselves _too much
+latitude_. The stability of the system required that they should be brought
+down, and he, for one, would exert all his powers of attraction to
+accomplish that end. If other bodies would cordially unite with him,
+particularly his noble friend next him, than whom no luminary possessed
+greater weight--
+
+JUPITER rose to order. He conceived his noble friend {305} had no right to
+allude to him in that manner, and was much surprised at his proposal,
+considering the matters which remained in dispute between them. In the
+present state of affairs, he would take care never to be in conjunction
+with his hon. neighbour one moment longer than he could help. (Cries of
+"Order, order, no long inequalities," during which he sat down.)
+
+SATURN proceeded to say, that he did not know till then that a planet with
+a ring could affront one who had only a belt, by proposing mutual
+co-operation. He would now come to the subject under discussion. He should
+think meanly of his hon. colleagues if they consented to bestow their
+approbation upon a mere astronomical production. Had they forgotten that
+they once were considered the arbiters of fate, and the prognosticators of
+man's destiny? What had lost them that proud position? Was it not the
+infernal march of intellect, which, after having turned the earth
+topsy-turvy, was now disturbing the very universe? For himself (others
+might do as they pleased), but he stuck to the venerable Partridge,[659]
+and the Stationers' Company, and trusted that they would outlive infidels
+and anarchists, whether of Astronomical or Diffusion of Knowledge
+Societies. (Cries of oh! oh!)
+
+MARS said he had been told, for he must confess he had not seen the work,
+that the places of the planets were given for Sundays. This, he must be
+allowed to say, was an indecorum he had not expected; and he was convinced
+the Lords of the Admiralty had given no orders to that effect. He hoped
+this point would be considered in the measure which had been introduced in
+another place, and that some {306} one would move that the prohibition
+against travelling on Sundays extend to the heavenly as well as earthly
+bodies.
+
+Several of the stars here declared, that they had been much annoyed by
+being observed on Sunday evenings, during the hours of divine service.
+
+The room was then cleared for a division, but we are unable to state what
+took place. Several comets-at-arms were sent for, and we heard rumors of a
+personal collision having taken place between two luminaries in opposition.
+We were afterwards told that the resolution was carried by a majority, and
+the luminaries elongated at 2 h. 15 m. 33,41 s. sidereal time.
+
+* * * It is reported, but we hope without foundation, that Saturn, and
+several other discontented planets, have accepted an invitation from Sirius
+to join his system, on the most liberal appointments. We believe the report
+to have originated in nothing more than the discovery of the annual
+parallax of Sirius from the orbit of Saturn; but we may safely assure our
+readers that no steps have as yet been taken to open any communication.
+
+We are also happy to state, that there is no truth in the rumor of the laws
+of gravitation being about to be repealed. We have traced this report, and
+find it originated with a gentleman living near Bath (Captain Forman,
+R.N),[660] whose name we forbear to mention.
+
+A great excitement has been observed among the nebulæ, visible to the
+earth's southern hemisphere, particularly among those which have not yet
+been discovered from thence. We are at a loss to conjecture the cause, but
+we shall not fail to report to our readers the news of any movement which
+may take place. (Sir J. Herschel's visit. He could just see this before he
+went out.)
+
+{307}
+
+
+
+WOODLEY'S DIVINE SYSTEM.
+
+    A Treatise on the Divine System of the Universe, by Captain Woodley,
+    R.N.,[661] and as demonstrated by his Universal Time-piece, and
+    universal method of determining a ship's longitude by the apparent true
+    place of the moon; with an introduction refuting the solar system of
+    Copernicus, the Newtonian philosophy, and mathematics. 1834.[662] 8vo.
+
+    Description of the Universal Time-piece. (4pp. 12mo.)
+
+I think this divine system was published several years before, and was
+republished with an introduction in 1834.[663] Capt. Woodley was very sure
+that the earth does not move: he pointed out to me, in a conversation I had
+with him, something--I forget what--in the motion of the Great Bear,
+visible to any eye, which could not possibly be if the earth moved. He was
+exceedingly ignorant, as the following quotation from his account of the
+usual opinion will show:
+
+"The north pole of the Earth's axis deserts, they say, the north star or
+pole of the Heavens, at the rate of 1° in 71¾ years.... The fact is,
+nothing can be more certain than that the Stars have not changed their
+latitudes or declinations _one degree_ in the last 71¾ years."
+
+This is a strong specimen of a class of men by whom all accessible persons
+who have made any name in science are hunted. It is a pity that they cannot
+be admitted into scientific societies, and allowed fairly to state their
+cases, and stand quiet cross-examination, being kept in their answers very
+close to the questions, and the answers written down. I am perfectly
+satisfied that if one meeting in the year were devoted to the hearing of
+those who chose to come forward on such conditions, much good would be
+done. But I strongly suspect few would come forward {308} at first, and
+none in a little while: and I have had some experience of the method I
+recommend, privately tried. Capt. Woodley was proposed, a little after
+1834, as a Fellow of the Astronomical Society; and, not caring whether he
+moved the sun or the earth, or both--I could not have stood _neither_--I
+signed the proposal. I always had a sneaking kindness for paradoxers, such
+a one, perhaps, as Petit André had for his _lambs_, as he called them.
+There was so little feeling against his opinions, that he only failed by a
+fraction of a ball. Had I myself voted, he would have been elected; but
+being engaged in conversation, and not having heard the slightest objection
+to him, I did not think it worth while to cross the room for the purpose. I
+regretted this at the time, but had I known how ignorant he was I should
+not have supported him. Probably those who voted against him knew more of
+his book than I did.
+
+I remember no other instance of exclusion from a scientific society on the
+ground of opinion, even if this be one; of which it may be that ignorance
+had more to do with it than paradoxy. Mr. Frend,[664] a strong
+anti-Newtonian, was a Fellow of the Astronomical Society, and for some
+years in the Council. Lieut. Kerigan[665] was elected to the Royal Society
+at a time when his proposers must have known that his immediate object was
+to put F.R.S. on the title-page of a work against the tides. To give all I
+know, I may add that the editor of some very ignorant bombast about the
+"forehead of the solar sky," who did not know the difference between
+_Bailly_[666] and _Baily_,[667] received hints which induced him to
+withdraw his proposal for election into the Astronomical Society. But this
+was an act of kindness; {309} for if he had seen Mr. Baily in the chair,
+with his head on, he might have been political historian enough to faint
+away.
+
+
+
+    De la formation des Corps. Par Paul Laurent.[668] Nancy, 1834, 8vo.
+
+Atoms, and ether, and ovules or eggs, which are planets, and their eggs,
+which are satellites. These speculators can create worlds, in which they
+cannot be refuted; but none of them dare attack the problem of a grain of
+wheat, and its passage from a seed to a plant, bearing scores of seeds like
+what it was itself.
+
+
+
+ON JOHN FLAMSTEED.
+
+    An account of the Rev. John Flamsteed,[669] the First
+    Astronomer-Royal.... By Francis Baily,[670] Esq. London, 1835, 4to.
+    Supplement, London, 1837, 4to.
+
+My friend Francis Baily was a paradoxer: he brought forward things counter
+to universal opinion. That Newton was impeccable in every point was the
+national creed; and failings of temper and conduct would have been utterly
+disbelieved, if the paradox had not come supported by very unusual
+evidence. Anybody who impeached Newton on existing evidence might as well
+have been squaring the circle, for any attention he would have got. About
+this book I will tell a story. It was published by the Admiralty for
+distribution; and the distribution was entrusted to Mr. Baily. On the eve
+of its appearance, rumors of its extraordinary revelations got about, and
+persons of influence applied to the Admiralty for copies. The Lords were in
+a difficulty: but on looking at the list they saw names, as they {310}
+thought, which were so obscure that they had a right to assume Mr. Baily
+had included persons who had no claim to such a compliment as presentation
+from the Admiralty. The Secretary requested Mr. Baily to call upon him.
+"Mr. Baily, my Lords are inclined to think that some of the persons in this
+list are perhaps not of that note which would justify their Lordships in
+presenting this work."--"To whom does your observation apply, Mr.
+Secretary?"--"Well, now, let us examine the list; let me see;
+now,--now,--now,--come!--here's Gauss[671]--_who's Gauss_?"--"Gauss, Mr.
+Secretary, is the oldest mathematician now living, and is generally thought
+to be the greatest."--"O-o-oh! Well, Mr. Baily, we will see about it, and I
+will write you a letter." The letter expressed their Lordships' perfect
+satisfaction with the list.
+
+There was a controversy about the revelations made in this work; but as the
+eccentric anomalies took no part in it, there is nothing for my purpose.
+The following valentine from Mrs. Flamsteed,[672] which I found among
+Baily's papers, illustrates some of the points:
+
+"3 Astronomers' Row, Paradise: February 14, 1836.
+
+"Dear Sir,--I suppose you hardly expected to receive a letter from me,
+dated from this place; but the truth is, a gentleman from our street was
+appointed guardian angel to the American Treaty, in which there is some
+astronomical question about boundaries. He has got leave to go back to
+fetch some instruments which he left behind, and I take this opportunity of
+making your acquaintance. That America has become a wonderful place since I
+was down among you; you have no idea how grand the fire at New York {311}
+looked up here. Poor dear Mr. Flamsteed does not know I am writing a letter
+to a gentleman on Valentine's day; he is walked out with Sir Isaac Newton
+(they are pretty good friends now, though they do squabble a little
+sometimes) and Sir William Herschel, to see a new nebula. Sir Isaac says he
+can't make out at all how it is managed; and I am sure I cannot help him. I
+never bothered my head about those things down below, and I don't intend to
+begin here.
+
+"I have just received the news of your having written a book about my poor
+dear man. It's a chance that I heard it at all; for the truth is, the
+scientific gentlemen are somehow or other become so wicked, and go so
+little to church, that very few of them are considered fit company for this
+place. If it had not been for Dr. Brinkley,[673] who came here of course, I
+should not have heard about it. He seems a nice man, but is not yet used to
+our ways. As to Mr. Halley,[674] he is of course not here; which is lucky
+for him, for Mr. Flamsteed swore the moment he caught him in a place where
+there are no magistrates, he would make a sacrifice of him to heavenly
+truth. It was very generous in Mr. F. not appearing against Sir Isaac when
+he came up, for I am told that if he had, Sir Isaac would not have been
+allowed to come in at all. I should have been sorry for that, for he is a
+companionable man enough, only holds his head rather higher than he should
+do. I met him the other day walking with Mr. Whiston,[675] and disputing
+about the deluge. 'Well, Mrs. Flamsteed,' says he, 'does old Poke-the-Stars
+understand gravitation yet?' Now you must know that is rather a sore point
+with poor dear Mr. Flamsteed. He says that Sir Isaac is as crochetty about
+the moon as ever; and as to {312} what some people say about what has been
+done since his time, he says he should like to see somebody who knows
+something about it of himself. For it is very singular that none of the
+people who have carried on Sir Isaac's notions have been allowed to come
+here.
+
+"I hope you have not forgotten to tell how badly Sir Isaac used Mr.
+Flamsteed about that book. I have never quite forgiven him; as for Mr.
+Flamsteed, he says that as long as he does not come for observations, he
+does not care about it, and that he will never trust him with any papers
+again as long as he lives. I shall never forget what a rage he came home in
+when Sir Isaac had called him a puppy. He struck the stairs all the way up
+with his crutch, and said puppy at every step, and all the evening, as soon
+as ever a star appeared in the telescope, he called it puppy. I could not
+think what was the matter, and when I asked, he only called me puppy.
+
+"I shall be very glad to see you if you come our way. Pray keep up some
+appearances, and go to church a little. St. Peter is always uncommonly
+civil to astronomers, and indeed to all scientific persons, and never
+bothers them with many questions. If they can make anything out of the
+case, he is sure to let them in. Indeed, he says, it is perfectly out of
+the question expecting a mathematician to be as religious as an apostle,
+but that it is as much as his place is worth to let in the greater number
+of those who come. So try if you cannot manage it, for I am very curious to
+know whether you found all the letters. I remain, dear sir, your faithful
+servant,
+
+"MARGARET FLAMSTEED.
+
+  Francis Baily, Esq.
+
+"P.S. Mr. Flamsteed has come in, and says he left Sir Isaac riding
+cockhorse upon the nebula, and poring over it as if it were a book. He has
+brought in his old acquaintance Ozanam,[676] who says that it was always
+his maxim on {313} earth, that 'il appartient aux docteurs de Sorbonne de
+disputer, au Pape de prononcer, et au mathématicien d'aller en Paradis en
+ligne perpendiculaire.'"[677]
+
+
+
+ON STEVIN.
+
+The Secretary of the Admiralty was completely extinguished. I can recall
+but two instances of demolition as complete, though no doubt there are many
+others. The first is in
+
+  Simon Stevin[678] and M. Dumortier. Nieuport, 1845, 12mo.
+
+M. Dumortier was a member of the Academy of Brussels: there was a
+discussion, I believe, about a national Pantheon for Belgium. The name of
+Stevinus suggested itself as naturally as that of Newton to an Englishman;
+probably no Belgian is better known to foreigners as illustrious in
+science. Stevinus is great in the _Mécanique Analytique_ of Lagrange;[679]
+Stevinus is great in the _Tristram Shandy_ of Sterne. M. Dumortier, who
+believed that not one Belgian in a thousand knew Stevinus, and who
+confesses with ironical shame that he was not the odd man, protested
+against placing the statue of an obscure man in the Pantheon, to give
+foreigners the notion that Belgium could show nothing greater. The work
+above named is a slashing retort: any one who knows the history of science
+ever so little may imagine what a dressing was given, by mere extract from
+foreign writers. The tract is a letter signed J. du Fan, but this is a
+pseudonym of Mr. Van de Weyer.[680] The Academician says Stevinus was a man
+who was not {314} without merit for the time at which he lived: Sir! is the
+answer, he was as much before his own time as you are behind yours. How
+came a man who had never heard of Stevinus to be a member of the Brussels
+Academy?
+
+The second story was told me by Mr. Crabb Robinson,[681] who was long
+connected with the _Times_, and intimately acquainted with Mr. W***.[682]
+When W*** was an undergraduate at Cambridge, taking a walk, he came to a
+stile, on which sat a bumpkin who did not make way for him: the gown in
+that day looked down on the town. "Why do you not make way for a
+gentleman?"--"Eh?"--"Yes, why do you not move? You deserve a good hiding,
+and you shall get it if you don't take care!" The bumpkin raised his
+muscular figure on its feet, patted his menacer on the head, and said, very
+quietly,--"Young man! I'm Cribb."[683] W*** seized the great pugilist's
+hand, and shook it warmly, got him to his own rooms in college, collected
+some friends, and had a symposium which lasted until the large end of the
+small hours.
+
+
+
+FINLEYSON AS A PARADOXER.
+
+    God's Creation of the Universe as it is, in support of the Scriptures.
+    By Mr. Finleyson.[684] Sixth Edition, 1835, 8vo.
+
+{315}
+
+This writer, by his own account, succeeded in delivering the famous Lieut.
+Richard Brothers[685] from the lunatic asylum, and tending him, not as a
+keeper but as a disciple, till he died. Brothers was, by his own account,
+the nephew of the Almighty, and Finleyson ought to have been the nephew of
+Brothers. For Napoleon came to him in a vision, with a broken sword and an
+arrow in his side, beseeching help: Finleyson pulled out the arrow, but
+refused to give a new sword; whereby poor Napoleon, though he got off with
+life, lost the battle of Waterloo. This story was written to the Duke of
+Wellington, ending with "I pulled out the arrow, but left the broken sword.
+Your Grace can supply the rest, and what followed is amply recorded in
+history." The book contains a long account of applications to Government to
+do three things: to pay 2,000l. for care taken of Brothers, to pay 10,000l.
+for discovery of the longitude, and to prohibit the teaching of the
+Newtonian system, which makes God a liar. The successive administrations
+were threatened that they would have to turn out if they refused, which, it
+is remarked, came to pass in every case. I have heard of a joke of Lord
+Macaulay, that the House of Commons must be the Beast of the Revelations,
+since 658 members, with the officers necessary for the action of the House,
+make 666. Macaulay read most things, and the greater part of the rest: so
+that he might be suspected of having appropriated as a joke one of
+Finleyson's serious points--"I wrote Earl Grey[686] upon the 13th of July,
+1831, informing him that his Reform {316} Bill could not be carried, as it
+reduced the members below the present amount of 658, which, with the eight
+principal clerks or officers of the House, make the number 666." But a
+witness has informed me that Macaulay's joke was made in his hearing a
+great many years before the Reform Bill was proposed; in fact, when both
+were students at Cambridge. Earl Grey was, according to Finleyson, a
+descendant of Uriah the Hittite. For a specimen of Lieut. Brothers, this
+book would be worth picking up. Perhaps a specimen of the Lieutenant's
+poetry may be acceptable: Brothers _loquitur_, remember:
+
+ "Jerusalem ! Jerusalem! shall be built again!
+    More rich, more grand then ever;
+  And through it shall Jordan flow!(!)
+    My people's favourite river.
+  There I'll erect a splendid throne,
+    And build on the wasted place;
+  To fulfil my ancient covenant
+    To King David and his race.
+      *    *    *    *    *    *
+ "Euphrates' stream shall flow with ships,
+    And also my wedded Nile;
+  And on my coast shall cities rise,
+    Each one distant but a mile.
+      *    *    *    *    *    *
+ "My friends the Russians on the north
+    With Persees and Arabs round,
+  Do show the limits of my land,
+    Here! Here! then I mark the ground."
+
+
+
+ON THEOLOGICAL PARADOXERS.
+
+Among the paradoxers are some of the theologians who in their own organs of
+the press venture to criticise science. These may hold their ground when
+they confine themselves to the geology of long past periods and to general
+cosmogony: for it is the tug of Greek against Greek; and both sides deal
+much in what is grand when called _hypothesis_, petty when called
+_supposition_. And very often they are not conspicuous when they venture
+upon things within knowledge; {317} wrong, but not quite wrong enough for a
+Budget of Paradoxes. One case, however, is destined to live, as an instance
+of a school which finds writers, editors, and readers. The double stars
+have been seen from the seventeenth century, and diligently observed by
+many from the time of Wm. Herschel, who first devoted continuous attention
+to them. The year 1836 was that of a remarkable triumph of astronomical
+prediction. The theory of gravitation had been applied to the motion of
+binary stars about each other, in elliptic orbits, and in that year the two
+stars of [gamma] Virginis, as had been predicted should happen within a few
+years of that time--for years are small quantities in such long
+revolutions--the two stars came to their nearest: in fact, they appeared to
+be one as much with the telescope as without it. This remarkable
+turning-point of the history of a long and widely-known branch of astronomy
+was followed by an article in the _Church of England Quarterly Review_ for
+April 1837, written against the Useful Knowledge Society. The notion that
+there are any such things as double stars is (p. 460) implied to be
+imposture or delusion, as in the following extract. I suspect that I myself
+am the _Sidrophel_, and that my companion to the maps of the stars, written
+for the Society and published in 1836, is the work to which the writer
+refers:
+
+"We have forgotten the name of that Sidrophel who lately discovered that
+the fixed stars were not single stars, but appear in the heavens like soles
+at Billingsgate, in pairs; while a second astronomer, under the influence
+of that competition in trade which the political economists tell us is so
+advantageous to the public, professes to show us, through his superior
+telescope, that the apparently single stars are really three. Before such
+wondrous mandarins of science, how continually must _homunculi_ like
+ourselves keep in the background, lest we come between the wind and their
+nobility."
+
+If the _homunculus_ who wrote this be still above ground, {318} how
+devoutly must he hope he may be able to keep in the background! But the
+chief blame falls on the editor. The title of the article is:
+
+"The new school of superficial pantology; a speech intended to be delivered
+before a defunct Mechanics' Institute. By Swallow Swift, late M.P. for the
+Borough of Cockney-Cloud, Witsbury: reprinted Balloon Island, Bubble year,
+month _Ventose_. Long live Charlatan!"
+
+As a rule, orthodox theologians should avoid humor, a weapon which all
+history shows to be very difficult to employ in favor of establishment, and
+which, nine times out of ten, leaves its wielder fighting on the side of
+heterodoxy. Theological argument, when not enlivened by bigotry, is seldom
+worse than narcotic: but theological fun, when not covert heresy, is almost
+always sialagogue. The article in question is a craze, which no editor
+should have admitted, except after severe inspection by qualified persons.
+The author of this wit committed a mistake which occurs now and then in old
+satire, the confusion between himself and the party aimed at. He ought to
+be reviewing this fictitious book, but every now and then the article
+becomes the book itself; not by quotation, but by the writer forgetting
+that _he_ is not Mr. Swallow Swift, but his reviewer. In fact he and Mr. S.
+Swift had each had a dose of the _Devil's Elixir_. A novel so called,
+published about forty years ago, proceeds upon a legend of this kind. If
+two parties both drink of the elixir, their identities get curiously
+intermingled; each turns up in the character of the other throughout the
+three volumes, without having his ideas clear as to whether he be himself
+or the other. There is a similar confusion in the answer made to the famous
+_Epistolæ Obscurorum Virorum_:[687] it is headed _Lamentationes Obscurorum
+Virorum_.[688] {319} This is not a retort of the writer, throwing back the
+imputation: the obscure men who had been satirized are themselves made, by
+name, to wince under the disapprobation which the Pope had expressed at the
+satire upon themselves.
+
+Of course the book here reviewed is a transparent forgery. But I do not
+know how often it may have happened that the book, in the journals which
+always put a title at the head, may have been written after the review.
+About the year 1830 a friend showed me the proof of an article of his on
+the malt tax, for the next number of the _Edinburgh Review_. Nothing was
+wanting except the title of the book reviewed; I asked what it was. He sat
+down, and wrote as follows at the head, "The Maltster's Guide (pp. 124),"
+and said that would do as well as anything.
+
+But I myself, it will be remarked, have employed such humor as I can
+command "in favor of establishment." What it is worth I am not to judge; as
+usual in such cases, those who are of my cabal pronounce it good, but
+cyclometers and other paradoxers either call it very poor, or commend it as
+sheer buffoonery. Be it one or the other, I observe that all the effective
+ridicule is, in this subject, on the side of establishment. This is partly
+due to the difficulty of quizzing plain and sober demonstration; but so
+much, if not more, to the ignorance of the paradoxers. For that which
+cannot be _ridiculed_, can be _turned into ridicule_ by those who know how.
+But by the time a person is deep enough in _negative_ quantities, and
+_impossible_ quantities, to be able to satirize them, he is caught, and
+being inclined to become a _user_, shrinks from being an _abuser_. Imagine
+a person with a gift of ridicule, and knowledge enough, trying his hand on
+the junction of the assertions which he will find in various books of
+algebra. First, that a negative quantity has no logarithm; secondly, that a
+{320} negative quantity has no square root; thirdly, that the first
+non-existent is to the second as the circumference of a circle to its
+diameter. One great reason of the allowance of such unsound modes of
+expression is the confidence felt by the writers that [root]-1 and log(-1)
+will make their way, however inaccurately described. I heartily wish that
+the cyclometers had knowledge enough to attack the weak points of
+algebraical diction: they would soon work a beneficial change.[689]
+
+
+
+AN EARLY METEOROLOGIST.
+
+    Recueil de ma vie, mes ouvrages et mes pensées. Par Thomas Ignace Marie
+    Forster.[690] Brussels, 1836, 12mo.
+
+Mr. Forster, an Englishman settled at Bruges, was an observer in many
+subjects, but especially in meteorology. He communicated to the
+Astronomical Society, in 1848, the information that, in the registers kept
+by his grandfather, his father, and himself, beginning in 1767, new moon on
+Saturday was followed, nineteen times out of twenty, by twenty days of rain
+and wind. This statement being published in the _Athenæum_, a cluster of
+correspondents averred that the belief is common among seamen, in all parts
+of the world, and among landsmen too. Some one quoted a distich:
+
+ "Saturday's moon and Sunday's full
+  Never were fine and never _wull_."
+
+{321} Another brought forward:
+
+ "If a Saturday's moon
+  Comes once in seven years it comes too soon."
+
+Mr. Forster did not say he was aware of the proverbial character of the
+phenomenon. He was a very eccentric man. He treated his dogs as friends,
+and buried them with ceremony. He quarrelled with the _curé_ of his parish,
+who remarked that he could not take his dogs to heaven with him. I will go
+nowhere, said he, where I cannot take my dog. He was a sincere Catholic:
+but there is a point beyond which even churches have no influence.
+
+The following is some account of the announcement of 1849. The _Athenæum_
+(Feb. 17), giving an account of the meeting of the Astronomical Society in
+December, 1858, says:
+
+"Dr. Forster of Bruges, who is well known as a meteorologist, made a
+communication at which our readers will stare: he declares that by journals
+of the weather kept by his grandfather, father, and himself, ever since
+1767, to the present time, _whenever the new moon has fallen on a Saturday,
+the following twenty days have been wet and windy_, in nineteen cases out
+of twenty. In spite of our friend Zadkiel[691] and the others who declare
+that we would smother every truth that does not happen to agree with us, we
+are glad to see that the Society had the sense to publish this
+communication, coming, as it does, from a veteran observer, and one whose
+love of truth is undoubted. It must be that the fact is so set down in the
+journals, because Dr. Forster says it: and whether it be only a fact of the
+journals, or one of the heavens, can soon be tried. The new moon of March
+next, falls on _Saturday_ the 24th, at 2 in the afternoon. We shall
+certainly look out."
+
+{322}
+
+The following appeared in the number of March 31:
+
+"The first _Saturday Moon_ since Dr. Forster's announcement came off a week
+ago. We had previously received a number of letters from different
+correspondents--all to the effect that the notion of new moon on Saturday
+bringing wet weather is one of widely extended currency. One correspondent
+(who gives his name) states that he has constantly heard it at sea, and
+among the farmers and peasantry in Scotland, Ireland, and the North of
+England. He proceeds thus: 'Since 1826, nineteen years of the time I have
+spent in a seafaring life. I have constantly observed, though unable to
+account for, the phenomenon. I have also heard the stormy qualities of a
+Saturday's moon remarked by American, French, and Spanish seamen; and,
+still more distant, a Chinese pilot, who was once doing duty on board my
+vessel seemed to be perfectly cognizant of the fact.' So that it seems we
+have, in giving currency to what we only knew as a very curious
+communication from an earnest meteorologist, been repeating what is common
+enough among sailors and farmers. Another correspondent affirms that the
+thing is most devoutly believed in by seamen; who would as soon sail on a
+Friday as be in the Channel after a Saturday moon.--After a tolerable
+course of dry weather, there was some snow, accompanied by wind on Saturday
+last, here in London; there were also heavy louring clouds. Sunday was
+cloudy and cold, with a little rain; Monday was louring, Tuesday unsettled;
+Wednesday quite overclouded, with rain in the morning. The present occasion
+shows only a general change of weather with a tendency towards rain. If Dr.
+Forster's theory be true, it is decidedly one of the minor instances, as
+far as London weather is concerned.--It will take a good deal of evidence
+to make us believe in the omen of a Saturday Moon. But, as we have said of
+the Poughkeepsie Seer, the thing is very curious whether true or false.
+Whence comes this universal proverb--and a hundred others--while the
+meteorological observer {323} cannot, when he puts down a long series of
+results, detect any weather cycles at all? One of our correspondents wrote
+us something of a lecture for encouraging, he said, the notion that _names_
+could influence the weather. He mistakes the question. If there be any
+weather cycles depending on the moon, it is possible that one of them may
+be so related to the week cycle of seven days, as to show recurrences which
+are of the kind stated, or any other. For example, we know that if the new
+moon of March fall on a Saturday in this year, it will most probably fall
+on a Saturday nineteen years hence. This is not connected with the spelling
+of Saturday--but with the connection between the motions of the sun and
+moon. Nothing but the Moon can settle the question--and we are willing to
+wait on her for further information. If the adage be true, then the
+philosopher has missed what lies before his eyes; if false, then the world
+can be led by the nose in spite of the eyes. Both these things happen
+sometimes; and we are willing to take whichever of the two solutions is
+borne out by future facts. In the mean time, we announce the next Saturday
+Moon for the 18th of August."
+
+How many coincidences are required to establish a law of connection? It
+depends on the way in which the mind views the matter in question. Many of
+the paradoxers are quite set up by a very few instances. I will now tell a
+story about myself, and then ask them a question.
+
+So far as instances can prove a law, the following is proved: no failure
+has occurred. Let a clergyman be known to me, whether by personal
+acquaintance or correspondence, or by being frequently brought before me by
+those with whom I am connected in private life: that clergyman does not,
+except in few cases, become a bishop; but _if_ he become a bishop, he is
+sure, first or last, to become an arch-bishop. This has happened in every
+case. As follows:
+
+1. My last schoolmaster, a former Fellow of Oriel, was {324} a very
+intimate college friend of Richard Whately[692], a younger man. Struck by
+his friend's talents, he used to talk of him perpetually, and predict his
+future eminence. Before I was sixteen, and before Whately had even given
+his Bampton Lectures, I was very familiar with his name, and some of his
+sayings. I need not say that he became Archbishop of Dublin.
+
+2. When I was a child, a first cousin of John Bird Sumner[693] married a
+sister of my mother. I cannot remember the time when I first heard his
+name, but it was made very familiar to me. In time he became Bishop of
+Chester, and then, Archbishop of Canterbury. My reader may say that Dr.
+C. R. Sumner,[694] Bishop of Winchester, has just as good a claim: but it
+is not so: those connected with me had more knowledge of Dr. J. B.
+Sumner;[695] and said nothing, or next to nothing, of the other. Rumor says
+that the Bishop of Winchester has _declined_ an Archbishopric: if so, my
+rule is a rule of gradations.
+
+3. Thomas Musgrave,[696] Fellow of Trinity College, Cambridge, was _Dean_
+of the college when I was an undergraduate: this brought me into connection
+with him, he giving impositions for not going to chapel, I writing them out
+according. We had also friendly intercourse in after life; I forgiving, he
+probably forgetting. Honest Tom {325} Musgrave, as he used to be called,
+became Bishop of Hereford, and Archbishop of York.
+
+4. About the time when I went to Cambridge, I heard a great deal about Mr.
+C. T. Longley,[697] of Christchurch, from a cousin of my own of the same
+college, long since deceased, who spoke of him much, and most
+affectionately. Dr. Longley passed from Durham to York, and thence to
+Canterbury. I cannot quite make out the two Archbishoprics; I do not
+remember any other private channel through which the name came to me:
+perhaps Dr. Longley, having two strings to his bow, would have been one
+archbishop if I had never heard of him.
+
+5. When Dr. Wm. Thomson[698] was appointed to the see of Gloucester in
+1861, he and I had been correspondents on the subject of logic--on which we
+had both written--for about fourteen years. On his elevation I wrote to
+him, giving the preceding instances, and informing him that he would
+certainly be an Archbishop. The case was a strong one, and the law acted
+rapidly; for Dr. Thomson's elevation to the see of York took place in 1862.
+
+Here are five cases; and there is no opposing instance. I have searched the
+almanacs since 1828, and can find no instance of a Bishop not finally
+Archbishop of whom I had known through private sources, direct or indirect.
+Now what do my paradoxers say? Is this a pre-established harmony, or a
+chain of coincidences? And how many instances will it require to establish
+a law?[699]
+
+{326}
+
+
+
+THE HERSCHEL HOAX.
+
+    Some account of the great astronomical discoveries lately made by Sir
+    John Herschel at the Cape of Good Hope. Second Edition. London, 12mo.
+    1836.
+
+This is a curious hoax, evidently written by a person versed in astronomy
+and clever at introducing probable circumstances and undesigned
+coincidences.[700] It first appeared in a newspaper. It makes Sir J.
+Herschel discover men, animals, etc. in the moon, of which much detail is
+given. There seems to have been a French edition, the original, and English
+editions in America, whence the work came into Britain: but whether the
+French was published in America or at Paris I do not know. There is no
+doubt that it was produced in the United States, by M. Nicollet,[701] an
+astronomer, once of Paris, and a fugitive of some kind. About him I have
+heard two stories. First that he fled to America with funds not his own,
+and that this book was a mere device to raise the wind. Secondly, that he
+was a protégé of Laplace, and of the Polignac party, and also an outspoken
+man. That after the revolution he was so obnoxious to the republican party
+that he judged it prudent to quit France; which he did in debt, leaving
+money for his creditors, but not enough, with M. Bouvard. In America he
+connected himself with an assurance office. {327} The moon-story was
+written, and sent to France, chiefly with the intention of entrapping M.
+Arago, Nicollet's especial foe, into the belief of it. And those who
+narrate this version of the story wind up by saying that M. Arago _was_
+entrapped, and circulated the wonders through Paris, until a letter from
+Nicollet to M. Bouvard[702] explained the hoax. I have no personal
+knowledge of either story: but as the poor man had to endure the first, it
+is but right that the second should be told with it.
+
+
+
+SOME MORE METEOROLOGY.
+
+    The Weather Almanac for the Year 1838. By P. Murphy,[703] Esq., M.N.S.
+
+By M. N. S. is meant _member of no society._. This almanac bears on the
+title-page two recommendations. The _Morning Post_ calls it one of the most
+important-if-true publications of our generation. The _Times_ says: "If the
+basis of his theory prove sound, and its principles be sanctioned by a more
+extended experience, it is not too much to say that the importance of the
+discovery is equal to that of the longitude." Cautious journalist! Three
+times that of the longitude would have been too little to say. That the
+landsman might predict the weather of all the year, at its beginning, Jack
+would cheerfully give up astronomical longitude--_the_ problem--altogether,
+and fall back on chronometers with the older Ls, lead, latitude, and
+look-out, applied to dead-reckoning. Mr. Murphy attempted to give the
+weather day by day: thus the first seven days of March {328} bore
+Changeable; Rain; Rain; Rain-_wind_; Changeable; Fair; Changeable. To aim
+at such precision as to put a fair day between two changeable ones by
+weather theory was going very near the wind and weather too. Murphy opened
+the year with cold and frost; and the weather did the same. But Murphy,
+opposite to Saturday, January 20, put down "Fair, Probable lowest degree of
+winter temperature." When this Saturday came, it was not merely the
+probably coldest of 1838, but certainly the coldest of many consecutive
+years. Without knowing anything of Murphy, I felt it prudent to cover my
+nose with my glove as I walked the street at eight in the morning. The
+fortune of the Almanac was made. Nobody waited to see whether the future
+would dement the prophecy: the shop was beset in a manner which brought the
+police to keep order; and it was said that the Almanac for 1838 was a gain
+of 5,000l. to the owners. It very soon appeared that this was only a lucky
+hit: the weather-prophet had a modified reputation for a few years; and is
+now no more heard of. A work of his will presently appear in the list.
+
+
+
+THE GREAT PYRAMIDS.
+
+    Letter from Alexandria on the evidence of the practical application of
+    the quadrature of the circle in the great pyramids of Gizeh. By H. C.
+    Agnew,[704] Esq. London, 1838, 4to.
+
+{329}
+
+Mr. Agnew detects proportions which he thinks were suggested by those of
+the circumference and diameter of a circle.
+
+
+
+THE MATHEMATICS OF A CREED.
+
+    The creed of St. Athanasius proved by a mathematical parallel. Before
+    you censure, condemn, or approve; read, examine, and understand. E. B.
+    REVILO.[705] London, 1839, 8vo.
+
+This author really believed himself, and was in earnest. He is not the only
+person who has written nonsense by confounding the mathematical infinite
+(of quantity) with what speculators now more correctly express by the
+unlimited, the unconditioned, or the absolute. This tract is worth
+preserving, as the extreme case of a particular kind. The following is a
+specimen. Infinity being represented by [infinity], as usual, and f, s, g,
+being finite integers, the three Persons are denoted by [infinity]^{f}, (m
+[infinity])^{s}, [infinity]^{g}, the finite fraction m representing human
+nature, as opposed to [infinity]. The clauses of the Creed are then given
+with their mathematical parallels. I extract a couple:
+
+ "But the Godhead of the
+  Father, of the Son, and of
+  the Holy Ghost, is all one:
+  the glory equal, the Majesty
+  co-eternal.
+
+ "It has been shown that
+  [infinity]^f, [infinity]^g, and (m [infinity])^s, together,
+  are but [infinity], and that
+  each is [infinity], and any magnitude
+  in existence represented
+  by [infinity] always was and always
+  will be: for it cannot
+  be made, or destroyed, and
+  yet exists.
+
+{330}
+
+ "Equal to the Father, as
+  touching his Godhead: and
+  inferior  to the  Father,
+  touching his Manhood."
+
+ "(m [infinity])^s is equal to [infinity]^f as
+  touching [infinity], but inferior to
+  [infinity]^f as touching m: because
+  m is not infinite."
+
+I might have passed this over, as beneath even my present subject, but for
+the way in which I became acquainted with it. A bookseller, _not the
+publisher_, handed it to me over his counter: one who had published
+mathematical works. He said, with an air of important communication, Have
+you seen _this_, Sir! In reply, I recommended him to show it to my friend
+Mr.----, for whom he had published mathematics. Educated men, used to books
+and to the converse of learned men, look with mysterious wonder on such
+productions as this: for which reason I have made a quotation which many
+will judge had better have been omitted. But it would have been an
+imposition on the public if I were, omitting this and some other uses of
+the Bible and Common Prayer, to pretend that I had given a true picture of
+my school.
+
+[Since the publication of the above, it has been stated that the author is
+Mr. Oliver Byrne, the author of the _Dual Arithmetic_ mentioned further on:
+E. B. Revilo seems to be obviously a reversal.]
+
+
+
+LOGIC HAS NO PARADOXERS.
+
+    Old and new logic contrasted: being an attempt to elucidate, for
+    ordinary comprehension, how Lord Bacon delivered the human mind from
+    its 2,000 years' enslavement under Aristotle. By Justin Brenan.[706]
+    London, 1839, 12mo.
+
+Logic, though the other exact science, has not had the sort of assailants
+who have clustered about mathematics. There is a sect which disputes the
+utility of logic, but there are no special points, like the quadrature of
+the circle, which {331} excite dispute among those who admit other things.
+The old story about Aristotle having one logic to trammel us, and Bacon
+another to set us free,--always laughed at by those who really knew either
+Aristotle or Bacon,--now begins to be understood by a large section of the
+educated world. The author of this tract connects the old logic with the
+indecencies of the classical writers, and the new with moral purity: he
+appeals to women, who, "when they see plainly the demoralizing tendency of
+syllogistic logic, they will no doubt exert their powerful influence
+against it, and support the Baconian method." This is the only work against
+logic which I can introduce, but it is a rare one, I mean in contents. I
+quote the author's idea of a syllogism:
+
+"The basis of this system is the syllogism. This is a form of couching the
+substance of your argument or investigation into one short line or
+sentence--then corroborating or supporting it in another, and drawing your
+conclusion or proof in a third."
+
+On this definition he gives an example, as follows: "Every sin deserves
+death," the substance of the "argument or investigation." Then comes,
+"Every unlawful wish is a sin," which "corroborates or supports" the
+preceding: and, lastly, "therefore every unlawful wish deserves death,"
+which is the "conclusion or proof." We learn, also, that "sometimes the
+first is called the premises (_sic_), and sometimes the first premiss"; as
+also that "the first is sometimes called the proposition, or subject, or
+affirmative, and the next the predicate, and sometimes the middle term." To
+which is added, with a mark of exclamation at the end, "but in analyzing
+the syllogism, there is a middle term, and a predicate too, in each of the
+lines!" It is clear that Aristotle never enslaved this mind.
+
+I have said that logic has no paradoxers, but I was speaking of old time.
+This science has slept until our own day: Hamilton[707] says there has been
+"no progress made in {332} the _general_ development of the syllogism since
+the time of Aristotle; and in regard to the few _partial_ improvements, the
+professed historians seem altogether ignorant." But in our time, the
+paradoxer, the opponent of common opinion, has appeared in this field. I do
+not refer to Prof. Boole,[708] who is not a _paradoxer_, but a
+_discoverer_: his system could neither oppose nor support common opinion,
+for its grounds were not in the conception of any one. I speak especially
+of two others, who fought like cat and dog: one was dogmatical, the other
+categorical. The first was Hamilton himself--Sir William Hamilton of
+Edinburgh, the metaphysician, not Sir William _Rowan_ Hamilton[709] of
+Dublin, the mathematician, a combination of peculiar genius with
+unprecedented learning, erudite in all he could want except mathematics,
+for which he had no turn, and in which he had not even a schoolboy's
+knowledge, thanks to the Oxford of his younger day. The other was the
+author of this work, so fully described in Hamilton's writings that there
+is no occasion to describe him here. I shall try to say a few words in
+common language about the paradoxers.
+
+Hamilton's great paradox was the _quantification of the predicate_; a
+fearful phrase, easily explained. We all know that when we say "Men are
+animals," a form wholly unquantified in phrase, we speak of _all_ men, but
+not of all animals: it is _some or all_, some may be all for aught the
+proposition says. This some-may-be-all-for-aught-we-say, or _not-none,_ is
+the logician's _some_. One would suppose {333} that "all men are some
+animals," would have been the logical phrase in all time: but the predicate
+never was quantified. The few who alluded to the possibility of such a
+thing found reasons for not adopting it over and above the great reason,
+that Aristotle did not adopt it. For Aristotle never ruled in physics or
+metaphysics _in the old time_ with near so much of absolute sway as he has
+ruled in logic _down to our own time_. The logicians knew that in the
+proposition "all men are animals" the "animal" is not _universal_, but
+_particular_ yet no one dared to say that _all_ men are _some_ animals, and
+to invent the phrase, "_some_ animals are _all_ men" until Hamilton leaped
+the ditch, and not only completed a system of enunciation, but applied it
+to syllogism.
+
+My own case is as peculiar as his: I have proposed to introduce
+mathematical _thought_ into logic to an extent which makes the old stagers
+cry:
+
+ "St. Aristotle! what wild notions!
+  Serve a _ne exeat regno_[710] on him!"
+
+Hard upon twenty years ago, a friend and opponent who stands high in these
+matters, and who is not nearly such a sectary of Aristotle and
+establishment as most, wrote to me as follows: "It is said that next to the
+man who forms the taste of the nation, the greatest genius is the man who
+corrupts it. I mean therefore no disrespect, but very much the reverse,
+when I say that I have hitherto always considered you as a great logical
+heresiarch." Coleridge says he thinks that it was Sir Joshua Reynolds who
+made the remark: which, to copy a bull I once heard, I cannot deny, because
+I was not there when he said it. My friend did not call me to repentance
+and reconciliation with the church: I think he had a guess that I was a
+reprobate sinner. My offences at that time were but small: I went on
+spinning syllogism systems, all alien from the common logic, until I had
+six, the initial letters of which, put together, from the {334} names I
+gave before I saw what they would make, bar all repentance by the words
+
+  RUE NOT!
+
+leaving to the followers of the old school the comfortable option of
+placing the letters thus:
+
+  TRUE? NO!
+
+It should however be stated that the question is not about absolute truth
+or falsehood. No one denies that anything I call an inference is an
+inference: they say that my alterations are _extra-logical_; that they are
+_material_, not _formal_; and that logic is a _formal_ science.
+
+The distinction between material and formal is easily made, where the usual
+perversions are not required. A _form_ is an empty machine, such as "Every
+X is Y"; it may be supplied with _matter_, as in "Every _man_ is _animal_."
+The logicians will not see that their _formal_ proposition, "Every X is Y,"
+is material in three points, the degree of assertion, the quantity of the
+proposition, and the copula. The purely formal proposition is "There is the
+probability [alpha] that X stands in the relation L to Y." The time will
+come when it will be regretted that logic went without paradoxers for two
+thousand years: and when much that has been said on the distinction of form
+and matter will breed jokes.
+
+I give one instance of one mood of each of the systems, in the order of the
+letters first written above.
+
+_Relative._--In this system the formal relation is taken, that is, the
+copula may be any whatever. As a material instance, in which the
+_relations_ are those of consanguinity (of men understood), take the
+following: X is the brother of Y; X is not the uncle of Z; therefore, Z is
+not the child of Y. The discussion of relation, and of the objections to
+the extension, is in the _Cambridge Transactions_, Vol. X, Part 2; a
+crabbed conglomerate.
+
+_Undecided._--In this system one premise, and want of power over another,
+infer want of power over a conclusion. {335} As "Some men are not capable
+of tracing consequences; we cannot be sure that there are beings
+responsible for consequences who are incapable of tracing consequences;
+therefore, we cannot be sure that all men are responsible for the
+consequences of their actions."
+
+_Exemplar._--This, long after it suggested itself to me as a means of
+correcting a defect in Hamilton's system, I saw to be the very system of
+Aristotle himself, though his followers have drifted into another. It makes
+its subject and predicate examples, thus: Any one man is an animal; any one
+animal is a mortal; therefore, any one man is a mortal.
+
+_Numerical._--Suppose 100 Ys to exist: then if 70 Xs be Ys, and 40 Zs be
+Ys, it follows that 10 Xs (at least) are Zs. Hamilton, whose mind could not
+generalize on symbols, saw that the word _most_ would come under this
+system, and admitted, as valid, such a syllogism as "most Ys are Xs; most
+Ys are Zs; therefore, some Xs are Zs."
+
+_Onymatic._--This is the ordinary system much enlarged in propositional
+forms. It is fully discussed in my _Syllabus of Logic_.
+
+_Transposed._--In this syllogism the quantity in one premise is transposed
+into the other. As, some Xs are not Ys; for every X there is a Y which is
+Z; therefore, some Zs are not Xs.
+
+Sir William Hamilton of Edinburgh was one of the best friends and allies I
+ever had. When I first began to publish speculation on this subject, he
+introduced me to the logical world as having plagiarized from him. This
+drew their attention: a mathematician might have written about logic under
+forms which had something of mathematical look long enough before the
+Aristotelians would have troubled themselves with him: as was done by John
+Bernoulli,[711] {336} James Bernoulli,[712] Lambert,[713] and
+Gergonne;[714] who, when our discussion began, were not known even to
+omnilegent Hamilton. He retracted his accusation of _wilful_ theft in a
+manly way when he found it untenable; but on this point he wavered a
+little, and was convinced to the last that I had taken his principle
+unconsciously. He thought I had done the same with Ploucquet[715] and
+Lambert. It was his pet notion that I did not understand the commonest
+principles of logic, that I did not always know the difference between the
+middle term of a syllogism and its conclusion. It went against his grain to
+imagine that a mathematician could be a logician. So long as he took me to
+be riding my own hobby, he laughed consumedly: but when he thought he could
+make out that I was mounted behind Ploucquet or Lambert, the current ran
+thus: "It would indeed have been little short of a miracle had he, ignorant
+even of the common principles of logic, been able of himself to rise to
+generalization so lofty and so accurate as are supposed in the peculiar
+doctrines of both the rival logicians, Lambert and Ploucquet--how useless
+soever these may in practice prove to be." All this has been sufficiently
+discussed elsewhere: "but, masters, remember that I am an ass."
+
+I know that I never saw Lambert's work until after all Hamilton supposed me
+to have taken was written: he himself, who read almost everything, knew
+nothing about it until after I did. I cannot prove what I say about my
+knowledge of Lambert: but the means of doing it may turn up. For, by the
+casual turning up of an old letter, I _have_ {337} found the means of
+clearing myself as to Ploucquet. Hamilton assumed that (unconsciously) I
+took from Ploucquet the notion of a logical notation in which the symbol of
+the conclusion is seen in the joint symbols of the premises. For example,
+in my own fashion I write down ( . ) ( . ), two symbols of premises. By
+these symbols I see that there is a valid conclusion, and that it may be
+written in symbol by striking out the two middle parentheses, which gives (
+. . ) and reading the two negative dots as an affirmative. And so I see in
+( . ) ( . ) that ( ) is the conclusion. This, in full, is the perception
+that "all are either Xs or Ys" and "all are either Ys or Zs" necessitates
+"some Xs are Zs." Now in Ploucquet's book of 1763, is found, "Deleatur in
+præmissis medius; id quod restat indicat conclusionem."[716] In the paper
+in which I explain my symbols--which are altogether different from
+Ploucquet's--there is found "Erase the symbols of the middle term; the
+remaining symbols show the inference." There is very great likeness: and I
+would have excused Hamilton for his notion if he had fairly given reference
+to the part of the book in which his quotation was found. For I had shown
+in my _Formal Logic_ what part of Ploucquet's book I had used: and a fair
+disputant would either have strengthened his point by showing that I had
+been at his part of the book, or allowed me the advantage of it being
+apparent that I had not given evidence of having seen that part of the
+book. My good friend, though an honest man, was sometimes unwilling to
+allow due advantage to controversial opponents.
+
+But to my point. The only work of Ploucquet I ever saw was lent me by my
+friend Dr. Logan,[717] with whom I have often corresponded on logic, etc. I
+chanced (in 1865) {338} to turn up the letter which he sent me (Sept. 12,
+1847) _with the book_. Part of it runs thus: "I congratulate you on your
+success in your logical researches [that is, in asking for the book, I had
+described some results]. Since the reading of your first paper I have been
+satisfied as to the possibility of inventing a logical notation in which
+the rationale of the inference is contained in the symbol, though I never
+attempted to verify it [what I communicated, then, satisfied the writer
+that I had done and communicated what he, from my previous paper, suspected
+to be practicable]. I send you Ploucquet's dissertation....'
+
+It now being manifest that I cannot be souring grapes which have been taken
+from me, I will say what I never said in print before. There is not the
+slightest merit in making the symbols of the premises yield that of the
+conclusion by erasure: _the thing must do itself in every system which
+symbolises quantities_. For in every syllogism (except the inverted
+_Bramantip_ of the Aristotelians) the conclusion is manifest in this way
+without symbols. This _Bramantip_ destroys system in the Aristotelian lot:
+and circumstances which I have pointed out destroy it in Hamilton's own
+collection. But in that enlargement of the reputed Aristotelian system
+which I have called _onymatic_, and in that correction of Hamilton's system
+which I have called _exemplar_, the rule of erasure is universal, and may
+be seen without symbols.
+
+Our first controversy was in 1846. In 1847, in my _Formal Logic_, I gave
+him back a little satire for satire, just to show, as I stated, that I
+could employ ridicule if I pleased. He was so offended with the appendix in
+which this was contained, that he would not accept the copy of the book I
+sent him, but returned it. Copies of controversial works, sent from
+opponent to opponent, are not _presents_, in the usual sense: it was a
+marked success to make him angry enough to forget this. It had some effect
+however: during the rest of his life I wished to avoid provocation; for I
+{339} could not feel sure that excitement might not produce consequences. I
+allowed his slashing account of me in the _Discussions_ to pass unanswered:
+and before that, when he proposed to open a controversy in the _Athenæum_
+upon my second Cambridge paper, I merely deferred the dispute until the
+next edition of my _Formal Logic_. I cannot expect the account in the
+_Discussions_ to amuse an unconcerned reader as much as it amused myself:
+but for a cut-and-thrust, might-and-main, tooth-and-nail, hammer-and-tongs
+assault, I can particularly recommend it. I never knew, until I read it,
+how much I should enjoy a thundering onslought on myself, done with racy
+insolence by a master hand, to whom my good genius had whispered _Ita feri
+ut se sentiat emori_.[718] Since that time I have, as the Irishman said,
+become "dry moulded for want of a bating." Some of my paradoxers have done
+their best: but theirs is mere twopenny--"small swipes," as Peter Peebles
+said. Brandy for heroes! I hope a reviewer or two will have mercy on me,
+and will give me as good discipline as Strafford would have given Hampden
+and his set: "much beholden," said he, "should they be to any one that
+should thoroughly take pains with them in that kind"--meaning _objective_
+flagellation. And I shall be the same to any one who will serve me so--but
+in a literary and periodical sense: my corporeal cuticle is as thin as my
+neighbors'.
+
+Sir W. H. was suffering under local paralysis before our controversy
+commenced: and though his mind was quite unaffected, a retort of as
+downright a character as the attack might have produced serious effect upon
+a person who had shown himself sensible of ridicule. Had a second attack of
+his disorder followed an answer from me, I should have been held to have
+caused it: though, looking at Hamilton's genial love of combat, I strongly
+suspected that a retort in kind
+
+{340}
+
+ "Would cheer his heart, and warm his blood,
+  And make him fight, and do him good."
+
+But I could not venture to risk it. So all I did, in reply to the article
+in the _Discussions_, was to write to him the following note: which, as
+illustrating an etiquette of controversy, I insert.
+
+"I beg to acknowledge and thank you for.... It is necessary that I should
+say a word on my retention of this work, with reference to your return of
+the copy of my _Formal Logic_, which I presented to you on its publication:
+a return made on the ground of your disapproval of the account of our
+controversy which that work contained. According to my view of the subject,
+any one whose dealing with the author of a book is specially attacked in
+it, has a right to expect from the author that part of the book in which
+the attack is made, together with so much of the remaining part as is
+fairly context. And I hold that the acceptance by the party assailed of
+such work or part of a work does not imply any amount of approval of the
+contents, or of want of disapproval. On this principle (though I am not
+prepared to add the word _alone_) I forwarded to you the whole of my work
+on _Formal Logic_ and my second Cambridge Memoir. And on this principle I
+should have held you wanting in due regard to my literary rights if you had
+not forwarded to me your asterisked pages, with all else that was necessary
+to a full understanding of their scope and meaning, so far as the contents
+of the book would furnish it. For the remaining portion, which it would be
+a hundred pities to separate from the pages in which I am directly
+concerned, I am your debtor on another principle; and shall be glad to
+remain so if you will allow me to make a feint of balancing the account by
+the offer of two small works on subjects as little connected with our
+discussion as the _Epistolæ Obscurorum Virorum_, or the Lutheran dispute. I
+trust that by accepting my _Opuscula_ you will enable me to avoid the {341}
+use of the knife, and leave me to cut you up with the pen as occasion shall
+serve, I remain, etc. (April 21, 1852)."
+
+I received polite thanks, but not a word about the body of the letter: my
+argument, I suppose, was admitted.
+
+
+
+SOME DOGGEREL AND COUNTER DOGGEREL.
+
+I find among my miscellaneous papers the following _jeu d'esprit_, or _jeu
+de bêtise_,[719] whichever the reader pleases--I care not--intended, before
+I saw ground for abstaining, to have, as the phrase is, come in somehow. I
+think I could manage to bring anything into anything: certainly into a
+Budget of Paradoxes. Sir W. H. rather piqued himself upon some caniculars,
+or doggerel verses, which he had put together _in memoriam_ [_technicam_]
+of the way in which A E I O are used in logic: he added U, Y, for the
+addition of _meet_, etc., to the system. I took the liberty of concocting
+some counter-doggerel, just to show that a mathematician may have
+architectonic power as well as a metaphysician.
+
+
+
+          DOGGEREL.
+      BY SIR W.  HAMILTON.
+  A it affirms of _this_, _these_, _all_,
+    Whilst E denies of _any_;
+  I it affirms (whilst O denies)
+    Of some (or few, or many).
+
+  Thus A affirms, as E denies,
+    And definitely either;
+  Thus I affirms, as O denies,
+    And definitely neither.
+
+  A half, left semidefinite,
+    Is worthy of its score;
+  U, then, affirms, as Y denies,
+    This, neither less nor more.
+
+  Indefinito-definites,
+    I, UI, YO, last we come;
+  {342}
+  And this affirms, as that denies
+    Of _more_, _most_ (_half_, _plus_, _some_).
+
+    COUNTER DOGGEREL.
+      BY PROF. DE MORGAN.
+          (1847.)
+  Great A affirms of all;
+    Sir William does so too:
+  When the subject is "my suspicion,"
+    And the predicate "must be true."
+
+  Great E denies of all;
+    Sir William of all but one:
+  When he speaks about this present time,
+    And of those who in logic have done.
+
+  Great I takes up but _some_;
+    Sir William! my dear soul!
+  Why then in all your writings,
+    Does "Great I" fill[720] the whole!
+
+  Great O says some are not;
+    Sir William's readers catch,
+  That some (modern) Athens is not without
+    An Aristotle to match.
+
+ "A half, left semi-definite,
+    Is worthy of its score:"
+  This looked very much like balderdash,
+    And neither less nor more.
+
+  It puzzled me like anything;
+    In fact, it puzzled me worse:
+  Isn't schoolman's logic hard enough,
+    Without being in Sibyl's verse?
+
+  {343}
+  At last, thinks I, 'tis German;
+    And I'll try it with some beer!
+  The landlord asked what bothered me so,
+    And at once he made it clear.
+
+  It's _half-and-half_, the gentleman means;
+    Don't you see he talks of _score_?
+  That's the bit of memorandum
+    That we chalk behind the door.
+
+  _Semi-definite_'s outlandish;
+    But I see, in half a squint,
+  That he speaks of the lubbers who call for a quart,
+    When they can't manage more than a pint.
+
+  Now I'll read it into English,
+    And then you'll answer me this:
+  If it isn't good logic all the world round,
+    I should like to know what is?
+
+  When you call for a pot of half-and-half,
+    If you're lost to sense of shame,
+  You may leave it _semi-definite_,
+    But you pay for it all just the same.
+      *    *    *    *    *    *
+
+I am unspeakably comforted when I look over the above in remembering that
+the question is not whether it be Pindaric or Horatian, but whether the
+copy be as good as the original. And I say it is: and will take no denial.
+
+Long live--long will live--the glad memory of William Hamilton, Good,
+Learned, Acute, and Disputatious! He fought upon principle: the motto of
+his book is:
+
+ "Truth, like a torch, the more it's shook it shines."
+
+There is something in this; but metaphors, like puddings, quarrels, rivers,
+and arguments, always have two sides to them. For instance,
+
+ "Truth, like a torch, the more it's shook it shines;
+    But those who want to use it, hold it steady.
+  They shake the flame who like a glare to gaze at,
+    They keep it still who want a light to see by."
+
+{344}
+
+
+
+ANOTHER THEORY OF PARALLELS.
+
+    Theory of Parallels. The proof of Euclid's axiom looked for in the
+    properties of the Equiangular Spiral. By Lieut-Col. G. Perronet
+    Thompson.[721] The same, second edition, revised and corrected. The
+    same, third edition, shortened, and freed from dependence on the theory
+    of limits. The same, fourth edition, ditto, ditto. All London, 1840,
+    8vo.
+
+To explain these editions it should be noted that General Thompson rapidly
+modified his notions, and republished his tracts accordingly.
+
+
+
+SOME PRIMITIVE DARWINISM.
+
+    Vestiges of the Natural History of Creation.[722] London, 1840, 12mo.
+
+This is the first edition of this celebrated work. Its form is a case of
+the theory: the book is an undeniable duodecimo, but the size of its paper
+gives it the look of not the smallest of octavos. Does not this illustrate
+the law of development, the gradation of families, the transference of
+species, and so on? If so, I claim the discovery of this esoteric testimony
+of the book to its own contents; I defy any one to point out the reviewer
+who has mentioned it. The work itself is described by its author as "the
+first attempt to connect the natural sciences into a history of creation."
+The attempt was commenced, and has been carried on, both with marked
+talent, and will be continued. Great advantage will result: at the worst we
+are but in the alchemy of some new chemistry, or the astrology of some new
+astronomy. Perhaps it would be as well not to be too sure on the matter,
+until we have an antidote to possible consequences as exhibited under
+another theory, on which {345} it is as reasonable to speculate as on that
+of the _Vestiges_. I met long ago with a splendid player on the guitar, who
+assured me, and was confirmed by his friends, that he _never practised_,
+except in thought, and did not possess an instrument: he kept his fingers
+acting in his mind, until they got their habits; and thus he learnt the
+most difficult novelties of execution. Now what if this should be a minor
+segment of a higher law? What if, by constantly thinking of ourselves as
+descended from primeval monkeys, we should--if it be true--actually _get
+our tails again_? What if the first man who was detected with such an
+appendage should be obliged to confess himself the author of the
+_Vestiges_--a person yet unknown--who would naturally get the start of his
+species by having had the earliest habit of thinking on the matter? I
+confess I never hear a man of note talk fluently about it without a curious
+glance at his proportions, to see whether there may be ground to conjecture
+that he may have more of "mortal coil" than others, in anaxyridical
+concealment. I do not feel sure that even a paternal love for his theory
+would induce him, in the case I am supposing, to exhibit himself at the
+British Association,
+
+  With a hole behind which his tail peeped through.
+
+The first sentence of this book (1840) is a cast of the log, which shows
+our rate of progress. "It is familiar knowledge that the earth which we
+inhabit is a globe of somewhat less than 8,000 miles in diameter, being one
+of a series of eleven which revolve at different distances around the sun."
+The _eleven_! Not to mention the Iscariot which Le Verrier and Adams
+calculated into existence, there is more than a septuagint of _new_
+planetoids.
+
+
+
+ON RELIGIOUS INSURANCE.
+
+    The Constitution and Rules of the Ancient and Universal 'Benefit
+    Society' established by Jesus Christ, exhibited, and its advantages and
+    claims maintained, against all Modern and {346} merely Human
+    Institutions of the kind: A Letter very respectfully addressed to the
+    Rev. James Everett,[723] and occasioned by certain remarks made by him,
+    in a speech to the Members of the 'Wesleyan Centenary Institute'
+    Benefit Society. Dated York, Dec. 7, 1840. By Thomas Smith.[724] 12mo,
+    (pp. 8.)
+
+The Wesleyan minister addressed had advocated provision against old age,
+etc.: the writer declares all _private_ provision un-Christian. After
+decent maintenance and relief of family claims of indigence, he holds that
+all the rest is to go to the "Benefit Society," of which he draws up the
+rules, in technical form, with chapters of "Officers," "Contributors" etc.,
+from the Acts of the Apostles, etc., and some of the early Fathers. He
+holds that a Christian may not "make a _private_ provision against the
+contingencies of the future": and that the great "Benefit Society" is the
+divinely-ordained recipient of all the surplus of his income; capital,
+beyond what is necessary for business, he is to have none. A real good
+speculator shuts his eyes by instinct, when opening them would not serve
+the purpose: he has the vizor of the Irish fairy tale, which fell of itself
+over the eyes of the wearer the moment he turned them upon the enchanted
+light which would have destroyed him if he had caught sight of it. "Whiles
+it remained, was it not thine own? and after it was sold, was it (the
+purchase-money) not in thine own power?" would have been awkward to quote,
+and accordingly nothing is stated except the well-known result, which is
+rule 3, cap. 5, "Prevention of Abuses." By putting his principles together,
+the author can be made, logically, to mean that the successors of the
+apostles should put to death all contributors who are detected in not
+paying their full premiums.
+
+{347}
+
+I have known one or two cases in which policy-holders have surrendered
+their policies through having arrived at a conviction that direct provision
+is unlawful. So far as I could make it out, these parties did not think it
+unlawful to lay by out of income, except when this was done in a manner
+which involved calculation of death-chances. It is singular they did not
+see that the entrance of chance of death was the entrance of the very
+principle of the benefit society described in the Acts of the Apostles. The
+family of the one who died young received more in proportion to _premiums_
+paid than the family of one who died old. Every one who understands life
+assurance sees that--_bonus_ apart--the difference between an assurance
+office and a savings bank consists in the adoption, _pro tanto_, of the
+principle of community of goods. In the original constitution of the oldest
+assurance office, the _Amicable Society_, the plan with which they started
+was nothing but this: persons of all ages under forty-five paid one common
+premium, and the proceeds were divided among the representatives of those
+who died within the year.
+
+
+
+THE TWO OLD PARADOXES AGAIN.
+
+[I omitted from its proper place a manuscript quadrature (3.1416 exactly)
+addressed to an eminent mathematician, dated in 1842 from the debtor's ward
+of a country gaol. The unfortunate speculator says, "I have labored many
+years to find the precise ratio." I have heard of several cases in which
+squaring the circle has produced an inability to square accounts. I remind
+those who feel a kind of inspiration to employ native genius upon
+difficulties, without gradual progression from elements, that the call is
+one which becomes stronger and stronger, and may lead, as it has led, to
+abandonment of the duties of life, and all the consequences.] {348}
+
+
+
+    1842. Provisional Prospectus of the Double Acting Rotary Engine
+    Company. Also Mechanic's Magazine, March 26, 1842.
+
+Perpetual motion by a drum with one vertical half in mercury, the other in
+a vacuum: the drum, I suppose, working round forever to find an easy
+position. Steam to be superseded: steam and electricity convulsions of
+nature never intended by Providence for the use of man. The price of the
+present engines, as old iron, will buy new engines that will work without
+fuel and at no expense. Guaranteed by the Count de Predaval,[725] the
+discoverer. I was to have been a Director, but my name got no further than
+ink, and not so far as official notification of the honor, partly owing to
+my having communicated to the _Mechanic's Magazine_ information privately
+given to me, which gave premature publicity, and knocked up the plan.
+
+
+
+    An Exposition of the Nature, Force, Action, and other properties of
+    Gravitation on the Planets. London, 1842, 12mo.
+
+    An Investigation of the principles of the Rules for determining the
+    Measures of the Areas and Circumferences of Circular Plane Surfaces ...
+    London, 1844, 8vo.
+
+These are anonymous; but the author (whom I believe to be Mr. Denison,[726]
+presently noted) is described as author of a new system of mathematics, and
+also of mechanics. He had need have both, for he shows that the line which
+has a square equal to a given circle, has a cube equal to the sphere on the
+same diameter: that is, in old mathematics, the diameter is to the
+circumference as 9 to 16! Again, admitting that the velocities of planets
+in circular orbits are inversely as the square roots of their distances,
+that is, admitting Kepler's law, he manages to prove that gravitation is
+inversely as the square _root_ of the distance: and suspects magnetism of
+doing the difference between this and Newton's law. {349} Magnetism and
+electricity are, in physics, the member of parliament and the cabman--at
+every man's bidding, as Henry Warburton[727] said.
+
+The above is an outrageous quadrature. In the preceding year, 1841, was
+published what I suppose at first to be a Maori quadrature, by Maccook. But
+I get it from a cutting out of some French periodical, and I incline to
+think that it must be by a Mr. M^cCook. He makes [pi] to be 2 +
+2[root](8[root]2 - 11).
+
+
+
+THE DUPLICATION PROBLEM.
+
+    Refutation of a Pamphlet written by the Rev. John Mackey, R.C.P.,[728]
+    entitled "A method of making a cube double of a cube, founded on the
+    principles of elementary geometry," wherein his principles are proved
+    erroneous, and the required solution not yet obtained. By Robert
+    Murphy.[729] Mallow, 1824, 12mo.
+
+This refutation was the production of an Irish boy of eighteen years old,
+self-educated in mathematics, the son of a shoemaker at Mallow. He died in
+1843, leaving a name which is well known among mathematicians. His works on
+the theory of equations and on electricity, and his papers in the
+_Cambridge Transactions_, are all of high genius. The only account of him
+which I know of is that which I wrote for the _Supplement_ of the _Penny
+Cyclopædia_. He was thrown by his talents into a good income at Cambridge,
+with no social training except penury, and very little intellectual
+training except mathematics. He fell into dissipation, and his scientific
+career was almost arrested: but he had great good in him, to my knowledge.
+A sentence in {350} a letter from the late Dean Peacock[730] to me--giving
+some advice about the means of serving Murphy--sets out the old case:
+"Murphy is a man whose _special_ education is in advance of his _general_;
+and such men are almost always difficult subjects to manage." This article
+having been omitted in its proper place, I put it at 1843, the date of
+Murphy's death.
+
+
+
+A NEW VALUE OF [pi].
+
+    The Invisible Universe disclosed; or, the real Plan and Government of
+    the Universe. By Henry Coleman Johnson, Esq. London, 1843, 8vo.
+
+The book opens abruptly with:
+
+"First demonstration. Concerning the centre: showing that, because the
+centre is an innermost point at an equal distance between two extreme
+points of a right line, and from every two relative and opposite
+intermediate points, it is composed of the two extreme internal points of
+each half of the line; each extreme internal point attracting towards
+itself all parts of that half to which it belongs...."
+
+Of course the circle is squared: and the circumference is 3-1/21 diameters.
+
+
+
+SOME MODERN ASTROLOGY.
+
+    Combination of the Zodiacal and Cometical Systems. Printed for the
+    London Society, Exeter Hall. Price Sixpence. (n. d. 1843.)
+
+What this London Society was, or the "combination," did not appear. There
+was a remarkable comet in 1843, the tail of which was at first confounded
+with what is called the _zodiacal light_. This nicely-printed little tract,
+evidently got up with less care for expense than is usual in such works,
+brings together all the announcements of the astronomers, and adds a short
+head and tail piece, which I shall quote entire. As the announcements are
+very ordinary {351} astronomy, the reader will be able to detect, if
+detection be possible, what is the meaning and force of the "Combination of
+the Zodiacal and Cometical Systems":
+
+"_Premonition._ It has pleased the AUTHOR _of_ CREATION to cause (to His
+_human and reasoning_ Creatures of this generation, by a '_combined_'
+appearance in His _Zodiacal_ and _Cometical_ system) a '_warning Crisis_'
+of universal concernment to this our GLOBE. It is this '_Crisis_' that has
+so generally 'ROUSED' at this moment the '_nations throughout the Earth_'
+that no equal interest has ever before been excited by MAN; unless it be in
+that caused by the 'PAGAN-TEMPLE IN ROME,' which is recorded by the elder
+Pliny, '_Nat. Hist._' i. 23. iii. 3. HARDOUIN."
+
+After the accounts given by the unperceiving astronomers, comes what
+follows:
+
+"Such has been (_hitherto_) the only object discerned by the '_Wise of this
+World_,' in this _twofold union_ of the '_Zodiacal_' and '_Cometical_'
+systems: yet it is nevertheless a most '_Thrilling Warning_,' to _all_ the
+inhabitants of this precarious and transitory EARTH. We have no authorized
+intimation or reasonable prospective contemplation, of '_current time_'
+beyond a year 1860, of the present century; or rather, except '_the
+interval which may now remain from the present year 1843, to a year 1860_'
+([Greek: hêmeras HEXÊKONTA]--'_threescore or sixty days_'--'_I have
+appointed each_ "DAY" _for a_ "YEAR,"' _Ezek._ iv. 6): and we know, from
+our '_common experience_,' how speedily such a measure of time will pass
+away.
+
+"No words can be '_more explicit_' than these of OUR BLESSED LORD: viz.
+'THIS GOSPEL _of the Kingdom shall be preached in_ ALL the EARTH, _for a
+Witness to_ ALL NATIONS; AND THEN, _shall the_ END COME.' The '_next 18
+years_' must therefore supply the interval of the '_special Episcopal
+forerunners_.'
+
+(Matt. xxiv. 14.)
+
+"See the 'JEWISH INTELLIGENCER' of the present month (_April_), p. 153, for
+the '_Debates in Parliament_,' respecting {352} the BISHOP OF JERUSALEM,
+_viz._ Dr. Bowring,[731] Mr. Hume,[732] Sir R. Inglis,[733] Sir R.
+Peel,[734] Viscount Palmerston.[735]"
+
+I have quoted this at length, to show the awful threats which were
+published at a time of some little excitement about the phenomenon, under
+the name of the _London Society_. The assumption of a corporate appearance
+is a very unfair trick: and there are junctures at which harm might be done
+by it.
+
+
+
+THE NUMBER OF THE BEAST.
+
+    _Wealth_ the name and number of the Beast, 666, in the Book of
+    Revelation. [by John Taylor.[736]] London, 1844, 8vo.
+
+Whether Junius or the Beast be the more difficult to identify, must be
+referred to Mr. Taylor, the only person who has attempted both. His cogent
+argument on the political secret is not unworthily matched in his treatment
+of the theological riddle. He sees the solution in [Greek: euporia], which
+occurs in the Acts of the Apostles as the word for wealth in one of its
+most disgusting forms, and makes 666 in the most straightforward way. This
+explanation has as good a chance as any other. The work contains a general
+{353} attempt at explanation of the Apocalypse, and some history of opinion
+on the subject. It has not the prolixity which is so common a fault of
+apocalyptic commentators.
+
+
+
+    A practical Treatise on Eclipses ... with remarks on the anomalies of
+    the present Theory of the Tides. By T. Kerigan,[737] F.R.S. 1844, 8vo.
+
+Containing also a refutation of the theory of the tides, and afterwards
+increased by a supplement, "Additional facts and arguments against the
+theory of the tides," in answer to a short notice in the _Athenæum_
+journal. Mr. Kerigan was a lieutenant in the Navy: he obtained admission to
+the Royal Society just before the publication of his book.
+
+
+
+    A new theory of Gravitation. By Joseph Denison,[738] Esq. London, 1844,
+    12mo.
+
+    Commentaries on the Principia. By the author of 'A new theory of
+    Gravitation.' London, 1846, 8vo.
+
+Honor to the speculator who can be put in his proper place by one sentence,
+be that place where it may.
+
+"But we have shown that the velocities are inversely as the square roots of
+the mean distances from the sun; wherefore, by equality of ratios, the
+forces of the sun's gravitation upon them are also inversely as the square
+roots of their distances from the sun."
+
+
+
+EASTER DAY PARADOXERS.
+
+In the years 1818 and 1845 the full moon fell on Easter Day, having been
+particularly directed to fall before it in the act for the change of style
+and in the English missals and prayer-books of all time: perhaps it would
+be more correct to say that Easter Day was directed to fall after the full
+moon; "but the principle is the same." No explanation was given in 1818,
+but Easter was kept by the tables, {354} in defiance of the rule, and of
+several protests. A chronological panic was beginning in December 1844,
+which was stopped by the _Times_ newspaper printing extracts from an
+article of mine in the _Companion to the Almanac_ for 1845, which had then
+just appeared. No one had guessed the true reason, which is that the thing
+called the moon in the Gregorian Calendar is not the moon of the heavens,
+but a fictitious imitation put wrong on purpose, as will presently appear,
+partly to keep Easter out of the way of the Jews' Passover, partly for
+convenience of calculation. The apparent error happens but rarely; and all
+the work will perhaps have to be gone over next time. I now give two bits
+of paradox.
+
+Some theologians were angry at this explanation. A review called the
+_Christian Observer_ (of which Christianity I do not know) got up a
+crushing article against me. I did not look at it, feeling sure that an
+article on such a subject which appeared on January 1, 1845, against a
+publication made in December 1844, must be a second-hand job. But some
+years afterwards (Sept. 10, 1850), the reviews, etc. having been just
+placed at the disposal of readers in the _old_ reading-room of the Museum,
+I made a tour of inspection, came upon my critic on his perch, and took a
+look at him. I was very glad to remember this, for, though expecting only
+second-hand, yet even of this there is good and bad; and I expected to find
+some hints in the good second-hand of a respectable clerical publication. I
+read on, therefore, attentively, but not long: I soon came to the
+information that some additions to Delambre's[739] statement of the rule
+for finding Easter, belonging to distant years, had been made by Sir Harris
+Nicolas![740] Now as I myself furnished my friend Sir H. N. with Delambre's
+digest of {355} Clavius's[741] rule, which I translated out of algebra into
+common language for the purpose, I was pretty sure this was the ignorant
+reading of a person to whom Sir H. N. was the highest _arithmetical_
+authority on the subject. A person pretending to chronology, without being
+able to distinguish the historical points--so clearly as they stand out--in
+which Sir H. N. speaks with authority, from the arithmetical points of pure
+reckoning on which he does not pretend to do more than directly repeat
+others, must be as fit to talk about the construction of Easter Tables as
+the Spanish are to talk French. I need hardly say that the additions for
+distant years are as much from Clavius as the rest: my reviewer was not
+deep enough in his subject to know that Clavius made and published, from
+his rules, the full table up to A.D. 5000, for all the movable feasts of
+every year! I gave only a glance at the rest: I found I was either knave or
+fool, with a leaning to the second opinion; and I came away satisfied that
+my critic was either ignoramus or novice, with a leaning to the first. I
+afterwards found an ambiguity of expression in Sir H. N.'s account--whether
+his or mine I could not tell--which might mislead a novice or content an
+ignoramus, but would have been properly read or further inquired into by a
+competent person.
+
+The second case is this. Shortly after the publication of my article, a
+gentleman called at my house, and, finding I was not at home, sent up his
+card--with a stylish west-end club on it--to my wife, begging for a few
+words on pressing business. With many well-expressed apologies, he stated
+that he had been alarmed by hearing that Prof. De M. had an intention of
+altering Easter next year. Mrs. De M. kept her countenance, and assured him
+that I had no such intention, and further, that she greatly doubted my
+having the power to do it. Was she quite sure? his authority was very good:
+fresh assurances given. He was greatly relieved, for he had some horses
+training for after Easter, which {356} would not be ready to run if it were
+altered the wrong way. A doubt comes over him: would Mrs. De M., in the
+event of her being mistaken, give him the very earliest information?
+Promise given; profusion of thanks; more apologies; and departure.
+
+Now, candid reader!--or uncandid either!--which most deserves to be laughed
+at? A public instructor, who undertakes to settle for the world whether a
+reader of Clavius, the constructor of the Gregorian Calendar, is fool or
+knave, upon information derived from a compiler--in this matter--of his own
+day; or a gentleman of horse and dog associations, who, misapprehending
+something which he heard about a current topic, infers that the reader of
+Clavius had the ear of the Government on a proposed alteration. I suppose
+the querist had heard some one say, perhaps, that the day ought to be set
+right, and some one else remark that I might be consulted, as the only
+person who had discussed the matter from the original source of the
+Calendar.
+
+To give a better chance of the explanation being at once produced, next
+time the real full moon and Easter Day shall fall together, I insert here a
+summary which was printed in the Irish Prayer-book of the Ecclesiastical
+Society. If the amusement given by paradoxers should prevent a useless
+discussion some years hence, I and the paradoxers shall have done a little
+good between us--at any rate, I have done my best to keep the heavy weight
+afloat by tying bladders to it. I think the next occurrence will be in
+1875.
+
+EASTER DAY.
+
+In the years 1818 and 1845, Easter Day, as given by the _rules in_ 24 Geo.
+II cap. 23. (known as the act for the _change of style_) contradicted the
+_precept_ given in the preliminary explanations. The precept is as follows:
+
+"_Easter Day_, on which the rest" of the moveable feasts "depend, is always
+the First Sunday after the Full Moon, which happens upon or next after the
+Twenty-first Day of {357} _March_; and if the Full Moon happens upon a
+Sunday, _Easter Day_ is the Sunday after."
+
+But in 1818 and 1845, the full moon fell on a Sunday, and yet the rules
+gave _that same Sunday_ for Easter Day. Much discussion was produced by
+this circumstance in 1818: but a repetition of it in 1845 was nearly
+altogether prevented by a timely[742] reference to the intention of those
+who conducted the Gregorian reformation of the Calendar. Nevertheless,
+seeing that the apparent error of the Calendar is due to the precept in the
+Act of Parliament, which is both erroneous and insufficient, and that the
+difficulty will recur so often as Easter Day falls on the day of full moon,
+it may be advisable to select from the two articles cited in the note such
+of their conclusions and rules, without proof or controversy, as will
+enable the reader to understand the main points of the Easter question,
+and, should he desire it, to calculate for himself the Easter of the old or
+new style, for any given year.
+
+1. In the very earliest age of Christianity, a controversy arose as to the
+mode of keeping Easter, some desiring to perpetuate the _Passover_, others
+to keep the _festival of the Resurrection_. The first afterwards obtained
+the name of _Quartadecimans_, from their Easter being always kept on the
+_fourteenth day_ of the moon (Exod. xii. 18, Levit. xxiii. 5.). But though
+it is unquestionable that a Judaizing party existed, it is also likely that
+many dissented on chronological grounds. It is clear that no _perfect_
+anniversary can take place, except when the fourteenth of the moon, and
+with it the passover, falls on a Friday. Suppose, for instance, it falls on
+a Tuesday: one of three things must be {358} done. Either (which seems
+never to have been proposed) the crucifixion and resurrection must be
+celebrated on Tuesday and Sunday, with a wrong interval; or the former on
+Tuesday, the latter on Thursday, abandoning the first day of the week; or
+the former on Friday, and the latter on Sunday, abandoning the paschal
+commemoration of the crucifixion.
+
+The last mode has been, as every one knows, finally adopted. The disputes
+of the first three centuries did not turn on any _calendar_ questions. The
+Easter question was merely the symbol of the struggle between what we may
+call the Jewish and Gentile sects of Christians: and it nearly divided the
+Christian world, the Easterns, for the most part, being _Quartadecimans_.
+It is very important to note that there is no recorded dispute about a
+method of predicting the new moon, that is, no general dispute leading to
+formation of sects: there may have been difficulties, and discussions about
+them. The Metonic cycle, presently mentioned, must have been used by many,
+perhaps most, churches.
+
+2. The question came before the Nicene Council (A.D. 325) not as an
+astronomical, but as a doctrinal, question: it was, in fact, this, Shall
+the _passover_[743] be treated as a part of Christianity? The Council
+resolved this question in the negative, and the only information on its
+premises and conclusion, or either, which comes from itself, is contained
+in the following sentence of the synodical epistle, which epistle is
+preserved by Socrates[744] and Theodoret.[745] "We also send {359} you the
+good news concerning the unanimous consent of all in reference to the
+celebration of the most solemn feast of Easter, for this difference also
+has been made up by the assistance of your prayers: so that all the
+brethren in the East, who formerly celebrated this festival _at the same
+time as the Jews_, will in future conform _to the Romans and to us_, and to
+all who have of old observed _our manner_ of celebrating Easter." This is
+all that can be found on the subject: none of the stories about the Council
+ordaining the astronomical mode of finding Easter, and introducing the
+Metonic cycle into ecclesiastical reckoning, have any contemporary
+evidence: the canons which purport to be those of the Nicene Council do not
+contain a word about Easter; and this is evidence, whether we suppose those
+canons to be genuine or spurious.
+
+3. The astronomical dispute about a lunar cycle for the prediction of
+Easter either commenced, or became prominent, by the extinction of greater
+ones, soon after the time of the Nicene Council. Pope Innocent I[746] met
+with difficulty in 414. S. Leo,[747] in 454, ordained that Easter of 455
+should be April 24; which is right. It is useless to record details of
+these disputes in a summary: the result was, that in the year 463, Pope
+Hilarius[748] employed Victorinus[749] of Aquitaine to correct the
+Calendar, and Victorinus formed a rule which lasted until the sixteenth
+century. He combined the Metonic cycle and the solar cycle presently
+described. But {360} this cycle bears the name of Dionysius Exiguus,[750] a
+Scythian settled at Rome, about A.D. 530, who adapted it to his new yearly
+reckoning, when he abandoned the era of Diocletian as a commencement, and
+constructed that which is now in common use.
+
+4. With Dionysius, if not before, terminated all difference as to the mode
+of keeping Easter which is of historical note: the increasing defects of
+the Easter Cycle produced in time the remonstrance of persons versed in
+astronomy, among whom may be mentioned Roger Bacon,[751] Sacrobosco,[752]
+Cardinal Cusa,[753] Regiomontanus,[754] etc. From the middle of the sixth
+to that of the sixteenth century, one rule was observed.
+
+5. The mode of applying astronomy to chronology has always involved these
+two principles. First, the actual position of the heavenly body is not the
+object of consideration, but what astronomers call its _mean place_, which
+may be described thus. Let a fictitious sun or moon move in the heavens, in
+such manner as to revolve among the fixed stars at an average rate,
+avoiding the alternate accelerations and retardations which take place in
+every planetary motion. Thus the fictitious (say _mean_) sun and moon are
+always very near to the real sun and moon. The ordinary clocks show time by
+the mean, not the real, sun: and it was always laid down that Easter
+depends on the opposition (or full moon) of the mean sun and moon, not of
+the real ones. Thus we see that, were the Calendar ever so correct {361} as
+to the _mean_ moon, it would be occasionally false as to the _true_ one:
+if, for instance, the opposition of the mean sun and moon took place at one
+second before midnight, and that of the real bodies only two seconds
+afterwards, the calendar day of full moon would be one day before that of
+the common almanacs. Here is a way in which the discussions of 1818 and
+1845 might have arisen: the British legislature has defined _the moon_ as
+the regulator of the paschal calendar. But this was only a part of the
+mistake.
+
+6. Secondly, in the absence of perfectly accurate knowledge of the solar
+and lunar motion (and for convenience, even if such knowledge existed),
+cycles are, and always have been taken, which serve to represent those
+motions nearly. The famous Metonic cycle, which is introduced into
+ecclesiastical chronology under the name of the cycle of the golden
+numbers, is a period of 19 Julian[755] years. This period, in the old
+Calendar, was taken to contain exactly 235 _lunations_, or intervals
+between new moons, of the mean moon. Now the state of the case is:
+
+19 average Julian years make 6939 days 18 hours.
+
+235 average lunations make 6939 days 16 hours 31 minutes.
+
+So that successive cycles of golden numbers, supposing the first to start
+right, amount to making the new moons fall too late, gradually, so that the
+mean moon _of this cycle_ gains 1 hour 29 minutes in 19 years upon the mean
+moon of the heavens, or about a day in 300 years. When the Calendar was
+reformed, the calendar new moons were four days in advance of the mean moon
+of the heavens: so that, for instance, calendar full moon on the 18th
+usually meant real full moon on the 14th.
+
+7. If the difference above had not existed, the moon of the heavens (the
+mean moon at least), would have returned {362} permanently to the same days
+of the month in 19 years; with an occasional slip arising from the unequal
+distribution of the leap years, of which a period contains sometimes five
+and sometimes four. As a general rule, the days of new and full moon in any
+one year would have been also the days of new and full moon of a year
+having 19 more units in its date. Again, if there had been no leap years,
+the days of the month would have returned to the same days of the week
+every seven years. The introduction of occasional 29ths of February
+disturbs this, and makes the permanent return of month days to week days
+occur only after 28 years. If all had been true, the lapse of 28 times 19,
+or 532 years, would have restored the year in every point: that is, A.D. 1,
+for instance, and A.D. 533, would have had the same almanac in every matter
+relating to week days, month days, sun, and moon (mean sun and moon at
+least). And on the supposition of its truth, the old system of Dionysius
+was framed. Its errors, are, first, that the moments of mean new moon
+advance too much by 1 h. 29 m. in 19 average Julian years; secondly, that
+the average Julian year of 365¼ days is too long by 11 m. 10 s.
+
+8. The Council of Trent, moved by the representations made on the state of
+the Calendar, referred the consideration of it to the Pope. In 1577,
+Gregory XIII[756] submitted to the Roman Catholic Princes and Universities
+a plan presented to him by the representatives of Aloysius Lilius,[757]
+then deceased. This plan being approved of, the Pope nominated a commission
+to consider its details, the working member of which was the Jesuit
+Clavius. A short work was prepared by Clavius, descriptive of the new
+Calendar: this {363} was published[758] in 1582, with the Pope's bull
+(dated February 24, 1581) prefixed. A larger work was prepared by Clavius,
+containing fuller explanation, and entitled _Romani Calendarii a Gregorio
+XIII. Pontifice Maximo restituti Explicatio_. This was published at Rome in
+1603, and again in the collection of the works of Clavius in 1612.
+
+9. The following extracts from Clavius settle the question of the meaning
+of the term _moon_, as used in the Calendar:
+
+"Who, except a few who think they are very sharp-sighted in this matter, is
+so blind as not to see that the 14th of the moon and the full moon are not
+the same things in the Church of God?... Although the Church, in finding
+the new moon, and from it the 14th day, _uses neither the true nor the mean
+motion of the moon_, but measures only according to the order of a cycle,
+it is nevertheless undeniable that the mean full moons found from
+astronomical tables are of the greatest use in determining the cycle which
+is to be preferred ... the new moons of which cycle, in order to the due
+celebration of Easter, should be so arranged that the 14th days of those
+moons, reckoning from the day of new moon _inclusive_, should not fall two
+or more days before the mean full moon, but only one day, or else on the
+very day itself, or not long after. And even thus far the Church need not
+take very great pains ... for it is sufficient that all should reckon by
+the 14th day of the moon in the cycle, even though sometimes it _should be
+more than one day before or after_ the mean full moon.... We have taken
+pains that in our cycle the new moons should _follow_ the real new moons,
+so that the 14th of the moon should fall either the day before the mean
+full moon, or on that day, or not long after; and this was done on purpose,
+for if the new moon of the cycle fell on the same day as the mean new moon
+of the {364} astronomers, it might chance that we should celebrate Easter
+on the same day as the Jews or the Quartadeciman heretics, which would be
+absurd, or else before them, which would be still more absurd."
+
+From this it appears that Clavius continued the Calendar of his
+predecessors in the choice of the _fourteenth_ day of the moon. Our
+legislature lays down the day of the _full moon_: and this mistake appears
+to be rather English than Protestant; for it occurs in missals published in
+the reign of Queen Mary. The calendar lunation being 29½ days, the middle
+day is the _fifteenth_ day, and this is and was reckoned as the day of the
+full moon. There is every right to presume that the original passover was a
+feast of the _real full moon_: but it is most probable that the moons were
+then reckoned, not from the astronomical conjunction with the sun, which
+nobody sees except at an eclipse, but from the day of _first visibility_ of
+the new moon. In fine climates this would be the day or two days after
+conjunction; and the fourteenth day from that of first visibility
+inclusive, would very often be the day of full moon. The following is then
+the proper correction of the precept in the Act of Parliament:
+
+Easter Day, on which the rest depend, is always the First Sunday after the
+_fourteenth day_ of the _calendar_ moon which happens upon or next after
+the Twenty-first day of March, _according to the rules laid down for the
+construction of the Calendar_; and if the _fourteenth day_ happens upon a
+Sunday, Easter Day is the Sunday after.
+
+10. Further, it appears that Clavius valued the celebration of the festival
+after the Jews, etc., more than astronomical correctness. He gives
+comparison tables which would startle a believer in the astronomical
+intention of his Calendar: they are to show that a calendar in which the
+moon is always made a day older than by him, _represents the heavens better
+than he has done, or meant to do_. But it must be observed that this
+diminution of the real moon's age has {365} a tendency to make the English
+explanation often practically accordant with the Calendar. For the
+fourteenth day of Clavius _is_ generally the fifteenth day of the mean moon
+of the heavens, and therefore most often that of the real moon. But for
+this, 1818 and 1845 would not have been the only instances of our day in
+which the English precept would have contradicted the Calendar.
+
+11. In the construction of the Calendar, Clavius adopted the ancient cycle
+of 532 years, but, we may say, without ever allowing it to run out. At
+certain periods, a shift is made from one part of the cycle into another.
+This is done whenever what should be Julian leap year is made a common
+year, as in 1700, 1800, 1900, 2100, etc. It is also done at certain times
+to correct the error of 1 h. 19 m., before referred to, in each cycle of
+golden numbers: Clavius, to meet his view of the amount of that error, put
+forward the moon's age a day 8 times in 2,500 years. As we cannot enter at
+full length into the explanation, we must content ourselves with giving a
+set of rules, independent of tables, by which the reader may find Easter
+for himself in any year, either by the old Calendar or the new. Any one who
+has much occasion to find Easters and movable feasts should procure
+Francoeur's[759] tables.
+
+12. _Rule for determining Easter Day of the Gregorian Calendar in any year
+of the new style._ To the several parts {366} of the rule are annexed, by
+way of example, the results for the year 1849.
+
+I. Add 1 to the given year. (1850).
+
+II. Take the quotient of the given year divided by 4, neglecting the
+remainder. (462).
+
+III. Take 16 from the centurial figures of the given year, if it can be
+done, and take the remainder. (2).
+
+IV. Take the quotient of III. divided by 4, neglecting the remainder. (0).
+
+V. From the sum of I, II, and IV., subtract III. (2310).
+
+VI. Find the remainder of V. divided by 7. (0).
+
+VII. Subtract VI. from 7; this is the number of the dominical letter
+
+  1  2  3  4  5  6  7  (7; dominical letter G).
+  A  B  C  D  E  F  G
+
+VIII. Divide I. by 19, the remainder (or 19, if no remainder) is the
+_golden number_. (7).
+
+IX. From the centurial figures of the year subtract 17, divide by 25, and
+keep the quotient. (0).
+
+X. Subtract IX. and 15 from the centurial figures, divide by 3, and keep
+the quotient. (1).
+
+XI. To VIII. add ten times the next less number, divide by 30, and keep the
+remainder. (7).
+
+XII. To XI. add X. and IV., and take away III., throwing out thirties, if
+any. If this give 24, change it into 25. If 25, change it into 26, whenever
+the golden number is greater than 11. If 0, change it into 30. Thus we have
+the epact, or age of the _Calendar_ moon at the beginning of the year. (6).
+
+_When the Epact is 23, or less._
+
+XIII. Subtract XII., the epact, from 45. (39).
+
+XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7,
+if there be no remainder. (7)
+
+_When the Epact is greater than 23._
+
+XIII. Subtract XII., the epact, from 75.
+
+XIV. Subtract the epact from 57, divide by 7, and keep the remainder, or 7,
+if there be no remainder.
+
+XV. To XIII. add VII., the dominical number, (and 7 besides, if XIV. be
+greater than VII.,) and subtract XIV., the result is the day of March, or
+if more than 31, subtract 31, and {367} the result is the day of April, on
+which Easter Sunday falls. (39; Easter Day is April 8).
+
+In the following examples, the several results leading to the final
+conclusion are tabulated.
+
+  ========================================================
+  GIVEN YEAR | 1592 | 1637 | 1723 | 1853 | 2018 | 4686
+  --------------------------------------------------------
+        I.   | 1593 | 1638 | 1724 | 1854 | 2019 |   4687
+       II.   |  398 |  409 |  430 |  463 |  504 |   1171
+      III.   |  --- |    0 |    1 |    2 |    4 |     30
+       IV.   |  --- |    0 |    0 |    0 |    1 |      7
+        V.   | 1991 | 2047 | 2153 | 2315 | 2520 |   5835
+       VI.   |    3 |    3 |    4 |    5 |    0 |      4
+      VII.   |    4 |    4 |    3 |    2 |    7 |      3
+     VIII.   |   16 |    4 |   14 |   11 |    5 |     13
+       IX.   |  --- |  --- |    0 |    0 |    0 |      1
+        X.   |    0 |    0 |    0 |    1 |    1 |     10
+       XI.   |   16 |    4 |   24 |   21 |   15 |     13
+      XII.   |   16 |    4 |   23 |   20 |   13 |0 say 30
+     XIII.   |   29 |   41 |   22 |   25 |   32 |     45
+      XIV.   |    4 |    2 |    4 |    7 |    7 |      6
+       XV.   |   29 |   43 |   28 |   27 |   32 |     49
+  Easter Day |Mar.29|Apr.12|Mar.28|Mar.27|Apr.1 | Apr.18
+  --------------------------------------------------------
+
+13. _Rule for determining Easter Day of the Antegregorian Calendar in any
+year of the old style._ To the several parts of the rule are annexed, by
+way of example, the results for the year 1287. The steps are numbered to
+correspond with the steps of the Gregorian rule, so that it can be seen
+what augmentations the latter requires.
+
+I. Set down the given year. (1287).
+
+II. Take the quotient of the given year divided by 4, neglecting the
+remainder (321).
+
+V. Take 4 more than the sum of I. and II. (1612).
+
+VI. Find the remainder of V. divided by 7. (2).
+
+VII. Subtract VI. from 7; this is the number of the dominical letter
+
+  1  2  3  4  5  6  7  (5; dominical letter E).
+  A  B  C  D  E  F  G
+
+VIII. Divide one more than the given year by 19, the remainder (or 19 if no
+remainder) is the golden number. (15).
+
+XII. Divide 3 less than 11 times VIII. by 30; the remainder (or 30 if there
+be no remainder) is the epact. (12).
+
+{368}
+
+_When the Epact is 23, or less._
+
+XIII. Subtract XII., the epact, from 45. (33).
+
+XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7,
+if there be no remainder, (1).
+
+_When the Epact is greater than 23._
+
+XIII. Subtract XII., the epact, from 75.
+
+XIV. Subtract the epact from 57, divide by 7, and keep the remainder, or 7,
+if there be no remainder.
+
+XV. To XIII. add VII., the dominical number, (and 7 besides if XIV. be
+greater than VII.,) and subtract XIV., the result is the day of March, or
+if more than 31, subtract 31, and the result is the day of April, on which
+Easter Sunday (old style) falls. (37; Easter Day is April 6).
+
+These rules completely represent the old and new Calendars, so far as
+Easter is concerned. For further explanation we must refer to the articles
+cited at the commencement.
+
+The annexed is the table of new and full moons of the Gregorian Calendar,
+cleared of the errors made for the purpose of preventing Easter from
+coinciding with the Jewish Passover.
+
+The second table (page 370) contains _epacts_, or ages of the moon at the
+beginning of the year: thus in 1913, the epact is 22, in 1868 it is 6. This
+table goes from 1850 to 1999: should the New Zealander not have arrived by
+that time, and should the churches of England and Rome then survive, the
+epact table may be continued from their liturgy-books. The way of using the
+table is as follows: Take the epact of the required year, and find it in
+the first or last column of the first table, in line with it are seen the
+calendar days of new and full moon. Thus, when the epact is 17, the new and
+full moons of March fall on the 13th and 28th. The result is, for the most
+part, correct: but in a minority of cases there is an error of a day. When
+this happens, the error is almost always a fraction of a day much less than
+twelve hours. Thus, when the table gives full moon on the 27th, and the
+real truth is the 28th, we may be sure it is early on the 28th.
+
+{369}
+
+  -------------------------------------------------------------------------
+        |Jan.|Feb.|Mar.|Apr.|May |June|July|Aug.|Sep.|Oct.|Nov.|Dec.|
+  -------------------------------------------------------------------------
+    1   | 29 | 27 | 29 | 27 | 27 | 25 | 25 | 23 | 22 | 21 | 20 | 19 |  1
+        | 14 | 13 | 14 | 13 | 12 | 11 | 10 |  9 |  7 |  7 |  5 |  5 |
+  -------------------------------------------------------------------------
+    2   | 28 | 26 | 28 | 26 | 26 | 24 | 24 | 22 | 21 | 20 | 19 | 18 |  2
+        | 13 | 12 | 13 | 12 | 11 | 10 |  9 |  8 |  6 |  6 |  4 |  4 |
+  -------------------------------------------------------------------------
+    3   | 27 | 25 | 27 | 25 | 25 | 23 | 23 | 21 | 20 | 19 | 18 | 17 |  3
+        | 12 | 11 | 12 | 11 | 10 |  9 |  8 |  7 |  5 |  5 |  3 |  3 |
+  -------------------------------------------------------------------------
+    4   | 26 | 24 | 26 | 24 | 24 | 22 | 22 | 20 | 19 | 18 | 17 | 16 |  4
+        | 11 | 10 | 11 | 10 |  9 |  8 |  7 |  6 |  4 |  4 |  2 |2,31|
+  -------------------------------------------------------------------------
+    5   | 25 | 23 | 25 | 23 | 23 | 21 | 21 | 19 | 18 | 17 | 16 | 15 |  5
+        | 10 |  9 | 10 |  9 |  8 |  7 |  6 |  5 |  3 |  3 |  1 |1,30|
+  -------------------------------------------------------------------------
+    6   | 24 | 22 | 24 | 22 | 22 | 20 | 20 | 18 | 17 | 16 | 15 | 14 |  6
+        |  9 |  8 |  9 |  8 |  7 |  6 |  5 |  4 |  2 |2,31| 30 | 29 |
+  -------------------------------------------------------------------------
+    7   | 23 | 21 | 23 | 21 | 21 | 19 | 19 | 17 | 16 | 15 | 14 | 13 |  7
+        |  8 |  7 |  8 |  7 |  6 |  5 |  4 |  3 |  1 |1,30| 29 | 28 |
+  -------------------------------------------------------------------------
+    8   | 22 | 20 | 22 | 20 | 20 | 18 | 18 | 16 | 15 | 14 | 13 | 12 |  8
+        |  7 |  6 |  7 |  6 |  5 |  4 |  3 |2,31| 30 | 29 | 28 | 27 |
+  -------------------------------------------------------------------------
+    9   | 21 | 19 | 21 | 19 | 19 | 17 | 17 | 15 | 14 | 13 | 12 | 11 |  9
+        |  6 |  5 |  6 |  5 |  4 |  3 |  2 |1,30| 29 | 28 | 27 | 26 |
+  -------------------------------------------------------------------------
+    10  | 20 | 18 | 20 | 18 | 18 | 16 | 16 | 14 | 13 | 12 | 11 | 10 |  10
+        |  5 |  4 |  5 |  4 |  3 |  2 |1,31| 29 | 28 | 27 | 26 | 25 |
+  -------------------------------------------------------------------------
+    11  | 19 | 17 | 19 | 17 | 17 | 15 | 15 | 13 | 12 | 11 | 10 |  9 |  11
+        |  4 |  3 |  4 |  3 |  2 |1,30| 30 | 28 | 27 | 26 | 25 | 24 |
+  -------------------------------------------------------------------------
+    12  | 18 | 16 | 18 | 16 | 16 | 14 | 14 | 12 | 11 | 10 |  9 |  8 |  12
+        |  3 |  2 |  3 |  2 |1,31| 29 | 29 | 27 | 26 | 25 | 24 | 23 |
+  -------------------------------------------------------------------------
+    13  | 17 | 15 | 17 | 15 | 15 | 13 | 13 | 11 | 10 |  9 |  8 |  7 |  13
+        |  2 |  1 |  2 |1,30| 30 | 28 | 28 | 26 | 25 | 24 | 23 | 22 |
+  -------------------------------------------------------------------------
+    14  | 16 | 14 | 16 | 14 | 14 | 12 | 12 | 10 |  9 |  8 |  7 |  6 |  14
+        |1,31| -- |1,31| 29 | 29 | 27 | 27 | 25 | 24 | 23 | 22 | 21 |
+  -------------------------------------------------------------------------
+    15  | 15 | 13 | 15 | 13 | 13 | 11 | 11 |  9 |  8 |  7 |  6 |  5 |  15
+        | 30 | 28 | 30 | 28 | 28 | 26 | 26 | 24 | 23 | 22 | 21 | 20 |
+  -------------------------------------------------------------------------
+    16  | 14 | 12 | 14 | 12 | 12 | 10 | 10 |  8 |  7 |  6 |  5 |  4 |  16
+        | 29 | 27 | 29 | 27 | 27 | 25 | 25 | 23 | 22 | 21 | 20 | 19 |
+  -------------------------------------------------------------------------
+    17  | 13 | 11 | 13 | 11 | 11 |  9 |  9 |  7 |  6 |  5 |  4 |  3 |  17
+        | 28 | 26 | 28 | 26 | 26 | 24 | 24 | 22 | 21 | 20 | 19 | 18 |
+  -------------------------------------------------------------------------
+    18  | 12 | 10 | 12 | 10 | 10 |  8 |  8 |  6 |  5 |  4 |  3 |  2 |  18
+        | 27 | 25 | 27 | 25 | 25 | 23 | 23 | 21 | 20 | 19 | 18 | 17 |
+  -------------------------------------------------------------------------
+    19  | 11 |  9 | 11 |  9 |  9 |  7 |  7 |  5 |  4 |  3 |  2 |1,31|  19
+        | 26 | 24 | 26 | 24 | 24 | 22 | 22 | 20 | 19 | 18 | 17 | 16 |
+  -------------------------------------------------------------------------
+    20  | 10 |  8 | 10 |  8 |  8 |  6 |  6 |  4 |  3 |  2 |1,31| 30 |  20
+        | 25 | 23 | 25 | 23 | 23 | 21 | 21 | 19 | 18 | 17 | 16 | 15 |
+  -------------------------------------------------------------------------
+    21  |  9 |  7 |  9 |  7 |  7 |  5 |  5 |  3 |  2 |1,31| 29 | 29 |  21
+        | 24 | 22 | 24 | 22 | 22 | 20 | 20 | 18 | 17 | 16 | 15 | 14 |
+  -------------------------------------------------------------------------
+    22  |  8 |  6 |  8 |  6 |  6 |  4 |  4 |  2 |1,30| 30 | 28 | 28 |  22
+        | 23 | 21 | 23 | 21 | 21 | 19 | 19 | 17 | 16 | 15 | 14 | 13 |
+  -------------------------------------------------------------------------
+    23  |  7 |  5 |  7 |  5 |  5 |  3 |  3 |1,31| 29 | 29 | 27 | 27 |  23
+        | 22 | 20 | 22 | 20 | 20 | 18 | 18 | 16 | 15 | 14 | 13 | 12 |
+  -------------------------------------------------------------------------
+    24  |  6 |  5 |  6 |  5 |  4 |  3 |  2 |1,30| 29 | 28 | 27 | 26 |  24
+        | 21 | 19 | 21 | 19 | 19 | 17 | 17 | 15 | 14 | 13 | 12 | 11 |
+  -------------------------------------------------------------------------
+    25  |  5 |  4 |  5 |  4 |  3 |  2 |1,31| 29 | 28 | 27 | 26 | 25 |  25
+        | 20 | 19 | 20 | 19 | 18 | 17 | 16 | 15 | 13 | 13 | 11 | 11 |
+  -------------------------------------------------------------------------
+    26  |  4 |  3 |  4 |  3 |  2 |1,30| 30 | 28 | 27 | 26 | 25 | 24 |  26
+        | 19 | 18 | 19 | 18 | 17 | 16 | 15 | 14 | 12 | 12 | 10 | 10 |
+  -------------------------------------------------------------------------
+    27  |  3 |  2 |  3 |  2 |1,31| 29 | 29 | 27 | 26 | 25 | 24 | 23 |  27
+        | 18 | 17 | 18 | 17 | 16 | 15 | 14 | 13 | 11 | 11 |  9 |  9 |
+  -------------------------------------------------------------------------
+    28  |  2 |  1 |  2 |1,30| 30 | 28 | 28 | 26 | 25 | 24 | 23 | 22 |  28
+        | 17 | 16 | 17 | 16 | 15 | 14 | 13 | 12 | 10 | 10 |  8 |  8 |
+  -------------------------------------------------------------------------
+    29  |1,31| -- |1,31| 29 | 29 | 27 | 27 | 25 | 24 | 23 | 22 | 21 |  29
+        | 16 | 15 | 16 | 15 | 14 | 13 | 12 | 11 |  9 |  9 |  7 |  7 |
+  -------------------------------------------------------------------------
+    30  | 30 | 28 | 30 | 28 | 28 | 26 | 26 | 24 | 23 | 22 | 21 | 20 |  30
+        | 15 | 14 | 15 | 14 | 13 | 12 | 11 | 10 |  8 |  8 |  6 |  6 |
+  -------------------------------------------------------------------------
+        |Jan.|Feb.|Mar.|Apr.|May |June|July|Aug.|Sep.|Oct.|Nov.|Dec.|
+  -------------------------------------------------------------------------
+
+{370}
+
+  =======================================================
+       |  0 |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9
+  -------------------------------------------------------
+   185 | 17 | 28 |  9 | 20 |  2 | 12 | 23 |  4 | 15 | 26
+  -------------------------------------------------------
+   186 |  7 | 18 | 30 | 11 | 22 |  3 | 14 | 25 |  6 | 17
+  -------------------------------------------------------
+   187 | 28 |  9 | 20 |  1 | 12 | 23 |  4 | 15 | 26 |  7
+  -------------------------------------------------------
+   188 | 18 | 30 | 11 | 22 |  3 | 14 | 25 |  6 | 17 | 28
+  -------------------------------------------------------
+   189 |  9 | 21 |  1 | 12 | 23 |  4 | 15 | 26 |  7 | 18
+  -------------------------------------------------------
+   190 | 29 | 10 | 21 |  2 | 13 | 24 |  5 | 16 | 27 |  8
+  -------------------------------------------------------
+   191 | 19 | 30 | 11 | 22 |  3 | 14 | 26 |  6 | 17 | 29
+  -------------------------------------------------------
+   192 | 10 | 21 |  2 | 13 | 24 |  5 | 16 | 27 |  8 | 19
+  -------------------------------------------------------
+   193 | 30 | 11 | 22 |  3 | 14 | 26 |  6 | 17 | 29 | 10
+  -------------------------------------------------------
+   194 | 21 |  2 | 13 | 24 |  5 | 16 | 27 |  8 | 19 | 30
+  -------------------------------------------------------
+   195 | 11 | 22 |  3 | 14 | 26 |  6 | 17 | 29 | 10 | 21
+  -------------------------------------------------------
+   196 |  2 | 13 | 24 |  5 | 16 | 27 |  8 | 19 | 30 | 11
+  -------------------------------------------------------
+   197 | 22 |  3 | 14 | 26 |  6 | 17 | 29 | 10 | 21 |  2
+  -------------------------------------------------------
+   198 | 13 | 24 |  5 | 16 | 27 |  8 | 19 | 30 | 11 | 22
+  -------------------------------------------------------
+   199 |  3 | 14 | 26 |  6 | 17 | 29 | 10 | 21 |  2 | 13
+  =======================================================
+
+For example, the year 1867. The epact is 25, and we find in the table:
+
+         J.   F.   M.   AP.  M.   JU.  JL.  AU.  S.   O.   N.   D.
+  New     5+   4    5+   4    3+   2  1,31  29   28-  27   26   25
+  Full   20   19-  20   19-  18   17   16   15   13-  13   11+  11
+
+When the truth is the day after + is written after the date; when the day
+before, -. Thus, the new moon of March is on the 6th; the full moon of
+April is on the 18th. {371}
+
+I now introduce a small paradox of my own; and as I am not able to prove
+it, I am compelled to declare that any one who shall dissent must be either
+very foolish or very dishonest, and will make me quite uncomfortable about
+the state of his soul. This being settled once for all, I proceed to say
+that the necessity of arriving at the truth about the assertions that the
+Nicene Council laid down astronomical tests led me to look at Fathers,
+Church histories, etc. to an extent which I never dreamed of before. One
+conclusion which I arrived at was, that the Nicene Fathers had a knack of
+sticking to the question which many later councils could not acquire. In
+our own day, it is not permitted to Convocation seriously to discuss any
+one of the points which are bearing so hard upon their resources of
+defence--the cursing clauses of the Athanasian Creed, for example. And it
+may be collected that the prohibition arises partly from fear that there is
+no saying where a beginning, if allowed, would end. There seems to be a
+suspicion that debate, once let loose, would play up old Trent with the
+liturgy, and bring the whole book to book. But if any one will examine the
+real Nicene Creed, without the augmentation, he will admire the way in
+which the framers stuck to the point, and settled what they had to decide,
+according to their view of it. With such a presumption of good sense in
+their favor, it becomes easier to believe in any claim which may be made on
+their behalf to tact or sagacity in settling any other matter. And I
+strongly suspect such a claim may be made for them on the Easter question.
+
+I collect from many little indications, both before and after the Council,
+that the division of the Christian world into Judaical and Gentile, though
+not giving rise to a sectarian distinction expressed by names, was of far
+greater force and meaning than historians prominently admit. I took _note_
+of many indications of this, but not _notes_, as it was not to my purpose.
+If it were so, we must admire the discretion of the Council. The Easter
+question was the {372} fighting ground of the struggle: the Eastern or
+Judaical Christians, with some varieties of usage and meaning, would have
+the Passover itself to be the great feast, but taken in a Christian sense;
+the Western or Gentile Christians, would have the commemoration of the
+Resurrection, connected with the Passover only by chronology. To shift the
+Passover in time, under its name, _Pascha_, without allusion to any of the
+force of the change, was gently cutting away the ground from under the feet
+of the Conservatives. And it was done in a very quiet way: no allusion to
+the precise character of the change; no hint that the question was about
+two different festivals: "all the brethren in the East, who formerly
+celebrated this festival at the same time as the Jews, will in future
+conform to the Romans and to us." The Judaizers meant to be keeping the
+Passover _as_ a Christian feast: they are gently assumed to be keeping,
+_not_ the Passover, _but_ a Christian feast; and a doctrinal decision is
+quietly, but efficiently, announced under the form of a chronological
+ordinance. Had the Council issued theses of doctrine, and excommunicated
+all dissentients, the rupture of the East and West would have taken place
+earlier by centuries than it did. The only place in which I ever saw any
+part of my paradox advanced, was in an article in the _Examiner_ newspaper,
+towards the end of 1866, after the above was written.
+
+A story about Christopher Clavius, the workman of the new Calendar. I
+chanced to pick up "Albertus Pighius Campensis de æquinoctiorum
+solsticiorumque inventione... Ejusdem de ratione Paschalis celebrationis,
+De que Restitutione ecclesiastici Kalendarii," Paris, 1520, folio.[760] On
+the title-page were decayed words followed by ".._hristophor.. C..ii_, 1556
+(or 8)," the last blank not entirely erased by time, but showing the lower
+halves of an _l_ and of an _a_, and {373} rather too much room for a _v_.
+It looked very like _E Libris Christophori Clavii_ 1556. By the courtesy of
+some members of the Jesuit body in London, I procured a tracing of the
+signature of Clavius from Rome, and the shapes of the letters, and the
+modes of junction and disjunction, put the matter beyond question. Even the
+extra space was explained; he wrote himself Cla_u_ius. Now in 1556, Clavius
+was nineteen years old: it thus appears probable that the framer of the
+Gregorian Calendar was selected, not merely as a learned astronomer, but as
+one who had attended to the calendar, and to works on its reformation, from
+early youth. When on the subject I found reason to think that Clavius had
+really read this work, and taken from it a phrase or two and a notion or
+two. Observe the advantage of writing the baptismal name at full length.
+
+
+
+A COUPLE OF MINOR PARADOXES.
+
+    The discovery of a general resolution of all superior finite equations,
+    of every numerical both algebraick and transcendent form. By A. P.
+    Vogel,[761] mathematician at Leipzick. Leipzick and London, 1845, 8vo.
+
+This work is written in the English of a German who has not mastered the
+idiom: but it is always intelligible. It professes to solve equations of
+every degree "in a more extent sense, and till to every degree of
+exactness." The general solution of equations of _all_ degrees is a vexed
+question, which cannot have the mysterious interest of the circle problem,
+and is of a comparatively modern date.[762] Mr. Vogel {374} announces a
+forthcoming treatise in which are resolved the "last impossibilities of
+pure mathematics."
+
+
+
+    Elective Polarity the Universal Agent. By Frances Barbara Burton,
+    authoress of 'Astronomy familiarized,' 'Physical Astronomy,' &c.
+    London, 1845, 8vo.[763]
+
+The title gives a notion of the theory. The first sentence states, that
+12,500 years ago [alpha] Lyræ was the pole-star, and attributes the immense
+magnitude of the now fossil animals to a star of such "polaric intensity as
+Vega pouring its magnetic streams through our planet." Miss Burton was a
+lady of property, and of very respectable acquirements, especially in
+Hebrew; she was eccentric in all things.
+
+1867.--Miss Burton is revived by the writer of a book on meteorology which
+makes use of the planets: she is one of his leading minds.[764]
+
+
+
+SPECULATIVE THOUGHT IN ENGLAND.
+
+In the year 1845 the old _Mathematical Society_ was merged in the
+Astronomical Society. The circle-squarers, etc., thrive more in England
+than in any other country: there are most weeds where there is the largest
+crop. Speculation, though not encouraged by our Government so much as by
+those of the Continent, has had, not indeed such forcing, but much wider
+diffusion: few tanks, but many rivulets. On this point I quote from the
+preface to the reprint of the work of Ramchundra,[765] which I
+superintended for the late Court of Directors of the East India Company.
+
+{375}
+
+"That sound judgment which gives men well to know what is best for them, as
+well as that faculty of invention which leads to development of resources
+and to the increase of wealth and comfort, are both materially advanced,
+perhaps cannot rapidly be advanced without, a great taste for pure
+speculation among the general mass of the people, down to the lowest of
+those who can read and write. England is a marked example. Many persons
+will be surprised at this assertion. They imagine that our country is the
+great instance of the refusal of all _unpractical_ knowledge in favor of
+what is _useful_. I affirm, on the contrary, that there is no country in
+Europe in which there has been so wide a diffusion of speculation, theory,
+or what other unpractical word the reader pleases. In our country, the
+scientific _society_ is always formed and maintained by the people; in
+every other, the scientific _academy_--most aptly named--has been the
+creation of the government, of which it has never ceased to be the
+nursling. In all the parts of England in which manufacturing pursuits have
+given the artisan some command of time, the cultivation of mathematics and
+other speculative studies has been, as is well known, a very frequent
+occupation. In no other country has the weaver at his loom bent over the
+_Principia_ of Newton; in no other country has the man of weekly wages
+maintained his own scientific periodical. With us, since the beginning of
+the last century, scores upon scores--perhaps hundreds, for I am far from
+knowing all--of annuals have run, some their ten years, some their
+half-century, some their century and a half, containing questions to be
+answered, from which many of our examiners in the universities have culled
+materials for the academical contests. And these questions have always been
+answered, and in cases without number by the lower order of purchasers, the
+mechanics, the weavers, and the printers' workmen. I cannot here digress to
+point out the manner in which the concentration of manufactures, and the
+general diffusion of education, have affected the {376} state of things; I
+speak of the time during which the present system took its rise, and of the
+circumstances under which many of its most effective promoters were
+trained. In all this there is nothing which stands out, like the
+state-nourished academy, with its few great names and brilliant single
+achievements. This country has differed from all others in the wide
+diffusion of the disposition to speculate, which disposition has found its
+place among the ordinary habits of life, moderate in its action, healthy in
+its amount."
+
+
+
+THE OLD MATHEMATICAL SOCIETY.
+
+Among the most remarkable proofs of the diffusion of speculation was the
+Mathematical Society, which flourished from 1717 to 1845. Its habitat was
+Spitalfields, and I think most of its existence was passed in Crispin
+Street. It was originally a plain society, belonging to the studious
+artisan. The members met for discussion once a week; and I believe I am
+correct in saying that each man had his pipe, his pot, and his problem. One
+of their old rules was that, "If any member shall so far forget himself and
+the respect due to the Society as in the warmth of debate to threaten or
+offer personal violence to any other member, he shall be liable to
+immediate expulsion, or to pay such fine as the majority of the members
+present shall decide." But their great rule, printed large on the back of
+the title page of their last book of regulations, was "By the constitution
+of the Society, it is the duty of every member, if he be asked any
+mathematical or philosophical question by another member, to instruct him
+in the plainest and easiest manner he is able." We shall presently see
+that, in old time, the rule had a more homely form.
+
+I have been told that De Moivre[766] was a member of this {377} Society.
+This I cannot verify: circumstances render it unlikely; even though the
+French refugees clustered in Spitalfields; many of them were of the
+Society, which there is some reason to think was founded by them. But
+Dolland,[767] Thomas Simpson,[768] Saunderson,[769] Crossley,[770] and
+others of known name, were certainly members. The Society gradually
+declined, and in 1845 was reduced to nineteen members. An arrangement was
+made by which sixteen of these members, who where not already in the
+Astronomical Society became Fellows without contribution, all the books and
+other property of the old Society being transferred to the new one. I was
+one of the committee which made the preliminary inquiries, and the reason
+of the decline was soon manifest. The only question which could arise was
+whether the members of the society of working men--for this repute still
+continued--were of that class of educated men who could associate with the
+Fellows of the Astronomical Society on terms agreeable to all parties. We
+found that the artisan element had been extinct for many years; there was
+not a man but might, as to education, manners, and position, have become a
+Fellow in the usual way. The fact was that life in Spitalfields had become
+harder: and the weaver could {378} only live from hand to mouth, and not up
+to the brain. The material of the old Society no longer existed.
+
+In 1798, experimental lectures were given, a small charge for admission
+being taken at the door: by this hangs a tale--and a song. Many years ago,
+I found among papers of a deceased friend, who certainly never had anything
+to do with the Society, and who passed all his life far from London, a
+song, headed "Song sung by the Mathematical Society in London, at a dinner
+given Mr. Fletcher,[771] a solicitor, who had defended the Society gratis."
+Mr. Williams,[772] the Assistant Secretary of the Astronomical Society,
+formerly Secretary of the Mathematical Society, remembered that the Society
+had had a solicitor named Fletcher among the members. Some years elapsed
+before it struck me that my old friend Benjamin Gompertz,[773] who had long
+been a member, might have some recollection of the matter. The following is
+an extract of a letter from him (July 9, 1861):
+
+"As to the Mathematical Society, of which I was a member when only 18 years
+of age, [Mr. G. was born in 1779], having been, contrary to the rules,
+elected under the age of 21. How I came to be a member of that Society--and
+continued so until it joined the Astronomical Society, and was then the
+President--was: I happened to pass a bookseller's small shop, of
+second-hand books, kept by a poor taylor, but a good mathematician, John
+Griffiths. I was very pleased to meet a mathematician, and I asked him if
+he would give me some lessons; and his reply was that I was more capable to
+teach him, but he belonged to a society of mathematicians, and he would
+introduce me. I accepted the offer, and I was elected, and had many
+scholars then to teach, as {379} one of the rules was, if a member asked
+for information, and applied to any one who could give it, he was obliged
+to give it, or fine one penny. Though I might say much with respect to the
+Society which would be interesting, I will for the present reply only to
+your question. I well knew Mr. Fletcher, who was a very clever and very
+scientific person. He did, as solicitor, defend an action brought by an
+informer against the Society--I think for 5,000l.--for giving lectures to
+the public in philosophical subjects [i.e., for unlicensed public
+exhibition with money taken at the doors]. I think the price for admission
+was one shilling, and we used to have, if I rightly recollect, from two to
+three hundred visitors. Mr. Fletcher was successful in his defence, and we
+got out of our trouble. There was a collection made to reward his services,
+but he did not accept of any reward: and I think we gave him a dinner, as
+you state, and enjoyed ourselves; no doubt with astronomical songs and
+other songs; but my recollection does not enable me to say if the
+astronomical song was a drinking song. I think the anxiety caused by that
+action was the cause of some of the members' death. [They had, no doubt,
+broken the law in ignorance; and by the sum named, the informer must have
+been present, and sued for a penalty on every shilling he could prove to
+have been taken]."
+
+I by no means guarantee that the whole song I proceed to give is what was
+sung at the dinner: I suspect, by the completeness of the chain, that
+augmentations have been made. My deceased friend was just the man to add
+some verses, or the addition may have been made before it came into his
+hands, or since his decease, for the scraps containing the verses passed
+through several hands before they came into mine. We may, however, be
+pretty sure that the original is substantially contained in what is given,
+and that the character is therefore preserved. I have had myself to repair
+damages every now and then, in the way of conjectural restoration of
+defects caused by ill-usage. {380}
+
+
+
+THE ASTRONOMER'S DRINKING SONG.
+
+ "Whoe'er would search the starry sky,
+    Its secrets to divine, sir,
+  Should take his glass--I mean, should try
+    A glass or two of wine, sir!
+  True virtue lies in golden mean,
+    And man must wet his clay, sir;
+  Join these two maxims, and 'tis seen
+    He should drink his bottle a day, sir!
+
+ "Old Archimedes, reverend sage!
+    By trump of fame renowned, sir,
+  Deep problems solved in every page,
+    And the sphere's curved surface found,[774] sir:
+  Himself he would have far outshone,
+    And borne a wider sway, sir,
+  Had he our modern secret known,
+    And drank a bottle a day, sir!
+
+ "When Ptolemy,[775] now long ago,
+    Believed the earth stood still, sir,
+  He never would have blundered so,
+    Had he but drunk his fill, sir:
+  He'd then have felt[776] it circulate,
+    And would have learnt to say, sir,
+  The true way to investigate
+    Is to drink your bottle a day, sir!
+
+ "Copernicus,[777] that learned wight,
+    The glory of his nation,
+  With draughts of wine refreshed his sight,
+    And saw the earth's rotation;
+  {381}
+  Each planet then its orb described,
+    The moon got under way, sir;
+  These truths from nature he imbibed
+    For he drank his bottle a day, sir!
+
+ "The noble[778] Tycho placed the stars,
+    Each in its due location;
+  He lost his nose[779] by spite of Mars,
+    But that was no privation:
+  Had he but lost his mouth, I grant
+    He would have felt dismay, sir,
+  Bless you! _he_ knew what he should want
+    To drink his bottle a day, sir!
+
+ "Cold water makes no lucky hits;
+    On mysteries the head runs:
+  Small drink let Kepler[780] time his wits
+    On the regular polyhedrons:
+  He took to wine, and it changed the chime,
+    His genius swept away, sir,
+  Through area varying[781] as the time
+    At the rate of a bottle a day, sir!
+
+ "Poor Galileo,[782] forced to rat
+    Before the Inquisition,
+  _E pur si muove_[783] was the pat
+    He gave them in addition:
+  {382}
+  He meant, whate'er you think you prove,
+    The earth must go its way, sirs;
+  Spite of your teeth I'll make it move,
+    For I'll drink my bottle a day, sirs!
+
+ "Great Newton, who was never beat
+    Whatever fools may think, sir;
+  Though sometimes he forgot to eat,
+    He never forgot to drink, sir:
+  Descartes[784] took nought but lemonade,
+    To conquer him was play, sir;
+  The first advance that Newton made
+    Was to drink his bottle a day, sir!
+
+ "D'Alembert,[785] Euler,[786] and Clairaut,[787]
+    Though they increased our store, sir,
+  Much further had been seen to go
+    Had they tippled a little more, sir!
+  Lagrange[788] gets mellow with Laplace,[789]
+    And both are wont to say, sir,
+  The _philosophe_ who's not an ass
+    Will drink his bottle a day, sir!
+
+ "Astronomers! what can avail
+    Those who calumniate us;
+  Experiment can never fail
+    With such an apparatus:
+  Let him who'd have his merits known
+    Remember what I say, sir;
+  Fair science shines on him alone
+    Who drinks his bottle a day, sir!
+
+  {383}
+ "How light we reck of those who mock
+    By this we'll make to appear, sir,
+  We'll dine by the sidereal[790] clock
+    For one more bottle a year, sir:
+  But choose which pendulum you will,
+    You'll never make your way, sir,
+  Unless you drink--and drink your fill,--
+    At least a bottle a day, sir!"
+
+Old times are changed, old manners gone!
+
+There is a new Mathematical Society,[791] and I am, at this present writing
+(1866), its first President. We are very high in the newest developments,
+and bid fair to take a place among the scientific establishments. Benjamin
+Gompertz, who was President of the old Society when it expired, was the
+link between the old and new body: he was a member of _ours_ at his death.
+But not a drop of liquor is seen at our meetings, except a decanter of
+water: all our heavy is a fermentation of symbols; and we do not draw it
+mild. There is no penny fine for reticence or occult science; and as to a
+song! not the ghost of a chance.
+
+
+
+1826. The time may have come when the original documents connected with the
+discovery of Neptune may be worth revising. The following are extracts from
+the _Athenæum_ of October 3 and October 17:
+
+
+
+LE VERRIER'S[792] PLANET.
+
+We have received, at the last moment before making up for press, the
+following letter from Sir John Herschel,[793] {384} in reference to the
+matter referred to in the communication from Mr. Hind[794] given below:
+
+"Collingwood, Oct. 1.
+
+"In my address to the British Association assembled at Southampton, on the
+occasion of my resigning the chair to Sir R. Murchison,[795] I stated,
+among the remarkable astronomical events of the last twelvemonth, that it
+had added a new planet to our list,--adding, 'it has done more,--it has
+given us the probable prospect of the discovery of another. We see it as
+Columbus saw America from the shores of Spain. Its movements have been
+felt, trembling along the far-reaching line of our analysis, with a
+certainty hardly inferior to that of ocular demonstration.'--These
+expressions are not reported in any of the papers which profess to give an
+account of the proceedings, but I appeal to all present whether they were
+not used.
+
+"Give me leave to state my reasons for this confidence; and, in so doing,
+to call attention to some facts which deserve to be put on record in the
+history of this noble discovery. On July 12, 1842, the late illustrious
+astronomer, Bessel,[796] honored me with a visit at my present residence.
+On the evening of that day, conversing on the great work of the planetary
+reductions undertaken by the Astronomer Royal[797]--then in progress, and
+since published,[798]--M. Bessel remarked that the motions of Uranus, as he
+had satisfied {385} himself by careful examination of the recorded
+observations, could not be accounted for by the perturbations of the known
+planets; and that the deviations far exceeded any possible limits of error
+of observation. In reply to the question, Whether the deviations in
+question might not be due to the action of an unknown planet?--he stated
+that he considered it highly probable that such was the case,--being
+systematic, and such as might be produced by an exterior planet. I then
+inquired whether he had attempted, from the indications afforded by these
+perturbations, to discover the position of the unknown body,--in order that
+'a hue and cry' might be raised for it. From his reply, the words of which
+I do not call to mind, I collected that he had not then gone into that
+inquiry; but proposed to do so, having now completed certain works which
+had occupied too much of his time. And, accordingly, in a letter which I
+received from him after his return to Königsberg, dated November 14, 1842,
+he says,--'In reference to our conversation at Collingwood, I _announce_ to
+you (_melde_ ich Ihnen) that Uranus is not forgotten.' Doubtless,
+therefore, among his papers will be found some researches on the subject.
+
+"The remarkable calculations of M. Le Verrier--which have pointed out, as
+now appears, nearly the true situation of the new planet, by resolving the
+inverse problem of the perturbations--if uncorroborated by repetition of
+the numerical calculations by another hand, or by independent investigation
+from another quarter, would hardly justify so strong an assurance as that
+conveyed by my expressions above alluded to. But it was known to me, at
+that time, (I will take the liberty to cite the Astronomer Royal as my
+authority) that a similar investigation had been independently entered
+into, and a conclusion as to the situation of the new planet very nearly
+coincident with M. Le Verrier's arrived at (in entire ignorance of his
+conclusions), by a young Cambridge mathematician, Mr. Adams;[799]--who
+will, I hope, {386} pardon this mention of his name (the matter being one
+of great historical moment),--and who will, doubtless, in his own good time
+and manner, place his calculations before the public.
+
+"J. F. W. HERSCHEL."
+
+_Discovery of Le Verrier's Planet._
+
+Mr. Hind announces to the _Times_ that he has received a letter from Dr.
+Brünnow, of the Royal Observatory at Berlin, giving the very important
+information that Le Verrier's planet was found by M. Galle, on the night of
+September 23. "In announcing this grand discovery," he says, "I think it
+better to copy Dr. Brünnow's[800] letter."
+
+
+
+"Berlin, Sept. 25.
+
+"My dear Sir--M. Le Verrier's planet was discovered here the 23d of
+September, by M. Galle.[801] It is a star of the 8th magnitude, but with a
+diameter of two or three seconds. Here are its places:
+
+             h. m. s.             R. A.           Declination.
+  Sept. 23,  12  0 14.6 M.T.      328° 19' 16.0"  -13° 24'  8.2"
+  Sept. 24,   8 54 40.9 M.T.      328° 18' 14.3"  -13° 24' 29.7"
+
+The planet is now retrograde, its motion amounting daily to four seconds of
+time.
+
+"Yours most respectfully, BRÜNNOW."
+
+"This discovery," Mr. Hind says, "may be justly considered one of the
+greatest triumphs of theoretical astronomy;" and he adds, in a postscript,
+that the planet was observed at Mr. Bishop's[802] Observatory, in the
+Regent's Park, {387} on Wednesday night, notwithstanding the moonlight and
+hazy sky. "It appears bright," he says, "and with a power of 320 I can see
+the disc. The following position is the result of instrumental comparisons
+with 33 Aquarii:
+
+  Sept. 30, at 8h. 16m. 21s. Greenwich mean time--
+      Right ascension of planet     21h. 52m. 47.15s.
+      South declination             13°  27'  20"."
+
+
+
+THE NEW PLANET.
+
+"Cambridge Observatory, Oct. 15.
+
+"The allusion made by Sir John Herschel, in his letter contained in the
+_Athenæum_ of October 3, to the theoretical researches of Mr. Adams,
+respecting the newly-discovered planet, has induced me to request that you
+would make the following communication public. It is right that I should
+first say that I have Mr. Adams's permission to make the statements that
+follow, so far as they relate to his labors. I do not propose to enter into
+a detail of the steps by which Mr. Adams was led, by his spontaneous and
+independent researches, to a conclusion that a planet must exist more
+distant than Uranus. The matter is of too great historical moment not to
+receive a more formal record than it would be proper to give here. My
+immediate object is to show, while the attention of the scientific public
+is more particularly directed to the subject, that, with respect to this
+remarkable discovery, English astronomers may lay claim to some merit.
+
+"Mr. Adams formed the resolution of trying, by calculation, to account for
+the anomalies in the motion of Uranus on the hypothesis of a more distant
+planet, when he was an undergraduate in this university, and when his
+exertions for the academical distinction, which he obtained in January
+1843, left him no time for pursuing the research. In the course of that
+year, he arrived at an approximation to the position of the supposed
+planet; which, however, he did not consider to be worthy of confidence, on
+account of his not {388} having employed a sufficient number of
+observations of Uranus. Accordingly, he requested my intervention to obtain
+for him the early Greenwich observations, then in course of
+reduction;--which the Astronomer Royal immediately supplied, in the kindest
+possible manner. This was in February, 1844. In September, 1845, Mr. Adams
+communicated to me values which he had obtained for the heliocentric
+longitude, excentricity of orbit, longitude of perihelion, and mass, of an
+assumed exterior planet,--deduced entirely from unaccounted-for
+perturbations of Uranus. The same results, somewhat corrected, he
+communicated, in October, to the Astronomer Royal. M. Le Verrier, in an
+investigation which was published in June of 1846, assigned very nearly the
+same heliocentric longitude for the probable position of the planet as Mr.
+Adams had arrived at, but gave no results respecting its mass and the form
+of its orbit. The coincidence as to position from two entirely independent
+investigations naturally inspired confidence; and the Astronomer Royal
+shortly after suggested the employing of the Northumberland telescope of
+this observatory in a systematic search after the hypothetical planet;
+recommending, at the same time, a definite plan of operations. I undertook
+to make the search,--and commenced observing on July 29. The observations
+were directed, in the first instance, to the part of the heavens which
+theory had pointed out as the most probable place of the planet; in
+selecting which I was guided by a paper drawn up for me by Mr. Adams. Not
+having hour xxi. of the Berlin star-maps--of the publication of which I was
+not aware--I had to proceed on the principle of comparison of observations
+made at intervals. On July 30, I went over a zone 9' broad, in such a
+manner as to include all stars to the eleventh magnitude. On August 4, I
+took a broader zone and recorded a place of the planet. My next
+observations were on August 12; when I met with a star of the eighth
+magnitude in the zone which I had gone over on July 30,--and which did not
+then {389} contain this star. Of course, this was the planet;--the place of
+which was, thus, recorded a second time in four days of observing. A
+comparison of the observations of July 30 and August 12 would, according to
+the principle of search which I employed, have shown me the planet. I did
+not make the comparison till after the detection of it at Berlin--partly
+because I had an impression that a much more extensive search was required
+to give any probability of discovery--and partly from the press of other
+occupation. The planet, however, was _secured_, and two positions of it
+recorded six weeks earlier here than in any other observatory,--and in a
+systematic search expressly undertaken for that purpose. I give now the
+positions of the planet on August 4 and August 12.
+
+  Greenwich mean time.
+
+  Aug. 4, 13h. 36m. 25s.     {R.A.   21h. 58m. 14.70s.
+                             {N.P.D. 102° 57'  32.2"
+
+  Aug. 12, 13h. 3m. 26s.     {R.A.   21h. 57m. 26.13s.
+                             {N.P.D. 103°  2'   0.2"
+
+"From these places compared with recent observations Mr. Adams has obtained
+the following results:
+
+  Distance of the planet from the sun       30.05
+  Inclination of the orbit                  1° 45'
+  Longitude of the descending node        309° 43'
+  Heliocentric longitude, Aug. 4          326° 39'
+
+"The present distance from the sun is, therefore, thirty times the earth's
+mean distance;--which is somewhat less than the theory had indicated. The
+other elements of the orbit cannot be approximated to till the observations
+shall have been continued for a longer period.
+
+"The part taken by Mr. Adams in the theoretical search after this planet
+will, perhaps, be considered to justify the suggesting of a name. With his
+consent, I mention _Oceanus_ as one which may possibly receive the votes of
+astronomers.--I {390} have authority to state that Mr. Adams's
+investigations will in a short time, be published in detail.
+
+"J. CHALLIS."[803]
+
+
+
+ASTRONOMICAL POLICE REPORT.
+
+"An ill-looking kind of a body, who declined to give any name, was brought
+before the Academy of Sciences, charged with having assaulted a gentleman
+of the name of Uranus in the public highway. The prosecutor was a youngish
+looking person, wrapped up in two or three great coats; and looked chillier
+than anything imaginable, except the prisoner,--whose teeth absolutely
+shook, all the time.
+
+Policeman Le Verrier[804] stated that he saw the prosecutor walking along
+the pavement,--and sometimes turning sideways, and sometimes running up to
+the railings and jerking about in a strange way. Calculated that somebody
+must be pulling his coat, or otherwise assaulting him. It was so dark that
+he could not see; but thought, if he watched the direction in which the
+next odd move was made, he might find out something. When the time came, he
+set Brünnow, a constable in another division of the same force, to watch
+where he told him; and Brünnow caught the prisoner lurking about in the
+very spot,--trying to look as if he was minding his own business. Had
+suspected for a long time that somebody was lurking about in the
+neighborhood. Brünnow was then called, and deposed to his catching the
+prisoner as described.
+
+_M. Arago._--Was the prosecutor sober?
+
+_Le Verrier._--Lord, yes, your worship; no man who had a drop in him ever
+looks so cold as he did.
+
+_M. Arago._--Did you see the assault?
+
+_Le Verrier._--I can't say I did; but I told Brünnow exactly how he'd be
+crouched down;--just as he was.
+
+{391}
+
+_M. Arago (to Brünnow)._--Did _you_ see the assault?
+
+_Brünnow._--No, your worship; but I caught the prisoner.
+
+_M. Arago._--How did you know there was any assault at all?
+
+_Le Verrier._--I reckoned it couldn't be otherwise, when I saw the
+prosecutor making those odd turns on the pavement.
+
+_M. Arago._--You reckon and you calculate! Why, you'll tell me, next, that
+you policemen may sit at home and find out all that's going on in the
+streets by arithmetic. Did you ever bring a case of this kind before me
+till now?
+
+_Le Verrier._--Why, you see, your worship, the police are growing cleverer
+and cleverer every day. We can't help it:--it grows upon us.
+
+_M. Arago._--You're getting too clever for me. What does the prosecutor
+know about the matter?
+
+The prosecutor said, all he knew was that he was pulled behind by somebody
+several times. On being further examined, he said that he had seen the
+prisoner often, but did not know his name, nor how he got his living; but
+had understood he was called Neptune. He himself had paid rates and taxes a
+good many years now. Had a family of six,--two of whom got their own
+living.
+
+The prisoner being called on for his defence, said that it was a quarrel.
+He had pushed the prosecutor--and the prosecutor had pushed him. They had
+known each other a long time, and were always quarreling;--he did not know
+why. It was their nature, he supposed. He further said, that the prosecutor
+had given a false account of himself;--that he went about under different
+names. Sometimes he was called Uranus, sometimes Herschel, and sometimes
+Georgium Sidus; and he had no character for regularity in the neighborhood.
+Indeed, he was sometimes not to be seen for a long time at once.
+
+The prosecutor, on being asked, admitted, after a little hesitation, that
+he had pushed and pulled the prisoner too. {392} In the altercation which
+followed, it was found very difficult to make out which began:--and the
+worthy magistrate seemed to think they must have begun together.
+
+_M. Arago._--Prisoner, have you any family?
+
+The prisoner declined answering that question at present. He said he
+thought the police might as well reckon it out whether he had or not.
+
+_M. Arago_ said he didn't much differ from that opinion.--He then addressed
+both prosecutor and prisoner; and told them that if they couldn't settle
+their differences without quarreling in the streets, he should certainly
+commit them both next time. In the meantime, he called upon both to enter
+into their own recognizances; and directed the police to have an eye upon
+both,--observing that the prisoner would be likely to want it a long time,
+and the prosecutor would be not a hair the worse for it."
+
+
+
+This quib was written by a person who was among the astronomers: and it
+illustrates the fact that Le Verrier had sole possession of the field until
+Mr. Challis's letter appeared. Sir John Herschel's previous communication
+should have paved the way: but the wonder of the discovery drove it out of
+many heads. There is an excellent account of the whole matter in Professor
+Grant's[805] _History of Physical Astronomy_. The squib scandalized some
+grave people, who wrote severe admonitions to the editor. There are
+formalists who spend much time in writing propriety to journals, to which
+they serve as foolometers. In a letter to the _Athenæum_, speaking of the
+way in which people hawk fine terms for common things, I said that these
+people ought to have a new translation of the Bible, which should contain
+the verse "gentleman and lady, created He them." The editor was handsomely
+fired and brimstoned!
+
+{393}
+
+
+
+A NEW THEORY OF TIDES.
+
+    A new theory of the tides: in which the errors of the usual theory are
+    demonstrated; and proof shewn that the full moon is not the cause of a
+    concomitant spring tide, but actually the cause of the neaps.... By
+    Comm^r. Debenham,[806] R.N. London, 1846, 8vo.
+
+The author replied to a criticism in the _Athenæum_, and I remember how, in
+a very few words, he showed that he had read nothing on the subject. The
+reviewer spoke of the forces of the planets (i.e., the Sun and Moon) on the
+ocean, on which the author remarks, "But N.B. the Sun is no planet, Mr.
+Critic." Had he read any of the actual investigations on the usual theory,
+he would have known that to this day the sun and moon continue to be called
+_planets_--though the phrase is disappearing--in speaking of the tides; the
+sense, of course, being the old one, wandering bodies.
+
+A large class of the paradoxers, when they meet with something which taken
+in their sense is absurd, do not take the trouble to find out the intended
+meaning, but walk off with the words laden with their own first
+construction. Such men are hardly fit to walk the streets without an
+interpreter. I was startled for a moment, at the time when a recent
+happy--and more recently happier--marriage occupied the public thoughts, by
+seeing in a haberdasher's window, in staring large letters, an unpunctuated
+sentence which read itself to me as "Princess Alexandra! collar and cuff!"
+It immediately occurred to me that had I been any one of some scores of my
+paradoxers, I should, no doubt, have proceeded to raise the mob against the
+unscrupulous person who dared to hint to a young bride such maleficent--or
+at least immellificent--conduct towards her new lord. But, as it was,
+certain material contexts in the shop window suggested a less {394} savage
+explanation. A paradoxer should not stop at reading the advertisements of
+Newton or Laplace; he should learn to look at the stock of goods.
+
+I think I must have an eye for double readings, when presented: though I
+never guess riddles. On the day on which I first walked into the _Panizzi_
+reading room[807]--as it ought to be called--at the Museum, I began my
+circuit of the wall-shelves at the ladies' end: and perfectly coincided in
+the propriety of the Bibles and theological works being placed there. But
+the very first book I looked on the back of had, in flaming gold letters,
+the following inscription--"Blast the Antinomians!"[808] If a line had been
+drawn below the first word, Dr. Blast's history of the Antinomians would
+not have been so fearfully misinterpreted. It seems that neither the binder
+nor the arranger of the room had caught my reading. The book was removed
+before the catalogue of books of reference was printed.
+
+
+
+AN ASTRONOMICAL PARADOXER.
+
+    Two systems of astronomy: first, the Newtonian system, showing the rise
+    and progress thereof, with a short historical account; the general
+    theory with a variety of remarks thereon: second, the system in
+    accordance with the Holy Scriptures, showing the rise and progress from
+    Enoch, the seventh from Adam, the prophets, Moses, and others, in the
+    first Testament; our Lord Jesus Christ, and his apostles, in the new or
+    second Testament; Reeve and Muggleton, in the third and last Testament;
+    with a variety of remarks thereon. By Isaac Frost.[809] London, 1846,
+    4to.
+
+{395}
+
+A very handsomely printed volume, with beautiful plates. Many readers who
+have heard of Muggletonians have never had any distinct idea of Lodowick
+Muggleton,[810] the inspired tailor, (1608-1698) who about 1650 received
+his commission from heaven, wrote a Testament, founded a sect, and
+descended to posterity. Of Reeve[811] less is usually said; according to
+Mr. Frost, he and Muggleton are the two "witnesses." I shall content myself
+with one specimen of Mr. Frost's science:
+
+"I was once invited to hear read over 'Guthrie[812] on Astronomy,' and when
+the reading was concluded I was asked my opinion thereon; when I said,
+'Doctor, it appears to me that Sir I. Newton has only given two proofs in
+support of his theory of the earth revolving round the sun: all the rest is
+assertion without any proofs.'--'What are they?' inquired the
+Doctor.--'Well,' I said, 'they are, first, the power of {396} attraction to
+keep the earth to the sun; the second is the power of repulsion, by virtue
+of the centrifugal motion of the earth: all the rest appears to me
+assertion without proof.' The Doctor considered a short time and then said,
+'It certainly did appear so.' I said, 'Sir Isaac has certainly obtained the
+credit of completing the system, but really he has only half done his
+work.'--'How is that,' inquired my friend the Doctor. My reply was this:
+'You will observe his system shows the earth traverses round the sun on an
+inclined plane; the consequence is, there are four powers required to make
+his system complete:
+
+  1st. The power of _attraction_.
+  2ndly. The power of _repulsion_.
+  3rdly. The power of _ascending_ the inclined plane.
+  4thly. The power of _descending_ the inclined plane.
+
+You will thus easily see the _four_ powers required, and Newton has only
+accounted for _two_; the work is therefore only half done.' Upon due
+reflection the Doctor said, 'It certainly was necessary to have these
+_four_ points cleared up before the system could be said to be complete.'"
+
+
+
+I have no doubt that Mr. Frost, and many others on my list, have really
+encountered doctors who could be puzzled by such stuff as this, or nearly
+as bad, among the votaries of existing systems, and have been encouraged
+thereby to print their objections. But justice requires me to say that from
+the words "power of repulsion by virtue of the centrifugal motion of the
+earth," Mr. Frost may be suspected of having something more like a notion
+of the much-mistaken term "centrifugal force" than many paradoxers of
+greater fame. The Muggletonian sect is not altogether friendless: over and
+above this handsome volume, the works of Reeve and Muggleton were printed,
+in 1832, in three quarto volumes. See _Notes and Queries, 1st Series_, v,
+80; 3d Series, iii, 303. {397}
+
+[The system laid down by Mr. Frost, though intended to be substantially
+that of Lodowick Muggleton, is not so vagarious. It is worthy of note how
+very different have been the fates of two contemporary paradoxers,
+Muggleton and George Fox.[813] They were friends and associates,[814] and
+commenced their careers about the same time, 1647-1650. The followers of
+Fox have made their sect an institution, and deserve to be called the
+pioneers of philanthropy. But though there must still be Muggletonians,
+since expensive books are published by men who take the name, no sect of
+that name is known to the world. Nevertheless, Fox and Muggleton are men of
+one type, developed by the same circumstances: it is for those who
+investigate such men to point out why their teachings have had fates so
+different. Macaulay says it was because Fox found followers of more sense
+than himself. True enough: but why did Fox find such followers and not
+Muggleton? The two were equally crazy, to all appearance: and the
+difference required must be sought in the doctrines themselves.
+
+Fox was not a _rational_ man: but the success of his sect and doctrines
+entitles him to a letter of alteration of the phrase which I am surprised
+has not become current. When Conduitt,[815] the husband of Newton's
+half-niece, wrote a circular to Newton's friends, just after his death,
+inviting them to bear their parts in a proper biography, he said, "As Sir
+I. Newton was a _national_ man, I think every one ought to contribute to a
+work intended to do him justice." Here is the very phrase which is often
+wanted to signify that {398} celebrity which puts its mark, good or bad, on
+the national history, in a manner which cannot be asserted of many
+notorious or famous historical characters. Thus George Fox and Newton are
+both _national_ men. Dr. Roget's[816] _Thesaurus_ gives more than fifty
+synonyms--_colleagues_ would be the better word--of "_celebrated_," any one
+of which might be applied, either in prose or poetry, to Newton or to his
+works, no one of which comes near to the meaning which Conduitt's adjective
+immediately suggests.
+
+The truth is, that we are too _monarchical_ to be _national_. We have the
+Queen's army, the Queen's navy, the Queen's highway, the Queen's English,
+etc.; nothing is national except the _debt_. That this remark is not new is
+an addition to its force; it has hardly been repeated since it was first
+made. It is some excuse that _nation_ is not vernacular English: the
+_country_ is our word, and _country man_ is appropriated.]
+
+
+
+    Astronomical Aphorisms, or Theory of Nature; founded on the immutable
+    basis of Meteoric Action. By P. Murphy,[817] Esq. London, 1847, 12mo.
+
+This is by the framer of the Weather Almanac, who appeals to that work as
+corroborative of his theory of planetary temperature, years after all the
+world knew by experience that this meteorological theory was just as good
+as the others.
+
+{399}
+
+
+
+    The conspiracy of the Bullionists as it affects the present system of
+    the money laws. By Caleb Quotem. Birmingham, 1847, 8vo. (pp. 16).
+
+This pamphlet is one of a class of which I know very little, in which the
+effects of the laws relating to this or that political bone of contention
+are imputed to deliberate conspiracy of one class to rob another of what
+the one knew ought to belong to the other. The success of such writers in
+believing what they have a bias to believe, would, if they knew themselves,
+make them think it equally likely that the inculpated classes might really
+believe what it is _their_ interest to believe. The idea of a _guilty_
+understanding existing among fundholders, or landholders, or any holders,
+all the country over, and never detected except by bouncing pamphleteers,
+is a theory which should have been left for Cobbett[818] to propose, and
+for Apella to believe.[819]
+
+[_August_, 1866. A pamphlet shows how to pay the National Debt. Advance
+paper to railways, etc., receivable in payment of taxes. The railways pay
+interest and principal in money, with which you pay your national debt, and
+redeem your notes. Twenty-five years of interest redeems the notes, and
+then the principal pays the debt. Notes to be kept up to value by
+penalties.]
+
+
+
+THEISM INDEPENDENT OF REVELATION.
+
+    The Reasoner. No. 45. Edited by G.J. Holyoake.[820] Price _2d._ Is
+    there sufficient proof of the existence of God? 8vo. 1847.
+
+This acorn of the holy oak was forwarded to me with a manuscript note,
+signed by the editor, on the part of the {400} "London Society of
+Theological Utilitarians," who say, "they trust you may be induced to give
+this momentous subject your consideration." The supposition that a
+middle-aged person, known as a student of thought on more subjects than
+one, had that particular subject yet to begin, is a specimen of what I will
+call the _assumption-trick_ of controversy, a habit which pervades all
+sides of all subjects. The tract is a proof of the good policy of letting
+opinions find their level, without any assistance from the Court of Queen's
+Bench. Twenty years earlier the thesis would have been positive, "There is
+sufficient proof of the non-existence of God," and bitter in its tone. As
+it stands, we have a moderate and respectful treatment--wrong only in
+making the opponent argue absurdly, as usually happens when one side
+invents the other--of a question in which a great many Christians have
+agreed with the atheist: that question being--Can the existence of God be
+proved independently of revelation? Many very religious persons answer this
+question in the negative, as well as Mr. Holyoake. And, this point being
+settled, all who agree in the negative separate into those who can endure
+scepticism, and those who cannot: the second class find their way to
+Christianity. This very number of _The Reasoner_ announces the secession of
+one of its correspondents, and his adoption of the Christian faith. This
+would not have happened twenty years before: nor, had it happened, would it
+have been respectfully announced.
+
+There are people who are very unfortunate in the expression of their
+meaning. Mr. Holyoake, in the name of the "London Society" etc., forwarded
+a pamphlet on the existence of God, and said that the Society trusted I
+"may be induced to give" the subject my "consideration." How could I know
+the Society was one person, who supposed I had arrived at a conclusion and
+wanted a "_guiding word_"? But so it seems it was: Mr. Holyoake, in the
+_English {401} Leader_ of October 15, 1864, and in a private letter to me,
+writes as follows:
+
+"The gentleman who was the author of the argument, and who asked me to send
+it to Mr. De Morgan, never assumed that that gentleman had 'that particular
+subject to begin'--on the contrary, he supposed that one whom we all knew
+to be eminent as a thinker _had_ come to a conclusion upon it, and would
+perhaps vouchsafe a guiding word to one who was, as yet, seeking the
+solution of the Great Problem of Theology. I told my friend that 'Mr. De
+Morgan was doubtless preoccupied, and that he must be content to wait. On
+some day of courtesy and leisure he might have the kindness to write.' Nor
+was I wrong--the answer appears in your pages at the lapse of seventeen
+years."
+
+I suppose Mr. Holyoake's way of putting his request was the _stylus curiæ_
+of the Society. A worthy Quaker who was sued for debt in the King's Bench
+was horrified to find himself charged in the declaration with detaining his
+creditor's money by force and arms, contrary to the peace of our Lord the
+King, etc. It's only the _stylus curiæ_, said a friend: I don't know
+_curiæ_, said the Quaker, but he shouldn't style us peace-breakers.
+
+The notion that the _non_-existence of God can be _proved_, has died out
+under the light of discussion: had the only lights shone from the pulpit
+and the prison, so great a step would never have been made. The question
+now is as above. The dictum that Christianity is "part and parcel of the
+law of the land" is also abrogated: at the same time, and the coincidence
+is not an accident, it is becoming somewhat nearer the truth that the law
+of the land is part and parcel of Christianity. It must also be noticed
+that _Christianity_ was part and parcel of the articles of _war_; and so
+was _duelling_. Any officer speaking against religion was to be cashiered;
+and any officer receiving an affront without, in the last resort,
+attempting to kill his opponent, was also to be cashiered. Though somewhat
+of a book-hunter, I {402} have never been able to ascertain the date of the
+collected remonstrances of the prelates in the House of Lords against this
+overt inculcation of murder, under the soft name of _satisfaction_: it is
+neither in Watt,[821] nor in Lowndes,[822] nor in any edition of
+Brunet;[823] and there is no copy in the British Museum. Was the collected
+edition really published?
+
+[The publication of the above in the _Athenæum_ has not produced reference
+to a single copy. The collected edition seems to be doubted. I have even
+met one or two persons who doubt the fact of the Bishops having
+remonstrated at all: but their doubt was founded on an absurd supposition,
+namely, that it was _no business of theirs_; that it was not the business
+of the prelates of the church in union with the state to remonstrate
+against the Crown commanding murder! Some say that the edition was
+published, but under an irrelevant title, which prevented people from
+knowing what it was about. Such things have happened: for example, arranged
+extracts from Wellington's general orders, which would have attracted
+attention, fell dead under the title of "Principles of War." It is surmised
+that the book I am looking for also contains the protests of the Reverend
+bench against other things besides the Thou-shalt-do-murder of the Articles
+(of war), and is called "First Elements of Religion" or some similar title.
+Time clears up all things.]
+
+       *       *       *       *       *
+
+
+Notes
+
+[1] See Mrs. De Morgan's _Memoir of Augustus De Morgan_, London, 1882, p
+61.
+
+[2] In the first edition this reference was to page 11.
+
+[3] In the first edition this read "at page 438," the work then appearing
+in a single volume.
+
+[4] "Just as it would surely have been better not to have considered it
+(i.e., the trinity) as a mystery, and with Cl. Kleckermann to have
+investigated by the aid of philosophy according to the teaching of true
+logic what it might be, before they determined what it was; just so would
+it have been better to withdraw zealously and industriously into the
+deepest caverns and darkest recesses of metaphysical speculations and
+suppositions in order to establish their opinion beyond danger from the
+weapons of their adversaries.... Indeed that great man so explains and
+demonstrates this dogma (although to theologians the word has not much
+charm) from the immovable foundations of philosophy, that with but few
+changes and additions a mind sincerely devoted to truth can desire nothing
+more."
+
+[5] Mrs. Wititterly, in _Nicholas Nickleby_.--A. De M.
+
+[6] The brackets mean that the paragraph is substantially from some one of
+the _Athenæum Supplements_.--S. E. De M.
+
+[7] "It is annoying that this ingenious naturalist who has already given us
+more useful works and has still others in preparation, uses for this odious
+task, a pen dipped in gall and wormwood. It is true that many of his
+remarks have some foundation, and that to each error that he points out he
+at the same time adds its correction. But he is not always just and never
+fails to insult. After all, what does his book prove except that a
+forty-fifth part of a very useful review is not free from mistakes? Must we
+confuse him with those superficial writers whose liberty of body does not
+permit them to restrain their fruitfulness, that crowd of savants of the
+highest rank whose writings have adorned and still adorn the
+_Transactions_? Has he forgotten that the names of the Boyles, Newtons,
+Halleys, De Moivres, Hans Sloanes, etc. have been seen frequently? and that
+still are found those of the Wards, Bradleys, Grahams, Ellicots, Watsons,
+and of an author whom Mr. Hill prefers to all others, I mean Mr. Hill
+himself?"
+
+[8] "Let no free man be seized or imprisoned or in any way harmed except by
+trial of his peers."
+
+[9] "The master can rob, wreck and punish his slave according to his
+pleasure save only that he may not maim him."
+
+[10] An Irish antiquary informs me that Virgil is mentioned in annals at
+A.D. 784, as "Verghil, i.e., the geometer, Abbot of Achadhbo [and Bishop of
+Saltzburg] died in Germany in the thirteenth year of his bishoprick." No
+allusion is made to his opinions; but it seems he was, by tradition, a
+mathematician. The Abbot of Aghabo (Queen's County) was canonized by
+Gregory IX, in 1233. The story of the second, or scapegoat, Virgil would be
+much damaged by the character given to the real bishop, if there were
+anything in it to dilapidate.--A. De M.
+
+[11] "He performed many acts befitting the Papal dignity, and likewise many
+excellent (to be sure!) works."
+
+[12] "After having been on the throne during ten years of pestilence."
+
+[13] The work is the _Questiones Joannis Buridani super X libros
+Aristotelis ad Nicomachum, curante Egidio Delfo_ ... Parisiis, 1489, folio.
+It also appeared at Paris in editions of 1499, 1513, and 1518, and at
+Oxford in 1637.
+
+[14] Jean Buridan was born at Béthune about 1298, and died at Paris about
+1358. He was professor of philosophy at the University of Paris and several
+times held the office of Rector. As a philosopher he was classed among the
+nominalists.
+
+[15] So in the original.
+
+[16] Baruch Spinoza, or Benedict de Spinoza as he later called himself, the
+pantheistic philosopher, excommunicated from the Jewish faith for heresy,
+was born at Amsterdam in 1632 and died there in 1677.
+
+[17] Michael Scott, or Scot, was born about 1190, probably in Fifeshire,
+Scotland, and died about 1291. He was one of the best known savants of the
+court of Emperor Frederick II, and wrote upon astrology, alchemy, and the
+occult sciences. He was looked upon as a great magician and is mentioned
+among the wizards in Dante's _Inferno_.
+
+             "That other, round the loins
+  So slender of his shape, was Michael Scot,
+  Practised in every slight of magic wile." _Inferno_, XX.
+
+Boccaccio also speaks of him: "It is not long since there was in this city
+(Florence) a great master in necromancy, who was called Michele Scotto,
+because he was a Scot." _Decameron_, Dec. Giorno.
+
+Scott's mention of him in Canto Second of his _Lay of the Last Minstrel_,
+is well known:
+
+ "In these fair climes, it was my lot
+  To meet the wondrous Michael Scott;
+    A wizard of such dreaded fame,
+  That when, in Salamanca's cave,
+  Him listed his magic wand to wave,
+    The bells would ring in Notre Dame!"
+
+Sir Walter's notes upon him are of interest.
+
+[18] These were some of the forgeries which Michel Chasles (1793-1880) was
+duped into buying. They purported to be a correspondence between Pascal and
+Newton and to show that the former had anticipated some of the discoveries
+of the great English physicist and mathematician. That they were forgeries
+was shown by Sir David Brewster in 1855.
+
+[19] "Let the serpent also break from its appointed path."
+
+[20] Guglielmo Brutus Icilius Timoleon Libri-Carucci della Sommaja, born at
+Florence in 1803; died at Fiesole in 1869. His _Histoire des Sciences
+Mathématiques_ appeared at Paris in 1838, the entire first edition of
+volume I, save some half dozen that he had carried home, being burned on
+the day that the printing was completed. He was a great collector of early
+printed works on mathematics, and was accused of having stolen large
+numbers of them from other libraries. This accusation took him to London,
+where he bitterly attacked his accusers. There were two auction sales of
+his library, and a number of his books found their way into De Morgan's
+collection.
+
+[21] Philo of Gadara lived in the second century B.C. He was a pupil of
+Sporus, who worked on the problem of the two mean proportionals.
+
+[22] In his _Histoire des Mathématiques_, the first edition of which
+appeared in 1758. Jean Etienne Montucla was born at Lyons in 1725 and died
+at Versailles in 1799. He was therefore only thirty-three years old when
+his great work appeared. The second edition, with additions by D'Alembert,
+appeared in 1799-1802. He also wrote a work on the quadrature of the
+circle, _Histoire des recherches sur la Quadrature du Cercle_, which
+appeared in 1754.
+
+[23] Eutocius of Ascalon was born in 480 A.D. He wrote commentaries on the
+first four books of the conics of Apollonius of Perga (247-222 B.C.). He
+also wrote on the Sphere and Cylinder and the Quadrature of the Circle, and
+on the two books on Equilibrium of Archimedes (287-212 B.C.)
+
+[24] Edward Cocker was born in 1631 and died between 1671 and 1677. His
+famous arithmetic appeared in 1677 and went through many editions. It was
+written in a style that appealed to teachers, and was so popular that the
+expression "According to Cocker" became a household phrase. Early in the
+nineteenth century there was a similar saying in America, "According to
+Daboll," whose arithmetic had some points of analogy to that of Cocker.
+Each had a well-known prototype in the ancient saying, "He reckons like
+Nicomachus of Gerasa."
+
+[25] So in the original, for Barrême. François Barrême was to France what
+Cocker was to England. He was born at Lyons in 1640, and died at Paris in
+1703. He published several arithmetics, dedicating them to his patron,
+Colbert. One of the best known of his works is _L'arithmétique, ou le livre
+facile pour apprendre l'arithmétique soi-mème_, 1677. The French word
+_barême_ or _barrême_, a ready-reckoner, is derived from his name.
+
+[26] Born at Rome, about 480 A.D.; died at Pavia, 524. Gibbon speaks of him
+as "the last of the Romans whom Cato or Tully could have acknowledged for
+their countryman." His works on arithmetic, music, and geometry were
+classics in the medieval schools.
+
+[27] Johannes Campanus, of Novarra, was chaplain to Pope Urban IV
+(1261-1264). He was one of the early medieval translators of Euclid from
+the Arabic into Latin, and the first printed edition of the _Elements_
+(Venice, 1482) was from his translation. In this work he probably depended
+not a little upon at least two or three earlier scholars. He also wrote _De
+computo ecclesiastico Calendarium_, and _De quadratura circuli_.
+
+[28] Archimedes gave 3-1/7, and 3-10/71 as the limits of the ratio of the
+circumference to the diameter of a circle.
+
+[29] Friedrich W. A. Murhard was born at Cassel in 1779 and died there in
+1853. His _Bibliotheca Mathematica_, Leipsic, 1797-1805, is ill arranged
+and inaccurate, but it is still a helpful bibliography. De Morgan speaks
+somewhere of his indebtedness to it.
+
+[30] Abraham Gotthelf Kästner was born at Leipsic in 1719, and died at
+Göttingen in 1800. He was professor of mathematics and physics at
+Göttingen. His _Geschichte der Mathematik_ (1796-1800) was a work of
+considerable merit. In the text of the _Budget of Paradoxes_ the name
+appears throughout as Kastner instead of Kästner.
+
+[31] Lucas Gauricus, or Luca Gaurico, born at Giffoni, near Naples, in
+1476; died at Rome in 1558. He was an astrologer and mathematician, and was
+professor of mathematics at Ferrara in 1531. In 1545 he became bishop of
+Cività Ducale.
+
+[32] John Couch Adams was born at Lidcot, Cornwall, in 1819, and died in
+1892. He and Leverrier predicted the discovery of Neptune from the
+perturbations in Uranus.
+
+[33] Urbain-Jean-Joseph Leverrier was born at Saint-Lô, Manche, in 1811,
+and died at Paris in 1877. It was his data respecting the perturbations of
+Uranus that were used by Adams and himself in locating Neptune.
+
+[34] Joseph-Juste Scaliger, the celebrated philologist, was born at Agen in
+1540, and died at Leyden in 1609. His _Cyclometrica elementa_, to which De
+Morgan refers, appeared at Leyden in 1594.
+
+[35] The title is: _In hoc libra contenta.... Introductio i
+geometri[=a].... Liber de quadratura circuli. Liber de cubicatione sphere.
+Perspectiva introductio_. Carolus Bovillus, or Charles Bouvelles (Boüelles,
+Bouilles, Bouvel), was born at Saucourt, Picardy, about 1470, and died at
+Noyon about 1533. He was canon and professor of theology at Noyon. His
+_Introductio_ contains considerable work on star polygons, a favorite study
+in the Middle Ages and early Renaissance. His work _Que hoc volumine
+contin[=e]tur. Liber de intellectu. Liber de sensu_, etc., appeared at
+Paris in 1509-10.
+
+[36] Nicolaus Cusanus, Nicolaus Chrypffs or Krebs, was born at Kues on the
+Mosel in 1401, and died at Todi, Umbria, August 11, 1464. He held positions
+of honor in the church, including the bishopric of Brescia. He was made a
+cardinal in 1448. He wrote several works on mathematics, his _Opuscula
+varia_ appearing about 1490, probably at Strasburg, but published without
+date or place. His _Opera_ appeared at Paris in 1511 and again in 1514, and
+at Basel in 1565.
+
+[37] Henry Stephens (born at Paris about 1528, died at Lyons in 1598) was
+one of the most successful printers of his day. He was known as
+_Typographus Parisiensis_, and to his press we owe some of the best works
+of the period.
+
+[38] Jacobus Faber Stapulensis (Jacques le Fèvre d'Estaples) was born at
+Estaples, near Amiens, in 1455, and died at Nérac in 1536. He was a priest,
+vicar of the bishop of Meaux, lecturer on philosophy at the Collège Lemoine
+in Paris, and tutor to Charles, son of Francois I. He wrote on philosophy,
+theology, and mathematics.
+
+[39] Claude-François Milliet de Challes was born at Chambéry in 1621, and
+died at Turin in 1678. He edited _Euclidis Elementorum libri octo_ in 1660,
+and published a _Cursus seu mundus mathematicus_, which included a short
+history of mathematics, in 1674. He also wrote on mathematical geography.
+
+[40] This date should be 1503, if he refers to the first edition. It is
+well known that this is the first encyclopedia worthy the name to appear in
+print. It was written by Gregorius Reisch (born at Balingen, and died at
+Freiburg in 1487), prior of the cloister at Freiburg and confessor to
+Maximilian I. The first edition appeared at Freiburg in 1503, and it passed
+through many editions in the sixteenth and seventeenth centuries. The title
+of the 1504 edition reads: _Aepitoma omnis phylosophiae. alias Margarita
+phylosophica tractans de omni genere scibili: Cum additionibus: Quae in
+alijs non habentur_.
+
+[41] This is the _Introductio in arithmeticam Divi S. Boetii.... Epitome
+rerum geometricarum ex geometrica introductio C. Bovilli. De quadratura
+circuli demonstratio ex Campano_, that appeared without date about 1507.
+
+[42] Born at Liverpool in 1805, and died there about 1872. He was a
+merchant, and in 1865 he published, at Liverpool, a work entitled _The
+Quadrature of the Circle, or the True Ratio between the Diameter and
+Circumference geometrically and mathematically demonstrated_. In this he
+gives the ratio as exactly 3-1/8.
+
+[43] "That it would be impossible to tell him exactly, since no one had yet
+been able to find precisely the ratio of the circumference to the
+diameter."
+
+[44] This is the Paris edition: "Parisiis: ex officina Ascensiana anno
+Christi ... MDXIIII," as appears by the colophon of the second volume to
+which De Morgan refers.
+
+[45] Regiomontanus, or Johann Müller of Königsberg (Regiomontanus), was
+born at Königsberg in Franconia, June 5, 1436, and died at Rome July 6,
+1476. He studied at Vienna under the great astronomer Peuerbach, and was
+his most famous pupil. He wrote numerous works, chiefly on astronomy. He is
+also known by the names Ioannes de Monte Regio, de Regiomonte, Ioannes
+Germanus de Regiomonte, etc.
+
+[46] Henry Cornelius Agrippa was born at Cologne in 1486 and died either at
+Lyons in 1534 or at Grenoble in 1535. He was professor of theology at
+Cologne and also at Turin. After the publication of his _De Occulta
+Philosophia_ he was imprisoned for sorcery. Both works appeared at Antwerp
+in 1530, and each passed through a large number of editions. A French
+translation appeared in Paris in 1582, and an English one in London in
+1651.
+
+[47] Nicolaus Remegius was born in Lorraine in 1554, and died at Nancy in
+1600. He was a jurist and historian, and held the office of procurator
+general to the Duke of Lorraine.
+
+[48] This was at the storming of the city by the British on May 4, 1799.
+From his having been born in India, all this appealed strongly to the
+interests of De Morgan.
+
+[49] Orontius Finaeus, or Oronce Finé, was born at Briançon in 1494 and
+died at Paris, October 6, 1555. He was imprisoned by François I for
+refusing to recognize the concordat (1517). He was made professor of
+mathematics in the Collège Royal (later called the Collège de France) in
+1532. He wrote extensively on astronomy and geometry, but was by no means a
+great scholar. He was a pretentious man, and his works went through several
+editions. His _Protomathesis_ appeared at Paris in 1530-32. The work
+referred to by De Morgan is the _Quadratura circuli tandem inventa &
+clarissime demonstrata_ ... Lutetiae Parisiorum, 1544, fol. In the 1556
+edition of his _De rebus mathematicis, hactenus desideratis, Libri IIII_,
+published at Paris, the subtitle is: _Quibus inter cætera, Circuli
+quadratura Centum modis, & suprà, per eundem Orontium recenter excogitatis,
+demonstratus_, so that he kept up his efforts until his death.
+
+[50] Johannes Buteo (Boteo, Butéon, Bateon) was born in Dauphiné c.
+1485-1489, and died in a cloister in 1560 or 1564. Some writers give
+Charpey as the place and 1492 as the date of his birth, and state that he
+died at Canar in 1572. He belonged to the order of St. Anthony, and wrote
+chiefly on geometry, exposing the pretenses of Finaeus. His _Opera
+geometrica_ appeared at Lyons in 1554, and his _Logistica_ and _De
+quadratura circuli libri duo_ at Lyons in 1559.
+
+[51] This is the great French algebraist, François Viète (Vieta), who was
+born at Fontenay-le-Comte in 1540, and died at Paris, December 13, 1603.
+His well-known _Isagoge in artem analyticam_ appeared at Tours in 1591. His
+_Opera mathematica_ was edited by Van Schooten in 1646.
+
+[52] This is the _De Rebus mathematicis hactenus desideratis, Libri IIII_,
+that appeared in Paris in 1556. For the title page see Smith, D. E., _Rara
+Arithmetica_, Boston, 1908, p. 280.
+
+[53] The title is correct except for a colon after _Astronomicum_. Nicolaus
+Raimarus Ursus was born in Henstede or Hattstede, in Dithmarschen, and died
+at Prague in 1599 or 1600. He was a pupil of Tycho Brahe. He also wrote _De
+astronomis hypothesibus_ (1597) and _Arithmetica analytica vulgo Cosa oder
+Algebra_ (1601).
+
+[54] Born at Dôle, Franche-Comté, about 1550, died in Holland about 1600.
+The work to which reference is made is the _Quadrature du cercle, ou
+manière de trouver un quarré égal au cercle donné_, which appeared at Delft
+in 1584. Duchesne had the courage of his convictions, not only on
+circle-squaring but on religion as well, for he was obliged to leave France
+because of his conversion to Calvinism. De Morgan's statement that his real
+name is Van der Eycke is curious, since he was French born. The Dutch may
+have translated his name when he became professor at Delft, but we might
+equally well say, that his real name was Quercetanus or à Quercu.
+
+[55] This was the father of Adriaan Metius (1571-1635). He was a
+mathematician and military engineer, and suggested the ratio 355/113 for
+[pi], a ratio afterwards published by his son. The ratio, then new to
+Europe, had long been known and used in China, having been found by Tsu
+Ch'ung-chih (428-499 A.D.).
+
+[56] This was Jost Bürgi, or Justus Byrgius, the Swiss mathematician of
+whom Kepler wrote in 1627: "Apices logistici Justo Byrgio multis annis ante
+editionem Neperianam viam præiverunt ad hos ipsissimos logarithmos." He
+constructed a table of antilogarithms (_Arithmetische und geometrische
+Progress-Tabulen_), but it was not published until after Napier's work
+appeared.
+
+[57] Ludolphus Van Ceulen, born at Hildesheim, and died at Leyden in 1610.
+It was he who first carried the computation of [pi] to 35 decimal places.
+
+[58] Jens Jenssen Dodt, van Flensburg, a Dutch historian, who died in 1847.
+
+[59] I do not know this edition. There was one "Antverpiae apud Petrum
+Bellerum sub scuto Burgundiae," 4to, in 1591.
+
+[60] Archytas of Tarentum (430-365 B.C.) who wrote on proportions,
+irrationals, and the duplication of the cube.
+
+[61]
+
+      _The Circle Speaks._
+ "At first a circle I was called,
+  And was a curve around about
+  Like lofty orbit of the sun
+  Or rainbow arch among the clouds.
+  A noble figure then was I--
+  And lacking nothing but a start,
+  And lacking nothing but an end.
+  But now unlovely do I seem
+  Polluted by some angles new.
+  This thing Archytas hath not done
+  Nor noble sire of Icarus
+  Nor son of thine, Iapetus.
+  What accident or god can then
+  Have quadrated mine area?"
+
+      _The Author Replies._
+ "By deepest mouth of Turia
+  And lake of limpid clearness, lies
+  A happy state not far removed
+  From old Saguntus; farther yet
+  A little way from Sucro town.
+  In this place doth a poet dwell,
+  Who oft the stars will closely scan,
+  And always for himself doth claim
+  What is denied to wiser men;--
+  An old man musing here and there
+  And oft forgetful of himself,
+  Not knowing how to rightly place
+  The compasses, nor draw a line,
+  As he doth of himself relate.
+  This craftsman fine, in sooth it is
+  Hath quadrated thine area."
+
+[62] Pietro Bongo, or Petrus Bungus, was born at Bergamo, and died there in
+1601. His work on the Mystery of Numbers is one of the most exhaustive and
+erudite ones of the mystic writers. The first edition appeared at Bergamo
+in 1583-84; the second, at Bergamo in 1584-85; the third, at Venice in
+1585; the fourth, at Bergamo in 1590; and the fifth, which De Morgan calls
+the second, in 1591. Other editions, before the Paris edition to which he
+refers, appeared in 1599 and 1614; and the colophon of the Paris edition is
+dated 1617. See the editor's _Rara Arithmetica_, pp. 380-383.
+
+[63] William Warburton (1698-1779), Bishop of Gloucester, whose works got
+him into numerous literary quarrels, being the subject of frequent satire.
+
+[64] Thomas Galloway (1796-1851), who was professor of mathematics at
+Sandhurst for a time, and was later the actuary of the Amicable Life
+Assurance Company of London. In the latter capacity he naturally came to be
+associated with De Morgan.
+
+[65] Giordano Bruno was born near Naples about 1550. He left the Dominican
+order to take up Calvinism, and among his publications was _L'expulsion de
+la bête triomphante_. He taught philosophy at Paris and Wittenberg, and
+some of his works were published in England in 1583-86. Whether or not he
+was roasted alive "for the maintenance and defence of the holy Church," as
+De Morgan states, depends upon one's religious point of view. At any rate,
+he was roasted as a heretic.
+
+[66] Referring to part of his _Discours de la méthode_, Leyden, 1637.
+
+[67] Bartholomew Legate, who was born in Essex about 1575. He denied the
+divinity of Christ and was the last heretic burned at Smithfield.
+
+[68] Edward Wightman, born probably in Staffordshire. He was
+anti-Trinitarian, and claimed to be the Messiah. He was the last man burned
+for heresy in England.
+
+[69] Gaspar Schopp, born at Neumarck in 1576, died at Padua in 1649;
+grammarian, philologist, and satirist.
+
+[70] Konrad Ritterhusius, born at Brunswick in 1560; died at Altdorf in
+1613. He was a jurist of some power.
+
+[71] Johann Jakob Brucker, born at Augsburg in 1696, died there in 1770. He
+wrote on the history of philosophy (1731-36, and 1742-44).
+
+[72] Daniel Georg Morhof, born at Wismar in 1639, died at Lübeck in 1691.
+He was rector of the University of Kiel, and professor of eloquence,
+poetry, and history.
+
+[73] In the _Histoire des Sciences Mathématiques_, vol. IV, note X, pp.
+416-435 of the 1841 edition.
+
+[74] Colenso (1814-1883), missionary bishop of Natal, was one of the
+leaders of his day in the field of higher biblical criticism. De Morgan
+must have admired his mathematical works, which were not without merit.
+
+[75] Samuel Roffey Maitland, born at London in 1792; died at Gloucester in
+1866. He was an excellent linguist and a critical student of the Bible. He
+became librarian at Lambeth in 1838.
+
+[76] Archbishop Howley (1766-1848) was a thorough Tory. He was one of the
+opponents of the Roman Catholic Relief bill, the Reform bill, and the
+Jewish Civil Disabilities Relief bill.
+
+[77] We have, in America at least, almost forgotten the great stir made by
+Edward B. Pusey (1800-1882) in the great Oxford movement in the middle of
+the nineteenth century. He was professor of Hebrew at Oxford, and canon of
+Christ Church.
+
+[78] That is, his _Magia universalis naturae et artis sive recondita
+naturalium et artificialium rerum scientia_, Würzburg, 1657, 4to, with
+editions at Bamberg in 1671, and at Frankfort in 1677. Gaspard Schott
+(Königshofen 1608, Würzburg 1666) was a physicist and mathematician,
+devoting most of his attention to the curiosities of his sciences. His type
+of mind must have appealed to De Morgan.
+
+[79] _Salicetti Quadratura circuli nova, perspicua, expedita, veraque tum
+naturalis, tum geometrica_, etc., 1608.--_Consideratio nova in opusculum
+Archimedis de circuli dimensione_, etc., 1609.
+
+[80] Melchior Adam, who died at Heidelberg in 1622, wrote a collection of
+biographies which was published at Heidelberg and Frankfort from 1615 to
+1620.
+
+[81] Born at Baden in 1524; died at Basel in 1583. The Erastians were
+related to the Zwinglians, and opposed all power of excommunication and the
+infliction of penalties by a church.
+
+[82] See Acts xii. 20.
+
+[83] Theodore de Bèse, a French theologian; born at Vezelay, in Burgundy,
+in 1519; died at Geneva, in 1605.
+
+[84] Dr. Robert Lee (1804-1868) had some celebrity in De Morgan's time
+through his attempt to introduce music and written prayers into the service
+of the Scotch Presbyterian church.
+
+[85] Born at Veringen, Hohenzollern, in 1512; died at Röteln in 1564.
+
+[86] Born at Kinnairdie, Bannfshire, in 1661; died at London in 1708. His
+_Astronomiae Physicae et Geometriae Elementa_, Oxford, 1702, was an
+influential work.
+
+[87] The title was carelessly copied by De Morgan, not an unusual thing in
+his case. The original reads: A Plaine Discovery, of the whole Revelation
+of S. Iohn: set downe in two treatises ... set foorth by John Napier L. of
+Marchiston ... whereunto are annexed, certaine Oracles of Sibylla ...
+London ... 1611.
+
+[88] I have not seen the first edition, but it seems to have appeared in
+Edinburgh, in 1593, with a second edition there in 1594. The 1611 edition
+was the third.
+
+[89] It seems rather certain that Napier felt his theological work of
+greater importance than that in logarithms. He was born at Merchiston, near
+(now a part of) Edinburgh, in 1550, and died there in 1617, three years
+after the appearance of his _Mirifici logarithmorum canonis descriptio_.
+
+[90] Followed, in the third edition, from which he quotes, by a comma.
+
+[91] There was an edition published at Stettin in 1633. An English
+translation by P. F. Mottelay appeared at London in 1893. Gilbert
+(1540-1603) was physician to Queen Elizabeth and President of the College
+of Physicians at London. His _De Magnete_ was the first noteworthy treatise
+on physics printed in England. He treated of the earth as a spherical
+magnet and suggested the variation and declination of the needle as a means
+of finding latitude at sea.
+
+[92] The title says "ab authoris fratre collectum," although it was edited
+by J. Gruterus.
+
+[93] Porta was born at Naples in 1550 and died there in 1615. He studied
+the subject of lenses and the theory of sight, did some work in hydraulics
+and agriculture, and was well known as an astrologer. His _Magiae naturalis
+libri XX_ was published at Naples in 1589. The above title should read
+_curvilineorum_.
+
+[94] Cataldi was born in 1548 and died at Bologna in 1626. He was professor
+of mathematics at Perugia, Florence, and Bologna, and is known in
+mathematics chiefly for his work in continued fractions. He was one of the
+scholarly men of his day.
+
+[95] Georg Joachim Rheticus was born at Feldkirch in 1514 and died at
+Caschau, Hungary, in 1576. He was one of the most prominent pupils of
+Copernicus, his _Narratio de libris revolutionum Copernici_ (Dantzig, 1540)
+having done much to make the theory of his master known.
+
+[96] Henry Briggs, who did so much to make logarithms known, and who used
+the base 10, was born at Warley Wood, in Yorkshire, in 1560, and died at
+Oxford in 1630. He was Savilian professor of mathematics at Oxford, and his
+grave may still be seen there.
+
+[97] He lived at "Reggio nella Emilia" in the 16th and 17th centuries. His
+_Regola e modo facilissimo di quadrare il cerchio_ was published at Reggio
+in 1609.
+
+[98] Christoph Klau (Clavius) was born at Bamberg in 1537, and died at Rome
+in 1612. He was a Jesuit priest and taught mathematics in the Jesuit
+College at Rome. He wrote a number of works on mathematics, including
+excellent text-books on arithmetic and algebra.
+
+[99] Christopher Gruenberger, or Grienberger, was born at Halle in Tyrol in
+1561, and died at Rome in 1636. He was, like Clavius, a Jesuit and a
+mathematician, and he wrote a little upon the subject of projections. His
+_Prospectiva nova coelestis_ appeared at Rome in 1612.
+
+[100] The name should, of course, be Lansbergii in the genitive, and is so
+in the original title. Philippus Lansbergius was born at Ghent in 1560, and
+died at Middelburg in 1632. He was a Protestant theologian, and was also a
+physician and astronomer. He was a well-known supporter of Galileo and
+Copernicus. His _Commentationes in motum terrae diurnum et annuum_ appeared
+at Middelburg in 1630 and did much to help the new theory.
+
+[101] I have never seen the work. It is rare.
+
+[102] The African explorer, born in Somersetshire in 1827, died at Bath in
+1864. He was the first European to cross Central Africa from north to
+south. He investigated the sources of the Nile.
+
+[103] Prester (Presbyter, priest) John, the legendary Christian king whose
+realm, in the Middle Ages, was placed both in Asia and in Africa, is first
+mentioned in the chronicles of Otto of Freisingen in the 12th century. In
+the 14th century his kingdom was supposed to be Abyssinia.
+
+[104] "It is a profane and barbarous nation, dirty and slovenly, who eat
+their meat half raw and drink mare's milk, and who use table-cloths and
+napkins only to wipe their hands and mouths."
+
+[105] "The great Prester John, who is the fourth in rank, is emperor of
+Ethiopia and of the Abyssinians, and boasts of his descent from the race of
+David, as having descended from the Queen of Sheba, Queen of Ethiopia. She,
+having gone to Jerusalem to see the wisdom of Solomon, about the year of
+the world 2952, returned pregnant with a son whom they called Moylech, from
+whom they claim descent in a direct line. And so he glories in being the
+most ancient monarch in the world, saying that his empire has endured for
+more than three thousand years, which no other empire is able to assert. He
+also puts into his titles the following: 'We, the sovereign in my realms,
+uniquely beloved of God, pillar of the faith, sprung from the race of
+Judah, etc.' The boundaries of this empire touch the Red Sea and the
+mountains of Azuma on the east, and on the western side it is bordered by
+the River Nile which separates it from Nubia. To the north lies Egypt, and
+to the south the kingdoms of Congo and Mozambique. It extends forty degrees
+in length, or one thousand twenty-five leagues, from Congo or Mozambique on
+the south to Egypt on the north; and in width it reaches from the Nile on
+the west to the mountains of Azuma on the east, seven hundred twenty-five
+leagues, or twenty-nine degrees. This empire contains thirty large
+provinces, namely Medra, Gaga, Alchy, Cedalon, Mantro, Finazam, Barnaquez,
+Ambiam, Fungy, Angoté, Cigremaon, Gorga, Cafatez, Zastanla, Zeth, Barly,
+Belangana, Tygra, Gorgany, Barganaza, d'Ancut, Dargaly, Ambiacatina,
+Caracogly, Amara, Maon (_sic_), Guegiera, Bally, Dobora, and Macheda. All
+of these provinces are situated directly under the equinoctial line between
+the tropics of Capricorn and Cancer; but they are two hundred fifty leagues
+nearer our tropic than the other. The name of Prester John signifies Great
+Lord, and is not Priest [Presbyter] as many think. He has always been a
+Christian, but often schismatic. At the present time he is a Catholic and
+recognizes the Pope as sovereign pontiff. I met one of his bishops in
+Jerusalem, and often conversed with him through the medium of our guide. He
+was of grave and serious bearing, pleasant of speech, but wonderfully
+subtle in everything he said. He took great delight in what I had to relate
+concerning our beautiful ceremonies and the dignity of our prelates in
+their pontifical vestments. As to other matters I will only say that the
+Ethiopian is joyous and merry, not at all like the Tartar in the matter of
+filth, nor like the wretched Arab. They are refined and subtle, trusting no
+one, wonderfully suspicious, and very devout. They are not at all black as
+is commonly supposed, by which I refer to those who do not live under the
+equator or too near to it, for these are Moors as we shall see."
+
+With respect to this translation it should be said that the original forms
+of the proper names have been preserved, although they are not those found
+in modern works. It should also be stated that the meaning of Prester is
+not the one that was generally accepted by scholars at the time the work
+was written, nor is it the one accepted to-day. There seems to be no doubt
+that the word is derived from Presbyter as stated in note 103 on page 71,
+since the above-mentioned chronicles of Otto, bishop of Freisingen about
+the middle of the twelfth century, states this fact clearly. Otto received
+his information from the bishop of Gabala (the Syrian Jibal) who told him
+the story of John, _rex et sacerdos_, or Presbyter John as he liked to be
+called. He goes on to say "Should it be asked why, with all this power and
+splendor, he calls himself merely 'presbyter,' this is because of his
+humility, and because it was not fitting for one whose server was a primate
+and king, whose butler an archbishop and king, whose chamberlain a bishop
+and king, whose master of the horse an archimandrite and king, whose chief
+cook an abbot and king, to be called by such titles as these."
+
+[106] Thomas Fienus (Fyens) was born at Antwerp in 1567 and died in 1631.
+He was professor of medicine at Louvain. Besides the editions mentioned
+below, his _De cometis anni 1618_ appeared at Leipsic in 1656. He also
+wrote a _Disputatio an coelum moveatur et terra quiescat_, which appeared
+at Antwerp in 1619, and again at Leipsic in 1656.
+
+[107] Libertus Fromondus (1587-c 1653), a Belgian theologian, dean of the
+College Church at Harcourt, and professor at Louvain. The name also appears
+as Froidmont and Froimont.
+
+[108] _L. Fromondi ... meteorologicorum libri sex.... Cui accessit T. Fieni
+et L. Fromondi dissertationes de cometa anni 1618...._ This is from the
+1670 edition. The 1619 edition was published at Antwerp. The
+_Meteorologicorum libri VI_, appeared at Antwerp in 1627. He also wrote
+_Anti-Aristarchus sive orbis terrae immobilis liber unicus_ (Antwerp,
+1631); _Labyrrinthus sive de compositione continui liber unus, Philosophis,
+Mathematicis, Theologis utilis et jucundus_ (Antwerp, 1631) and _Vesta sive
+Anti-Aristarchi vindex adversus Jac. Lansbergium (Philippi filium) et
+copernicanos_ (Antwerp, 1634).
+
+[109] Snell was born at Leyden in 1591, and died there in 1626. He studied
+under Tycho Brahe and Kepler, and is known for Snell's law of the
+refraction of light. He was the first to determine the size of the earth by
+measuring the arc of a meridian with any fair degree of accuracy. The title
+should read: _Willebrordi Snellii R. F. Cyclometricus, de circuli
+dimensione secundum Logistarum abacos, et ad Mechanicem accuratissima...._
+
+[110] Bacon was born at York House, London, in 1561, and died near
+Highgate, London, in 1626. His _Novum Organum Scientiarum or New Method of
+employing the reasoning faculties in the pursuits of Truth_ appeared at
+London in 1620. He had previously published a work entitled _Of the
+Proficience and Advancement of Learning, divine and humane_ (London, 1605),
+which again appeared in 1621. His _De augmentis scientiarum Libri IX_
+appeared at Paris in 1624, and his _Historia naturalis et experimentalis de
+ventis_ at Leyden in 1638. He was successively solicitor general, attorney
+general, lord chancellor (1619), Baron Verulam and Viscount St. Albans. He
+was deprived of office and was imprisoned in the Tower of London in 1621,
+but was later pardoned.
+
+[111] The Greek form, _Organon_, is sometimes used.
+
+[112] James Spedding (1808-1881), fellow of Cambridge, who devoted his life
+to his edition of Bacon.
+
+[113] R. Leslie Ellis (1817-1859), editor of the _Cambridge Mathematical
+Journal_. He also wrote on Roman aqueducts, on Boole's Laws of Thought, and
+on the formation of a Chinese dictionary.
+
+[114] Douglas Derion Heath (1811-1897), a classical and mathematical
+scholar.
+
+[115] There have been numerous editions of Bacon's complete works,
+including the following: Frankfort, 1665; London, 1730, 1740, 1764, 1765,
+1778, 1803, 1807, 1818, 1819, 1824, 1825-36, 1857-74, 1877. The edition to
+which De Morgan refers is that of 1857-74, 14 vols., of which five were
+apparently out at the time he wrote. There were also French editions in
+1800 and 1835.
+
+[116] So in the original for Tycho Brahe.
+
+[117] In general these men acted before Baron wrote, or at any rate, before
+he wrote the _Novum Organum_, but the statement must not be taken too
+literally. The dates are as follows: Copernicus, 1473-1543; Tycho Brahe,
+1546-1601; Gilbert, 1540-1603; Kepler, 1571-1630; Galileo, 1564-1642;
+Harvey, 1578-1657. For example, Harvey's _Exercitatio Anatomica de Motu
+Cordis et Sanguinis_ did not appear until 1628, and his _Exercitationes de
+Generatione_ until 1651.
+
+[118] Robert Hooke (1635-1703) studied under Robert Boyle at Oxford. He was
+"Curator of Experiments" to the Royal Society and its secretary, and was
+professor of geometry at Gresham College, London. It is true that he was
+"very little of a mathematician" although he wrote on the motion of the
+earth (1674), on helioscopes and other instruments (1675), on the rotation
+of Jupiter (1666), and on barometers and sails.
+
+[119] The son of the Sir William mentioned below. He was born in 1792 and
+died in 1871. He wrote a treatise on light (1831) and one on astronomy
+(1836), and established an observatory at the Cape of Good Hope where he
+made observations during 1834-1838, publishing them in 1847. On his return
+to England he was knighted, and in 1848 was made president of the Royal
+Society. The title of the work to which reference is made is: _A
+preliminary discourse on the Study of Natural Philosophy_. It appeared at
+London in 1831.
+
+[120] Sir William was horn at Hanover in 1738 and died at Slough, near
+Windsor in 1822. He discovered the planet Uranus and six satellites,
+besides two satellites of Saturn. He was knighted by George III.
+
+[121] This was the work of 1836. He also published a work entitled
+_Outlines of Astronomy_ in 1849.
+
+[122] While Newton does not tell the story, he refers in the _Principia_
+(1714 edition, p. 293) to the accident caused by his cat.
+
+[123] Marino Ghetaldi (1566-1627), whose _Promotus Archimedes_ appeared at
+Rome in 1603, _Nonnullae propositiones de parabola_ at Rome in 1603. and
+_Apollonius redivivus_ at Venice in 1607. He was a nobleman and was
+ambassador from Venice to Rome.
+
+[124] Simon Stevin (born at Bruges, 1548; died at the Hague, 1620). He was
+an engineer and a soldier, and his _La Disme_ (1585) was the first separate
+treatise on the decimal fraction. The contribution referred to above is
+probably that on the center of gravity of three bodies (1586).
+
+[125] Habakuk Guldin (1577-1643), who took the name Paul on his conversion
+to Catholicism. He became a Jesuit, and was professor of mathematics at
+Vienna and later at Gratz. In his _Centrobaryca seu de centro gravitatis
+trium specierum quantitatis continuae_ (1635), of the edition of 1641,
+appears the Pappus rule for the volume of a solid formed by the revolution
+of a plane figure about an axis, often spoken of as Guldin's Theorem.
+
+[126] Edward Wright was born at Graveston, Norfolkshire, in 1560, and died
+at London in 1615. He was a fellow of Caius College, Cambridge, and in his
+work entitled _The correction of certain errors in Navigation_ (1599) he
+gives the principle of Mercator's projection. He translated the _Portuum
+investigandorum ratio_ of Stevin in 1599.
+
+[127] De Morgan never wrote a more suggestive sentence. Its message is not
+for his generation alone.
+
+[128] The eminent French physicist, Jean Baptiste Biot (1779-1862),
+professor in the Collège de France. His work _Sur les observatoires
+météorologiques_ appeared in 1855.
+
+[129] George Biddell Airy (1801-1892), professor of astronomy and physics
+at Cambridge, and afterwards director of the Observatory at Greenwich.
+
+[130] De Morgan would have rejoiced in the rôle played by Intuition in the
+mathematics of to-day, notably among the followers of Professor Klein.
+
+[131] Colburn was the best known of the calculating boys produced in
+America. He was born at Cabot, Vermont, in 1804, and died at Norwich,
+Vermont, in 1840. Having shown remarkable skill in numbers as early as
+1810, he was taken to London in 1812, whence he toured through Great
+Britain and to Paris. The Earl of Bristol placed him in Westminster School
+(1816-1819). On his return to America he became a preacher, and later a
+teacher of languages.
+
+[132] The history of calculating boys is interesting. Mathieu le Coc (about
+1664), a boy of Lorraine, could extract cube roots at sight at the age of
+eight. Tom Fuller, a Virginian slave of the eighteenth century, although
+illiterate, gave the number of seconds in 7 years 17 days 12 hours after
+only a minute and a half of thought. Jedediah Buxton, an Englishman of the
+eighteenth century, was studied by the Royal Society because of his
+remarkable powers. Ampère, the physicist, made long calculations with
+pebbles at the age of four. Gauss, one of the few infant prodigies to
+become an adult prodigy, corrected his father's payroll at the age of
+three. One of the most remarkable of the French calculating boys was Henri
+Mondeux. He was investigated by Arago, Sturm, Cauchy, and Liouville, for
+the Académie des Sciences, and a report was written by Cauchy. His
+specialty was the solution of algebraic problems mentally. He seems to have
+calculated squares and cubes by a binomial formula of his own invention. He
+died in obscurity, but was the subject of a _Biographie_ by Jacoby (1846).
+George P. Bidder, the Scotch engineer (1806-1878), was exhibited as an
+arithmetical prodigy at the age of ten, and did not attend school until he
+was twelve. Of the recent cases two deserve special mention, Inaudi and
+Diamandi. Jacques Inaudi (born in 1867) was investigated for the Académie
+in 1892 by a commission including Poincaré, Charcot, and Binet. (See the
+_Revue des Deux Mondes_, June 15, 1892, and the laboratory bulletins of the
+Sorbonne). He has frequently exhibited his remarkable powers in America.
+Périclès Diamandi was investigated by the same commission in 1893. See
+Alfred Binet, _Psychologie des Grands Calculateurs et Joueurs d'Echecs_,
+Paris, 1894.
+
+[133] John Flamsteed's (1646-1719) "old white house" was the first
+Greenwich observatory. He was the Astronomer Royal and first head of this
+observatory.
+
+[134] It seems a pity that De Morgan should not have lived to lash those of
+our time who are demanding only the immediately practical in mathematics.
+His satire would have been worth the reading against those who seek to
+stifle the science they pretend to foster.
+
+[135] Ismael Bouillaud, or Boulliau, was born in 1605 and died at Paris in
+1694. He was well known as an astronomer, mathematician, and jurist. He
+lived with De Thou at Paris, and accompanied him to Holland. He traveled
+extensively, and was versed in the astronomical work of the Persians and
+Arabs. It was in his _Astronomia philolaica, opus novum_ (Paris, 1645) that
+he attacked Kepler's laws. His tables were shown to be erroneous by the
+fact that the solar eclipse did not take place as predicted by him in 1645.
+
+[136] As it did, until 1892, when Airy had reached the ripe age of
+ninety-one.
+
+[137] _Didaci a Stunica ... In Job commentaria_ appeared at Toledo in 1584.
+
+[138] "The false Pythagorean doctrine, absolutely opposed to the Holy
+Scriptures, concerning the mobility of the earth and the immobility of the
+sun."
+
+[139] Paolo Antonio Foscarini (1580-1616), who taught theology and
+philosophy at Naples and Messina, was one of the first to champion the
+theories of Copernicus. This was in his _Lettera sopra l'opinione de'
+Pittagorici e del Copernico, della mobilità della Terra e stabilità del
+Sole, e il nuovo pittagorico sistema del mondo_, 4to, Naples, 1615. The
+condemnation of the Congregation was published in the following spring, and
+in the year of Foscarini's death at the early age of thirty-six.
+
+[140] "To be wholly prohibited and condemned," because "it seeks to show
+that the aforesaid doctrine is consonant with truth and is not opposed to
+the Holy Scriptures."
+
+[141] "As repugnant to the Holy Scriptures and to its true and Catholic
+interpretation (which in a Christian man cannot be tolerated in the least),
+he does not hesitate to treat (of his subject) '_by hypothesis_', but he
+even adds '_as most true_'!"
+
+[142] "To the places in which he discusses not by hypothesis but by making
+assertions concerning the position and motion of the earth."
+
+[143] "_Copernicus._ If by chance there shall be vain talkers who, although
+ignorant of all mathematics, yet taking it upon themselves to sit in
+judgment upon the subject on account of a certain passage of Scripture
+badly distorted for their purposes, shall have dared to criticize and
+censure this teaching of mine, I pay no attention to them, even to the
+extent of despising their judgment as rash. For it is not unknown that
+Lactantius, a writer of prominence in other lines although but little
+versed in mathematics, spoke very childishly about the form of the earth
+when he ridiculed those who declared that it was spherical. Hence it should
+not seem strange to the learned if some shall look upon us in the same way.
+Mathematics is written for mathematicians, to whom these labors of ours
+will seem, if I mistake not, to add something even to the republic of the
+Church.... _Emend._ Here strike out everything from 'if by chance' to the
+words 'these labors of ours,' and adapt it thus: 'But these labors of
+ours.'"
+
+[144] "_Copernicus._ However if we consider the matter more carefully it
+will be seen that the investigation is not yet completed, and therefore
+ought by no means to be condemned. _Emend._ However, if we consider the
+matter more carefully it is of no consequence whether we regard the earth
+as existing in the center of the universe or outside of the center, so far
+as the solution of the phenomena of celestial movements is concerned."
+
+[145] "The whole of this chapter may be cut out, since it avowedly treats
+of the earth's motion, while it refutes the reasons of the ancients proving
+its immobility. Nevertheless, since it seems to speak problematically, in
+order that it may satisfy the learned and keep intact the sequence and
+unity of the book let it be emended as below."
+
+[146] "_Copernicus._ Therefore why do we still hesitate to concede to it
+motion which is by nature consistent with its form, the more so because the
+whole universe is moving, whose end is not and cannot be known, and not
+confess that there is in the sky an appearance of daily revolution, while
+on the earth there is the truth of it? And in like manner these things are
+as if Virgil's Æneas should say, 'We are borne from the harbor' ...
+_Emend._ Hence I cannot concede motion to this form, the more so because
+the universe would fall, whose end is not and cannot be known, and what
+appears in the heavens is just as if ..."
+
+[147] "_Copernicus_. I also add that it would seem very absurd that motion
+should be ascribed to that which contains and locates, and not rather to
+that which is contained and located, that is the earth. _Emend._ I also add
+that it is not more difficult to ascribe motion to the contained and
+located, which is the earth, than to that which contains it."
+
+[148] "_Copernicus._ You see, therefore, that from all these things the
+motion of the earth is more probable than its immobility, especially in the
+daily revolution which is as it were a particular property of it. _Emend._
+Omit from 'You see' to the end of the chapter."
+
+[149] "_Copernicus._ Therefore, since there is nothing to hinder the motion
+of the earth, it seems to me that we should consider whether it has several
+motions, to the end that it may be looked upon as one of the moving stars.
+_Emend._ Therefore, since I have assumed that the earth moves, it seems to
+me that we should consider whether it has several motions."
+
+[150] "_Copernicus._ We are not ashamed to acknowledge ... that this is
+preferably verified in the motion of the earth. _Emend._ We are not ashamed
+to assume ... that this is consequently verified in the motion."
+
+[151] "_Copernicus._ So divine is surely this work of the Best and
+Greatest. _Emend._ Strike out these last words."
+
+[152] This should be Cap. 11, lib. i, p. 10.
+
+[153] "_Copernicus._ Demonstration of the threefold motion of the earth.
+_Emend._ On the hypothesis of the threefold motion of the earth and its
+demonstration."
+
+[154] This should be Cap. 20, lib. iv, p. 122.
+
+[155] "_Copernicus._ Concerning the size of these three stars, the sun, the
+moon and the earth. _Emend._ Strike out the words 'these three stars,'
+because the earth is not a star as Copernicus would make it."
+
+[156] He seems to speak problematically in order to satisfy the learned.
+
+[157] One of the Church Fathers, born about 250 A.D., and died about 330,
+probably at Trèves. He wrote _Divinarum Institutionum Libri VII._ and other
+controversial and didactic works against the learning and philosophy of the
+Greeks.
+
+[158] Giovanni Battista Riccioli (1598-1671) taught philosophy and theology
+at Parma and Bologna, and was later professor of astronomy. His _Almagestum
+novum_ appeared in 1651, and his _Argomento fisico-matematico contro il
+moto diurno della terra_ in 1668.
+
+[159] He was a native of Arlington, Sussex, and a pensioner of Christ's
+College, Cambridge. In 1603 he became a master of arts at Oxford.
+
+[160] Straying, i.e., from the right way.
+
+[161] "Private subjects may, in the presence of danger, defend themselves
+or their families against a monarch as against any malefactor, if the
+monarch assaults them like a bandit or a ravisher, and provided they are
+unable to summon the usual protection and cannot in any way escape the
+danger."
+
+[162] Daniel Neal (1678-1743), an independent minister, wrote a _History of
+the Puritans_ that appeared in 1732. The account may be found in the New
+York edition of 1843-44, vol. I, p. 271.
+
+[163] Anthony Wood (1632-1695), whose _Historia et Antiquitates
+Universitatis Oxoniensis_ (1674) and _Athenae Oxoniensis_ (1691) are among
+the classics on Oxford.
+
+[164] Part of the title, not here quoted, shows the nature of the work more
+clearly: "liber unicus, in quo decretum S. Congregationis S. R. E.
+Cardinal. an. 1616, adversus Pythagorico-Copernicanos editum defenditur."
+
+[165] This was John Elliot Drinkwater Bethune (1801-1851), the statesman
+who did so much for legislative and educational reform in India. His
+father, John Drinkwater Bethune, wrote a history of the siege of Gibraltar.
+
+[166] The article referred to is about thirty years old; since it appeared
+another has been given (_Dubl. Rev._, Sept. 1865) which is of much greater
+depth. In it will also be found the Roman view of Bishop Virgil (_ante_, p.
+32).--A. De M.
+
+[167] Jean Baptiste Morin (1583-1656), in his younger days physician to the
+Bishop of Boulogne and the Duke of Luxemburg, became in 1630 professor of
+mathematics at the Collège Royale. His chief contribution to the problem of
+the determination of longitude is his _Longitudinum terrestrium et
+coelestium nova et hactenus optata scientia_ (1634). He also wrote against
+Copernicus in his _Famosi problematis de telluris motu vel quiete hactenus
+optata solutio_ (1631), and against Lansberg in his _Responsio pro telluris
+quiete_ (1634).
+
+[168] The work appeared at Leyden in 1626, at Amsterdam in 1634, at
+Copenhagen in 1640 and again at Leyden in 1650. The title of the 1640
+edition is _Arithmeticae Libri II et Geometriae Libri VI_. The work on
+which it is based is the _Arithmeticae et Geometriae Practica_, which
+appeared in 1611.
+
+[169] The father's name was Adriaan, and Lalande says that it was Montucla
+who first made the mistake of calling him Peter, thinking that the initials
+P. M. stood for Petrus Metius, when in reality they stood for _piae
+memoriae_! The ratio 355/113 was known in China hundreds of years before
+his time. See note 55, page 52.
+
+[170] Adrian Metius (1571-1635) was professor of medicine at the University
+of Franeker. His work was, however, in the domain of astronomy, and in this
+domain he published several treatises.
+
+[171] The first edition was entitled: _The Discovery of a World in the
+Moone. Or, a Discourse Tending to prove that 'tis probable there may be
+another habitable World in that Planet_. 1638, 8vo. The fourth edition
+appeared in 1684. John Wilkins (1614-1672) was Warden of Wadham College,
+Oxford; master of Trinity, Cambridge; and, later, Bishop of Chester. He was
+influential in founding the Royal Society.
+
+[172] The first edition was entitled: _C. Hugenii_ [Greek: Kosmotheôros],
+_sive de Terris coelestibus, earumque ornatu, conjecturae_, The Hague,
+1698, 4to. There were several editions. It was also translated into French
+(1718), and there was another English edition (1722). Huyghens (1629-1695)
+was one of the best mathematical physicists of his time.
+
+[173] It is hardly necessary to say that science has made enormous advance
+in the chemistry of the universe since these words were written.
+
+[174] William Whewell (1794-1866) is best known through his _History of the
+Inductive Sciences_ (1837) and _Philosophy of the Inductive Sciences_
+(1840).
+
+[175] Thomas Chalmers (1780-1847), the celebrated Scotch preacher. These
+discourses were delivered while he was minister in a large parish in the
+poorest part of Glasgow, and in them he attempted to bring science into
+harmony with the Bible. He was afterwards professor of moral philosophy at
+St. Andrew's (1823-28), and professor of theology at Edinburgh (1828). He
+became the leader of a schism from the Scotch Presbyterian Church,--the
+Free Church.
+
+[176] That is, in Robert Watt's (1774-1819) _Bibliotheca Britannica_
+(posthumous, 1824). Nor is it given in the _Dictionary of National
+Biography_.
+
+[177] The late Greek satirist and poet, c. 120-c. 200 A.D.
+
+[178] François Rabelais (c. 1490-1553) the humorist who created Pantagruel
+(1533) and Gargantua (1532). His work as a physician and as editor of the
+works of Galen and Hippocrates is less popularly known.
+
+[179] Francis Godwin (1562-1633) bishop of Llandaff and Hereford. Besides
+some valuable historical works he wrote _The Man in the Moone, or a
+Discourse of a voyage thither by Domingo Gonsales, the Speed Messenger of
+London_, 1638.
+
+[180] Bernard Le Bovier de Fontenelle (1657-1757), historian, critic,
+mathematician, Secretary of the Académie des Sciences, and member of the
+Académie Française. His _Entretien sur la pluralité des mondes_ appeared at
+Paris in 1686.
+
+[181] Athanasius Kircher (1602-1680), Jesuit, professor of mathematics and
+philosophy, and later of Hebrew and Syriac, at Wurzburg; still later
+professor of mathematics and Hebrew at Rome. He wrote several works on
+physics. His collection of mathematical instruments and other antiquities
+became the basis of the Kircherian Museum at Rome.
+
+[182] "Both belief and non-belief are dangerous. Hippolitus died because
+his stepmother was believed. Troy fell because Cassandra was not believed.
+Therefore the truth should be investigated long before foolish opinion can
+properly judge." (Prove = probe?).
+
+[183] Jacobus Grandamicus (Jacques Grandami) was born at Nantes in 1588 and
+died at Paris in 1672. He was professor of theology and philosophy in the
+Jesuit colleges at Rennes, Tours, Rouen, and other places. He wrote several
+works on astronomy.
+
+[184] "And I, if I be lifted up from the earth, will draw all men unto me."
+John xii. 32.
+
+[185] Andrea Argoli (1568-1657) wrote a number of works on astronomy, and
+computed ephemerides from 1621 to 1700.
+
+[186] So in the original edition of the _Budget_. It is Johannem Pellum in
+the original title. John Pell (1610 or 1611-1685) studied at Cambridge and
+Oxford, and was professor of mathematics at Amsterdam (1643-46) and Breda
+(1646-52). He left many manuscripts but published little. His name attaches
+by accident to an interesting equation recently studied with care by Dr.
+E. E. Whitford (New York, 1912).
+
+[187] Christianus Longomontanus (Christen Longberg or Lumborg) was born in
+1569 at Longberg, Jutland, and died in 1647 at Copenhagen. He was an
+assistant of Tycho Brahe and accepted the diurnal while denying the orbital
+motion of the earth. His _Cyclometria e lunulis reciproce demonstrata_
+appeared in 1612 under the name of Christen Severin, the latter being his
+family name. He wrote several other works on the quadrature problem, and
+some treatises on astronomy.
+
+[188] The names are really pretty well known. Giles Persone de Roberval was
+born at Roberval near Beauvais in 1602, and died at Paris in 1675. He was
+professor of philosophy at the Collège Gervais at Paris, and later at the
+Collège Royal. He claimed to have discovered the theory of indivisibles
+before Cavalieri, and his work is set forth in his _Traité des
+indivisibles_ which appeared posthumously in 1693.
+
+Hobbes (1588-1679), the political and social philosopher, lived a good part
+of his time (1610-41) in France where he was tutor to several young
+noblemen, including the Cavendishes. His _Leviathan_ (1651) is said to have
+influenced Spinoza, Leibnitz, and Rousseau. His _Quadratura circuli,
+cubatio sphaerae, duplicatio cubi ..._ (London, 1669), _Rosetum geometricum
+..._ (London, 1671), and _Lux Mathematica, censura doctrinae Wallisianae
+contra Rosetum Hobbesii_ (London, 1674) are entirely forgotten to-day. (See
+a further note, _infra_.)
+
+Pierre de Carcavi, a native of Lyons, died at Paris in 1684. He was a
+member of parliament, royal librarian, and member of the Académie des
+Sciences. His attempt to prove the impossibility of the quadrature appeared
+in 1645. He was a frequent correspondent of Descartes.
+
+Cavendish (1591-1654) was Sir (not Lord) Charles. He was, like De Morgan
+himself, a bibliophile in the domain of mathematics. His life was one of
+struggle, his term as member of parliament under Charles I being followed
+by gallant service in the royal army. After the war he sought refuge on the
+continent where he met most of the mathematicians of his day. He left a
+number of manuscripts on mathematics, which his widow promptly disposed of
+for waste paper. If De Morgan's manuscripts had been so treated we should
+not have had his revision of his _Budget of Paradoxes_.
+
+Marin Mersenne (1588-1648), a minorite, living in the cloisters at Nevers
+and Paris, was one of the greatest Franciscan scholars. He edited Euclid,
+Apollonius, Archimedes, Theodosius, and Menelaus (Paris, 1626), translated
+the Mechanics of Galileo into French (1634), wrote _Harmonicorum Libri XII_
+(1636), and _Cogitata physico-mathematica_ (1644), and taught theology and
+philosophy at Nevers.
+
+Johann Adolph Tasse (Tassius) was born in 1585 and died at Hamburg in 1654.
+He was professor of mathematics in the Gymnasium at Hamburg, and wrote
+numerous works on astronomy, chronology, statics, and elementary
+mathematics.
+
+Johann Ludwig, Baron von Wolzogen, seems to have been one of the early
+unitarians, called _Fratres Polonorum_ because they took refuge in Poland.
+Some of his works appear in the _Bibliotheca Fratrum Polonorum_ (Amsterdam,
+1656). I find no one by the name who was contributing to mathematics at
+this time.
+
+Descartes is too well known to need mention in this connection.
+
+Bonaventura Cavalieri (1598-1647) was a Jesuit, a pupil of Galileo, and
+professor of mathematics at Bologna. His greatest work, _Geometria
+indivisibilibus continuorum nova quadam ratione promota_, in which he makes
+a noteworthy step towards the calculus, appeared in 1635.
+
+Jacob (Jacques) Golius was born at the Hague in 1596 and died at Leyden in
+1667. His travels in Morocco and Asia Minor (1622-1629) gave him such
+knowledge of Arabic that he became professor of that language at Leyden.
+After Snell's death he became professor of mathematics there. He translated
+Arabic works on mathematics and astronomy into Latin.
+
+[189] It would be interesting to follow up these rumors, beginning perhaps
+with the tomb of Archimedes. The Ludolph van Ceulen story is very likely a
+myth. The one about Fagnano may be such. The Bernoulli tomb does have the
+spiral, however (such as it is), as any one may see in the cloisters at
+Basel to-day.
+
+[190] Collins (1625-1683) was secretary of the Royal Society, and was "a
+kind of register of all new improvements in mathematics." His office
+brought him into correspondence with all of the English scientists, and he
+was influential in the publication of various important works, including
+Branker's translation of the algebra by Rhonius, with notes by Pell, which
+was the first work to contain the present English-American symbol of
+division. He also helped in the publication of editions of Archimedes and
+Apollonius, of Kersey's Algebra, and of the works of Wallis. His profession
+was that of accountant and civil engineer, and he wrote three unimportant
+works on mathematics (one published posthumously, and the others in 1652
+and 1658).
+
+Heinrich Christian Schumacher (1780-1850) was professor of astronomy at
+Copenhagen and director of the observatory at Altona. His translation of
+Carnot's _Géométrie de position_ (1807) brought him into personal relations
+with Gauss, and the friendship was helpful to Schumacher. He was a member
+of many learned societies and had a large circle of acquaintances. He
+published numerous monographs and works on astronomy.
+
+Gassendi (1592-1655) might well have been included by De Morgan in the
+group, since he knew and was a friend of most of the important
+mathematicians of his day. Like Mersenne, he was a minorite, but he was a
+friend of Galileo and Kepler, and wrote a work under the title _Institutio
+astronomica, juxta hypotheses Copernici, Tychonis-Brahaei et Ptolemaei_
+(1645). He taught philosophy at Aix, and was later professor of mathematics
+at the College Royal at Paris.
+
+Burnet is the Bishop Gilbert Burnet (1643-1715) who was so strongly
+anti-Romanistic that he left England during the reign of James II and
+joined the ranks of the Prince of Orange. William made him bishop of
+Salisbury.
+
+[191] There is some substantial basis for De Morgan's doubts as to the
+connection of that _mirandula_ of his age, Sir Kenelm Digby (1603-1665),
+with the famous _poudre de sympathie_. It is true that he was just the one
+to prepare such a powder. A dilletante in everything,--learning, war,
+diplomacy, religion, letters, and science--he was the one to exploit a
+fraud of this nature. He was an astrologer, an alchemist, and a fabricator
+of tales, and well did Henry Stubbes characterize him as "the very Pliny of
+our age for lying." He first speaks of the powder in a lecture given at
+Montpellier in 1658, and in the same year he published the address at Paris
+under the title: _Discours fait en une célèbre assemblée par le chevalier
+Digby .... touchant la guérison de playes par la poudre de sympathie_. The
+London edition referred to by De Morgan also came out in 1658, and several
+editions followed it in England, France and Germany. But Nathaniel Highmore
+in his _History of Generation_ (1651) referred to the concoction as
+"Talbot's Powder" some years before Digby took it up. The basis seems to
+have been vitriol, and it was claimed that it would heal a wound by simply
+being applied to a bandage taken from it.
+
+[192] This work by Thomas Birch (1705-1766) came out in 1756-57. Birch was
+a voluminous writer on English history. He was a friend of Dr. Johnson and
+of Walpole, and he wrote a life of Robert Boyle.
+
+[193] We know so much about John Evelyn (1620-1706) through the diary which
+he began at the age of eleven, that we forget his works on navigation and
+architecture.
+
+[194] I suppose this was the seventh Earl of Shrewsbury (1553-1616).
+
+[195] This is interesting in view of the modern aseptic practice of surgery
+and the antiseptic treatment of wounds inaugurated by the late Lord Lister.
+
+[196] Perhaps De Morgan had not heard the _bon mot_ of Dr. Holmes: "I
+firmly believe that if the whole _materia medica_ could be sunk to the
+bottom of the sea, it would be all the better for mankind and all the worse
+for the fishes."
+
+[197] The full title is worth giving, because it shows the mathematical
+interests of Hobbes, and the nature of the six dialogues: _Examinatio et
+emendatio mathematicae hodiernae qualis explicatur in libris Johannis
+Wallisii geometriae professoris Saviliani in Academia Oxoniensi: distributa
+in sex dialogos (1. De mathematicae origine ...; 2. De principiis traditis
+ab Euclide; 3. De demonstratione operationum arithmeticarum ...; 4. De
+rationibus; 5. De angula contactus, de sectionibus coni, et arithmetica
+infinitorum; 6. Dimensio circuli tribus methodis demonstrata ... item
+cycloidis verae descriptio et proprietates aliquot.)_ Londini, 1660 (not
+1666). For a full discussion of the controversy over the circle, see George
+Croom Robertson's biography of Hobbes in the eleventh edition of the
+_Encyclopaedia Britannica_.
+
+[198] This is his _Animadversions upon Mr. Hobbes' late book De principiis
+et ratiocinatione geometrarum_, 1666, or his _Hobbianae quadraturae
+circuli, cubationis sphaerae et duplicationis cubi confutatio_, also of
+1669.
+
+[199] This is the work of 1669 referred to above.
+
+[200] Gregoire de St. Vincent (1584-1667) published his _Opus geometricum
+quadraturae circuli et sectionum coni_ at Antwerp in 1647.
+
+[201] This appears in _J. Scaligeri cyclometrica elementa duo_, Lugduni
+Batav., 1594.
+
+[202] Adriaen van Roomen (1561-1615) gave the value of [pi] to sixteen
+decimal places in his _Ideae mathematicae pars prima_ (1593), and wrote his
+_In Archimedis circuli dimensionem expositio & analysis_ in 1597.
+
+[203] Kästner. See note 30 on page 43.
+
+[204] Bentley (1662-1742) might have done it, for as the head of Trinity
+College, Cambridge, and a follower of Newton, he knew some mathematics.
+Erasmus (1466-1536) lived a little too early to attempt it, although his
+brilliant satire might have been used to good advantage against those who
+did try.
+
+[205] "In grammar, to give the winds to the ships and to give the ships to
+the winds mean the same thing. But in geometry it is one thing to assume
+the circle BCD not greater than thirty-six segments BCDF, and another (to
+assume) the thirty-six segments BCDF not greater than the circle. The one
+assumption is true, the other false."
+
+[206] The Greek scholar (1559-1614) who edited a Greek and Latin edition of
+Aristotle in 1590.
+
+[207] Jacques Auguste de Thou (1553-1617), the historian and statesman.
+
+[208] "To value Scaliger higher even when wrong, than the multitude when
+right."
+
+[209] "I would rather err with Scaliger than be right with Clavius."
+
+[210] "The perimeter of the dodecagon to be inscribed in a circle is
+greater than the perimeter of the circle. And the more sides a polygon to
+be inscribed in a circle successively has, so much the greater will the
+perimeter of the polygon be than the perimeter of the circle."
+
+[211] De Morgan took, perhaps, the more delight in speaking thus of Sir
+William Hamilton (1788-1856) because of a spirited controversy that they
+had in 1847 over the theory of logic. Possibly, too, Sir William's low
+opinion of mathematics had its influence.
+
+[212] Edwards (1699-1757) wrote _The canons of criticism_ (1747) in which
+he gave a scathing burlesque on Warburton's Shakespeare. It went through
+six editions.
+
+[213] Antoine Teissier (born in 1632) published his _Eloges des hommes
+savants, tirés de l'histoire de M. de Thou_ in 1683.
+
+[214] "He boasted without reason of having found the quadrature of the
+circle. The glory of this admirable discovery was reserved for Joseph
+Scaliger, as Scévole de St. Marthe has written."
+
+[215] _Natural and political observations mentioned in the following Index,
+and made upon the Bills of Mortality.... With reference to the government,
+religion, trade, growth, ayre, and diseases of the said city._ London,
+1662, 4to. The book went through several editions.
+
+[216] _Ne sutor ultra crepidam_, "Let the cobbler stick to his last," as we
+now say.
+
+[217] The author (1632-1695) of the _Historia et Antiquitates Universitatis
+Oxoniensis_ (1674). See note 163, page 98.
+
+[218] The mathematical guild owes Samuel Pepys (1633-1703) for something
+besides his famous diary (1659-1669). Not only was he president of the
+Royal Society (1684), but he was interested in establishing Sir William
+Boreman's mathematical school at Greenwich.
+
+[219] John Graunt (1620-1674) was a draper by trade, and was a member of
+the Common Council of London until he lost office by turning Romanist.
+Although a shopkeeper, he was elected to the Royal Society on the special
+recommendation of Charles II. Petty edited the fifth edition of his work,
+adding much to its size and value, and this may be the basis of Burnet's
+account of the authorship.
+
+[220] Petty (1623-1687) was a mathematician and economist, and a friend of
+Pell and Sir Charles Cavendish. His survey of Ireland, made for Cromwell,
+was one of the first to be made on a large scale in a scientific manner. He
+was one of the founders of the Royal Society.
+
+[221] The story probably arose from Graunt's recent conversion to the Roman
+Catholic faith.
+
+[222] He was born in 1627 and died in 1704. He published a series of
+ephemerides, beginning in 1659. He was imprisoned in 1679, at the time of
+the "Popish Plot," and again for treason in 1690. His important
+astrological works are the _Animal Cornatum, or the Horn'd Beast_ (1654)
+and _The Nativity of the late King Charls_ (1659).
+
+[223] Isaac D'Israeli (1766-1848), in his _Curiosities of Literature_
+(1791), speaking of Lilly, says: "I shall observe of this egregious
+astronomer, that there is in this work, so much artless narrative, and at
+the same time so much palpable imposture, that it is difficult to know when
+he is speaking what he really believes to be the truth." He goes on to say
+that Lilly relates that "those adepts whose characters he has drawn were
+the lowest miscreants of the town. Most of them had taken the air in the
+pillory, and others had conjured themselves up to the gallows. This seems a
+true statement of facts."
+
+[224] It is difficult to estimate William Lilly (1602-1681) fairly. His
+_Merlini Anglici ephemeris_, issued annually from 1642 to 1681, brought him
+a great deal of money. Sir George Wharton (1617-1681) also published an
+almanac annually from 1641 to 1666. He tried to expose John Booker
+(1603-1677) by a work entitled _Mercurio-Coelicio-Mastix; or, an
+Anti-caveat to all such, as have (heretofore) had the misfortune to be
+Cheated and Deluded by that Grand and Traiterous Impostor of this
+Rebellious Age, John Booker_, 1644. Booker was "licenser of mathematical
+[astrological] publications," and as such he had quarrels with Lilly,
+Wharton, and others.
+
+[225] See note 171 on page 100.
+
+[226] This is the _Ars Signorum, vulgo character universalis et lingua
+philosophica_, that appeared at London in 1661, 8vo. George Dalgarno
+anticipated modern methods in the teaching of the deaf and dumb.
+
+[227] See note 200 on page 110.
+
+[228] If the hyperbola is referred to the asymptotes as axes, the area
+between two ordinates (x = a, x = b) is the difference of the logarithms of
+a and b to the base e. E.g., in the case of the hyperbola xy = 1, the area
+between x = a and x = 1 is log a.
+
+[229] "On ne peut lui refuser la justice de remarquer que personne avant
+lui ne s'est porté dans cette recherche avec autant de génie, & même, si
+nous en exceptons son objet principal, avec autant de succès." _Quadrature
+du Cercle_, p. 66.
+
+[230] The title proceeds: _Seu duae mediae proportionales inter extremas
+datas per circulum et per infinitas hyperbolas, vel ellipses et per
+quamlibet exhibitae_.... René Francois, Baron de Sluse (1622-1685) was
+canon and chancellor of Liège, and a member of the Royal Society. He also
+published a work on tangents (1672). The word _mesolabium_ is from the
+Greek [Greek: mesolabion] or [Greek: mesolabon], an instrument invented by
+Eratosthenes for finding two mean proportionals.
+
+[231] The full title has some interest: _Vera circuli et hyperbolae
+quadratura cui accedit geometriae pars universalis inserviens quantitatum
+curvarum transmutationi et mensurae. Authore Jacobo Gregorio Abredonensi
+Scoto ... Patavii_, 1667. That is, James Gregory (1638-1675) of Aberdeen
+(he was really born near but not in the city), a good Scot, was publishing
+his work down in Padua. The reason was that he had been studying in Italy,
+and that this was a product of his youth. He had already (1663) published
+his _Optica promota_, and it is not remarkable that his brilliancy brought
+him a wide circle of friends on the continent and the offer of a pension
+from Louis XIV. He became professor of mathematics at St Andrews and later
+at Edinburgh, and invented the first successful reflecting telescope. The
+distinctive feature of his _Vera quadratura_ is his use of an infinite
+converging series, a plan that Archimedes used with the parabola.
+
+[232] Jean de Beaulieu wrote several works on mathematics, including _La
+lumière de l'arithmétique_ (n.d.), _La lumière des mathématiques_ (1673),
+_Nouvelle invention d'arithmétique_ (1677), and some mathematical tables.
+
+[233] A just estimate. There were several works published by Gérard
+Desargues (1593-1661), of which the greatest was the _Brouillon Proiect_
+(Paris, 1639). There is an excellent edition of the _Oeuvres de Desargues_
+by M. Poudra, Paris, 1864.
+
+[234] "A certain M. de Beaugrand, a mathematician, very badly treated by
+Descartes, and, as it appears, rightly so."
+
+[235] This is a very old approximation for [pi]. One of the latest
+pretended geometric proofs resulting in this value appeared in New York in
+1910, entitled _Quadrimetry_ (privately printed).
+
+[236] "Copernicus, a German, made himself no less illustrious by his
+learned writings; and we might say of him that he stood alone and unique in
+the strength of his problems, if his excessive presumption had not led him
+to set forth in this science a proposition so absurd that it is contrary to
+faith and reason, namely that the circumference of a circle is fixed and
+immovable while the center is movable: on which geometrical principle he
+has declared in his astrological treatise that the sun is fixed and the
+earth is in motion."
+
+[237] So in the original.
+
+[238] Franciscus Maurolycus (1494-1575) was really the best mathematician
+produced by Sicily for a long period. He made Latin translations of
+Theodosius, Menelaus, Euclid, Apollonius, and Archimedes, and wrote on
+cosmography and other mathematical subjects.
+
+[239] "Nicolaus Copernicus is also tolerated who asserted that the sun is
+fixed and that the earth whirls about it; and he rather deserves a whip or
+a lash than a reproof."
+
+[240] "Algebra is the curious science of scholars, and particularly for a
+general of an army, or a captain, in order quickly to draw up an army in
+battle array and to number the musketeers and pikemen who compose it,
+without the figures of arithmetic. This science has five special figures of
+this kind: P means _plus_ in commerce and _pikemen_ in the army; M means
+_minus_, and _musketeer_ in the art of war;... R signifies _root_ in the
+measurement of a cube, and _rank_ in _the army_; Q means _square_ (French
+_quarè_, as then spelled) in both cases; C means _cube_ in mensuration, and
+_cavalry_ in arranging batallions and squadrons. As for the operations of
+this science, they are as follows: to add a _plus_ and a _plus_, the sum
+will be _plus_; to add _minus_ with _plus_, take the less from the greater
+and the remainder will be the sum required or the number to be found. I say
+this only in passing, for the benefit of those who are wholly ignorant of
+it."
+
+[241] He refers to the _Joannis de Beaugrand ... Geostatice, seu de vario
+pondere gravium secundum varia a terrae (centro) intervalla dissertatio
+mathematica_, Paris, 1636. Pascal relates that de Beaugrand sent all of
+Roberval's theorems on the cycloid and Fermat's on maxima and minima to
+Galileo in 1638, pretending that they were his own.
+
+[242] More (1614-1687) was a theologian, a fellow of Christ College,
+Cambridge, and a Christian Platonist.
+
+[243] Matthew Hale (1609-1676) the famous jurist, wrote a number of tracts
+on scientific, moral, and religious subjects. These were collected and
+published in 1805.
+
+[244] They might have been attributed to many a worse man than Dr. Hales
+(1677-1761), who was a member of the Royal Society and of the Paris
+Academy, and whose scheme for the ventilation of prisons reduced the
+mortality at the Savoy prison from one hundred to only four a year. The
+book to which reference is made is _Vegetable Staticks or an Account of
+some statical experiments on the sap in Vegetables_, 1727.
+
+[245] _Pleas of the Crown; or a Methodical Summary of the Principal Matters
+relating to the subject_, 1678.
+
+[246] _Thomae Streete Astronomia Carolina, a new theory of the celestial
+motions_, 1661. It also appeared at Nuremberg in 1705, and at London in
+1710 and 1716 (Halley's editions). He wrote other works on astronomy.
+
+[247] This was the Sir Thomas Street (1626-1696) who passed sentence of
+death on a Roman Catholic priest for saying mass. The priest was reprieved
+by the king, but in the light of the present day one would think the
+justice more in need of pardon. He took part in the trial of the Rye House
+Conspirators in 1683.
+
+[248] Edmund Halley (1656-1742), who succeeded Wallis (1703) as Savilian
+professor of mathematics at Oxford, and Flamsteed (1720) as head of the
+Greenwich observatory. It is of interest to note that he was instrumental
+in getting Newton's _Principia_ printed.
+
+[249] Shepherd (born in 1760) was one of the most famous lawyers of his
+day. He was knighted in 1814 and became Attorney General in 1817.
+
+[250] This was William Hone (1780-1842), a book publisher, who wrote
+satires against the government, and who was tried three times because of
+his parodies on the catechism, creed, and litany (illustrated by
+Cruikshank). He was acquitted on all of the charges.
+
+[251] Valentinus was a Benedictine monk and was still living at Erfurt in
+1413. His _Currus triumphalis antimonii_ appeared in 1624. Synesius was
+Bishop of Ptolemaide, who died about 430. His works were printed at Paris
+in 1605. Theodor Kirckring (1640-1693) was a fellow-student of Spinoza's.
+Besides the commentary on Valentine he left several works on anatomy. His
+commentary appeared at Amsterdam in 1671. There were several editions of
+the _Chariot_.
+
+[252] The chief difficulty with this curious "monk-bane" etymology is its
+absurdity. The real origin of the word has given etymologists a good deal
+of trouble.
+
+[253] Robert Boyle (1627-1691), son of "the Great Earl" (of Cork). Perhaps
+his best-known discovery is the law concerning the volume of gases.
+
+[254] The real name of Eirenaeus Philalethes (born in 1622) is unknown. It
+may have been Childe. He claimed to have discovered the philosopher's stone
+in 1645. His tract in this work is _The Secret of the Immortal Liquor
+Alkahest or Ignis-Aqua_. See note 260, _infra_.
+
+[255] Johann Baptist van Helmont, Herr von Merode, Royenborg etc.
+(1577-1644). His chemical discoveries appeared in his _Ortus medicinae_
+(1648), which went through many editions.
+
+[256] De Morgan should have written up Francis Anthony (1550-1623), whose
+_Panacea aurea sive tractatus duo de auro potabili_ (Hamburg, 1619)
+described a panacea that he gave for every ill. He was repeatedly
+imprisoned for practicing medicine without a license from the Royal College
+of Physicians.
+
+[257] Bernardus Trevisanus (1406-1490), who traveled even through Barbary,
+Egypt, Palestine, and Persia in search of the philosopher's stone. He wrote
+several works on alchemy,--_De Chemica_ (1567), _De Chemico Miraculo_
+(1583), _Traité de la nature de l'oeuf des philosophes_ (1659), etc., all
+published long after his death.
+
+[258] George Ripley (1415-1490) was an Augustinian monk, later a
+chamberlain of Innocent VIII, and still later a Carmelite monk. His _Liber
+de mercuris philosophico_ and other tracts first appeared in _Opuscula
+quaedam chymica_ (Frankfort, 1614).
+
+[259] Besides the _Opus majus_, and other of the better known works of this
+celebrated Franciscan (1214-1294), there are numerous tracts on alchemy
+that appeared in the _Thesaurus chymicus_ (Frankfort, 1603).
+
+[260] George Starkey (1606-1665 or 1666) has special interest for American
+readers. He seems to have been born in the Bermudas and to have obtained
+the bachelor's degree in England. He then went to America and in 1646
+obtained the master's degree at Harvard, apparently under the name of
+Stirk. He met Eirenaeus Philalethes (see note 254 above) in America and
+learned alchemy from him. Returning to England, he sold quack medicines
+there, and died in 1666 from the plague after dissecting a patient who had
+died of the disease. Among his works was the _Liquor Alcahest, or a
+Discourse of that Immortal Dissolvent of Paracelsus and Helmont_, which
+appeared (1675) some nine years after his death.
+
+[261] Platt (1552-1611) was the son of a London brewer. Although he left a
+manuscript on alchemy, and wrote a book entitled _Delights for Ladies to
+adorne their Persons_ (1607), he was knighted for some serious work on the
+chemistry of agriculture, fertilizing, brewing, and the preserving of
+foods, published in _The Jewell House of Art and Nature_ (1594).
+
+[262] "Those who wish to call a man a liar and deceiver speak of him a
+writer of almanacs; but those who (would call him) a scoundrel and an
+imposter (speak of him as) a chemist."
+
+[263] "Trust your barque to the winds but not your body to a chemist; any
+breeze is safer than the faith of a chemist."
+
+[264] Probably the Jesuit, Père Claude François Menestrier (1631-1705), a
+well known historian.
+
+[265] The author was Christopher Nesse (1621-1705), a belligerent
+Calvinist, who wrote many controversial works and succeeded in getting
+excommunicated four times. One of his most virulent works was _A Protestant
+Antidote against the Poison of Popery_.
+
+[266] John Case (c. 1660-1700) was a famous astrologer and physician. He
+succeeded to Lilly's practice in London. In a darkened room, wherein he
+kept an array of mystical apparatus, he pretended to show the credulous the
+ghosts of their departed relatives. Besides his astrological works he wrote
+one serious treatise, the _Compendium Anatomicum nova methodo institutum_
+(1695), in which he defends Harvey's theories of embryology.
+
+[267] Marcelis (1636-after 1714) was a soap maker of Amsterdam. It is to be
+hoped that he made better soap than values of [pi].
+
+[268] John Craig (died in 1731) was a Scotchman, but most of his life was
+spent at Cambridge reading and writing on mathematics. He endeavored to
+introduce the Leibnitz differential calculus into England. His mathematical
+works include the _Methodus Figurarum ... Quadraturas determinandi_ (1685),
+_Tractatus ... de Figurarum Curvilinearum Quadraturis et locis Geometricis_
+(1693), and _De Calculo Fluentium libri duo_ (1718).
+
+[269] As is well known, this subject owes much to the Bernoullis. Craig's
+works on the calculus brought him into controversy with them. He also wrote
+on other subjects in which they were interested, as in his memoir _On the
+Curve of the quickest descent_ (1700), _On the Solid of least resistance_
+(1700), and the _Solution of Bernoulli's problem on Curves_ (1704).
+
+[270] This is Samuel Lee (1783-1852), the young prodigy in languages. He
+was apprenticed to a carpenter at twelve and learned Greek while working at
+the trade. Before he was twenty-five he knew Hebrew, Chaldee, Syriac,
+Samaritan, Persian, and Hindustani. He later became Regius professor of
+Hebrew at Cambridge.
+
+[271] "Where the devil, Master Ludovico, did you pick up such a
+collection?"
+
+[272] Lord William Brounker (c. 1620-1684), the first president of the
+Royal Society, is best known in mathematics for his contributions to
+continued fractions.
+
+[273] Horace Walpole (1717-1797) published his _Catalogue of the Royal and
+Noble Authors of England_ in 1758. Since his time a number of worthy names
+in the domain of science in general and of mathematics in particular might
+be added from the peerage of England.
+
+[274] It was written by Charles Hayes (1678-1760), a mathematician and
+scholar of no mean attainments. He travelled extensively, and was deputy
+governor of the Royal African Company. His _Treatise on Fluxions_ (London,
+1704) was the first work in English to explain Newton's calculus. He wrote
+a work entitled _The Moon_ (1723) to prove that our satellite shines by its
+own as well as by reflected light. His _Chronographia Asiatica & Aegyptica_
+(1758) gives the results of his travels.
+
+[275] _Publick_ in the original.
+
+[276] Whiston (1667-1752) succeeded Newton as Lucasian professor of
+mathematics at Cambridge. In 1710 he turned Arian and was expelled from the
+university. His work on _Primitive Christianity_ appeared the following
+year. He wrote many works on astronomy and religion.
+
+[277] Ditton (1675-1715) was, on Newton's recommendation, made Head of the
+mathematical school at Christ's Hospital, London. He wrote a work on
+fluxions (1706). His idea for finding longitude at sea was to place
+stations in the Atlantic to fire off bombs at regular intervals, the time
+between the sound and the flash giving the distance. He also corresponded
+with Huyghens concerning the use of chronometers for the purpose.
+
+[278] This was John Arbuthnot (c. 1658-1735), the mathematician, physician
+and wit. He was intimate with Pope and Swift, and was Royal physician to
+Queen Anne. Besides various satires he published a translation of
+Huyghens's work on probabilities (1692) and a well-known treatise on
+ancient coins, weights, and measures (1727).
+
+[279] Greene (1678-1730) was a very eccentric individual and was generally
+ridiculed by his contemporaries. In his will he directed that his body be
+dissected and his skeleton hung in the library of King's College,
+Cambridge. Unfortunately for his fame, this wish was never carried out.
+
+[280] This was the historian, Robert Sanderson (1660-1741), who spent most
+of his life at Cambridge.
+
+[281] I presume this was William Jones (1675-1749) the friend of Newton and
+Halley, vice-president of the Royal Society, in whose _Synopsis Palmariorum
+Matheseos_ (1706) the symbol [pi] is first used for the circle ratio.
+
+[282] This was the _Geometrica solidorum, sive materiae, seu de varia
+compositione, progressione, rationeque velocitatum_, Cambridge, 1712. The
+work was parodied in _A Taste of Philosophical Fanaticism ... by a
+gentleman of the University of Gratz_.
+
+[283] The antiquary and scientist (1690-1754), president of the Royal
+Society, member of the Académie, friend of Newton, and authority on
+numismatics.
+
+[284] She was Catherine Barton, Newton's step-niece. She married John
+Conduitt, master of the mint, who collected materials for a life of Newton.
+
+_A propos_ of Mrs. Conduitt's life of her illustrious uncle, Sir George
+Greenhill tells a very good story on Poincaré, the well-known French
+mathematician. At an address given by the latter at the International
+Congress of Mathematicians held in Rome in 1908 he spoke of the story of
+Newton and the apple as a mere fable. After the address Sir George asked
+him why he had done so, saying that the story was first published by
+Voltaire, who had heard it from Newton's niece, Mrs. Conduitt. Poincaré
+looked blank and said, "Newton, et la nièce de Newton, et Voltaire,--non!
+je ne vous comprends pas!" He had thought Sir George meant Professor
+Volterra of Rome, whose name in French is Voltaire, and who could not
+possibly have known a niece of Newton without bridging a century or so.
+
+[285] This was the Edmund Turnor (1755-1829) who wrote the _Collections for
+the Town and Soke of Grantham, containing authentic Memoirs of Sir Isaac
+Newton, from Lord Portsmouth's Manuscripts_, London, 1806.
+
+[286] It may be recalled to mind that Sir David (1781-1868) wrote a life of
+Newton (1855).
+
+[287] "They are in the country. We rejoice."
+
+[288] "I am here, chatterbox, suck!"
+
+[289] "I have been graduated! I decline!"
+
+[290] Giovanni Castiglioni (Castillon, Castiglione), was born at
+Castiglione, in Tuscany, in 1708, and died at Berlin in 1791. He was
+professor of mathematics at Utrecht and at Berlin. He wrote on De Moivre's
+equations (1762), Cardan's rule (1783), and Euclid's treatment of parallels
+(1788-89).
+
+[291] This was the _Isaaci Newtoni, equitis aurati, opuscula mathematica,
+philosophica et philologica_, Lausannae & Genevae, 1744.
+
+[292] At London, 4to.
+
+[293] "All the English attribute it to Newton."
+
+[294] Stephen Peter Rigaud (1774-1839), Savilian professor of geometry at
+Oxford (1810-27) and later professor of astronomy and head of the Radcliffe
+Observatory. He wrote _An historical Essay on first publication of Sir
+Isaac Newton's Principia_, Oxford, 1838, and a two-volume work entitled
+_Correspondence of Scientific Men of the 17th Century_, 1841.
+
+[295] It is no longer considered by scholars as the work of Newton.
+
+[296] J. Edleston, the author of the _Correspondence of Sir Isaac Newton
+and Professor Cotes_, London, 1850.
+
+[297] Palmer (1601-1647) was Master of Queen's College, Cambridge, a
+Puritan but not a separatist. His work, _The Characters of a believing
+Christian, in Paradoxes and seeming contradictions_, appeared in 1645.
+
+[298] Grosart (1827-1899) was a Presbyterian clergyman. He was a great
+bibliophile, and issued numerous reprints of rare books.
+
+[299] This was the year after Palmer's death. The title was, _The Remaines
+of ... Francis Lord Verulam....; being Essays and severall Letters to
+severall great personages, and other pieces of various and high concernment
+not heretofore published_, London, 1648, 4to.
+
+[300] Shaw (1694-1763) was physician extraordinary to George II. He wrote
+on chemistry and medicine, and his edition of the _Philosophical Works of
+Francis Bacon_ appeared at London in 1733.
+
+[301] John Locke (1632-1704), the philosopher. This particular work
+appeared in 1695. There was an edition in 1834 (vol. 25 of the _Sacred
+Classics_) and one in 1836 (vol. 2 of the _Christian Library_).
+
+[302] I use the word _Socinian_ because it was so much used in Locke's
+time: it is used in our own day by the small fry, the unlearned clergy and
+their immediate followers, as a term of reproach for _all_ Unitarians. I
+suspect they have a kind of liking for the _word_; it sounds like _so
+sinful_. The learned clergy and the higher laity know better: they know
+that the bulk of the modern Unitarians go farther than Socinus, and are not
+correctly named as his followers. The Unitarians themselves neither desire
+nor deserve a name which puts them one point nearer to orthodoxy than they
+put themselves. That point is the doctrine that direct prayer to Jesus
+Christ is lawful and desirable: this Socinus held, and the modern
+Unitarians do not hold. Socinus, in treating the subject in his own
+_Institutio_, an imperfect catechism which he left, lays much more stress
+on John xiv. 13 than on xv. 16 and xvi. 23. He is not disinclined to think
+that _Patrem_ should be in the first citation, where some put it; but he
+says that to ask the Father in the name of the Son is nothing but praying
+to the Son in prayer to the Father. He labors the point with obvious wish
+to secure a conclusive sanction. In the Racovian Catechism, of which
+Faustus Socinus probably drew the first sketch, a clearer light is arrived
+at. The translation says: "But wherein consists the divine honor due to
+Christ? In adoration likewise and invocation. For we ought at all times to
+adore Christ, and may in our necessities address our prayers to him as
+often as we please; and there are many reasons to induce us to do this
+freely." There are some who like accuracy, even in aspersion--A. De M.
+
+Socinus, or Fausto Paolo Sozzini (1539-1604), was an antitrinitarian who
+believed in prayer and homage to Christ. Leaving Italy after his views
+became known, he repaired to Basel, but his opinions were too extreme even
+for the Calvinists. He then tried Transylvania, attempting to convert to
+his views the antitrinitarian Bishop Dávid. The only result of his efforts
+was the imprisonment of Dávid and his own flight to Poland, in which
+country he spent the rest of his life (1579-1604). His complete works
+appeared first at Amsterdam in 1668, in the _Bibliotheca Fratres
+Polonorum_. The _Racovian Catechism_ (1605) appeared after his death, but
+it seems to have been planned by him.
+
+[303] "As much of faith as is necessary to salvation is contained in this
+article, Jesus is the Christ."
+
+[304] Edwards (1637-1716) was a Cambridge fellow, strongly Calvinistic. He
+published many theological works, attacking the Arminians and Socinians.
+Locke and Whiston were special objects of attack.
+
+[305] _Sir I. Newton's views on points of Trinitarian Doctrine; his
+Articles of Faith, and the General Coincidence of his Opinions with those
+of J. Locke; a Selection of Authorities, with Observations_, London, 1856.
+
+[306] _A Confession of the Faith_, Bristol, 1752, 8vo.
+
+[307] This was really very strange, because Laud (1573-1644), while he was
+Archbishop of Canterbury, forced a good deal of High Church ritual on the
+Puritan clergy, and even wished to compel the use of a prayer book in
+Scotland. It was this intolerance that led to his impeachment and
+execution.
+
+[308] The name is Jonchère. He was a man of some merit, proposing (1718) an
+important canal in Burgundy, and publishing a work on the _Découverte des
+longitudes estimées généralement impossible à trouver_, 1734 (or 1735).
+
+[309] Locke invented a kind of an instrument for finding longitude, and it
+is described in the appendix, but I can find nothing about the man. There
+was published some years later (London, 1751) another work of his, _A new
+Problem to discover the longitude at sea_.
+
+[310] Baxter, concerning whom I know merely that he was a schoolmaster,
+starts with the assumption of this value, and deduces from it some fourteen
+properties relating to the circle.
+
+[311] John, who died in 1780, was a well-known character in his way. He was
+a bookseller on Fleet Street, and his shop was a general rendezvous for the
+literary men of his time. He wrote the _Memoirs of the Life and Writings of
+Mr. William Whiston_ (1749, with another edition in 1753). He was one of
+the first to issue regular catalogues of books with prices affixed.
+
+[312] The name appears both as Hulls and as Hull. He was born in
+Gloucestershire in 1699. In 1754 he published _The Art of Measuring made
+Easy by the help of a new Sliding Scale_.
+
+[313] Thomas Newcomen (1663-1729) invented the first practical steam engine
+about 1710. It was of about five and a half horse power, and was used for
+pumping water from coal mines. Savery had described such an engine in 1702,
+but Newcomen improved upon it and made it practical.
+
+[314] The well-known benefactor of art (1787-1863).
+
+[315] The tract was again reprinted in 1860.
+
+[316] Hulls made his experiment on the Avon, at Evesham, in 1737, having
+patented his machine in 1736. He had a Newcomen engine connected with six
+paddles. This was placed in the front of a small tow boat. The experiment
+was a failure.
+
+[317] William Symington (1763-1831). In 1786 he constructed a working model
+of a steam road carriage. The machinery was applied to a small boat in
+1788, and with such success as to be tried on a larger boat in 1789. The
+machinery was clumsy, however, and in 1801 he took out a new patent for the
+style of engine still used on paddle wheel steamers. This engine was
+successfully used in 1802, on the Charlotte Dundas. Fulton (1765-1815) was
+on board, and so impressed Robert Livingston with the idea that the latter
+furnished the money to build the Clermont (1807), the beginning of
+successful river navigation.
+
+[318] Louis Bertrand Castel (1688-1757), most of whose life was spent in
+trying to perfect his _Clavecin oculaire_, an instrument on the order of
+the harpsichord, intended to produce melodies and harmonies of color. He
+also wrote _L'Optique des couleurs_ (1740) and _Sur le fond de la Musique_
+(1754).
+
+[319] Dr. Robinson (1680-1754) was professor of physic at Trinity College,
+Dublin, and three times president of King and Queen's College of
+Physicians. In his _Treatise on the Animal Economy_ (1732-3, with a third
+edition in 1738) he anticipated the discoveries of Lavoisier and Priestley
+on the nature of oxygen.
+
+[320] There was another edition, published at London in 1747, 8vo.
+
+[321] The author seems to have shot his only bolt in this work. I can find
+nothing about him.
+
+[322] _Quod Deus sit, mundusque ab ipso creatus fuerit in tempore, ejusque
+providentia gubernetur. Selecta aliquot theoremata adversos atheos_, etc.,
+Paris, 1635, 4to.
+
+[323] The British Museum Catalogue mentions a copy of 1740, but this is
+possibly a misprint.
+
+[324] This was Johann II (1710-1790), son of Johann I, who succeeded his
+father as professor of mathematics at Basel.
+
+[325] Samuel Koenig (1712-1757), who studied under Johann Bernoulli I. He
+became professor of mathematics at Franeker (1747) and professor of
+philosophy at the Hague (1749).
+
+[326] "In accordance with the hypotheses laid down in this memoir it is so
+evident that t must = 34, y = 1, and z = 1, that there is no need of proof
+or authority for it to be recognized by every one."
+
+[327] "I subscribe to the judgment of Mr. Bernoulli as a result of these
+hypotheses."
+
+[328] "It clearly appears from my present analysis and demonstration that
+they have already recognized and perfectly agreed to the fact that the
+quadrature of the circle is mathematically demonstrated."
+
+[329] Dr. Knight (died in 1772) made some worthy contributions to the
+literature of the mariner's compass. As De Morgan states, he was librarian
+of the British Museum.
+
+[330] Sir Anthony Panizzi (1797-1879) fled from Italy under sentence of
+death (1822). He became assistant (1831) and chief (1856) librarian of the
+British Museum, and was knighted in 1869. He began the catalogue of printed
+books of the Museum.
+
+[331] Wright (1711-1786) was a physicist. He was offered the professorship
+of mathematics at the Imperial Academy of St. Petersburg but declined to
+accept it. This work is devoted chiefly to the theory of the Milky Way, the
+_via lactea_ as he calls it after the manner of the older writers.
+
+[332] Troughton (1753-1835) was one of the world's greatest instrument
+makers. He was apprenticed to his brother John, and the two succeeded
+(1770) Wright and Cole in Fleet Street. Airy called his method of
+graduating circles the greatest improvement ever made in instrument making.
+He constructed (1800) the first modern transit circle, and his instruments
+were used in many of the chief observatories of the world.
+
+[333] William Simms (1793-1860) was taken into partnership by Troughton
+(1826) after the death of the latter's brother. The firm manufactured some
+well-known instruments.
+
+[334] This was George Horne (1730-1792), fellow of Magdalen College,
+Oxford, vice-Chancellor of the University (1776), Dean of Canterbury
+(1781), and Bishop of Norwich (1790). He was a great satirist, but most of
+his pamphlets against men like Adam Smith, Swedenborg, and Hume, were
+anonymous, as in the case of this one against Newton. He was so liberal in
+his attitude towards the Methodists that he would not have John Wesley
+forbidden to preach in his diocese. He was twenty-one when this tract
+appeared.
+
+[335] Martin (1704-1782) was by no means "old Benjamin Martin" when Horne
+wrote this pamphlet in 1749. In fact he was then only forty-five. He was a
+physicist and a well-known writer on scientific instruments. He also wrote
+_Philosophia Britannica or a new and comprehensive system of the Newtonian
+Philosophy_ (1759).
+
+[336] Jean Théophile Desaguliers, or Des Aguliers (1683-1744) was the son
+of a Protestant who left France after the revocation of the Edict of
+Nantes. He became professor of physics at Oxford, and afterwards gave
+lectures in London. Later he became chaplain to the Prince of Wales. He
+published several works on physics.
+
+[337] Charles Hutton (1737-1823), professor of mathematics at Woolwich
+(1772-1807). His _Mathematical Tables_ (1785) and _Mathematical and
+Philosophical Dictionary_ (1795-1796) are well known.
+
+[338] James Epps (1773-1839) contributed a number of memoirs on the use and
+corrections of instruments. He was assistant secretary of the Astronomical
+Society.
+
+[339] John Hutchinson (1674-1737) was one of the first to try to reconcile
+the new science of geology with Genesis. He denied the Newtonian hypothesis
+as dangerous to religion, and because it necessitated a vacuum. He was a
+mystic in his interpretation of the Scriptures, and created a sect that
+went under the name of Hutchinsonians.
+
+[340] John Rowning, a Lincolnshire rector, died in 1771. He wrote on
+physics, and published a memoir on _A machine for finding the roots of
+equations universally_ (1770).
+
+[341] It is always difficult to sanction this spelling of the name of this
+Jesuit father who is so often mentioned in the analytic treatment of
+conics. He was born in Ragusa in 1711, and the original spelling was
+Ru[=d]er Josip Bo[vs]kovi['c]. When he went to live in Italy, as professor
+of mathematics at Rome (1740) and at Pavia, the name was spelled Ruggiero
+Giuseppe Boscovich, although Boscovicci would seem to a foreigner more
+natural. His astronomical work was notable, and in his _De maculis
+solaribus_ (1736) there is the first determination of the equator of a
+planet by observing the motion of spots on its surface. Boscovich came near
+having some contact with America, for he was delegated to observe in
+California the transit of Venus in 1755, being prevented by the dissolution
+of his order just at that time. He died in 1787, at Milan.
+
+[342] James Granger (1723-1776) who wrote the _Biographical History of
+England_, London, 1769. His collection of prints was remarkable, numbering
+some fourteen thousand.
+
+[343] He was curator of experiments for the Royal Society. He wrote a large
+number of books and monographs on physics. He died about 1713.
+
+[344] Lee seems to have made no impression on biographers.
+
+[345] This work appeared at London in 1852.
+
+[346] Of course this is no longer true. The most scholarly work to-day is
+that of Rudio, _Archimedes, Huygens, Lambert, Legendre, vier Abhandlungen
+über die Kreismessung ... mit einer Uebersicht über die Geschichte des
+Problems von der Quadratur des Zirkels, von den ältesten Zeiten bis auf
+unsere Tage_, Leipsic, 1892.
+
+[347] Joseph Jérome le François de Lalande (1732-1807), professor of
+astronomy in the Collège de France (1753) and director of the Paris
+Observatory (1761). His writings on astronomy and his _Bibliographie
+astronomique, avec l'histoire de l'astronomie depuis 1781 jusqu'en 1802_
+(Paris, 1803) are well known.
+
+[348] De Morgan refers to his _Histoire de l'Astronomie au 18e siècle_,
+which appeared in 1827, five years after Delambre's death. Jean Baptiste
+Joseph Delambre (1749-1822) was a pupil of and a collaborator with Lalande,
+following his master as professor of astronomy in the Collège de France.
+His work on the measurements for the metric system is well known, and his
+four histories of astronomy, _ancienne_ (1817), _au moyen âge_ (1819),
+_moderne_ (1821), and _au 18e siècle_ (posthumous, 1827) are highly
+esteemed.
+
+[349] Jean-Joseph Rive (1730-1792), a priest who left his cure under grave
+charges, and a quarrelsome character. His attack on Montucla was a case of
+the pot calling the kettle black; for while he was a brilliant writer he
+was a careless bibliographer.
+
+[350] Isaac Barrow (1630-1677) was quite as well known as a theologian as
+he was from his Lucasian professorship of mathematics at Cambridge.
+
+[351] "Besides we can see by this that Barrow was a poor philosopher; for
+he believed in the immortality of the soul and in a Divinity other than
+universal nature."
+
+[352] The _Récréations mathématiques et physiques_ (Paris, 1694) of Jacques
+Ozanam (1640-1717) is a work that is still highly esteemed. Among various
+other works he wrote a _Dictionnaire mathématique ou Idée générale des
+mathématiques_ (1690) that was not without merit. The _Récréations_ went
+through numerous editions (Paris, 1694, 1696, 1741, 1750, 1770, 1778, and
+the Montucla edition of 1790; London, 1708, the Montucla-Hutton edition of
+1803 and the Riddle edition of 1840; Dublin, 1790).
+
+[353] Hendryk van Etten, the _nom de plume_ of Jean Leurechon (1591-1670),
+rector of the Jesuit college at Bar, and professor of philosophy and
+mathematics. He wrote on astronomy (1619) and horology (1616), and is known
+for his _Selecta Propositiones in tota sparsim mathematica pulcherrime
+propositae in solemni festo SS. Ignatii et Francesci Xaverii_, 1622. The
+book to which De Morgan refers is his _Récréation mathématicque, composée
+de plusieurs problèmes plaisants et facetieux_, Lyons, 1627, with an
+edition at Pont-à-Mousson, 1629. There were English editions published at
+London in 1633, 1653, and 1674, and Dutch editions in 1662 and 1672.
+
+I do not understand how De Morgan happened to miss owning the work by
+Claude Gaspar Bachet de Meziriac (1581-1638), _Problèmes plaisans et
+délectables_, which appeared at Lyons in 1612, 8vo, with a second edition
+in 1624. There was a fifth edition published at Paris in 1884.
+
+[354] His title page closes with "Paris, Chez Ch. Ant. Jombert.... M DCC
+LIV."
+
+This was Charles-Antoine Jombert (1712-1784), a printer and bookseller with
+some taste for painting and architecture. He wrote several works and edited
+a number of early treatises.
+
+[355] The late Professor Newcomb made the matter plain even to the
+non-mathematical mind, when he said that "ten decimal places are sufficient
+to give the circumference of the earth to the fraction of an inch, and
+thirty decimal places would give the circumference of the whole visible
+universe to a quantity imperceptible with the most powerful microscope."
+
+[356] _Antinewtonianismi pars prima, in qua Newtoni de coloribus systema ex
+propriis principiis geometrice evertitur, et nova de coloribus theoria
+luculentissimis experimentis demonstrantur_.... Naples, 1754; _pars
+secunda_, Naples, 1756.
+
+[357] Celestino Cominale (1722-1785) was professor of medicine at the
+University of Naples.
+
+[358] The work appeared in the years from 1844 to 1849.
+
+[359] There was a Vienna edition in 1758, 4to, and another in 1759, 4to.
+This edition is described on the title page as _Editio Veneta prima ipso
+auctore praesente, et corrigente_.
+
+[360] The first edition was entitled _De solis ac lunae defectibus libri
+V. P. Rogerii Josephi Boscovich ... cum ejusdem auctoris adnotationibus_,
+London, 1760. It also appeared in Venice in 1761, and in French translation
+by the Abbé de Baruel in 1779, and was a work of considerable influence.
+
+[361] Paulian (1722-1802) was professor of physics at the Jesuit college at
+Avignon. He wrote several works, the most popular of which, the
+_Dictionnaire de physique_ (Avignon, 1761), went through nine editions by
+1789.
+
+[362] This is correct.
+
+[363] Probably referring to the fact that Hill (1795-1879), who had done so
+much for postal reform, was secretary to the postmaster general (1846), and
+his name was a synonym for the post office directory.
+
+[364] Richard Lovett (1692-1780) was a good deal of a charlatan. He claimed
+to have studied electrical phenomena, and in 1758 advertised that he could
+effect marvelous cures, especially of sore throat, by means of electricity.
+Before publishing the works mentioned by De Morgan he had issued others of
+similar character, including _The Subtile Medium proved_ (London, 1756) and
+_The Reviewers Reviewed_ (London, 1760).
+
+[365] Jean Sylvain Bailly (1736-1793), member of the _Académie française_
+and of the _Académie des sciences_, first deputy elected to represent Paris
+in the _Etats-généraux_ (1789), president of the first National Assembly,
+and mayor of Paris (1789-1791). For his vigor as mayor in keeping the
+peace, and for his manly defence of the Queen, he was guillotined. He was
+an astronomer of ability, but is best known for his histories of the
+science.
+
+[366] These were the _Histoire de l'Astronomie ancienne_ (1775), _Histoire
+de l'Astronomie moderne_ (1778-1783), _Histoire de l'Astronomie indienne et
+orientale_ (1787), and _Lettres sur l'origine des peuples de l'Asie_
+(1775).
+
+[367] "The sick old man of Ferney, V., a boy of a hundred years." Voltaire
+was born in 1694, and hence was eighty-three at this time.
+
+[368] In Palmézeaux's _Vie de Bailly_, in Bailly's _Ouvrage Posthume_
+(1810), M. de Sales is quoted as saying that the _Lettres sur l'Atlantide_
+were sent to Voltaire and that the latter did not approve of the theory set
+forth.
+
+[369] The British Museum catalogue gives two editions, 1781 and 1782.
+
+[370] A mystic and a spiritualist. His chief work was the one mentioned
+here.
+
+[371] Jacob Behmen, or Böhme (1575-1624), known as "the German
+theosophist," was founder of the sect of Boehmists, a cult allied to the
+Swedenborgians. He was given to the study of alchemy, and brought the
+vocabulary of the science into his mystic writings. His sect was revived in
+England in the eighteenth century through the efforts of William Law.
+Saint-Martin translated into French two of his Latin works under the titles
+_L'Aurore naissante, ou la Racine de la philosophie_ (1800), and _Les trois
+principes de l'essence divine_ (1802). The originals had appeared nearly
+two hundred years earlier,--_Aurora_ in 1612, and _De tribus principiis_ in
+1619.
+
+[372] "Unknown."
+
+[373] "Skeptical."
+
+[374] "Man, man, man."
+
+[375] "Men, men, men."
+
+[376] It is interesting to read De Morgan's argument against Saint-Martin's
+authorship of this work. It is attributed to Saint-Martin both by the
+_Biographie Universelle_ and by the _British Museum Catalogue_, and De
+Morgan says by "various catalogues and biographies."
+
+[377] "To explain things by man and not man by things. _On Errors and
+Truth_, by a Ph.... Inc...."
+
+[378] "If we would preserve ourselves from all illusions, and above all
+from the allurements of pride, by which man is so often seduced, we should
+never take man, but always God, for our term of comparison."
+
+[379] "And here is found already an explanation of the numbers four and
+nine which caused some perplexity in the work cited above. Man is lost in
+passing from four to nine."
+
+[380] Williams also took part in the preparation of some tables for the
+government to assist in the determination of longitude. He had published a
+work two years before the one here cited, on the same subject,--_An entire
+new work and method to discover the variation of the Earth's Diameters_,
+London, 1786.
+
+[381] This is Gabriel Mouton (1618-1694), a vicar at Lyons, who suggested
+as a basis for a natural system of measures the _mille_, a minute of a
+degree of the meridian. This appeared in his _Observationes diametrorum
+solis et lunae apparentium, meridianarumque aliquot altitudinum cum tabula
+declinationum solis_.... Lyons, 1670.
+
+[382] Jacques Cassini (1677-1756), one of the celebrated Cassini family of
+astronomers. After the death of his father he became director of the
+observatory at Paris. The basis for a metric unit was set forth by him in
+his _Traité de la grandeur et de la figure de la terre_, Paris, 1720. He
+was a prolific writer on astronomy.
+
+[383] Alexis Jean Pierre Paucton (1732-1798). He was, for a time, professor
+of mathematics at Strassburg, but later (1796) held office in Paris. His
+leading contribution to metrology was his _Métrologie ou Traité des
+mesures_, Paris, 1780.
+
+[384] He was an obscure writer, born at Deptford.
+
+[385] He was also a writer of no scientific merit, his chief contributions
+being religious tracts. One of his productions, however, went through many
+editions, even being translated into French; _Three dialogues between a
+Minister and one of his Parishioners; on the true principles of Religion
+and salvation for sinners by Jesus Christ_. The twentieth edition appeared
+at Cambridge in 1786.
+
+[386] This was the _Reflections on the Revolution in France, and on the
+proceedings in certain societies in London relative to that event_ (London,
+1790) by Edmund Burke (1729-1797). Eleven editions of the work appeared the
+first year.
+
+[387] Paine (1736-1809) was born in Norfolkshire, of Quaker parents. He
+went to America at the beginning of the Revolution and published, in
+January 1776, a violent pamphlet entitled _Common Sense_. He was a private
+soldier under Washington, and on his return to England after the war he
+published _The Rights of Man_. He was indicted for treason and was outlawed
+to France. He was elected to represent Calais at the French convention, but
+his plea for moderation led him perilously near the guillotine. His _Age of
+Reason_ (1794) was dedicated to Washington. He returned to America in 1802
+and remained there until his death.
+
+[388] Part I appeared in 1791 and was so popular that eight editions
+appeared in that year. It was followed in 1792 by Part II, of which nine
+editions appeared in that year. Both parts were immediately republished in
+Paris, and there have been several subsequent editions.
+
+[389] Mary Wollstonecraft (1759-1797) was only thirty-three when this work
+came out. She had already published _An historical and moral View of the
+Origin and Progress of the French Revolution_ (1790), and _Original Stories
+from Real Life_ (1791). She went to Paris in 1792 and remained during the
+Reign of Terror.
+
+[390] Samuel Parr (1747-1827) was for a time head assistant at Harrow
+(1767-1771), afterwards headmaster in other schools. At the time this book
+was written he was vicar of Hatton, where he took private pupils
+(1785-1798) to the strictly limited number of seven. He was a violent Whig
+and a caustic writer.
+
+[391] On Mary Wollstonecraft's return from France she married (1797)
+William Godwin (1756-1836). He had started as a strong Calvinistic
+Nonconformist minister, but had become what would now be called an
+anarchist, at least by conservatives. He had written an _Inquiry concerning
+Political Justice_ (1793) and a novel entitled _Caleb Williams, or Things
+as they are_ (1794), both of which were of a nature to attract his future
+wife.
+
+[392] This child was a daughter. She became Shelley's wife, and Godwin's
+influence on Shelley was very marked.
+
+[393] This was John Nichols (1745-1826), the publisher and antiquary. He
+edited the _Gentleman's Magazine_ (1792-1826) and his works include the
+_Literary Anecdotes of the Eighteenth Century_ (1812-1815), to which De
+Morgan here refers.
+
+[394] William Bellenden, a Scotch professor at the University of Paris, who
+died about 1633. His textbooks are now forgotten, but Parr edited an
+edition of his works in 1787. The Latin preface, _Praefatio ad Bellendum de
+Statu_, was addressed to Burke, North, and Fox, and was a satire on their
+political opponents.
+
+[395] As we have seen, he had been head-master before he began taking "his
+handful of private pupils."
+
+[396] The story has evidently got mixed up in the telling, for Tom Sheridan
+(1721-1788), the great actor, was old enough to have been Dr. Parr's
+father. It was his son, Richard Brinsley Sheridan (1751-1816), the
+dramatist and politician, who was the pupil of Parr. He wrote _The Rivals_
+(1775) and _The School for Scandal_ (1777) soon after Parr left Harrow.
+
+[397] Horner (1785-1864) was a geologist and social reformer. He was very
+influential in improving the conditions of child labor.
+
+[398] William Cobbett (1762-1835), the journalist, was a character not
+without interest to Americans. Born in Surrey, he went to America at the
+age of thirty and remained there eight years. Most of this time he was
+occupied as a bookseller in Philadelphia, and while thus engaged he was
+fined for libel against the celebrated Dr. Rush. On his return to England
+he edited the _Weekly Political Register_ (1802-1835), a popular journal
+among the working classes. He was fined and imprisoned for two years
+because of his attack (1810) on military flogging, and was also (1831)
+prosecuted for sedition. He further showed his paradox nature by his
+_History of the Protestant Reformation_ (1824-1827), an attack on the
+prevailing Protestant opinion. He also wrote a _Life of Andrew Jackson_
+(1834). After repeated attempts he succeeded in entering parliament, a
+result of the Reform Bill.
+
+[399] Robinson (1735-1790) was a Baptist minister who wrote several
+theological works and a number of hymns. His work at Cambridge so offended
+the students that they at one time broke up the services.
+
+[400] This work had passed through twelve editions by 1823.
+
+[401] Dyer (1755-1841), the poet and reformer, edited Robinson's
+_Ecclesiastical Researches_ (1790). He was a life-long friend of Charles
+Lamb, and in their boyhood they were schoolmates at Christ's Hospital. His
+_Complaints of the Poor People of England_ (1793) made him a worthy
+companion of the paradoxers above mentioned.
+
+[402] These were John Thelwall (1764-1834) whose _Politics for the People
+or Hogswash_ (1794) took its title from the fact that Burke called the
+people the "swinish multitude." The book resulted in sending the author to
+the Tower for sedition. In 1798 he gave up politics and started a school of
+elocution which became very famous. Thomas Hardy (1752-1832), who kept a
+bootmaker's shop in Piccadilly, was a fellow prisoner with Thelwall, being
+arrested for high treason. He was founder (1792) of The London
+Corresponding Society, a kind of clearing house for radical associations
+throughout the country. Horne Tooke was really John Horne (1736-1812), he
+having taken the name of his friend William Tooke in 1782. He was a radical
+of the radicals, and organized a number of reform societies. Among these
+was the Constitutional Society that voted money (1775) to assist the
+American revolutionists, appointing him to give the contribution to
+Franklin. For this he was imprisoned for a year. With his fellow rebels in
+the Tower in 1794, however, he was acquitted. As a philologist he is known
+for his early advocacy of the study of Anglo-Saxon and Gothic, and his
+_Diversions of Purley_ (1786) is still known to readers.
+
+[403] This was the admiral, Adam Viscount Duncan (1731-1804), who defeated
+the Dutch off Camperdown in 1797.
+
+[404] He was created Duke of Clarence and St. Andrews in 1789 and was
+Admiral of the Fleet escorting Louis XVIII on his return to France in 1814.
+He became Lord High Admiral in 1827, and reigned as William IV from 1830 to
+1837.
+
+[405] This was Charles Abbott (1762-1832) first Lord Tenterden. He
+succeeded Lord Ellenborough as Chief Justice (1818) and was raised to the
+peerage in 1827. He was a strong Tory and opposed the Catholic Relief Bill,
+the Reform Bill, and the abolition of the death penalty for forgery.
+
+[406] Edward Law (1750-1818), first Baron Ellenborough. He was chief
+counsel for Warren Hastings, and his famous speech in defense of his client
+is well known. He became Chief Justice and was raised to the peerage in
+1802. He opposed all efforts to modernize the criminal code, insisting upon
+the reactionary principle of new death penalties.
+
+[407] Edmund Law (1703-1787), Bishop of Carlisle (1768), was a good deal
+more liberal than his son. His _Considerations on the Propriety of
+requiring subscription to the Articles of Faith_ (1774) was published
+anonymously. In it he asserts that not even the clergy should be required
+to subscribe to the thirty-nine articles.
+
+[408] Joe Miller (1684-1738), the famous Drury Lane comedian, was so
+illiterate that he could not have written the _Joe Miller's Jests, or the
+Wit's Vade-Mecum_ that appeared the year after his death. It was often
+reprinted and probably contained more or less of Miller's own jokes.
+
+[409] The sixth duke (1766-1839) was much interested in parliamentary
+reform. He was a member of the Society of Friends of the People. He was for
+fourteen years a member of parliament (1788-1802) and was later Lord
+Lieutenant of Ireland (1806-1807). He afterwards gave up politics and
+became interested in agricultural matters.
+
+[410] George Jeffreys (c. 1648-1689), the favorite of James II, who was
+active in prosecuting the Rye House conspirators. He was raised to the
+peerage in 1684 and held the famous "bloody assize" in the following year,
+being made Lord Chancellor as a result. He was imprisoned in the Tower by
+William III and died there.
+
+[411] _The Every Day Book, forming a Complete History of the Year, Months,
+and Seasons, and a perpetual Key to the Almanack_, 1826-1827.
+
+[412] The first and second editions appeared in 1820. Two others followed
+in 1821.
+
+[413] _The three trials of W. H., for publishing three parodies; viz the
+late John Wilkes' Catechism, the Political Litany, and the Sinecurists
+Creed; on three ex-officio informations, at Guildhall, London, ... Dec. 18,
+19, & 20, 1817_,... London, 1818.
+
+[414] The _Political Litany_ appeared in 1817.
+
+[415] That is, Castlereagh's.
+
+[416] The well-known caricaturist (1792-1878), then only twenty-nine years
+old.
+
+[417] Robert Stewart (1769-1822) was second Marquis of Londonderry and
+Viscount Castlereagh. As Chief Secretary for Ireland he was largely
+instrumental in bringing about the union of Ireland and Great Britain. He
+was at the head of the war department during most of the Napoleonic wars,
+and was to a great extent responsible for the European coalition against
+the Emperor. He suicided in 1822.
+
+[418] John Murray (1778-1843), the well-known London publisher. He refused
+to finish the publication of Don Juan, after the first five cantos, because
+of his Tory principles.
+
+[419] Only the first two cantos appeared in 1819.
+
+[420] Proclus (412-485), one of the greatest of the neo-Platonists, studied
+at Alexandria and taught philosophy at Athens. He left commentaries on
+Plato and on part of Euclid's _Elements_.
+
+[421] Thomas Taylor (1758-1835), called "the Platonist," had a liking for
+mathematics, and was probably led by his interest in number mysticism to a
+study of neo-Platonism. He translated a number of works from the Latin and
+Greek, and wrote two works on theoretical arithmetic (1816, 1823).
+
+[422] There was an earlier edition, 1788-89.
+
+[423] Georgius Gemistus, or Georgius Pletho (Plethon), lived in the
+fourteenth and fifteenth centuries. He was a native of Constantinople, but
+spent most of his time in Greece. He devoted much time to the propagation
+of the Platonic philosophy, but also wrote on divinity, geography, and
+history.
+
+[424] Hannah More (1745-1833), was, in her younger days, a friend of Burke,
+Reynolds, Dr. Johnson, and Garrick. At this time she wrote a number of
+poems and aspired to become a dramatist. Her _Percy_ (1777), with a
+prologue and epilogue by Garrick, had a long run at Covent Garden. Somewhat
+later she came to believe that the playhouse was a grave public evil, and
+refused to attend the revival of her own play with Mrs. Siddons in the
+leading part. After 1789 she and her sisters devoted themselves to starting
+schools for poor children, teaching them religion and housework, but
+leaving them illiterate.
+
+[425] These were issued at the rate of three each month,--a story, a
+ballad, and a Sunday tract. They were collected and published in one volume
+in 1795. It is said that two million copies were sold the first year. There
+were also editions in 1798, 1819, 1827, and 1836-37.
+
+[426] That is, Dr. Johnson (1709-1784). The _Rambler_ was published in
+1750-1752, and was an imitation of Addison's _Spectator_.
+
+[427] Dr. Moore, referred to below.
+
+[428] Dr. John Moore (1729-1802), physician and novelist, is now best known
+for his _Journal during a Residence in France from the beginning of August
+to the middle of December, 1792_, a work quoted frequently by Carlyle in
+his _French Revolution_.
+
+[429] Sir John Moore (1761-1809), Lieutenant General in the Napoleonic
+wars. He was killed in the battle of Corunna. The poem by Charles Wolfe
+(1791-1823), _The Burial of Sir John Moore_ (1817), is well known.
+
+[430] Referring to the novels of Thomas Love Peacock (1785-1866), who
+succeeded James Mill as chief examiner of the East India Company, and was
+in turn succeeded by John Stuart Mill.
+
+[431] Frances Burney, Madame d'Arblay (1752-1840), married General
+d'Arblay, a French officer and companion of Lafayette, in 1793. She was
+only twenty-five when she acquired fame by her _Evelina, or a Young Lady's
+Entrance into the World_. Her _Letters and Diaries_ appeared posthumously
+(1842-45).
+
+[432] Henry Peter, Baron Brougham and Vaux (1778-1868), well known in
+politics, science, and letters. He was one of the founders of the
+_Edinburgh Review_, became Lord Chancellor in 1830, and took part with men
+like William Frend, De Morgan's father-in-law, in the establishing of
+London University. He was also one of the founders of the Society for the
+Diffusion of Useful Knowledge. He was always friendly to De Morgan, who
+entered the faculty of London University, whose work on geometry was
+published by the Society mentioned, and who was offered the degree of
+doctor of laws by the University of Edinburgh while Lord Brougham was Lord
+Rector. The Edinburgh honor was refused by De Morgan who said he "did not
+feel like an LL.D."
+
+[433] Maria Edgeworth (1767-1849).
+
+[434] Sydney Owenson (c. 1783-1859) married Sir Thomas Morgan, a well-known
+surgeon, in 1812. Her Irish stories were very popular with the patriots but
+were attacked by the _Quarterly Review_. _The Wild Irish Girl_ (1806) went
+through seven editions in two years.
+
+[435] 1775-1817.
+
+[436] 1771-1832.
+
+[437] The famous preacher (1732-1808). He was the first chairman of the
+Religious Tract Society. He is also known as one of the earliest advocates
+of vaccination, in his _Cow-pock Inoculation vindicated and recommended
+from matters of fact_, 1806.
+
+[438] Sir Rowland Hill (1795-1879), the father of penny postage.
+
+[439] Beilby Porteus (1731-1808), Bishop of Chester (1776) and Bishop of
+London (1787). He encouraged the Sunday-school movement and the
+dissemination of Hannah More's tracts. He was an active opponent of
+slavery, but also of Catholic emancipation.
+
+[440] Henrietta Maria Bowdler (1754-1830), generally known as Mrs. Harriet
+Bowdler. She was the author of many religious tracts and poems. Her _Poems
+and Essays_ (1786) were often reprinted. The story goes that on the
+appearance of her _Sermons on the Doctrines and duties of Christianity_
+(published anonymously), Bishop Porteus offered the author a living under
+the impression that it was written by a man.
+
+[441] William Frend (1757-1841), whose daughter Sophia Elizabeth became De
+Morgan's wife (1837), was at one time a clergyman of the Established
+Church, but was converted to Unitarianism (1787). He came under De Morgan's
+definition of a true paradoxer, carrying on a zealous warfare for what he
+thought right. As a result of his _Address to the Inhabitants of Cambridge_
+(1787), and his efforts to have abrogated the requirement that candidates
+for the M.A. must subscribe to the thirty-nine articles, he was deprived of
+his tutorship in 1788. A little later he was banished (see De Morgan's
+statement in the text) from Cambridge because of his denunciation of the
+abuses of the Church and his condemnation of the liturgy. His eccentricity
+is seen in his declining to use negative quantities in the operations of
+algebra. He finally became an actuary at London and was prominent in
+radical associations. He was a mathematician of ability, having been second
+wrangler and having nearly attained the first place, and he was also an
+excellent scholar in Latin, Greek, and Hebrew.
+
+[442] George Peacock (1791-1858), Fellow of Trinity College, Cambridge,
+Lowndean professor of astronomy, and Dean of Ely Cathedral (1839). His tomb
+may be seen at Ely where he spent the latter part of his life. He was one
+of the group that introduced the modern continental notation of the
+calculus into England, replacing the cumbersome notation of Newton, passing
+from "the _dot_age of fluxions to the _de_ism of the calculus."
+
+[443] Robert Simson (1687-1768); professor of mathematics at Glasgow. His
+restoration of Apollonius (1749) and his translation and restoration of
+Euclid (1756, and 1776--posthumous) are well known.
+
+[444] Francis Maseres (1731-1824), a prominent lawyer. His mathematical
+works had some merit.
+
+[445] These appeared annually from 1804 to 1822.
+
+[446] Henry Gunning (1768-1854) was senior esquire bedell of Cambridge. The
+_Reminiscences_ appeared in two volumes in 1854.
+
+[447] John Singleton Copley, Baron Lyndhurst (1772-1863), the son of John
+Singleton Copley the portrait painter, was born in Boston. He was educated
+at Trinity College, Cambridge, and became a lawyer. He was made Lord
+Chancellor in 1827.
+
+[448] Sir William Rough (c. 1772-1838), a lawyer and poet, became Chief
+Justice of Ceylon in 1836. He was knighted in 1837.
+
+[449] Herbert Marsh, afterwards Bishop of Peterborough, a relation of my
+father.--S. E. De M.
+
+He was born in 1757 and died in 1839. On the trial of Frend he publicly
+protested against testifying against a personal confidant, and was excused.
+He was one of the first of the English clergy to study modern higher
+criticism of the Bible, and amid much opposition he wrote numerous works on
+the subject. He was professor of theology at Cambridge (1707), Bishop of
+Llandaff (1816), and Bishop of Peterborough.
+
+[450] George Butler (1774-1853), Headmaster of Harrow (1805-1829),
+Chancellor of Peterborough (1836), and Dean of Peterborough (1842).
+
+[451] James Tate (1771-1843), Headmaster of Richmond School (1796-1833) and
+Canon of St. Paul's Cathedral (1833). He left several works on the
+classics.
+
+[452] Francis Place (1771-1854), at first a journeyman breeches maker, and
+later a master tailor. He was a hundred years ahead of his time as a strike
+leader, but was not so successful as an agitator as he was as a tailor,
+since his shop in Charing Cross made him wealthy. He was a well-known
+radical, and it was largely due to his efforts that the law against the
+combinations of workmen was repealed in 1824. His chief work was _The
+Principles of Population_ (1822).
+
+[453] Speed (1552-1629) was a tailor until Grevil (Greville) made him
+independent of his trade. He was not only an historian of some merit, but a
+skilful cartographer. His maps of the counties were collected in the
+_Theatre of the Empire of Great Britaine_, 1611. About this same time he
+also published _Genealogies recorded in Sacred Scripture_, a work that had
+passed through thirty-two editions by 1640.
+
+[454] _The history of Great Britaine under the conquests of ye Romans,
+Saxons, Danes, and Normans...._ London, 1611, folio. The second edition
+appeared in 1623; the third, to which De Morgan here refers, posthumously
+in 1632; and the fourth in 1650.
+
+[455] William Nicolson (1655-1727) became Bishop of Carlisle in 1702, and
+Bishop of Derry in 1718. His chief work was the _Historical Library_
+(1696-1724), in the form of a collection of documents and chronicles. It
+was reprinted in 1736 and in 1776.
+
+[456] Sir Fulk Grevil, or Fulke Greville (1554-1628), was a favorite of
+Queen Elizabeth, Chancellor of the Exchequer under James I, a patron of
+literature, and a friend of Sir Philip Sidney.
+
+[457] See note 443 on page 197.
+
+[458] See note 444 on page 197.
+
+[459] See note 439 on page 193.
+
+[460] Edward Waring (1736-1796) was Lucasian professor of mathematics at
+Cambridge. He published several works on analysis and curves. The work
+referred to was the _Miscellanea Analytica de aequationibus algebraicis et
+curvarum proprietatibus_, Cambridge, 1762.
+
+[461] _A Dissertation on the use of the Negative Sign in Algebra...; to
+which is added, Machin's Quadrature of the Circle_, London, 1758.
+
+[462] The paper was probably one on complex numbers, or possibly one on
+quaternions, in which direction as well as absolute value is involved.
+
+[463] De Morgan quotes from one of the Latin editions. Descartes wrote in
+French, the title of his first edition being: _Discours de la méthode pour
+bien conduire sa raison et chercher la vérité dans les sciences, plus la
+dioptrique, les météores et la géométrie qui sont des essais de cette
+méthode_, Leyden, 1637, 4to.
+
+[464] "I have observed that algebra indeed, as it is usually taught, is so
+restricted by definite rules and formulas of calculation, that it seems
+rather a confused kind of an art, by the practice of which the mind is in a
+certain manner disturbed and obscured, than a science by which it is
+cultivated and made acute."
+
+[465] It appeared in 93 volumes, from 1758 to 1851.
+
+[466] _The principles of the doctrine of life-annuities; explained in a
+familiar manner ... with a variety of new tables_ ..., London, 1783.
+
+[467] I suppose the one who wrote _Conjectures on the physical causes of
+Earthquakes and Volcanoes_, Dublin, 1820.
+
+[468] _Scriptores Logarithmici; or, a Collection of several curious_
+_tracts on the nature and construction of Logarithms ... together with same
+tracts on the Binomial Theorem_ ..., 6 vols., London, 1791-1807.
+
+[469] Charles Babbage (1792-1871), whose work on the calculating machine is
+well known. Maseres was, it is true, ninety-two at this time, but Babbage
+was thirty-one instead of twenty-nine. He had already translated Lacroix's
+_Treatise on the differential and integral calculus_ (1816), in
+collaboration with Herschel and Peacock. He was Lucasian professor of
+mathematics at Cambridge from 1828 to 1839.
+
+[470] _The great and new Art of weighing Vanity, or a discovery of the
+ignorance of the great and new artist in his pseudo-philosophical
+writings._ The "great and new artist" was Sinclair.
+
+[471] George Sinclair, probably a native of East Lothian, who died in 1696.
+He was professor of philosophy and mathematics at Glasgow, and was one of
+the first to use the barometer in measuring altitudes. The work to which De
+Morgan refers is his _Hydrostaticks_ (1672). He was a firm believer in evil
+spirits, his work on the subject going through four editions: _Satan's
+Invisible World Discovered; or, a choice collection of modern relations,
+proving evidently against the Saducees and Athiests of this present age,
+that there are Devils, Spirits, Witches, and Apparitions_, Edinburgh, 1685.
+
+[472] This was probably William Sanders, Regent of St. Leonard's College,
+whose _Theses philosophicae_ appeared in 1674, and whose _Elementa
+geometriae_ came out a dozen years later.
+
+[473] _Ars nova et magna gravitatis et levitatis; sive dialogorum
+philosophicorum libri sex de aeris vera ac reali gravitate_, Rotterdam,
+1669, 4to.
+
+[474] Volume I, Nos. 1 and 2, appeared in 1803.
+
+[475] His daughter, Mrs. De Morgan, says in her _Memoir_ of her husband:
+"My father had been second wrangler in a year in which the two highest were
+close together, and was, as his son-in-law afterwards described him, an
+exceedingly clear thinker. It is possible, as Mr. De Morgan said, that this
+mental clearness and directness may have caused his mathematical heresy,
+the rejection of the use of negative quantities in algebraical operations;
+and it is probable that he thus deprived himself of an instrument of work,
+the use of which might have led him to greater eminence in the higher
+branches." _Memoir of Augustus De Morgan_, London, 1882, p. 19.
+
+[476] "If it is not true it is a good invention." A well-known Italian
+proverb.
+
+[477] See page 86, note 132.
+
+[478] He was born at Paris in 1713, and died there in 1765.
+
+[479] _Recherches sur les courbes à double courbure_, Paris, 1731. Clairaut
+was then only eighteen, and was in the same year made a member of the
+Académie des sciences. His _Elémens de géométrie_ appeared in 1741.
+Meantime he had taken part in the measurement of a degree in Lapland
+(1736-1737). His _Traité de la figure de la terre_ was published in 1741.
+The Academy of St. Petersburg awarded him a prize for his _Théorie de la
+lune_ (1750). His various works on comets are well known, particularly his
+_Théorie du mouvement des comètes_ (1760) in which he applied the "problem
+of three bodies" to Halley's comet as retarded by Jupiter and Saturn.
+
+[480] Joseph Privat, Abbé de Molières (1677-1742), was a priest of the
+Congregation of the Oratorium. In 1723 he became a professor in the Collège
+de France. He was well known as an astronomer and a mathematician, and
+wrote in defense of Descartes's theory of vortices (1728, 1729). He also
+contributed to the methods of finding prime numbers (1705).
+
+[481] "Deserves not only to be printed, but to be admired as a marvel of
+imagination, of understanding, and of ability."
+
+[482] Blaise Pascal (1623-1662), the well-known French philosopher and
+mathematician. He lived for some time with the Port Royalists, and defended
+them against the Jesuits in his _Provincial Letters_. Among his works are
+the following: _Essai pour les coniques_ (1640); _Recit de la grande
+expérience de l'équilibre des liqueurs_ (1648), describing his experiment
+in finding altitudes by barometric readings; _Histoire de la roulette_
+(1658); _Traité du triangle arithmétique_ (1665); _Aleae geometria_ (1654).
+
+[483] This proposition shows that if a hexagon is inscribed in a conic (in
+particular a circle) and the opposite sides are produced to meet, the three
+points determined by their intersections will be in the same straight line.
+
+[484] Jacques Curabelle, _Examen des Oeuvres du Sr. Desargues_, Paris,
+1644. He also published without date a work entitled: _Foiblesse pitoyable
+du Sr. G. Desargues employée contre l'examen fait de ses oeuvres_.
+
+[485] See page 119, note 233.
+
+[486] Until "this great proposition called Pascal's should see the light."
+
+[487] The story is that his father, Etienne Pascal, did not wish him to
+study geometry until he was thoroughly grounded in Latin and Greek. Having
+heard the nature of the subject, however, he began at the age of twelve to
+construct figures by himself, drawing them on the floor with a piece of
+charcoal. When his father discovered what he was doing he was attempting to
+demonstrate that the sum of the angles of a triangle equals two right
+angles. The story is given by his sister, Mme. Perier.
+
+[488] Sir John Wilson (1741-1793) was knighted in 1786 and became
+Commissioner of the Great Seal in 1792. He was a lawyer and jurist of
+recognized merit. He stated his theorem without proof, the first
+demonstration having been given by Lagrange in the Memoirs of the Berlin
+Academy for 1771,--_Demonstration d'un théorème nouveau concernant les
+nombres premiers_. Euler also gave a proof in his _Miscellanea Analytica_
+(1773). Fermat's works should be consulted in connection with the early
+history of this theorem.
+
+[489] He wrote, in 1760, a tract in defense of Waring, a point of whose
+algebra had been assailed by a Dr. Powell. Waring wrote another tract of
+the same date.--A. De M.
+
+William Samuel Powell (1717-1775) was at this time a fellow of St. John's
+College, Cambridge. In 1765 he became Vice Chancellor of the University.
+Waring was a Magdalene man, and while candidate for the Lucasian
+professorship he circulated privately his _Miscellanea Analytica_. Powell
+attacked this in his _Observations on the First Chapter of a Book called
+Miscellanea_ (1760). This attack was probably in the interest of another
+candidate, a man of his own college (St. John's), William Ludlam.
+
+[490] William Paley (1743-1805) was afterwards a tutor at Christ's College,
+Cambridge. He never contributed anything to mathematics, but his _Evidences
+of Christianity_ (1794) was long considered somewhat of a classic. He also
+wrote _Principles of Morality and Politics_ (1785), and _Natural Theology_
+(1802).
+
+[491] Edward, first Baron Thurlow (1731-1806) is known to Americans because
+of his strong support of the Royal prerogative during the Revolution. He
+was a favorite of George III, and became Lord Chancellor in 1778.
+
+[492] George Wilson Meadley (1774-1818) published his _Memoirs of ...
+Paley_ in 1809. He also published _Memoirs of Algernon Sidney_ in 1813. He
+was a merchant and banker, and had traveled extensively in Europe and the
+East. He was a convert to unitarianism, to which sect Paley had a strong
+leaning.
+
+[493] Watson (1737-1816) was a strange kind of man for a bishopric. He was
+professor of chemistry at Cambridge (1764) at the age of twenty-seven. It
+was his experiments that led to the invention of the black-bulb
+thermometer. He is said to have saved the government £100,000 a year by his
+advice on the manufacture of gunpowder. Even after he became professor of
+divinity at Cambridge (1771) he published four volumes of _Chemical Essays_
+(vol. I, 1781). He became Bishop of Llandaff in 1782.
+
+[494] James Adair (died in 1798) was counsel for the defense in the trial
+of the publishers of the _Letters of Junius_ (1771). As King's Serjeant he
+assisted in prosecuting Hardy and Horne Tooke.
+
+[495] Morgan (1750-1833) was actuary of the Equitable Assurance Society of
+London (1774-1830), and it was to his great abilities that the success of
+that company was due at a time when other corporations of similar kind were
+meeting with disaster. The Royal Society awarded him a medal (1783) for a
+paper on _Probability of Survivorship_. He wrote several important works on
+insurance and finance.
+
+[496] Dr. Price (1723-1791) was a non-conformist minister and a writer on
+ethics, economics, politics, and insurance. He was a defender of the
+American Revolution and a personal friend of Franklin. In 1778 Congress
+invited him to America to assist in the financial administration of the new
+republic, but he declined. His famous sermon on the French Revolution is
+said to have inspired Burke's _Reflections on the Revolution in France_.
+
+[497] Elizabeth Gurney (1780-1845), a Quaker, who married Joseph Fry
+(1800), a London merchant. She was the prime mover in the Association for
+the Improvement of the Female Prisoners in Newgate, founded in 1817. Her
+influence in prison reform extended throughout Europe, and she visited the
+prisons of many countries in her efforts to improve the conditions of penal
+servitude. The friendship of Mrs. Fry with the De Morgans began in 1837.
+Her scheme for a female benefit society proved worthless from the actuarial
+standpoint, and would have been disastrous to all concerned if it had been
+carried out, and it was therefore fortunate that De Morgan was consulted in
+time. Mrs. De Morgan speaks of the consultation in these words: "My
+husband, who was very sensitive on such points, was charmed with Mrs. Fry's
+voice and manner as much as by the simple self-forgetfulness with which she
+entered into this business; her own very uncomfortable share of it not
+being felt as an element in the question, as long as she could be useful in
+promoting good or preventing mischief. I can see her now as she came into
+our room, took off her little round Quaker cap, and laying it down, went at
+once into the matter. 'I have followed thy advice, and I think nothing
+further can be done in this case; but all harm is prevented.' In the
+following year I had an opportunity of seeing the effect of her most
+musical tones. I visited her at Stratford, taking my little baby and nurse
+with me, to consult her on some articles on prison discipline, which I had
+written for a periodical. The baby--three months old--was restless, and the
+nurse could not quiet her, neither could I entirely, until Mrs. Fry began
+to read something connected with the subject of my visit, when the infant,
+fixing her large eyes on the reader, lay listening till she fell asleep."
+_Memoirs_, p. 91.
+
+[498] Mrs. Fry certainly believed that the writer was the old actuary of
+the Equitable, when she first consulted him upon the benevolent Assurance
+project; but we were introduced to her by our old and dear friend Lady Noel
+Byron, by whom she had been long known and venerated, and who referred her
+to Mr. De Morgan for advice. An unusual degree of confidence in, and
+appreciation of each other, arose on their first meeting between the two,
+who had so much that was externally different, and so much that was
+essentially alike, in their natures.--S. E. De M.
+
+Anne Isabella Milbanke (1792-1860) married Lord Byron in 1815, when both
+took the additional name of Noel, her mother's name. They were separated in
+1816.
+
+[499] An obscure writer not mentioned in the ordinary biographies.
+
+[500] Not mentioned in the ordinary biographies, and for obvious reasons.
+
+[501] "Before" and "after."
+
+[502] On Bishop Wilkins see note 171 on page 100.
+
+[503] Provision for a journey.
+
+[504] See note 179 on page 103.
+
+[505] Thomas Bradwardine (1290-1349), known as _Doctor Profundus_, proctor
+and professor of theology at Oxford, and afterwards Chancellor of St.
+Paul's and confessor to Edward III. The English ascribed their success at
+Crécy to his prayers.
+
+[506] He was consecrated Archbishop of Canterbury by the Pope at Avignon,
+July 13, 1349, and died of the plague at London in the same year.
+
+[507] "One paltry little year."
+
+[508] The title is carelessly copied, as is so frequently the case in
+catalogues, even of the Libri class. It should read: _Arithmetica thome
+brauardini_ || _Olivier Senant_ || _Venum exponuntur ab Oliuiario senant in
+vico diui Jacobi sub signo beate Barbare sedente_. The colophon reads:
+_Explicit arithmetica speculatiua th[=o]e brauardini b[=n] reuisa et
+correcta a Petro sanchez Ciruelo aragonensi mathematicas leg[=e]te
+Parisius, [=i]pressa per Thom[=a] anguelart_. There were Paris editions of
+1495, 1496, 1498, s. a. (c. 1500), 1502, 1504, 1505, s. a. (c. 1510), 1512,
+1530, a Valencia edition of 1503, two Wittenberg editions of 1534 and 1536,
+and doubtless several others. The work is not "very rare," although of
+course no works of that period are common. See the editor's _Rara
+Arithmetica_, page 61.
+
+[509] This is his _Tractatus de proportionibus_, Paris, 1495; Venice, 1505;
+Vienna, 1515, with other editions.
+
+[510] The colophon of the 1495 edition reads: _Et sic explicit Geometria
+Thome brauardini c[=u] tractatulo de quadratura circuli bene reuisa a Petro
+sanchez ciruelo: operaqz Guidonis mercatoris dilig[=e]tissime impresse
+parisi^o in c[=a]po gaillardi. Anno d[=n]i. 1495. die. 20, maij._
+
+This Petro Ciruelo was born in Arragon, and died in 1560 at Salamanca. He
+studied mathematics and philosophy at Paris, and took the doctor's degree
+there. He taught at the University of Alcalà and became canon of the
+Cathedral at Salamanca. Besides his editions of Bradwardine he wrote
+several works, among them the _Liber arithmeticae practicae qui dicitur
+algorithmus_ (Paris, 1495) and the _Cursus quatuor mathematicarum artium
+liberalium_ (Alcalà, 1516).
+
+[511] Star polygons, a subject of considerable study in the later Middle
+Ages. See note 35 on page 44.
+
+[512] "A new theory that adds lustre to the fourteenth century."
+
+[513] There is nothing in the edition of 1495 that leads to this
+conclusion.
+
+[514] The full title is: _Nouvelle théorie des parallèles, avec un
+appendice contenant la manière de perfectionner la théorie des parallèles
+de A. M. Legendre_. The author had no standing as a scientist.
+
+[515] Adrien Marie Legendre (1752-1833) was one of the great mathematicians
+of the opening of the nineteenth century. His _Eléments de géométrie_
+(1794) had great influence on the geometry of the United States. His _Essai
+sur la théorie des nombres_ (1798) is one of the classics upon the subject.
+The work to which Kircher refers is the _Nouvelle théorie des parallèles_
+(1803), in which the attempt is made to avoid using Euclid's postulate of
+parallels, the result being merely the substitution of another assumption
+that was even more unsatisfactory. The best presentations of the general
+theory are W. B. Frankland's _Theories of Parallelism_, Cambridge, 1910,
+and Engel and Stäckel's _Die Theorie der Parallellinien von Euclid bis auf
+Gauss_, Leipsic, 1895. Legendre published a second work on the theory the
+year of his death, _Réflexions sur ... la théorie des parallèles_ (1833).
+His other works include the _Nouvelles méthodes pour la détermination des
+orbites des comètes_ (1805), in which he uses the method of least squares;
+the _Traité des fonctions elliptiques et des intégrales_ (1827-1832), and
+the _Exercises de calcul intégral_ (1811, 1816, 1817).
+
+[516] Johann Joseph Ignatz von Hoffmann (1777-1866), professor of
+mathematics at Aschaffenburg, published his _Theorie der Parallellinien_ in
+1801. He supplemented this by his _Kritik der Parallelen-Theorie_ in 1807,
+and his _Das eilfte Axiom der Elemente des Euclidis neu bewiesen_ in 1859.
+He wrote other works on mathematics, but none of his contributions was of
+any importance.
+
+[517] Johann Karl Friedrich Hauff (1766-1846) was successively professor of
+mathematics at Marburg, director of the polytechnic school at Augsburg,
+professor at the Gymnasium at Cologne, and professor of mathematics and
+physics at Ghent. The work to which Kircher refers is his memoirs on the
+Euclidean _Theorie der Parallelen_ in Hindenburg's _Archiv_, vol. III
+(1799), an article of no merit in the general theory.
+
+[518] Wenceslaus Johann Gustav Karsten (1732-1787) was professor of logic
+at Rostock (1758) and Butzow (1760), and later became professor of
+mathematics and physics at Halle. His work on parallels is the _Versuch
+einer völlig berichtigten Theorie der Parallellinien_ (1779). He also wrote
+a work entitled _Anfangsgründe der mathematischen Wissenschaften_ (1780),
+but neither of these works was more than mediocre.
+
+[519] Johann Christoph Schwab (not Schwal) was born in 1743 and died in
+1821. He was professor at the Karlsschule at Stuttgart. De Morgan's wish
+was met, for the catalogues give "c. fig. 8," so that it evidently had
+eight illustrations instead of eight volumes. He wrote several other works
+on the principles of geometry, none of any importance.
+
+[520] Gaetano Rossi of Catanzaro. This was the libretto writer (1772-1855),
+and hence the imperfections of the work can better be condoned. De Morgan
+should have given a little more of the title: _Solusione esatta e regolare
+... del ... problema della quadratura del circolo_. There was a second
+edition, London, 1805.
+
+[521] This identifies Rossi, for Joséphine Grassini (1773-1850) was a
+well-known contralto, _prima donna_ at Napoleon's court opera.
+
+[522] William Spence (1783-1860) was an entomologist and economist of some
+standing, a fellow of the Royal Society, and one of the founders of the
+Entomological Society of London. The work here mentioned was a popular one,
+the first edition appearing in 1807, and four editions being justified in a
+single year. He also wrote _Agriculture the Source of Britain's Wealth_
+(1808) and _Objections against the Corn Bill refuted_ (1815), besides a
+work in four volumes on entomology (1815-1826) in collaboration with
+William Kirby.
+
+[523] "That used to be so, but we have changed all that."
+
+[524] "Meet the coming disease."
+
+[525] George Douglas (or Douglass) was a Scotch writer. He got out an
+edition of the _Elements of Euclid_ in 1776, with an appendix on
+trigonometry and a set of tables. His work on _Mathematical Tables_
+appeared in 1809, and his _Art of Drawing in Perspective, from mathematical
+principles_, in 1810.
+
+[526] See note 443, on page 197.
+
+[527] John Playfair (1748-1848) was professor of mathematics (1785) and
+natural philosophy (1805) at the University of Edinburgh. His _Elements of
+Geometry_ went through many editions.
+
+[528] "Tell Apella" was an expression current in classical Rome to indicate
+incredulity and to show the contempt in which the Jew was held. Horace
+says: _Credat Judæus Apella_, "Let Apella the Jew believe it." Our "Tell it
+to the marines," is a similar phrase.
+
+[529] As De Morgan says two lines later, "No mistake is more common than
+the natural one of imagining that the"--University of Virginia is at
+Richmond. The fact is that it is not there, and that it did not exist in
+1810. It was not chartered until 1819, and was not opened until 1825, and
+then at Charlottesville. The act establishing the Central College, from
+which the University of Virginia developed, was passed in 1816. The Jean
+Wood to whom De Morgan refers was one John Wood who was born about 1775 in
+Scotland and who emigrated to the United States in 1800. He published a
+_History of the Administration of J. Adams_ (New York, 1802) that was
+suppressed by Aaron Burr. This act called forth two works, a _Narrative of
+the Suppression, by Col. Burr, of the 'History of the Administration of
+John Adams'_ (1802), in which Wood was sustained; and the _Antidote to John
+Wood's Poison_ (1802), in which he was attacked. The work referred to in
+the "printed circular" may have been the _New theory of the diurnal
+rotation of the earth_ (Richmond, Va., 1809). Wood spent the last years of
+his life in Richmond, Va., making county maps. He died there in 1822. A
+careful search through works relating to the University of Virginia fails
+to show that Wood had any connection with it.
+
+[530] There seems to be nothing to add to Dobson's biography beyond what De
+Morgan has so deliciously set forth.
+
+[531] "Give to each man his due."
+
+[532] Hester Lynch Salusbury (1741-1821), the friend of Dr. Johnson,
+married Henry Thrale (1763), a brewer, who died in 1781. She then married
+Gabriel Piozzi (1784), an Italian musician. Her _Anecdotes of the late
+Samuel Johnson_ (1786) and _Letters to and from Samuel Johnson_ (1788) are
+well known. She also wrote numerous essays and poems.
+
+[533] Samuel Pike (c. 1717-1773) was an independent minister, with a chapel
+in London and a theological school in his house. He later became a disciple
+of Robert Sandeman and left the Independents for the Sandemanian church
+(1765). The _Philosophia Sacra_ was first published at London in 1753. De
+Morgan here cites the second edition.
+
+[534] Pike had been dead over forty years when Kittle published this second
+edition. Kittle had already published a couple of works: _King Solomon's
+portraiture of Old Age_ (Edinburgh, 1813), and _Critical and Practical
+Lectures on the Apocalyptical Epistles to the Seven Churches of Asia Minor_
+(London, 1814).
+
+[535] See note 334, on page 152.
+
+[536] William Stukely (1687-1765) was a fellow of the Royal Society and of
+the College of Physicians and Surgeons. He afterwards (1729) entered the
+Church. He was prominent as an antiquary, especially in the study of the
+Roman and Druidic remains of Great Britain. He was the author of numerous
+works, chiefly on paleography.
+
+[537] William Jones (1726-1800), who should not be confused with his
+namesake who is mentioned in note 281 on page 135. He was a lifelong friend
+of Bishop Horne, and his vicarage at Nayland was a meeting place of an
+influential group of High Churchmen. Besides the _Physiological
+Disquisitions_ (1781) he wrote _The Catholic Doctrine of the Trinity_
+(1756) and _The Grand Analogy_ (1793).
+
+[538] Robert Spearman (1703-1761) was a pupil of John Hutchinson, and not
+only edited his works but wrote his life. He wrote a work against the
+Newtonian physics, entitled _An Enquiry after Philosophy and Theology_
+(Edinburgh, 1755), besides the _Letters to a Friend concerning the
+Septuagint Translation_ (Edinburgh, 1759) to which De Morgan refers.
+
+[539] A writer of no importance, at least in the minds of British
+biographers.
+
+[540] Alexander Catcott (1725-1779), a theologian and geologist, wrote not
+only a work on the creation (1756) but a _Treatise on the Deluge_ (1761,
+with a second edition in 1768). Sir Charles Lyell considered the latter
+work a valuable contribution to geology.
+
+[541] James Robertson (1714-1795), professor of Hebrew at the University of
+Edinburgh. Probably De Morgan refers to his _Grammatica Linguae Hebrææ_
+(Edinburgh, 1758; with a second edition in 1783). He also wrote _Clavis
+Pentateuchi_ (1770).
+
+[542] Benjamin Holloway (c. 1691-1759), a geologist and theologian. He
+translated Woodward's _Naturalis Historia Telluris_, and was introduced by
+Woodward to Hutchinson. The work referred to by De Morgan appeared at
+Oxford in two volumes in 1754.
+
+[543] His work was _The Christian plan exhibited in the interpretation of
+Elohim: with observations upon a few other matters relative to the same
+subject_, Oxford, 1752, with a second edition in 1755.
+
+[544] Duncan Forbes (1685-1747) studied Oriental languages and Civil law at
+Leyden. He was Lord President of the Court of Sessions (1737). He wrote a
+number of theological works.
+
+[545] Should be 1756.
+
+[546] Edward Henry Bickersteth (1825-1906), bishop of Exeter (1885-1900);
+published _The Rock of Ages; or scripture testimony to the one Eternal
+Godhead of the Father, and of the Son, and of the Holy Ghost_ at Hampstead
+in 1859. A second edition appeared at London in 1860.
+
+[547] Thomas Sadler (1822-1891) took his Ph.D. at Erlangen in 1844, and
+became a Unitarian minister at Hampstead, where Bickersteth's work was
+published. Besides writing the _Gloria Patri_ (1859), he edited Crabb
+Robinson's Diaries.
+
+[548] This was his _Virgil's Bucolics and the two first Satyrs of Juvenal_,
+1634.
+
+[549] Possibly in his _Twelve Questions or Arguments drawn out of
+Scripture, wherein the commonly received Opinion touching the Deity of the
+Holy Spirit is clearly and fully refuted_, 1647. This was his first
+heretical work, and it was followed by a number of others that were written
+during the intervals in which the Puritan parliament allowed him out of
+prison. It was burned by the hangman as blasphemous. Biddle finally died in
+prison, unrepentant to the last.
+
+[550] The first edition of the anonymous [Greek: Haireseôn anastasis] (by
+Vicars?) appeared in 1805.
+
+[551] Possibly by Thomas Pearne (c. 1753-1827), a fellow of St. Peter's
+College, Cambridge, and a Unitarian minister.
+
+[552] Thomas Wentworth, Earl of Strafford, was borne in London in 1593, and
+was executed there in 1641. He was privy councilor to Charles I, and was
+Lord Deputy of Ireland. On account of his repressive measures to uphold the
+absolute power of the king he was impeached by the Long Parliament and was
+executed for treason. The essence of his defence is in the sentence quoted
+by De Morgan, to which Pym replied that taken as a whole, the acts tended
+to show an intention to change the government, and this was in itself
+treason.
+
+[553] The name assumed by a writer who professed to give a mathematical
+explanation of the Trinity, see farther on.--S. E. De M.
+
+[554] Sabellius (fl. 230 A.D.) was an early Christian of Libyan origin. He
+taught that Father, Son, and Holy Spirit were different names for the same
+person.
+
+[555] Sir Richard Phillips was born in London in 1767 (not 1768 as stated
+above), and died there in 1840. He was a bookseller and printer in
+Leicester, where he also edited a radical newspaper. He went to London to
+live in 1795 and started the _Monthly Magazine_ there in 1796. Besides the
+works mentioned by De Morgan he wrote on law and economics.
+
+[556] It was really eighteen months.
+
+[557] While he was made sheriff in 1807 he was not knighted until the
+following year.
+
+[558] James Mitchell (c. 1786-1844) was a London actuary, or rather a
+Scotch actuary living a good part of his life in London. Besides the work
+mentioned he compiled a _Dictionary of Chemistry, Mineralogy, and Geology_
+(1823), and wrote _On the Plurality of Worlds_ (1813) and _The Elements of
+Astronomy_ (1820).
+
+[559] Richarda Smith, wife of Sir George Biddell Airy (see note 129, page
+85) the astronomer. In 1835 Sir Robert Peel offered a pension of £300 a
+year to Airy, who requested that it be settled on his wife.
+
+[560] Mary Fairfax (1780-1872) married as her second husband Dr. William
+Somerville. In 1826 she presented to the Royal Society a paper on _The
+Magnetic Properties of the Violet Rays of the Solar Spectrum_, which
+attracted much attention. It was for her _Mechanism of the Heavens_ (1831),
+a popular translation of Laplace's _Mécanique Céleste_, that she was
+pensioned.
+
+[561] Dominique François Jean Arago (1786-1853) the celebrated French
+astronomer and physicist.
+
+[562] For there is a well-known series
+
+  1 + 1/2^2 + 1/3^2 + ... = [pi]^2/6.
+
+If, therefore, the given series equals 1, we have
+
+  2 = 1/6 [pi]^2
+
+  or [pi]^2 = 12,
+
+  whence [pi] = 2 [root]3.
+
+But c = [pi]d, and twice the diagonal of a cube on the diameter is 2d
+[root]3.
+
+[563] There was a second edition in 1821.
+
+[564] London, 1830.
+
+[565] He was a resident of Chatham, and seems to have published no other
+works.
+
+[566] Richard Whately (1787-1863) was, as a child, a calculating prodigy
+(see note 132, page 86), but lost the power as is usually the case with
+well-balanced minds. He was a fellow of Oriel College, Oxford, and in 1825
+became principal of St. Alban Hall. He was a friend of Newman, Keble, and
+others who were interested in the religious questions of the day. He became
+archbishop of Dublin in 1831. He was for a long time known to students
+through his _Logic_ (1826) and _Rhetoric_ (1828).
+
+[567] William King, D.C.L. (1663-1712), student at Christ Church, Oxford,
+and celebrated as a wit and scholar. His _Dialogues of the Dead_ (1699) is
+a satirical attack on Bentley.
+
+[568] Thomas Ebrington (1760-1835) was a fellow of Trinity College, Dublin,
+and taught divinity, mathematics, and natural philosophy there. He became
+provost of the college in 1811, bishop of Limerick in 1820, and bishop of
+Leighlin and Ferns in 1822. His edition of Euclid was reprinted a dozen
+times. The _Reply to John Search's Considerations on the Law of Libel_
+appeared at Dublin in 1834.
+
+[569] Joseph Blanco White (1775-1841) was the son of an Irishman living in
+Spain. He was born at Seville and studied for orders there, being ordained
+priest in 1800. He lost his faith in the Roman Catholic Church, and gave up
+the ministry, escaping to England at the time of the French invasion. At
+London he edited _Español_, a patriotic journal extensively circulated in
+Spain, and for this service he was pensioned after the expulsion of the
+French. He then studied at Oriel College, Oxford, and became intimate with
+men like Whately, Newman, and Keble. In 1835 he became a Unitarian. Among
+his theological writings is his _Evidences against Catholicism_ (1825). The
+"rejoinder" to which De Morgan refers consisted of two letters: _The law of
+anti-religious Libel reconsidered_ (Dublin, 1834) and _An Answer to some
+Friendly Remarks on "The Law of Anti-Religious Libel Reconsidered"_
+(Dublin, 1834).
+
+[570] The work was translated from the French.
+
+[571] J. Hoëné Wronski (1778-1853) served, while yet a mere boy, as an
+artillery officer in Kosciusko's army (1791-1794). He was imprisoned after
+the battle of Maciejowice. He afterwards lived in Germany, and (after 1810)
+in Paris. For the bibliography of his works see S. Dickstein's article in
+the _Bibliotheca Mathematica_, vol. VI (2), page 48.
+
+[572] Perhaps referring to his _Introduction à la philosophie des
+mathématiques_ (1811).
+
+[573] Read "equation of the."
+
+[574] Thomas Young (1773-1829), physician and physicist, sometimes called
+the founder of physiological optics. He seems to have initiated the theory
+of color blindness that was later developed by Helmholtz. The attack
+referred to was because of his connection with the Board of Longitude, he
+having been made (1818) superintendent of the Nautical Almanac and
+secretary of the Board. He opposed introducing into the Nautical Almanac
+anything not immediately useful to navigation, and this antagonized many
+scientists.
+
+[575] Isaac Milner (1750-1820) was professor of natural philosophy at
+Cambridge (1783) and later became, as De Morgan states, president of
+Queens' College (1788). In 1791 he became dean of Carlisle, and in 1798
+Lucasian professor of mathematics. His chief interest was in chemistry and
+physics, but he contributed nothing of importance to these sciences or to
+mathematics.
+
+[576] Thomas Perronet Thompson (1783-1869), fellow of Queens' College,
+Cambridge, saw service in Spain and India, but after 1822 lived in England.
+He became major general in 1854, and general in 1868. Besides some works on
+economics and politics he wrote a _Geometry without Axioms_ (1830) that De
+Morgan includes later on in his _Budget_. In it Thompson endeavored to
+prove the parallel postulate.
+
+[577] De Morgan's father-in-law. See note 441, page 196.
+
+[578] Johann Friedrich Herbart (1776-1841), successor of Kant as professor
+of philosophy at Königsberg (1809-1833), where he established a school of
+pedagogy. From 1833 until his death he was professor of philosophy at
+Göttingen. The title of the pamphlet is: _De Attentionis mensura causisque
+primariis. Psychologiae principia statica et mechanica exemplo
+illustraturus.... Regiomonti,... 1822_. The formulas in question are given
+on pages 15 and 17, and De Morgan has omitted the preliminary steps, which
+are, for the first one:
+
+  [beta] ([phi] - z) [delta]t = [delta]z
+
+  unde [beta]t= Const / ([phi] - z).
+
+  Pro t = 0 etiam z = 0; hinc [beta]t = log [phi]/([phi] - z).
+
+  z = [phi] (1 - [epsilon]^{-[beta]t});
+
+  et   [delta]z/[delta]t = [beta][phi][epsilon]^{-[beta]t}
+
+These are, however, quite elementary as compared with other portions of the
+theory.
+
+[579] See note 371, page 168.
+
+[580] William Law (1686-1761) was a clergyman, a fellow of Emanuel College,
+Cambridge, and in later life a convert to Behmen's philosophy. He was so
+free in his charities that the village in which he lived became so infested
+by beggars that he was urged by the citizens to leave. He wrote _A serious
+call to a devout and holy life_ (1728).
+
+[581] He was a curate at Cheshunt, and wrote the _Spiritual voice to the
+Christian Church and to the Jews_ (London, 1760), _A second warning to the
+world by the Spirit of Prophecy_ (London, 1760), and _Signs of the Times;
+or a Voice to Babylon_ (London, 1773).
+
+[582] His real name was Thomas Vaughan (1622-1666). He was a fellow of
+Jesus College, Oxford, taking orders, but was deprived of his living on
+account of drunkenness. He became a mystic philosopher and gave attention
+to alchemy. His works had a large circulation, particularly on the
+continent. He wrote _Magia Adamica_ (London, 1650), _Euphrates; or the
+Waters of the East_ (London, 1655), and _The Chymist's key to shut, and to
+open; or the True Doctrine of Corruption and Generation_ (London, 1657).
+
+[583] Emanuel Swedenborg, or Svedberg (1688-1772) the mystic. It is not
+commonly known to mathematicians that he was one of their guild, but he
+wrote on both mathematics and chemistry. Among his works are the
+_Regelkonst eller algebra_ (Upsala, 1718) and the _Methodus nova inveniendi
+longitudines locorum, terra marique, ope lunae_ (Amsterdam, 1721, 1727, and
+1766). After 1747 he devoted his attention to mystic philosophy.
+
+[584] Pierre Simon Laplace (1749-1827), whose _Exposition du système du
+monde_ (1796) and _Traité de mécanique celeste_ (1799) are well known.
+
+[585] See note 117, page 76.
+
+[586] John Dalton (1766-1844), who taught mathematics and physics at New
+College, Manchester (1793-1799) and was the first to state the law of the
+expansion of gases known by his name and that of Gay-Lussac. His _New
+system of Chemical Philosophy_ (Vol. I, pt. i, 1808; pt. ii, 1810; vol. II,
+1827) sets forth his atomic theory.
+
+[587] Howison was a poet and philosopher. He lived in Edinburgh and was a
+friend of Sir Walter Scott. This work appeared in 1822.
+
+[588] He was a shoemaker, born about 1765 at Haddiscoe, and his
+"astro-historical" lectures at Norwich attracted a good deal of attention
+at one time. He traced all geologic changes to differences in the
+inclination of the earth's axis to the plane of its orbit. Of the works
+mentioned by De Morgan the first appeared at Norwich in 1822-1823, and
+there was a second edition in 1824. The second appeared in 1824-1825. The
+fourth was _Urania's Key to the Revelation; or the analyzation of the
+writings of the Jews..._, and was first published at Norwich in 1823, there
+being a second edition at London in 1833. His books were evidently not a
+financial success, for Mackey died in an almshouse at Norwich.
+
+[589] Godfrey Higgins (1773-1833), the archeologist, was interested in the
+history of religious beliefs and in practical sociology. He wrote _Horae
+Sabbaticae_ (1826), _The Celtic Druids_ (1827 and 1829), and _Anacalypsis,
+an attempt to draw aside the veil of the Saitic Isis; or an Inquiry into
+the Origin of Languages, Nations, and Religions_ (posthumously published,
+1836), and other works. See also page 274, _infra_.
+
+[590] The work also appeared in French. Wirgman wrote, or at least began,
+two other works: _Divarication of the New Testament into Doctrine and
+History; part I, The Four Gospels_ (London, 1830), and _Mental Philosophy;
+part I, Grammar of the five senses; being the first step to infant
+education_ (London, 1838).
+
+[591] He was born at Shandrum, County Limerick, and supported himself by
+teaching writing and arithmetic. He died in an almshouse at Cork.
+
+[592] George Boole (1815-1864), professor of mathematics at Queens'
+College, Cork. His _Laws of Thought_ (1854) was the first work on the
+algebra of logic.
+
+[593] Oratio Grassi (1582-1654), the Jesuit who became famous for his
+controversy with Galileo over the theory of comets. Galileo ridiculed him
+in _Il Saggiatore_, although according to the modern view Grassi was the
+more nearly right. It is said that the latter's resentment led to the
+persecution of Galileo.
+
+[594] De Morgan might have found much else for his satire in the letters of
+Walsh. He sought, in his _Theory of Partial Functions_, to substitute
+"partial equations" for the differential calculus. In his diary there is an
+entry: "Discovered the general solution of numerical equations of the fifth
+degree at 114 Evergreen Street, at the Cross of Evergreen, Cork, at nine
+o'clock in the forenoon of July 7th, 1844; exactly twenty-two years after
+the invention of the Geometry of Partial Equations, and the expulsion of
+the differential calculus from Mathematical Science."
+
+[595] "It has been ordered, sir, it has been ordered."
+
+[596] Bartholomew Prescot was a Liverpool accountant. De Morgan gives this
+correct spelling on page 278. He died after 1849. His _Inverted Scheme of
+Copernicus_ appeared in Liverpool in 1822.
+
+[597] Robert Taylor (1784-1844) had many more ups and downs than De Morgan
+mentions. He was a priest of the Church of England, but resigned his parish
+in 1818 after preaching against Christianity. He soon recanted and took
+another parish, but was dismissed by the Bishop almost immediately on the
+ground of heresy. As stated in the text, he was convicted of blasphemy in
+1827 and was sentenced to a year's imprisonment, and again for two years on
+the same charge in 1831. He then married a woman who was rich in money and
+in years, and was thereupon sued for breach of promise by another woman. To
+escape paying the judgment that was rendered against him he fled to Tours
+where he took up surgery.
+
+[598] Herbert Marsh, Bishop of Peterborough. See note 449 on page 199.
+
+[599] "Argument from the prison."
+
+[600] Richard Carlile (1790-1843), one of the leading radicals of his time.
+He published Hone's parodies (see note 250, page 124) after they had been
+suppressed, and an edition of Thomas Paine (1818). He was repeatedly
+imprisoned, serving nine years in all. His continued conflict with the
+authorities proved a good advertisement for his bookshop.
+
+[601] Wilhelm Ludwig Christmann (1780-1835) was a protestant clergyman and
+teacher of mathematics. For a while he taught under Pestalozzi.
+Disappointed in his ambition to be professor of mathematics at Tubingen, he
+became a confirmed misanthrope and is said never to have left his house
+during the last ten years of his life. He wrote several works: _Ein Wort
+über Pestalozzi und Pestalozzismus_ (1812); _Ars cossae promota_ (1814);
+_Philosophia cossica_ (1815); _Aetas argentea cossae_ (1819); _Ueber
+Tradition und Schrift, Logos und Kabbala_ (1829), besides the one mentioned
+above. The word _coss_ in the above titles was a German name for algebra,
+from the Italian _cosa_ (thing), the name for the unknown quantity. It
+appears in English in the early name for algebra, "the cossic art."
+
+[602] See note 174, page 101.
+
+[603] See note 589, page 257.
+
+[604] He seems to have written nothing else.
+
+[605] See note 596 on page 270. The name is here spelled correctly.
+
+[606] Joseph Jacotot (1770-1840), the father of this Fortuné Jacotot, was
+an infant prodigy. At nineteen he was made professor of the humanities at
+Dijon. He served in the army, and then became professor of mathematics at
+Dijon. He continued in his chair until the restoration of the Bourbons, and
+then fled to Louvain. It was here that he developed the method with which
+his name is usually connected. He wrote a _Mathématiques_ in 1827, which
+went through four editions. The _Epitomé_ is by his son, Fortuné.
+
+[607] He wrote on educational topics and a _Sacred History_ that went
+through several editions.
+
+[608] "All is in all."
+
+[609] "Know one thing and refer everything else to it," as it is often
+translated.
+
+[610] A writer of no reputation.
+
+[611] Sir John Lubbock (1803-1865), banker, scientist, publicist,
+astronomer, one of the versatile men of his time.
+
+[612] See note 165, page 99.
+
+[613] "Those about to die salute you."
+
+[614] Georges Louis Leclerc Buffon (1707-1788), the well-known biologist.
+He also experimented with burning mirrors, his results appearing in his
+_Invention des miroirs ardens pour brûler à une grande distance_ (1747).
+The reference here may be to his _Resolution des problèmes qui regardent le
+jeu du franc carreau_ (1733). The prominence of his _Histoire naturelle_
+(36 volumes, 1749-1788) has overshadowed the credit due to him for his
+translation of Newton's work on Fluxions.
+
+[615] See page 285. This article was a supplement to No. 14 in the
+_Athenæum_ Budget.--A. De M.
+
+[616] There are many similar series and products. Among the more
+interesting are the following:
+
+  [pi]   2·2·4·4·6·6·8...
+  ---- = ----------------,
+    2    1·3·3·5·5·7·7...
+
+  [pi]-3  =   1       1       1
+  ------  = ----- - ----- + ----- - ...,
+    4       2·3·4   4·5·6   6·7·8
+
+  [pi]        1         1      1       1       1
+  ---- = sqrt - · (1 - --- + ----- - ----- + ----- - ...),
+    6         3        3·3   3^2·5   3^3·7   3^4·9
+
+  [pi]       1     1       1       1
+  ---- = 4 ( - - ----- + ----- - ----- + ...)
+   4         5   3·5^3   5·5^5   7·5^7
+
+              1       1         1
+         - ( --- - ------- + ------- - ...).
+             239   3·239^3   5·239^5
+
+[617] "To a privateer, a privateer and a half."
+
+[618] Joshua Milne (1776-1851) was actuary of the Sun Life Assurance
+Society. He wrote _A Treatise on the Valuation of Annuities and Assurances
+on Lives and Survivorships; on the Construction of tables of mortality; and
+on the Probabilities and Expectations of Life_, London, 1815. Upon the
+basis of the Carlisle bills of mortality of Dr. Heysham he reconstructed
+the mortality tables then in use and which were based upon the Northampton
+table of Dr. Price. His work revolutionized the actuarial science of the
+time. In later years he devoted his attention to natural history.
+
+[619] See note 576, page 252. He also wrote the _Theory of Parallels. The
+proof of Euclid's axiom looked for in the properties of the equiangular
+spiral_ (London, 1840), which went through four editions, and the _Theory
+of Parallels. The proof that the three angles of a triangle are equal to
+two right angles looked for in the inflation of the sphere_ (London, 1853),
+of which there were three editions.
+
+[620] For the latest summary, see W. B. Frankland, _Theories of
+Parallelism, an historical critique_, Cambridge, 1910.
+
+[621] Joseph Louis Lagrange (1736-1813), author of the _Mécanique
+analytique_ (1788), _Théorie des functions analytiques_ (1797), _Traité de
+la résolution des équations numériques de tous degrés_ (1798), _Leçons sur
+le calcul des fonctions_ (1806), and many memoirs. Although born in Turin
+and spending twenty of his best years in Germany, he is commonly looked
+upon as the great leader of French mathematicians. The last twenty-seven
+years of his life were spent in Paris, and his remarkable productivity
+continued to the time of his death. His genius in the theory of numbers was
+probably never excelled except by Fermat. He received very high honors at
+the hands of Napoleon and was on the first staff of the Ecole polytechnique
+(1797).
+
+[622] "I shall have to think it over again."
+
+[623] Henry Goulburn (1784-1856) held various government posts. He was
+under-secretary for war and the colonies (1813), commissioner to negotiate
+peace with America (1814), chief secretary to the Lord Lieutenant of
+Ireland (1821), and several times Chancellor of the Exchequer. On the
+occasion mentioned by De Morgan he was standing for parliament, and was
+successful.
+
+[624] On Drinkwater Bethune see note 165, page 99.
+
+[625] Charles Henry Cooper (1808-1866) was a biographer and antiquary. He
+was town clerk of Cambridge (1849-1866) and wrote the _Annals of Cambridge_
+(1842-1853). His _Memorials of Cambridge_ (1874) appeared after his death.
+Thompson Cooper was his son, and the two collaborated in the _Athenae
+Cantabrigiensis_ (1858).
+
+[626] William Yates Peel (1789-1858) was a brother of Sir Robert Peel, he
+whose name degenerated into the familiar title of the London "Bobby" or
+"Peeler." Yates Peel was a member of parliament almost continuously from
+1817 to 1852. He represented Cambridge at Westminster from 1831 to 1835.
+
+[627] Henry John Temple, third Viscount of Palmerston (1784-1865), was
+member for Cambridge in 1811, 1818, 1820, 1826 (defeating Goulburn), and
+1830. He failed of reelection in 1831 because of his advocacy of reform.
+This must have been the time when Goulburn defeated him. He was Foreign
+Secretary (1827) and Secretary of State for Foreign Affairs (1830-1841, and
+1846-1851). It is said of him that he "created Belgium, saved Portugal and
+Spain from absolutism, rescued Turkey from Russia and the highway to India
+from France." He was Prime Minister almost continuously from 1855 to 1865,
+a period covering the Indian Mutiny and the American Civil War.
+
+[628] William Cavendish, seventh Duke of Devonshire (1808-1891). He was
+member for Cambridge from 1829 to 1831, but was defeated in 1831 because he
+had favored parliamentary reform. He became Earl of Burlington in 1834, and
+Duke of Devonshire in 1858. He was much interested in the promotion of
+railroads and in the iron and steel industries.
+
+[629] Richard Sheepshanks (1794-1855) was a brother of John Sheepshanks the
+benefactor of art. (See note 314, p. 147.) He was a fellow of Trinity
+College, Cambridge, a fellow of the Royal Society and secretary of the
+Astronomical Society. Babbage (See note 469, p. 207) suspected him of
+advising against the government support of his calculating machine and
+attacked him severely in his _Exposition of 1851_, in the chapter on _The
+Intrigues of Science_. Babbage also showed that Sheepshanks got an
+astronomical instrument of French make through the custom house by having
+Troughton's (See note 332, page 152) name engraved on it. Sheepshanks
+admitted this second charge, but wrote a _Letter in Reply to the Calumnies
+of Mr. Babbage_, which was published in 1854. He had a highly controversial
+nature.
+
+[630] See note 469, page 207. The work referred to is _Passages from the
+Life of a Philosopher_, London, 1864.
+
+[631] Drinkwater Bethune. See note 165, page 99.
+
+[632] Siméon-Denis Poisson (1781-1840) was professor of calculus and
+mechanics at the Ecole polytechnique. He was made a baron by Napoleon, and
+was raised to the peerage in 1837. His chief works are the _Traité de
+mécanìque_ (1811) and the _Traité mathématique de la chaleur_ (1835).
+
+[633] "As to M. Poisson, I really wish I had a thousandth part of his
+mathematical knowledge that I might prove my system to the incredulous."
+
+[634] This list includes most of the works of Antoine-Louis-Guénard
+Demonville. There was also the _Nouveau système du monde ... et hypothèses
+conformes aux expériences sur les vents, sur la lumière et sur le fluide
+électro-magnétique_, Paris, 1830.
+
+[635] Paris, 1835.
+
+[636] Paris, 1833.
+
+[637] The second part appeared in 1837. There were also editions in 1850
+and 1852, and one edition appeared without date.
+
+[638] Paris, 1842.
+
+[639] Parsey also wrote _The Art of Miniature Painting on Ivory_ (1831),
+_Perspective Rectified_ (1836), and _The Science of Vision_ (1840), the
+third being a revision of the second.
+
+[640] William Ritchie (1790-1837) was a physicist who had studied at Paris
+under Biot and Gay-Lussac. He contributed several papers on electricity,
+heat, and elasticity, and was looked upon as a good experimenter. Besides
+the geometry he wrote the _Principles of the Differential and Integral
+Calculus_ (1836).
+
+[641] Alfred Day (1810-1849) was a man who was about fifty years ahead of
+his time in his attempt to get at the logical foundations of geometry. It
+is true that he laid himself open to criticism, but his work was by no
+means bad. He also wrote _A Treatise on Harmony_ (1849, second edition
+1885), _The Rotation of the Pendulum_ (1851), and several works on Greek
+and Latin Grammar.
+
+[642] Walter Forman wrote a number of controversial tracts. His first seems
+to have been _A plan for improving the Revenue without adding to the
+burdens of the people_, a letter to Canning in 1813. He also wrote _A New
+Theory of the Tides_ (1822). His _Letter to Lord John Russell, on Lord
+Brougham's most extraordinary conduct; and another to Sir J. Herschel, on
+the application of Kepler's third law_ appeared in 1832.
+
+[643] Lord John Russell (1792-1878) first Earl Russell, was one of the
+strongest supporters of the reform measures of the early Victorian period.
+He became prime minister in 1847, and again in 1865.
+
+[644] Lauder seems never to have written anything else.
+
+[645] See note 22, page 40.
+
+[646] The names of Alphonso Cano de Molina, Yvon, and Robert Sara have no
+standing in the history of the subject beyond what would be inferred from
+De Morgan's remark.
+
+[647] Claude Mydorge (1585-1647), an intimate friend of Descartes, was a
+dilletante in mathematics who read much but accomplished little. His
+_Récréations mathématiques_ is his chief work. Boncompagni published the
+"Problèmes de Mydorge" in his _Bulletino_.
+
+[648] Claude Hardy was born towards the end of the 16th century and died at
+Paris in 1678. In 1625 he edited the _Data Euclidis_, publishing the Greek
+text with a Latin translation. He was a friend of Mydorge and Descartes,
+but an opponent of Fermat.
+
+[649] That is, in the _Bibliotheca Realis_ of Martin Lipen, or Lipenius
+(1630-1692), which appeared in six folio volumes, at Frankfort, 1675-1685.
+
+[650] See note 29, page 43.
+
+[651] Baldassare Boncompagni (1821-1894) was the greatest general collector
+of mathematical works that ever lived, possibly excepting Libri. His
+magnificent library was dispersed at his death. His _Bulletino_ (1868-1887)
+is one of the greatest source books on the history of mathematics that we
+have. He also edited the works of Leonardo of Pisa.
+
+[652] He seems to have attracted no attention since De Morgan's search, for
+he is not mentioned in recent bibliographies.
+
+[653] Joseph-Louis Vincens de Mouléon de Causans was born about the
+beginning of the l8th century. He was a Knight of Malta, colonel in the
+infantry, prince of Conti, and governor of the principality of Orange. His
+works on geometry are the _Prospectus apologétique pour la quadrature du
+cercle_ (1753), and _La vraie géométrie transcendante_ (1754).
+
+[654] See note 119, page 80.
+
+[655] See note 120, page 81.
+
+[656] Lieut. William Samuel Stratford (1791-1853), was in active service
+during the Napoleonic wars but retired from the army in 1815. He was first
+secretary of the Astronomical Society (1820) and became superintendent of
+the Nautical Almanac in 1831. With Francis Baily he compiled a star
+catalogue, and wrote on Halley's (1835-1836) and Encke's (1838) comets.
+
+[657] See Sir J. Herschel's _Astronomy_, p. 369.--A. De M.
+
+[658] Captain Ross had just stuck a bit of brass there.--A. De M.
+
+Sir James Clark Ross (1800-1862) was a rear admiral in the British navy and
+an arctic and antarctic explorer of prominence. De Morgan's reference is to
+Ross's discovery of the magnetic pole on June 1, 1831. In 1838 he was
+employed by the Admiralty on a magnetic survey of the United Kingdom. He
+was awarded the gold medal of the geographical societies of London and
+Paris in 1842.
+
+[659] John Partridge (1644-1715), the well-known astrologer and almanac
+maker. Although bound to a shoemaker in his early boyhood, he had acquired
+enough Latin at the age of eighteen to read the works of the astrologers.
+He then mastered Greek and Hebrew and studied medicine. In 1680 he began
+the publication of his almanac, the _Merlinus Liberatus_, a book that
+acquired literary celebrity largely through the witty comments upon it by
+such writers as Swift and Steele.
+
+[660] See note 642 on page 296.
+
+[661] William Woodley also published several almanacs (1838, 1839, 1840)
+after his rejection by the Astronomical Society in 1834.
+
+[662] It appeared at London.
+
+[663] The first edition appeared in 1830, also at London.
+
+[664] See note 441, page 196.
+
+[665] Thomas Kerigan wrote _The Young Navigator's Guide to the siderial and
+planetary parts of Nautical Astronomy_ (London, 1821, second edition 1828),
+a work on eclipses (London, 1844), and the work on tides (London, 1847) to
+which De Morgan refers.
+
+[666] Jean Sylvain Bailly, who was guillotined. See note 365, page 166.
+
+[667] See note 670, page 309.
+
+[668] Laurent seems to have had faint glimpses of the modern theory of
+matter. He is, however, unknown.
+
+[669] See note 133, page 87.
+
+[670] Francis Baily (1774-1844) was a London stockbroker. His interest in
+science in general and in astronomy in particular led to his membership in
+the Royal Society and to his presidency of the Astronomical Society. He
+wrote on interest and annuities (1808), but his chief works were on
+astronomy.
+
+[671] If the story is correctly told Baily must have enjoyed his statement
+that Gauss was "the oldest mathematician now living." As a matter of fact
+he was then only 58, three years the junior of Baily himself. Gauss was
+born in 1777 and died in 1855, and Baily was quite right in saying that he
+was "generally thought to be the greatest" mathematician then living.
+
+[672] Margaret Cooke, who married Flamsteed in 1692.
+
+[673] John Brinkley (1763-1835), senior wrangler, first Smith's prize-man
+(1788), Andrews professor of astronomy at Dublin, first Astronomer Royal
+for Ireland (1792), F.R.S. (1803), Copley medallist, president of the Royal
+Society and Bishop of Cloyne. His _Elements of Astronomy_ appeared in 1808.
+
+[674] See note 248, page 124.
+
+[675] See note 276, page 133.
+
+[676] See note 352, page 161.
+
+[677] "It becomes the doctors of the Sorbonne to dispute, the Pope to
+decree, and the mathematician to go to Paradise on a perpendicular line."
+
+[678] See note 124, page 83.
+
+[679] See note 621, page 288.
+
+[680] Sylvain van de Weyer, who was born at Louvain in 1802. He was a
+jurist and statesman, holding the portfolio for foreign affairs
+(1831-1833), and being at one time ambassador to England.
+
+[681] Henry Crabb Robinson (1775-1867), correspondent of the _Times_ at
+Altona and in the Peninsula, and later foreign editor. He was one of the
+founders of the Athenæum Club and of University College, London. He seems
+to have known pretty much every one of his day, and his posthumous _Diary_
+attracted attention when it appeared.
+
+[682] Was this Whewell, who was at Trinity from 1812 to 1816 and became a
+fellow in 1817?
+
+[683] Tom Cribb (1781-1848) the champion pugilist. He had worked as a coal
+porter and hence received his nickname, the Black Diamond.
+
+[684] John Finleyson, or Finlayson, was born in Scotland in 1770 and died
+in London in 1854. He published a number of pamphlets that made a pretense
+to being scientific. Among his striking phrases and sentences are the
+statements that the stars were made "to amuse us in observing them"; that
+the earth is "not shaped like a garden turnip as the Newtonians make it,"
+and that the stars are "oval-shaped immense masses of frozen water." The
+first edition of the work here mentioned appeared at London in 1830.
+
+[685] Richard Brothers (1757-1824) was a native of Newfoundland. He went to
+London when he was about 30, and a little later set forth his claim to
+being a descendant of David, prince of the Hebrews, and ruler of the world.
+He was confined as a criminal lunatic in 1795 but was released in 1806.
+
+[686] Charles Grey (1764-1845), second Earl Grey, Viscount Howick, was then
+Prime Minister. The Reform Bill was introduced and defeated in 1831. The
+following year, with the Royal guarantees to allow him to create peers, he
+finally carried the bill in spite of "the number of the beast."
+
+[687] The letters of obscure men, the _Epistolæ obscurorum virorum ad
+venerabilem virum Magistrum Ortuinum Gratium Dauentriensem_, by Joannes
+Crotus, Ulrich von Hutten, and others appeared at Venice about 1516.
+
+[688] The lamentations of obscure men, the _Lamentationes obscurorum
+virorum, non prohibete per sedem Apostolicam. Epistola D. Erasmi
+Roterodami: quid de obscuris sentiat_, by G. Ortwinus, appeared at Cologne
+in 1518.
+
+[689] The criticism was timely when De Morgan wrote it. At present it would
+have but little force with respect to the better class of algebras.
+
+[690] Thomas Ignatius Maria Forster (1789-1860) was more of a man than one
+would infer from this satire upon his theory. He was a naturalist,
+astronomer, and physiologist. In 1812 he published his _Researches about
+Atmospheric Phenomena_, and seven years later (July 3, 1819) he discovered
+a comet. With Sir Richard Phillips he founded a Meteorological Society, but
+it was short lived. He declined a fellowship in the Royal Society because
+he disapproved of certain of its rules, so that he had a recognized
+standing in his day. The work mentioned by De Morgan is the second edition,
+the first having appeared at Frankfort on the Main in 1835 under the title,
+_Recueil des ouvrages et des pensées d'un physicien et metaphysicien_.
+
+[691] Zadkiel, whose real name was Richard James Morrison (1795-1874), was
+in his early years an officer in the navy. In 1831 he began the publication
+of the _Herald of Astrology_, which was continued as _Zadkiel's Almanac_.
+His name became familiar throughout Great Britain as a result.
+
+[692] See note 566, page 246.
+
+[693] Sumner (1780-1862) was an Eton boy. He went to King's College,
+Cambridge, and was elected fellow in 1801. He took many honors, and in 1807
+became M.A. He was successively Canon of Durham (1820), Bishop of Chester
+(1828), and Archbishop of Canterbury (1848). Although he voted for the
+Catholic Relief Bill (1829) and the Reform Bill (1832), he opposed the
+removal of Jewish disabilities.
+
+[694] Charles Richard Sumner (1790-1874) was not only Bishop of Winchester
+(1827), but also Bishop of Llandaff and Dean of St. Paul's, London (1826).
+He lost the king's favor by voting for the Catholic Relief Bill.
+
+[695] John Bird Sumner, brother of Charles Richard.
+
+[696] Thomas Musgrave (1788-1860) became Fellow of Trinity in 1812, and
+senior proctor in 1831. He was also Dean of Bristol.
+
+[697] Charles Thomas Longley (1794-1868) was educated at Westminster School
+and at Christ Church, Oxford. He became M.A. in 1818 and D.D. in 1829.
+Besides the bishoprics mentioned he was Bishop of Ripon (1836-1856), and
+before that was headmaster of Harrow (1829-1836).
+
+[698] Thomson (1819-1890) was scholar and fellow of Queen's College,
+Oxford. He became chaplain to the Queen in 1859.
+
+[699] This is worthy of the statistical psychologists of the present day.
+
+[700] The famous Moon Hoax was written by Richard Adams Locke, who was born
+in New York in 1800 and died in Staten Island in 1871. He was at one time
+editor of the _Sun_, and the Hoax appeared in that journal in 1835. It was
+reprinted in London (1836) and Germany, and was accepted seriously by most
+readers. It was published in book form in New York in 1852 under the title
+_The Moon Hoax_. Locke also wrote another hoax, the _Lost Manuscript of
+Mungo Park_, but it attracted relatively little attention.
+
+[701] It is true that Jean-Nicolas Nicollet (1756-1843) was at that time in
+the United States, but there does not seem to be any very tangible evidence
+to connect him with the story. He was secretary and librarian of the Paris
+observatory (1817), member of the Bureau of Longitudes (1822), and teacher
+of mathematics in the Lycée Louis-le-Grand. Having lost his money through
+speculations he left France for the United States in 1831 and became
+connected with the government survey of the Mississippi Valley.
+
+[702] This was Alexis Bouvard (1767-1843), who made most of the
+computations for Laplace's _Mécanique céleste_ (1793). He discovered eight
+new comets and calculated their orbits. In his tables of Uranus (1821) he
+attributed certain perturbations to the presence of an undiscovered planet,
+but unlike Leverrier and Adams he did not follow up this clue and thus
+discover Neptune.
+
+[703] Patrick Murphy (1782-1847) awoke to find himself famous because of
+his natural guess that there would be very cold weather on January 20,
+although that is generally the season of lowest temperature. It turned out
+that his forecasts were partly right on 168 days and very wrong on 197
+days.
+
+[704] He seems to have written nothing else. If one wishes to enter into
+the subject of the mathematics of the Great Pyramid there is an extensive
+literature awaiting him. Richard William Howard Vyse (1784-1853) published
+in 1840 his _Operations carried on at the Pyramids of Gizeh in 1837_, and
+in this he made a beginning of a scientific metrical study of the subject.
+Charles Piazzi Smyth (1819-1900), astronomer Royal for Scotland (1845-1888)
+was much carried away with the number mysticism of the Great Pyramid, so
+much so that he published in 1864 a work entitled _Our Inheritance in the
+Great Pyramid_, in which his vagaries were set forth. Although he was then
+a Fellow of the Royal Society (1857), his work was so ill received that
+when he offered a paper on the subject it was rejected (1874) and he
+resigned in consequence of this action. The latest and perhaps the most
+scholarly of all investigators of the subject is William Matthew Flinders
+Petrie (born in 1853), Edwards professor of Egyptology at University
+College, London, whose _Pyramids and Temples of Gizeh_ (1883) and
+subsequent works are justly esteemed as authorities.
+
+[705] As De Morgan subsequently found, this name reversed becomes Oliver
+B...e, for Oliver Byrne, one of the odd characters among the minor
+mathematical writers of the middle of the last century. One of his most
+curious works is _The first six Books of the Elements of Euclid; in which
+coloured diagrams and symbols are used instead of letters_ (1847). There is
+some merit in speaking of the red triangle instead of the triangle ABC, but
+not enough to give the method any standing. His _Dual Arithmetic_
+(1863-1867) was also a curious work.
+
+[706] Brenan also wrote on English composition (1829), a work that went
+through fourteen editions by 1865; a work entitled _The Foreigner's English
+Conjugator_ (1831), and a work on the national debt.
+
+[707] See note 211, page 112.
+
+[708] See note 592, page 261.
+
+[709] Sir William Rowan Hamilton (1805-1865), the discoverer of quaternions
+(1852), was an infant prodigy, competing with Zerah Colburn as a child. He
+was a linguist of remarkable powers, being able, at thirteen years of age,
+to boast that he knew as many languages as he had lived years. When only
+sixteen he found an error in Laplace's _Mécanique céleste_. When only
+twenty-two he was appointed Andrews professor of astronomy, and he soon
+after became Astronomer Royal of Ireland. He was knighted in 1835. His
+earlier work was on optics, his _Theory of Systems of Rays_ appearing in
+1823. In 1827 he published a paper on the principle of _Varying Action_. He
+also wrote on dynamics.
+
+[710] "Let him not leave the kingdom,"--a legal phrase.
+
+[711] Probably De Morgan is referring to Johann Bernoulli III (1744-1807),
+who edited Lambert's _Logische und philosophische Abhandlungen_, Berlin,
+1782. He was astronomer of the Academy of Sciences at Berlin.
+
+[712] Jacob Bernoulli (1654-1705) was one of the two brothers who founded
+the famous Bernoulli family of mathematicians, the other being Johann I.
+His _Ars conjectandi_ (1713), published posthumously, was the first
+distinct treatise on probabilities.
+
+[713] Johann Heinrich Lambert (1728-1777) was one of the most learned men
+of his time. Although interested chiefly in mathematics, he wrote also on
+science, logic, and philosophy.
+
+[714] Joseph Diez Gergonne (1771-1859), a soldier under Napoleon, and
+founder of the _Annales de mathématiques_ (1810).
+
+[715] Gottfried Ploucquet (1716-1790) was at first a clergyman, but
+afterwards became professor of logic at Tübingen.
+
+[716] "In the premises let the middle term be omitted; what remains
+indicates the conclusion."
+
+[717] Probably Sir William Edmond Logan (1789-1875), who became so
+interested in geology as to be placed at the head of the geological survey
+of Canada (1842). The University of Montreal conferred the title LL.D. upon
+him, and Napoleon III gave him the cross of the Legion of Honor.
+
+[718] "So strike that he may think himself to die."
+
+[719] "Witticism or piece of stupidity."
+
+[720] A very truculently unjust assertion: for Sir W. was as great a setter
+up of some as he was a puller down of others. His writings are a congeries
+of praises and blames, both _cruel smart_, as they say in the States. But
+the combined instigation of prose, rhyme, and retort would send Aristides
+himself to Tartarus, if it were not pretty certain that Minos would grant a
+_stet processus_ under the circumstances. The first two verses are
+exaggerations standing on a basis of truth. The fourth verse is quite true:
+Sir W. H. was an Edinburgh Aristotle, with the difference of ancient and
+modern Athens well marked, especially the _perfervidum ingenium
+Scotorum_.--A. De M.
+
+[721] See note 576, p. 252. There was also a _Theory of Parallels_ that
+differed from these, London, 1853, second edition 1856, third edition 1856.
+
+[722] The work was written by Robert Chambers (1802-1871), the Edinburgh
+publisher, a friend of Scott and of many of his contemporaries in the
+literary field. He published the _Vestiges of the Natural History of
+Creation_ in 1844, not 1840.
+
+[723] Everett (1784-1872) was at that time a good Wesleyan, but was
+expelled from the ministry in 1849 for having written _Wesleyan Takings_
+and as under suspicion for having started the _Fly Sheets_ in 1845. In 1857
+he established the United Methodist Free Church.
+
+[724] Smith was a Primitive Methodist preacher. He also wrote an _Earnest
+Address to the Methodists_ (1841) and _The Wealth Question_ (1840?).
+
+[725] He wrote the _Nouveau traité de Balistique_, Paris, 1837.
+
+[726] Joseph Denison, known to fame only through De Morgan. See also page
+353.
+
+[727] The radical (1784?-1858), advocate of the founding of London
+university (1826), of medical reform (1827-1834), and of the repeal of the
+duties on newspapers and corn, and an ardent champion of penny postage.
+
+[728] I. e., Roman Catholic Priest.
+
+[729] Murphy (1806-1843) showed extraordinary powers in mathematics even
+before the age of thirteen. He became a fellow of Caius College, Cambridge,
+in 1829, dean in 1831, and examiner in mathematics in London University in
+1838.
+
+[730] See note 442, page 196.
+
+[731] Sir John Bowring (1792-1872), the linguist, writer, and traveler,
+member of many learned societies and a writer of high reputation in his
+time. His works were not, however, of genuine merit.
+
+[732] Joseph Hume (1777-1855) served as a surgeon with the British army in
+India early in the nineteenth century. He returned to England in 1808 and
+entered parliament as a radical in 1812. He was much interested in all
+reform movements.
+
+[733] Sir Robert Harry Inglis (1786-1855), a strong Tory, known for his
+numerous addresses in the House of Commons rather than for any real
+ability.
+
+[734] Sir Robert Peel (1788-1850) began his parliamentary career in 1809
+and was twice prime minister. He was prominent in most of the great reforms
+of his time.
+
+[735] See note 627, page 290.
+
+[736] John Taylor (1781-1864) was a publisher, and published several
+pamphlets opposed to Peel's currency measures. De Morgan refers to his work
+on the Junius question. This was done early in his career, and resulted in
+_A Discovery of the author of the Letters of Junius_ (1813), and _The
+Identity of Junius with a distinguished living character established_
+(1816), this being Sir Philip Francis.
+
+[737] See note 665, page 308.
+
+[738] See page 348.
+
+[739] See note 348, page 160.
+
+[740] Sir Nicholas Harris Nicolas (1799-1848) was a reformer in various
+lines,--the Record Commission, the Society of Antiquaries, and the British
+Museum,--and his work was not without good results.
+
+[741] See note 98, page 69.
+
+[742] In the _Companion to the Almanac_ for 1845 is a paper by Prof. De
+Morgan, "On the Ecclesiastical Calendar," the statements of which, so far
+as concerns the Gregorian Calendar, are taken direct from the work of
+Clavius, the principal agent in the arrangement of the reformed reckoning.
+This was followed, in the _Companion to the Almanac_ for 1846, by a second
+paper, by the same author, headed "On the Earliest Printed Almanacs," much
+of which is written in direct supplement to the former article.--S. E. De
+Morgan.
+
+[743] It may be necessary to remind some English readers that in Latin and
+its derived European languages, what we call Easter is called the passover
+(_pascha_). The Quartadecimans had the _name_ on their side: a possession
+which often is, in this world, nine points of the law.--A. De M.
+
+[744] Socrates Scholasticus was born at Constantinople c. 379, and died
+after 439. His _Historia Ecclesiastica_ (in Greek) covers the period from
+Constantine the Great to about 439, and includes the Council of Nicæa. The
+work was printed in Paris 1544.
+
+[745] Theodoretus or Theodoritus was born at Antioch and died about 457. He
+was one of the greatest divines of the fifth century, a man of learning,
+piety, and judicial mind, and a champion of freedom of opinion in all
+religious matters.
+
+[746] He died in 417. He was a man of great energy and of high attainments.
+
+[747] He died in 461, having reigned as pope for twenty-one years. It was
+he who induced Attila to spare Rome in 452.
+
+[748] He succeeded Leo as pope in 461, and reigned for seven years.
+
+[749] Victorinus or Victorius Marianus seems to have been born at Limoges.
+He was a mathematician and astronomer, and the cycle mentioned by De Morgan
+is one of 532 years, a combination of the Metonic cycle of 19 years with
+the solar cycle of 28 years. His canon was published at Antwerp in 1633 or
+1634, _De doctrina temporum sive commentarius in Victorii Aquitani et
+aliorum canones paschales_.
+
+[750] He went to Rome about 497, and died there in 540. He wrote his _Liber
+de paschate_ in 525, and it was in this work that the Christian era was
+first used for calendar purposes.
+
+[751] See note 259, page 126.
+
+[752] Johannes de Sacrobosco (Holy wood), or John of Holywood. The name was
+often written, without regard to its etymology, Sacrobusto. He was educated
+at Oxford and taught in Paris until his death (1256). He did much to make
+the Hindu-Arabic numerals known to European scholars.
+
+[753] See note 36, page 44.
+
+[754] See note 45, page 48.
+
+[755] The Julian year is a year of the Julian Calendar, in which there is
+leap year every fourth year. Its average length is therefore 365 days and a
+quarter.--A. De M.
+
+[756] Ugo Buoncompagno (1502-1585) was elected pope in 1572.
+
+[757] He was a Calabrian, and as early as 1552 was professor of medicine at
+Perugia. In 1576 his manuscript on the reform of the calendar was presented
+to the Roman Curia by his brother, Antonius. The manuscript was not printed
+and it has not been preserved.
+
+[758] The title of this work, which is the authority on all points of the
+new Calendar, is _Kalendarium Gregorianum Perpetuum. Cum Privilegio Summi
+Pontificis Et Aliorum Principum. Romæ, Ex Officina Dominici Basæ. MDLXXXII.
+Cum Licentia Superiorum_ (quarto, pp. 60).--A. De M.
+
+[759] _Manuels-Roret. Théorie du Calendrier et collection de tous les
+Calendriers des Années passées et futures_.... Par L. B. Francoeur,...
+Paris, à la librairie encyclopédique de Roret, rue Hautefeuille, 10 bis.
+1842. (12mo.) In this valuable manual, the 35 possible almanacs are given
+at length, with such preliminary tables as will enable any one to find, by
+mere inspection, which almanac he is to choose for any year, whether of old
+or new style. [1866. I may now refer to my own _Book of Almanacs_, for the
+same purpose].--A. De M.
+
+Louis Benjamin Francoeur (1773-1849), after holding positions in the Ecole
+polytechnique (1804) and the Lycée Charlemagne (1805), became professor of
+higher algebra in the University of Paris (1809). His _Cours complet des
+mathématiques pures_ was well received, and he also wrote on mechanics,
+astronomy, and geodesy.
+
+[760] Albertus Pighius, or Albert Pigghe, was born at Kempen c. 1490 and
+died at Utrecht in 1542. He was a mathematician and a firm defender of the
+faith, asserting the supremacy of the Pope and attacking both Luther and
+Calvin. He spent some time in Rome. His greatest work was his _Hierarchiæ
+ecclesiasticæ assertio_ (1538).
+
+[761] This was A. F. Vogel. The work was his translation from the German
+edition which appeared at Leipsic the same year, _Entdeckung einer
+numerischen General-Auflösung aller höheren endlichen Gleichungen von jeder
+beliebigen algebraischen und transcendenten Form_.
+
+[762] The latest edition of Burnside and Panton's _Theory of Equations_ has
+this brief summary of the present status of the problem: "Demonstrations
+have been given by Abel and Wantzel (see Serret's _Cours d'Algèbre
+Supérieure_, Art. 516) of the impossibility of resolving algebraically
+equations unrestricted in form, of a degree higher than the fourth. A
+transcendental solution, however, of the quintic has been given by M.
+Hermite, in a form involving elliptic integrals."
+
+[763] There was a second edition of this work in 1846. The author's
+_Astronomy Simplified_ was published in 1838, and the _Thoughts on Physical
+Astronomy_ in 1840, with a second edition in 1842.
+
+[764] This was _The Science of the Weather, by several authors... edited by
+B._, Glasgow, 1867.
+
+[765] This was Y. Ramachandra, son of Sundara L[=a]la. He was a teacher of
+science in Delhi College, and the work to which De Morgan refers is _A
+Treatise on problems of Maxima and Minima solved by Algebra_, which
+appeared at Calcutta in 1850. De Morgan's edition was published at London
+nine years later.
+
+[766] Abraham de Moivre (1667-1754), French refugee in London, poor,
+studying under difficulties, was a man with tastes in some respects like
+those of De Morgan. For one thing, he was a lover of books, and he had a
+good deal of interest in the theory of probabilities to which De Morgan
+also gave much thought. His introduction of imaginary quantities into
+trigonometry was an event of importance in the history of mathematics, and
+the theorem that bears his name, (cos [phi] + i sin [phi])^{n} = cos n[phi]
++ i sin n[phi], is one of the most important ones in all analysis.
+
+[767] John Dolland (1706-1761), the silk weaver who became the greatest
+maker of optical instruments in his time.
+
+[768] Thomas Simpson (1710-1761), also a weaver, taking his leisure from
+his loom at Spitalfields to teach mathematics. His _New Treatise on
+Fluxions_ (1737) was written only two years after he began working in
+London, and six years later he was appointed professor of mathematics at
+Woolwich. He wrote many works on mathematics and Simpson's Formulas for
+computing trigonometric tables are still given in the text-books.
+
+[769] Nicholas Saunderson (1682-1739), the blind mathematician. He lost his
+eyesight through smallpox when only a year old. At the age of 25 he began
+lecturing at Cambridge on the principles of the Newtonian philosophy. His
+_Algebra_, in two large volumes, was long the standard treatise on the
+subject.
+
+[770] He was not in the class with the others mentioned.
+
+[771] Not known in the literature of mathematics.
+
+[772] Probably J. Butler Williams whose _Practical Geodesy_ appeared in
+1842, with a third edition in 1855.
+
+[773] Benjamin Gompertz (1779-1865) was debarred as a Jew from a university
+education. He studied mathematics privately and became president of the
+Mathematical Society. De Morgan knew him professionally through the fact
+that he was prominent in actuarial work.
+
+[774] Referring to the contributions of Archimedes (287-212 B.C.) to the
+mensuration of the sphere.
+
+[775] The famous Alexandrian astronomer (c. 87-c. 165 A.D.), author of the
+_Almagest_, a treatise founded on the works of Hipparchus.
+
+[776] Dr. Whewell, when I communicated this song to him, started the
+opinion, which I had before him, that this was a very good idea, of which
+too little was made.--A. De M.
+
+[777] See note 117, page 76.
+
+[778] The common epithet of rank: _nobilis Tycho_, as he was a nobleman.
+The writer had been at history.--A. De M.
+
+See note 117, page 76.
+
+[779] He lost it in a duel, with Manderupius Pasbergius. A contemporary,
+T. B. Laurus, insinuates that they fought to settle which was the best
+mathematician! This seems odd, but it must be remembered they fought in the
+dark, "_in tenebris densis_"; and it is a nice problem to shave off a nose
+in the dark, without any other harm.--A. De M.
+
+Was this T. B. Laurus Joannes Baptista Laurus or Giovanni Battista Lauro
+(1581-1621), the poet and writer?
+
+[780] See note 117, page 76.
+
+[781] Referring to Kepler's celebrated law of planetary motion. He had
+previously wasted his time on analogies between the planetary orbits and
+the polyhedrons.--A. De M.
+
+[782] See note 117, page 76.
+
+[783] "It does move though."
+
+[784] As great a lie as ever was told: but in 1800 a compliment to Newton
+without a fling at Descartes would have been held a lopsided structure.--A.
+De M.
+
+[785] Jean-le-Rond D'Alembert (1717-1783), the foundling who was left on
+the steps of Jean-le-Rond in Paris, and who became one of the greatest
+mathematical physicists and astronomers of his century.
+
+[786] Leonhard Euler (1707-1783), friend of the Bernoullis, the greatest of
+Swiss mathematicians, prominent in the theory of numbers, and known for
+discoveries in all lines of mathematics as then studied.
+
+[787] See notes 478, 479, page 219.
+
+[788] See note 621, page 288.
+
+[789] See note 584, page 255.
+
+[790] The _siderial_ day is about four minutes short of the solar; there
+are 366 sidereal days in the year.--A. De M.
+
+[791] The founding of the London Mathematical Society is discussed by Mrs.
+De Morgan in her _Memoir_ (p. 281). The idea came from a conversation
+between her brilliant son, George Campbell De Morgan, and his friend Arthur
+Cowper Ranyard in 1864. The meeting of organization was held on Nov. 7,
+1864, with Professor De Morgan in the chair, and the first regular meeting
+on January 16, 1865.
+
+[792] See note 33, page 43.
+
+[793] See note 119, page 80.
+
+[794] John Russell Hind (b. 1823), the astronomer. Between 1847 and 1854 he
+discovered ten planetoids.
+
+[795] Sir Roderick Impey Murchison (1792-1871), the great geologist. He was
+knighted in 1846 and devoted the latter part of his life to the work of the
+Royal Geographical Society and to the geology of Scotland.
+
+[796] Friedrich Wilhelm Bessel (1784-1846), the astronomer and physicist.
+He was professor of astronomy at Königsberg.
+
+[797] This was the _Reduction of the Observations of Planets made ... from
+1750 to 1830: computed ... under the superintendence of George Biddell
+Airy_ (1848). See note 129, page 85.
+
+[798] The expense of this magnificent work was defrayed by Government
+grants, obtained, at the instance of the British Association, in 1833--A.
+De M.
+
+[799] See note 32, page 43.
+
+[800] Franz Friedrich Ernst Brünnow (1821-1891) was at that time or shortly
+before director of the observatory at Dusseldorf. He then went to Berlin
+and thence (1854) to Ann Arbor, Michigan. He then went to Dublin and
+finally became Royal Astronomer of Ireland.
+
+[801] Johann Gottfried Galle (1812-1910), at that time connected with the
+Berlin observatory, and later professor of astronomy at Breslau.
+
+[802] George Bishop (1785-1861), in whose observatory in Regent's Park
+important observations were made by Dawes, Hind, and Marth.
+
+[803] James Challis (1803-1882), director of the Cambridge observatory, and
+successor of Airy as Plumian professor of astronomy.
+
+[804] On Leverrier and Arago see note 33, page 43, and note 561, page 243.
+
+[805] Robert Grant's (1814-1892) _History of Physical Astronomy from the
+Earliest Ages to the Middle of the Nineteenth Century_ appeared in 1852. He
+was professor of astronomy and director of the observatory at Glasgow.
+
+[806] John Debenham was more interested in religion than in astronomy. He
+wrote _The Strait Gate; or, the true scripture doctrine of salvation
+clearly explained_, London, 1843, and _Tractatus de magis et Bethlehemæ
+stella et Christi in deserto tentatione_, privately printed at London in
+1845.
+
+[807] More properly the Sydney Smirke reading room, since it was built from
+his designs.
+
+[808] The Antinomians were followers of Johannes Agricola (1494-1566). They
+believed that Christians as such were released from all obligations to the
+Old Testament. Some went so far as to assert that, since all Christians
+were sanctified, they could not lose this sanctity even though they
+disobeyed God. The sect was prominent in England in the seventeenth
+century, and was transferred to New England. Here it suffered a check in
+the condemnation of Mrs. Ann Hutchinson (1636) by the Newton Synod.
+
+[809] Aside from this work and his publications on Reeve and Muggleton he
+wrote nothing. With Joseph Frost he published _A list_ _of Books and
+general index to J. Reeve and L. Muggleton's works_ (1846), _Divine Songs
+of the Muggletonians_ (1829), and the work mentioned on page 396. _The
+works of J. Reeve and L. Muggleton_ (1832).
+
+[810] About 1650 he and his cousin John Reeve (1608-1658) began to have
+visions. As part of their creed they taught that astronomy was opposed by
+the Bible. They asserted that the sun moves about the earth, and Reeve
+figured out that heaven was exactly six miles away. Both Muggleton and
+Reeve were imprisoned for their unitarian views. Muggleton wrote a
+_Transcendant Spirituall Treatise_ (1652). I have before me _A true
+Interpretation of All the Chief Texts ... of the whole Book of the
+Revelation of St. John.... By Lodowick Muggleton, one of the two last
+Commissioned Witnesses & Prophets of the onely high, immortal, glorious
+God, Christ Jesus_ (1665), in which the interpretation of the "number of
+the beast" occupies four pages without arriving anywhere.
+
+[811] In 1652 he was, in a vision, named as the Lord's "last messenger,"
+with Muggleton as his "mouth," and died six years later, probably of
+nervous tension resulting from his divine "illumination." He was the more
+spiritual of the two.
+
+[812] William Guthrie (1708-1770) was a historian and political writer. His
+_History of England_ (1744-1751) was the first attempt to base history on
+parliamentary records. He also wrote a _General History of Scotland_ in 10
+volumes (1767). The work to which Frost refers is the _Geographical,
+Historical, and Commercial Grammar_ (1770) which contained an astronomical
+part by J. Ferguson. By 1827 it had passed through 24 editions.
+
+[813] George Fox (1624-1691), founder of the Society of Friends; a mystic
+and a disciple of Boehme. He was eight times imprisoned for heresy.
+
+[814] If they were friends they were literary antagonists, for Muggleton
+wrote against Fox _The Neck of the Quakers Broken_ (1663), and Fox replied
+in 1667. Muggleton also wrote _A Looking Glass for George Fox_.
+
+[815] John Conduitt (1688-1737), who married (1717) Newton's half niece,
+Mrs. Katherine Barton. See note 284, page 136.
+
+[816] Probably Peter Mark Roget's (1779-1869) _Thesaurus of English Words_
+(1852) is not much used at present, but it went through 28 editions in his
+lifetime. Few who use the valuable work are aware that Roget was a
+professor of physiology at the Royal Institution (London), that he achieved
+his title of F. R. S. because of his work in perfecting the slide rule, and
+that he followed Sir John Herschel as secretary of the Royal Society.
+
+[817] See note 703, page 327. This work went into a second edition in the
+year of its first publication.
+
+[818] See note 398, page 177.
+
+[819] See note 528, page 233.
+
+[820] George Jacob Holyoake (1817-1906) entered into a controversial life
+at an early age. In 1841 he was imprisoned for six months for blasphemy. He
+founded and edited _The Reasoner_ (Vols. 1-26, 1846-1861). In his later
+life he did much to promote cooperation among the working class.
+
+[821] See note 176, page 102.
+
+[822] William Thomas Lowndes (1798-1843), whose _Bibliographer's Manual of
+English Literature_, 4 vols., London, 1834 (also 1857-1864, and 1869) is a
+classic in its line.
+
+[823] Jacques Charles Brunet (1780-1867), the author of the great French
+bibliography, the _Manuel du Libraire_ (1810).
+
+       *       *       *       *       *
+
+
+Corrections made to printed original.
+
+Page 5, "direct acquaintance with the whole of his mental ancestry":
+'acquantance' in original.
+
+Page 100, "The error is at the rate": 'it' (for 'is') in original.
+
+Page 192, "the lineal successor of the Repository association":
+'successsor' in original.
+
+Page 211, "the doctors had finished their compliments": 'docters' in
+original.
+
+Page 302, "causing mutual perturbations": 'peturbations' in original.
+
+Page 344, "The work itself is described": 'decribed' in original.
+
+Page 370, The entry for 1852 is printed as 19, it appears that the correct
+value should be 9.
+
+Page 392, "Sir John Herschel's previous communication": 'pervious' in
+original.
+
+Note 317, "he constructed a working model of a steam road carriage":
+'contructed' in original.
+
+Note 380, "the variation of the Earth's Diameters": 'Diaameters' in
+original.
+
+Note 550, "The first edition of the anonymous [Greek]": 'anonynous' in
+original.
+
+
+
+
+
+
+End of the Project Gutenberg EBook of A Budget of Paradoxes, Volume I (of II), by 
+Augustus De Morgan
+
+*** END OF THIS PROJECT GUTENBERG EBOOK A BUDGET OF PARADOXES ***
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+
+The Project Gutenberg EBook of A Budget of Paradoxes, Volume I (of II), by 
+Augustus De Morgan
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: A Budget of Paradoxes, Volume I (of II)
+
+Author: Augustus De Morgan
+
+Editor: David Eugene Smith
+
+Release Date: October 20, 2007 [EBook #23100]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK A BUDGET OF PARADOXES ***
+
+
+
+
+Produced by David Starner, Keith Edkins and the Online
+Distributed Proofreading Team at http://www.pgdp.net
+
+
+
+
+
+
+</pre>
+
+
+<table border="0" cellpadding="10" style="background-color: #ccccff;">
+<tr>
+<td style="width:25%; vertical-align:top">
+Transcriber's note:
+</td>
+<td>
+A few typographical errors have been corrected. They
+appear in the text <span class="correction" title="explanation will pop up">like this</span>, and the
+explanation will appear when the mouse pointer is moved over the marked
+passage.
+</td>
+</tr>
+</table>
+
+<h3>BY AUGUSTUS DE MORGAN</h3>
+
+<h1>A BUDGET OF<br />
+PARADOXES</h1>
+
+<p class="cenhead"><span class="scac">REPRINTED WITH THE AUTHOR'S ADDITIONS FROM THE ATHENAEUM</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">SECOND EDITION EDITED BY DAVID EUGENE SMITH</p>
+
+<p class="cenhead">WITH A NEW INTRODUCTION BY ERNEST NAGEL</p>
+
+<p class="cenhead">PROFESSOR OF PHILOSOPHY, COLUMBIA UNIVERSITY</p>
+
+<p class="cenhead">UNABRIDGED EDITION&mdash;TWO VOLUMES BOUND AS ONE</p>
+
+  <p>&nbsp;</p>
+
+<h1>Volume I</h1>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">DOVER PUBLICATIONS, INC., NEW YORK</p>
+
+<hr class="full" >
+
+<h3>PREFACE TO THE FIRST EDITION.</h3>
+
+<p class="cenhead">(1872)</p>
+
+  <p>It is not without hesitation that I have taken upon myself the
+  editorship of a work left avowedly imperfect by the author, and, from its
+  miscellaneous and discursive character, difficult of completion with due
+  regard to editorial limitations by a less able hand.</p>
+
+  <p>Had the author lived to carry out his purpose he would have looked
+  through his Budget again, amplifying and probably rearranging some of its
+  contents. He had collected materials for further illustration of Paradox
+  of the kind treated of in this book; and he meant to write a second part,
+  in which the contradictions and inconsistencies of orthodox learning
+  would have been subjected to the same scrutiny and castigation as
+  heterodox ignorance had already received.</p>
+
+  <p>It will be seen that the present volume contains more than the
+  <i>Athenæum</i> Budget. Some of the additions formed a Supplement to the
+  original articles. These supplementary paragraphs were, by the author,
+  placed after those to which they respectively referred, being
+  distinguished from the rest of the text by brackets. I have omitted these
+  brackets as useless, except where they were needed to indicate subsequent
+  writing.</p>
+
+  <p>Another and a larger portion of the work consists of discussion of
+  matters of contemporary interest, for the Budget was in some degree a
+  receptacle for the author's thoughts on any literary, scientific, or
+  social question. Having grown thus gradually to its present size, the
+  book as it was left was not quite in a fit condition for publication, but
+  the alterations which have been made are slight and few, being in most
+  cases verbal, and such as the sense absolutely required, or
+  transpositions of sentences to secure coherence with the rest, in places
+  where the author, in his more recent insertion of them, had overlooked
+  the connection in which they stood. In no case has the meaning been in
+  any degree modified or interfered with.</p>
+
+  <p>One rather large omission must be mentioned here. It is an account of
+  the quarrel between Sir James South and Mr. Troughton on the mounting,
+  etc. of the equatorial telescope at Campden Hill. At some future time
+  when the affair has passed entirely out of the memory of living
+  Astronomers, the appreciative sketch, which is omitted in this edition of
+  the Budget, will be an interesting piece of history and study of
+  character.<a name="NtA_1" href="#Nt_1"><sup>[1]</sup></a></p>
+
+  <p>A very small portion of Mr. James Smith's circle-squaring has been
+  left out, with a still smaller portion of Mr. De Morgan's answers to that
+  Cyclometrical Paradoxer.</p>
+
+  <p>In more than one place repetitions, which would have disappeared under
+  the author's revision, have been allowed to remain, because they could
+  not have been taken away without leaving a hiatus, not easy to fill up
+  without damage to the author's meaning.</p>
+
+  <p>I give these explanations in obedience to the rules laid down for the
+  guidance of editors at page <a href="#page15">15</a>.<a name="NtA_2"
+  href="#Nt_2"><sup>[2]</sup></a> If any apology for the fragmentary
+  character of the book be thought necessary, it may be found in the
+  author's own words at page 281 of the second volume.<a name="NtA_3"
+  href="#Nt_3"><sup>[3]</sup></a></p>
+
+  <p>The publication of the Budget could not have been delayed without
+  lessening the interest attaching to the writer's thoughts upon questions
+  of our own day. I trust that, incomplete as the work is compared with
+  what it might have been, I shall not be held mistaken in giving it to the
+  world. Rather let me hope that it will be welcomed as an old friend
+  returning under great disadvantages, but bringing a pleasant remembrance
+  of the amusement which its weekly appearance in the <i>Athenæum</i> gave
+  to both writer and reader.</p>
+
+  <p>The Paradoxes are dealt with in chronological order. This will be a
+  guide to the reader, and with the alphabetical Index of Names, etc.,
+  will, I trust, obviate all difficulty of reference.</p>
+
+  <p class="author"><span class="sc">Sophia De Morgan</span>.
+
+<blockquote class="b1n">
+
+  <p>6 <span class="sc">Merton Road, Primrose Hill</span>.</p>
+
+</blockquote>
+
+<hr class="full" >
+
+<h3>PREFACE TO THE SECOND EDITION.</h3>
+
+  <p>If Mrs. De Morgan felt called upon to confess her hesitation at taking
+  upon herself the labor of editing these Paradoxes, much more should one
+  who was born two generations later, who lives in another land and who was
+  reared amid different influences, confess to the same feeling when
+  undertaking to revise this curious medley. But when we consider the
+  nature of the work, the fact that its present rarity deprives so many
+  readers of the enjoyment of its delicious satire, and the further fact
+  that allusions that were commonplace a half century ago are now
+  forgotten, it is evident that some one should take up the work and
+  perform it <i>con amore</i>.</p>
+
+  <p>Having long been an admirer of De Morgan, having continued his work in
+  the bibliography of early arithmetics, and having worked in his library
+  among the books of which he was so fond, it is possible that the present
+  editor, whatever may be his other shortcomings, may undertake the labor
+  with as much of sympathy as any one who is in a position to perform it.
+  With this thought in mind, two definite rules were laid down at the
+  beginning of the task: (1) That no alteration in the text should be made,
+  save in slightly modernizing spelling and punctuation and in the case of
+  manifest typographical errors; (2) That whenever a note appeared it
+  should show at once its authorship, to the end that the material of the
+  original edition might appear intact.</p>
+
+  <p>In considering, however, the unbroken sequence of items that form the
+  Budget, it seems clear that readers would be greatly aided if the various
+  leading topics were separated in some convenient manner. After
+  considerable thought it was decided to insert brief captions from time to
+  time that might aid the eye in selecting the larger subjects of the text.
+  In some parts of the work these could easily be taken from the original
+  folio heads, but usually they had to be written anew. While, therefore,
+  the present editor accepts the responsibility for the captions of the
+  various subdivisions, he has endeavored to insert them in harmony with
+  the original text.</p>
+
+  <p>As to the footnotes, the first edition had only a few, some due to De
+  Morgan himself and others to Mrs. De Morgan. In the present edition those
+  due to the former are signed A. De M., and those due to Mrs. De Morgan
+  appear with her initials, S.&nbsp;E. De M. For all other footnotes the present
+  editor is responsible. In preparing them the effort has been made to
+  elucidate the text by supplying such information as the casual reader
+  might wish as he passes over the pages. Hundreds of names are referred to
+  in the text that were more or less known in England half a century ago,
+  but are now forgotten there and were never familiar elsewhere. Many books
+  that were then current have now passed out of memory, and much that
+  agitated England in De Morgan's prime seems now like ancient history.
+  Even with respect to well-known names, a little information as to dates
+  and publications will often be welcome, although the editor recognizes
+  that it will quite as often be superfluous. In order, therefore, to
+  derive the pleasure that should come from reading the Budget, the reader
+  should have easy access to the information that the notes are intended to
+  supply. That they furnish too much here and too little there is to be
+  expected. They are a human product, and if they fail to serve their
+  purpose in all respects it is hoped that this failure will not seriously
+  interfere with the reader's pleasure.</p>
+
+  <p>In general the present editor has refrained from expressing any
+  opinions that would strike a discordant note in the reading of the text
+  as De Morgan left it. The temptation is great to add to the discussion at
+  various points, but it is a temptation to be resisted. To furnish such
+  information as shall make the reading more pleasant, rather than to
+  attempt to improve upon one of the most delicious bits of satire of the
+  nineteenth century, has been the editor's wish. It would have been an
+  agreeable task to review the history of circle squaring, of the
+  trisection problem, and of the duplication of the cube. This, however,
+  would be to go too far afield. For the benefit of those who wish to
+  investigate the subject the editor can only refer to such works and
+  articles as the following: F. Rudio, <i>Archimedes, Huygens, Lambert,
+  Legendre,&mdash;mit einer Uebersicht über die Geschichte des Problemes
+  von der Quadratur des Zirkels</i>, Leipsic, 1892; Thomas Muir, "Circle,"
+  in the eleventh edition of the <i>Encyclopædia Britannica</i>; the
+  various histories of mathematics; and to his own article on "The
+  Incommensurability of <span class="grk">&pi;</span>" in Prof. J. W. A.
+  Young's <i>Monographs on Topics of Modern Mathematics</i>, New York,
+  1911.</p>
+
+  <p>The editor wishes to express his appreciation and thanks to Dr. Paul
+  Carus, editor of <i>The Monist</i> and <i>The Open Court</i> for the
+  opportunity of undertaking this work; to James Earl Russell, LL.D., Dean
+  of Teachers College, Columbia University, for his encouragement in its
+  prosecution; to Miss Caroline Eustis Seely for her intelligent and
+  painstaking assistance in securing material for the notes; and to Miss
+  Lydia G. Robinson and Miss Anna A. Kugler for their aid and helpful
+  suggestions in connection with the proof-sheets. Without the generous
+  help of all five this work would have been impossible.</p>
+
+  <p class="author"><span class="sc">David Eugene Smith</span>.
+
+<blockquote class="b1n">
+
+  <p><span class="sc">Teachers College, Columbia University</span>.</p>
+
+</blockquote>
+
+<hr class="full" >
+
+<h2>A BUDGET OF PARADOXES</h2>
+
+<p><!-- Page 1 --><span class="pagenum"><a name="page1"></a>[1]</span></p>
+
+<h3>INTRODUCTORY.</h3>
+
+  <p>If I had before me a fly and an elephant, having never seen more than
+  one such magnitude of either kind; and if the fly were to endeavor to
+  persuade me that he was larger than the elephant, I might by possibility
+  be placed in a difficulty. The apparently little creature might use such
+  arguments about the effect of distance, and might appeal to such laws of
+  sight and hearing as I, if unlearned in those things, might be unable
+  wholly to reject. But if there were a thousand flies, all buzzing, to
+  appearance, about the great creature; and, to a fly, declaring, each one
+  for himself, that he was bigger than the quadruped; and all giving
+  different and frequently contradictory reasons; and each one despising
+  and opposing the reasons of the others&mdash;I should feel quite at my
+  ease. I should certainly say, My little friends, the case of each one of
+  you is destroyed by the rest. I intend to show flies in the swarm, with a
+  few larger animals, for reasons to be given.</p>
+
+  <p>In every age of the world there has been an established system, which
+  has been opposed from time to time by isolated and dissentient reformers.
+  The established system has sometimes fallen, slowly and gradually: it has
+  either been upset by the rising influence of some one man, or it has been
+  sapped by gradual change of opinion in the many.</p>
+
+  <p>I have insisted on the isolated character of the dissentients, as an
+  element of the <i>a priori</i> probabilities of the case. Show me a
+  schism, especially a growing schism, and it is another thing. The
+  homeopathists, for instance, shall be, if any one so think, as wrong as
+  St. John Long; but an <!-- Page 2 --><span class="pagenum"><a
+  name="page2"></a>[2]</span>organized opposition, supported by the efforts
+  of many acting in concert, appealing to common arguments and experience,
+  with perpetual succession and a common seal, as the Queen says in the
+  charter, is, be the merit of the schism what it may, a thing wholly
+  different from the case of the isolated opponent in the mode of
+  opposition to it which reason points out.</p>
+
+  <p>During the last two centuries and a half, physical knowledge has been
+  gradually made to rest upon a basis which it had not before. It has
+  become <i>mathematical</i>. The question now is, not whether this or that
+  hypothesis is better or worse to the pure thought, but whether it accords
+  with observed phenomena in those consequences which can be shown
+  necessarily to follow from it, if it be true. Even in those sciences
+  which are not yet under the dominion of mathematics, and perhaps never
+  will be, a working copy of the mathematical process has been made. This
+  is not known to the followers of those sciences who are not themselves
+  mathematicians and who very often exalt their horns against the
+  mathematics in consequence. They might as well be squaring the circle,
+  for any sense they show in this particular.</p>
+
+  <p>A great many individuals, ever since the rise of the mathematical
+  method, have, each for himself, attacked its direct and indirect
+  consequences. I shall not here stop to point out how the very accuracy of
+  exact science gives better aim than the preceding state of things could
+  give. I shall call each of these persons a <i>paradoxer</i>, and his
+  system a <i>paradox</i>. I use the word in the old sense: a paradox is
+  something which is apart from general opinion, either in subject-matter,
+  method, or conclusion.</p>
+
+  <p>Many of the things brought forward would now be called
+  <i>crotchets</i>, which is the nearest word we have to old
+  <i>paradox</i>. But there is this difference, that by calling a thing a
+  <i>crotchet</i> we mean to speak lightly of it; which was not the
+  necessary sense of <i>paradox</i>. Thus in the sixteenth century many
+  spoke of the earth's motion as the <i>paradox of <!-- Page 3 --><span
+  class="pagenum"><a name="page3"></a>[3]</span>Copernicus</i>, who held
+  the ingenuity of that theory in very high esteem, and some, I think, who
+  even inclined towards it. In the seventeenth century, the depravation of
+  meaning took place, in England at least. Phillips says <i>paradox</i> is
+  "a thing which seemeth strange"&mdash;here is the old meaning: after a
+  colon he proceeds&mdash;"and absurd, and is contrary to common opinion,"
+  which is an addition due to his own time.</p>
+
+  <p>Some of my readers are hardly inclined to think that the word
+  <i>paradox</i> could once have had no disparagement in its meaning; still
+  less that persons could have applied it to themselves. I chance to have
+  met with a case in point against them. It is Spinoza's <i>Philosophia
+  Scripturæ Interpres, Exercitatio Paradoxa</i>, printed anonymously at
+  Eleutheropolis, in 1666. This place was one of several cities in the
+  clouds, to which the cuckoos resorted who were driven away by the other
+  birds; that is, a feigned place of printing, adopted by those who would
+  have caught it if orthodoxy could have caught them. Thus, in 1656, the
+  works of Socinus could only be printed at Irenopolis. The author deserves
+  his self-imposed title, as in the following:<a name="NtA_4"
+  href="#Nt_4"><sup>[4]</sup></a></p>
+
+  <p>"Quanto sane satius fuisset illam [Trinitatem] pro mysterio non
+  habuisse, et Philosophiæ ope, antequam quod esset statuerent, secundum
+  veræ logices præcepta quid esset cum Cl. Kleckermanno investigasse; tanto
+  fervore ac labore in profundissimas speluncas et obscurissimos
+  metaphysicarum speculationum atque fictionum recessus se recipere ut ab
+  adversariorum telis sententiam suam in tuto collocarent. <!-- Page 4
+  --><span class="pagenum"><a name="page4"></a>[4]</span>Profecto magnus
+  ille vir ... dogma illud, quamvis apud theologos eo nomine non multum
+  gratiæ iniverit, ita ex immotis Philosophiæ fundamentis explicat ac
+  demonstrat, ut paucis tantum immutatis, atque additis, nihil amplius
+  animus veritate sincere deditus desiderare possit."</p>
+
+  <p>This is properly paradox, though also heterodox. It supposes, contrary
+  to all opinion, orthodox and heterodox, that philosophy can, with slight
+  changes, explain the Athanasian doctrine so as to be at least compatible
+  with orthodoxy. The author would stand almost alone, if not quite; and
+  this is what he meant. I have met with the counter-paradox. I have heard
+  it maintained that the doctrine as it stands, in all its mystery is <i>a
+  priori</i> more likely than any other to have been Revelation, if such a
+  thing were to be; and that it might almost have been predicted.</p>
+
+  <p>After looking into books of paradoxes for more than thirty years, and
+  holding conversation with many persons who have written them, and many
+  who might have done so, there is one point on which my mind is fully made
+  up. The manner in which a paradoxer will show himself, as to sense or
+  nonsense, will not depend upon what he maintains, but upon whether he has
+  or has not made a sufficient knowledge of what has been done by others,
+  <i>especially as to the mode of doing it</i>, a preliminary to inventing
+  knowledge for himself. That a little knowledge is a dangerous thing is
+  one of the most fallacious of proverbs. A person of small knowledge is in
+  danger of trying to make his <i>little</i> do the work of <i>more</i>;
+  but a person without any is in more danger of making his <i>no</i>
+  knowledge do the work of <i>some</i>. Take the speculations on the tides
+  as an instance. Persons with nothing but a little geometry have certainly
+  exposed themselves in their modes of objecting to results which require
+  the higher mathematics to be known before an independent opinion can be
+  formed on sufficient grounds. But persons with no geometry at all have
+  done the same thing much more completely. <!-- Page 5 --><span
+  class="pagenum"><a name="page5"></a>[5]</span></p>
+
+  <p>There is a line to be drawn which is constantly put aside in the
+  arguments held by paradoxers in favor of their right to instruct the
+  world. Most persons must, or at least will, like the lady in Cadogan
+  Place,<a name="NtA_5" href="#Nt_5"><sup>[5]</sup></a> form and express an
+  immense variety of opinions on an immense variety of subjects; and all
+  persons must be their own guides in many things. So far all is well. But
+  there are many who, in carrying the expression of their own opinions
+  beyond the usual tone of private conversation, whether they go no further
+  than attempts at oral proselytism, or whether they commit themselves to
+  the press, do not reflect that they have ceased to stand upon the ground
+  on which their process is defensible. Aspiring to lead <i>others</i>,
+  they have never given themselves the fair chance of being first led by
+  <i>other</i> others into something better than they can start for
+  themselves; and that they should first do this is what both those classes
+  of others have a fair right to expect. New knowledge, when to any
+  purpose, must come by contemplation of old knowledge in every matter
+  which concerns thought; mechanical contrivance sometimes, not very often,
+  escapes this rule. All the men who are now called discoverers, in every
+  matter ruled by thought, have been men versed in the minds of their
+  predecessors, and learned in what had been before them. There is not one
+  exception. I do not say that every man has made direct <span
+  class="correction" title="text reads `acquantance'">acquaintance</span>
+  with the whole of his mental ancestry; many have, as I may say, only
+  known their grandfathers by the report of their fathers. But even on this
+  point it is remarkable how many of the greatest names in all departments
+  of knowledge have been real antiquaries in their several subjects.</p>
+
+  <p>I may cite, among those who have wrought strongly upon opinion or
+  practice in science, Aristotle, Plato, Ptolemy, Euclid, Archimedes, Roger
+  Bacon, Copernicus, Francis Bacon, Ramus, Tycho Brahé, Galileo, Napier,
+  Descartes, Leibnitz, Newton, Locke. I take none but names known out of
+  their <!-- Page 6 --><span class="pagenum"><a
+  name="page6"></a>[6]</span>fields of work; and all were learned as well
+  as sagacious. I have chosen my instances: if any one will undertake to
+  show a person of little or no knowledge who has established himself in a
+  great matter of pure thought, let him bring forward his man, and we shall
+  see.</p>
+
+  <p>This is the true way of putting off those who plague others with their
+  great discoveries. The first demand made should be&mdash;Mr. Moses,
+  before I allow you to lead me over the Red Sea, I must have you show that
+  you are learned in all the wisdom of the Egyptians upon your own subject.
+  The plea that it is unlikely that this or that unknown person should
+  succeed where Newton, etc. have failed, or should show Newton, etc. to be
+  wrong, is utterly null and void. It was worthily versified by Sylvanus
+  Morgan (the great herald who in his <i>Sphere of Gentry</i> gave coat
+  armor to "Gentleman Jesus," as he said), who sang of Copernicus as
+  follows (1652):</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"If Tellus winged be,</p>
+      <p>The earth a motion round;</p>
+      <p>Then much deceived are they</p>
+      <p>Who nere before it found.</p>
+      <p>Solomon was the wisest,</p>
+      <p>His wit nere this attained;</p>
+      <p>Cease, then, Copernicus,</p>
+      <p>Thy hypothesis is vain."</p>
+    </div>
+  </div>
+  <p>Newton, etc. were once unknown; but they made themselves known by what
+  they knew, and then brought forward what they could do; which I see is as
+  good verse as that of Herald Sylvanus. The demand for previous knowledge
+  disposes of twenty-nine cases out of thirty, and the thirtieth is worth
+  listening to.</p>
+
+  <p>I have not set down Copernicus, Galileo, etc. among the paradoxers,
+  merely because everybody knows them; if my list were quite complete, they
+  would have been in it. But the reader will find Gilbert, the great
+  precursor of sound magnetical theory; and several others on whom no
+  censure can be cast, though some of their paradoxes are inadmissible,
+  <!-- Page 7 --><span class="pagenum"><a name="page7"></a>[7]</span>some
+  unprovoked, and some capital jokes, true or false: the author of
+  <i>Vestiges of Creation</i> is an instance. I expect that my old
+  correspondent, General Perronet Thompson, will admit that his geometry is
+  part and parcel of my plan; and also that, if that plan embraced
+  politics, he would claim a place for his <i>Catechism on the Corn
+  Laws</i>, a work at one time paradoxical, but which had more to do with
+  the abolition of the bread-tax than Sir Robert Peel.</p>
+
+  <p>My intention in publishing this Budget in the <i>Athenæum</i> is <i>to
+  enable those who have been puzzled by one or two discoverers to see how
+  they look in a lump</i>. The only question is, has the selection been
+  fairly made? To this my answer is, that no selection at all has been
+  made. The books are, without exception, those which I have in my own
+  library; and I have taken <i>all</i>&mdash;I mean all of the kind: Heaven
+  forbid that I should be supposed to have no other books! But I may have
+  been a collector, influenced in choice by bias? I answer that I never
+  have collected books of this sort&mdash;that is, I have never searched
+  for them, never made up my mind to look out for this book or that. I have
+  bought what happened to come in my way at show or auction; I have
+  retained what came in as part of the <i>undescribed</i> portion of
+  miscellaneous auction lots; I have received a few from friends who found
+  them among what they called their rubbish; and I have preserved books
+  sent to me for review. In not a few instances the books have been bound
+  up with others, unmentioned at the back; and for years I knew no more I
+  had them than I knew I had Lord Macclesfield's speech on moving the
+  change of Style, which, after I had searched shops, etc. for it in vain,
+  I found had been reposing on my own shelves for many years, at the end of
+  a summary of Leibnitz's philosophy. Consequently, I may positively affirm
+  that the following list is formed by accident and circumstance alone, and
+  that it truly represents the casualties of about a third of a century.
+  For instance, the large proportion of works <!-- Page 8 --><span
+  class="pagenum"><a name="page8"></a>[8]</span>on the quadrature of the
+  circle is not my doing: it is the natural share of this subject in the
+  actual run of events.</p>
+
+  <p>[I keep to my plan of inserting only such books as I possessed in
+  1863, except by casual notice in aid of my remarks. I have found several
+  books on my shelves which ought to have been inserted. These have their
+  titles set out at the commencement of their articles, in leading
+  paragraphs; the casuals are without this formality.<a name="NtA_6"
+  href="#Nt_6"><sup>[6]</sup></a>]</p>
+
+  <p>Before proceeding to open the Budget, I say something on my personal
+  knowledge of the class of discoverers who square the circle, upset
+  Newton, etc. I suspect I know more of the English class than any man in
+  Britain. I never kept any reckoning; but I know that one year with
+  another&mdash;and less of late years than in earlier time&mdash;I have
+  talked to more than five in each year, giving more than a hundred and
+  fifty specimens. Of this I am sure, that it is my own fault if they have
+  not been a thousand. Nobody knows how they swarm, except those to whom
+  they naturally resort. They are in all ranks and occupations, of all ages
+  and characters. They are very earnest people, and their purpose is
+  <i>bona fide</i> the dissemination of their paradoxes. A great
+  many&mdash;the mass, indeed&mdash;are illiterate, and a great many waste
+  their means, and are in or approaching penury. But I must say that never,
+  in any one instance, has the quadrature of the circle, or the like, been
+  made a pretext for begging; even to be asked to purchase a book is of the
+  very rarest occurrence&mdash;it has happened, and that is all.</p>
+
+  <p>These discoverers despise one another: if there were the concert among
+  them which there is among foreign mendicants, a man who admitted one to a
+  conference would be plagued to death. I once gave something to a very
+  genteel French applicant, who overtook me in the street, at my own door,
+  saying he had picked up my handkerchief: whether he picked it up in my
+  pocket for an introduction, I know not. <!-- Page 9 --><span
+  class="pagenum"><a name="page9"></a>[9]</span>But that day week came
+  another Frenchman to my house, and that day fortnight a French lady; both
+  failed, and I had no more trouble. The same thing happened with Poles. It
+  is not so with circle-squarers, etc.: they know nothing of each other.
+  Some will read this list, and will say I am right enough, generally
+  speaking, but that there <i>is</i> an exception, if I could but see
+  it.</p>
+
+  <p>I do not mean, by my confession of the manner in which I have sinned
+  against the twenty-four hours, to hold myself out as accessible to
+  personal explanation of new plans. Quite the contrary: I consider myself
+  as having made my report, and being discharged from further attendance on
+  the subject. I will not, from henceforward, talk to any squarer of the
+  circle, trisector of the angle, duplicator of the cube, constructor of
+  perpetual motion, subverter of gravitation, stagnator of the earth,
+  builder of the universe, etc. I will receive any writings or books which
+  require no answer, and read them when I please: I will certainly preserve
+  them&mdash;this list may be enlarged at some future time.</p>
+
+  <p>There are three subjects which I have hardly anything upon; astrology,
+  mechanism, and the infallible way of winning at play. I have never cared
+  to preserve astrology. The mechanists make models, and not books. The
+  infallible winners&mdash;though I have seen a few&mdash;think their
+  secret too valuable, and prefer <i>mutare quadrata rotundis</i>&mdash;to
+  turn dice into coin&mdash;at the gaming-house: verily they have their
+  reward.</p>
+
+  <p>I shall now select, to the mystic number seven, instances of my
+  personal knowledge of those who think they have discovered, in
+  illustration of as many misconceptions.</p>
+
+  <p>1. <i>Attempt by help of the old philosophy, the discoverer not being
+  in possession of modern knowledge.</i> A poor schoolmaster, in rags,
+  introduced himself to a scientific friend with whom I was talking, and
+  announced that he had found out the composition of the sun. "How was that
+  done?"&mdash;"By consideration of the four elements."&mdash;"What are
+  <!-- Page 10 --><span class="pagenum"><a
+  name="page10"></a>[10]</span>they?"&mdash;"Of course, fire, air, earth,
+  and water."&mdash;"Did you not know that air, earth, and water, have long
+  been known to be no elements at all, but compounds?"&mdash;"What do you
+  mean, sir? Who ever heard of such a thing?"</p>
+
+  <p>2. <i>The notion that difficulties are enigmas, to be overcome in a
+  moment by a lucky thought.</i> A nobleman of very high rank, now long
+  dead, read an article by me on the quadrature, in an early number of the
+  <i>Penny Magazine</i>. He had, I suppose, school recollections of
+  geometry. He put pencil to paper, drew a circle, and constructed what
+  seemed likely to answer, and, indeed, was&mdash;as he said&mdash;certain,
+  if only this bit were equal to that; which of course it was not. He
+  forwarded his diagram to the Secretary of the Diffusion Society, to be
+  handed to the author of the article, in case the difficulty should happen
+  to be therein overcome.</p>
+
+  <p>3. <i>Discovery at all hazards, to get on in the world.</i> Thirty
+  years ago, an officer of rank, just come from foreign service, and trying
+  for a decoration from the Crown, found that his claims were of doubtful
+  amount, and was told by a friend that so and so, who had got the order,
+  had the additional claim of scientific distinction. Now this officer,
+  while abroad, had bethought himself one day, that there really could be
+  no difficulty in finding the circumference of a circle: if a circle were
+  rolled upon a straight line until the undermost point came undermost
+  again, there would be the straight line equal to the circle. He came to
+  me, saying that he did not feel equal to the statement of his claim in
+  this respect, but that if some clever fellow would put the thing in a
+  proper light, he thought his affair might be managed. I was clever enough
+  to put the thing in a proper light to himself, to this extent at least,
+  that, though perhaps they were wrong, the advisers of the Crown would
+  never put the letters K.C.B. to such a circle as his.</p>
+
+  <p>4. <i>The notion that mathematicians cannot find the circle for common
+  purposes.</i> A working man measured the altitude of a cylinder
+  accurately, and&mdash;I think the process of <!-- Page 11 --><span
+  class="pagenum"><a name="page11"></a>[11]</span>Archimedes was one of his
+  proceedings&mdash;found its bulk. He then calculated the ratio of the
+  circumference to the diameter, and found it answered very well on other
+  modes of trial. His result was about 3.14. He came to London, and
+  somebody sent him to me. Like many others of his pursuit, he seemed to
+  have turned the whole force of his mind upon one of his points, on which
+  alone he would be open to refutation. He had read some of Kater's
+  experiments, and had got the Act of 1825 on weights and measures. Say
+  what I would, he had for a long time but one answer&mdash;"Sir! I go upon
+  Captain Kater and the Act of Parliament." But I fixed him at last. I
+  happened to have on the table a proof-sheet of the <i>Astronomical
+  Memoirs</i>, in which were a large number of observed places of the
+  planets compared with prediction, and asked him whether it could be
+  possible that persons who did not know the circle better than he had
+  found it could make the calculations, of which I gave him a notion, so
+  accurately? He was perfectly astonished, and took the titles of some
+  books which he said he would read.</p>
+
+  <p>5. <i>Application for the reward from abroad.</i> Many years ago,
+  about twenty-eight, I think, a Jesuit came from South America, with a
+  quadrature, and a cutting from a newspaper announcing that a reward was
+  ready for the discovery in England. On this evidence he came over. After
+  satisfying him that nothing had ever been offered here, I discussed his
+  quadrature, which was of no use. I succeeded better when I told him of
+  Richard White, also a Jesuit, and author of a quadrature published before
+  1648, under the name of <i>Chrysæspis</i>, of which I can give no
+  account, having never seen it. This White (<i>Albius</i>) is the only
+  quadrator who was ever convinced of his error. My Jesuit was struck by
+  the instance, and promised to read more geometry&mdash;he was no
+  Clavius&mdash;before he published his book. He relapsed, however, for I
+  saw his book advertised in a few days. I may say, as sufficient proof of
+  my being no collector, that I had not the curiosity to buy his book; and
+  my friend the <!-- Page 12 --><span class="pagenum"><a
+  name="page12"></a>[12]</span>Jesuit did not send me a copy, which he
+  ought to have done, after the hour I had given him.</p>
+
+  <p>6. <i>Application for the reward at home.</i> An agricultural laborer
+  squared the circle, and brought the proceeds to London. He left his
+  papers with me, one of which was the copy of a letter to the Lord
+  Chancellor, desiring his Lordship to hand over forthwith 100,000 pounds,
+  the amount of the alleged offer of reward. He did not go quite so far as
+  M. de Vausenville, who, I think in 1778, brought an action against the
+  Academy of Sciences to recover a reward to which he held himself
+  entitled. I returned the papers, with a note, stating that he had not the
+  knowledge requisite to see in what the problem consisted. I got for
+  answer a letter in which I was told that a person who could not see that
+  he had done the thing should "change his business, and appropriate his
+  time and attention to a Sunday-school, to learn what he could, and keep
+  the <i>litle</i> children from <i>durting</i> their <i>close</i>." I also
+  received a letter from a friend of the quadrator, informing me that I
+  knew his friend had succeeded, and had been heard to say so. These
+  letters were printed&mdash;without the names of the writers&mdash;for the
+  amusement of the readers of <i>Notes and Queries</i>, First Series, xii.
+  57, and they will appear again in the sequel.</p>
+
+  <p>[There are many who have such a deep respect for any attempt at
+  thought that they are shocked at ridicule even of those who have made
+  themselves conspicuous by pretending to lead the world in matters which
+  they have not studied. Among my anonyms is a gentleman who is angry at my
+  treatment of the "poor but thoughtful" man who is described in my
+  introduction as recommending me to go to a Sunday-school because I
+  informed him that he did not know in what the difficulty of quadrature
+  consisted. My impugner quite forgets that this man's "thoughtfulness"
+  chiefly consisted in his demanding a hundred thousand pounds from the
+  Lord Chancellor for his discovery; and I may add, that his greatest
+  stretch of invention was finding out that "the clergy" <!-- Page 13
+  --><span class="pagenum"><a name="page13"></a>[13]</span>were the means
+  of his modest request being unnoticed. I mention this letter because it
+  affords occasion to note a very common error, namely, that men unread in
+  their subjects have, by natural wisdom, been great benefactors of
+  mankind. My critic says, "Shakspeare, whom the Pro<sup>r</sup>
+  (<i>sic</i>) may admit to be a wisish man, though an object of contempt
+  as to learning ..." Shakespeare an object of contempt as to learning!
+  Though not myself a thoroughgoing Shakespearean&mdash;and adopting the
+  first half of the opinion given by George III, "What! is there not sad
+  stuff? only one must not say so"&mdash;I am strongly of opinion that he
+  throws out the masonic signs of learning in almost every scene, to all
+  who know what they are. And this over and above every kind of direct
+  evidence. First, foremost, and enough, the evidence of Ben Jonson that he
+  had "little Latin and less Greek"; then Shakespeare had as much Greek as
+  Jonson would call <i>some</i>, even when he was depreciating. To have any
+  Greek at all was in those days exceptional. In Shakespeare's youth St.
+  Paul's and Merchant Taylor's schools were to have masters learned in good
+  and clean Latin literature, <i>and also in Greek if such may be
+  gotten</i>. When Jonson spoke as above, he intended to put Shakespeare
+  low among the learned, but not out of their pale; and he spoke as a rival
+  dramatist, who was proud of his own learned sock; and it may be a subject
+  of inquiry how much Latin <i>he</i> would call <i>little</i>. If
+  Shakespeare's learning on certain points be very much less visible than
+  Jonson's, it is partly because Shakespeare's writings hold it in chemical
+  combination, Jonson's in mechanical aggregation.]</p>
+
+  <p>7. An elderly man came to me to show me how the universe was created.
+  There was one molecule, which by vibration became&mdash;Heaven knows
+  how!&mdash;the Sun. Further vibration produced Mercury, and so on. I
+  suspect the nebular hypothesis had got into the poor man's head by
+  reading, in some singular mixture with what it found there. Some
+  modifications of vibration gave heat, electricity, etc. I <!-- Page 14
+  --><span class="pagenum"><a name="page14"></a>[14]</span>listened until
+  my informant ceased to vibrate&mdash;which is always the shortest
+  way&mdash;and then said, "Our knowledge of elastic fluids is imperfect."
+  "Sir!" said he, "I see you perceive the truth of what I have said, and I
+  will reward your attention by telling you what I seldom disclose, never,
+  except to those who can receive my theory&mdash;the little molecule whose
+  vibrations have given rise to our solar system is the Logos of St. John's
+  Gospel!" He went away to Dr. Lardner, who would not go into the solar
+  system at all&mdash;the first molecule settled the question. So hard upon
+  poor discoverers are men of science who are not antiquaries in their
+  subject! On leaving, he said, "Sir, Mr. De Morgan received me in a very
+  different way! he heard me attentively, and I left him perfectly
+  satisfied of the truth of my system." I have had much reason to think
+  that many discoverers, of all classes, believe they have convinced every
+  one who is not peremptory to the verge of incivility.</p>
+
+  <p>My list is given in chronological order. My readers will understand
+  that my general expressions, where slighting or contemptuous, refer to
+  the ignorant, who teach before they have learned. In every instance,
+  those of whom I am able to speak with respect, whether as right or wrong,
+  have sought knowledge in the subject they were to handle before they
+  completed their speculations. I shall further illustrate this at the
+  conclusion of my list.</p>
+
+  <p>Before I begin the list, I give prominence to the following letter,
+  addressed by me to the <i>Correspondent</i> of October 28, 1865. Some of
+  my paradoxers attribute to me articles in this or that journal; and
+  others may think&mdash;I know some do think&mdash;they know me as the
+  writer of reviews of some of the very books noticed here. The following
+  remarks will explain the way in which they may be right, and in which
+  they may be wrong. <!-- Page 15 --><span class="pagenum"><a
+  name="page15"></a>[15]</span></p>
+
+<hr class="short" >
+
+<p class="cenhead">THE EDITORIAL SYSTEM.</p>
+
+  <p>"Sir,&mdash;I have reason to think that many persons have a very
+  inaccurate notion of the <i>Editorial System</i>. What I call by this
+  name has grown up in the last <i>centenary</i>&mdash;a word I may use to
+  signify the hundred years now ending, and to avoid the ambiguity of
+  <i>century</i>. It cannot conveniently be explained by editors
+  themselves, and <i>edited</i> journals generally do not like to say much
+  about it. In <i>your</i> paper perhaps, in which editorial duties differ
+  somewhat from those of ordinary journals, the common system may be freely
+  spoken of.</p>
+
+  <p>"When a reviewed author, as very often happens, writes to the editor
+  of the reviewing journal to complain of what has been said of him, he
+  frequently&mdash;even more often than not&mdash;complains of 'your
+  reviewer.' He sometimes presumes that 'you' have, 'through inadvertence'
+  in this instance, 'allowed some incompetent person to lower the character
+  of your usually accurate pages.' Sometimes he talks of 'your scribe,'
+  and, in extreme cases, even of 'your hack.' All this shows perfect
+  ignorance of the journal system, except where it is done under the notion
+  of letting the editor down easy. But the editor never accepts the
+  mercy.</p>
+
+  <p>"All that is in a journal, except what is marked as from a
+  correspondent, either by the editor himself or by the correspondent's
+  real or fictitious signature, is published entirely on editorial
+  responsibility, as much as if the editor had written it himself. The
+  editor, therefore, may claim, and does claim and exercise, unlimited
+  right of omission, addition, and alteration. This is so well understood
+  that the editor performs his last function on the last revise without the
+  'contributor' knowing what is done. The word <i>contributor</i> is the
+  proper one; it implies that he furnishes materials without stating what
+  he furnishes or how much of it is accepted, or whether he be the only
+  contributor. All this applies both to political and literary journals. No
+  editor acknowledges <!-- Page 16 --><span class="pagenum"><a
+  name="page16"></a>[16]</span>the right of a contributor to withdraw an
+  article, if he should find alterations in the proof sent to him for
+  correction which would make him wish that the article should not appear.
+  If the <i>demand</i> for suppression were made&mdash;I say nothing about
+  what might be granted to <i>request</i>&mdash;the answer would be, 'It is
+  not your article, but mine; I have all the responsibility; if it should
+  contain a libel, I could not give you up, even at your own desire. You
+  have furnished me with materials, on the known and common understanding
+  that I was to use them at my discretion, and you have no right to impede
+  my operations by making the appearance of the article depend on your
+  approbation of my use of your materials.'</p>
+
+  <p>"There is something to be said for this system, and something against
+  it&mdash;I mean simply on its own merits. But the all-conquering argument
+  in its favor is, that the only practicable alternative is the modern
+  French plan of no articles without the signature of the writers. I need
+  not discuss this plan; there is no collective party in favor of it. Some
+  may think it is not the only alternative; they have not produced any
+  intermediate proposal in which any dozen of persons have concurred. Many
+  will say, Is not all this, though perfectly correct, well known to be
+  matter of form? Is it not practically the course of events that an
+  engaged contributor writes the article, and sends it to the editor, who
+  admits it as written&mdash;substantially, at least? And is it not often
+  very well known, by style and in other ways, who it was wrote the
+  article? This system is matter of form just as much as loaded pistols are
+  matter of form so long as the wearer is not assailed; but matter of form
+  takes the form of matter in the pulling of a trigger, so soon as the need
+  arises. Editors and contributors who can work together find each other
+  out by elective affinity, so that the common run of events settles down
+  into most articles appearing much as they are written. And there are two
+  safety-valves; that is, when judicious persons come together. In the
+  first place, the editor himself, when he has selected his contributor,
+  feels that <!-- Page 17 --><span class="pagenum"><a
+  name="page17"></a>[17]</span>the contributor is likely to know his
+  business better than an editor can teach him; in fact, it is on that
+  principle that the selection is made. But he feels that he is more
+  competent than the writer to judge questions of strength and of tone,
+  especially when the general purpose of the journal is considered, of
+  which the editor is the judge without appeal. An editor who meddles with
+  substantive matter is likely to be wrong, even when he knows the subject;
+  but one who prunes what he deems excess, is likely to be right, even when
+  he does not know the subject. In the second place, a contributor knows
+  that he is supplying an editor, and learns, without suppressing truth or
+  suggesting falsehood, to make the tone of his communications suit the
+  periodical in which they are to appear. Hence it very often arises that a
+  reviewed author, who thinks he knows the name of his reviewer, and
+  proclaims it with expressions of dissatisfaction, is only wrong in
+  supposing that his critic has given all his mind. It has happened to
+  myself more than once, to be announced as the author of articles which I
+  could not have signed, because they did not go far enough to warrant my
+  affixing my name to them as to a sufficient expression of my own
+  opinion.</p>
+
+  <p>"There are two other ways in which a reviewed author may be wrong
+  about his critic. An editor frequently makes slight insertions or
+  omissions&mdash;I mean slight in quantity of type&mdash;as he goes over
+  the last proof; this he does in a comparative hurry, and it may chance
+  that he does not know the full sting of his little alteration. The very
+  bit which the writer of the book most complains of may not have been seen
+  by the person who is called the writer of the article until after the
+  appearance of the journal; nay, if he be one of those&mdash;few, I
+  daresay&mdash;who do not read their own articles, may never have been
+  seen by him at all. Possibly, the insertion or omission would not have
+  been made if the editor could have had one minute's conversation with his
+  contributor. Sometimes it actually contradicts something which is <!--
+  Page 18 --><span class="pagenum"><a name="page18"></a>[18]</span>allowed
+  to remain in another part of the article; and sometimes, especially in
+  the case of omission, it renders other parts of the article
+  unintelligible. These are disadvantages of the system, and a judicious
+  editor is not very free with his <i>unus et alter pannus</i>. Next,
+  readers in general, when they see the pages of a journal with the
+  articles so nicely fitting, and so many ending with the page or column,
+  have very little notion of the cutting and carving which goes to the
+  process. At the very last moment arises the necessity of some trimming of
+  this kind; and the editor, who would gladly call the writer to counsel if
+  he could, is obliged to strike out ten or twelve lines. He must do his
+  best, but it may chance that the omission selected would take from the
+  writer the power of owning the article. A few years ago, an able opponent
+  of mine wrote to a journal some criticisms upon an article which he
+  expressly attributed to me. I replied as if I were the writer, which, in
+  a sense, I was. But if any one had required of me an unmodified 'Yes' or
+  'No' to the question whether I wrote the article, I must, of two
+  falsehoods, have chosen 'No': for certain omissions, dictated by the
+  necessities of space and time, would have amounted, had my signature been
+  affixed, to a silent surrender of points which, in my own character, I
+  must have strongly insisted on, unless I had chosen to admit certain
+  inferences against what I had previously published in my own name. I may
+  here add that the forms of journalism obliged me in this case to remind
+  my opponent that it could not be permitted to me, <i>in that journal</i>,
+  either to acknowledge or deny the authorship of the articles. The
+  cautions derived from the above remarks are particularly wanted with
+  reference to the editorial comments upon letters of complaint. There is
+  often no time to send these letters to the contributor, and even when
+  this can be done, an editor is&mdash;and very properly&mdash;never of so
+  editorial a mind as when he is revising the comments of a contributor
+  upon an assailant of the article. He is then in a better position as to
+  information, and a more <!-- Page 19 --><span class="pagenum"><a
+  name="page19"></a>[19]</span>critical position as to responsibility. Of
+  course, an editor never meddles, except under notice, with the letter of
+  a correspondent, whether of a complainant, of a casual informant, or of a
+  contributor who sees reason to become a correspondent. Omissions must
+  sometimes be made when a grievance is too highly spiced. It did once
+  happen to me that a waggish editor made an insertion without notice in a
+  letter signed by me with some fiction, which insertion contained the name
+  of a friend of mine, with a satire which I did not believe, and should
+  not have written if I had. To my strong rebuke, he replied&mdash;'I know
+  it was very wrong; but human nature could not resist.' But this was the
+  only occasion on which such a thing ever happened to me.</p>
+
+  <p>"I daresay what I have written may give some of your readers to
+  understand some of the <i>pericula et commoda</i> of modern journalism. I
+  have known men of deep learning and science as ignorant of the prevailing
+  system as any uneducated reader of a newspaper in a country town. I may
+  perhaps induce some writers not to be too sure about this, that, or the
+  other person. They may detect their reviewer, and they may be safe in
+  attributing to him the general matter and tone of the article. But about
+  one and another point, especially if it be a short and stinging point,
+  they may very easily chance to be wrong. It has happened to myself, and
+  within a few weeks to publication, to be wrong in two ways in reading a
+  past article&mdash;to attribute to editorial insertion what was really my
+  own, and to attribute to myself what was really editorial insertion."</p>
+
+  <p>&nbsp;</p>
+
+  <p>What is a man to do who is asked whether he wrote an article? He may,
+  of course, refuse to answer; which is regarded as an admission. He may
+  say, as Swift did to Serjeant Bettesworth, "Sir, when I was a young man,
+  a friend of mine advised me, whenever I was asked whether I had written a
+  certain paper, to deny it; and I accordingly tell that I did <i>not</i>
+  write it." He may say, as I often do, <!-- Page 20 --><span
+  class="pagenum"><a name="page20"></a>[20]</span>when charged with having
+  invented a joke, story, or epigram, "I want all the credit I can get, and
+  therefore I always acknowledge all that is attributed to me, truly or
+  not; the story, etc. <i>is</i> mine." But for serious earnest, in the
+  matter of imputed criticism, the answer may be, "The article was of my
+  material, but the editor has not let it stand as I gave it; I cannot own
+  it as a whole." He may then refuse to be particular as to the amount of
+  the editor's interference. Of this there are two extreme cases. The
+  editor may have expunged nothing but a qualifying adverb. Or he may have
+  done as follows. We all remember the account of Adam which satirizes
+  woman, but eulogizes her if every second and third line be transposed. As
+  in:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Adam could find no solid peace</p>
+      <p class="i2">When Eve was given him for a mate,</p>
+      <p>Till he beheld a woman's face,</p>
+      <p class="i2">Adam was in a happy state."</p>
+    </div>
+  </div>
+  <p>If this had been the article, and a gallant editor had made the
+  transpositions, the author could not with truth acknowledge. If the
+  alteration were only an omitted adverb, or a few things of the sort, the
+  author could not with truth deny. In all that comes between, every man
+  must be his own casuist. I stared, when I was a boy, to hear grave
+  persons approve of Sir Walter Scott's downright denial that he was the
+  author of Waverley, in answer to the Prince Regent's downright question.
+  If I remember rightly, Samuel Johnson would have approved of the same
+  course.</p>
+
+  <p>It is known that, whatever the law gives, it also gives all that is
+  necessary to full possession; thus a man whose land is environed by land
+  of others has a right of way over the land of these others. By analogy,
+  it is argued that when a man has a right to his secret, he has a right to
+  all that is necessary to keep it, and that is not unlawful. If, then, he
+  can only keep his secret by denial, he has a right to denial. This I
+  admit to be an answer against all men except the denier himself; if
+  conscience and self-respect will allow <!-- Page 21 --><span
+  class="pagenum"><a name="page21"></a>[21]</span>it, no one can impeach
+  it. But the question cannot be solved on a case. That question is, A lie,
+  is it <i>malum in se</i>, without reference to meaning and circumstances?
+  This is a question with two sides to it. Cases may be invented in which a
+  lie is the only way of preventing a murder, or in which a lie may
+  otherwise save a life. In these cases it is difficult to acquit, and
+  almost impossible to blame; discretion introduced, the line becomes very
+  hard to draw.</p>
+
+  <p>I know but one work which has precisely&mdash;as at first
+  appears&mdash;the character and object of my Budget. It is the <i>Review
+  of the Works of the Royal Society of London</i>, by Sir John Hill, M.D.
+  (1751 and 1780, 4to.). This man offended many: the Royal Society, by his
+  work, the medical profession, by inventing and selling
+  extra-pharmacop&oelig;ian doses; Garrick, by resenting the rejection of a
+  play. So Garrick wrote:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"For physic and farces his equal there scarce is;</p>
+      <p>His farces are physic; his physic a farce is."</p>
+    </div>
+  </div>
+  <p>I have fired at the Royal Society and at the medical profession, but I
+  have given a wide berth to the drama and its wits; so there is no epigram
+  out against me, as yet. He was very able and very eccentric. Dr. Thomson
+  (<i>Hist. Roy. Soc.</i>) says he has no humor, but Dr. Thomson was a man
+  who never would have discovered humor.</p>
+
+  <p>Mr. Weld (<i>Hist. Roy. Soc.</i>) backs Dr. Thomson, but with a
+  remarkable addition. Having followed his predecessor in observing that
+  the <i>Transactions</i> in Martin Folkes's time have an unusual
+  proportion of trifling and puerile papers, he says that Hill's book is a
+  poor attempt at humor, and glaringly exhibits the feelings of a
+  disappointed man. It is probable, he adds, that the points told with some
+  effect on the Society; for shortly after its publication the
+  <i>Transactions</i> possess a much higher scientific value.</p>
+
+  <p>I copy an account which I gave elsewhere.</p>
+
+  <p>When the Royal Society was founded, the Fellows set <!-- Page 22
+  --><span class="pagenum"><a name="page22"></a>[22]</span>to work to prove
+  all things, that they might hold fast that which was good. They bent
+  themselves to the question whether sprats were young herrings. They made
+  a circle of the powder of a unicorn's horn, and set a spider in the
+  middle of it; "but it immediately ran out." They tried several times, and
+  the spider "once made some stay in the powder." They inquired into Kenelm
+  Digby's sympathetic powder. "Magnetic cures being discoursed of, Sir
+  Gilbert Talbot promised to communicate what he knew of sympathetical
+  cures; and those members who had any of the powder of sympathy, were
+  desired to bring some of it at the next meeting."</p>
+
+  <p>June 21, 1661, certain gentlemen were appointed "curators of the
+  proposal of tormenting a man with the sympathetic powder"; I cannot find
+  any record of the result. And so they went on until the time of Sir John
+  Hill's satire, in 1751. This once well-known work is, in my judgment, the
+  greatest compliment the Royal Society ever received. It brought forward a
+  number of what are now feeble and childish researches in the
+  Philosophical Transactions. It showed that the inquirers had actually
+  been inquiring; and that they did not pronounce decision about "natural
+  <i>knowledge</i>" by help of "<i>natural</i> knowledge." But for this,
+  Hill would neither have known what to assail, nor how. Matters are now
+  entirely changed. The scientific bodies are far too well established to
+  risk themselves. <i>Ibit qui zonam perdidit:</i></p>
+
+<blockquote class="b1n">
+
+  <p>"Let him take castles who has ne'er a groat."</p>
+
+</blockquote>
+
+  <p>These great institutions are now without any collective purpose,
+  except that of promoting individual energy; they print for their
+  contributors, and guard themselves by a general declaration that they
+  will not be answerable for the things they print. Of course they will not
+  put forward anything for everybody; but a writer of a certain reputation,
+  or matter of a certain look of plausibility and safety, <!-- Page 23
+  --><span class="pagenum"><a name="page23"></a>[23]</span>will find
+  admission. This is as it should be; the pasturer of flocks and herds and
+  the hunters of wild beasts are two very different bodies, with very
+  different policies. The scientific academies are what a spiritualist
+  might call "publishing mediums," and <i>their</i> spirits fall
+  occasionally into writing which looks as if minds in the higher state
+  were not always impervious to nonsense.</p>
+
+  <p>The following joke is attributed to Sir John Hill. I cannot honestly
+  say I believe it; but it shows that his contemporaries did not believe he
+  had no humor. Good stories are always in some sort of keeping with the
+  characters on which they are fastened. Sir John Hill contrived a
+  communication to the Royal Society from Portsmouth, to the effect that a
+  sailor had broken his leg in a fall from the mast-head; that bandages and
+  a plentiful application of tarwater had made him, in three days, able to
+  use his leg as well as ever. While this communication was under grave
+  discussion&mdash;it must be remembered that many then thought tarwater
+  had extraordinary remedial properties&mdash;the joker contrived that a
+  second letter should be delivered, which stated that the writer had
+  forgotten, in his previous communication, to mention that the leg was a
+  wooden leg! Horace Walpole told this story, I suppose for the first time;
+  he is good authority for the fact of circulation, but for nothing
+  more.</p>
+
+  <p>Sir John Hill's book is droll and cutting satire. Dr. Maty, (Sec.
+  Royal Society) wrote thus of it in the <i>Journal Britannique</i> (Feb.
+  1751), of which he was editor:</p>
+
+  <p>"Il est fâcheux que cet ingénieux Naturaliste, qui nous a déjà donné
+  et qui nous prépare encore des ouvrages plus utiles, emploie à cette
+  odieuse tâche une plume qu'il trempe dans le fiel et dans l'absinthe. Il
+  est vrai que plusieurs de ses remarques sont fondées, et qu'à l'erreur
+  qu'il indique, il joint en même tems la correction. Mais il n'est pas
+  toujours équitable, et ne manque jamais d'insulter. Que peut <!-- Page 24
+  --><span class="pagenum"><a name="page24"></a>[24]</span>après tout
+  prouver son livre, si ce n'est que la quarante-cinquième partie d'un
+  très-ample et très-utile Recueil n'est pas exempte d'erreurs? Devoit-il
+  confondre avec des Ecrivains superficiels, dont la Liberté du Corps ne
+  permet pas de restreindre la fertilité, cette foule de savans du Premier
+  ordre, dont les Ecrits ont orné et ornent encore les Transactions? A-t-il
+  oublié qu'on y a vu fréquemment les noms des Boyle, des Newton, des
+  Halley, des De Moivres, des Hans Sloane, etc.? Et qu'on y trouve encore
+  ceux des Ward, des Bradley, des Graham, des Ellicot, des Watson, et d'un
+  Auteur que Mr. Hill préfère à tous les autres, je veux dire de Mr. Hill
+  lui-même?"<a name="NtA_7" href="#Nt_7"><sup>[7]</sup></a></p>
+
+  <p>This was the only answer; but it was no answer at all. Hill's object
+  was to expose the absurdities; he therefore collected the absurdities. I
+  feel sure that Hill was a benefactor of the Royal Society; and much more
+  than he would have been if he had softened their errors and enhanced
+  their praises. No reviewer will object to me that I have omitted Young,
+  Laplace, etc. But then my book has a true title. Hill should not have
+  called his a review of the "Works."</p>
+
+  <p>It was charged against Sir John Hill that he had tried to become a
+  Fellow of the Royal Society and had failed. This he denied, and
+  challenged the production of the certificate which a candidate always
+  sends in, and which is preserved. <!-- Page 25 --><span
+  class="pagenum"><a name="page25"></a>[25]</span>But perhaps he could not
+  get so far as a certificate&mdash;that is, could not find any one to
+  recommend him; he was a likely man to be in such a predicament. As I have
+  myself run foul of the Society on some little points, I conceive it
+  possible that I may fall under a like suspicion. Whether I could have
+  been a Fellow, I cannot know; as the gentleman said who was asked if he
+  could play the violin, I never tried. I have always had a high opinion of
+  the Society upon its whole history. A person used to historical inquiry
+  learns to look at wholes; the Universities of Oxford and Cambridge, the
+  College of Physicians, etc. are taken in all their duration. But those
+  who are not historians&mdash;I mean not possessed of the habit of
+  history&mdash;hold a mass of opinions about current things which lead
+  them into all kinds of confusion when they try to look back. Not to give
+  an instance which will offend any set of existing men&mdash;this merely
+  because I can do without it&mdash;let us take the country at large. Magna
+  Charta for ever! glorious safeguard of our liberties! <i>Nullus liber
+  homo capiatur aut imprisonetur ... aut aliquo modo destruatur, nisi per
+  judicium parium</i> ....<a name="NtA_8" href="#Nt_8"><sup>[8]</sup></a>
+  <i>Liber homo: frank home</i>; a capital thing for him&mdash;but how
+  about the <i>villeins</i>? Oh, there are none <i>now</i>! But there were.
+  Who cares for villains, or barbarians, or helots? And so England, and
+  Athens, and Sparta, were free States; all the freemen in them were free.
+  Long after Magna Charta, villains were sold with their "chattels and
+  offspring," named in that order. Long after Magna Charta, it was law that
+  "Le Seigniour poit rob, naufrer, et chastiser son villein a son volunt,
+  salve que il ne poit luy maim."<a name="NtA_9"
+  href="#Nt_9"><sup>[9]</sup></a></p>
+
+  <p>The Royal Society was founded as a co-operative body, and co-operation
+  was its purpose. The early charters, etc. do not contain a trace of the
+  intention to create a <i>scientific distinction</i>, a kind of Legion of
+  Honor. It is clear that the <!-- Page 26 --><span class="pagenum"><a
+  name="page26"></a>[26]</span>qualification was ability and willingness to
+  do good work for the promotion of natural knowledge, no matter in how
+  many persons, nor of what position in society. Charles II gave a smart
+  rebuke for exclusiveness, as elsewhere mentioned. In time arose, almost
+  of course, the idea of distinction attaching to the title; and when I
+  first began to know the Society, it was in this state. Gentlemen of good
+  social position were freely elected if they were really educated men; but
+  the moment a claimant was announced as resting on his science, there was
+  a disposition to inquire whether he was scientific enough. The maxim of
+  the poet was adopted; and the Fellows were practically divided into
+  <i>Drink-deeps</i> and <i>Taste-nots</i>.</p>
+
+  <p>I was, in early life, much repelled by the tone taken by the Fellows
+  of the Society with respect to their very mixed body. A man high in
+  science&mdash;some thirty-seven years ago (about 1830)&mdash;gave me some
+  encouragement, as he thought. "We shall have you a Fellow of the Royal
+  Society in time," said he. Umph! thought I: for I had that day heard of
+  some recent elections, the united science of which would not have
+  demonstrated I. 1, nor explained the action of a pump. Truly an elevation
+  to look up at! It came, further, to my knowledge that the Royal
+  Society&mdash;if I might judge by the claims made by very influential
+  Fellows&mdash;considered itself as entitled to the best of everything:
+  second-best being left for the newer bodies. A secretary, in returning
+  thanks for the Royal at an anniversary of the Astronomical, gave rather a
+  lecture to the company on the positive duty of all present to send the
+  very best to the old body, and the absolute right of the old body to
+  expect it. An old friend of mine, on a similar occasion, stated as a fact
+  that the thing was always done, as well as that it ought to be done.</p>
+
+  <p>Of late years this pretension has been made by a President of the
+  Society. In 1855, Lord Rosse presented a confidential memorandum to the
+  Council on the expediency of enlarging their number. He says, "In a
+  Council so small it <!-- Page 27 --><span class="pagenum"><a
+  name="page27"></a>[27]</span>is impossible to secure a satisfactory
+  representation of the leading scientific Societies, and it is scarcely to
+  be expected that, under such circumstances, they will continue to publish
+  inferior papers while they send the best to our <i>Transactions</i>."</p>
+
+  <p>And, again, with all the Societies represented on the Council, "even
+  if every Science had its Society, and if they published everything,
+  withholding their best papers [i.e., from the Royal Society], which they
+  would not be likely to do, still there would remain to the Royal Society
+  ...." Lord Rosse seems to imagine that the minor Societies themselves
+  transfer their best papers to the Royal Society; that if, for instance,
+  the Astronomical Society were to receive from A.B. a paper of unusual
+  merit, the Society would transfer it to the Royal Society. This is quite
+  wrong: any preference of the Royal to another Society is the work of the
+  contributor himself. But it shows how well hafted is the Royal Society's
+  claim, that a President should acquire the notion that it is acknowledged
+  and acted upon by the other Societies, in their joint and corporate
+  capacities. To the pretension thus made I never could give any sympathy.
+  When I first heard Mr. Christie, Sec. R.&nbsp;S., set it forth at the
+  anniversary dinner of the Astronomical Society, I remembered the Baron in
+  Walter Scott:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Of Gilbert the Galliard a heriot he sought,</p>
+      <p>Saying, Give thy best steed as a vassal ought."</p>
+    </div>
+  </div>
+  <p>And I remembered the answer:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Lord and Earl though thou be, I trow</p>
+      <p>I can rein Buck's-foot better than thou."</p>
+    </div>
+  </div>
+  <p>Fully conceding that the Royal Society is entitled to preeminent rank
+  and all the respect due to age and services, I could not, nor can I now,
+  see any more obligation in a contributor to send his best to that Society
+  than he can make out to be due to himself. This pretension, in my mind,
+  was hooked on, by my historical mode of viewing things already mentioned,
+  to my knowledge of the fact that the Royal <!-- Page 28 --><span
+  class="pagenum"><a name="page28"></a>[28]</span>Society&mdash;the chief
+  fault, perhaps, lying with its President, Sir Joseph Banks&mdash;had
+  sternly set itself against the formation of other societies; the
+  Geological and Astronomical, for instance, though it must be added that
+  the chief rebels came out of the Society itself. And so a certain not
+  very defined dislike was generated in my mind&mdash;an anti-aristocratic
+  affair&mdash;to the body which seemed to me a little too uplifted. This
+  would, I daresay, have worn off; but a more formidable objection arose.
+  My views of physical science gradually arranged themselves into a form
+  which would have rendered F.R.S., as attached to my name, a false
+  representation symbol. The Royal Society is the great fortress of general
+  physics: and in the philosophy of our day, as to general physics, there
+  is something which makes the banner of the R.S. one under which I cannot
+  march. Everybody who saw the three letters after my name would infer
+  certain things as to my mode of thought which would not be true
+  inference. It would take much space to explain this in full. I may
+  hereafter, perhaps, write a budget of collected results of the <i>a
+  priori philosophy</i>, the nibbling at the small end of omniscience, and
+  the effect it has had on common life, from the family parlor to the
+  jury-box, from the girls'-school to the vestry-meeting. There are in the
+  Society those who would, were there no others, prevent my criticism, be
+  its conclusions true or false, from having any basis; but they are in the
+  minority.</p>
+
+  <p>There is no objection to be made to the principles of philosophy in
+  vogue at the Society, when they are stated as principles; but there is an
+  omniscience in daily practice which the principles repudiate. In like
+  manner, the most retaliatory Christians have a perfect form of round
+  words about behavior to those who injure them; none of them are as candid
+  as a little boy I knew, who, to his mother's admonition, You should love
+  your enemies, answered&mdash;Catch me at it!</p>
+
+  <p>Years ago, a change took place which would alone have <!-- Page 29
+  --><span class="pagenum"><a name="page29"></a>[29]</span>put a sufficient
+  difficulty in the way. The co-operative body got tired of getting funds
+  from and lending name to persons who had little or no science, and wanted
+  F.R.S. to be in every case a Fellow Really Scientific. Accordingly, the
+  number of yearly elections was limited to fifteen recommended by the
+  Council, unless the general body should choose to elect more; which it
+  does not do. The election is now a competitive examination: it is no
+  longer&mdash;Are you able and willing to promote natural knowledge; it
+  is&mdash;Are you one of the upper fifteen of those who make such claim.
+  In the list of candidates&mdash;a list rapidly growing in
+  number&mdash;each year shows from thirty to forty of those whom Newton
+  and Boyle would have gladly welcomed as fellow-laborers. And though the
+  rejected of one year may be the accepted of the next&mdash;or of the next
+  but one, or but two, if self-respect will permit the candidate to hang
+  on&mdash;yet the time is clearly coming when many of those who ought to
+  be welcomed will be excluded for life, or else shelved at last, when past
+  work, with a scientific peerage. Coupled with this attempt to create a
+  kind of order of knighthood is an absurdity so glaring that it should
+  always be kept before the general eye. This distinction, this mark set by
+  science upon successful investigation, is of necessity a
+  class-distinction. Rowan Hamilton, one of the greatest names of our day
+  in mathematical science, never could attach F.R.S. to his
+  name&mdash;<i>he could not afford it</i>. There is a condition
+  precedent&mdash;Four Red Sovereigns. It is four pounds a year,
+  or&mdash;to those who have contributed to the Transactions&mdash;forty
+  pounds down. This is as it should be: the Society must be supported. But
+  it is not as it should be that a kind of title of honor should be forged,
+  that a body should take upon itself to confer distinctions <i>for
+  science</i>, when it is in the background&mdash;and kept there when the
+  distinction is trumpeted&mdash;that the wearer is a man who can spare
+  four pounds a year. I am well aware that in England a person who is not
+  gifted either by nature or art, with this amount of money power, <!--
+  Page 30 --><span class="pagenum"><a name="page30"></a>[30]</span>is, with
+  the mass, a very second-rate sort of Newton, whatever he may be in the
+  field of investigation. Even men of science, so called, have this
+  feeling. I know that the <i>scientific advisers</i> of the Admiralty,
+  who, years ago, received 100 pounds a year each for his trouble, were
+  sneered at by a wealthy pretender as "fellows to whom a hundred a year is
+  an object." Dr. Thomas Young was one of them. To a bookish man&mdash;I
+  mean a man who can manage to collect books&mdash;there is no tax. To
+  myself, for example, 40 pounds worth of books deducted from my shelves,
+  and the life-use of the Society's splendid library instead, would have
+  been a capital exchange. But there may be, and are, men who want books,
+  and cannot pay the Society's price. The Council would be very liberal in
+  allowing books to be consulted. I have no doubt that if a known
+  investigator were to call and ask to look at certain books, the
+  Assistant-Secretary would forthwith seat him with the books before him,
+  absence of F.R.S. not in any wise withstanding. But this is not like
+  having the right to consult any book on any day, and to take it away, if
+  farther wanted.</p>
+
+  <p>So much for the Royal Society as concerns myself. I must add that
+  there is not a spark of party feeling against those who wilfully remain
+  outside. The better minds of course know better; and the smaller
+  <i>savants</i> look complacently on the idea of an outer world which
+  makes <i>élite</i> of them. I have done such a thing as serve on a
+  committee of the Society, and report on a paper: they had the sense to
+  ask, and I had the sense to see that none of my opinions were compromised
+  by compliance. And I will be of any use which does not involve the status
+  of <i>homo trium literarum</i>; as I have elsewhere explained, I would
+  gladly be <i>Fautor Realis Scientiæ</i>, but I would not be taken for
+  <i>Falsæ Rationis Sacerdos</i>.</p>
+
+  <p>Nothing worse will ever happen to me than the smile which individuals
+  bestow on a man who does not <i>groove</i>. Wisdom, like religion,
+  belongs to majorities; who can <!-- Page 31 --><span class="pagenum"><a
+  name="page31"></a>[31]</span>wonder that it should be so thought, when it
+  is so clearly pictured in the New Testament from one end to the
+  other?</p>
+
+  <p>The counterpart of <i>paradox</i>, the isolated opinion of one or of
+  few, is the general opinion held by all the rest; and the counterpart of
+  false and absurd paradox is what is called the "vulgar error," the
+  <i>pseudodox</i>. There is one great work on this last subject, the
+  <i>Pseudodoxia Epidemica</i> of Sir Thomas Browne, the famous author of
+  the <i>Religio Medici</i>; it usually goes by the name of Browne "On
+  Vulgar Errors" (1st ed. 1646; 6th, 1672). A careful analysis of this work
+  would show that vulgar errors are frequently opposed by scientific
+  errors; but good sense is always good sense, and Browne's book has a vast
+  quantity of it.</p>
+
+  <p>As an example of bad philosophy brought against bad observation. The
+  Amphisbæna serpent was supposed to have two heads, one at each end;
+  partly from its shape, partly because it runs backwards as well as
+  forwards. On this Sir Thomas Browne makes the following remarks:</p>
+
+  <p>"And were there any such species or natural kind of animal, it would
+  be hard to make good those six positions of body which, according to the
+  three dimensions, are ascribed unto every Animal; that is, <i>infra</i>,
+  <i>supra</i>, <i>ante</i>, <i>retro</i>, <i>dextrosum</i>,
+  <i>sinistrosum</i>: for if (as it is determined) that be the anterior and
+  upper part wherein the senses are placed, and that the posterior and
+  lower part which is opposite thereunto, there is no inferior or former
+  part in this Animal; for the senses, being placed at both extreams, doth
+  make both ends anterior, which is impossible; the terms being Relative,
+  which mutually subsist, and are not without each other. And therefore
+  this duplicity was ill contrived to place one head at both extreams, and
+  had been more tolerable to have settled three or four at one. And
+  therefore also Poets have been more reasonable than Philosophers, and
+  <i>Geryon</i> or <i>Cerberus</i> less monstrous than <i>Amphisbæna</i>."
+  <!-- Page 32 --><span class="pagenum"><a
+  name="page32"></a>[32]</span></p>
+
+  <p>There may be paradox upon paradox: and there is a good instance in the
+  eighth century in the case of Virgil, an Irishman, Bishop of Salzburg and
+  afterwards Saint, and his quarrels with Boniface, an Englishman,
+  Archbishop of Mentz, also afterwards Saint. All we know about the matter
+  is, that there exists a letter of 748 from Pope Zachary, citing
+  Virgil&mdash;then, it seems, at most a simple priest, though the Pope was
+  not sure even of that&mdash;to Rome to answer the charge of maintaining
+  that there is another world (<i>mundus</i>) under our earth
+  (<i>terra</i>), with another sun and another moon. Nothing more is known:
+  the letter contains threats in the event of the charge being true; and
+  there history drops the matter. Since Virgil was afterwards a Bishop and
+  a Saint, we may fairly conclude that he died in the full flower of his
+  orthodox reputation. It has been supposed&mdash;and it seems
+  probable&mdash;that Virgil maintained that the earth is peopled all the
+  way round, so that under some spots there are antipodes; that his
+  contemporaries, with very dim ideas about the roundness of the earth, and
+  most of them with none at all, interpreted him as putting another earth
+  under ours&mdash;turned the other way, probably, like the second piece of
+  bread-and-butter in a sandwich, with a sun and moon of its own. In the
+  eighth century this would infallibly have led to an underground Gospel,
+  an underground Pope, and an underground Avignon for him to live in. When,
+  in later times, the idea of inhabitants for the planets was started, it
+  was immediately asked whether they had sinned, whether Jesus Christ died
+  for <i>them</i>, whether their wine and their water could be lawfully
+  used in the sacraments, etc.</p>
+
+  <p>On so small a basis as the above has been constructed a companion case
+  to the persecution of Galileo. On one side the positive assertion, with
+  indignant comment, that Virgil was deposed for antipodal heresy, on the
+  other, serious attempts at justification, palliation, or mystification.
+  Some writers say that Virgil was found guilty; others that he gave
+  satisfactory explanation, and became very good friends with <!-- Page 33
+  --><span class="pagenum"><a name="page33"></a>[33]</span>Boniface: for
+  all which see Bayle. Some have maintained that the antipodist was a
+  different person from the canonized bishop: there is a second Virgil,
+  made to order. When your shoes pinch, and will not stretch, always throw
+  them away and get another pair: the same with your facts. Baronius was
+  not up to the plan of a substitute: his commentator Pagi (probably
+  writing about 1690) argues for it in a manner which I think Baronius
+  would not have approved. This Virgil was perhaps a slippery fellow. The
+  Pope says he hears that Virgil pretended licence from him to claim one of
+  some new bishoprics: this he declares is totally false. It is part of the
+  argument that such a man as this could not have been created a Bishop and
+  a Saint: on this point there will be opinions and opinions.<a
+  name="NtA_10" href="#Nt_10"><sup>[10]</sup></a></p>
+
+  <p>Lactantius, four centuries before, had laughed at the antipodes in a
+  manner which seems to be ridicule thrown on the idea of the earth's
+  roundness. Ptolemy, without reference to the antipodes, describes the
+  extent of the inhabited part of the globe in a way which shows that he
+  could have had no objection to men turned opposite ways. Probably, in the
+  eighth century, the roundness of the earth was matter of thought only to
+  astronomers. It should always be remembered, especially by those who
+  affirm persecution of a true opinion, that but for our knowing from
+  Lactantius that the antipodal notion had been matter of assertion and
+  denial among theologians, we could never have had any great confidence in
+  Virgil really having maintained the simple theory of the existence of
+  antipodes. And even now we are not entitled to affirm it as having
+  historical proof: the evidence <!-- Page 34 --><span class="pagenum"><a
+  name="page34"></a>[34]</span>goes to Virgil having been charged with very
+  absurd notions, which it seems more likely than not were the absurd
+  constructions which ignorant contemporaries put upon sensible opinions of
+  his.</p>
+
+  <p>One curious part of this discussion is that neither side has allowed
+  Pope Zachary to produce evidence to character. He shall have been an
+  Urban, say the astronomers; an Urban he ought to have been, say the
+  theologians. What sort of man was Zachary? He was eminently sensible and
+  conciliatory; he contrived to make northern barbarians hear reason in a
+  way which puts him high among that section of the early popes who had the
+  knack of managing uneducated swordsmen. He kept the peace in Italy to an
+  extent which historians mention with admiration. Even Bale, that
+  Maharajah of pope-haters, allows himself to quote in favor of Zachary,
+  that "multa Papalem dignitatem decentia, eademque præclara (scilicet)
+  opera confecit."<a name="NtA_11" href="#Nt_11"><sup>[11]</sup></a> And
+  this, though so willing to find fault that, speaking of Zachary putting a
+  little geographical description of the earth on the portico of the
+  Lateran Church, he insinuates that it was intended to affirm that the
+  Pope was lord of the whole. Nor can he say how long Zachary held the see,
+  except by announcing his death in 752, "cum decem annis pestilentiæ sedi
+  præfuisset."<a name="NtA_12" href="#Nt_12"><sup>[12]</sup></a></p>
+
+  <p>There was another quarrel between Virgil and Boniface which is an
+  illustration. An ignorant priest had baptized "in nomine Patri<i>a</i>,
+  et Fili<i>a</i> et Spiritu<i>a</i> Sanct<i>a</i>." Boniface declared the
+  rite null and void: Virgil maintained the contrary; and Zachary decided
+  in favor of Virgil, on the ground that the absurd form was only ignorance
+  of Latin, and not heresy. It is hard to believe that this man deposed a
+  priest for asserting the whole globe to be inhabited. To me the little
+  information that we have seems <!-- Page 35 --><span class="pagenum"><a
+  name="page35"></a>[35]</span>to indicate&mdash;but not with
+  certainty&mdash;that Virgil maintained the antipodes: that his ignorant
+  contemporaries travestied his theory into that of an underground cosmos;
+  that the Pope cited him to Rome to explain his system, which, as
+  reported, looked like what all would then have affirmed to be heresy;
+  that he gave satisfactory explanations, and was dismissed with honor. It
+  may be that the educated Greek monk, Zachary, knew his Ptolemy well
+  enough to guess what the asserted heretic would say; we have seen that he
+  seems to have patronized geography. The <i>description</i> of the earth,
+  according to historians, was a <i>map</i>; this Pope may have been more
+  ready than another to prick up his ears at any rumor of geographical
+  heresy, from hope of information. And Virgil, who may have entered the
+  sacred presence as frightened as Jacquard, when Napoleon I sent for him
+  and said, with a stern voice and threatening gesture, "You are the man
+  who can tie a knot in a stretched string," may have departed as well
+  pleased as Jacquard with the riband and pension which the interview was
+  worth to him.</p>
+
+  <p>A word more about Baronius. If he had been pope, as he would have been
+  but for the opposition of the Spaniards, and if he had lived ten years
+  longer than he did, and if Clavius, who would have been his astronomical
+  adviser, had lived five years longer than he did, it is probable, nay
+  almost certain, that the great exhibition, the proceeding against
+  Galileo, would not have furnished a joke against theology in all time to
+  come. For Baronius was sensible and witty enough to say that in the
+  Scriptures the Holy Spirit intended to teach how to go to Heaven, not how
+  Heaven goes; and Clavius, in his last years, confessed that the whole
+  system of the heavens had broken down, and must be mended.</p>
+
+  <p>The manner in which the Galileo case, a reality, and the Virgil case,
+  a fiction, have been hawked against the Roman see are enough to show that
+  the Pope and his adherents have not cared much about physical philosophy.
+  In truth, orthodoxy has always had other fish to fry. Physics, which <!--
+  Page 36 --><span class="pagenum"><a name="page36"></a>[36]</span>in
+  modern times has almost usurped the name <i>philosophy</i>, in England at
+  least, has felt a little disposed to clothe herself with all the honors
+  of persecution which belong to the real owner of the name. But the
+  bishops, etc. of the Middle Ages knew that the contest between nominalism
+  and realism, for instance, had a hundred times more bearing upon
+  orthodoxy than anything in astronomy, etc. A wrong notion about
+  <i>substance</i> might play the mischief with
+  <i>transubstantiation</i>.</p>
+
+  <p>The question of the earth's motion was the single point in which
+  orthodoxy came into real contact with science. Many students of physics
+  were suspected of magic, many of atheism: but, stupid as the mistake may
+  have been, it was <i>bona fide</i> the magic or the atheism, not the
+  physics, which was assailed. In the astronomical case it was the very
+  doctrine, as a doctrine, independently of consequences, which was the
+  <i>corpus delicti</i>: and this because it contradicted the Bible. And so
+  it did; for the stability of the earth is as clearly assumed from one end
+  of the Old Testament to the other as the solidity of iron. Those who take
+  the Bible to be <i>totidem verbis</i> dictated by the God of Truth can
+  refuse to believe it; and they make strange reasons. They undertake, <i>a
+  priori</i>, to settle Divine intentions. The Holy Spirit did not
+  <i>mean</i> to teach natural philosophy: this they know beforehand; or
+  else they infer it from finding that the earth does move, and the Bible
+  says it does not. Of course, ignorance apart, every word is truth, or the
+  writer did not mean truth. But this puts the whole book on its trial: for
+  we never can find out what the writer meant, until we otherwise find out
+  what is true. Those who like may, of course, declare for an inspiration
+  over which they are to be viceroys; but common sense will either accept
+  verbal meaning or deny verbal inspiration.</p>
+
+<hr class="full" >
+
+<p><!-- Page 37 --><span class="pagenum"><a name="page37"></a>[37]</span></p>
+
+<h2>A BUDGET OF PARADOXES.</h2>
+
+<h3>VOLUME I.</h3>
+
+<p class="cenhead">THE STORY OF BURIDAN'S ASS.</p>
+
+<blockquote class="b1n">
+
+  <p>Questiones Morales, folio, 1489 [Paris]. By T. Buridan.</p>
+
+</blockquote>
+
+  <p>This is the title from the Hartwell Catalogue of Law Books. I suppose
+  it is what is elsewhere called the "Commentary on the Ethics of
+  Aristotle," printed in 1489.<a name="NtA_13"
+  href="#Nt_13"><sup>[13]</sup></a> Buridan<a name="NtA_14"
+  href="#Nt_14"><sup>[14]</sup></a> (died about 1358) is the creator of the
+  famous ass which, as <i>Burdin's</i><a name="NtA_15"
+  href="#Nt_15"><sup>[15]</sup></a> ass, was current in Burgundy, perhaps
+  is, as a vulgar proverb. Spinoza<a name="NtA_16"
+  href="#Nt_16"><sup>[16]</sup></a> says it was a jenny ass, and that a man
+  would not have been so foolish; but whether the compliment is paid to
+  human or to masculine character does not appear&mdash;perhaps to both in
+  one. The story <i>told</i> about the famous paradox is very curious. The
+  Queen of France, Joanna or Jeanne, was in the habit of sewing her lovers
+  up in sacks, and throwing them into the Seine; not for blabbing, but that
+  they might not blab&mdash;certainly the safer plan. Buridan was exempted,
+  and, in gratitude, invented the sophism. What it has to do with the
+  matter <!-- Page 38 --><span class="pagenum"><a
+  name="page38"></a>[38]</span>has never been explained. Assuredly <i>qui
+  facit per alium facit per se</i> will convict Buridan of prating. The
+  argument is as follows, and is seldom told in full. Buridan was for
+  free-will&mdash;that is, will which determines conduct, let motives be
+  ever so evenly balanced. An ass is <i>equally</i> pressed by hunger and
+  by thirst; a bundle of hay is on one side, a pail of water on the other.
+  Surely, you will say, he will not be ass enough to die for want of food
+  or drink; he will then make a choice&mdash;that is, will choose between
+  alternatives of equal force. The problem became famous in the schools;
+  some allowed the poor donkey to die of indecision; some denied the
+  possibility of the balance, which was no answer at all.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">MICHAEL SCOTT'S DEVILS.</p>
+
+  <p>The following question is more difficult, and involves free-will to
+  all who answer&mdash;"Which you please." If the northern hemisphere were
+  land, and all the southern hemisphere water, ought we to call the
+  northern hemisphere an island, or the southern hemisphere a lake? Both
+  the questions would be good exercises for paradoxers who must be kept
+  employed, like Michael Scott's<a name="NtA_17"
+  href="#Nt_17"><sup>[17]</sup></a> devils. The wizard <!-- Page 39
+  --><span class="pagenum"><a name="page39"></a>[39]</span>knew nothing
+  about squaring the circle, etc., so he set them to make ropes out of sea
+  sand, which puzzled them. Stupid devils; much of our glass is sea sand,
+  and it makes beautiful thread. Had Michael set them to square the circle
+  or to find a perpetual motion, he would have done his work much better.
+  But all this is conjecture: who knows that I have not hit on the very
+  plan he adopted? Perhaps the whole race of paradoxers on hopeless
+  subjects are Michael's subordinates, condemned to transmigration after
+  transmigration, until their task is done.</p>
+
+  <p>The above was not a bad guess. A little after the time when the famous
+  Pascal papers<a name="NtA_18" href="#Nt_18"><sup>[18]</sup></a> were
+  produced, I came into possession of a correspondence which, but for these
+  papers, I should have held too incredible to be put before the world. But
+  when one sheep leaps the ditch, another will follow: so I gave the
+  following account in the <i>Athenæum</i> of October 5, 1867:</p>
+
+  <p>"The recorded story is that Michael Scott, being bound by contract to
+  produce perpetual employment for a number of young demons, was worried
+  out of his life in inventing jobs for them, until at last he set them to
+  make ropes out of sea sand, which they never could do. We have obtained a
+  very curious correspondence between the wizard Michael and his
+  demon-slaves; but we do not feel at liberty to say how it came into our
+  hands. We much regret that we did not receive it in time for the British
+  Association. It appears that the story, true as far as it goes, was never
+  finished. The demons easily conquered the rope difficulty, by the simple
+  process of making the sand into glass, and spinning the glass into
+  thread, which they twisted. Michael, thoroughly disconcerted, hit upon
+  the plan of setting some to <!-- Page 40 --><span class="pagenum"><a
+  name="page40"></a>[40]</span>square the circle, others to find the
+  perpetual motion, etc. He commanded each of them to transmigrate from one
+  human body into another, until their tasks were done. This explains the
+  whole succession of cyclometers, and all the heroes of the Budget. Some
+  of this correspondence is very recent; it is much blotted, and we are not
+  quite sure of its meaning: it is full of figurative allusions to driving
+  something illegible down a steep into the sea. It looks like a humble
+  petition to be allowed some diversion in the intervals of transmigration;
+  and the answer is&mdash;</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>Rumpat et serpens iter institutum,<a name="NtA_19" href="#Nt_19"><sup>[19]</sup></a></p>
+    </div>
+  </div>
+  <p>&mdash;a line of Horace, which the demons interpret as a direction to
+  come athwart the proceedings of the Institute by a sly trick. Until we
+  saw this, we were suspicious of M. Libri,<a name="NtA_20"
+  href="#Nt_20"><sup>[20]</sup></a> the unvarying blunders of the
+  correspondence look like knowledge. To be always out of the road requires
+  a map: genuine ignorance occasionally lapses into truth. We thought it
+  possible M. Libri might have played the trick to show how easily the
+  French are deceived; but with our present information, our minds are at
+  rest on the subject. We see M. Chasles does not like to avow the real
+  source of information: he will not confess himself a spiritualist."</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">PHILO OF GADARA.</p>
+
+  <p>Philo of Gadara<a name="NtA_21" href="#Nt_21"><sup>[21]</sup></a> is
+  asserted by Montucla,<a name="NtA_22" href="#Nt_22"><sup>[22]</sup></a>
+  on the <!-- Page 41 --><span class="pagenum"><a
+  name="page41"></a>[41]</span>authority of Eutocius,<a name="NtA_23"
+  href="#Nt_23"><sup>[23]</sup></a> the commentator on Archimedes, to have
+  squared the circle within the <i>ten-thousandth</i> part of a unit, that
+  is, to <i>four</i> places of decimals. A modern classical dictionary
+  represents it as done by Philo to <i>ten thousand</i> places of decimals.
+  Lacroix comments on Montucla to the effect that <i>myriad</i> (in Greek
+  <i>ten thousand</i>) is here used as we use it, vaguely, for an immense
+  number. On looking into Eutocius, I find that not one definite word is
+  said about the extent to which Philo carried the matter. I give a
+  translation of the passage:</p>
+
+  <p>"We ought to know that Apollonius Pergæus, in his Ocytocium [this work
+  is lost], demonstrated the same by other numbers, and came nearer, which
+  seems more accurate, but has nothing to do with Archimedes; for, as
+  before said, he aimed only at going near enough for the wants of life.
+  Neither is Porus of Nicæa fair when he takes Archimedes to task for not
+  giving a line accurately equal to the circumference. He says in his Cerii
+  that his teacher, Philo of Gadara, had given a more accurate
+  approximation (<span title="eis akribesterous arithmous agagein" class="grk"
+  >&epsilon;&#x1F30;&sigmaf;
+  &#x1F00;&kappa;&rho;&iota;&beta;&epsilon;&sigma;&tau;&#x1F73;&rho;&omicron;&upsilon;&sigmaf;
+  &#x1F00;&rho;&iota;&theta;&mu;&omicron;&#x1F7A;&sigmaf;
+  &#x1F00;&gamma;&#x1F71;&gamma;&epsilon;&iota;&nu;</span>) than that of
+  Archimedes, or than 7 to 22. But all these [the rest as well as Philo]
+  miss the intention. They multiply and divide by <i>tens of thousands</i>,
+  which no one can easily do, unless he be versed in the logistics
+  [fractional computation] of Magnus [now unknown]."</p>
+
+  <p>Montucla, or his source, ought not to have made this mistake. He had
+  been at the Greek to correct Philo <i>Gadetanus</i>, as he had often been
+  called, and he had brought away <!-- Page 42 --><span class="pagenum"><a
+  name="page42"></a>[42]</span>and quoted <span title="apo Gadarôn" class="grk"
+  >&#x1F00;&pi;&#x1F78;
+  &Gamma;&#x1F71;&delta;&alpha;&rho;&omega;&nu;</span>. Had he read two
+  sentences further, he would have found the mistake.</p>
+
+  <p>We here detect a person quite unnoticed hitherto by the moderns,
+  Magnus the arithmetician. The phrase is ironical; it is as if we should
+  say, "To do this a man must be deep in Cocker."<a name="NtA_24"
+  href="#Nt_24"><sup>[24]</sup></a> Accordingly, Magnus, Baveme,<a
+  name="NtA_25" href="#Nt_25"><sup>[25]</sup></a> and Cocker, are three
+  personifications of arithmetic; and there may be more.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON SQUARING THE CIRCLE.</p>
+
+  <p>Aristotle, treating of the category of relation, denies that the
+  quadrature has been found, but appears to assume that it can be done.
+  Boethius,<a name="NtA_26" href="#Nt_26"><sup>[26]</sup></a> in his
+  comment on the passage, says that it has been done since Aristotle, but
+  that the demonstration is too long for him to give. Those who have no
+  notion of the quadrature question may look at the <i>English
+  Cyclopædia</i>, art. "Quadrature of the Circle."</p>
+
+<blockquote class="b1n">
+
+  <p>Tetragonismus. Id est circuli quadratura per Campanum, Archimedem
+  Syracusanum, atque Boetium mathematicæ perspicacissimos
+  adinventa.&mdash;At the end, Impressum Venetiis per Ioan. Bapti. Sessa.
+  Anno ab incarnatione Domini, 1503. Die 28 Augusti.</p>
+
+</blockquote>
+
+<p><!-- Page 43 --><span class="pagenum"><a name="page43"></a>[43]</span></p>
+
+  <p>This book has never been noticed in the history of the subject, and I
+  cannot find any mention of it. The quadrature of Campanus<a name="NtA_27"
+  href="#Nt_27"><sup>[27]</sup></a> takes the ratio of Archimedes,<a
+  name="NtA_28" href="#Nt_28"><sup>[28]</sup></a> 7 to 22 to be absolutely
+  correct; the account given of Archimedes is not a translation of his
+  book; and that of Boetius has more than is in Boet<i>h</i>ius. This book
+  must stand, with the next, as the earliest in print on the subject, until
+  further showing: Murhard<a name="NtA_29"
+  href="#Nt_29"><sup>[29]</sup></a> and Kastner<a name="NtA_30"
+  href="#Nt_30"><sup>[30]</sup></a> have nothing so early. It is edited by
+  Lucas Gauricus,<a name="NtA_31" href="#Nt_31"><sup>[31]</sup></a> who has
+  given a short preface. Luca Gaurico, Bishop of Civita Ducale, an
+  astrologer of astrologers, published this work at about thirty years of
+  age, and lived to eighty-two. His works are collected in folios, but I do
+  not know whether they contain this production. The poor fellow could
+  never tell his own fortune, because his father neglected to note the hour
+  and minute of his birth. But if there had been anything in astrology, he
+  could have worked back, as Adams<a name="NtA_32"
+  href="#Nt_32"><sup>[32]</sup></a> and Leverrier<a name="NtA_33"
+  href="#Nt_33"><sup>[33]</sup></a> did when they caught <!-- Page 44
+  --><span class="pagenum"><a name="page44"></a>[44]</span>Neptune: at
+  sixty he could have examined every minute of his day of birth, by the
+  events of his life, and so would have found the right minute. He could
+  then have gone on, by rules of prophecy. Gauricus was the mathematical
+  teacher of Joseph Scaliger,<a name="NtA_34"
+  href="#Nt_34"><sup>[34]</sup></a> who did him no credit, as we shall
+  see.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">BOVILLUS ON THE QUADRATURE PROBLEM.</p>
+
+<blockquote class="b1n">
+
+  <p>In hoc opere contenta Epitome.... Liber de quadratura Circuli....
+  Paris, 1503, folio.</p>
+
+</blockquote>
+
+  <p>The quadrator is Charles Bovillus,<a name="NtA_35"
+  href="#Nt_35"><sup>[35]</sup></a> who adopted the views of Cardinal
+  Cusa,<a name="NtA_36" href="#Nt_36"><sup>[36]</sup></a> presently
+  mentioned. Montucla is hard on his compatriot, who, he says, was only
+  saved from the laughter of geometers by his obscurity. Persons must guard
+  against most historians of mathematics in one point: they frequently
+  attribute to <i>his own</i> age the obscurity which a writer has in
+  <i>their own</i> time. This tract was printed by Henry Stephens,<a
+  name="NtA_37" href="#Nt_37"><sup>[37]</sup></a> at the instigation of
+  Faber Stapulensis,<a name="NtA_38" href="#Nt_38"><sup>[38]</sup></a> <!--
+  Page 45 --><span class="pagenum"><a name="page45"></a>[45]</span>and is
+  recorded by Dechales,<a name="NtA_39" href="#Nt_39"><sup>[39]</sup></a>
+  etc. It was also introduced into the <i>Margarita Philosophica</i> of
+  1815,<a name="NtA_40" href="#Nt_40"><sup>[40]</sup></a> in the same
+  appendix with the new perspective from Viator. This is not extreme
+  obscurity, by any means. The quadrature deserved it; but that is another
+  point.</p>
+
+  <p>It is stated by Montucla that Bovillus makes <span
+  class="grk">&pi;</span> = &radic;10. But Montucla cites a work of 1507,
+  <i>Introductorium Geometricum</i>, which I have never seen.<a
+  name="NtA_41" href="#Nt_41"><sup>[41]</sup></a> He finds in it an account
+  which Bovillus gives of the quadrature of the peasant laborer, and
+  describes it as agreeing with his own. But the description makes <span
+  class="grk">&pi;</span> = 3-1/8, which it thus appears Bovillus could not
+  distinguish from &radic;10. It seems also that this 3-1/8, about which we
+  shall see so much in the sequel, takes its rise in the thoughtful head of
+  a poor laborer. It does him great honor, being so near the truth, and he
+  having no means of instruction. In our day, when an ignorant person
+  chooses to bring his fancy forward in opposition to demonstration which
+  he will not study, he is deservedly laughed at.</p>
+
+<p><!-- Page 46 --><span class="pagenum"><a name="page46"></a>[46]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE STORY OF LACOMME'S ATTEMPT AT QUADRATURE.</p>
+
+  <p>Mr. James Smith,<a name="NtA_42" href="#Nt_42"><sup>[42]</sup></a> of
+  Liverpool&mdash;hereinafter notorified&mdash;attributes the first
+  announcement of 3-1/8 to M. Joseph Lacomme, a French well-sinker, of whom
+  he gives the following account:</p>
+
+  <p>"In the year 1836, at which time Lacomme could neither read nor write,
+  he had constructed a circular reservoir and wished to know the quantity
+  of stone that would be required to pave the bottom, and for this purpose
+  called on a professor of mathematics. On putting his question and giving
+  the diameter, he was surprised at getting the following answer from the
+  Professor: <i>'Qu'il lui était impossible de le lui dire au juste,
+  attendu que personne n'avait encore pu trouver d'une manière exacte le
+  rapport de la circonférence au diametre.'</i><a name="NtA_43"
+  href="#Nt_43"><sup>[43]</sup></a> From this he was led to attempt the
+  solution of the problem. His first process was purely mechanical, and he
+  was so far convinced he had made the discovery that he took to educating
+  himself, and became an expert arithmetician, and then found that
+  arithmetical results agreed with his mechanical experiments. He appears
+  to have eked out a bare existence for many years by teaching arithmetic,
+  all the time struggling to get a hearing from some of the learned
+  societies, but without success. In the year 1855 he found his way to
+  Paris, where, as if by accident, he made the acquaintance of a young
+  gentleman, son of M. Winter, a commissioner of police, and taught him his
+  peculiar methods of calculation. The young man was so enchanted that he
+  strongly recommended Lacomme to his father, and <!-- Page 47 --><span
+  class="pagenum"><a name="page47"></a>[47]</span>subsequently through M.
+  Winter he obtained an introduction to the President of the Society of
+  Arts and Sciences of Paris. A committee of the society was appointed to
+  examine and report upon his discovery, and the society at its
+  <i>séance</i> of March 17, 1856, awarded a silver medal of the first
+  class to M. Joseph Lacomme for his discovery of the true ratio of
+  diameter to circumference in a circle. He subsequently received three
+  other medals from other societies. While writing this I have his likeness
+  before me, with his medals on his breast, which stands as a frontispiece
+  to a short biography of this extraordinary man, for which I am indebted
+  to the gentleman who did me the honor to publish a French translation of
+  the pamphlet I distributed at the meeting of the British Association for
+  the Advancement of Science, at Oxford, in
+  1860."&mdash;<i>Correspondent</i>, May 3, 1866.</p>
+
+  <p>My inquiries show that the story of the medals is not incredible.
+  There are at Paris little private societies which have not so much claim
+  to be exponents of scientific opinion as our own Mechanics' Institutes.
+  Some of them were intended to give a false lustre: as the "Institut
+  Historique," the members of which are "Membre de l'Institut Historique."
+  That M. Lacomme should have got four medals from societies of this class
+  is very possible: that he should have received one from any society at
+  Paris which has the least claim to give one is as yet simply
+  incredible.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">NICOLAUS OF CUSA'S ATTEMPT.</p>
+
+<blockquote class="b1n">
+
+  <p>Nicolai de Cusa Opera Omnia. Venice, 1514. 3 vols. folio.</p>
+
+</blockquote>
+
+  <p>The real title is "Hæc accurata recognitio trium voluminum operum
+  clariss. P. Nicolai Cusæ ... proxime sequens pagina monstrat."<a
+  name="NtA_44" href="#Nt_44"><sup>[44]</sup></a> Cardinal Cusa, who died
+  in 1464, is one of the earliest modern attempters. His quadrature is
+  found in the second volume, and is now quite unreadable.</p>
+
+<p><!-- Page 48 --><span class="pagenum"><a name="page48"></a>[48]</span></p>
+
+  <p>In these early days every quadrator found a geometrical opponent, who
+  finished him. Regimontanus<a name="NtA_45"
+  href="#Nt_45"><sup>[45]</sup></a> did this office for the Cardinal.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">HENRY CORNELIUS AGRIPPA.</p>
+
+<blockquote class="b1n">
+
+  <p>De Occulta Philosophia libri III. By Henry Cornelius Agrippa. Lyons,
+  1550, 8vo.</p>
+
+  <p>De incertitudine et vanitate scientiarum. By the same. Cologne, 1531,
+  8vo.</p>
+
+</blockquote>
+
+  <p>The first editions of these works were of 1530, as well as I can make
+  out; but the first was in progress in 1510.<a name="NtA_46"
+  href="#Nt_46"><sup>[46]</sup></a> In the second work Agrippa repents of
+  having wasted time on the magic of the first; but all those who actually
+  deal with demons are destined to eternal fire with Jamnes and Mambres and
+  Simon Magus. This means, as is the fact, that his occult philosophy did
+  not actually enter upon <i>black</i> magic, but confined itself to the
+  power of the stars, of numbers, etc. The fourth book, which appeared
+  after the death of Agrippa, and really concerns dealing with evil
+  spirits, is undoubtedly spurious. It is very difficult to make out what
+  Agrippa really believed on the subject. I have introduced his books as
+  the most marked specimens of treatises on magic, a paradox of our day,
+  though not far from orthodoxy in his; and here I should have ended my
+  notice, if I had not casually found something more interesting to the
+  reader of our day.</p>
+
+<p><!-- Page 49 --><span class="pagenum"><a name="page49"></a>[49]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">WHICH LEADS TO WALTER SCOTT.</p>
+
+  <p>Walter Scott, it is well known, was curious on all matters connected
+  with magic, and has used them very widely. But it is hardly known how
+  much pains he has taken to be correct, and to give the real thing. The
+  most decided detail of a magical process which is found in his writings
+  is that of Dousterswivel in <i>The Antiquary</i>; and it is obvious, by
+  his accuracy of process, that he does not intend the adept for a mere
+  impostor, but for one who had a lurking belief in the efficacy of his own
+  processes, coupled with intent to make a fraudulent use of them. The
+  materials for the process are taken from Agrippa. I first quote Mr.
+  Dousterswivel:</p>
+
+  <p>"... I take a silver plate when she [the moon] is in her fifteenth
+  mansion, which mansion is in de head of <i>Libra</i>, and I engrave upon
+  one side de worts <i>Schedbarschemoth Scharta</i>ch<i>an</i> [<i>ch</i>
+  should be <i>t</i>]&mdash;dat is, de Intelligence of de Intelligence of
+  de moon&mdash;and I make his picture like a flying serpent with a
+  turkey-cock's head&mdash;vary well&mdash;Then upon this side I make de
+  table of de moon, which is a square of nine, multiplied into itself, with
+  eighty-one numbers [nine] on every side and diameter nine...."</p>
+
+  <p>In the <i>De Occulta Philosophia</i>, p. 290, we find that the
+  fifteenth mansion of the moon <i>incipit capite Libræ</i>, and is good
+  <i>pro extrahendis thesauris</i>, the object being to discover hidden
+  treasure. In p. 246, we learn that a <i>silver</i> plate must be used
+  with the moon. In p. 248, we have the words which denote the
+  Intelligence, etc. But, owing to the falling of a number into a wrong
+  line, or the misplacement of a line, one or other&mdash;which takes place
+  in all the editions I have examined&mdash;Scott has, sad to say, got hold
+  of the wrong words; he has written down the <i>demon of the demons</i> of
+  the moon. Instead of the gibberish above, it should have been <i>Malcha
+  betarsisim hed beruah schenhakim</i>. In p. 253, we have the magic square
+  of the moon, with eighty-one numbers, and the symbol for the
+  Intelligence, which Scott likens to a flying <!-- Page 50 --><span
+  class="pagenum"><a name="page50"></a>[50]</span>serpent with a
+  turkey-cock's head. He was obliged to say something; but I will stake my
+  character&mdash;and so save a woodcut&mdash;on the scratches being more
+  like a pair of legs, one shorter than the other, without a body, jumping
+  over a six-barred gate placed side uppermost. Those who thought that
+  Scott forged his own nonsense, will henceforth stand corrected. As to the
+  spirit Peolphan, etc., no doubt Scott got it from the authors he
+  elsewhere mentions, Nicolaus Remigius<a name="NtA_47"
+  href="#Nt_47"><sup>[47]</sup></a> and Petrus Thyracus; but this last word
+  should be Thyræus.</p>
+
+  <p>The tendency of Scott's mind towards prophecy is very marked, and it
+  is always fulfilled. Hyder, in his disguise, calls out to Tippoo: "Cursed
+  is the prince who barters justice for lust; he shall die in the gate by
+  the sword of the stranger." Tippoo was killed in a gateway at
+  Seringapatam.<a name="NtA_48" href="#Nt_48"><sup>[48]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">FINAEUS ON CIRCLE SQUARING.</p>
+
+<blockquote class="b1n">
+
+  <p>Orontii Finaei ... Quadratura Circuli. Paris, 1544, 4to.</p>
+
+</blockquote>
+
+  <p>Orontius<a name="NtA_49" href="#Nt_49"><sup>[49]</sup></a> squared the
+  circle out of all comprehension; but he was killed by a feather from his
+  own wing. His <!-- Page 51 --><span class="pagenum"><a
+  name="page51"></a>[51]</span>former pupil, John Buteo,<a name="NtA_50"
+  href="#Nt_50"><sup>[50]</sup></a> the same who&mdash;I believe for the
+  first time&mdash;calculated the question of Noah's ark, as to its power
+  to hold all the animals and stores, unsquared him completely. Orontius
+  was the author of very many works, and died in 1555. Among the laudatory
+  verses which, as was usual, precede this work, there is one of a rare
+  character: a congratulatory ode to the wife of the author. The French now
+  call this writer Oronce Finée; but there is much difficulty about
+  delatinization. Is this more correct than Oronce Fine, which the
+  translator of De Thou uses? Or than Horonce Phine, which older writers
+  give? I cannot understand why M. de Viette<a name="NtA_51"
+  href="#Nt_51"><sup>[51]</sup></a> should be called Viète, because his
+  Latin name is Vieta. It is difficult to restore Buteo; for not only now
+  is <i>butor</i> a blockhead as well as a bird, but we really cannot know
+  what kind of bird Buteo stood for. We may be sure that Madame Fine was
+  Denise Blanche; for Dionysia Candida can mean nothing else. Let her shade
+  rejoice in the fame which Hubertus Sussannæus has given her.</p>
+
+  <p>I ought to add that the quadrature of Orontius, and solutions of all
+  the other difficulties, were first published in <i>De Rebus Mathematicis
+  Hactenus Desideratis</i>,<a name="NtA_52"
+  href="#Nt_52"><sup>[52]</sup></a> of which I have not the date.</p>
+
+  <p>&nbsp;</p>
+
+<p><!-- Page 52 --><span class="pagenum"><a name="page52"></a>[52]</span></p>
+
+<p class="cenhead">DUCHESNE, AND A DISQUISITION ON ETYMOLOGY.</p>
+
+<blockquote class="b1n">
+
+  <p>Nicolai Raymari Ursi Dithmarsi Fundamentum Astronomicum, id est, nova
+  doctrina sinuum et triangulorum.... Strasburg, 1588, 4to.<a name="NtA_53"
+  href="#Nt_53"><sup>[53]</sup></a></p>
+
+</blockquote>
+
+  <p>People choose the name of this astronomer for themselves: I take
+  <i>Ursus</i>, because he <i>was</i> a bear. This book gave the quadrature
+  of Simon Duchesne,<a name="NtA_54" href="#Nt_54"><sup>[54]</sup></a> or à
+  Quercu, which excited Peter Metius,<a name="NtA_55"
+  href="#Nt_55"><sup>[55]</sup></a> as presently noticed. It also gave that
+  unintelligible reference to Justus Byrgius which has been used in the
+  discussion about the invention of logarithms.<a name="NtA_56"
+  href="#Nt_56"><sup>[56]</sup></a></p>
+
+  <p>The real name of Duchesne is Van der Eycke. I have met with a tract in
+  Dutch, <i>Letterkundige Aanteekeningen</i>, upon Van Eycke, Van Ceulen,<a
+  name="NtA_57" href="#Nt_57"><sup>[57]</sup></a> etc., by J.&nbsp;J. Dodt van
+  Flensburg,<a name="NtA_58" href="#Nt_58"><sup>[58]</sup></a> which I make
+  out to be since 1841 in date. I should <!-- Page 53 --><span
+  class="pagenum"><a name="page53"></a>[53]</span>much like a translation
+  of this tract to be printed, say in the <i>Phil. Mag.</i> Dutch would be
+  clear English if it were properly spelt. For example, <i>learn-master</i>
+  would be seen at once to be <i>teacher</i>; but they will spell it
+  <i>leermeester</i>. <i>Of these</i> they write as <i>van deze</i>;
+  <i>widow</i> they make <i>weduwe</i>. All this is plain to me, who never
+  saw a Dutch dictionary in my life; but many of their misspellings are
+  quite unconquerable.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">FALCO'S RARE TRACT.</p>
+
+<blockquote class="b1n">
+
+  <p>Jacobus Falco Valentinus, miles Ordinis Montesiani, hanc circuli
+  quadraturam invenit. Antwerp, 1589, 4to.<a name="NtA_59"
+  href="#Nt_59"><sup>[59]</sup></a></p>
+
+</blockquote>
+
+  <p>The attempt is more than commonly worthless; but as Montucla and
+  others have referred to the verses at the end, and as the tract is of the
+  rarest, I will quote them:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="i4"><i>Circulus loquitur.</i></p>
+      <p>Vocabar ante circulus</p>
+      <p>Eramque curvus undique</p>
+      <p>Ut alta solis orbita</p>
+      <p>Et arcus ille nubium.</p>
+      <p>Eram figura nobilis</p>
+      <p>Carensque sola origine</p>
+      <p>Carensque sola termino.</p>
+      <p>Modo indecora prodeo</p>
+      <p>Novisque f&oelig;dor angulis.</p>
+      <p>Nec hoc peregit Archytas<a name="NtA_60" href="#Nt_60"><sup>[60]</sup></a></p>
+      <p>Neque Icari pater neque</p>
+      <p>Tuus, Iapete, filius.</p>
+      <p>Quis ergo casus aut Deus</p>
+      <p>Meam quadravit aream?</p>
+    </div>
+
+    <div class="stanza">
+      <p class="i4"><i>Respondet auctor.</i></p>
+      <p>Ad alta Turiæ ostia</p>
+      <p>Lacumque limpidissimum</p>
+      <p>Sita est beata civitas</p>
+<!-- Page 54 --><span class="pagenum"><a name="page54"></a>[54]</span>
+      <p>Parum Saguntus abfuit</p>
+      <p>Abestque Sucro plusculum.</p>
+      <p>Hic est poeta quispiam</p>
+      <p>Libenter astra consulens</p>
+      <p>Sibique semper arrogans</p>
+      <p>Negata doctioribus,</p>
+      <p>Senex ubique cogitans</p>
+      <p>Sui frequenter immemor</p>
+      <p>Nec explicare circinum</p>
+      <p>Nec exarare lineas</p>
+      <p>Sciens ut ipse prædicat.</p>
+      <p>Hic ergo bellus artifex</p>
+      <p>Tuam quadravit aream.<a name="NtA_61" href="#Nt_61"><sup>[61]</sup></a></p>
+    </div>
+  </div>
+  <p>Falco's verses are pretty, if the &#x2D8;-mysteries be correct; but of
+  these things I have forgotten&mdash;what I knew. [One mistake has been
+  pointed out to me: it is Arch<span class="over">y</span>tas].</p>
+
+  <p>As a specimen of the way in which history is written, I copy the
+  account which Montucla&mdash;who is accurate when he writes about what he
+  has seen&mdash;gives of these verses. He gives the date 1587; he places
+  the verses at the beginning instead of the end; he says the circle thanks
+  its quadrator affectionately; and he says the good and modest chevalier
+  gives all the glory to the patron saint of his order. All of little
+  consequence, as it happens; but writing at second-hand makes as complete
+  mistakes about more important matters.</p>
+
+<p><!-- Page 55 --><span class="pagenum"><a name="page55"></a>[55]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">BUNGUS ON THE MYSTERY OF NUMBER.</p>
+
+<blockquote class="b1n">
+
+  <p>Petri Bungi Bergomatis Numerorum mysteria. Bergomi [Bergamo], 1591,
+  4to. Second Edition.</p>
+
+</blockquote>
+
+  <p>The first edition is said to be of 1585;<a name="NtA_62"
+  href="#Nt_62"><sup>[62]</sup></a> the third, Paris, 1618. Bungus is not
+  for my purpose on his own score, but those who gave the numbers their
+  mysterious characters: he is but a collector. He quotes or uses 402
+  authors, as we are informed by his list; this just beats Warburton,<a
+  name="NtA_63" href="#Nt_63"><sup>[63]</sup></a> whom some eulogist or
+  satirist, I forget which, holds up as having used 400 authors in some one
+  work. Bungus goes through 1, 2, 3, etc., and gives the account of
+  everything remarkable in which each number occurs; his accounts not being
+  always mysterious. The numbers which have nothing to say for themselves
+  are omitted: thus there is a gap between 50 and 60. In treating 666,
+  Bungus, a good Catholic, could not compliment the Pope with it, but he
+  fixes it on Martin Luther with a little forcing. If from A to I represent
+  1-10, from K to S 10-90, and from T to Z 100-500, we see:</p>
+
+<table class="nobctr" width="50%" summary="Martin Lutera 666" title="Martin Lutera 666">
+<tr><td style="width:2%" align="center">M</td>
+<td style="width:2%" align="center">A</td>
+<td style="width:2%" align="center">R</td>
+<td style="width:2%" align="center">T</td>
+<td style="width:2%" align="center">I</td>
+<td style="width:2%" align="center">N</td>
+<td style="width:2%" align="center">&nbsp;</td>
+<td style="width:2%" align="center">L</td>
+<td style="width:2%" align="center">U</td>
+<td style="width:2%" align="center">T</td>
+<td style="width:2%" align="center">E</td>
+<td style="width:2%" align="center">R</td>
+<td style="width:2%" align="center">A</td></tr>
+<tr><td align="center">30</td>
+<td align="center">1</td>
+<td align="center">80</td>
+<td align="center">100</td>
+<td align="center">9</td>
+<td align="center">40</td>
+<td align="center">&nbsp;</td>
+<td align="center">20</td>
+<td align="center">200</td>
+<td align="center">100</td>
+<td align="center">5</td>
+<td align="center">80</td>
+<td align="center">1</td></tr>
+</table>
+
+  <p>which gives 666. Again, in Hebrew, <i>Lulter</i> does the same:</p>
+
+<table class="nobctr" width="25%" summary="Hebrew Lulter 666" title="Hebrew Lulter 666">
+<tr>
+<td style="width:2%" align="center"><span lang="he" class="heb" title="R" ><bdo dir="rtl">&#x5E8;</bdo></span></td>
+<td style="width:2%" align="center"><span lang="he" class="heb" title="T" ><bdo dir="rtl">&#x5EA;</bdo></span></td>
+<td style="width:2%" align="center"><span lang="he" class="heb" title="L" ><bdo dir="rtl">&#x5DC;</bdo></span></td>
+<td style="width:2%" align="center"><span lang="he" class="heb" title="W" ><bdo dir="rtl">&#x5D5;</bdo></span></td>
+<td style="width:2%" align="center"><span lang="he" class="heb" title="L" ><bdo dir="rtl">&#x5DC;</bdo></span></td>
+</tr>
+<tr><td align="center">200</td>
+<td align="center">400</td>
+<td align="center">30</td>
+<td align="center">6</td>
+<td align="center">30</td></tr>
+</table>
+
+  <p>And thus two can play at any game. The second is better than the
+  first: to Latinize the surname and not the Christian <!-- Page 56
+  --><span class="pagenum"><a name="page56"></a>[56]</span>name is very
+  unscholarlike. The last number mentioned is a thousand millions; all
+  greater numbers are dismissed in half a page. Then follows an accurate
+  distinction between <i>number</i> and <i>multitude</i>&mdash;a thing much
+  wanted both in arithmetic and logic.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">WHICH LEADS TO A STORY ABOUT THE ROYAL SOCIETY.</p>
+
+  <p>What may be the use of such a book as this? The last occasion on which
+  it was used was the following. Fifteen or sixteen years ago the Royal
+  Society determined to restrict the number of yearly admissions to fifteen
+  men of science, and noblemen <i>ad libitum</i>; the men of science being
+  selected and recommended by the Council, with a power, since practically
+  surrendered, to the Society to elect more. This plan appears to me to be
+  directly against the spirit of their charter, the true intent of which
+  is, that all who are fit should be allowed to promote natural knowledge
+  in association, from and after the time at which they are both fit and
+  willing. It is also working more absurdly from year to year; the tariff
+  of fifteen per annum will soon amount to the practical exclusion of many
+  who would be very useful. This begins to be felt already, I suspect. But,
+  as appears above, the body of the Society has the remedy in its own
+  hands. When the alteration was discussed by the Council, my friend the
+  late Mr. Galloway,<a name="NtA_64" href="#Nt_64"><sup>[64]</sup></a> then
+  one of the body, opposed it strongly, and inquired particularly into the
+  reason why <i>fifteen</i>, of all numbers, was the one to be selected.
+  Was it because fifteen is seven and eight, typifying the Old Testament
+  Sabbath, and the New Testament day of the resurrection following? Was it
+  because Paul strove fifteen days against Peter, proving that he was a
+  doctor both of the Old and New Testament? Was it because the prophet
+  Hosea bought a lady <!-- Page 57 --><span class="pagenum"><a
+  name="page57"></a>[57]</span>for fifteen pieces of silver? Was it
+  because, according to Micah, seven shepherds and eight chiefs should
+  waste the Assyrians? Was it because Ecclesiastes commands equal reverence
+  to be given to both Testaments&mdash;such was the interpretation&mdash;in
+  the words "Give a portion to seven, and also to eight"? Was it because
+  the waters of the Deluge rose fifteen cubits above the
+  mountains?&mdash;or because they lasted fifteen decades of days? Was it
+  because Ezekiel's temple had fifteen steps? Was it because Jacob's ladder
+  has been supposed to have had fifteen steps? Was it because fifteen years
+  were added to the life of Hezekiah? Was it because the feast of
+  unleavened bread was on the fifteenth day of the month? Was it because
+  the scene of the Ascension was fifteen stadia from Jerusalem? Was it
+  because the stone-masons and porters employed in Solomon's temple
+  amounted to fifteen myriads? etc. The Council were amused and astounded
+  by the volley of fifteens which was fired at them; they knowing nothing
+  about Bungus, of which Mr. Galloway&mdash;who did not, as the French say,
+  indicate his sources&mdash;possessed the copy now before me. In giving
+  this anecdote I give a specimen of the book, which is exceedingly rare.
+  Should another edition ever appear, which is not very probable, he would
+  be but a bungling Bungus who should forget the <i>fifteen</i> of the
+  Royal Society.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">AND ALSO TO A QUESTION OF EVIDENCE.</p>
+
+  <p>[I make a remark on the different colors which the same person gives
+  to one story, according to the bias under which he tells it. My friend
+  Galloway told me how he had quizzed the Council of the Royal Society, to
+  my great amusement. Whenever I am struck by the words of any one, I carry
+  away a vivid recollection of position, gestures, tones, etc. I do not
+  know whether this be common or uncommon. I never recall this joke without
+  seeing before me my friend, leaning against his bookcase, with Bungus
+  open in his hand, and a certain half-depreciatory tone which he often
+  used <!-- Page 58 --><span class="pagenum"><a
+  name="page58"></a>[58]</span>when speaking of himself. Long after his
+  death, an F.R.S. who was present at the discussion, told me the story. I
+  did not say I had heard it, but I watched him, with Galloway at the
+  bookcase before me. I wanted to see whether the two would agree as to the
+  fact of an enormous budget of fifteens having been fired at the Council,
+  and they did agree perfectly. But when the paragraph of the Budget
+  appeared in the <i>Athenæum</i>, my friend, who seemed rather to object
+  to the <i>showing-up</i>, assured me that the thing was grossly
+  exaggerated; there was indeed a fifteen or two, but nothing like the
+  number I had given. I had, however, taken sharp note of the previous
+  narration.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">AND TO ANOTHER QUESTION OF EVIDENCE.</p>
+
+  <p>I will give another instance. An Indian officer gave me an account of
+  an elephant, as follows. A detachment was on the march, and one of the
+  gun-carriages got a wheel off the track, so that it was also off the
+  ground, and hanging over a precipice. If the bullocks had moved a step,
+  carriages, bullocks, and all must have been precipitated. No one knew
+  what could be done until some one proposed to bring up an elephant, and
+  let him manage it his own way. The elephant took a moment's survey of the
+  fix, put his trunk under the axle of the free wheel, and waited. The
+  surrounders, who saw what he meant, moved the bullocks gently forward,
+  the elephant followed, supporting the axle, until there was ground under
+  the wheel, when he let it quietly down. From all I had heard of the
+  elephant, this was not too much to believe. But when, years afterwards, I
+  reminded my friend of his story, he assured me that I had misunderstood
+  him, that the elephant was <i>directed</i> to put his trunk under the
+  wheel, and saw in a moment why. This is reasonable sagacity, and very
+  likely the correct account; but I am quite sure that, in the fit of
+  elephant-worship under which the story was first told, it was told as I
+  have first stated it.] <!-- Page 59 --><span class="pagenum"><a
+  name="page59"></a>[59]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">GIORDANO BRUNO AND HIS PARADOXES.</p>
+
+<blockquote class="b1n">
+
+  <p>[Jordani Bruni Nolani de Monade, Numero et Figura ... item de
+  Innumerabilibus, Immenso, et Infigurabili ... Frankfort, 1591, 8vo.<a
+  name="NtA_65" href="#Nt_65"><sup>[65]</sup></a></p>
+
+</blockquote>
+
+  <p>I cannot imagine how I came to omit a writer whom I have known so many
+  years, unless the following story will explain it. The officer reproved
+  the boatswain for perpetual swearing; the boatswain answered that he
+  heard the officers swear. "Only in an emergency," said the officer.
+  "That's just it," replied the other; "a boatswain's life is a life of
+  'mergency." Giordano Bruno was all paradox; and my mind was not alive to
+  his paradoxes, just as my ears might have become dead to the boatswain's
+  oaths. He was, as has been said, a vorticist before Descartes,<a
+  name="NtA_66" href="#Nt_66"><sup>[66]</sup></a> an optimist before
+  Leibnitz, a Copernican before Galileo. It would be easy to collect a
+  hundred strange opinions of his. He was born about 1550, and was roasted
+  alive at Rome, February 17, 1600, for the maintenance and defence of the
+  holy Church, and the rights and liberties of the same. These last words
+  are from the writ of our own good James I, under which Leggatt<a
+  name="NtA_67" href="#Nt_67"><sup>[67]</sup></a> was roasted at
+  Smithfield, in March 1612; and if I had a copy of the instrument under
+  which Wightman<a name="NtA_68" href="#Nt_68"><sup>[68]</sup></a> was
+  roasted at Lichfield, a month afterwards, I daresay I should <!-- Page 60
+  --><span class="pagenum"><a name="page60"></a>[60]</span>find something
+  quite as edifying. I extract an account which I gave of Bruno in the
+  <i>Comp. Alm.</i> for 1855:</p>
+
+  <p>"He was first a Dominican priest, then a Calvinist; and was roasted
+  alive at Rome, in 1600, for as many heresies of opinion, religious and
+  philosophical, as ever lit one fire. Some defenders of the papal cause
+  have at least worded their accusations so to be understood as imputing to
+  him villainous actions. But it is positively certain that his death was
+  due to opinions alone, and that retractation, even after sentence, would
+  have saved him. There exists a remarkable letter, written from Rome on
+  the very day of the murder, by Scioppius<a name="NtA_69"
+  href="#Nt_69"><sup>[69]</sup></a> (the celebrated scholar, a waspish
+  convert from Lutheranism, known by his hatred to Protestants and Jesuits)
+  to Rittershusius,<a name="NtA_70" href="#Nt_70"><sup>[70]</sup></a> a
+  well-known Lutheran writer on civil and canon law, whose works are in the
+  index of prohibited books. This letter has been reprinted by Libri (vol.
+  iv. p. 407). The writer informs his friend (whom he wished to convince
+  that even a Lutheran would have burnt Bruno) that all Rome would tell him
+  that Bruno died for Lutheranism; but this is because the Italians do not
+  know the difference between one heresy and another, in which simplicity
+  (says the writer) may God preserve them. That is to say, they knew the
+  difference between a live heretic and a roasted one by actual inspection,
+  but had no idea of the difference between a Lutheran and a Calvinist. The
+  countrymen of Boccaccio would have smiled at the idea which the German
+  scholar entertained of them. They said Bruno was burnt for Lutheranism, a
+  name under which they classed all Protestants: and they are better
+  witnesses than Schopp, or Scioppius. He then proceeds to describe to his
+  Protestant friend (to whom he would certainly not have omitted any act
+  which both their churches would have condemned) the mass of opinions with
+  which Bruno was charged; as that there <!-- Page 61 --><span
+  class="pagenum"><a name="page61"></a>[61]</span>are innumerable worlds,
+  that souls migrate, that Moses was a magician, that the Scriptures are a
+  dream, that only the Hebrews descended from Adam and Eve, that the devils
+  would be saved, that Christ was a magician and deservedly put to death,
+  etc. In fact, says he, Bruno has advanced all that was ever brought
+  forward by all heathen philosophers, and by all heretics, ancient and
+  modern. A time for retractation was given, both before sentence and
+  after, which should be noted, as well for the wretched palliation which
+  it may afford, as for the additional proof it gives that opinions, and
+  opinions only, brought him to the stake. In this medley of charges the
+  Scriptures are a dream, while Adam, Eve, devils, and salvation are
+  truths, and the Saviour a deceiver. We have examined no work of Bruno
+  except the <i>De Monade</i>, etc., mentioned in the text. A strong though
+  strange <i>theism</i> runs through the whole, and Moses, Christ, the
+  Fathers, etc., are cited in a manner which excites no remark either way.
+  Among the versions of the cause of Bruno's death is <i>atheism</i>: but
+  this word was very often used to denote rejection of revelation, not
+  merely in the common course of dispute, but by such writers, for
+  instance, as Brucker<a name="NtA_71" href="#Nt_71"><sup>[71]</sup></a>
+  and Morhof.<a name="NtA_72" href="#Nt_72"><sup>[72]</sup></a> Thus Morhof
+  says of the <i>De Monade, etc.</i>, that it exhibits no manifest signs of
+  atheism. What he means by the word is clear enough, when he thus speaks
+  of a work which acknowledges God in hundreds of places, and rejects
+  opinions as blasphemous in several. The work of Bruno in which his
+  astronomical opinions are contained is <i>De Monade, etc.</i> (Frankfort,
+  1591, 8vo). He is the most thorough-going Copernican possible, and throws
+  out almost every opinion, true or false, which has ever been discussed by
+  astronomers, from the theory of innumerable inhabited worlds and systems
+  to that <!-- Page 62 --><span class="pagenum"><a
+  name="page62"></a>[62]</span>of the planetary nature of comets. Libri
+  (vol. iv)<a name="NtA_73" href="#Nt_73"><sup>[73]</sup></a> has reprinted
+  the most striking part of his expressions of Copernican opinion."</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THIS LEADS TO THE CHURCH QUESTION.</p>
+
+  <p>The Satanic doctrine that a church may employ force in aid of its
+  dogma is supposed to be obsolete in England, except as an individual
+  paradox; but this is difficult to settle. Opinions are much divided as to
+  what the Roman Church would do in England, if she could: any one who
+  doubts that she claims the right does not deserve an answer. When the
+  hopes of the Tractarian section of the High Church were in bloom, before
+  the most conspicuous intellects among them had <i>transgressed</i> their
+  ministry, that they might go to their own place, I had the curiosity to
+  see how far it could be ascertained whether they held the only doctrine
+  which makes me the personal enemy of a sect. I found in one of their
+  tracts the assumption of a right to persecute, modified by an asserted
+  conviction that force was not efficient. I cannot now say that this tract
+  was one of the celebrated ninety; and on looking at the collection I find
+  it so poorly furnished with contents, etc., that nothing but searching
+  through three thick volumes would decide. In these volumes I find,
+  augmenting as we go on, declarations about the character and power of
+  "the Church" which have a suspicious appearance. The suspicion is
+  increased by that curious piece of sophistry, No. 87, on religious
+  reserve. The queer paradoxes of that tract leave us in doubt as to
+  everything but this, that the church(man) is not bound to give his whole
+  counsel in all things, and not bound to say what the things are in which
+  he does not give it. It is likely enough that some of the "rights and
+  liberties" are but scantily described. There is now no fear; but the time
+  was when, if not fear, there might be a looking for of fear to come;
+  nobody could then be so <!-- Page 63 --><span class="pagenum"><a
+  name="page63"></a>[63]</span>sure as we now are that the lion was only
+  asleep. There was every appearance of a harder fight at hand than was
+  really found needful.</p>
+
+  <p>Among other exquisite quirks of interpretation in the No. 87 above
+  mentioned is the following. God himself employs reserve; he is said to be
+  decked with light as with a garment (the old or prayer-book version of
+  Psalm civ. 2). To an ordinary apprehension this would be a strong image
+  of display, manifestation, revelation; but there is something more. "Does
+  not a garment veil in some measure that which it clothes? Is not that
+  very light concealment?"</p>
+
+  <p>This No. 87, admitted into a series, fixes upon the managers of the
+  series, who permitted its introduction, a strong presumption of that
+  underhand intent with which they were charged. At the same time it is
+  honorable to our liberty that this series could be published: though its
+  promoters were greatly shocked when the Essayists and Bishop Colenso<a
+  name="NtA_74" href="#Nt_74"><sup>[74]</sup></a> took a swing on the other
+  side. When No. 90 was under discussion, Dr. Maitland,<a name="NtA_75"
+  href="#Nt_75"><sup>[75]</sup></a> the librarian at Lambeth, asked
+  Archbishop Howley<a name="NtA_76" href="#Nt_76"><sup>[76]</sup></a> a
+  question about No. 89. "I did not so much as know there <i>was</i> a No.
+  89," was the answer. I am almost sure I have seen this in print, and
+  quite sure that Dr. Maitland told it to me. It is creditable that there
+  was so much freedom; but No. 90 was <i>too bad</i>, and was stopped.</p>
+
+  <p>The Tractarian mania has now (October 1866) settled down into a
+  chronic vestment disease, complicated with fits of transubstantiation,
+  which has taken the name of <!-- Page 64 --><span class="pagenum"><a
+  name="page64"></a>[64]</span><i>Ritualism</i>. The common sense of our
+  national character will not put up with a continuance of this grotesque
+  folly; millinery in all its branches will at last be advertised only over
+  the proper shops. I am told that the Ritualists give short and practical
+  sermons; if so, they may do good in the end. The English Establishment
+  has always contained those who want an excitement; the New Testament, in
+  its plain meaning, can do little for them. Since the Revolution,
+  Jacobitism, Wesleyanism, Evangelicism, Puseyism,<a name="NtA_77"
+  href="#Nt_77"><sup>[77]</sup></a> and Ritualism, have come on in turn,
+  and have furnished hot water for those who could not wash without it. If
+  the Ritualists should succeed in substituting short and practical
+  teaching for the high-spiced lectures of the doctrinalists, they will be
+  remembered with praise. John the Baptist would perhaps not have brought
+  all Jerusalem out into the wilderness by his plain and good sermons: it
+  was the camel's hair and the locusts which got him a congregation, and
+  which, perhaps, added force to his precepts. When at school I heard a
+  dialogue, between an usher and the man who cleaned the shoes, about Mr.
+  &mdash;&mdash;, a minister, a very corporate body with due area of
+  waistcoat. "He is a man of great erudition," said the first. "Ah, yes
+  sir," said Joe; "any one can see that who looks at that silk
+  waistcoat."]</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">OF THOMAS GEPHYRANDER SALICETUS.</p>
+
+  <p>[When I said at the outset that I had only taken books from my own
+  store, I should have added that I did not make any search for information
+  given as <i>part</i> of a work. Had I looked <i>through</i> all my books,
+  I might have made some curious additions. For instance, in Schott's
+  <i>Magia Naturalis</i><a name="NtA_78" href="#Nt_78"><sup>[78]</sup></a>
+  <!-- Page 65 --><span class="pagenum"><a
+  name="page65"></a>[65]</span>(vol. iii. pp. 756-778) is an account of the
+  quadrature of Gephyra<i>u</i>der, as he is misprinted in Montucla. He was
+  Thomas Gephyrander Salicetus; and he published two editions, in 1608 and
+  1609.<a name="NtA_79" href="#Nt_79"><sup>[79]</sup></a> I never even
+  heard of a copy of either. His work is of the extreme of absurdity: he
+  makes a distinction between geometrical and arithmetical fractions, and
+  evolves theorems from it. More curious than his quadrature is his name;
+  what are we to make of it? If a German, he is probably a German form of
+  <i>Bridgeman</i>. and Salicetus refers him to <i>Weiden</i>. But
+  <i>Thomas</i> was hardly a German Christian name of his time; of 526
+  German philosophers, physicians, lawyers, and theologians who were
+  biographed by Melchior Adam,<a name="NtA_80"
+  href="#Nt_80"><sup>[80]</sup></a> only two are of this name. Of these one
+  is Thomas Erastus,<a name="NtA_81" href="#Nt_81"><sup>[81]</sup></a> the
+  physician whose theological writings against the Church as a separate
+  power have given the name of Erastians to those who follow his doctrine,
+  whether they have heard of him or not. Erastus is little known;
+  accordingly, some have supposed that he must be Erastus, the friend of
+  St. Paul and Timothy (Acts xix. 22; 2 Tim. iv. 20; Rom. xvi. 23), but
+  what this gentleman did to earn the character is not hinted at. Few words
+  would have done: Gaius (Rom. xvi. 23) has an immortality which many more
+  noted men have missed, given by John Bunyan, out of seven words of St.
+  Paul. I was once told that the Erastians got their name from
+  <i>Blastus</i>, and I could not solve <i>bl = er</i>: at last I
+  remembered that Blastus was a <i>chamberlain</i><a name="NtA_82"
+  href="#Nt_82"><sup>[82]</sup></a> as well as Erastus; hence the
+  association which <!-- Page 66 --><span class="pagenum"><a
+  name="page66"></a>[66]</span>caused the mistake. The real heresiarch was
+  a physician who died in 1583; his heresy was promulgated in a work,
+  published immediately after his death by his widow, <i>De
+  Excommunicatione Ecclesiastica</i>. He denied the power of
+  excommunication on the principle above stated; and was answered by
+  Besa.<a name="NtA_83" href="#Nt_83"><sup>[83]</sup></a> The work was
+  translated by Dr. R. Lee<a name="NtA_84"
+  href="#Nt_84"><sup>[84]</sup></a> (Edinb. 1844, 8vo). The other is Thomas
+  Grynæus,<a name="NtA_85" href="#Nt_85"><sup>[85]</sup></a> a theologian,
+  nephew of Simon, who first printed Euclid in Greek; of him Adam says that
+  of works he published none, of learned sons four. If Gephyrander were a
+  Frenchman, his name is not so easily guessed at; but he must have been of
+  La Saussaye. The account given by Schott is taken from a certain Father
+  Philip Colbinus, who wrote against him.</p>
+
+  <p>In some manuscripts lately given to the Royal Society, David
+  Gregory,<a name="NtA_86" href="#Nt_86"><sup>[86]</sup></a> who seems to
+  have seen Gephyrander's work, calls him Salicetus <i>Westphalus</i>,
+  which is probably on the title-page. But the only Weiden I can find is in
+  Bavaria. Murhard has both editions in his Catalogue, but had plainly
+  never seen the books: he gives the author as Thomas Gep. Hyandrus,
+  Salicettus Westphalus. Murhard is a very old referee of mine; but who the
+  <i>non nominandus</i> was to see Montucla's <i>Gephyrander</i> in
+  Murhard's <i>Gep. Hyandrus</i>, both writers being usually accurate?]</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">NAPIER ON REVELATIONS.</p>
+
+<blockquote class="b1n">
+
+  <p>A plain discoverie of the whole Revelation of St. John ... whereunto
+  are annexed certain oracles of Sibylla.... Set Foorth by John Napeir L.
+  of Marchiston. London, 1611, 4to.<a name="NtA_87"
+  href="#Nt_87"><sup>[87]</sup></a></p>
+
+</blockquote>
+
+<p><!-- Page 67 --><span class="pagenum"><a name="page67"></a>[67]</span></p>
+
+  <p>The first edition was Edinburgh, 1593,<a name="NtA_88"
+  href="#Nt_88"><sup>[88]</sup></a> 4to. Napier<a name="NtA_89"
+  href="#Nt_89"><sup>[89]</sup></a> always believed that his great mission
+  was to upset the Pope, and that logarithms, and such things, were merely
+  episodes and relaxations. It is a pity that so many books have been
+  written about this matter, while Napier, as good as any, is forgotten and
+  unread. He is one of the first who gave us the six thousand years. "There
+  is a sentence of the house of Elias reserved in all ages, bearing these
+  words: The world shall stand six thousand years, and then it shall be
+  consumed by fire: two thousand yeares voide or without lawe, two thousand
+  yeares under the law, and two thousand yeares shall be the daies of the
+  Messias...."</p>
+
+  <p>I give Napier's parting salute: it is a killing dilemma:</p>
+
+  <p>"In summar conclusion, if thou o <i>Rome</i> aledges thyselfe
+  reformed, and to beleeue true Christianisme, then beleeue Saint
+  <i>John</i> the Disciple, whome Christ loued, publikely here in this
+  Reuelation proclaiming thy wracke, but if thou remain Ethnick in thy
+  priuate thoghts, beleeuing<a name="NtA_90"
+  href="#Nt_90"><sup>[90]</sup></a> the old Oracles of the <i>Sibyls</i>
+  reuerently keeped somtime in thy <i>Capitol</i>: then doth here this
+  <i>Sibyll</i> proclame also thy wracke. Repent therefore alwayes, in this
+  thy latter breath, as thou louest thine Eternall salvation.
+  <i>Amen</i>."</p>
+
+  <p>&mdash;Strange that Napier should not have seen that this appeal could
+  not succeed, unless the prophecies of the Apocalypse were no true
+  prophecies at all.</p>
+
+<p><!-- Page 68 --><span class="pagenum"><a name="page68"></a>[68]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">OF GILBERT'S DE MAGNETE.</p>
+
+<blockquote class="b1n">
+
+  <p>De Magnete magneticisque corporibus, et de magno magnete tellure. By
+  William Gilbert. London, 1600, folio.&mdash;There is a second edition;
+  and a third, according to Watt.<a name="NtA_91"
+  href="#Nt_91"><sup>[91]</sup></a></p>
+
+</blockquote>
+
+  <p>Of the great work on the magnet there is no need to speak, though it
+  was a paradox in its day. The posthumous work of Gilbert, "De Mundo
+  nostro sublunari philosophia nova" (Amsterdam, 1651, 4to)<a name="NtA_92"
+  href="#Nt_92"><sup>[92]</sup></a> is, as the title indicates, confined to
+  the physics of the globe and its atmosphere. It has never excited
+  attention: I should hope it would be examined with our present
+  lights.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">OF GIOVANNI BATISTA PORTA.</p>
+
+<blockquote class="b1n">
+
+  <p>Elementorum Curvilineorium Libri tres. By John Baptista Porta. Rome,
+  1610, 4to.<a name="NtA_93" href="#Nt_93"><sup>[93]</sup></a></p>
+
+</blockquote>
+
+  <p>This is a ridiculous attempt, which defies description, except that it
+  is all about lunules. Porta was a voluminous writer. His printer
+  announces fourteen works printed, and four to come, besides thirteen
+  plays printed, and eleven waiting. His name is, and will be, current in
+  treatises on physics for more reasons than one.</p>
+
+<p><!-- Page 69 --><span class="pagenum"><a name="page69"></a>[69]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">CATALDI ON THE QUADRATURE.</p>
+
+<blockquote class="b1n">
+
+  <p>Trattato della quadratura del cerchio. Di Pietro Antonio Cataldi.
+  Bologna, 1612, folio.<a name="NtA_94"
+  href="#Nt_94"><sup>[94]</sup></a></p>
+
+</blockquote>
+
+  <p>Rheticus,<a name="NtA_95" href="#Nt_95"><sup>[95]</sup></a> Vieta, and
+  Cataldi are the three untiring computers of Germany, France, and Italy;
+  Napier in Scotland, and Briggs<a name="NtA_96"
+  href="#Nt_96"><sup>[96]</sup></a> in England, come just after them. This
+  work claims a place as beginning with the quadrature of Pellegrino
+  Borello<a name="NtA_97" href="#Nt_97"><sup>[97]</sup></a> of Reggio, who
+  will have the circle to be exactly 3 diameters and 69/484 of a diameter.
+  Cataldi, taking Van Ceulen's approximation, works hard at the finding of
+  integers which nearly represent the ratio. He had not then the
+  <i>continued fraction</i>, a mode of representation which he gave the
+  next year in his work on the square root. He has but twenty of Van
+  Ceulen's thirty places, which he takes from Clavius<a name="NtA_98"
+  href="#Nt_98"><sup>[98]</sup></a>: and any one might be puzzled to know
+  whence the Italians got the result; Van Ceulen, in 1612, not having been
+  translated from Dutch. But Clavius names his comrade Gruenberger, and
+  attributes the approximation to them <!-- Page 70 --><span
+  class="pagenum"><a name="page70"></a>[70]</span>jointly; "Lud. a Collen
+  et Chr. Gruenbergerus<a name="NtA_99" href="#Nt_99"><sup>[99]</sup></a>
+  invenerunt," which he had no right to do, unless, to his private
+  knowledge, Gruenberger had verified Van Ceulen. And Gruenberger only
+  handed over twenty of the places. But here is one instance, out of many,
+  of the polyglot character of the Jesuit body, and its advantages in
+  literature.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">OF LANSBERGIUS.</p>
+
+<blockquote class="b1n">
+
+  <p>Philippi Lausbergii Cyclometriæ Novæ Libri Duo. Middleburg, 1616,
+  4to.<a name="NtA_100" href="#Nt_100"><sup>[100]</sup></a></p>
+
+</blockquote>
+
+  <p>This is one of the legitimate quadratures, on which I shall here only
+  remark that by candlelight it is quadrature under difficulties, for all
+  the diagrams are in red ink.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A TEXT LEADING TO REMARKS ON PRESTER JOHN.</p>
+
+<blockquote class="b1n">
+
+  <p>Recherches Curieuses des Mesures du Monde. By S. C. de V. Paris, 1626,
+  8vo (pp. 48).<a name="NtA_101" href="#Nt_101"><sup>[101]</sup></a></p>
+
+</blockquote>
+
+  <p>It is written by some Count for his son; and if all the French
+  nobility would have given their sons the same kind of instruction about
+  rank, the old French aristocracy would have been as prosperous at this
+  moment as the English peerage and squireage. I sent the tract to Capt.
+  Speke,<a name="NtA_102" href="#Nt_102"><sup>[102]</sup></a> shortly after
+  his arrival in England, thinking he might like <!-- Page 71 --><span
+  class="pagenum"><a name="page71"></a>[71]</span>to see the old names of
+  the Ethiopian provinces. But I first made a copy of all that relates to
+  Prester John,<a name="NtA_103" href="#Nt_103"><sup>[103]</sup></a>
+  himself a paradox. The tract contains, <i>inter alia</i>, an account of
+  the four empires; of the great Turk, the great Tartar, the great Sophy,
+  and the great Prester John. This word <i>great</i> (<i>grand</i>), which
+  was long used in the phrase "the great Turk," is a generic adjunct to an
+  emperor. Of the Tartars it is said that "c'est vne nation prophane et
+  barbaresque, sale et vilaine, qui mangent la chair demie cruë, qui
+  boiuent du laict de jument, et qui n'vsent de nappes et seruiettes que
+  pour essuyer leurs bouches et leurs mains."<a name="NtA_104"
+  href="#Nt_104"><sup>[104]</sup></a> Many persons have heard of Prester
+  John, and have a very indistinct idea of him. I give all that is said
+  about him, since the recent discussions about the Nile may give an
+  interest to the old notions of geography.</p>
+
+  <p>"Le grand Prestre Jean qui est le quatriesme en rang, est Empereur
+  d'Ethiopie, et des Abyssins, et se vante d'estre issu de la race de
+  Dauid, comme estant descendu de la Royne de Saba, Royne d'Ethiopie,
+  laquelle estant venuë en Hierusalem pour voir la sagesse de Salomon,
+  enuiron l'an du monde 2952, s'en retourna grosse d'vn fils qu'ils nomment
+  Moylech, duquel ils disent estre descendus en ligne directe. Et ainsi il
+  se glorifie d'estre le plus ancien Monarque de la terre, disant que son
+  Empire a duré plus de trois mil ans, ce que nul autre Empire ne peut
+  dire. Aussi met-il en ses tiltres ce qui s'ensuit: Nous, N. Souuerain en
+  mes Royaumes, vniquement aymé de Dieu, colomne de la foy, sorty de la
+  race de Inda, etc. Les limites de cet Empire touchent à la mer Rouge, et
+  aux montagnes d'Azuma vers <!-- Page 72 --><span class="pagenum"><a
+  name="page72"></a>[72]</span>l'Orient, et du costé de l'Occident, il est
+  borné du fleuue du Nil, qui le separe de la Nubie, vers le Septentrion il
+  a l'Ægypte, et au Midy les Royaumes de Congo, et de Mozambique, sa
+  longueur contenant quarante degré, qui font mille vingt cinq lieuës, et
+  ce depuis Congo ou Mozambique qui sont au Midy, iusqu'en Ægypte qui est
+  au Septentrion, et sa largeur contenant depuis le Nil qui est à
+  l'Occident, iusqu'aux montagnes d'Azuma, qui sont à l'Orient, sept cens
+  vingt cinq lieues, qui font vingt neuf degrez. Cét empire a sous soy
+  trente grandes Prouinces, sçavoir, Medra, Gaga, Alchy, Cedalon, Mantro,
+  Finazam, Barnaquez, Ambiam, Fungy, Angoté, Cigremaon, Gorga, Cafatez,
+  Zastanla, Zeth, Barly, Belangana, Tygra, Gorgany, Barganaza, d'Ancut,
+  Dargaly, Ambiacatina, Caracogly, Amara, Maon (<i>sic</i>), Guegiera,
+  Bally, Dobora et Macheda. Toutes ces Prouinces cy dessus sont situées
+  iustement sous la ligne equinoxiale, entres les Tropiques de Capricorne,
+  et de Cancer. Mais elles s'approchent de nostre Tropique, de deux cens
+  cinquante lieuës plus qu'elles ne font de l'autre Tropique. Ce mot de
+  Prestre Jean signifie grand Seigneur, et n'est pas Prestre comme
+  plusieurs pense, il a esté tousiours Chrestien, mais souuent
+  Schismatique: maintenant il est Catholique, et reconnaist le Pape pour
+  Souuerain Pontife. I'ay veu quelqu'vn des ses Euesques, estant en
+  Hierusalem, auec lequel i'ay conferé souuent par le moyen de nostre
+  trucheman: il estoit d'vn port graue et serieux, succiur (<i>sic</i>) en
+  son parler, mais subtil à merueilles en tout ce qu'il disoit. Il prenoit
+  grand plaisir au recit que je luy faisais de nos belles ceremonies, et de
+  la grauité de nos Prelats en leurs habits Pontificaux, et autres choses
+  que je laisse pour dire, que l'Ethiopien est ioyoux et gaillard, ne
+  ressemblant en rien a la saleté du Tartare, ny à l'affreux regard du
+  miserable Arabe, mais ils sont fins et cauteleux, et ne se fient en
+  personne, soupçonneux à merueilles, et fort devotieux, ils ne sont du
+  tout noirs comme l'on croit, i'entens parler de ceux qui ne sont pas sous
+  la ligne Equinoxiale, ny trop proches <!-- Page 73 --><span
+  class="pagenum"><a name="page73"></a>[73]</span>d'icelle, car ceux qui
+  sont dessous sont les Mores que nous voyons."<a name="NtA_105"
+  href="#Nt_105"><sup>[105]</sup></a></p>
+
+  <p>It will be observed that the author speaks of his conversation with an
+  Ethiopian bishop, about that bishop's sovereign. Something must have
+  passed between the two which satisfied the writer that the bishop
+  acknowledged his own sovereign under some title answering to Prester
+  John.</p>
+
+<p><!-- Page 74 --><span class="pagenum"><a name="page74"></a>[74]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">CONCERNING A TRACT BY FIENUS.</p>
+
+<blockquote class="b1n">
+
+  <p>De Cometa anni 1618 dissertationes Thomæ Fieni<a name="NtA_106"
+  href="#Nt_106"><sup>[106]</sup></a> et Liberti Fromondi<a name="NtA_107"
+  href="#Nt_107"><sup>[107]</sup></a> ... Equidem Thomæ Fieni epistolica
+  quæstio, An verum sit C&oelig;lum moveri et Terram quiescere? London,
+  1670, 8vo.</p>
+
+</blockquote>
+
+  <p>This tract of Fienus against the motion of the earth is a reprint of
+  one published in 1619.<a name="NtA_108"
+  href="#Nt_108"><sup>[108]</sup></a> I have given an account of it as a
+  good summary of arguments of the time, in the <i>Companion to the
+  Almanac</i> for 1836.</p>
+
+<p><!-- Page 75 --><span class="pagenum"><a name="page75"></a>[75]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON SNELL'S WORK.</p>
+
+<blockquote class="b1n">
+
+  <p>Willebrordi Snellii. R. F. Cyclometricus. Leyden, 1621, 4to.</p>
+
+</blockquote>
+
+  <p>This is a celebrated work on the approximative quadrature, which,
+  having the suspicious word <i>cyclometricus</i>, must be noticed here for
+  distinction.<a name="NtA_109" href="#Nt_109"><sup>[109]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON BACON'S NOVUM ORGANUM.</p>
+
+  <p>1620. In this year, Francis Bacon<a name="NtA_110"
+  href="#Nt_110"><sup>[110]</sup></a> published his <i>Novum Organum</i>,<a
+  name="NtA_111" href="#Nt_111"><sup>[111]</sup></a> which was long held in
+  England&mdash;but not until the last century&mdash;to be the work which
+  taught Newton and all his successors how to philosophize. That Newton
+  never mentions Bacon, nor alludes in any way to his works, passed for
+  nothing. Here and there a paradoxer ventured not to find all this
+  teaching in Bacon, but he was pronounced blind. In our day it begins to
+  be seen that, great as Bacon was, and great as his book really is, he is
+  not the philosophical father of modern discovery.</p>
+
+  <p>But old prepossession will find reason for anything. A learned friend
+  of mine wrote to me that he had discovered proof that Newton owned Bacon
+  for his master: the proof was that Newton, in some of his earlier
+  writings, used the <!-- Page 76 --><span class="pagenum"><a
+  name="page76"></a>[76]</span>phrase <i>experimentum crucis</i>, which is
+  Bacon's. Newton may have read some of Bacon, though no proof of it
+  appears. I have a dim idea that I once saw the two words attributed to
+  the alchemists: if so, there is another explanation; for Newton was
+  deeply read in the alchemists.</p>
+
+  <p>I subjoin a review which I wrote of the splendid edition of Bacon by
+  Spedding,<a name="NtA_112" href="#Nt_112"><sup>[112]</sup></a> Ellis,<a
+  name="NtA_113" href="#Nt_113"><sup>[113]</sup></a> and Heath.<a
+  name="NtA_114" href="#Nt_114"><sup>[114]</sup></a> All the opinions
+  therein expressed had been formed by me long before: most of the
+  materials were collected for another purpose.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>The Works of Francis Bacon. Edited by James Spedding, R. Leslie Ellis,
+  and Douglas D. Heath. 5 vols.<a name="NtA_115"
+  href="#Nt_115"><sup>[115]</sup></a></p>
+
+</blockquote>
+
+  <p>No knowledge of nature without experiment and observation: so said
+  Aristotle, so said Bacon, so acted Copernicus, Tycho Brahé,<a
+  name="NtA_116" href="#Nt_116"><sup>[116]</sup></a> Gilbert, Kepler,
+  Galileo, Harvey, etc., before Bacon wrote.<a name="NtA_117"
+  href="#Nt_117"><sup>[117]</sup></a> No derived knowledge <i>until</i>
+  experiment and observation are concluded: so said Bacon, and no one else.
+  We do not mean to say that he laid down his principle in these words, or
+  that he carried it to the utmost extreme: we mean that Bacon's ruling
+  idea was the <!-- Page 77 --><span class="pagenum"><a
+  name="page77"></a>[77]</span>collection of enormous masses of facts, and
+  then digested processes of arrangement and elimination, so artistically
+  contrived, that a man of common intelligence, without any unusual
+  sagacity, should be able to announce the truth sought for. Let Bacon
+  speak for himself, in his editor's English:</p>
+
+  <p>"But the course I propose for the discovery of sciences is such as
+  leaves but little to the acuteness and strength of wits, but places all
+  wits and understandings nearly on a level. For, as in the drawing of a
+  straight line or a perfect circle, much depends on the steadiness and
+  practice of the hand, if it be done by aim of hand only, but if with the
+  aid of rule or compass little or nothing, so it is exactly with my
+  plan.... For my way of discovering sciences goes far to level men's wits,
+  and leaves but little to individual excellence; because it performs
+  everything by the surest rules and demonstrations."</p>
+
+  <p>To show that we do not strain Bacon's meaning, we add what is said by
+  Hooke,<a name="NtA_118" href="#Nt_118"><sup>[118]</sup></a> whom we have
+  already mentioned as his professed disciple, and, we believe, his only
+  disciple of the day of Newton. We must, however, remind the reader that
+  Hooke was very little of a mathematician, and spoke of algebra from his
+  own idea of what others had told him:</p>
+
+  <p>"The intellect is not to be suffered to act without its helps, but is
+  continually to be assisted by some method or engine, which shall be as a
+  guide to regulate its actions, so as that it shall not be able to act
+  amiss. Of this engine, no man except the incomparable Verulam hath had
+  any thoughts and he indeed hath promoted it to a very good pitch; but
+  there is yet somewhat more to be added, which he seemed to want time to
+  complete. By this, as by that <!-- Page 78 --><span class="pagenum"><a
+  name="page78"></a>[78]</span>art of algebra in geometry, 'twill be very
+  easy to proceed in any natural inquiry, regularly and certainly.... For
+  as 'tis very hard for the most acute wit to find out any difficult
+  problem in geometry without the help of algebra ... and altogether as
+  easy for the meanest capacity acting by that method to complete and
+  perfect it, so will it be in the inquiry after natural knowledge."</p>
+
+  <p>Bacon did not live to mature the whole of this plan. Are we really to
+  believe that if he had completed the <i>Instauratio</i> we who write
+  this&mdash;and who feel ourselves growing bigger as we write
+  it&mdash;should have been on a level with Newton in physical discovery?
+  Bacon asks this belief of us, and does not get it. But it may be said,
+  Your business is with what he <i>did</i> leave, and with its
+  consequences. Be it so. Mr. Ellis says: "That his method is impracticable
+  cannot, I think, be denied, if we reflect not only that it never has
+  produced any result, but also that the process by which scientific truths
+  have been established cannot be so presented as even to appear to be in
+  accordance with it." That this is very true is well known to all who have
+  studied the history of discovery: those who deny it are bound to
+  establish either that some great discovery has been made by Bacon's
+  method&mdash;we mean by the part peculiar to Bacon&mdash;or, better
+  still, to show that some new discovery can be made, by actually making
+  it. No general talk about <i>induction</i>: no reliance upon the mere
+  fact that certain experiments or observations have been made; let us see
+  where <i>Bacon's induction</i> has been actually used or can be used.
+  Mere induction, <i>enumeratio simplex</i>, is spoken of by himself with
+  contempt, as utterly incompetent. For Bacon knew well that a thousand
+  instances may be contradicted by the thousand and first: so that no
+  enumeration of instances, however large, is "sure demonstration," so long
+  any are left.</p>
+
+  <p>The immortal Harvey, who was <i>inventing</i>&mdash;we use the word in
+  its old sense&mdash;the circulation of the blood, while <!-- Page 79
+  --><span class="pagenum"><a name="page79"></a>[79]</span>Bacon was in the
+  full flow of thought upon his system, may be trusted to say whether, when
+  the system appeared, he found any likeness in it to his own processes, or
+  what would have been any help to him, if he had waited for the <i>Novum
+  Organum</i>. He said of Bacon, "He writes philosophy like a Lord
+  Chancellor." This has been generally supposed to be only a sneer at the
+  <i>sutor ultra crepidam</i>; but we cannot help suspecting that there was
+  more intended by it. To us, Bacon is eminently the philosopher of
+  <i>error prevented</i>, not of <i>progress facilitated</i>. When we throw
+  off the idea of being <i>led right</i>, and betake ourselves to that of
+  being <i>kept from going wrong</i>, we read his writings with a sense of
+  their usefulness, his genius, and their probable effect upon purely
+  experimental science, which we can be conscious of upon no other
+  supposition. It amuses us to have to add that the part of Aristotle's
+  logic of which he saw the value was the book on <i>refutation of
+  fallacies</i>. Now is this not the notion of things to which the bias of
+  a practised lawyer might lead him? In the case which is before the Court,
+  generally speaking, truth lurks somewhere about the facts, and the
+  elimination of all error will show it in the residuum. The two senses of
+  the word <i>law</i> come in so as to look almost like a play upon words.
+  The judge can apply the law so soon as the facts are settled: the
+  physical philosopher has to deduce the law from the facts. Wait, says the
+  judge, until the facts are determined: did the prisoner take the goods
+  with felonious intent? did the defendant give what amounts to a warranty?
+  or the like. Wait, says Bacon, until all the facts, or all the obtainable
+  facts, are brought in: apply my rules of separation to the facts, and the
+  result shall come out as easily as by ruler and compasses. We think it
+  possible that Harvey might allude to the legal character of Bacon's
+  notions: we can hardly conceive so acute a man, after seeing what manner
+  of writer Bacon was, meaning only that he was a lawyer and had better
+  stick to his business. We do ourselves believe that Bacon's philosophy
+  <!-- Page 80 --><span class="pagenum"><a
+  name="page80"></a>[80]</span>more resembles the action of mind of a
+  common-law judge&mdash;not a Chancellor&mdash;than that of the physical
+  inquirers who have been supposed to follow in his steps. It seems to us
+  that Bacon's argument is, there can be nothing of law but what must be
+  either perceptible, or mechanically deducible, when all the results of
+  law, as exhibited in phenomena, are before us. Now the truth is, that the
+  physical philosopher has frequently to conceive law which never was in
+  his previous thought&mdash;to educe the unknown, not to choose among the
+  known. Physical discovery would be very easy work if the inquirer could
+  lay down his this, his that, and his t'other, and say, "Now, one of these
+  it must be; let us proceed to try which." Often has he done this, and
+  failed; often has the truth turned out to be neither this, that, nor
+  t'other. Bacon seems to us to think that the philosopher is a judge who
+  has to choose, upon ascertained facts, which of known statutes is to rule
+  the decision: he appears to us more like a person who is to write the
+  statute-book, with no guide except the cases and decisions presented in
+  all their confusion and all their conflict.</p>
+
+  <p>Let us take the well-known first aphorism of the <i>Novum
+  Organum</i>:</p>
+
+  <p>"Man being the servant and interpreter of nature, can do and
+  understand so much, and so much only, as he has observed in fact or in
+  thought of the course of nature: beyond this he neither knows anything
+  nor can do anything."</p>
+
+  <p>This aphorism is placed by Sir John Herschel<a name="NtA_119"
+  href="#Nt_119"><sup>[119]</sup></a> at the head of his <i>Discourse on
+  the Study of Natural Philosophy</i>: a book containing notions of
+  discovery far beyond any of which Bacon ever dreamed; and this because it
+  was written <!-- Page 81 --><span class="pagenum"><a
+  name="page81"></a>[81]</span>after discovery, instead of before. Sir John
+  Herschel, in his version, has avoided the translation of <i>re vel mente
+  observaverit</i>, and gives us only "by his observation of the order of
+  nature." In making this the opening of an excellent sermon, he has
+  imitated the theologians, who often employ the whole time of the
+  discourse in stuffing matter into the text, instead of drawing matter out
+  of it. By <i>observation</i> he (Herschel) means the whole course of
+  discovery, observation, hypothesis, deduction, comparison, etc. The type
+  of the Baconian philosopher as it stood in his mind, had been derived
+  from a noble example, his own father, William Herschel,<a name="NtA_120"
+  href="#Nt_120"><sup>[120]</sup></a> an inquirer whose processes would
+  have been held by Bacon to have been vague, insufficient, compounded of
+  chance work and sagacity, and too meagre of facts to deserve the name of
+  induction. In another work, his treatise on Astronomy,<a name="NtA_121"
+  href="#Nt_121"><sup>[121]</sup></a> Sir John Herschel, after noting that
+  a popular account can only place the reader on the threshold, proceeds to
+  speak as follows of all the higher departments of science. The italics
+  are his own:</p>
+
+  <p>"Admission to its sanctuary, and to the privileges and feelings of a
+  votary, is only to be gained by one means&mdash;<i>sound and sufficient
+  knowledge of mathematics, the great instrument of all exact inquiry,
+  without which no man can ever make such advances in this or any other of
+  the higher departments of science as can entitle him to form an
+  independent opinion on any subject of discussion within their
+  range</i>."</p>
+
+  <p>How is this? Man can know no more than he gets from observation, and
+  yet mathematics is the great instrument of all exact inquiry. Are the
+  results of mathematical deduction results of observation? We think it
+  likely that <!-- Page 82 --><span class="pagenum"><a
+  name="page82"></a>[82]</span>Sir John Herschel would reply that Bacon, in
+  coupling together <i>observare re</i> and <i>observare mente</i>, has
+  done what some wags said Newton afterwards did in his
+  study-door&mdash;cut a large hole of exit for the large cat, and a little
+  hole for the little cat.<a name="NtA_122"
+  href="#Nt_122"><sup>[122]</sup></a> But Bacon did no such thing: he never
+  included any deduction under observation. To mathematics he had a
+  dislike. He averred that logic and mathematics should be the handmaids,
+  not the mistresses, of philosophy. He meant that they should play a
+  subordinate and subsequent part in the dressing of the vast mass of facts
+  by which discovery was to be rendered equally accessible to Newton and to
+  us. Bacon himself was very ignorant of all that had been done by
+  mathematics; and, strange to say, he especially objected to astronomy
+  being handed over to the mathematicians. Leverrier and Adams, calculating
+  an unknown planet into visible existence by enormous heaps of algebra,
+  furnish the last comment of note on this specimen of the goodness of
+  Bacon's views. The following account of his knowledge of what had been
+  done in his own day or before it, is Mr. Spedding's collection of casual
+  remarks in Mr. Ellis's several prefaces:</p>
+
+  <p>"Though he paid great attention to astronomy, discussed carefully the
+  methods in which it ought to be studied, constructed for the satisfaction
+  of his own mind an elaborate theory of the heavens, and listened eagerly
+  for the news from the stars brought by Galileo's telescope, he appears to
+  have been utterly ignorant of the discoveries which had just been made by
+  Kepler's calculations. Though he complained in 1623 of the want of
+  compendious methods for facilitating arithmetical computations,
+  especially with regard to the doctrine of Series, and fully recognized
+  the importance of them as an aid to physical inquiries&mdash;he does not
+  say a word about Napier's Logarithms, which had been published only nine
+  years before and reprinted more than once in the <!-- Page 83 --><span
+  class="pagenum"><a name="page83"></a>[83]</span>interval. He complained
+  that no considerable advance had made in geometry beyond Euclid, without
+  taking any notice of what had been done by Archimedes and Apollonius. He
+  saw the importance of determining accurately the specific gravity of
+  different substances, and himself attempted to form a table of them by a
+  rude process of his own, without knowing of the more scientific though
+  still imperfect methods previously employed by Archimedes, Ghetaldus,<a
+  name="NtA_123" href="#Nt_123"><sup>[123]</sup></a> and Porta. He speaks
+  of the <span title="heurêka" class="grk"
+  >&epsilon;&#x1F55;&rho;&eta;&kappa;&alpha;</span> of Archimedes in a
+  manner which implies that he did not clearly apprehend either the nature
+  of the problem to be solved or the principles upon which the solution
+  depended. In reviewing the progress of mechanics, he makes no mention of
+  Archimedes himself, or of Stevinus,<a name="NtA_124"
+  href="#Nt_124"><sup>[124]</sup></a> Galileo, Guldinus,<a name="NtA_125"
+  href="#Nt_125"><sup>[125]</sup></a> or Ghetaldus. He makes no allusion to
+  the theory of equilibrium. He observes that a ball of one pound weight
+  will fall nearly as fast through the air as a ball of two, without
+  alluding to the theory of the acceleration of falling bodies, which had
+  been made known by Galileo more than thirty years before. He proposes an
+  inquiry with regard to the lever&mdash;namely, whether in a balance with
+  arms of different length but equal weight the distance from the fulcrum
+  has any effect upon the inclination,&mdash;though the theory of the lever
+  was as well understood in his own time as it is now. In making an
+  experiment <!-- Page 84 --><span class="pagenum"><a
+  name="page84"></a>[84]</span>of his own to ascertain the cause of the
+  motion of a windmill, he overlooks an obvious circumstance which makes
+  the experiment inconclusive, and an equally obvious variation of the same
+  experiment which would have shown him that his theory was false. He
+  speaks of the poles of the earth as fixed, in a manner which seems to
+  imply that he was not acquainted with the precession of the equinoxes;
+  and in another place, of the north pole being above and the south pole
+  below, as a reason why in our hemisphere the north winds predominate over
+  the south."</p>
+
+  <p>Much of this was known before, but such a summary of Bacon's want of
+  knowledge of the science of his own time was never yet collected in one
+  place. We may add, that Bacon seems to have been as ignorant of
+  Wright's<a name="NtA_126" href="#Nt_126"><sup>[126]</sup></a> memorable
+  addition to the resources of navigation as of Napier's addition to the
+  means of calculation. Mathematics was beginning to be the great
+  instrument of exact inquiry: Bacon threw the science aside, from
+  ignorance, just at the time when his enormous sagacity, applied to
+  knowledge, would have made him see the part it was to play. If Newton had
+  taken Bacon for his master, not he, but somebody else, would have been
+  Newton.<a name="NtA_127" href="#Nt_127"><sup>[127]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON METEOROLOGICAL OBSERVATORIES.</p>
+
+  <p>There is an attempt at induction going on, which has yielded little or
+  no fruit, the observations made in the meteorological observatories. This
+  attempt is carried on in a manner which would have caused Bacon to dance
+  for joy; for he lived in times when Chancellors did dance. <!-- Page 85
+  --><span class="pagenum"><a name="page85"></a>[85]</span>Russia, says M.
+  Biot,<a name="NtA_128" href="#Nt_128"><sup>[128]</sup></a> is covered by
+  an army of meteorographs, with generals, high officers, subalterns, and
+  privates with fixed and defined duties of observation. Other countries
+  have also their systematic observations. And what has come of it?
+  Nothing, says M. Biot, and nothing will ever come of it; the veteran
+  mathematician and experimental philosopher declares, as does Mr. Ellis,
+  that no single branch of science has ever been fruitfully explored in
+  this way. There is no <i>special object</i>, he says. Any one would
+  suppose that M. Biot's opinion, given to the French Government upon the
+  proposal to construct meteorological observatories in Algeria (<i>Comptes
+  Rendus</i>, vol. xli, Dec. 31, 1855), was written to support the mythical
+  Bacon, modern physics, against the real Bacon of the <i>Novum
+  Organum</i>. There is no <i>special object</i>. In these words lies the
+  difference between the two methods.</p>
+
+  <p>&nbsp;</p>
+
+  <p>[In the report to the Greenwich Board of Visitors for 1867 Mr. Airy,<a
+  name="NtA_129" href="#Nt_129"><sup>[129]</sup></a> speaking of the
+  increase of meteorological observatories, remarks, "Whether the effect of
+  this movement will be that millions of useless observations will be added
+  to the millions that already exist, or whether something may be expected
+  to result which will lead to a meteorological theory, I cannot hazard a
+  conjecture." This <i>is</i> a conjecture, and a very obvious one: if Mr.
+  Airy would have given 2-3/4<i>d.</i> for the chance of a meteorological
+  theory formed by masses of observations, he would never have said what I
+  have quoted.]</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">BASIS OF MODERN DISCOVERY.</p>
+
+  <p>Modern discoveries have not been made by large collections of facts,
+  with subsequent discussion, separation, and <!-- Page 86 --><span
+  class="pagenum"><a name="page86"></a>[86]</span>resulting deduction of a
+  truth thus rendered perceptible. A few facts have suggested an
+  <i>hypothesis</i>, which means a <i>supposition</i>, proper to explain
+  them. The necessary results of this supposition are worked out, and then,
+  and not till then, other facts are examined to see if these ulterior
+  results are found in nature. The trial of the hypothesis is the
+  <i>special object</i>: prior to which, hypothesis must have been started,
+  not by rule, but by that sagacity of which no description can be given,
+  precisely because the very owners of it do not act under laws perceptible
+  to themselves.<a name="NtA_130" href="#Nt_130"><sup>[130]</sup></a> The
+  inventor of hypothesis, if pressed to explain his method, must answer as
+  did Zerah Colburn,<a name="NtA_131" href="#Nt_131"><sup>[131]</sup></a>
+  when asked for his mode of instantaneous calculation. When the poor boy
+  had been bothered for some time in this manner, he cried out in a huff,
+  "God put it into my head, and I can't put it into yours."<a
+  name="NtA_132" href="#Nt_132"><sup>[132]</sup></a> <!-- Page 87 --><span
+  class="pagenum"><a name="page87"></a>[87]</span>Wrong hypotheses, rightly
+  worked from, have produced more useful results than unguided observation.
+  But this is not the Baconian plan. Charles the Second, when informed of
+  the state of navigation, founded a Baconian observatory at Greenwich, to
+  observe, observe, observe away at the moon, until her motions were known
+  sufficiently well to render her useful in guiding the seaman. And no
+  doubt Flamsteed's<a name="NtA_133" href="#Nt_133"><sup>[133]</sup></a>
+  observations, twenty or thirty of them at least, were of signal use. But
+  how? A somewhat fanciful thinker, one Kepler, had hit upon the
+  approximate orbits of the planets by trying one hypothesis after another:
+  he found the <i>ellipse</i>, which the Platonists, well despised of
+  Bacon, and who would have despised him as heartily if they had known him,
+  had investigated and put ready to hand nearly 2000 years before.<a
+  name="NtA_134" href="#Nt_134"><sup>[134]</sup></a> The sun in the focus,
+  the motions of the planet more and more rapid as they approach the sun,
+  led Kepler&mdash;and Bacon would have reproved him for his
+  rashness&mdash;to imagine that a force residing in the sun might move the
+  planets, a force inversely as the distance. Bouillaud,<a name="NtA_135"
+  href="#Nt_135"><sup>[135]</sup></a> upon a fanciful analogy, rejected the
+  inverse distance, <!-- Page 88 --><span class="pagenum"><a
+  name="page88"></a>[88]</span>and, rejecting the force altogether,
+  declared that if such a thing there were, it would be as the inverse
+  <i>square</i> of the distance. Newton, ready prepared with the
+  mathematics of the subject, tried the fall of the moon towards the earth,
+  away from her tangent, and found that, as compared with the fall of a
+  stone, the law of the inverse square did hold for the moon. He deduced
+  the ellipse, he proceeded to deduce the effect of the disturbance of the
+  sun upon the moon, upon the assumed theory of <i>universal</i>
+  gravitation. He found result after result of his theory in conformity
+  with observed fact: and, by aid of Flamsteed's observations, which
+  amended what mathematicians call his <i>constants</i>, he constructed his
+  lunar theory. Had it not been for Newton, the whole dynasty of Greenwich
+  astronomers, from Flamsteed of happy memory, to Airy whom Heaven
+  preserve,<a name="NtA_136" href="#Nt_136"><sup>[136]</sup></a> might have
+  worked away at nightly observation and daily reduction, without any
+  remarkable result: looking forward, as to a millennium, to the time when
+  any man of moderate intelligence was to see the whole explanation. What
+  are large collections of facts for? To make theories <i>from</i>, says
+  Bacon: to try ready-made theories <i>by</i>, says the history of
+  discovery: it's all the same, says the idolater: nonsense, say we!</p>
+
+  <p>Time and space run short: how odd it is that of the three leading
+  ideas of mechanics, time, space, and matter, the first two should always
+  fail a reviewer before the third. We might dwell upon many points,
+  especially if we attempted a more descriptive account of the valuable
+  edition before us. No one need imagine that the editors, by their
+  uncompromising attack upon the notion of Bacon's influence common even
+  among mathematicians and experimental philosophers, have lowered the
+  glory of the great man whom it was, many will think, their business to
+  defend through thick and thin. They have given a clearer notion of his
+  <!-- Page 89 --><span class="pagenum"><a
+  name="page89"></a>[89]</span>excellencies, and a better idea of the power
+  of his mind, than ever we saw given before. Such a correction as theirs
+  must have come, and soon, for as Hallam says&mdash;after noting that the
+  <i>Novum Organum</i> was <i>never published separately in England</i>,
+  Bacon has probably been more read in the last thirty years&mdash;now
+  forty&mdash;than in the two hundred years which preceded. He will now be
+  more read than ever he was. The history of the intellectual world is the
+  history of the worship of one idol after another. No sooner is it clear
+  that a Hercules has appeared among men, than all that imagination can
+  conceive of strength is attributed to him, and his labors are recorded in
+  the heavens. The time arrives when, as in the case of Aristotle, a new
+  deity is found, and the old one is consigned to shame and reproach. A
+  reaction may afterwards take place, and this is now happening in the case
+  of the Greek philosopher. The end of the process is, that the opposing
+  deities take their places, side by side, in a Pantheon dedicated not to
+  gods, but to heroes.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE REAL VALUE OF BACON'S WORKS.</p>
+
+  <p>Passing over the success of Bacon's own endeavors to improve the
+  details of physical science, which was next to nothing, and of his method
+  as a whole, which has never been practised, we might say much of the good
+  influence of his writings. Sound wisdom, set in sparkling wit, must
+  instruct and amuse to the end of time: and, as against error, we repeat
+  that Bacon is soundly wise, so far as he goes. There is hardly a form of
+  human error within his scope which he did not detect, expose, and attach
+  to a satirical metaphor which never ceases to sting. He is largely
+  indebted to a very extensive reading; but the thoughts of others fall
+  into his text with such a close-fitting compactness that he can make even
+  the words of the Sacred Writers pass for his own. A saying of the prophet
+  Daniel, rather a hackneyed quotation in our day, <i>Multi pertransibunt,
+  et augebitur scientia</i>, stands in the title-page of the first edition
+  <!-- Page 90 --><span class="pagenum"><a name="page90"></a>[90]</span>of
+  Montucla's <i>History of Mathematics</i> as a quotation from
+  Bacon&mdash;and it is not the only place in which this mistake occurs.
+  When the truth of the matter, as to Bacon's system, is fully recognized,
+  we have little fear that there will be a reaction against the man. First,
+  because Bacon will always live to speak for himself, for he will not
+  cease to be read: secondly, because those who seek the truth will find it
+  in the best edition of his works, and will be most ably led to know what
+  Bacon was, in the very books which first showed at large what he <i>was
+  not</i>.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE CONGREGATION OF THE INDEX, ON COPERNICUS.</p>
+
+  <p>In this year (1620) appeared the corrections under which the
+  Congregation of the Index&mdash;i.e., the Committee of Cardinals which
+  superintended the <i>Index</i> of forbidden books&mdash;proposed to allow
+  the work of Copernicus to be read. I insert these conditions in full,
+  because they are often alluded to, and I know of no source of reference
+  accessible to a twentieth part of those who take interest in the
+  question.</p>
+
+  <p>By a decree of the Congregation of the Index, dated March 5, 1616, the
+  work of Copernicus, and another of Didacus Astunica,<a name="NtA_137"
+  href="#Nt_137"><sup>[137]</sup></a> are suspended <i>donec
+  corrigantur</i>, as teaching:</p>
+
+  <p>"Falsam illam doctrinam Pythagoricam, divinæ que Scripturæ omnino
+  adversantem, de mobilitate Terræ et immobilitate Solis."<a name="NtA_138"
+  href="#Nt_138"><sup>[138]</sup></a></p>
+
+  <p>But a work of the Carmelite Foscarini<a name="NtA_139"
+  href="#Nt_139"><sup>[139]</sup></a> is:</p>
+
+<p><!-- Page 91 --><span class="pagenum"><a name="page91"></a>[91]</span></p>
+
+  <p>"Omnino prohibendum atque damnandum," because "ostendere conatur
+  præfatam doctrinam ... consonam esse veritati et non adversari Sacræ
+  Scripturæ."<a name="NtA_140" href="#Nt_140"><sup>[140]</sup></a></p>
+
+  <p>Works which teach the false doctrine of the earth's motion are to be
+  corrected; those which declare the doctrine conformable to Scripture are
+  to be utterly prohibited.</p>
+
+  <p>In a "Monitum ad Nicolai Copernici lectorem, ejusque emendatio,
+  permissio, et correctio," dated 1620 without the month or day, permission
+  is given to reprint the work of Copernicus with certain alterations; and,
+  by implication, to read existing copies after correction in writing. In
+  the preamble the author is called <i>nobilis astrologus</i>; not a
+  compliment to his birth, which was humble, but to his fame. The
+  suspension was because:</p>
+
+  <p>"Sacræ Scripturæ, ejusque veræ et Catholicæ interpretationi
+  repugnantia (quod in homine Christiano minime tolerandum) non <i>per
+  hypothesin</i> tractare, sed <i>ut verissima</i> adstruere non
+  dubitat!"<a name="NtA_141" href="#Nt_141"><sup>[141]</sup></a></p>
+
+  <p>And the corrections relate:</p>
+
+  <p>"Locis in quibus non <i>ex hypothesi</i>, sed <i>asserendo</i> de situ
+  et motu Terræ disputat."<a name="NtA_142"
+  href="#Nt_142"><sup>[142]</sup></a></p>
+
+  <p>That is, the earth's motion may be an hypothesis for elucidation of
+  the heavenly motions, but must not be asserted as a fact.</p>
+
+  <p>&nbsp;</p>
+
+  <p>(In Pref. circa finem.) "<i>Copernicus.</i> Si fortasse erunt <span
+  title="mataiologoi" class="grk"
+  >&mu;&alpha;&tau;&alpha;&iota;&#x1F79;&lambda;&omicron;&gamma;&omicron;&iota;</span>,
+  qui cum omnium Mathematum ignari sint, tamen de illis judicium sibi
+  summunt, propter aliquem locum scripturæ, male ad suum propositum
+  detortum, ausi fuerint meum <!-- Page 92 --><span class="pagenum"><a
+  name="page92"></a>[92]</span>hoc institutum reprehendere ac insectari:
+  illos nihil moror adeo ut etiam illorum judicium tanquam temerarium
+  contemnam. Non enim obscurum est Lactantium, celebrem alioqui scriptorem,
+  sed Mathematicum parum, admodum pueriliter de forma terræ loqui, cum
+  deridet eos, qui terram globi formam habere prodiderunt. Itaque non debet
+  mirum videri studiosis, si qui tales nos etiam videbunt. Mathemata
+  Mathematicis scribuntur, quibus et hi nostri labores, si me non fallit
+  opinio, videbuntur etiam Reipub. ecclesiasticæ conducere aliquid....
+  <i>Emend.</i> Ibi <i>si fortasse</i> dele omnia, usque ad verbum <i>hi
+  nostri labores</i> et sic accommoda&mdash;<i>C&oelig;terum hi nostri
+  labores</i>."<a name="NtA_143" href="#Nt_143"><sup>[143]</sup></a></p>
+
+  <p>All the allusion to Lactantius, who laughed at the notion of the earth
+  being round, which was afterwards found true, is to be struck out.</p>
+
+  <p>&nbsp;</p>
+
+  <p>(Cap. 5. lib. i. p. 3) "<i>Copernicus.</i> Si tamen attentius rem
+  consideremus, videbitur hæc quæstio nondum absoluta, et ideireo minime
+  contemnenda. <i>Emend.</i> Si tamen attentius rem consideremus, nihil
+  refert an Terram in medio Mundi, an extra Medium existere, quoad
+  solvendas c&oelig;lestium motuum apparentias existimemus."<a
+  name="NtA_144" href="#Nt_144"><sup>[144]</sup></a></p>
+
+<p><!-- Page 93 --><span class="pagenum"><a name="page93"></a>[93]</span></p>
+
+  <p>We must not say the question is not yet settled, but only that it may
+  be settled either way, so far as mere explanation of the celestial
+  motions is concerned.</p>
+
+  <p>&nbsp;</p>
+
+  <p>(Cap. 8. lib. i.) "Totum hoc caput potest expungi, quia ex professo
+  tractat de veritate motus Terræ, dum solvit veterum rationes probantes
+  ejus quietem. Cum tamen problematice videatur loqui; ut studiosis
+  satisfiat, seriesque et ordo libri integer maneat; emendetur ut infra."<a
+  name="NtA_145" href="#Nt_145"><sup>[145]</sup></a></p>
+
+  <p>A chapter which seems to assert the motion should perhaps be expunged;
+  but it may perhaps be problematical; and, not to break up the book, must
+  be amended as below.</p>
+
+  <p>&nbsp;</p>
+
+  <p>(p. 6.) "<i>Copernicus.</i> Cur ergo hesitamus adhuc, mobilitatem illi
+  formæ suæ a natura congruentem concedere, magisquam quod totus labatur
+  mundus, cujus finis ignoratur, scirique nequit, neque fateamur ipsius
+  cotidianæ revolutionis in c&oelig;lo apparentiam esse, et in terra
+  veritatem? Et hæc perinde se habere, ac si diceret Virgilianus Æneas:
+  Provehimur portu ... <i>Emend.</i> Cur ergo non possum mobilitatem illi
+  formæ suæ concedere, magisque quod totus labatur mundus, cujus finis
+  ignoratur scirique nequit, et quæ apparent in c&oelig;lo, perinde se
+  habere ac si ..."<a name="NtA_146"
+  href="#Nt_146"><sup>[146]</sup></a></p>
+
+<p><!-- Page 94 --><span class="pagenum"><a name="page94"></a>[94]</span></p>
+
+  <p>"Why should we hesitate to allow the earth's motion," must be altered
+  into "I cannot concede the earth's motion."</p>
+
+  <p>&nbsp;</p>
+
+  <p>(p. 7.) "<i>Copernicus.</i> Addo etiam, quod satis absurdum videretur,
+  continenti sive locanti motum adscribi, et non potius contento et locato,
+  quod est terra. <i>Emend.</i> Addo etiam difficilius non esse contento et
+  locato, quod est Terra, motum adscribere, quam continenti."<a
+  name="NtA_147" href="#Nt_147"><sup>[147]</sup></a></p>
+
+  <p>We must not say it is absurd to refuse motion to the <i>contained</i>
+  and <i>located</i>, and to give it to the containing and locating; say
+  that neither is more difficult than the other.</p>
+
+  <p>&nbsp;</p>
+
+  <p>(p. 7.) "<i>Copernicus.</i> Vides ergo quod ex his omnibus probabilior
+  sit mobilitas Terræ, quam ejus quies, præsertim in cotidiana revolutione,
+  tanquam terræ maxime propria. <i>Emend.</i> <i>Vides</i> ... delendus est
+  usque ad finem capitis."<a name="NtA_148"
+  href="#Nt_148"><sup>[148]</sup></a></p>
+
+  <p>Strike out the whole of the chapter from this to the end; it says that
+  the motion of the earth is the most probable hypothesis.</p>
+
+  <p>&nbsp;</p>
+
+  <p>(Cap. 9. lib. i. p. 7.) "<i>Copernicus.</i> Cum igitur nihil prohibeat
+  mobilitatem Terræ, videndum nunc arbitror, an etiam plures illi motus
+  conveniant, ut possit una errantium syderum existimari. <i>Emend.</i> Cum
+  igitur Terram moveri assumpserim, videndum nunc arbitror, an etiam illi
+  plures possint convenire motus."<a name="NtA_149"
+  href="#Nt_149"><sup>[149]</sup></a></p>
+
+<p><!-- Page 95 --><span class="pagenum"><a name="page95"></a>[95]</span></p>
+
+  <p>We must not say that nothing prohibits the motion of the earth, only
+  that having <i>assumed</i> it, we may inquire whether our explanations
+  require several motions.</p>
+
+  <p>&nbsp;</p>
+
+  <p>(Cap. 10. lib. i. p. 9.) "<i>Copernicus.</i> Non pudet nos fateri ...
+  hoc potius in mobilitate terræ verificari. <i>Emend.</i> Non pudet nos
+  assumere ... hoc consequenter in mobilitate verificari."<a name="NtA_150"
+  href="#Nt_150"><sup>[150]</sup></a></p>
+
+  <p>(Cap. 10. lib. i. p. 10.) "<i>Copernicus.</i> Tanta nimirum est divina
+  hæc. Opt. Max. fabrica. <i>Emend.</i> Dele illa verba postrema."<a
+  name="NtA_151" href="#Nt_151"><sup>[151]</sup></a></p>
+
+  <p>(Cap. ii. lib. i.<a name="NtA_152"
+  href="#Nt_152"><sup>[152]</sup></a>) "<i>Copernicus.</i> De triplici motu
+  telluris demonstratio. <i>Emend.</i> De hypothesi triplicis motus Terræ,
+  ejusque demonstratione."<a name="NtA_153"
+  href="#Nt_153"><sup>[153]</sup></a></p>
+
+  <p>(Cap. 10. lib. iv. p. 122.<a name="NtA_154"
+  href="#Nt_154"><sup>[154]</sup></a>) "<i>Copernicus.</i> De magnitudine
+  horum trium siderum, Solis, Lunæ, et Terræ. <i>Emend.</i> Dele verba
+  <i>horum trium siderum</i>, quia terra non est sidus, ut facit eam
+  Copernicus."<a name="NtA_155" href="#Nt_155"><sup>[155]</sup></a></p>
+
+  <p>We must not say we are not ashamed to <i>acknowledge</i>;
+  <i>assume</i> is the word. We must not call this assumption a <i>Divine
+  work</i>. A chapter must not be headed <i>demonstration</i>, but
+  <i>hypothesis</i>. The earth must not be called a <i>star</i>; the word
+  implies motion.</p>
+
+  <p>It will be seen that it does not take much to reduce Copernicus to
+  pure hypothesis. No personal injury being done to the author&mdash;who
+  indeed had been 17 years out of <!-- Page 96 --><span class="pagenum"><a
+  name="page96"></a>[96]</span>reach&mdash;the treatment of his book is now
+  an excellent joke. It is obvious that the Cardinals of the Index were a
+  little ashamed of their position, and made a mere excuse of a few
+  corrections. Their mode of dealing with chap. 8, this <i>problematice
+  videtur loqui, ut studiosis satisfiat</i>,<a name="NtA_156"
+  href="#Nt_156"><sup>[156]</sup></a> is an excuse to avoid corrections.
+  But they struck out the stinging allusion to Lactantius<a name="NtA_157"
+  href="#Nt_157"><sup>[157]</sup></a> in the preface, little thinking,
+  honest men, for they really believed what they said&mdash;that the light
+  of Lactantius would grow dark before the brightness of their own.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE CONVOCATION AT OXFORD EQUALLY AT FAULT.</p>
+
+  <p>1622. I make no reference to the case of Galileo, except this. I have
+  pointed out (<i>Penny Cycl. Suppl.</i> "Galileo"; <i>Engl. Cycl.</i>
+  "Motion of the Earth") that it is clear the absurdity was the act of the
+  <i>Italian</i> Inquisition&mdash;for the private and personal pleasure of
+  the Pope, who <i>knew</i> that the course he took would not commit him as
+  <i>Pope</i>&mdash;and not of the body which calls itself the
+  <i>Church</i>. Let the dirty proceeding have its right name. The Jesuit
+  Riccioli,<a name="NtA_158" href="#Nt_158"><sup>[158]</sup></a> the
+  stoutest and most learned Anti-Copernican in Europe, and the Puritan
+  Wilkins, a strong Copernican and Pope-hater, are equally positive that
+  the Roman <i>Church</i> never pronounced any decision: and this in the
+  time immediately following the ridiculous proceeding of the Inquisition.
+  In like manner a decision of the Convocation of Oxford is not a law of
+  the <i>English</i> Church; which is fortunate, for that Convocation, in
+  1622, came to a decision quite as absurd, and a great deal <!-- Page 97
+  --><span class="pagenum"><a name="page97"></a>[97]</span>more wicked than
+  the declaration against the motion of the earth. The second was a foolish
+  mistake; the first was a disgusting surrender of right feeling. The story
+  is told without disapprobation by Anthony Wood, who never exaggerated
+  anything against the university of which he is writing eulogistic
+  history.</p>
+
+  <p>In 1622, one William Knight<a name="NtA_159"
+  href="#Nt_159"><sup>[159]</sup></a> put forward in a sermon preached
+  before the University certain theses which, looking at the state of the
+  times, may have been improper and possibly of seditious intent. One of
+  them was that the bishop might excommunicate the civil magistrate: this
+  proposition the clerical body could not approve, and designated it by the
+  term <i>erronea</i>,<a name="NtA_160" href="#Nt_160"><sup>[160]</sup></a>
+  the mildest going. But Knight also declared as follows:</p>
+
+  <p>"Subditis mere privatis, si Tyrannus tanquam latro aut stuprator in
+  ipsos faciat impetum, et ipsi nec potestatem ordinariam implorare, nec
+  alia ratione effugere periculum possint, in presenti periculo se et suos
+  contra tyrannum, sicut contra privatum grassatorem, defendere licet."<a
+  name="NtA_161" href="#Nt_161"><sup>[161]</sup></a></p>
+
+  <p>That is, a man may defend his purse or a woman her honor, against the
+  personal attack of a king, as against that of a private person, if no
+  other means of safety can be found. The Convocation sent Knight to
+  prison, declared the proposition <i>"falsa</i>, periculosa, et
+  <i>impia</i>," and enacted that all applicants for degrees should
+  subscribe this censure, and make oath that they would neither hold,
+  teach, nor defend Knight's opinions.</p>
+
+  <p>The thesis, in the form given, was unnecessary and improper. Though
+  strong opinions of the king's rights were advanced at the time, yet no
+  one ventured to say that, <!-- Page 98 --><span class="pagenum"><a
+  name="page98"></a>[98]</span>ministers and advisers apart, the king might
+  <i>personally</i> break the law; and we know that the first and only
+  attempt which his successor made brought on the crisis which cost him his
+  throne and his head. But the declaration that the proposition was
+  <i>false</i> far exceeds in all that is disreputable the decision of the
+  Inquisition against the earth's motion. We do not mention this little
+  matter in England. Knight was a Puritan, and Neal<a name="NtA_162"
+  href="#Nt_162"><sup>[162]</sup></a> gives a short account of his sermon.
+  From comparison with Wood,<a name="NtA_163"
+  href="#Nt_163"><sup>[163]</sup></a> I judge that the theses, as given,
+  were not Knight's words, but the digest which it was customary to make in
+  criminal proceedings against opinion. This heightens the joke, for it
+  appears that the qualifiers of the Convocation took pains to present
+  their condemnation of Knight in the terms which would most unequivocally
+  make their censure condemn themselves. This proceeding took place in the
+  interval between the two proceedings against Galileo: it is left
+  undetermined whether we must say pot-kettle-pot or kettle-pot-kettle.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Liberti Fromondi.... Ant-Aristarchus, sive orbis terræ immobilis.
+  Antwerp, 1631, 8vo.<a name="NtA_164"
+  href="#Nt_164"><sup>[164]</sup></a></p>
+
+</blockquote>
+
+  <p>This book contains the evidence of an ardent opponent of Galileo to
+  the fact, that Roman Catholics of the day did not consider the decree of
+  the <i>Index</i> or of the <i>Inquisition</i> as a declaration of their
+  <i>Church</i>. Fromond would have been glad to say as much, and tries to
+  come near it, but confesses he must abstain. See <i>Penny Cyclop.
+  Suppl.</i> "Galileo," and <i>Eng. Cycl.</i> "Motion of the Earth." The
+  author of a celebrated article in the <i>Dublin Review</i>, in defence of
+  the <!-- Page 99 --><span class="pagenum"><a
+  name="page99"></a>[99]</span>Church of Rome, seeing that Drinkwater
+  Bethune<a name="NtA_165" href="#Nt_165"><sup>[165]</sup></a> makes use of
+  the authority of Fromondus, but for another purpose, sneers at him for
+  bringing up a "musty old Professor." If he had known Fromondus, and used
+  him he would have helped his own case, which is very meagre for want of
+  knowledge.<a name="NtA_166" href="#Nt_166"><sup>[166]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Advis à Monseigneur l'eminentissime Cardinal Duc de Richelieu, sur la
+  Proposition faicte par le Sieur Morin pour l'invention des longitudes.
+  Paris, 1634, 8vo.<a name="NtA_167"
+  href="#Nt_167"><sup>[167]</sup></a></p>
+
+</blockquote>
+
+  <p>This is the Official Report of the Commissioners appointed by the
+  Cardinal, of whom Pascal is the one now best known, to consider Morin's
+  plan. See the full account in Delambre, <i>Hist. Astr. Mod.</i> ii. 236,
+  etc.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE METIUS APPROXIMATION.</p>
+
+<blockquote class="b1n">
+
+  <p>Arithmetica et Geometria practica. By Adrian Metius. Leyden, 1640,
+  4to.<a name="NtA_168" href="#Nt_168"><sup>[168]</sup></a></p>
+
+</blockquote>
+
+  <p>This book contains the celebrated approximation <i>guessed at</i> by
+  his father, Peter Metius,<a name="NtA_169"
+  href="#Nt_169"><sup>[169]</sup></a> namely that the diameter is <!-- Page
+  100 --><span class="pagenum"><a name="page100"></a>[100]</span>to the
+  circumference as 113 to 355. The error <span class="correction"
+  title="text reads `it'">is</span> at the rate of about a foot in 2,000
+  miles. Peter Metius, having his attention called to the subject by the
+  false quadrature of Duchesne, found that the ratio lay between 333/106
+  and 377/120. He then took the liberty of taking the mean of both
+  numerators and denominators, giving 355/113. He had no right to presume
+  that this mean was better than either of the extremes; nor does it appear
+  positively that he did so. He published nothing; but his son Adrian,<a
+  name="NtA_170" href="#Nt_170"><sup>[170]</sup></a> when Van Ceulen's work
+  showed how near his father's result came to the truth, first made it
+  known in the work above. (See <i>Eng. Cyclop.</i>, art.
+  "Quadrature.")</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON INHABITABLE PLANETS.</p>
+
+<blockquote class="b1n">
+
+  <p>A discourse concerning a new world and another planet, in two books.
+  London, 1640, 8vo.<a name="NtA_171"
+  href="#Nt_171"><sup>[171]</sup></a></p>
+
+  <p>Cosmotheoros: or conjectures concerning the planetary worlds and their
+  inhabitants. Written in Latin, by Christianus Huyghens. This translation
+  was first published in 1698. Glasgow, 1757, 8vo. [The original is also of
+  1698.]<a name="NtA_172" href="#Nt_172"><sup>[172]</sup></a></p>
+
+</blockquote>
+
+  <p>The first work is by Bishop Wilkins, being the third edition, [first
+  in 1638] of the first book, "That the Moon may be a Planet"; and the
+  first edition of the second work, <!-- Page 101 --><span
+  class="pagenum"><a name="page101"></a>[101]</span>"That the Earth may be
+  a Planet." [See more under the reprint of 1802.] Whether other planets be
+  inhabited or not, that is, crowded with organisations some of them having
+  consciousness, is not for me to decide; but I should be much surprised
+  if, on going to one of them, I should find it otherwise. The whole
+  dispute tacitly assumes that, if the stars and planets be inhabited, it
+  must be by things of which we can form some idea. But for aught we know,
+  what number of such bodies there are, so many organisms may there be, of
+  which we have no way of thinking nor of speaking. This is seldom
+  remembered. In like manner it is usually forgotten that the <i>matter</i>
+  of other planets may be of different chemistry from ours. There may be no
+  oxygen and hydrogen in Jupiter, which may have <i>gens</i> of its own.<a
+  name="NtA_173" href="#Nt_173"><sup>[173]</sup></a> But this must not be
+  said: it would limit the omniscience of the <i>a priori</i> school of
+  physical inquirers, the larger half of the whole, and would be very
+  <i>unphilosophical</i>. Nine-tenths of my best paradoxers come out from
+  among this larger half, because they are just a little more than of it at
+  their entrance.</p>
+
+  <p>There was a discussion on the subject some years ago, which began
+  with</p>
+
+<blockquote class="b1n">
+
+  <p>The plurality of worlds: an Essay. London, 1853, 8vo. [By Dr. Wm.
+  Whewell, Master of Trinity College, Cambridge]. A dialogue on the
+  plurality of worlds, being a supplement to the Essay on that subject.
+  [First found in the second edition, 1854; removed to the end in
+  subsequent editions, and separate copies issued.]<a name="NtA_174"
+  href="#Nt_174"><sup>[174]</sup></a></p>
+
+</blockquote>
+
+  <p>A work of skeptical character, insisting on analogies which prohibit
+  the positive conclusion that the planets, stars, etc., are what we should
+  call <i>inhabited</i> worlds. It produced <!-- Page 102 --><span
+  class="pagenum"><a name="page102"></a>[102]</span>several works and a
+  large amount of controversy in reviews. The last predecessor of whom I
+  know was</p>
+
+<blockquote class="b1n">
+
+  <p>Plurality of Worlds.... By Alexander Maxwell. Second Edition. London,
+  1820, 8vo.</p>
+
+</blockquote>
+
+  <p>This work is directed against the plurality by an author who does not
+  admit modern astronomy. It was occasioned by Dr. Chalmers's<a
+  name="NtA_175" href="#Nt_175"><sup>[175]</sup></a> celebrated discourses
+  on religion in connection with astronomy. The notes contain many
+  citations on the gravity controversy, from authors now very little read:
+  and this is its present value. I find no mention of Maxwell, not even in
+  Watt.<a name="NtA_176" href="#Nt_176"><sup>[176]</sup></a> He
+  communicated with mankind without the medium of a publisher; and, from
+  Vieta till now, this method has always been favorable to loss of
+  books.</p>
+
+  <p>A correspondent informs me that Alex. Maxwell, who wrote on the
+  plurality of worlds, in 1820, was a law-bookseller and publisher
+  (probably his own publisher) in Bell Yard. He had peculiar notions, which
+  he was fond of discussing with his customers. He was a bit of a
+  Swedenborgian.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">INHABITED PLANETS IN FICTION.</p>
+
+  <p>There is a class of hypothetical creations which do not belong to my
+  subject, because they are <i>acknowledged</i> to be fictions, as those of
+  Lucian,<a name="NtA_177" href="#Nt_177"><sup>[177]</sup></a> Rabelais,<a
+  name="NtA_178" href="#Nt_178"><sup>[178]</sup></a> Swift, Francis <!--
+  Page 103 --><span class="pagenum"><a
+  name="page103"></a>[103]</span>Godwin,<a name="NtA_179"
+  href="#Nt_179"><sup>[179]</sup></a> Voltaire, etc. All who have more
+  positive notions as to either the composition or organization of other
+  worlds, than the reasonable conclusion that our Architect must be quite
+  able to construct millions of other buildings on millions of other plans,
+  ought to rank with the writers just mentioned, in all but self-knowledge.
+  Of every one of their systems I say, as the Irish Bishop said of
+  Gulliver's book,&mdash;I don't believe half of it. Huyghens had been
+  preceded by Fontenelle,<a name="NtA_180"
+  href="#Nt_180"><sup>[180]</sup></a> who attracted more attention.
+  Huyghens is very fanciful and very positive; but he gives a true account
+  of his method. "But since there's no hopes of a Mercury to carry us such
+  a journey, we shall e'en be contented with what's in our power: we shall
+  suppose ourselves there...." And yet he says, "We have proved that they
+  live in societies, have hands and feet...." Kircher<a name="NtA_181"
+  href="#Nt_181"><sup>[181]</sup></a> had gone to the stars before him, but
+  would not find any life in them, either animal or vegetable.</p>
+
+  <p>The question of the inhabitants of a particular planet is one which
+  has truth on one side or the other: either there are some inhabitants, or
+  there are none. Fortunately, it is of no consequence which is true. But
+  there are many cases where the balance is equally one of truth and
+  falsehood, in which the choice is a matter of importance. My work
+  selects, for the most part, sins against demonstration: but the world is
+  full of questions of fact or opinion, in which a struggling minority will
+  become a majority, or else will <!-- Page 104 --><span class="pagenum"><a
+  name="page104"></a>[104]</span>be gradually annihilated: and each of the
+  cases subdivides into results of good, and results of evil. What is to be
+  done?</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Periculosum est credere et non credere;</p>
+      <p>Hippolitus obiit quia novercæ creditum est;</p>
+      <p>Cassandræ quia non creditum ruit Ilium:</p>
+      <p>Ergo exploranda est veritas multum prius</p>
+      <p>Quam stulta prove judicet sententia."<a name="NtA_182" href="#Nt_182"><sup>[182]</sup></a></p>
+    </div>
+  </div>
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Nova Demonstratio immobilitatis terræ petita ex virtute magnetica. By
+  Jacobus Grandamicus. Flexiae (La Flèche), 1645, 4to.<a name="NtA_183"
+  href="#Nt_183"><sup>[183]</sup></a></p>
+
+</blockquote>
+
+  <p>No magnetic body can move about its poles: the earth is a magnetic
+  body, therefore, etc. The iron and its magnetism are typical of two
+  natures in one person; so it is said, "Si exaltatus fuero à terra, omnia
+  traham ad me ipsum."<a name="NtA_184"
+  href="#Nt_184"><sup>[184]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A VENETIAN BUDGET OF PARADOXES.</p>
+
+<blockquote class="b1n">
+
+  <p>Le glorie degli incogniti, o vero gli huomini illustri dell' accademia
+  de' signori incogniti di Venetia. Venice, 1647, 4to.</p>
+
+</blockquote>
+
+  <p>This work is somewhat like a part of my own: it is a budget of
+  Venetian nobodies who wished to be somebodies; but paradox is not the
+  only means employed. It is of a serio-comic character, gives genuine
+  portraits in copperplate, and grave lists of works; but satirical
+  accounts. The astrologer Andrew Argoli<a name="NtA_185"
+  href="#Nt_185"><sup>[185]</sup></a> is there, and his son; both of whom,
+  with some of the others, have place in modern works <!-- Page 105
+  --><span class="pagenum"><a name="page105"></a>[105]</span>on biography.
+  Argoli's discovery that logarithms facilitate easy processes, but
+  increase the labor of difficult ones, is worth recording.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Controversiæ de vera circuli mensura ... inter ... C.&nbsp;S. Longomontanum
+  et Jo. Pellium.<a name="NtA_186" href="#Nt_186"><sup>[186]</sup></a>
+  Amsterdam, 1647, 4to.</p>
+
+</blockquote>
+
+  <p>Longomontanus,<a name="NtA_187" href="#Nt_187"><sup>[187]</sup></a> a
+  Danish astronomer of merit, squared the circle in 1644: he found out that
+  the diameter 43 gives the square root of 18252 for the circumference;
+  which gives 3.14185... for the ratio. Pell answered him, and being a kind
+  of circulating medium, managed to engage in the controversy names known
+  and unknown, as Roberval, Hobbes, Carcavi, Lord Charles Cavendish,
+  Pallieur, Mersenne, Tassius, Baron Wolzogen, Descartes, Cavalieri and
+  Golius.<a name="NtA_188" href="#Nt_188"><sup>[188]</sup></a> Among them,
+  of course, Longomontanus was made <!-- Page 106 --><span
+  class="pagenum"><a name="page106"></a>[106]</span>mincemeat: but he is
+  said to have insisted on the discovery of his epitaph.<a name="NtA_189"
+  href="#Nt_189"><sup>[189]</sup></a></p>
+
+<p><!-- Page 107 --><span class="pagenum"><a name="page107"></a>[107]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE CIRCULATING MEDIA OF MATHEMATICS.</p>
+
+  <p>The great circulating mediums, who wrote to everybody, heard from
+  everybody, and sent extracts to everybody else, have been Father
+  Mersenne, John Collins, and the late Professor Schumacher: all "late" no
+  doubt, but only the last recent enough to be so styled. If M.C.S. should
+  ever again stand for "Member of the Corresponding Society," it should
+  raise an acrostic thought of the three. There is an allusion to
+  Mersenne's occupation in Hobbes's reply to him. He wanted to give Hobbes,
+  who was very ill at Paris, the Roman Eucharist: but Hobbes said, "I have
+  settled all that long ago; when did you hear from Gassendi?" We are
+  reminded of William's answer to Burnet. John Collins disseminated Newton,
+  among others. Schumacher ought to have been called the postmaster-general
+  of astronomy, as Collins was called the attorney-general of
+  mathematics.<a name="NtA_190" href="#Nt_190"><sup>[190]</sup></a></p>
+
+<p><!-- Page 108 --><span class="pagenum"><a name="page108"></a>[108]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE SYMPATHETIC POWDER.</p>
+
+<blockquote class="b1n">
+
+  <p>A late discourse ... by Sir Kenelme Digby.... Rendered into English by
+  R. White. London, 1658, 12mo.</p>
+
+</blockquote>
+
+  <p>On this work see <i>Notes and Queries</i>, 2d series, vii. 231, 299,
+  445, viii. 190. It contains the celebrated sympathetic powder. I am still
+  in much doubt as to the connection of Digby with this tract.<a
+  name="NtA_191" href="#Nt_191"><sup>[191]</sup></a> Without entering on
+  the subject here, I observe that in Birch's <i>History of the Royal
+  Society</i>,<a name="NtA_192" href="#Nt_192"><sup>[192]</sup></a> to
+  which both Digby and White belonged, Digby, though he brought many things
+  before the Society, never mentioned the powder, which is connected only
+  with the names of Evelyn<a name="NtA_193"
+  href="#Nt_193"><sup>[193]</sup></a> and Sir Gilbert Talbot.<a
+  name="NtA_194" href="#Nt_194"><sup>[194]</sup></a> The sympathetic powder
+  was that which cured by anointing the weapon with its salve instead of
+  the wound. I have long been convinced that it was efficacious. The
+  directions were to keep the <!-- Page 109 --><span class="pagenum"><a
+  name="page109"></a>[109]</span>wound clean and cool, and to take care of
+  diet, rubbing the salve on the knife or sword.<a name="NtA_195"
+  href="#Nt_195"><sup>[195]</sup></a> If we remember the dreadful notions
+  upon drugs which prevailed, both as to quantity and quality, we shall
+  readily see that any way of <i>not</i> dressing the wound would have been
+  useful. If the physicians had taken the hint, had been careful of diet
+  etc., and had poured the little barrels of medicine down the throat of a
+  practicable doll, <i>they</i> would have had their magical cures as well
+  as the surgeons.<a name="NtA_196" href="#Nt_196"><sup>[196]</sup></a>
+  Matters are much improved now; the quantity of medicine given, even by
+  orthodox physicians, would have been called infinitesimal by their
+  professional ancestors. Accordingly, the College of Physicians has a
+  right to abandon its motto, which is <i>Ars longa, vita brevis</i>,
+  meaning <i>Practice is long, so life is short</i>.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">HOBBES AS A MATHEMATICIAN.</p>
+
+<blockquote class="b1n">
+
+  <p>Examinatio et emendatio Mathematicæ Hodiernæ. By Thomas Hobbes.
+  London, 1666, 4to.</p>
+
+</blockquote>
+
+  <p>In six dialogues: the sixth contains a quadrature of the circle.<a
+  name="NtA_197" href="#Nt_197"><sup>[197]</sup></a> But there is another
+  edition of this work, without place or date on the title-page, in which
+  the quadrature is omitted. This seems to be connected with the
+  publication <!-- Page 110 --><span class="pagenum"><a
+  name="page110"></a>[110]</span>of another quadrature, without date, but
+  about 1670, as may be judged from its professing to answer a tract of
+  Wallis, printed in 1669.<a name="NtA_198"
+  href="#Nt_198"><sup>[198]</sup></a> The title is "Quadratura circuli,
+  cubatio sphæræ, duplicatio cubi," 4to.<a name="NtA_199"
+  href="#Nt_199"><sup>[199]</sup></a> Hobbes, who began in 1655, was very
+  wrong in his quadrature; but, though not a Gregory St. Vincent,<a
+  name="NtA_200" href="#Nt_200"><sup>[200]</sup></a> he was not the
+  ignoramus in geometry that he is sometimes supposed. His writings,
+  erroneous as they are in many things, contain acute remarks on points of
+  principle. He is wronged by being coupled with Joseph Scaliger, as the
+  two great instances of men of letters who have come into geometry to help
+  the mathematicians out of their difficulty. I have never seen Scaliger's
+  quadrature,<a name="NtA_201" href="#Nt_201"><sup>[201]</sup></a> except
+  in the answers of Adrianus Romanus,<a name="NtA_202"
+  href="#Nt_202"><sup>[202]</sup></a> Vieta and Clavius, and in the
+  extracts of Kastner.<a name="NtA_203" href="#Nt_203"><sup>[203]</sup></a>
+  Scaliger had no right to such strong opponents: Erasmus or Bentley might
+  just as well have tried the problem, and either would have done much
+  better in any twenty minutes of his life.<a name="NtA_204"
+  href="#Nt_204"><sup>[204]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">AN ESTIMATE OF SCALIGER.</p>
+
+  <p>Scaliger inspired some mathematicians with great respect for his
+  geometrical knowledge. Vieta, the first man of his time, who answered
+  him, had such regard for his opponent <!-- Page 111 --><span
+  class="pagenum"><a name="page111"></a>[111]</span>as made him conceal
+  Scaliger's name. Not that he is very respectful in his manner of
+  proceeding: the following dry quiz on his opponent's logic must have been
+  very cutting, being true. "In grammaticis, dare navibus Austros, et dare
+  naves Austris, sunt æque significantia. Sed in Geometricis, aliud est
+  adsumpsisse circulum <span class="scac">BCD</span> non esse majorem
+  triginta sex segmentis <span class="scac">BCDF</span>, aliud circulo
+  <span class="scac">BCD</span> non esse majora triginta sex segmenta <span
+  class="scac">BCDF</span>. Illa adsumptiuncula vera est, hæc falsa."<a
+  name="NtA_205" href="#Nt_205"><sup>[205]</sup></a> Isaac Casaubon,<a
+  name="NtA_206" href="#Nt_206"><sup>[206]</sup></a> in one of his letters
+  to De Thou,<a name="NtA_207" href="#Nt_207"><sup>[207]</sup></a> relates
+  that, he and another paying a visit to Vieta, the conversation fell upon
+  Scaliger, of whom the host said that he believed Scaliger was the only
+  man who perfectly understood mathematical writers, especially the Greek
+  ones: and that he thought more of Scaliger when wrong than of many others
+  when right; "pluris se Scaligerum vel errantem facere quam multos <span
+  title="katorthountas" class="grk"
+  >&kappa;&alpha;&tau;&omicron;&rho;&theta;&omicron;&#x1F7B;&nu;&tau;&alpha;&sigmaf;</span>."<a
+  name="NtA_208" href="#Nt_208"><sup>[208]</sup></a> This must have been
+  before Scaliger's quadrature (1594). There is an old story of some one
+  saying, "Mallem cum Scaligero errare, quam cum Clavio recte sapere."<a
+  name="NtA_209" href="#Nt_209"><sup>[209]</sup></a> This I cannot help
+  suspecting to have been a version of Vieta's speech with Clavius
+  satirically inserted, on account of the great hostility which Vieta
+  showed towards Clavius in the latter years of his life.</p>
+
+  <p>Montucla could not have read with care either Scaliger's quadrature or
+  Clavius's refutation. He gives the first a wrong date: he assures the
+  world that there is no question about Scaliger's quadrature being wrong,
+  in the eyes of geometers at least: and he states that Clavius mortified
+  him <!-- Page 112 --><span class="pagenum"><a
+  name="page112"></a>[112]</span>extremely by showing that it made the
+  circle less than its inscribed dodecagon, which is, of course, equivalent
+  to asserting that a straight line is not always the shortest distance
+  between two points. Did <i>Clavius</i> show this? No, it was Scaliger
+  himself who showed it, boasted of it, and declared it to be a "noble
+  paradox" that a theorem false in geometry is true in arithmetic; a thing,
+  he says with great triumph, not noticed by Archimedes himself! He says in
+  so many words that the periphery of the dodecagon is greater than that of
+  the circle; and that the more sides there are to the inscribed figure,
+  the more does it exceed the circle in which it is. And here <i>are</i>
+  the words, on the independent testimonies of Clavius and Kastner:</p>
+
+  <p>"Ambitus dodecagoni circulo inscribendi plus potest quam circuli
+  ambitus. Et quanto deinceps plurium laterum fuerit polygonum circulo
+  inscribendum, tanto plus poterit ambitus polygoni quam ambitus
+  circuli."<a name="NtA_210" href="#Nt_210"><sup>[210]</sup></a></p>
+
+  <p>There is much resemblance between Joseph Scaliger and William
+  Hamilton,<a name="NtA_211" href="#Nt_211"><sup>[211]</sup></a> in a
+  certain impetuousity of character, and inaptitude to think of quantity.
+  Scaliger maintained that the arc of a circle is less than its chord in
+  arithmetic, though greater in geometry; Hamilton arrived at two
+  quantities which are identical, but the greater the one the less the
+  other. But, on the whole, I liken Hamilton rather to Julius than to
+  Joseph. On this last hero of literature I repeat Thomas Edwards,<a
+  name="NtA_212" href="#Nt_212"><sup>[212]</sup></a> who says that a man is
+  unlearned who, be his other knowledge what it may, does not <!-- Page 113
+  --><span class="pagenum"><a name="page113"></a>[113]</span>understand the
+  subject he writes about. And now one of many instances in which
+  literature gives to literature character in science. Anthony Teissier,<a
+  name="NtA_213" href="#Nt_213"><sup>[213]</sup></a> the learned annotator
+  of De Thou's biographies, says of Finæus, "Il se vanta sans raison avoir
+  trouvé la quadrature du cercle; la gloire de cette admirable découverte
+  était réservée à Joseph Scalinger, comme l'a écrit Scévole de St.
+  Marthe."<a name="NtA_214" href="#Nt_214"><sup>[214]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">JOHN GRAUNT AS A PARADOXER.</p>
+
+<blockquote class="b1n">
+
+  <p>Natural and Political Observations ... upon the Bills of Mortality. By
+  John Graunt, citizen of London. London, 1662, 4to.<a name="NtA_215"
+  href="#Nt_215"><sup>[215]</sup></a></p>
+
+</blockquote>
+
+  <p>This is a celebrated book, the first great work upon mortality. But
+  the author, going <i>ultra crepidam</i>, has attributed to the motion of
+  the moon in her orbit all the tremors which she gets from a shaky
+  telescope.<a name="NtA_216" href="#Nt_216"><sup>[216]</sup></a> But there
+  is another paradox about this book: the above absurd opinion is
+  attributed to that excellent mechanist, Sir William Petty, who passed his
+  days among the astronomers. Graunt did not write his own book! Anthony
+  Wood<a name="NtA_217" href="#Nt_217"><sup>[217]</sup></a> hints that
+  Petty "assisted, or put into a way" his old benefactor: no doubt the two
+  friends talked the matter over many a time. Burnet and Pepys<a
+  name="NtA_218" href="#Nt_218"><sup>[218]</sup></a> state that Petty wrote
+  the book. It is enough for me that <!-- Page 114 --><span
+  class="pagenum"><a name="page114"></a>[114]</span>Graunt, whose honesty
+  was never impeached, uses the plainest incidental professions of
+  authorship throughout; that he was elected into the Royal Society because
+  he was the author; that Petty refers to him as author in scores of
+  places, and published an edition, as editor, after Graunt's death, with
+  Graunt's name of course. The note on Graunt in the <i>Biographia
+  Britannica</i> may be consulted; it seems to me decisive. Mr. C.&nbsp;B.
+  Hodge, an able actuary, has done the best that can be done on the other
+  side in the <i>Assurance Magazine</i>, viii. 234. If I may say what is in
+  my mind, without imputation of disrespect, I suspect some actuaries have
+  a bias: they would rather have Petty the greater for their Coryphæus than
+  Graunt the less.<a name="NtA_219" href="#Nt_219"><sup>[219]</sup></a></p>
+
+  <p>Pepys is an ordinary gossip: but Burnet's account has an animus which
+  is of a worse kind. He talks of "one Graunt, a Papist, under whose name
+  Sir William Petty<a name="NtA_220" href="#Nt_220"><sup>[220]</sup></a>
+  published his observations on the bills of mortality." He then gives the
+  cock without a bull story of Graunt being a trustee of the New River
+  Company, and shutting up the cocks and carrying off their keys, just
+  before the fire of London, by which a supply of water was delayed.<a
+  name="NtA_221" href="#Nt_221"><sup>[221]</sup></a> It was one of the
+  first objections made to Burnet's work, that Graunt was <i>not</i> a
+  trustee at the time; and Maitland, the historian of London, ascertained
+  from the books of the Company that he was not admitted until twenty-three
+  days after the breaking out of the fire. Graunt's first admission <!--
+  Page 115 --><span class="pagenum"><a name="page115"></a>[115]</span>to
+  the Company took place on the very day on which a committee was appointed
+  to inquire into the cause of the fire. So much for Burnet. I incline to
+  the view that Graunt's setting London on fire strongly corroborates his
+  having written on the bills of mortality: every practical man takes stock
+  before he commences a grand operation in business.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">MANKIND A GULLIBLE LOT.</p>
+
+<blockquote class="b1n">
+
+  <p>De Cometis: or a discourse of the natures and effects of Comets, as
+  they are philosophically, historically, and astrologically considered.
+  With a brief (yet full) account of the III late Comets, or blazing stars,
+  visible to all Europe. And what (in a natural way of judicature) they
+  portend. Together with some observations on the nativity of the Grand
+  Seignior. By John Gadbury, <span title="Philomathêmatikos" class="grk"
+  >&Phi;&iota;&lambda;&omicron;&mu;&alpha;&theta;&eta;&mu;&alpha;&tau;&iota;&kappa;&#x1F79;&sigmaf;</span>.
+  London, 1665, 4to.</p>
+
+</blockquote>
+
+  <p>Gadbury, though his name descends only in astrology, was a
+  well-informed astronomer.<a name="NtA_222"
+  href="#Nt_222"><sup>[222]</sup></a> D'Israeli<a name="NtA_223"
+  href="#Nt_223"><sup>[223]</sup></a> sets down Gadbury, Lilly, Wharton,
+  Booker, etc., as rank rogues: I think him quite wrong. The easy belief in
+  roguery and intentional imposture which prevails in educated society is,
+  to my mind, a greater presumption against the honesty of mankind than all
+  the roguery and imposture itself. Putting aside mere swindling for the
+  sake of gain, and looking at speculation and paradox, I find very little
+  reason to suspect wilful deceit.<a name="NtA_224"
+  href="#Nt_224"><sup>[224]</sup></a> My opinion of mankind is founded upon
+  the <!-- Page 116 --><span class="pagenum"><a
+  name="page116"></a>[116]</span>mournful fact that, so far as I can see,
+  they find within themselves the means of believing in a thousand times as
+  much as there is to believe in, judging by experience. I do not say
+  anything against Isaac D'Israeli for talking his time. We are all in the
+  team, and we all go the road, but we do not all draw.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A FORERUNNER OF A WRITTEN ESPERANTO.</p>
+
+<blockquote class="b1n">
+
+  <p>An essay towards a real character and a philosophical language. By
+  John Wilkins [Dean of Ripon, afterwards Bishop of Chester].<a
+  name="NtA_225" href="#Nt_225"><sup>[225]</sup></a> London, 1668,
+  folio.</p>
+
+</blockquote>
+
+  <p>This work is celebrated, but little known. Its object gives it a right
+  to a place among paradoxes. It proposes a language&mdash;if that be the
+  proper name&mdash;in which <i>things</i> and their relations shall be
+  denoted by signs, not <i>words</i>: so that any person, whatever may be
+  his mother tongue, may read it in his own words. This is an obvious
+  possibility, and, I am afraid, an obvious impracticability. One man may
+  construct such a system&mdash;Bishop Wilkins has done it&mdash;but where
+  is the man who will learn it? The second tongue makes a language, as the
+  second blow makes a fray. There has been very little curiosity about his
+  performance, the work is scarce; and I do not know where to refer the
+  reader for any account of its details, except, to the partial reprint of
+  Wilkins presently mentioned under 1802, in which there is an
+  unsatisfactory abstract. There is nothing in the <i>Biographia
+  Britannica</i>, except discussion of Anthony Wood's statement that the
+  hint was derived from Dalgarno's book, <!-- Page 117 --><span
+  class="pagenum"><a name="page117"></a>[117]</span><i>De Signis</i>,
+  1661.<a name="NtA_226" href="#Nt_226"><sup>[226]</sup></a> Hamilton
+  (<i>Discussions</i>, Art. 5, "Dalgarno") does not say a word on this
+  point, beyond quoting Wood; and Hamilton, though he did now and then
+  write about his countrymen with a rough-nibbed pen, knew perfectly well
+  how to protect their priorities.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">GREGOIRE DE ST. VINCENT.</p>
+
+<blockquote class="b1n">
+
+  <p>Problema Austriacum. Plus ultra Quadratura Circuli. Auctore P.
+  Gregorio a Sancto Vincentio Soc. Jesu., Antwerp, 1647, folio.&mdash;Opus
+  Geometricum posthumum ad Mesolabium. By the same. Gandavi [Ghent], 1668,
+  folio.<a name="NtA_227" href="#Nt_227"><sup>[227]</sup></a></p>
+
+</blockquote>
+
+  <p>The first book has more than 1200 pages, on all kinds of geometry.
+  Gregory St. Vincent is the greatest of circle-squarers, and his
+  investigations led him into many truths: he found the property of the
+  area of the hyperbola<a name="NtA_228"
+  href="#Nt_228"><sup>[228]</sup></a> which led to Napier's logarithms
+  being called <i>hyperbolic</i>. Montucla says of him, with sly truth,
+  that no one has ever squared the circle with so much genius, or,
+  excepting his principal object, with so much success.<a name="NtA_229"
+  href="#Nt_229"><sup>[229]</sup></a> His reputation, and the many merits
+  of his work, led to a sharp controversy on his quadrature, which ended in
+  its complete exposure by Huyghens and others. He had a small school of
+  followers, who defended him in print.</p>
+
+<p><!-- Page 118 --><span class="pagenum"><a name="page118"></a>[118]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">RENE DE SLUSE.</p>
+
+<blockquote class="b1n">
+
+  <p>Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liège], 1668,
+  4to.<a name="NtA_230" href="#Nt_230"><sup>[230]</sup></a></p>
+
+</blockquote>
+
+  <p>The Mesolabum is the solution of the problem of finding two mean
+  proportionals, which Euclid's geometry does not attain. Slusius is a true
+  geometer, and uses the ellipse, etc.: but he is sometimes ranked with the
+  trisecters, for which reason I place him here, with this explanation.</p>
+
+  <p>The finding of two mean proportionals is the preliminary to the famous
+  old problem of the duplication of the cube, proposed by Apollo (not
+  Apollonius) himself. D'Israeli speaks of the "six follies of
+  science,"&mdash;the quadrature, the duplication, the perpetual motion,
+  the philosopher's stone, magic, and astrology. He might as well have
+  added the trisection, to make the mystic number seven: but had he done
+  so, he would still have been very lenient; only seven follies in all
+  science, from mathematics to chemistry! Science might have said to such a
+  judge&mdash;as convicts used to say who got seven years, expecting it for
+  life, "Thank you, my Lord, and may you sit there till they are
+  over,"&mdash;may the Curiosities of Literature outlive the Follies of
+  Science!</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">JAMES GREGORY.</p>
+
+  <p>1668. In this year James Gregory, in his <i>Vera Circuli et Hyperbolæ
+  Quadratura</i>,<a name="NtA_231" href="#Nt_231"><sup>[231]</sup></a> held
+  himself to have proved that <!-- Page 119 --><span class="pagenum"><a
+  name="page119"></a>[119]</span>the <i>geometrical</i> quadrature of the
+  circle is impossible. Few mathematicians read this very abstruse
+  speculation, and opinion is somewhat divided. The regular circle-squarers
+  attempt the <i>arithmetical</i> quadrature, which has long been proved to
+  be impossible. Very few attempt the geometrical quadrature. One of the
+  last is Malacarne, an Italian, who published his <i>Solution
+  Géométrique</i>, at Paris, in 1825. His method would make the
+  circumference less than three times the diameter.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">BEAULIEU'S QUADRATURE.</p>
+
+<blockquote class="b1n">
+
+  <p>La Géométrie Françoise, ou la Pratique aisée.... La quadracture du
+  cercle. Par le Sieur de Beaulieu, Ingénieur, Géographe du Roi ... Paris,
+  1676, 8vo. [not Pontault de Beaulieu, the celebrated topographer; he died
+  in 1674].<a name="NtA_232" href="#Nt_232"><sup>[232]</sup></a></p>
+
+</blockquote>
+
+  <p>If this book had been a fair specimen, I might have pointed to it in
+  connection with contemporary English works, and made a scornful
+  comparison. But it is not a fair specimen. Beaulieu was attached to the
+  Royal Household, and throughout the century it may be suspected that the
+  household forced a royal road to geometry. Fifty years before, Beaugrand,
+  the king's secretary, made a fool of himself, and [so?] contrived to pass
+  for a geometer. He had interest enough to get Desargues, the most
+  powerful geometer of his time,<a name="NtA_233"
+  href="#Nt_233"><sup>[233]</sup></a> the teacher and friend of Pascal,
+  prohibited from <!-- Page 120 --><span class="pagenum"><a
+  name="page120"></a>[120]</span>lecturing. See some letters on the History
+  of Perspective, which I wrote in the <i>Athenæum</i>, in October and
+  November, 1861. Montucla, who does not seem to know the true secret of
+  Beaugrand's greatness, describes him as "un certain M. de Beaugrand,
+  mathématicien, fort mal traité par Descartes, et à ce qu'il paroit avec
+  justice."<a name="NtA_234" href="#Nt_234"><sup>[234]</sup></a></p>
+
+  <p>Beaulieu's quadrature amounts to a geometrical construction<a
+  name="NtA_235" href="#Nt_235"><sup>[235]</sup></a> which gives <span
+  class="grk">&pi;</span> = &radic;10. His depth may be ascertained from
+  the following extracts. First on Copernicus:</p>
+
+  <p>"Copernic, Allemand, ne s'est pas moins rendu illustre par ses doctes
+  écrits; et nous pourrions dire de luy, qu'il seroit le seul et unique en
+  la force de ses Problèmes, si sa trop grande présomption ne l'avoit porté
+  à avancer en cette Science une proposition aussi absurde, qu'elle est
+  contre la Foy et raison, en faisant la circonférence d'un Cercle fixe,
+  immobile, et le centre mobile, sur lequel principe Géométrique, il a
+  avancé en son Traitté Astrologique le Soleil fixe, et la Terre mobile."<a
+  name="NtA_236" href="#Nt_236"><sup>[236]</sup></a></p>
+
+  <p>I digress here to point out that though our quadrators, etc., very
+  often, and our historians sometimes, assert that men of the character of
+  Copernicus, etc., were treated with contempt and abuse until their day of
+  ascendancy came, nothing can be more incorrect. From Tycho Brahé<a
+  name="NtA_237" href="#Nt_237"><sup>[237]</sup></a> to Beaulieu, there is
+  but one expression of admiration for the genius of Copernicus. There is
+  an exception, which, I <!-- Page 121 --><span class="pagenum"><a
+  name="page121"></a>[121]</span>believe, has been quite misunderstood.
+  Maurolycus,<a name="NtA_238" href="#Nt_238"><sup>[238]</sup></a> in his
+  <i>De Sphæra</i>, written many years before its posthumous publication in
+  1575, and which it is not certain he would have published, speaking of
+  the safety with which various authors may be read after his cautions,
+  says, "Toleratur et Nicolaus Copernicus qui Solem fixum et Terram <i>in
+  girum circumverti</i> posuit: et scutica potius, aut flagello, quam
+  reprehensione dignus est."<a name="NtA_239"
+  href="#Nt_239"><sup>[239]</sup></a> Maurolycus was a mild and somewhat
+  contemptuous satirist, when expressing disapproval: as we should now say,
+  he pooh-poohed his opponents; but, unless the above be an instance, he
+  was never savage nor impetuous. I am fully satisfied that the meaning of
+  the sentence is, that Copernicus, who turned the earth like a boy's top,
+  ought rather to have a whip given him wherewith to keep up his plaything
+  than a serious refutation. To speak of <i>tolerating</i> a person <i>as
+  being</i> more worthy of a flogging than an argument, is almost a
+  contradiction.</p>
+
+  <p>I will now extract Beaulieu's treatise on algebra, entire.</p>
+
+  <p>"L'Algebre est la science curieuse des Sçavans et specialement d'un
+  General d'Armée ou Capitaine, pour promptement ranger une Armée en
+  bataille, et nombre de Mousquetaires et Piquiers qui composent les
+  bataillons d'icelle, outre les figures de l'Arithmetique. Cette science a
+  5 figures particulieres en cette sorte. P signifie <i>plus</i> au
+  commerce, et à l'Armée <i>Piquiers</i>. M signifie <i>moins</i>, et
+  <i>Mousquetaire</i> en l'Art des bataillons. [It is quite true that P and
+  M were used for <i>plus</i> and <i>minus</i> in a great many old works.]
+  R signifie <i>racine</i> en la mesure du Cube, et en l'Armée <i>rang</i>.
+  Q signifie <i>quaré</i> en l'un et l'autre usage. C signifie <i>cube</i>
+  en la mesure, et <i>Cavallerie</i> en la composition des bataillons et
+  escadrons. Quant à l'operation de cette science, c'est <!-- Page 122
+  --><span class="pagenum"><a name="page122"></a>[122]</span>d'additionner
+  un <i>plus</i> d'avec <i>plus</i>, la somme sera <i>plus</i>, et
+  <i>moins</i> d'avec <i>plus</i>, on soustrait le moindre du <i>plus</i>,
+  et la reste est la somme requise ou nombre trouvé. Je dis seulement cecy
+  en passant pour ceux qui n'en sçavent rien du tout."<a name="NtA_240"
+  href="#Nt_240"><sup>[240]</sup></a></p>
+
+  <p>This is the algebra of the Royal Household, seventy-three years after
+  the death of Vieta. Quære, is it possible that the fame of Vieta, who
+  himself held very high stations in the household all his life, could have
+  given people the notion that when such an officer chose to declare
+  himself an algebraist, he must be one indeed? This would explain
+  Beaugrand, Beaulieu, and all the <i>beaux</i>. Beaugrand&mdash;not only
+  secretary to the king, but "mathematician" to the Duke of Orleans&mdash;I
+  wonder what his "fool" could have been like, if indeed he kept the
+  offices separate,&mdash;would have been in my list if I had possessed his
+  <i>Geostatique</i>, published about 1638.<a name="NtA_241"
+  href="#Nt_241"><sup>[241]</sup></a> He makes bodies diminish in weight as
+  they approach the earth, because the effect of a weight on a lever is
+  less as it approaches the fulcrum.</p>
+
+<p><!-- Page 123 --><span class="pagenum"><a name="page123"></a>[123]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">SIR MATTHEW HALE.</p>
+
+<blockquote class="b1n">
+
+  <p>Remarks upon two late ingenious discourses.... By Dr. Henry More.<a
+  name="NtA_242" href="#Nt_242"><sup>[242]</sup></a> London, 1676, 8vo.</p>
+
+</blockquote>
+
+  <p>In 1673 and 1675, Matthew Hale,<a name="NtA_243"
+  href="#Nt_243"><sup>[243]</sup></a> then Chief Justice, published two
+  tracts, an "Essay touching Gravitation," and "Difficiles Nugæ" on the
+  Torricellian experiment. Here are the answers by the learned and
+  voluminous Henry More. The whole would be useful to any one engaged in
+  research about ante-Newtonian notions of gravitation.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Observations touching the principles of natural motions; and
+  especially touching rarefaction and condensation.... By the author of
+  <i>Difficiles Nugæ</i>. London, 1677, 8vo.</p>
+
+</blockquote>
+
+  <p>This is another tract of Chief Justice Hale, published the year after
+  his death. The reader will remember that <i>motion</i>, in old
+  philosophy, meant any change from state to state: what we now describe as
+  <i>motion</i> was <i>local motion</i>. This is a very philosophical book,
+  about <i>flux</i> and <i>materia prima</i>, <i>virtus activa</i> and
+  <i>essentialis</i>, and other fundamentals. I think Stephen Hales, the
+  author of the "Vegetable Statics," has the writings of the Chief Justice
+  sometimes attributed to him, which is very puny justice indeed.<a
+  name="NtA_244" href="#Nt_244"><sup>[244]</sup></a> Matthew Hale died in
+  1676, and from his devotion to science it probably arose that his famous
+  <i>Pleas of the Crown</i><a name="NtA_245"
+  href="#Nt_245"><sup>[245]</sup></a> and other law works did not appear
+  until after his death. One of his <!-- Page 124 --><span
+  class="pagenum"><a name="page124"></a>[124]</span>contemporaries was the
+  astronomer Thomas Street, whose <i>Caroline Tables</i><a name="NtA_246"
+  href="#Nt_246"><sup>[246]</sup></a> were several times printed: another
+  contemporary was his brother judge, Sir Thomas Street.<a name="NtA_247"
+  href="#Nt_247"><sup>[247]</sup></a> But of the astronomer absolutely
+  nothing is known: it is very unlikely that he and the judge were the same
+  person, but there is not a bit of positive evidence either for or
+  against, so far as can be ascertained. Halley<a name="NtA_248"
+  href="#Nt_248"><sup>[248]</sup></a>&mdash;no less a
+  person&mdash;published two editions of the <i>Caroline Tables</i>, no
+  doubt after the death of the author: strange indeed that neither Halley
+  nor any one else should leave evidence that Street was born or died.</p>
+
+  <p>Matthew Hale gave rise to an instance of the lengths a lawyer will go
+  when before a jury who cannot detect him. Sir Samuel Shepherd,<a
+  name="NtA_249" href="#Nt_249"><sup>[249]</sup></a> the Attorney General,
+  in opening Hone's<a name="NtA_250" href="#Nt_250"><sup>[250]</sup></a>
+  first trial, calls him "one who was the most learned man that ever
+  adorned the Bench, the most even man that ever blessed domestic life, the
+  <i>most eminent man that ever advanced the progress of science</i>, and
+  one of the [very moderate] best and most purely religious men that ever
+  lived."</p>
+
+<p><!-- Page 125 --><span class="pagenum"><a name="page125"></a>[125]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON THE DISCOVERY OF ANTIMONY.</p>
+
+<blockquote class="b1n">
+
+  <p>Basil Valentine his triumphant Chariot of Antimony, with annotations
+  of Theodore Kirkringius, M.D. With the true book of the learned Synesius,
+  a Greek abbot, taken out of the Emperour's library, concerning the
+  Philosopher's Stone. London, 1678, 8vo.<a name="NtA_251"
+  href="#Nt_251"><sup>[251]</sup></a></p>
+
+</blockquote>
+
+  <p>There are said to be three Hamburg editions of the collected works of
+  Valentine, who discovered the common antimony, and is said to have given
+  the name <i>antimoine</i>, in a curious way. Finding that the pigs of his
+  convent throve upon it, he gave it to his brethren, who died of it.<a
+  name="NtA_252" href="#Nt_252"><sup>[252]</sup></a> The impulse given to
+  chemistry by R. Boyle<a name="NtA_253"
+  href="#Nt_253"><sup>[253]</sup></a> seems to have brought out a vast
+  number of translations, as in the following tract:</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON ALCHEMY.</p>
+
+<blockquote class="b1n">
+
+  <p><i>Collectanea Chymica</i>: A collection of ten several treatises in
+  chymistry, concerning the liquor Alkehest, the Mercury of Philosophers,
+  and other curiosities worthy the perusal. Written by Eir. Philaletha,<a
+  name="NtA_254" href="#Nt_254"><sup>[254]</sup></a> Anonymus, J. B.
+  Van-Helmont,<a name="NtA_255" href="#Nt_255"><sup>[255]</sup></a> Dr. Fr.
+  <!-- Page 126 --><span class="pagenum"><a
+  name="page126"></a>[126]</span>Antonie,<a name="NtA_256"
+  href="#Nt_256"><sup>[256]</sup></a> Bernhard Earl of Trevisan,<a
+  name="NtA_257" href="#Nt_257"><sup>[257]</sup></a> Sir Geo. Ripley,<a
+  name="NtA_258" href="#Nt_258"><sup>[258]</sup></a> Rog. Bacon,<a
+  name="NtA_259" href="#Nt_259"><sup>[259]</sup></a> Geo. Starkie,<a
+  name="NtA_260" href="#Nt_260"><sup>[260]</sup></a> Sir Hugh Platt,<a
+  name="NtA_261" href="#Nt_261"><sup>[261]</sup></a> and the Tomb of
+  Semiramis. See more in the contents. London, 1684, 8vo.</p>
+
+</blockquote>
+
+  <p>In the advertisements at the ends of these tracts there are upwards of
+  a hundred English tracts, nearly all of the period, and most of them
+  translations. Alchemy looks up since the chemists have found perfectly
+  different substances composed of the same elements and proportions. It is
+  true the chemists cannot yet <i>transmute</i>; but they may in time: they
+  poke about most assiduously. It seems, then, that the conviction that
+  alchemy <i>must</i> be impossible was a delusion: but we do not mention
+  it.</p>
+
+<p><!-- Page 127 --><span class="pagenum"><a name="page127"></a>[127]</span></p>
+
+  <p>The astrologers and the alchemists caught it in company in the
+  following, of which I have an unreferenced note.</p>
+
+  <p>"Mendacem et futilem hominem nominare qui volunt, calendariographum
+  dicunt; at qui sceleratum simul ac impostorem, chimicum.<a name="NtA_262"
+  href="#Nt_262"><sup>[262]</sup></a></p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Crede ratem ventis corpus ne crede chimistis;</p>
+      <p class="i4">Est quævis chimica tutior aura fide."<a name="NtA_263" href="#Nt_263"><sup>[263]</sup></a></p>
+    </div>
+  </div>
+  <p>Among the smaller paradoxes of the day is that of the <i>Times</i>
+  newspaper, which always spells it <i>chymistry</i>: but so, I believe, do
+  Johnson, Walker, and others. The Arabic work is very likely formed from
+  the Greek: but it may be connected either with <span title="chêmeia" class="grk"
+  >&chi;&eta;&mu;&epsilon;&iota;&alpha;</span> or with <span
+  title="chumeia" class="grk"
+  >&chi;&upsilon;&mu;&epsilon;&iota;&alpha;</span>.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Lettre d'un gentil-homme de province à une dame de qualité, sur le
+  sujet de la Comète. Paris, 1681, 4to.</p>
+
+</blockquote>
+
+  <p>An opponent of astrology, whom I strongly suspect to have been one of
+  the members of the Academy of Sciences under the name of a country
+  gentleman,<a name="NtA_264" href="#Nt_264"><sup>[264]</sup></a> writes
+  very good sense on the tremors excited by comets.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>The Petitioning-Comet: or a brief Chronology of all the famous Comets
+  and their events, that have happened from the birth of Christ to this
+  very day. Together with a modest enquiry into this present comet, London,
+  1681, 4to.</p>
+
+</blockquote>
+
+  <p>A satirical tract against the cometic prophecy:</p>
+
+  <p>"This present comet (it's true) is of a menacing aspect, but if the
+  <i>new parliament</i> (for whose convention so many good men pray)
+  continue long to sit, I fear not but the star will lose its virulence and
+  malignancy, or at least its portent be averted from this our nation;
+  which being the humble request to God of all good men, makes me thus
+  entitle it, a Petitioning-Comet."</p>
+
+<p><!-- Page 128 --><span class="pagenum"><a name="page128"></a>[128]</span></p>
+
+  <p>The following anecdote is new to me:</p>
+
+  <p>"Queen Elizabeth (1558) being then at Richmond, and being disswaded
+  from looking on a comet which did then appear, made answer, <i>jacta est
+  alea</i>, the dice are thrown; thereby intimating that the pre-order'd
+  providence of God was above the influence of any star or comet."</p>
+
+  <p>The argument was worth nothing: for the comet might have been <i>on
+  the dice</i> with the event; the astrologers said no more, at least the
+  more rational ones, who were about half of the whole.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>An astrological and theological discourse upon this present great
+  conjunction (the like whereof hath not (likely) been in some ages)
+  ushered in by a great comet. London, 1682, 4to. By C. N.<a name="NtA_265"
+  href="#Nt_265"><sup>[265]</sup></a></p>
+
+</blockquote>
+
+  <p>The author foretells the approaching "sabbatical jubilee," but will
+  not fix the date: he recounts the failures of his predecessors.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>A judgment of the comet which became first generally visible to us in
+  Dublin, December 13, about 15 minutes before 5 in the evening, <span
+  class="scac">A.D.</span> 1680. By a person of quality. Dublin, 1682,
+  4to.</p>
+
+</blockquote>
+
+  <p>The author argues against cometic astrology with great ability.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>A prophecy on the conjunction of Saturn and Jupiter in this present
+  year 1682. With some prophetical predictions of what is likely to ensue
+  therefrom in the year 1684. By John Case, Student in physic and
+  astrology.<a name="NtA_266" href="#Nt_266"><sup>[266]</sup></a> London,
+  1682, 4to.</p>
+
+</blockquote>
+
+<p><!-- Page 129 --><span class="pagenum"><a name="page129"></a>[129]</span></p>
+
+  <p>According to this writer, great conjunctions of Jupiter and Saturn
+  occur "in the fiery trigon," about once in 800 years. Of these there are
+  to be seven: six happened in the several times of Enoch, Noah, Moses,
+  Solomon, Christ, Charlemagne. The seventh, which is to happen at "the
+  lamb's marriage with the bride," seems to be that of 1682; but this is
+  only vaguely hinted.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>De Quadrature van de Circkel. By Jacob Marcelis. Amsterdam, 1698,
+  4to.</p>
+
+  <p>Ampliatie en demonstratie wegens de Quadrature ... By Jacob Marcelis.
+  Amsterdam, 1699, 4to.</p>
+
+  <p>Eenvoudig vertoog briev-wys geschrevem am J. Marcelis ... Amsterdam,
+  1702, 4to.</p>
+
+  <p>De sleutel en openinge van de quadrature ... Amsterdam, 1704, 4to.</p>
+
+</blockquote>
+
+  <p>Who shall contradict Jacob Marcelis?<a name="NtA_267"
+  href="#Nt_267"><sup>[267]</sup></a> He says the circumference contains
+  the diameter exactly times</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="i2">1008449087377541679894282184894</p>
+      <p>3 &mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;&mdash;</p>
+      <p class="i2">6997183637540819440035239271702</p>
+    </div>
+  </div>
+  <p>But he does not come very near, as the young arithmetician will
+  find.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">MATHEMATICAL THEOLOGY.</p>
+
+<blockquote class="b1n">
+
+  <p>Theologiæ Christianæ Principia Mathematica. Auctore Johanne Craig.<a
+  name="NtA_268" href="#Nt_268"><sup>[268]</sup></a> London, 1699, 4to.</p>
+
+</blockquote>
+
+  <p>This is a celebrated speculation, and has been reprinted abroad, and
+  seriously answered. Craig is known in the early history of fluxions, and
+  was a good mathematician. <!-- Page 130 --><span class="pagenum"><a
+  name="page130"></a>[130]</span>He professed to calculate, on the
+  hypothesis that the suspicions against historical evidence increase with
+  the square of the time, how long it will take the evidence of
+  Christianity to die out. He finds, by formulæ, that had it been oral
+  only, it would have gone out A.D. 800; but, by aid of the written
+  evidence, it will last till A.D. 3150. At this period he places the
+  second coming, which is deferred until the extinction of evidence, on the
+  authority of the question "When the Son of Man cometh, shall he find
+  faith on the earth?" It is a pity that Craig's theory was not adopted: it
+  would have spared a hundred treatises on the end of the world, founded on
+  no better knowledge than his, and many of them falsified by the event.
+  The most recent (October, 1863) is a tract in proof of Louis Napoleon
+  being Antichrist, the Beast, the eighth Head, etc.; and the present
+  dispensation is to close soon after 1864.</p>
+
+  <p>In order rightly to judge Craig, who added speculations on the
+  variations of pleasure and pain treated as functions of time, it is
+  necessary to remember that in Newton's day the idea of force, as a
+  quantity to be measured, and as following a law of variation, was very
+  new: so likewise was that of probability, or belief, as an object of
+  measurement.<a name="NtA_269" href="#Nt_269"><sup>[269]</sup></a> The
+  success of the <i>Principia</i> of Newton put it into many heads to
+  speculate about applying notions of quantity to other things not then
+  brought under measurement. Craig imitated Newton's title, and evidently
+  thought he was making a step in advance: but it is not every one who can
+  plough with Samson's heifer.</p>
+
+  <p>It is likely enough that Craig took a hint, directly or indirectly,
+  from Mohammedan writers, who make a reply to the argument that the Koran
+  has not the evidence derived <!-- Page 131 --><span class="pagenum"><a
+  name="page131"></a>[131]</span>from miracles. They say that, as evidence
+  of Christian miracles is daily becoming weaker, a time must at last
+  arrive when it will fail of affording assurance that they were miracles
+  at all: whence would arise the necessity of another prophet and other
+  miracles. Lee,<a name="NtA_270" href="#Nt_270"><sup>[270]</sup></a> the
+  Cambridge Orientalist, from whom the above words are taken, almost
+  certainly never heard of Craig or his theory.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE ARISTOCRAT AS A SCIENTIST.</p>
+
+<blockquote class="b1n">
+
+  <p>Copernicans of all sorts convicted ... to which is added a Treatise of
+  the Magnet. By the Hon. Edw. Howard, of Berks. London, 1705, 8vo.</p>
+
+</blockquote>
+
+  <p>Not all the blood of all the Howards will gain respect for a writer
+  who maintains that eclipses admit no possible explanation under the
+  Copernican hypothesis, and who asks how a man can "go 200 yards to any
+  place if the moving superficies of the earth does carry it from him?"
+  Horace Walpole, at the beginning of his <i>Royal and Noble Authors</i>,
+  has mottoed his book with the Cardinal's address to Ariosto, "Dove
+  diavolo, Messer Ludovico, avete pigliato tante coglionerie?"<a
+  name="NtA_271" href="#Nt_271"><sup>[271]</sup></a> Walter Scott says you
+  could hardly pick out, on any principle of selection&mdash;except badness
+  itself, he means of course&mdash;the same number of plebeian authors
+  whose works are so bad. But his implied satire on aristocratic writing
+  forgets two points. First, during a large period of our history, when
+  persons of rank condescended to write, they veiled themselves under "a
+  person of honor," "a person of quality," and the like, when not wholly
+  undescribed. Not one of these has Walpole got; he omits, <!-- Page 132
+  --><span class="pagenum"><a name="page132"></a>[132]</span>for instance,
+  Lord Brounker's<a name="NtA_272" href="#Nt_272"><sup>[272]</sup></a>
+  translation of Descartes on Music. Secondly, Walpole only takes the heads
+  of houses: this cuts both ways; he equally eliminates the Hon. Robert
+  Boyle and the precious Edward Howard. The last writer is hardly out of
+  the time in which aristocracy suppressed its names; the avowal was then
+  usually meant to make the author's greatness useful to the book. In our
+  day, literary peers and honorables are very favorably known, and contain
+  an eminent class.<a name="NtA_273" href="#Nt_273"><sup>[273]</sup></a>
+  They rough it like others, and if such a specimen as Edw. Howard were now
+  to appear, he would be greeted with</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Hereditary noodle! knowest thou not</p>
+      <p>Who would be wise, himself must make him so?"</p>
+    </div>
+  </div>
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE LONGITUDE PROBLEM.</p>
+
+<blockquote class="b1n">
+
+  <p>A new and easy method to find the longitude at land or sea. London,
+  1710, 4to.</p>
+
+</blockquote>
+
+  <p>This tract is a little earlier than the great epoch of such
+  publications (1714), and professes to find the longitude by the observed
+  altitudes of the moon and two stars.<a name="NtA_274"
+  href="#Nt_274"><sup>[274]</sup></a> <!-- Page 133 --><span
+  class="pagenum"><a name="page133"></a>[133]</span></p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>A new method for discovering the longitude both at sea and land,
+  humbly proposed to the consideration of the public.<a name="NtA_275"
+  href="#Nt_275"><sup>[275]</sup></a> By Wm. Whiston<a name="NtA_276"
+  href="#Nt_276"><sup>[276]</sup></a> and Humphry Ditton.<a name="NtA_277"
+  href="#Nt_277"><sup>[277]</sup></a> London, 1714, 8vo.</p>
+
+</blockquote>
+
+  <p>This is the celebrated tract, written by the two Arian heretics.
+  Swift, whose orthodoxy was as undoubted as his meekness, wrote upon it
+  the epigram&mdash;if, indeed, that be epigram of which the point is pious
+  wish&mdash;which has been so often recited for the purity of its style, a
+  purity which transcends modern printing. Perhaps some readers may think
+  that Swift cared little for Whiston and Ditton, except as a chance
+  hearing of their plan pointed them out as good marks. But it was not so:
+  the clique had their eye on the guilty pair before the publication of the
+  tract. The preface is dated July 7; and ten days afterwards Arbuthnot<a
+  name="NtA_278" href="#Nt_278"><sup>[278]</sup></a> writes as follows to
+  Swift:</p>
+
+  <p>"Whiston has at last published his project of the longitude; the most
+  ridiculous thing that ever was thought on. But a pox on him! he has
+  spoiled one of my papers of Scriblerus, which was a proposition for the
+  longitude not very unlike his, to this purpose; that since there was no
+  pole for east and west, that all the princes of Europe should join and
+  build two prodigious poles, upon high mountains, <!-- Page 134 --><span
+  class="pagenum"><a name="page134"></a>[134]</span>with a vast lighthouse
+  to serve for a polestar. I was thinking of a calculation of the time,
+  charges, and dimensions. Now you must understand his project is by
+  lighthouses, and explosion of bombs at a certain hour."</p>
+
+  <p>The plan was certainly impracticable; but Whiston and Ditton might
+  have retorted that they were nearer to the longitude than their satirist
+  to the kingdom of heaven, or even to a bishopric. Arbuthnot, I think,
+  here and elsewhere, reveals himself as the calculator who kept Swift
+  right in his proportions in the matter of the Lilliputians,
+  Brobdingnagians, etc. Swift was very ignorant about things connected with
+  number. He writes to Stella that he has discovered that leap-year comes
+  every four years, and that all his life he had thought it came every
+  three years. Did he begin with the mistake of Cæsar's priests? Whether or
+  no, when I find the person who did not understand leap-year inventing
+  satellites of Mars in correct accordance with Kepler's third law, I feel
+  sure he must have had help.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE AURORA BOREALIS.</p>
+
+<blockquote class="b1n">
+
+  <p>An essay concerning the late apparition in the heavens on the 6th of
+  March. Proving by mathematical, logical, and moral arguments, that it
+  cou'd not have been produced meerly by the ordinary course of nature, but
+  must of necessity be a prodigy. Humbly offered to the consideration of
+  the Royal Society. London, 1716, 8vo.</p>
+
+</blockquote>
+
+  <p>The prodigy, as described, was what we should call a very decided and
+  unusual aurora borealis. The inference was, that men's sins were bringing
+  on the end of the world. The author thinks that if one of the old
+  "threatening prophets" were then alive, he would give "something like the
+  following." I quote a few sentences of the notion which the author had of
+  the way in which Ezekiel, for instance, would have addressed his Maker in
+  the reign of George the First:</p>
+
+  <p>"Begin! Begin! O Sovereign, for once, with an <!-- Page 135 --><span
+  class="pagenum"><a name="page135"></a>[135]</span>effectual clap of
+  thunder.... O Deity! either thunder to us no more, or when you thunder,
+  do it home, and strike with vengeance to the mark.... 'Tis not enough to
+  raise a storm, unless you follow it with a blow, and the thunder without
+  the bolt, signifies just nothing at all.... Are then your lightnings of
+  so short a sight, that they don't know how to hit, unless a mountain
+  stands like a barrier in their way? Or perhaps so many eyes open in the
+  firmament make you lose your aim when you shoot the arrow? Is it this?
+  No! but, my dear Lord, it is your custom never to take hold of your arms
+  till you have first bound round your majestic countenance with gathered
+  mists and clouds."</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>The principles of the Philosophy of the Expansive and Contractive
+  Forces ... By Robert Greene,<a name="NtA_279"
+  href="#Nt_279"><sup>[279]</sup></a> M.A., Fellow of Clare Hall.
+  Cambridge, 1727, folio.</p>
+
+</blockquote>
+
+  <p>Sanderson<a name="NtA_280" href="#Nt_280"><sup>[280]</sup></a> writes
+  to Jones,<a name="NtA_281" href="#Nt_281"><sup>[281]</sup></a> "The
+  gentleman has been reputed mad for these two years last past, but never
+  gave the world such ample testimony of it before." This was said of a
+  former work of Greene's, on solid geometry, published in 1712, in which
+  he gives a quadrature.<a name="NtA_282"
+  href="#Nt_282"><sup>[282]</sup></a> He gives the same or another, I do
+  not know which, in the present work, in which the circle is 3-1/5
+  diameters. This volume is of 981 good folio pages, and treats of all
+  things, mental and material. The author is not at all mad, only wrong on
+  <!-- Page 136 --><span class="pagenum"><a
+  name="page136"></a>[136]</span>many points. It is the weakness of the
+  orthodox follower of any received system to impute insanity to the
+  solitary dissentient: which is voted (in due time) a very wrong opinion
+  about Copernicus, Columbus, or Galileo, but quite right about Robert
+  Greene. If misconceptions, acted on by too much self-opinion, be
+  sufficient evidence of madness, it would be a curious inquiry what is the
+  least per-centage of the reigning school which has been insane at any one
+  time. Greene is one of the sources for Newton being led to think of
+  gravitation by the fall of an apple: his authority is the gossip of
+  Martin Folkes.<a name="NtA_283" href="#Nt_283"><sup>[283]</sup></a>
+  Probably Folkes had it from Newton's niece, Mrs. Conduitt, whom Voltaire
+  acknowledges as <i>his authority</i>.<a name="NtA_284"
+  href="#Nt_284"><sup>[284]</sup></a> It is in the draft found among
+  Conduitt's papers of memoranda to be sent to Fontenelle. But Fontenelle,
+  though a great retailer of anecdote, does not mention it in his
+  <i>éloge</i> of Newton; whence it may be suspected that it was left out
+  in the copy forwarded to France. D'Israeli has got an improvement on the
+  story: the apple "struck him a smart blow on the head": no doubt taking
+  him just on the organ of causality. He was "surprised at the force of the
+  stroke" from so small an apple: but then the apple had a mission; Homer
+  would have said <!-- Page 137 --><span class="pagenum"><a
+  name="page137"></a>[137]</span>it was Minerva in the form of an apple.
+  "This led him to consider the accelerating motion of falling bodies,"
+  which Galileo had settled long before: "from whence he deduced the
+  principle of gravity," which many had considered before him, but no one
+  had <i>deduced anything from it</i>. I cannot imagine whence D'Israeli
+  got the rap on the head, I mean got it for Newton: this is very unlike
+  his usual accounts of things. The story is pleasant and possible: its
+  only defect is that various writings, well known to Newton, a very
+  <i>learned</i> mathematician, had given more suggestion than a whole sack
+  of apples could have done, if they had tumbled on that mighty head all at
+  once. And Pemberton, speaking from Newton himself, says nothing more than
+  that the idea of the moon being retained by the same force which causes
+  the fall of bodies struck him for the first time while meditating in a
+  garden. One particular tree at Woolsthorpe has been selected as the
+  gallows of the appleshaped goddess: it died in 1820, and Mr. Turnor<a
+  name="NtA_285" href="#Nt_285"><sup>[285]</sup></a> kept the wood; but Sir
+  D. Brewster<a name="NtA_286" href="#Nt_286"><sup>[286]</sup></a> brought
+  away a bit of root in 1814, and must have had it on his conscience for 43
+  years that he may have killed the tree. Kepler's suggestion of
+  gravitation with the inverse distance, and Bouillaud's proposed
+  substitution of the inverse square of the distance, are things which
+  Newton knew better than his modern readers. I discovered two anagrams on
+  his name, which are quite conclusive; the notion of gravitation was
+  <i>not new</i>; but Newton <i>went on</i>. Some wandering spirit,
+  probably whose business it was to resent any liberty taken with Newton's
+  name, put into the head of a friend of mine <i>eighty-one</i> anagrams on
+  my own pair, some of which hit harder than any apple.</p>
+
+<p><!-- Page 138 --><span class="pagenum"><a name="page138"></a>[138]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">DE MORGAN ANAGRAMS.</p>
+
+  <p>This friend, whom I must not name, has since made it up to about 800
+  anagrams on my name, of which I have seen about 650. Two of them I have
+  joined in the title-page: the reader may find the sense. A few of the
+  others are personal remarks.</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Great gun! do us a sum!"</p>
+    </div>
+  </div>
+  <p>is a sneer at my pursuits: but,</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Go! great sum! &int;<i>a u<sup><i>n</i></sup> du</i>"</p>
+    </div>
+  </div>
+  <p>is more dignified.</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Sunt agro! gaudemus,"<a name="NtA_287" href="#Nt_287"><sup>[287]</sup></a></p>
+    </div>
+  </div>
+  <p>is happy as applied to one of whom it may be said:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Ne'er out of town; 'tis such a horrid life;</p>
+      <p class="i1">But duly sends his family and wife."</p>
+    </div>
+  </div>
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Adsum, nugator, suge!"<a name="NtA_288" href="#Nt_288"><sup>[288]</sup></a></p>
+    </div>
+  </div>
+  <p>is addressed to a student who continues talking after the lecture has
+  commenced: oh! the rascal!</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Graduatus sum! nego"<a name="NtA_289" href="#Nt_289"><sup>[289]</sup></a></p>
+    </div>
+  </div>
+  <p>applies to one who declined to subscribe for an M.A. degree.</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Usage mounts guard"</p>
+    </div>
+  </div>
+  <p>symbolizes a person of very fixed habits.</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Gus! Gus! a mature don!</p>
+      <p class="i2">August man! sure, god!</p>
+      <p>And Gus must argue, O!</p>
+      <p class="i2">Snug as mud to argue,</p>
+      <p>Must argue on gauds.</p>
+      <p class="i2">A mad rogue stung us.</p>
+      <p>Gag a numerous stud</p>
+      <p class="i2">Go! turn us! damage us!</p>
+      <p>Tug us! O drag us! Amen.</p>
+      <p class="i2">Grudge us! moan at us!</p>
+<!-- Page 139 --><span class="pagenum"><a name="page139"></a>[139]</span>
+      <p>Daunt us! gag us more!</p>
+      <p class="i2">Dog-ear us, man! gut us!</p>
+      <p>D&mdash;&mdash; us! a rogue tugs!"</p>
+    </div>
+  </div>
+  <p>are addressed to me by the circle-squarers; and,</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"O! Gus! tug a mean surd!"</p>
+    </div>
+  </div>
+  <p>is smart upon my preference of an incommensurable value of <span
+  class="grk">&pi;</span> to 3-1/5, or some such simple substitute.
+  While,</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Gus! Gus! at 'em a' round!"</p>
+    </div>
+  </div>
+  <p>ought to be the backing of the scientific world to the author of the
+  <i>Budget of Paradoxes</i>.</p>
+
+  <p>The whole collection commenced existence in the head of a powerful
+  mathematician during some sleepless nights. Seeing how large a number was
+  practicable, he amused himself by inventing a digested plan of finding
+  more.</p>
+
+  <p>Is there any one whose name cannot be twisted into either praise or
+  satire? I have had given to me,</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Thomas Babington Macaulay</p>
+      <p class="i1">Mouths big: a Cantab anomaly."</p>
+    </div>
+  </div>
+  <p>&nbsp;</p>
+
+<p class="cenhead">NEWTON'S DE MUNDI SYSTEMATE LIBER.</p>
+
+<blockquote class="b1n">
+
+  <p>A treatise of the system of the world. By Sir Isaac Newton. Translated
+  into English. London, 1728, 8vo.</p>
+
+</blockquote>
+
+  <p>I think I have a right to one little paradox of my own: I greatly
+  doubt that Newton wrote this book. Castiglione,<a name="NtA_290"
+  href="#Nt_290"><sup>[290]</sup></a> in his <i>Newtoni Opuscula</i>,<a
+  name="NtA_291" href="#Nt_291"><sup>[291]</sup></a> gives it in the Latin
+  which appeared in 1731,<a name="NtA_292"
+  href="#Nt_292"><sup>[292]</sup></a> not for the first time; he says
+  <i>Angli omnes Newtono tribuunt</i>.<a name="NtA_293"
+  href="#Nt_293"><sup>[293]</sup></a> It appeared just after Newton's
+  death, without the name of any editor, or any allusion to Newton's <!--
+  Page 140 --><span class="pagenum"><a
+  name="page140"></a>[140]</span>recent departure, purporting to be that
+  popular treatise which Newton, at the beginning of the third book of the
+  <i>Principia</i>, says he wrote, intending it to be the third book. It is
+  very possible that some observant turnpenny might construct such a
+  treatise as this from the third book, that it might be ready for
+  publication the moment Newton could not disown it. It has been treated
+  with singular silence: the name of the editor has never been given.
+  Rigaud<a name="NtA_294" href="#Nt_294"><sup>[294]</sup></a> mentions it
+  without a word: I cannot find it in Brewster's <i>Newton</i>, nor in the
+  <i>Biographia Britannica</i>. There is no copy in the Catalogue of the
+  Royal Society's Library, either in English or Latin, except in
+  Castiglione. I am open to correction; but I think nothing from Newton's
+  acknowledged works will prove&mdash;as laid down in the suspected
+  work&mdash;that he took Numa's temple of Vesta, with a central fire, to
+  be intended to symbolize the sun as the center of our system, in the
+  Copernican sense.<a name="NtA_295"
+  href="#Nt_295"><sup>[295]</sup></a></p>
+
+  <p>Mr. Edleston<a name="NtA_296" href="#Nt_296"><sup>[296]</sup></a>
+  gives an account of the <i>lectures</i> "de motu corporum," and gives the
+  corresponding pages of the <i>Latin</i> "De Systemate Mundi" of 1731. But
+  no one mentions the <i>English</i> of 1728. This English seems to agree
+  with the Latin; but there is a mystery about it. The preface says, "That
+  this work as here published is genuine will so clearly appear by the
+  intrinsic marks it bears, that it will be but losing words and the
+  reader's time to take pains in giving him any other satisfaction." Surely
+  fewer words would have been lost if the prefator had said at once that
+  the work was from the manuscript preserved at Cambridge. Perhaps it was a
+  mangled copy clandestinely taken and interpreted. <!-- Page 141 --><span
+  class="pagenum"><a name="page141"></a>[141]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A BACONIAN CONTROVERSY.</p>
+
+<blockquote class="b1n">
+
+  <p>Lord Bacon not the author of "The Christian Paradoxes," being a
+  reprint of "Memorials of Godliness and Christianity," by Herbert Palmer,
+  B.D.<a name="NtA_297" href="#Nt_297"><sup>[297]</sup></a> With
+  Introduction, Memoir, and Notes, by the Rev. Alexander B. Grosart,<a
+  name="NtA_298" href="#Nt_298"><sup>[298]</sup></a> Kenross. (Private
+  circulation, 1864).</p>
+
+</blockquote>
+
+  <p>I insert the above in this place on account of a slight connection
+  with the last. Bacon's Paradoxes,&mdash;so attributed&mdash;were first
+  published as his in some asserted "Remains," 1648.<a name="NtA_299"
+  href="#Nt_299"><sup>[299]</sup></a> They were admitted into his works in
+  1730, and remain there to this day. The title is "The Character of a
+  believing Christian, set forth in paradoxes and seeming contradictions."
+  The following is a specimen:</p>
+
+  <p>"He believes three to be one and one to be three; a father not to be
+  older than his son; a son to be equal with his father; and one proceeding
+  from both to be equal with both: he believes three persons in one nature,
+  and two natures in one person.... He believes the God of all grace to
+  have been angry with one that never offended Him; and that God that hates
+  sin to be reconciled to himself though sinning continually, and never
+  making or being able to make Him any satisfaction. He believes a most
+  just God to have punished a most just person, and to have justified
+  himself, though a most ungodly sinner. He believes himself freely
+  pardoned, and yet a sufficient satisfaction was made for him."</p>
+
+  <p>Who can doubt that if Bacon had written this it must have been wrong?
+  Many writers, especially on the <!-- Page 142 --><span class="pagenum"><a
+  name="page142"></a>[142]</span>Continent, have taken him as sneering at
+  (Athanasian) Christianity right and left. Many Englishmen have taken him
+  to be quite in earnest, and to have produced a body of edifying doctrine.
+  More than a century ago the Paradoxes were published as a penny tract;
+  and, again, at the same price, in the <i>Penny Sunday Reader</i>, vol.
+  vi, No. 148, a few passages were omitted, as <i>too strong</i>. But all
+  did not agree: in my copy of Peter Shaw's <a name="NtA_300"
+  href="#Nt_300"><sup>[300]</sup></a> edition (vol. ii, p. 283) the
+  Paradoxes have been cut out by the binder, who has left the backs of the
+  leaves. I never had the curiosity to see whether other copies of the
+  edition have been served in the same way. The Religious Tract Society
+  republished them recently in <i>Selections from the Writings of Lord
+  Bacon</i>, (no date; bad plan; about 1863, I suppose). No omissions were
+  made, so far as I find.</p>
+
+  <p>I never believed that Bacon wrote this paper; it has neither his
+  <i>sparkle</i> nor his idiom. I stated my doubts even before I heard that
+  Mr. Spedding, one of Bacon's editors, was of the same mind.
+  (<i>Athenæum</i>, July 16, 1864). I was little moved by the wide consent
+  of orthodox men: for I knew how Bacon, Milton, Newton, Locke, etc., were
+  always claimed as orthodox until almost the present day. Of this there is
+  a remarkable instance.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">LOCKE AND SOCINIANISM.</p>
+
+  <p>Among the books which in my younger day were in some orthodox
+  publication lists&mdash;I think in the list of the Christian Knowledge
+  Society, but I am not sure&mdash;was Locke's <a name="NtA_301"
+  href="#Nt_301"><sup>[301]</sup></a> "Reasonableness of Christianity." It
+  seems to have come down from the eighteenth century, when the battle was
+  belief in Christ against unbelief, <i>simpliciter</i>, as the <!-- Page
+  143 --><span class="pagenum"><a name="page143"></a>[143]</span>logicians
+  say. Now, if ever there was a Socinian<a name="NtA_302"
+  href="#Nt_302"><sup>[302]</sup></a> book in the world, it is this work of
+  Locke. "These two," says Locke, "faith and repentance, i.e., believing
+  Jesus to be the Messiah, and a good life, are the indispensable
+  conditions of the new covenant, to be performed by all those who would
+  obtain eternal life." All the book is amplification of this doctrine.
+  Locke, in this and many other things, followed Hobbes, whose doctrine, in
+  the Leviathan, is <i>fidem, quanta ad salutem necessaria est, contineri
+  in hoc articulo, Jesus est Christus</i>.<a name="NtA_303"
+  href="#Nt_303"><sup>[303]</sup></a> For this Hobbes was called an
+  atheist, which <!-- Page 144 --><span class="pagenum"><a
+  name="page144"></a>[144]</span>many still believe him to have been: some
+  of his contemporaries called him, rightly, a Socinian. Locke was known
+  for a Socinian as soon as his work appeared: Dr. John Edwards,<a
+  name="NtA_304" href="#Nt_304"><sup>[304]</sup></a> his assailant, says he
+  is "Socinianized all over." Locke, in his reply, says "there is not one
+  word of Socinianism in it:" and he was right: the positive Socinian
+  doctrine has <i>not one word of Socinianism in it</i>; Socinianism
+  consists in omissions. Locke and Hobbes did not dare <i>deny</i> the
+  Trinity: for such a thing Hobbes might have been roasted, and Locke might
+  have been strangled. Accordingly, the well-known way of teaching
+  Unitarian doctrine was the collection of the asserted essentials of
+  Christianity, without naming the Trinity, etc. This is the plan Newton
+  followed, in the papers which have at last been published.<a
+  name="NtA_305" href="#Nt_305"><sup>[305]</sup></a></p>
+
+  <p>So I, for one, thought little about the general tendency of orthodox
+  writers to claim Bacon by means of the Paradoxes. I knew that, in his
+  "Confession of Faith"<a name="NtA_306"
+  href="#Nt_306"><sup>[306]</sup></a> he is a Trinitarian of a heterodox
+  stamp. His second Person takes human nature before he took flesh, not for
+  redemption, but as a condition precedent of creation. "God is so holy,
+  pure, and jealous, that it is impossible for him to be pleased in any
+  creature, though the work of his own hands.... [Gen. i. 10, 12, 18, 21,
+  25, 31, freely rendered]. But&mdash;purposing to become a Creator, and to
+  communicate to his creatures, he ordained in his eternal counsel that one
+  person of the Godhead should be united to one nature, and to one
+  particular of his creatures; that so, in the person of the Mediator, the
+  true ladder might be fixed, whereby God might <!-- Page 145 --><span
+  class="pagenum"><a name="page145"></a>[145]</span>descend to his
+  creatures and his creatures might ascend to God...."</p>
+
+  <p>This is republished by the Religious Tract Society, and seems to suit
+  their theology, for they confess to having omitted some things of which
+  they disapprove.</p>
+
+  <p>In 1864, Mr. Grosart published his discovery that the Paradoxes are by
+  Herbert Palmer; that they were first published surreptitiously, and
+  immediately afterwards by himself, both in 1645; that the "Remains" of
+  Bacon did not appear until 1648; that from 1645 to 1708, thirteen
+  editions of the "Memorials" were published, all containing the Paradoxes.
+  In spite of this, the Paradoxes were introduced into Bacon's works in
+  1730, where they have remained.</p>
+
+  <p>Herbert Palmer was of good descent, and educated as a Puritan. He was
+  an accomplished man, one of the few of his day who could speak French as
+  well as English. He went into the Church, and was beneficed by Laud,<a
+  name="NtA_307" href="#Nt_307"><sup>[307]</sup></a> in spite of his
+  puritanism; he sat in the Assembly of Divines, and was finally President
+  of Queens' College, Cambridge, in which post he died, August 13, 1647, in
+  the 46th year of his age.</p>
+
+  <p>Mr. Grosart says, speaking of Bacon's "Remains," "All who have had
+  occasion to examine our early literature are aware that it was a common
+  trick to issue imperfect, false, and unauthorized writings under any
+  recently deceased name that might be expected to take. The Puritans, down
+  to John Bunyan, were perpetually expostulating and protesting against
+  such procedure." I have met with instances of all this; but I did not
+  know that there was so much of it: a good collection would be very
+  useful. The work of 1728, attributed to Newton, is likely enough to be
+  one of the class.</p>
+
+<p><!-- Page 146 --><span class="pagenum"><a name="page146"></a>[146]</span></p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Demonstration de l'immobilitez de la Terre.... Par M. de la
+  Jonchere,<a name="NtA_308" href="#Nt_308"><sup>[308]</sup></a> Ingénieur
+  Français. Londres, 1728, 8vo.</p>
+
+</blockquote>
+
+  <p>A synopsis which is of a line of argument belonging to the beginning
+  of the preceding century.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">TWO FORGOTTEN CIRCLE SQUARERS.</p>
+
+<blockquote class="b1n">
+
+  <p>The Circle squared; together with the Ellipsis and several reflections
+  on it. The finding two geometrical mean proportionals, or doubling the
+  cube geometrically. By Richard Locke<a name="NtA_309"
+  href="#Nt_309"><sup>[309]</sup></a>.... London, no date, probably about
+  1730, 8vo.</p>
+
+</blockquote>
+
+  <p>According to Mr. Locke, the circumference is three diameters,
+  three-fourths the difference of the diameter and the side of the
+  inscribed equilateral triangle, and three-fourths the difference between
+  seven-eighths of the diameter and the side of the same triangle. This
+  gives, he says, 3.18897. There is an addition to this tract, being an
+  appendix to a book on the longitude.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>The Circle squar'd. By Thos. Baxter, Crathorn, Cleaveland, Yorkshire.
+  London, 1732, 8vo.</p>
+
+</blockquote>
+
+  <p>Here <span class="grk">&pi;</span> = 3.0625. No proof is offered.<a
+  name="NtA_310" href="#Nt_310"><sup>[310]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>The longitude discovered by the Eclipses, Occultations, and
+  Conjunctions of Jupiter's planets. By William Whiston. London, 1738.</p>
+
+</blockquote>
+
+  <p>This tract has, in some copies, the celebrated preface containing the
+  account of Newton's appearance before the Parliamentary Committee on the
+  longitude question, in 1714 <!-- Page 147 --><span class="pagenum"><a
+  name="page147"></a>[147]</span>(Brewster, ii. 257-266). This "historical
+  preface," is an insertion and is dated April 28, 1741, with four
+  additional pages dated August 10, 1741. The short "preface" is by the
+  publisher, John Whiston,<a name="NtA_311"
+  href="#Nt_311"><sup>[311]</sup></a> the author's son.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE STEAMSHIP SUGGESTED.</p>
+
+<blockquote class="b1n">
+
+  <p>A description and draught of a new-invented machine for carrying
+  vessels or ships out of, or into any harbour, port, or river, against
+  wind and tide, or in a calm. For which, His Majesty has granted letters
+  patent, for the sole benefit of the author, for the space of fourteen
+  years. By Jonathan Hulls.<a name="NtA_312"
+  href="#Nt_312"><sup>[312]</sup></a> London: printed for the author, 1737.
+  Price sixpence (folding plate and pp. 48, beginning from title).</p>
+
+</blockquote>
+
+  <p>(I ought to have entered this tract in its place. It is so rare that
+  its existence was once doubted. It is the earliest description of
+  steam-power applied to navigation. The plate shows a barge, with smoking
+  funnel, and paddles at the stem, towing a ship of war. The engine, as
+  described, is Newcomen's.<a name="NtA_313"
+  href="#Nt_313"><sup>[313]</sup></a></p>
+
+  <p>In 1855, John Sheepshanks,<a name="NtA_314"
+  href="#Nt_314"><sup>[314]</sup></a> so well known as a friend of Art and
+  a public donor, reprinted this tract, in fac-simile, from his own copy;
+  twenty-seven copies of the original 12mo size, and twelve on old paper,
+  small 4to. I have an original copy, wanting the plate, and with "Price
+  sixpence" carefully erased, to the honor of the book.<a name="NtA_315"
+  href="#Nt_315"><sup>[315]</sup></a></p>
+
+<p><!-- Page 148 --><span class="pagenum"><a name="page148"></a>[148]</span></p>
+
+  <p>It is not known whether Hulls actually constructed a boat.<a
+  name="NtA_316" href="#Nt_316"><sup>[316]</sup></a> In all probability his
+  tract suggested to Symington, as Symington<a name="NtA_317"
+  href="#Nt_317"><sup>[317]</sup></a> did to Fulton.)</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE NEWTONIANS ATTACKED.</p>
+
+<blockquote class="b1n">
+
+  <p>Le vrai système de physique générale de M. Isaac Newton exposé et
+  analysé en parallèle avec celui de Descartes. By Louis Castel<a
+  name="NtA_318" href="#Nt_318"><sup>[318]</sup></a> [Jesuit and F.R.S.]
+  Paris, 1743, 4to.</p>
+
+</blockquote>
+
+  <p>This is an elaborate correction of Newton's followers, and of Newton
+  himself, who it seems did not give his own views with perfect fidelity.
+  Father Castel, for instance, assures us that Newton placed the sun <i>at
+  rest</i> in the center of the system. Newton left the sun to arrange that
+  matter with the planets and the rest of the universe. In this volume of
+  500 pages there is right and wrong, both clever.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>A dissertation on the Æther of Sir Isaac Newton. By Bryan Robinson,<a
+  name="NtA_319" href="#Nt_319"><sup>[319]</sup></a> M.D. Dublin, 1743,
+  8vo.<a name="NtA_320" href="#Nt_320"><sup>[320]</sup></a></p>
+
+</blockquote>
+
+<p><!-- Page 149 --><span class="pagenum"><a name="page149"></a>[149]</span></p>
+
+  <p>A mathematical work professing to prove that the assumed ether causes
+  gravitation.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">MATHEMATICAL THEOLOGY.</p>
+
+<blockquote class="b1n">
+
+  <p>Mathematical principles of theology, or the existence of God
+  geometrically demonstrated. By Richard Jack, teacher of Mathematics.
+  London, 1747, 8vo.<a name="NtA_321"
+  href="#Nt_321"><sup>[321]</sup></a></p>
+
+</blockquote>
+
+  <p>Propositions arranged after the manner of Euclid, with beings
+  represented by circles and squares. But these circles and squares are
+  logical symbols, not geometrical ones. I brought this book forward to the
+  Royal Commission on the British Museum as an instance of the absurdity of
+  attempting a <i>classed</i> catalogue from the <i>titles</i> of books.
+  The title of this book sends it either to theology or geometry: when, in
+  fact, it is a logical vagary. Some of the houses which Jack built were
+  destroyed by the fortune of war in 1745, at Edinburgh: who will say the
+  rebels did no good whatever? I suspect that Jack copied the ideas of J.B.
+  Morinus, "Quod Deus sit," Paris, 1636,<a name="NtA_322"
+  href="#Nt_322"><sup>[322]</sup></a> 4to, containing an attempt of the
+  same kind, but not stultified with diagrams.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">TWO MODEL INDORSEMENTS.</p>
+
+<blockquote class="b1n">
+
+  <p>Dissertation, découverte, et démonstrations de la quadrature
+  mathématique du cercle. Par M. de Fauré, géomètre. [<i>s. l.</i>,
+  probably Geneva] 1747, 8vo.</p>
+
+  <p>Analyse de la Quadrature du Cercle. Par M. de Fauré, Gentilhomme
+  Suisse. Hague, 1749,<a name="NtA_323" href="#Nt_323"><sup>[323]</sup></a>
+  4to.</p>
+
+</blockquote>
+
+  <p>According to this octavo geometer and quarto gentleman, a diameter of
+  81 gives a circumference of 256. There is an amusing circumstance about
+  the quarto which has been overlooked, if indeed the book has ever been
+  <!-- Page 150 --><span class="pagenum"><a
+  name="page150"></a>[150]</span>examined. John Bernoulli (the one of the
+  day)<a name="NtA_324" href="#Nt_324"><sup>[324]</sup></a> and Koenig<a
+  name="NtA_325" href="#Nt_325"><sup>[325]</sup></a> have both given an
+  attestation: my mathematical readers may stare as they please, such is
+  the fact. But, on examination, there will be reason to think the two sly
+  Swiss played their countryman the same trick as the medical man played
+  Miss Pickle, in the novel of that name. The lady only wanted to get his
+  authority against sousing her little nephew, and said, "Pray, doctor, is
+  it not both dangerous and cruel to be the means of letting a poor tender
+  infant perish by sousing it in water as cold as ice?"&mdash;"Downright
+  murder, I affirm," said the doctor; and certified accordingly. De Fauré
+  had built a tremendous scaffolding of equations, quite out of place, and
+  feeling cock-sure that his solutions, if correct, would square the
+  circle, applied to Bernoulli and Koenig&mdash;who after his tract of two
+  years before, must have known what he was at&mdash;for their approbation
+  of the solutions. And he got it, as follows, well guarded:</p>
+
+<blockquote class="b1n">
+
+  <p>"Suivant les suppositions posées dans ce Mémoire, il est si évident
+  que <i>t</i> doit être = 34, <i>y</i> = 1, et <i>z</i> = 1, que cela n'a
+  besoin ni de preuve ni d'autorité pour être reconnu par tout le monde.<a
+  name="NtA_326" href="#Nt_326"><sup>[326]</sup></a></p>
+
+  <p class="author">"à Basle le 7e Mai 1749. <span class="sc">Jean Bernoulli.</span>"
+
+  <p>"Je souscris au jugement de Mr. Bernoulli, en conséquence de ces
+  suppositions.<a name="NtA_327" href="#Nt_327"><sup>[327]</sup></a></p>
+
+  <p class="author">"à la Haye le 21 Juin 1749. <span class="sc">S. Koenig.</span>"
+
+</blockquote>
+
+  <p>On which de Fauré remarks with triumph&mdash;as I have no doubt it was
+  intended he should do&mdash;"il conste clairement par ma présente Analyse
+  et Démonstration, qu'ils y ont déja <!-- Page 151 --><span
+  class="pagenum"><a name="page151"></a>[151]</span>reconnu et approuvé
+  parfaitement que la quadrature du cercle est mathématiquement
+  démontrée."<a name="NtA_328" href="#Nt_328"><sup>[328]</sup></a> It
+  should seem that it is easier to square the circle than to get round a
+  mathematician.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>An attempt to demonstrate that all the Phenomena in Nature may be
+  explained by two simple active principles, Attraction and Repulsion,
+  wherein the attraction of Cohesion, Gravity and Magnetism are shown to be
+  one the same. By Gowin Knight. London, 1748, 4to.</p>
+
+</blockquote>
+
+  <p>Dr. Knight<a name="NtA_329" href="#Nt_329"><sup>[329]</sup></a> was
+  Mr. Panizzi's<a name="NtA_330" href="#Nt_330"><sup>[330]</sup></a>
+  archetype, the first Principal Librarian of the British Museum. He was
+  celebrated for his magnetical experiments. This work was long neglected;
+  but is now recognized as of remarkable resemblance to modern
+  speculations.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THOMAS WRIGHT OF DURHAM.</p>
+
+<blockquote class="b1n">
+
+  <p>An original theory or Hypothesis of the Universe. By Thomas Wright<a
+  name="NtA_331" href="#Nt_331"><sup>[331]</sup></a> of Durham. London,
+  4to, 1750.</p>
+
+</blockquote>
+
+  <p>Wright is a speculator whose thoughts are now part of our current
+  astronomy. He took that view&mdash;or most of it&mdash;of the milky way
+  which afterwards suggested itself to William Herschel. I have given an
+  account of him and his work in the <i>Philosophical Magazine</i> for
+  April, 1848.</p>
+
+  <p>Wright was mathematical instrument maker to the King, <!-- Page 152
+  --><span class="pagenum"><a name="page152"></a>[152]</span>and kept a
+  shop in Fleet Street. Is the celebrated business of Troughton &amp;
+  Simms, also in Fleet Street, a lineal descendant of that of Wright? It is
+  likely enough, more likely that that&mdash;as I find him reported to have
+  affirmed&mdash;Prester John was the descendant of Solomon and the Queen
+  of Sheba. Having settled it thus, it struck me that I might apply to Mr.
+  Simms, and he informs me that it is as I thought, the line of descent
+  being Wright, Cole, John Troughton, Edward Troughton,<a name="NtA_332"
+  href="#Nt_332"><sup>[332]</sup></a> Troughton &amp; Simms.<a
+  name="NtA_333" href="#Nt_333"><sup>[333]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">BISHOP HORNE ON NEWTON.</p>
+
+<blockquote class="b1n">
+
+  <p>The theology and philosophy in Cicero's <i>Somnium Scipionis</i>
+  explained. Or, a brief attempt to demonstrate, that the Newtonian system
+  is perfectly agreeable to the notions of the wisest ancients: and that
+  mathematical principles are the only sure ones. [By Bishop Horne,<a
+  name="NtA_334" href="#Nt_334"><sup>[334]</sup></a> at the age of
+  nineteen.] London, 1751, 8vo.</p>
+
+</blockquote>
+
+  <p>This tract, which was not printed in the collected works, and is now
+  excessively rare, is mentioned in <i>Notes and Queries</i>, 1st S., v,
+  490, 573; 2d S., ix, 15. The boyish satire on Newton is amusing. Speaking
+  of old Benjamin Martin,<a name="NtA_335"
+  href="#Nt_335"><sup>[335]</sup></a> he goes on as follows:</p>
+
+<p><!-- Page 153 --><span class="pagenum"><a name="page153"></a>[153]</span></p>
+
+  <p>"But the most elegant account of the matter [attraction] is by that
+  hominiform animal, Mr. Benjamin Martin, who having attended Dr.
+  Desaguliers'<a name="NtA_336" href="#Nt_336"><sup>[336]</sup></a> fine,
+  raree, gallanty shew for some years [Desaguliers was one of the first who
+  gave public experimental lectures, before the saucy boy was born] in the
+  capacity of a turnspit, has, it seems, taken it into his head to set up
+  for a philosopher."</p>
+
+  <p>Thus is preserved the fact, unknown to his biographers, that Benj.
+  Martin was an assistant to Desaguliers in his lectures. Hutton<a
+  name="NtA_337" href="#Nt_337"><sup>[337]</sup></a> says of him, that "he
+  was well skilled in the whole circle of the mathematical and
+  philosophical sciences, and wrote useful books on every one of them":
+  this is quite true; and even at this day he is read by twenty where Horne
+  is read by one; see the stalls, <i>passim</i>. All that I say of him,
+  indeed my knowledge of the tract, is due to this contemptuous mention of
+  a more durable man than himself. My assistant secretary at the
+  Astronomical Society, the late Mr. Epps,<a name="NtA_338"
+  href="#Nt_338"><sup>[338]</sup></a> bought the copy at a stall because
+  his eye was caught by the notice of "Old Ben Martin," of whom he was a
+  great reader. Old Ben could not be a Fellow of the Royal Society, because
+  he kept a shop: even though the shop sold nothing but philosophical
+  instruments. Thomas Wright, similarly situated as to shop and goods,
+  never was a Fellow. The Society of our day has greatly degenerated: those
+  of the old time would be pleased, no doubt, that the glories of their day
+  <!-- Page 154 --><span class="pagenum"><a
+  name="page154"></a>[154]</span>should be commemorated. In the early days
+  of the Society, there was a similar difficulty about Graunt, the author
+  of the celebrated work on mortality. But their royal patron, "who never
+  said a foolish thing," sent them a sharp message, and charged them if
+  they found any more such tradesmen, they should "elect them without more
+  ado."</p>
+
+  <p>Horne's first pamphlet was published when he was but twenty-one years
+  old. Two years afterwards, being then a Fellow of his college, and having
+  seen more of the world, he seems to have felt that his manner was a
+  little too pert. He endeavored, it is said, to suppress his first tract:
+  and copies are certainly of extreme rarity. He published the following as
+  his maturer view:</p>
+
+<blockquote class="b1n">
+
+  <p>A fair, candid, and impartial state of the case between Sir Isaac
+  Newton and Mr. Hutchinson.<a name="NtA_339"
+  href="#Nt_339"><sup>[339]</sup></a> In which is shown how far a system of
+  physics is capable of mathematical demonstration; how far Sir Isaac's, as
+  such a system, has that demonstration; and consequently, what regard Mr.
+  Hutchinson's claim may deserve to have paid to it. By George Horne, M.A.
+  Oxford, 1753, 8vo.</p>
+
+</blockquote>
+
+  <p>It must be remembered that the successors of Newton were very apt to
+  declare that Newton had demonstrated attraction as a <i>physical</i>
+  cause: he had taken reasonable pains to show that he did not pretend to
+  this. If any one had said to Newton, I hold that every particle of matter
+  is a responsible being of vast intellect, ordered by the Creator to move
+  as it would do if every other particle attracted it, and gifted with
+  power to make its way in true accordance with that law, as easily as a
+  lady picks her way across the street; what have you to say against
+  it?&mdash;Newton must have replied, Sir! if you really undertake to
+  maintain this as <i>demonstrable</i>, your soul had better borrow a
+  little power <!-- Page 155 --><span class="pagenum"><a
+  name="page155"></a>[155]</span>from the particles of which your body is
+  made: if you merely ask me to refute it, I tell you that I neither can
+  nor need do it; for whether attraction comes in this way or in any other,
+  <i>it comes</i>, and that is all I have to do with it.</p>
+
+  <p>The reader should remember that the word attraction, as used by Newton
+  and the best of his followers, only meant a <i>drawing towards</i>,
+  without any implication as to the cause. Thus whether they said that
+  matter attracts matter, or that young lady attracts young gentleman, they
+  were using one word in one sense. Newton found that the law of the first
+  is the inverse square of the distance: I am not aware that the law of the
+  second has been discovered; if there be any chance, we shall see it at
+  the year 1856 in this list.</p>
+
+  <p>In this point young Horne made a hit. He justly censures those who
+  fixed upon Newton a more positive knowledge of what attraction is than he
+  pretended to have. "He has owned over and over he did not know what he
+  meant by it&mdash;it might be this, or it might be that, or it might be
+  anything, or it might be nothing." With the exception of the
+  <i>nothing</i> clause, this is true, though Newton might have answered
+  Horne by "Thou hast said it."</p>
+
+  <p>(I thought everybody knew the meaning of "Thou hast said it": but I
+  was mistaken. In three of the evangelists <span title="Su legeis" class="grk"
+  >&Sigma;&#x1F7A; &lambda;&#x1F73;&gamma;&epsilon;&iota;&sigmaf;</span> is
+  the answer to "Art thou a king?" The force of this answer, as always
+  understood, is "That is your way of putting it." The Puritans, who lived
+  in Bible phrases, so understood it: and Walter Scott, who caught all
+  peculiarities of language with great effect, makes a marked instance,
+  "Were you armed?&mdash;I was not&mdash;I went in my calling, as a
+  preacher of God's word, to encourage them that drew the sword in His
+  cause. In other words, to aid and abet the rebels, said the Duke. <i>Thou
+  hast spoken it</i>, replied the prisoner.")</p>
+
+  <p>Again, Horne quotes Rowning<a name="NtA_340"
+  href="#Nt_340"><sup>[340]</sup></a> as follows:</p>
+
+<p><!-- Page 156 --><span class="pagenum"><a name="page156"></a>[156]</span></p>
+
+  <p>"Mr. Rowning, pt. 2, p. 5 in a note, has a very pretty conceit upon
+  this same subject of attraction, about every particle of a fluid being
+  intrenched in three spheres of attraction and repulsion, one within
+  another, 'the innermost of which (he says) is a sphere of repulsion,
+  which keeps them from approaching into contact; the next, a sphere of
+  attraction, diffused around this of repulsion, by which the particles are
+  disposed to run together into drops; and the outermost of all, a sphere
+  of repulsion, whereby they repel each other, when removed out of the
+  attraction.' So that between the <i>urgings</i>, and
+  <i>solicitations</i>, of one and t'other, a poor unhappy particle must
+  ever be at his wit's end, not knowing which way to turn, or whom to obey
+  first."</p>
+
+  <p>Rowning has here started the notion which Boscovich<a name="NtA_341"
+  href="#Nt_341"><sup>[341]</sup></a> afterwards developed.</p>
+
+  <p>I may add to what precedes that it cannot be settled that, as
+  Granger<a name="NtA_342" href="#Nt_342"><sup>[342]</sup></a> says,
+  Desaguliers was the first who gave experimental lectures in London.
+  William Whiston gave some, and Francis Hauksbee<a name="NtA_343"
+  href="#Nt_343"><sup>[343]</sup></a> made the experiments. The prospectus,
+  as we should now call it, is extant, a quarto tract of plates and
+  descriptions, without date. Whiston, in his life, <!-- Page 157 --><span
+  class="pagenum"><a name="page157"></a>[157]</span>gives 1714 as the first
+  date of publication, and therefore, no doubt, of the lectures.
+  Desaguliers removed to London soon after 1712, and commenced his lectures
+  soon after that. It will be rather a nice point to settle which lectured
+  first; probabilities seem to go in favor of Whiston.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">FALLACIES IN A THEORY OF ANNUITIES.</p>
+
+<blockquote class="b1n">
+
+  <p>An Essay to ascertain the value of leases, and annuities for years and
+  lives. By W[eyman] L[ee]. London, 1737, 8vo.</p>
+
+  <p>A valuation of Annuities and Leases certain, for a single life. By
+  Weyman Lee, Esq. of the Inner Temple. London, 1751, 8vo. Third edition,
+  1773.</p>
+
+</blockquote>
+
+  <p>Every branch of exact science has its paradoxer. The world at large
+  cannot tell with certainty who is right in such questions as squaring the
+  circle, etc. Mr. Weyman Lee<a name="NtA_344"
+  href="#Nt_344"><sup>[344]</sup></a> was the assailant of what all who had
+  studied called demonstration in the question of annuities. He can be
+  exposed to the world: for his error arose out of his not being able to
+  see that the whole is the sum of all its parts.</p>
+
+  <p>By an annuity, say of £100, now bought, is meant that the buyer is to
+  have for his money £100 in a year, if he be then alive, £100 at the end
+  of two years, if then alive, and so on. It is clear that he would buy a
+  life annuity if he should buy the first £100 in one office, the second in
+  another, and so on. All the difference between buying the whole from one
+  office and buying all the separate contingent payments at different
+  offices, is immaterial to calculation. Mr. Lee would have agreed with the
+  rest of the world about the payments to be made to the several different
+  offices, in consideration of their several contracts: but he differed
+  from every one else about the sum to be paid to <i>one</i> office. He
+  contended that the way to value an annuity is to find out the term of
+  years which the individual has an even chance of surviving, and to charge
+  for the life annuity the value of an annuity certain for that term.</p>
+
+<p><!-- Page 158 --><span class="pagenum"><a name="page158"></a>[158]</span></p>
+
+  <p>It is very common to say that Lee took the average life, or
+  expectation, as it is wrongly called, for his term: and this I have done
+  myself, taking the common story. Having exposed the absurdity of this
+  second supposition, taking it for Lee's, in my <i>Formal Logic</i>,<a
+  name="NtA_345" href="#Nt_345"><sup>[345]</sup></a> I will now do the same
+  with the first.</p>
+
+  <p>A mathematical truth is true in its extreme cases. Lee's principle is
+  that an annuity on a life is the annuity made certain for the term within
+  which it is an even chance the life drops. If, then, of a thousand
+  persons, 500 be sure to die within a year, and the other 500 be immortal,
+  Lee's price of an annuity to any one of these persons is the present
+  value of one payment: for one year is the term which each one has an even
+  chance of surviving and not surviving. But the true value is obviously
+  half that of a perpetual annuity: so that at 5 percent Lee's rule would
+  give less than the tenth of the true value. It must be said for the poor
+  circle-squarers, that they never err so much as this.</p>
+
+  <p>Lee would have said, if alive, that I have put an <i>extreme case</i>:
+  but any <i>universal</i> truth is true in its extreme cases. It is not
+  fair to bring forward an extreme case against a person who is speaking as
+  of usual occurrences: but it is quite fair when, as frequently happens,
+  the proposer insists upon a perfectly general acceptance of his
+  assertion. And yet many who go the whole hog protest against being
+  tickled with the tail. Counsel in court are good instances: they are
+  paradoxers by trade. June 13, 1849, at Hertford, there was an action
+  about a ship, insured against a <i>total</i> loss: some planks were
+  saved, and the underwriters refused to pay. Mr.&nbsp;Z. (for deft.) "There can
+  be no degrees of totality; and some timbers were saved."&mdash;L.&nbsp;C.&nbsp;B.
+  "Then if the vessel were burned to the water's edge, and some rope saved
+  in the boat, there would be no total loss."&mdash;Mr.&nbsp;Z. "This is putting
+  a very extreme case."&mdash;L.&nbsp;C.&nbsp;B. "The argument <!-- Page 159 --><span
+  class="pagenum"><a name="page159"></a>[159]</span>would go that length."
+  What would <i>Judge</i> Z.&mdash;as he now is&mdash;say to the extreme
+  case beginning somewhere between six planks and a bit of rope?</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">MONTUCLA'S WORK ON THE QUADRATURE.</p>
+
+<blockquote class="b1n">
+
+  <p>Histoire des recherches sur la quadrature du cercle ... avec une
+  addition concernant les problèmes de la duplication du cube et de la
+  trisection de l'angle. Paris, 1754, 12mo. [By Montucla.]</p>
+
+</blockquote>
+
+  <p>This is <i>the</i> history of the subject.<a name="NtA_346"
+  href="#Nt_346"><sup>[346]</sup></a> It was a little episode to the great
+  history of mathematics by Montucla, of which the first edition appeared
+  in 1758. There was much addition at the end of the fourth volume of the
+  second edition; this is clearly by Montucla, though the bulk of the
+  volume is put together, with help from Montucla's papers, by Lalande.<a
+  name="NtA_347" href="#Nt_347"><sup>[347]</sup></a> There is also a second
+  edition of the history of the quadrature, Paris, 1831, 8vo, edited, I
+  think, by Lacroix; of which it is the great fault that it makes hardly
+  any use of the additional matter just mentioned.</p>
+
+  <p>Montucla is an admirable historian when he is writing from his own
+  direct knowledge: it is a sad pity that he did not tell us when he was
+  depending on others. We are not to trust a quarter of his book, and we
+  must read many other books to know which quarter. The fault is common
+  enough, but Montucla's good three-quarters is so good that the fault is
+  greater in him than in most others: I mean the fault of not
+  acknowledging; for an historian cannot read everything. But it must be
+  said that mankind give little encouragement to candor on this point.
+  Hallam, in his <!-- Page 160 --><span class="pagenum"><a
+  name="page160"></a>[160]</span><i>History of Literature</i>, states with
+  his own usual instinct of honesty every case in which he depends upon
+  others: Montucla does not. And what is the consequence?&mdash;Montucla is
+  trusted, and believed in, and cried up in the bulk; while the smallest
+  talker can lament that Hallam should be so unequal and apt to depend on
+  others, without remembering to mention that Hallam himself gives the
+  information. As to a universal history of any great subject being written
+  entirely upon primary knowledge, it is a thing of which the possibility
+  is not yet proved by an example. Delambre attempted it with astronomy,
+  and was removed by death before it was finished,<a name="NtA_348"
+  href="#Nt_348"><sup>[348]</sup></a> to say nothing of the gaps he
+  left.</p>
+
+  <p>Montucla was nothing of a bibliographer, and his descriptions of books
+  in the first edition were insufficient. The Abbé Rive<a name="NtA_349"
+  href="#Nt_349"><sup>[349]</sup></a> fell foul of him, and as the phrase
+  is, gave it him. Montucla took it with great good humor, tried to mend,
+  and, in his second edition, wished his critic had lived to see the
+  <i>vernis de bibliographe</i> which he had given himself.</p>
+
+  <p>I have seen Montucla set down as an <i>esprit fort</i>, more than
+  once: wrongly, I think. When he mentions Barrow's<a name="NtA_350"
+  href="#Nt_350"><sup>[350]</sup></a> address to the Almighty, he adds, "On
+  voit, au reste, par là, que Barrow étoit un pauvre philosophe; car il
+  croyait en l'immortalité de l'âme, et en une Divinité autre que la nature
+  <!-- Page 161 --><span class="pagenum"><a
+  name="page161"></a>[161]</span>universelle."<a name="NtA_351"
+  href="#Nt_351"><sup>[351]</sup></a> This is irony, not an expression of
+  opinion. In the book of mathematical recreations which Montucla
+  constructed upon that of Ozanam,<a name="NtA_352"
+  href="#Nt_352"><sup>[352]</sup></a> and Ozanam upon that of Van Etten,<a
+  name="NtA_353" href="#Nt_353"><sup>[353]</sup></a> now best known in
+  England by Hutton's similar treatment of Montucla, there is an amusing
+  chapter on the quadrators. Montucla refers to his own anonymous book of
+  1754 as a curious book published by Jombert.<a name="NtA_354"
+  href="#Nt_354"><sup>[354]</sup></a> He seems to have been a little
+  ashamed of writing about circle-squarers: what a slap on the face for an
+  unborn Budgeteer!</p>
+
+  <p>Montucla says, speaking of France, that he finds three notions
+  prevalent among the cyclometers: (1) that there is a large reward offered
+  for success; (2) that the longitude problem depends on that success; (3)
+  that the solution is the great end and object of geometry. The same three
+  <!-- Page 162 --><span class="pagenum"><a
+  name="page162"></a>[162]</span>notions are equally prevalent among the
+  same class in England. No reward has ever been offered by the government
+  of either country. The longitude problem in no way depends upon perfect
+  solution; existing approximations are sufficient to a point of accuracy
+  far beyond what can be wanted.<a name="NtA_355"
+  href="#Nt_355"><sup>[355]</sup></a> And geometry, content with what
+  exists, has long passed on to other matters. Sometimes a cyclometer
+  persuades a skipper who has made land in the wrong place that the
+  astronomers are in fault, for using a wrong measure of the circle; and
+  the skipper thinks it a very comfortable solution! And this is the utmost
+  that the problem ever has to do with longitude.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ANTINEWTONIANISMUS.</p>
+
+<blockquote class="b1n">
+
+  <p>Antinewtonianismus.<a name="NtA_356"
+  href="#Nt_356"><sup>[356]</sup></a> By Cælestino Cominale,<a
+  name="NtA_357" href="#Nt_357"><sup>[357]</sup></a> M.D. Naples, 1754 and
+  1756, 2 vols. 4to.</p>
+
+</blockquote>
+
+  <p>The first volume upsets the theory of light; the second vacuum, vis
+  inertiæ, gravitation, and attraction. I confess I never attempted these
+  big Latin volumes, numbering 450 closely-printed quarto pages. The man
+  who slays Newton in a pamphlet is the man for me. But I will lend them to
+  anybody who will give security, himself in £500, and two sureties in £250
+  each, that he will read them through, and give a full abstract; and I
+  will not exact security for their return. I have never seen any mention
+  of this book: it has a printer, but not a publisher, as happens with so
+  many unrecorded books.</p>
+
+<p><!-- Page 163 --><span class="pagenum"><a name="page163"></a>[163]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">OFFICIAL BLOW TO CIRCLE SQUARERS.</p>
+
+  <p>1755. The French Academy of Sciences came to the determination not to
+  examine any more quadratures or kindred problems. This was the
+  consequence, no doubt, of the publication of Montucla's book: the time
+  was well chosen; for that book was a full justification of the
+  resolution. The Royal Society followed the same course, I believe, a few
+  years afterwards. When our Board of Longitude was in existence, most of
+  its time was consumed in listening to schemes, many of which included the
+  quadrature of the circle. It is certain that many quadrators have
+  imagined the longitude problem to be connected with theirs: and no doubt
+  the notion of a reward offered by Government for a true quadrature is a
+  result of the reward offered for the longitude. Let it also be noted that
+  this longitude reward was not a premium upon excogitation of a mysterious
+  difficulty. The legislature was made to know that the rational hopes of
+  the problem were centered in the improvement of the lunar tables and the
+  improvement of chronometers. To these objects alone, and by name, the
+  offer was directed: several persons gained rewards for both; and the
+  offer was finally repealed.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">AN INTERESTING HOAX.</p>
+
+<blockquote class="b1n">
+
+  <p>Fundamentalis Figura Geometrica, primas tantum lineas circuli
+  quadraturæ possibilitatis ostendens. By Niels Erichsen (Nicolaus
+  Ericius), shipbuilder, of Copenhagen. Copenhagen, 1755, 12mo.</p>
+
+</blockquote>
+
+  <p>This was a gift from my oldest friend who was not a relative, Dr.
+  Samuel Maitland of the "Dark Ages."<a name="NtA_358"
+  href="#Nt_358"><sup>[358]</sup></a> He found it among his books, and
+  could not imagine how he came by it: I could have told him. He once
+  collected interpretations of the Apocalypse: and auction lots of such
+  <!-- Page 164 --><span class="pagenum"><a
+  name="page164"></a>[164]</span>books often contain quadratures. The
+  wonder is he never found more than one.</p>
+
+  <p>The quadrature is not worth notice. Erichsen is the only squarer I
+  have met with who has distinctly asserted the particulars of that reward
+  which has been so frequently thought to have been offered in England. He
+  says that in 1747 the Royal Society on the 2d of June, offered to give a
+  large reward for the quadrature of the circle and a true explanation of
+  magnetism, in addition to £30,000 previously promised for the same. I
+  need hardly say that the Royal Society had not £30,000 at that time, and
+  would not, if it had had such a sum, have spent it on the circle, nor on
+  magnetic theory; nor would it have coupled the two things. On this book,
+  see <i>Notes and Queries</i>, 1st S., xii, 306. Perhaps Erichsen meant
+  that the £30,000 had been promised by the Government, and the addition by
+  the Royal Society.</p>
+
+  <p>October 8, 1866. I receive a letter from a cyclometer who understands
+  that a reward is offered to any one who will square the circle, and that
+  all competitors are to send their plans to me. The hoaxers have not yet
+  failed out of the land.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">TWO JESUIT CONTRIBUTIONS.</p>
+
+<blockquote class="b1n">
+
+  <p>Theoria Philosophiæ Naturalis redacta ad unicam legem virium in natura
+  existentium. Editio <i>Veneta</i> prima. By Roger Joseph Boscovich.
+  Venice, 1763, 4to.</p>
+
+</blockquote>
+
+  <p>The first edition is said to be of Vienna, 1758.<a name="NtA_359"
+  href="#Nt_359"><sup>[359]</sup></a> This is a celebrated work on the
+  molecular theory of matter, grounded on the hypothesis of spheres of
+  alternate attraction and repulsion. Boscovich was a Jesuit of varied
+  pursuit. During his measurement of a degree of the meridian, while on
+  horseback or waiting for his observations, he composed a Latin poem of
+  about five thousand verses on eclipses, <!-- Page 165 --><span
+  class="pagenum"><a name="page165"></a>[165]</span>with notes, which he
+  dedicated to the Royal Society: <i>De Solis et Lunæ defectibus</i>,<a
+  name="NtA_360" href="#Nt_360"><sup>[360]</sup></a> London, Millar and
+  Dodsley, 1760, 4to.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Traité de paix entre Des Cartes et Newton, <i>précédé</i> des vies
+  littéraires de ces deux chefs de la physique moderne.... By Aimé Henri
+  Paulian.<a name="NtA_361" href="#Nt_361"><sup>[361]</sup></a> Avignon,
+  1763, 12mo.</p>
+
+</blockquote>
+
+  <p>I have had these books for many years without feeling the least desire
+  to see how a lettered Jesuit would atone Descartes and Newton. On looking
+  at my two volumes, I find that one contains nothing but the literary life
+  of Descartes; the other nothing but the literary life of Newton. The
+  preface indicates more: and Watt mentions <i>three</i> volumes.<a
+  name="NtA_362" href="#Nt_362"><sup>[362]</sup></a> I dare say the first
+  two contain all that is valuable. On looking more attentively at the two
+  volumes, I find them both readable and instructive; the account of Newton
+  is far above that of Voltaire, but not so popular. But he should not have
+  said that Newton's family came from Newton in Ireland. Sir Rowland Hill
+  gives fourteen <i>Newtons</i> in Ireland;<a name="NtA_363"
+  href="#Nt_363"><sup>[363]</sup></a> twice the number of the cities that
+  contended for the birth of Homer may now contend for the origin of
+  Newton, on the word of Father Paulian.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Philosophical Essays, in three parts. By R. Lovett, Lay Clerk of the
+  Cathedral Church of Worcester. Worcester, 1766, 8vo.</p>
+
+  <p>The Electrical Philosopher: containing a new system of physics <!--
+  Page 166 --><span class="pagenum"><a
+  name="page166"></a>[166]</span>founded upon the principle of an universal
+  Plenum of elementary fire.... By R. Lovett, Worcester, 1774, 8vo.</p>
+
+</blockquote>
+
+  <p>Mr. Lovett<a name="NtA_364" href="#Nt_364"><sup>[364]</sup></a> was
+  one of those ether philosophers who bring in elastic fluid as an
+  explanation by imposition of words, without deducing any one phenomenon
+  from what we know of it. And yet he says that attraction has received no
+  support from geometry; though geometry, applied to a particular law of
+  attraction, had shown how to predict the motions of the bodies of the
+  solar system. He, and many of his stamp, have not the least idea of the
+  confirmation of a theory by accordance of deduced results with
+  observation posterior to the theory.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">BAILLY'S EXAGGERATED VIEW OF ASTRONOMY.</p>
+
+<blockquote class="b1n">
+
+  <p>Lettres sur l'Atlantide de Platon, et sur l'ancien Histoire de l'Asie,
+  pour servir de suite aux lettres sur l'origine des Sciences, adressées à
+  M. de Voltaire, par M. Bailly.<a name="NtA_365"
+  href="#Nt_365"><sup>[365]</sup></a> London and Paris, 1779, 8vo.</p>
+
+</blockquote>
+
+  <p>I might enter here all Bailly's histories of astronomy.<a
+  name="NtA_366" href="#Nt_366"><sup>[366]</sup></a> The paradox which runs
+  through them all more or less, is the doctrine that astronomy is of
+  immense antiquity, coming from some forgotten source, probably the
+  drowned island of Plato, peopled by a race whom Bailly makes, as has <!--
+  Page 167 --><span class="pagenum"><a name="page167"></a>[167]</span>been
+  said, to teach us everything except their existence and their name. These
+  books, the first scientific histories which belong to readable
+  literature, made a great impression by power of style: Delambre created a
+  strong reaction, of injurious amount, in favor of history founded on
+  contemporary documents, which early astronomy cannot furnish. These
+  letters are addressed to Voltaire, and continue the discussion. There is
+  one letter of Voltaire, being the fourth, dated Feb. 27, 1777, and signed
+  "le vieux malade de Ferney, V. puer centum annorum."<a name="NtA_367"
+  href="#Nt_367"><sup>[367]</sup></a> Then begin Bailly's letters, from
+  January 16 to May 12, 1778. From some ambiguous expressions in the
+  Preface, it would seem that these are fictitious letters, supposed to be
+  addressed to Voltaire at their dates. Voltaire went to Paris February 10,
+  1778, and died there May 30. Nearly all this interval was his closing
+  scene, and it is very unlikely that Bailly would have troubled him with
+  these letters.<a name="NtA_368" href="#Nt_368"><sup>[368]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>An inquiry into the cause of motion, or a general theory of physics.
+  By S. Miller. London, 1781, 4to</p>
+
+</blockquote>
+
+  <p>Newton all wrong: matter consists of two kinds of particles, one
+  inert, the other elastic and capable of expanding themselves <i>ad
+  infinitum</i>.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">SAINT-MARTIN ON ERRORS AND TRUTH.</p>
+
+<blockquote class="b1n">
+
+  <p>Des Erreurs et de la Vérité, ou les hommes rappelés au principe
+  universel de la science; ouvrage dans lequel, en faisant remarquer aux
+  observateurs l'incertitude de leurs recherches, et leurs méprises
+  continuelles, on leur indique la route qu'ils auroient dû suivre, pour
+  acquérir l'évidence physique sur l'origine du bien et du mal, sur
+  l'homme, sur la nature matérielle, et la nature sacrée; sur la base des
+  gouvernements <!-- Page 168 --><span class="pagenum"><a
+  name="page168"></a>[168]</span>politiques, sur l'autorité des souverains,
+  sur la justice civile et criminelle, sur les sciences, les langues, et
+  les arts. Par un Ph.... Inc.... A Edimbourg. 1782.<a name="NtA_369"
+  href="#Nt_369"><sup>[369]</sup></a> Two vols. 8vo.</p>
+
+</blockquote>
+
+  <p>This is the famous work of Louis Claude de Saint-Martin<a
+  name="NtA_370" href="#Nt_370"><sup>[370]</sup></a> (1743-1803), for whose
+  other works, vagaries included, the reader must look elsewhere: among
+  other things, he was a translator of Jacob Behmen.<a name="NtA_371"
+  href="#Nt_371"><sup>[371]</sup></a> The title promises much, and the
+  writer has smart thoughts now and then; but the whole is the wearisome
+  omniscience of the author's day and country, which no reader of our time
+  can tolerate. Not that we dislike omniscience; but we have it of our own
+  country, both home-made and imported; and fashions vary. But surely there
+  can be but one omniscience? Must a man have but one wife? Nay, may not a
+  man have a new wife while the old one is living? There was a famous
+  instrumental professor forty years ago, who presented a friend to Madame
+  &mdash;&mdash;. The friend started, and looked surprised; for, not many
+  weeks before, he had been presented to another lady, with the same title,
+  at Paris. The musician observed his surprise, and quietly said, "Celle-ci
+  est Madame &mdash;&mdash; de Londres." In like manner we have a London
+  omniscience now current, which would make any one start who only knew the
+  old French article.</p>
+
+  <p>The book was printed at Lyons, but it was a trick of French authors to
+  pretend to be afraid of prosecution: it <!-- Page 169 --><span
+  class="pagenum"><a name="page169"></a>[169]</span>made a book look
+  wicked-like to have a feigned place of printing, and stimulated readers.
+  A Government which had undergone Voltaire would never have drawn its
+  sword upon quiet Saint-Martin. To make himself look still worse, he was
+  only ph[ilosophe] Inc...., which is generally read <i>Inconnu</i><a
+  name="NtA_372" href="#Nt_372"><sup>[372]</sup></a> but sometimes
+  <i>Incrédule</i>; <a name="NtA_373" href="#Nt_373"><sup>[373]</sup></a>
+  most likely the ambiguity was intended. There is an awful paradox about
+  the book, which explains, in part, its leaden sameness. It is all about
+  <i>l'homme</i>, <i>l'homme</i>, <i>l'homme</i>,<a name="NtA_374"
+  href="#Nt_374"><sup>[374]</sup></a> except as much as treats of <i>les
+  hommes</i>, <i>les hommes</i>, <i>les hommes</i>;<a name="NtA_375"
+  href="#Nt_375"><sup>[375]</sup></a> but not one single man is mentioned
+  by name in its 500 pages. It reminds one of</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Water, water everywhere,</p>
+      <p>And not a drop to drink."</p>
+    </div>
+  </div>
+  <p>Not one opinion of any other man is referred to, in the way of
+  agreement or of opposition. Not even a town is mentioned: there is
+  nothing which brings a capital letter into the middle of a sentence,
+  except, by the rarest accident, such a personification as <i>Justice</i>.
+  A likely book to want an <i>Edimbourg</i> godfather!</p>
+
+  <p>Saint-Martin is great in mathematics. The number <i>four</i>
+  essentially belongs to straight lines, and <i>nine</i> to curves. The
+  object of a straight line is to perpetuate <i>ad infinitum</i> the
+  production of a point from which it emanates. A circle <a
+  href="images/adem_177.png"><img src="images/adem_177.png" class="middle"
+  style="height:2ex" alt="circle" /></a> bounds the production of all its
+  radii, tends to destroy them, and is in some sort their enemy. How is it
+  possible that things so distinct should not be distinguished in their
+  <i>number</i> as well as in their action? If this important observation
+  had been made earlier, immense trouble would have been saved to the
+  mathematicians, who would have been prevented from searching for a common
+  measure to lines which have nothing in common. But, though all straight
+  lines have the number <i>four</i>, it must not be supposed that they are
+  all equal, for a line is the result of its law and <!-- Page 170 --><span
+  class="pagenum"><a name="page170"></a>[170]</span>its number; but though
+  both are the same for all lines of a sort, they act differently, as to
+  force, energy, and duration, in different individuals; which explains all
+  differences of length, etc. I congratulate the reader who understands
+  this; and I do not pity the one who does not.</p>
+
+  <p>Saint-Martin and his works are now as completely forgotten as if they
+  had never been born, except so far as this, that some one may take up one
+  of the works as of heretical character, and lay it down in
+  disappointment, with the reflection that it is as dull as orthodoxy. For
+  a person who was once in some vogue, it would be difficult to pick out a
+  more fossil writer, from Aa to Zyp&oelig;us, except,&mdash;though it is
+  unusual for (,&mdash;) to represent an interval of more than a
+  year&mdash;his unknown opponent. This opponent, in the very year of the
+  <i>Des Erreurs</i> ... published a book in two parts with the same
+  fictitious place of printing;</p>
+
+<blockquote class="b1n">
+
+  <p>Tableau Naturel des Rapports qui existent entre Dieu, l'Homme, et
+  l'Univers. A Edimbourg, 1782, 8vo.<a name="NtA_376"
+  href="#Nt_376"><sup>[376]</sup></a></p>
+
+</blockquote>
+
+  <p>There is a motto from the <i>Des Erreurs</i> itself, "Expliquer les
+  choses par l'homme, et non l'homme par les choses. <i>Des Erreurs et de
+  la Vérité</i>, par un PH.... INC...., p. 9."<a name="NtA_377"
+  href="#Nt_377"><sup>[377]</sup></a> This work is set down in various
+  catalogues and biographies as written by the PH.... INC.... himself. But
+  it is not usual for a writer to publish two works in the same year, one
+  of which takes a motto from the other. And the second work is profuse in
+  capitals and italics, and uses Hebrew learning: its style differs much
+  from the first work. The first work sets out from man, and has nothing to
+  do with God: the second is religious and raps the knuckles of the first
+  as follows: "Si nous voulons nous préserver de toutes <!-- Page 171
+  --><span class="pagenum"><a name="page171"></a>[171]</span>les illusions,
+  et surtout des amorces de l'orgueil par lesquelles l'homme est si souvent
+  séduit, ne prenons jamais les hommes, mais toujours <i>Dieu</i> pour
+  notre terme de comparaison."<a name="NtA_378"
+  href="#Nt_378"><sup>[378]</sup></a> The first uses <i>four</i> and
+  <i>nine</i> in various ways, of which I have quoted one: the second says,
+  "Et ici se trouve déjà une explication des nombres <i>quatre</i> et
+  <i>neuf</i>, qui ont peu embarrassé dans l'ouvrage déjà cité. L'homme
+  s'est égaré en allant de <i>quatre</i> à <i>neuf</i>...."<a
+  name="NtA_379" href="#Nt_379"><sup>[379]</sup></a> The work cited is the
+  <i>Erreurs</i>, etc., and the citation is in the motto, which is the text
+  of the opposition sermon.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A FORERUNNER OF THE METRIC SYSTEM.</p>
+
+<blockquote class="b1n">
+
+  <p>Method to discover the difference of the earth's diameters; proving
+  its true ratio to be not less variable than as 45 is to 46, and shortest
+  in its pole's axis 174 miles.... likewise a method for fixing an
+  universal standard for weights and measures. By Thomas Williams.<a
+  name="NtA_380" href="#Nt_380"><sup>[380]</sup></a> London, 1788, 8vo.</p>
+
+</blockquote>
+
+  <p>Mr. Williams was a paradoxer in his day, and proposed what was, no
+  doubt, laughed at by some. He proposed the sort of plan which the
+  French&mdash;independently of course&mdash;carried into effect a few
+  years after. He would have the 52d degree of latitude divided into
+  100,000 parts and each part a geographical yard. The geographical ton was
+  to be the cube of a geographical yard filled with sea-water taken some
+  leagues from land. All multiples and sub-divisions were to be
+  decimal.</p>
+
+  <p>I was beginning to look up those who had made similar proposals, when
+  a learned article on the proposal of a <!-- Page 172 --><span
+  class="pagenum"><a name="page172"></a>[172]</span>metrical system came
+  under my eye in the <i>Times</i> of Sept. 15, 1863. The author cites
+  Mouton,<a name="NtA_381" href="#Nt_381"><sup>[381]</sup></a> who would
+  have the minute of a degree divided into 10,000 <i>virgulæ</i>; James
+  Cassini,<a name="NtA_382" href="#Nt_382"><sup>[382]</sup></a> whose foot
+  was to be six thousandths of a minute; and Paucton,<a name="NtA_383"
+  href="#Nt_383"><sup>[383]</sup></a> whose foot was the 400,000th of a
+  degree. I have verified the first and third statements; surely the second
+  ought to be the <i>six-thousandth</i>.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>An inquiry into the Copernican system ... wherein it is proved, in the
+  clearest manner, that the earth has only her diurnal motion ... with an
+  attempt to point out the only true way whereby mankind can receive any
+  real benefit from the study of the heavenly bodies. By John Cunningham.<a
+  name="NtA_384" href="#Nt_384"><sup>[384]</sup></a> London, 1789, 8vo.</p>
+
+</blockquote>
+
+  <p>The "true way" appears to be the treatment of heaven and earth as
+  emblematical of the Trinity.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Cosmology. An inquiry into the cause of what is called gravitation or
+  attraction, in which the motions of the heavenly bodies, and the
+  preservation and operations of all nature, are deduced from an universal
+  principle of efflux and reflux. By T. Vivian,<a name="NtA_385"
+  href="#Nt_385"><sup>[385]</sup></a> vicar of Cornwood, Devon. Bath, 1792,
+  12mo.</p>
+
+</blockquote>
+
+<p><!-- Page 173 --><span class="pagenum"><a name="page173"></a>[173]</span></p>
+
+  <p>Attraction, an influx of matter to the sun; centrifugal force, the
+  solar rays; cohesion, the pressure of the atmosphere. The confusion about
+  centrifugal <i>force</i>, so called, as demanding an external agent, is
+  very common.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THOMAS PAINE'S RIGHTS OF MAN.</p>
+
+<blockquote class="b1n">
+
+  <p>The rights of <span class="sc">Man</span>, being an answer to Mr.
+  Burke's attack on the French Revolution.<a name="NtA_386"
+  href="#Nt_386"><sup>[386]</sup></a> By Thomas Paine.<a name="NtA_387"
+  href="#Nt_387"><sup>[387]</sup></a> In two parts. 1791-1792. 8vo.
+  (Various editions.)<a name="NtA_388"
+  href="#Nt_388"><sup>[388]</sup></a></p>
+
+  <p>A vindication of the rights of <span class="sc">Woman</span>, with
+  strictures on political and moral subjects. By Mary Wollstonecraft.<a
+  name="NtA_389" href="#Nt_389"><sup>[389]</sup></a> 1792. 8vo.</p>
+
+  <p>A sketch of the rights of <span class="sc">Boys</span> and <span
+  class="sc">Girls</span>. By Launcelot Light, of Westminster School; and
+  Lætitia Lookabout, of Queen's Square, Bloomsbury. [By the Rev. Samuel
+  Parr,<a name="NtA_390" href="#Nt_390"><sup>[390]</sup></a> LL.D.] 1792.
+  8vo. (pp.64).</p>
+
+</blockquote>
+
+  <p>When did we three meet before? The first work has sunk into oblivion:
+  had it merited its title, it might have <!-- Page 174 --><span
+  class="pagenum"><a name="page174"></a>[174]</span>lived. It is what the
+  French call a <i>pièce de circonstance</i>; it belongs in time to the
+  French Revolution, and in matter to Burke's opinion of that movement.
+  Those who only know its name think it was really an attempt to write a
+  philosophical treatise on what we now call socialism. Silly government
+  prosecutions gave it what it never could have got for itself.</p>
+
+  <p>Mary Wollstonecraft seldom has her name spelled right. I suppose the
+  O! O! character she got made her W<i>oo</i>lstonecraft. Watt gives double
+  insinuation, for his cross-reference sends us to G<i>oo</i>dwin.<a
+  name="NtA_391" href="#Nt_391"><sup>[391]</sup></a> No doubt the title of
+  the book was an act of discipleship to Paine's <i>Rights of Man</i>; but
+  this title is very badly chosen. The book was marred by it, especially
+  when the authoress and her husband assumed the right of dispensing with
+  legal sanction until the approach of offspring brought them to a sense of
+  their child's interest.<a name="NtA_392"
+  href="#Nt_392"><sup>[392]</sup></a> Not a hint of such a claim is found
+  in the book, which is mostly about female education. The right claimed
+  for woman is to have the education of a rational human being, and not to
+  be considered as nothing but woman throughout youthful training. The
+  maxims of Mary Wollstonecraft are now, though not derived from her,
+  largely followed in the education of girls, especially in home education:
+  just as many of the political principles of Tom Paine, again not derived
+  from him, are the guides of our actual legislation. I remember, forty
+  years ago, an old lady used to declare that she disliked girls from the
+  age of sixteen to five-and-twenty. "They are full," said she, "of
+  <i>femalities</i>." She spoke of their behavior to women as well as to
+  men. She <!-- Page 175 --><span class="pagenum"><a
+  name="page175"></a>[175]</span>would have been shocked to know that she
+  was a follower of Mary Wollstonecraft, and had packed half her book into
+  one sentence.</p>
+
+  <p>The third work is a satirical attack on Mary Wollstonecraft and Tom
+  Paine. The details of the attack would convince any one that neither has
+  anything which would now excite reprobation. It is utterly unworthy of
+  Dr. Parr, and has quite disappeared from lists of his works, if it were
+  ever there. That it was written by him I take to be evident, as follows.
+  Nichols,<a name="NtA_393" href="#Nt_393"><sup>[393]</sup></a> who could
+  not fail to know, says (<i>Anecd.</i>, vol. ix, p. 120): "This is a
+  playful essay by a first-rate scholar, who is elsewhere noticed in this
+  volume, but whose name I shall not bring forward on so trifling an
+  occasion." Who the scholar was is made obvious by Master Launcelot being
+  made to talk of Bellendenus.<a name="NtA_394"
+  href="#Nt_394"><sup>[394]</sup></a> Further, the same boy is made to say,
+  "Let Dr. Parr lay his hand upon his heart, if his conscience will let
+  him, and ask himself how many thousands of wagon-loads of this article
+  [birch] he has cruelly misapplied." How could this apply to Parr, with
+  his handful of private pupils,<a name="NtA_395"
+  href="#Nt_395"><sup>[395]</sup></a> and no reputation for severity? Any
+  one except himself would have called on the head-master of Westminster or
+  Eton. I doubt whether the name of Parr could be connected with the rod by
+  anything in print, except the above and an anecdote of his pupil, Tom
+  Sheridan.<a name="NtA_396" href="#Nt_396"><sup>[396]</sup></a> The Doctor
+  had dressed for a dinner visit, and <!-- Page 176 --><span
+  class="pagenum"><a name="page176"></a>[176]</span>was ready a quarter of
+  an hour too soon to set off. "Tom," said he, "I think I had better whip
+  you now; you are sure to do something while I am out."&mdash;"I wish you
+  would, sir!" said the boy; "it would be a letter of licence for the whole
+  evening." The Doctor saw the force of the retort: my two tutelaries will
+  see it by this time. They paid in advance; and I have given liberal
+  interpretation to the order.</p>
+
+  <p>The following story of Dr. Parr was told me and others, about 1829, by
+  the late Leonard Horner,<a name="NtA_397"
+  href="#Nt_397"><sup>[397]</sup></a> who knew him intimately. Parr was
+  staying in a house full of company, I think in the north of England. Some
+  gentlemen from America were among the guests, and after dinner they
+  disputed some of Parr's assertions or arguments. So the Doctor broke out
+  with "Do you know what country you come from? You come from the place to
+  which we used to send our thieves!" This made the host angry, and he gave
+  Parr such a severe rebuke as sent him from the room in ill-humor. The
+  rest walked on the lawn, amusing the Americans with sketches of the
+  Doctor. There was a dark cloud overhead, and from that cloud presently
+  came a voice which called <i>Tham</i> (Parr-lisp for <i>Sam</i>). The
+  company were astonished for a moment, but thought the Doctor was calling
+  his servant in the house, and that the apparent direction was an illusion
+  arising out of inattention. But presently the sound was repeated,
+  certainly from the cloud,</p>
+
+<blockquote class="b1n">
+
+  <p>"And nearer, clearer, deadlier than before."</p>
+
+</blockquote>
+
+  <p>There was now a little alarm: where could the Doctor have got to? They
+  ran to his bedroom, and there they discovered a sufficient rather than
+  satisfactory explanation. The Doctor had taken his pipe into his bedroom,
+  and had seated himself, in sulky mood, upon the higher bar of a large and
+  deep old-fashioned grate with a high mantelshelf. Here he had <!-- Page
+  177 --><span class="pagenum"><a name="page177"></a>[177]</span>tumbled
+  backwards, and doubled himself up between the bars and the back of the
+  grate. He was fixed tight, and when he called for help, he could only
+  throw his voice up the chimney. The echo from the cloud was the warning
+  which brought his friends to the rescue.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ATTACKS ON RELIGIOUS CUSTOMS.</p>
+
+  <p>Days of political paradox were coming, at which we now stare.
+  Cobbett<a name="NtA_398" href="#Nt_398"><sup>[398]</sup></a> said, about
+  1830, in earnest, that in the country every man who did not take off his
+  hat to the clergyman was suspected, and ran a fair chance of having
+  something brought against him. I heard this assertion canvassed, when it
+  was made, in a party of elderly persons. The Radicals backed it, the old
+  Tories rather denied it, but in a way which satisfied me they ought to
+  have denied it less if they could not deny it more. But it must be said
+  that the Governments stopped far short of what their partisans would have
+  had them do. All who know Robert Robinson's<a name="NtA_399"
+  href="#Nt_399"><sup>[399]</sup></a> very quiet assault on church-made
+  festivals in his <i>History and Mystery of Good Friday</i> (1777)<a
+  name="NtA_400" href="#Nt_400"><sup>[400]</sup></a> will hear or remember
+  with surprise that the <i>British Critic</i> pronounced it a direct,
+  unprovoked, and malicious libel on the most <!-- Page 178 --><span
+  class="pagenum"><a name="page178"></a>[178]</span>sacred institutions of
+  the national Church. It was reprinted again and again: in 1811 it was in
+  a cheap form at 6s. 6d. a hundred. When the Jacobin day came, the State
+  was really in a fright: people thought twice before they published what
+  would now be quite disregarded. I examined a quantity of letters
+  addressed to George Dyer<a name="NtA_401"
+  href="#Nt_401"><sup>[401]</sup></a> (Charles Lamb's G.D.) and what
+  between the autographs of Thelwall, Hardy, Horne Tooke, and all the
+  rebels,<a name="NtA_402" href="#Nt_402"><sup>[402]</sup></a> put together
+  a packet which produced five guineas, or thereabouts, for the widow.
+  Among them were the following verses, sent by the author&mdash;who would
+  not put his name, even in a private letter, for fear of
+  accidents&mdash;for consultation whether they could safely be sent to an
+  editor: and they were <i>not</i> sent. The occasion was the public
+  thanksgiving at St. Paul's for the naval victories, December 19,
+  1797.</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"God bless me! what a thing!</p>
+      <p>Have you heard that the King</p>
+      <p class="i2">Goes to St. Paul's?</p>
+<!-- Page 179 --><span class="pagenum"><a name="page179"></a>[179]</span>
+      <p>Good Lord! and when he's there,</p>
+      <p>He'll roll his eyes in prayer,</p>
+      <p>To make poor Johnny stare</p>
+      <p class="i2">At this fine thing.</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"No doubt the plan is wise</p>
+      <p>To blind poor Johnny's eyes</p>
+      <p class="i2">By this grand show;</p>
+      <p>For should he once suppose</p>
+      <p>That he's led by the nose,</p>
+      <p>Down the whole fabric goes,</p>
+      <p class="i2">Church, lords, and king.</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"As he shouts Duncan's<a name="NtA_403" href="#Nt_403"><sup>[403]</sup></a> praise,</p>
+      <p>Mind how supplies they'll raise</p>
+      <p class="i2">In wondrous haste.</p>
+      <p>For while upon the sea</p>
+      <p>We gain one victory,</p>
+      <p>John still a dupe will be</p>
+      <p class="i2">And taxes pay.</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"Till from his little store</p>
+      <p>Three-fourths or even more</p>
+      <p class="i2">Goes to the Crown.</p>
+      <p>Ah, John! you little think</p>
+      <p>How fast we downward sink</p>
+      <p>And touch the fatal brink</p>
+      <p class="i2">At which we're slaves."</p>
+    </div>
+  </div>
+  <p>I would have indicted the author for not making his thirds and
+  sevenths rhyme. As to the rhythm, it is not much better than what the
+  French sang in the Calais theater when the Duke of Clarence<a
+  name="NtA_404" href="#Nt_404"><sup>[404]</sup></a> took over Louis XVIII
+  in 1814.</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"God save noble Clarence,</p>
+      <p>Who brings our king to France;</p>
+      <p class="i2">God save Clarence!</p>
+      <p>He maintains the glory</p>
+      <p>Of the British navy,</p>
+      <p class="i2">etc., etc."</p>
+    </div>
+  </div>
+<p><!-- Page 180 --><span class="pagenum"><a name="page180"></a>[180]</span></p>
+
+  <p>Perhaps had this been published, the Government would have assailed it
+  as a libel on the church service. They got into the way of defending
+  themselves by making libels on the Church, of what were libels, if on
+  anything, on the rulers of the State; until the celebrated trials of Hone
+  settled the point for ever, and established that juries will not convict
+  for one offence, even though it have been committed, when they know the
+  prosecution is directed at another offence and another intent.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">HONE'S FAMOUS TRIALS.</p>
+
+  <p>The results of Hone's trials (William Hone, 1779-1842) are among the
+  important constitutional victories of our century. He published parodies
+  on the Creeds, the Lord's Prayer, the Catechism, etc., with intent to
+  bring the Ministry into contempt: everybody knew that was his
+  <i>purpose</i>. The Government indicted him for impious, profane,
+  blasphemous intent, but not for seditious intent. They hoped to wear him
+  out by proceeding day by day. December 18, 1817, they hid themselves
+  under the Lord's Prayer, the Creed, and the Commandments; December 19,
+  under the Litany; December 20, under the Athanasian Creed, an odd place
+  for shelter when they could not find it in the previous places. Hone
+  defended himself for six, seven, and eight hours on the several days: and
+  the jury acquitted him in 15, 105, and 20 minutes. In the second trial
+  the offense was laid both as profanity and as sedition, which seems to
+  have made the jury hesitate. And they probably came to think that the
+  second count was false pretence: but the length of their deliberation is
+  a satisfactory addition to the value of the whole. In the first trial the
+  Attorney-General (Shepherd) had the impudence to say that the libel had
+  nothing of a political tendency about it, but was <i>avowedly</i> set off
+  against the religion and worship of the Church of England. The whole <!--
+  Page 181 --><span class="pagenum"><a name="page181"></a>[181]</span>is
+  political in every sentence; neither more nor less political than the
+  following, which is part of the parody on the Catechism: "What is thy
+  duty towards the Minister? My duty towards the Minister is, to trust him
+  as much as I can; to honor him with all my words, with all my bows, with
+  all my scrapes, and with all my cringes; to flatter him; to give him
+  thanks; to give up my whole soul to him; to idolize his name, and obey
+  his word, and serve him blindly all the days of his political life." And
+  the parody on the Creed begins, "I believe in George, the Regent
+  almighty, maker of new streets and Knights of the Bath." This is what the
+  Attorney-General said had nothing of a political tendency about it. But
+  this was <i>on the first trial</i>: Hone was not known. The first day's
+  trial was under Justice Abbott (afterwards C.&nbsp;J. Tenterden).<a
+  name="NtA_405" href="#Nt_405"><sup>[405]</sup></a> It was perfectly
+  understood, when Chief Justice Ellenborough<a name="NtA_406"
+  href="#Nt_406"><sup>[406]</sup></a> appeared in Court on the second day,
+  that he was very angry at the first result, and put his junior aside to
+  try his own rougher dealing. But Hone tamed the lion. An eye-witness told
+  me that when he implored of Hone not to detail his own father Bishop
+  Law's<a name="NtA_407" href="#Nt_407"><sup>[407]</sup></a> views on the
+  Athanasian Creed, which humble petition Hone kindly granted, he held by
+  the desk for support. And the same when&mdash;which is not
+  reported&mdash;the Attorney-General appealed to the Court for protection
+  against a <!-- Page 182 --><span class="pagenum"><a
+  name="page182"></a>[182]</span>stinging attack which Hone made on the
+  Bar: he <i>held on</i>, and said, "Mr. Attorney, what <i>can</i> I do!" I
+  was a boy of twelve years old, but so strong was the feeling of
+  exultation at the verdicts that boys at school were not prohibited from
+  seeing the parodies, which would have been held at any other time quite
+  unfit to meet their eyes. I was not able to comprehend all about the Lord
+  Chief Justice until I read and heard again in after years. In the
+  meantime, Joe Miller had given me the story of the leopard which was sent
+  home on board a ship of war, and was in two days made as docile as a cat
+  by the sailors.<a name="NtA_408" href="#Nt_408"><sup>[408]</sup></a> "You
+  have got that fellow well under," said an officer. "Lord bless your
+  Honor!" said Jack, "if the Emperor of Marocky would send us a cock
+  rhinoceros, we'd bring him to his bearings in no time!" When I came to
+  the subject again, it pleased me to entertain the question whether, if
+  the Emperor had sent a cock rhinoceros to preside on the third day in the
+  King's Bench, Hone would have mastered <i>him</i>: I forget how I settled
+  it. There grew up a story that Hone caused Lord Ellenborough's death, but
+  this could not have been true. Lord Ellenborough resigned his seat in a
+  few months, and died just a year after the trials; but sixty-eight years
+  may have had more to do with it than his defeat.</p>
+
+  <p>A large subscription was raised for Hone, headed by the Duke of
+  Bedford<a name="NtA_409" href="#Nt_409"><sup>[409]</sup></a> for £105.
+  Many of the leading anti-ministerialists joined: but there were many of
+  the other side who avowed their disapprobation of the false pretense.
+  Many could not venture their names. In the list I find: <!-- Page 183
+  --><span class="pagenum"><a name="page183"></a>[183]</span>A member of
+  the House of Lords, an enemy to persecution, and especially to religious
+  persecution employed for political purposes&mdash;No parodist, but an
+  enemy to persecution&mdash;A juryman on the third day's trial&mdash;Ellen
+  Borough&mdash;My name would ruin me&mdash;Oh! minions of Pitt&mdash;Oil
+  for the Hone&mdash;The Ghosts of Jeffries<a name="NtA_410"
+  href="#Nt_410"><sup>[410]</sup></a> and Sir William Roy [Ghosts of
+  Jeffries in abundance]&mdash;A conscientious Jury and a conscientious
+  Attorney, £1 6s. 8d.&mdash;To Mr. Hone, for defending in his own person
+  the freedom of the press, attacked for a political object, under the old
+  pretense of supporting Religion&mdash;A cut at corruption&mdash;An
+  Earldom for myself and a translation for my brother&mdash;One who
+  disapproves of parodies, but abhors persecution&mdash;From a schoolboy
+  who wishes Mr. Hone to have a very grand subscription&mdash;"For
+  delicacy's sake forbear," and "Felix trembled"&mdash;"I will go myself
+  to-morrow"&mdash;Judge Jeffries' works rebound in calf by Law&mdash;Keep
+  us from Law, and from the Shepherd's paw&mdash;I must not give you my
+  name, but God bless you!&mdash;As much like Judge Jeffries as the present
+  times will permit&mdash;May Jeffries' fame and Jeffries' fate on every
+  modern Jeffries wait&mdash;No parodist, but an admirer of the man who has
+  proved the fallacy of the Lawyer's Law, that when a man is his own
+  advocate he has a fool for his client&mdash;A Mussulman who thinks it
+  would not be an impious libel to parody the Koran&mdash;May the
+  suspenders of the Habeas Corpus Act be speedily suspended&mdash;Three
+  times twelve for thrice-tried Hone, who cleared the cases himself alone,
+  and won three heats by twelve to one, £1 16s.&mdash;A conscientious
+  attorney, £1 6s. 8d.&mdash;Rev. T.&nbsp;B. Morris, rector of Shelfanger, who
+  disapproves of the parodies, but abhors the making an affected zeal for
+  religion the pretext for political persecution&mdash;A Lawyer opposed in
+  principle to <!-- Page 184 --><span class="pagenum"><a
+  name="page184"></a>[184]</span>Law&mdash;For the Hone that set the razor
+  that shaved the rats&mdash;Rev. Dr. Samuel Parr, who most seriously
+  disapproves of all parodies upon the hallowed language of Scripture and
+  the contents of the Prayer-book, but acquits Mr. Hone of intentional
+  impiety, admires his talents and fortitude, and applauds the good sense
+  and integrity of his juries&mdash;Religion without hypocrisy, and Law
+  without impartiality&mdash;O Law! O Law! O Law!</p>
+
+  <p>These are specimens of a great many allusive mottoes. The subscription
+  was very large, and would have bought a handsome annuity, but Hone
+  employed it in the bookselling trade, and did not thrive. His <i>Everyday
+  Book</i><a name="NtA_411" href="#Nt_411"><sup>[411]</sup></a> and his
+  <i>Apocryphal New Testament</i>,<a name="NtA_412"
+  href="#Nt_412"><sup>[412]</sup></a> are useful books. On an annuity he
+  would have thriven as an antiquarian writer and collector. It is well
+  that the attack upon the right to ridicule Ministers roused a dormant
+  power which was equal to the occasion. Hone declared, on his honor, that
+  he had never addressed a meeting in his life, nor spoken a word before
+  more than twelve persons. Had he&mdash;which however could not then be
+  done&mdash;employed counsel and had a <i>guilty defense</i> made for him,
+  he would very likely have been convicted, and the work would have been
+  left to be done by another. No question that the parodies disgusted all
+  who reverenced Christianity, and who could not separate the serious and
+  the ludicrous, and prevent their existence in combination.</p>
+
+  <p>My extracts, etc., are from the nineteenth, seventeenth, and sixteenth
+  editions of the three trials, which seem to have been contemporaneous
+  (all in 1818) as they are made up into one book, with additional title
+  over all, and the motto "Thrice the brindled cat hath mew'd." They are
+  published by Hone himself, who I should have said was a publisher <!--
+  Page 185 --><span class="pagenum"><a name="page185"></a>[185]</span>as
+  well as was to be. And though the trials only ended Dec. 20, 1817, the
+  preface attached to this common title is dated Jan. 23, 1818.<a
+  name="NtA_413" href="#Nt_413"><sup>[413]</sup></a></p>
+
+  <p>The spirit which was roused against the false dealing of the
+  Government, i.e., the pretense of prosecuting for impiety when all the
+  world knew the real offense was, if anything, sedition&mdash;was not got
+  up at the moment: there had been previous exhibitions of it. For example,
+  in the spring of 1818 Mr. Russell, a little printer in Birmingham, was
+  indicted for publishing the Political Litany<a name="NtA_414"
+  href="#Nt_414"><sup>[414]</sup></a> on which Hone was afterwards tried.
+  He took his witnesses to the summer Warwick assizes, and was told that
+  the indictment had been removed by certiorari into the King's Bench. He
+  had notice of trial for the spring assizes at Warwick: he took his
+  witnesses there, and the trial was postponed by the Crown. He then had
+  notice for the summer assizes at Warwick; and so on. The policy seems to
+  have been to wear out the obnoxious parties, either by delays or by
+  heaping on trials. The Government was odious, and knew it could
+  <i>not</i> get verdicts against ridicule, and <i>could</i> get verdicts
+  against impiety. No difficulty was found in convicting the sellers of
+  Paine's works, and the like. When Hone was held to bail it was seen that
+  a crisis was at hand. All parties in politics furnished him with parodies
+  in proof of religious persons having made instruments of them. The
+  parodies by Addison and Luther were contributed by a Tory lawyer, who was
+  afterwards a judge.</p>
+
+  <p>Hone had published, in 1817, tracts of purely political ridicule:
+  <i>Official Account of the Noble Lord's Bite,</i><a name="NtA_415"
+  href="#Nt_415"><sup>[415]</sup></a> <i>Trial of the Dog for Biting the
+  Noble Lord</i>, etc. These were not touched. After the trials, it is
+  manifest that Hone was <!-- Page 186 --><span class="pagenum"><a
+  name="page186"></a>[186]</span>to be unassailed, do what he might. <i>The
+  Political House that Jack built</i>, in 1819; <i>The Man in the Moon</i>,
+  1820; <i>The Queen's Matrimonial Ladder</i>, <i>Non mi ricordo</i>,
+  <i>The R&mdash;l Fowls</i>, 1820; <i>The Political Showman at Home</i>,
+  with plates by G. Cruickshank,<a name="NtA_416"
+  href="#Nt_416"><sup>[416]</sup></a> 1821 [he did all the plates]; <i>The
+  Spirit of Despotism</i>, 1821&mdash;would have been legitimate marks for
+  prosecution in previous years. The biting caricature of several of these
+  works are remembered to this day. <i>The Spirit of Despotism</i> was a
+  tract of 1795, of which a few copies had been privately circulated with
+  great secrecy. Hone reprinted it, and prefixed the following address to
+  "Robert Stewart, <i>alias</i> Lord Castlereagh"<a name="NtA_417"
+  href="#Nt_417"><sup>[417]</sup></a>: "It appears to me that if,
+  unhappily, your counsels are allowed much longer to prevail in the
+  Brunswick Cabinet, they will bring on a crisis, in which the king may be
+  dethroned or the people enslaved. Experience has shown that the people
+  will not be enslaved&mdash;the alternative is the affair of your
+  employers." Hone might say this without notice.</p>
+
+  <p>In 1819 Mr. Murray<a name="NtA_418"
+  href="#Nt_418"><sup>[418]</sup></a> published Lord Byron's <i>Don
+  Juan</i>,<a name="NtA_419" href="#Nt_419"><sup>[419]</sup></a> and Hone
+  followed it with <i>Don John, or Don Juan Unmasked</i>, a little account
+  of what the publisher to the Admiralty was allowed to issue without
+  prosecution. The parody on the Commandments was a case very much in
+  point: and Hone makes a stinging allusion to the use of the
+  "<i>unutterable Name</i>, with a profane levity unsurpassed by <!-- Page
+  187 --><span class="pagenum"><a name="page187"></a>[187]</span>any other
+  two lines in the English language." The lines are</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"'Tis strange&mdash;the Hebrew noun which means 'I am,'</p>
+      <p>The English always use to govern d&mdash;&mdash;n."</p>
+    </div>
+  </div>
+  <p>Hone ends with: "Lord Byron's dedication of 'Don Juan' to Lord
+  Castlereagh was suppressed by Mr. Murray from delicacy to Ministers. Q.
+  Why did not Mr. Murray suppress Lord Byron's <i>parody</i> on the Ten
+  Commandments? <i>A.</i> Because it contains nothing in ridicule of
+  Ministers, and therefore nothing that <i>they</i> could suppose would
+  lead to the displeasure of Almighty God."</p>
+
+  <p>The little matters on which I have dwelt will never appear in history
+  from their political importance, except in a few words of result. As a
+  mode of thought, silly evasions of all kinds belong to such a work as the
+  present. Ignorance, which seats itself in the chair of knowledge, is a
+  mother of revolutions in politics, and of unread pamphlets in
+  circle-squaring. From 1815 to 1830 the question of revolution or no
+  revolution lurked in all our English discussions. The high classes must
+  govern; the high classes shall not govern; and thereupon issue was to be
+  joined. In 1828-33 the question came to issue; and it was, Revolution
+  with or without civil war; choose. The choice was wisely made; and the
+  Reform Bill started a new system so well dovetailed into the old that the
+  joinings are hardly visible. And now, in 1867, the thing is repeated with
+  a marked subsidence of symptoms; and the party which has taken the place
+  of the extinct Tories is carrying through Parliament a wider extension of
+  the franchise than their opponents would have ventured. Napoleon used to
+  say that a decided nose was a sign of power: on which it has been
+  remarked that he had good reason to say so before the play was done. And
+  so had our country; it was saved from a religious war, and from a civil
+  war, by the power of that nose over its colleagues. <!-- Page 188
+  --><span class="pagenum"><a name="page188"></a>[188]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THOMAS TAYLOR, THE PLATONIST.</p>
+
+<blockquote class="b1n">
+
+  <p>The Commentaries of Proclus.<a name="NtA_420"
+  href="#Nt_420"><sup>[420]</sup></a> Translated by Thomas Taylor.<a
+  name="NtA_421" href="#Nt_421"><sup>[421]</sup></a> London, 1792, 2 vols.
+  4to.<a name="NtA_422" href="#Nt_422"><sup>[422]</sup></a></p>
+
+</blockquote>
+
+  <p>The reputation of "the Platonist" begins to grow, and will continue to
+  grow. The most authentic account is in the <i>Penny Cyclopædia</i>,
+  written by one of the few persons who knew him well, and one of the fewer
+  who possess all his works. At page lvi of the Introduction is Taylor's
+  notion of the way to find the circumference. It is not geometrical, for
+  it proceeds on the motion of a point: the words "on account of the
+  simplicity of the impulsive motion, such a line must be either straight
+  or circular" will suffice to show how Platonic it is. Taylor certainly
+  professed a kind of heathenism. D'lsraeli said, "Mr. T. Taylor, the
+  Platonic philosopher and the modern Plethon,<a name="NtA_423"
+  href="#Nt_423"><sup>[423]</sup></a> consonant to that philosophy,
+  professes polytheism." Taylor printed this in large type, in a page by
+  itself after the dedication, without any disavowal. I have seen the
+  following, Greek and translation both, in his handwriting: "<span
+  title="Pas agathos hêi agathos ethnikos; kai pas christianos hêi christianos kakos." class="grk"
+  >&Pi;&#x1FB6;&sigmaf; &#x1F00;&gamma;&alpha;&theta;&#x1F78;&sigmaf;
+  &#x1F97; &#x1F00;&gamma;&alpha;&theta;&#x1F78;&sigmaf;
+  &#x1F10;&theta;&nu;&iota;&kappa;&#x1F79;&sigmaf;&#x387;
+  &kappa;&alpha;&#x1F76; &pi;&#x1FB6;&sigmaf;
+  &chi;&rho;&iota;&sigma;&tau;&iota;&alpha;&nu;&#x1F78;&sigmaf; &#x1F97;
+  &chi;&rho;&iota;&sigma;&tau;&iota;&alpha;&nu;&#x1F78;&sigmaf;
+  &kappa;&alpha;&kappa;&#x1F79;&sigmaf;.</span> Every good man, so far as
+  he is a good man, is a heathen; and every Christian, so far as he is a
+  Christian, is a bad man." Whether Taylor had in his head the Christian of
+  the New Testament, or whether he drew from those members of the
+  "religious world" who make manifest the religious flesh and the religious
+  devil, <!-- Page 189 --><span class="pagenum"><a
+  name="page189"></a>[189]</span>cannot be decided by us, and perhaps was
+  not known to himself. If a heathen, he was a virtuous one.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A NEW ERA IN FICTION.</p>
+
+  <p>(1795.) This is the date of a very remarkable paradox. The religious
+  world&mdash;to use a name claimed by a doctrinal sect&mdash;had long set
+  its face against amusing literature, and all works of imagination.
+  Bunyan, Milton, and a few others were irresistible; but a long face was
+  pulled at every attempt to produce something readable for poor people and
+  <i>poor children</i>. In 1795, a benevolent association began to
+  circulate the works of a lady who had been herself a dramatist, and had
+  nourished a pleasant vein of satire in the society of Garrick and his
+  friends; all which is carefully suppressed in some biographies. Hannah
+  More's<a name="NtA_424" href="#Nt_424"><sup>[424]</sup></a> <i>Cheap
+  Repository Tracts</i>,<a name="NtA_425"
+  href="#Nt_425"><sup>[425]</sup></a> which were bought by millions of
+  copies, destroyed the vicious publications with which the hawkers deluged
+  the country, by the simple process of furnishing the hawkers with
+  something more saleable.</p>
+
+  <p><i>Dramatic fiction</i>, in which the <i>characters</i> are drawn by
+  themselves, was, at the middle of the last century, the monopoly of
+  writers who required indecorum, such as Fielding and Smollett. All, or
+  nearly all, which could be permitted to the young, was dry narrative,
+  written by people who could not make their personages <i>talk
+  character</i>; they all spoke <!-- Page 190 --><span class="pagenum"><a
+  name="page190"></a>[190]</span>alike. The author of the <i>Rambler</i><a
+  name="NtA_426" href="#Nt_426"><sup>[426]</sup></a> is ridiculed, because
+  his young ladies talk Johnsonese; but the satirists forget that all the
+  presentable novel-writers were equally incompetent; even the author of
+  <i>Zeluco</i> (1789)<a name="NtA_427" href="#Nt_427"><sup>[427]</sup></a>
+  is the strongest possible case in point.</p>
+
+  <p>Dr. Moore,<a name="NtA_428" href="#Nt_428"><sup>[428]</sup></a> the
+  father of the hero of Corunna,<a name="NtA_429"
+  href="#Nt_429"><sup>[429]</sup></a> with good narrative power, some sly
+  humor, and much observation of character, would have been, in our day, a
+  writer of the <i>Peacock</i><a name="NtA_430"
+  href="#Nt_430"><sup>[430]</sup></a> family. Nevertheless, to one who is
+  accustomed to our style of things, it is comic to read the dialogue of a
+  jealous husband, a suspected wife, a faithless maid-servant, a tool of a
+  nurse, a wrong-headed pomposity of a priest, and a sensible physician,
+  all talking Dr. Moore through their masks. Certainly an Irish soldier
+  does say "by Jasus," and a cockney footman "this here" and "that there";
+  and this and the like is all the painting of characters which is effected
+  out of the mouths of the bearers by a narrator of great power. I suspect
+  that some novelists repressed their power under a rule that a narrative
+  should narrate, and that the dramatic should be confined to the
+  drama.</p>
+
+  <p>I make no exception in favor of Miss Burney;<a name="NtA_431"
+  href="#Nt_431"><sup>[431]</sup></a> though she was the forerunner of a
+  new era. Suppose a country <!-- Page 191 --><span class="pagenum"><a
+  name="page191"></a>[191]</span>in which dress is always of one color;
+  suppose an importer who brings in cargoes of blue stuff, red stuff, green
+  stuff, etc., and exhibits dresses of these several colors, that person is
+  the similitude of Miss Burney. It would be a delightful change from a
+  universal dull brown, to see one person all red, another all blue, etc.;
+  but the real inventor of pleasant dress would be the one who could mix
+  his colors and keep down the bright and gaudy. Miss Burney's introduction
+  was so charming, by contrast, that she nailed such men as Johnson, Burke,
+  Garrick, etc., to her books. But when a person who has read them with
+  keen pleasure in boyhood, as I did, comes back to them after a long
+  period, during which he has made acquaintance with the great novelists of
+  our century, three-quarters of the pleasure is replaced by wonder that he
+  had not seen he was at a puppet-show, not at a drama. Take some
+  <i>labeled</i> characters out of our humorists, let them be put together
+  into one piece, to speak only as labeled: let there be a Dominie with
+  nothing but "Prodigious!" a Dick Swiveller with nothing but adapted
+  quotations; a Dr. Folliott with nothing but sneers at Lord Brougham;<a
+  name="NtA_432" href="#Nt_432"><sup>[432]</sup></a> and the whole will
+  pack up into one of Miss Burney's novels.</p>
+
+  <p>Maria Edgeworth,<a name="NtA_433" href="#Nt_433"><sup>[433]</sup></a>
+  Sydney Owenson (Lady Morgan),<a name="NtA_434"
+  href="#Nt_434"><sup>[434]</sup></a> Jane Austen,<a name="NtA_435"
+  href="#Nt_435"><sup>[435]</sup></a> Walter Scott,<a name="NtA_436"
+  href="#Nt_436"><sup>[436]</sup></a> etc., are all of our century; as <!--
+  Page 192 --><span class="pagenum"><a name="page192"></a>[192]</span>are,
+  I believe, all the Minerva Press novels, as they were called, which show
+  some of the power in question. Perhaps dramatic talent found its best
+  encouragement in the drama itself. But I cannot ascertain that any such
+  power was directed at the multitude, whether educated or uneducated, with
+  natural mixture of character, under the restraints of decorum, until the
+  use of it by two religious writers of the school called "evangelical,"
+  Hannah More and Rowland Hill.<a name="NtA_437"
+  href="#Nt_437"><sup>[437]</sup></a> The <i>Village Dialogues</i>, though
+  not equal to the <i>Repository Tracts</i>, are in many parts an approach,
+  and perhaps a copy; there is frequently humorous satire, in that most
+  effective form, self-display. They were published in 1800, and, partly at
+  least, by the Religious Tract Society, the lineal <span
+  class="correction" title="text reads `successsor'">successor</span> of
+  the <i>Repository</i> association, though knowing nothing about its
+  predecessor. I think it right to add that Rowland Hill here mentioned is
+  not the regenerator of the Post Office.<a name="NtA_438"
+  href="#Nt_438"><sup>[438]</sup></a> Some do not distinguish accurately; I
+  have heard of more than one who took me to have had a logical controversy
+  with a diplomatist who died some years before I was born.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE RELIGIOUS TRACT SOCIETY.</p>
+
+  <p>A few years ago, an attempt was made by myself and others to collect
+  some information about the <i>Cheap Repository</i> (see <i>Notes and
+  Queries</i>, 3d Series, vi. 241, 290, 353; <i>Christian Observer</i>,
+  Dec. 1864, pp. 944-49). It appeared that after the Religious Tract
+  Society had existed more than fifty years, a friend presented it with a
+  copy of the original prospectus of the <i>Repository</i>, a thing the
+  existence of which was not known. In this prospectus it is announced that
+  from the plan "will be carefully excluded whatever is enthusiastic,
+  absurd, or superstitious." The "evangelical" <!-- Page 193 --><span
+  class="pagenum"><a name="page193"></a>[193]</span>party had, from the
+  foundation of the Religious Tract Society, regretted that the
+  <i>Repository Tracts</i> "did not contain a fuller statement of the great
+  evangelical principles"; while in the prospectus it is also stated that
+  "no cause of any particular party is intended to be served by it, but
+  general Christianity will be promoted upon practical principles." This
+  explains what has often been noticed, that the tracts contain a mild form
+  of "evangelical" doctrine, free from that more fervid dogmatism which
+  appears in the <i>Village Dialogues</i>; and such as H. More's friend,
+  Bishop Porteus<a name="NtA_439"
+  href="#Nt_439"><sup>[439]</sup></a>&mdash;a great promoter of the
+  scheme&mdash;might approve. The Religious Tract Society (in 1863)
+  republished some of H. More's tracts, with alterations, additions, and
+  omissions <i>ad libitum</i>. This is an improper way of dealing with the
+  works of the dead; especially when the reprints are of popular works. A
+  small type addition to the preface contains: "Some alterations and
+  abridgements have been made to adapt them to the present times and the
+  aim of the Religious Tract Society." I think every publicity ought to be
+  given to the existence of such a practice; and I reprint what I said on
+  the subject in <i>Notes and Queries</i>.</p>
+
+  <p>Alterations in works which the Society republishes are a necessary
+  part of their plan, though such notes as they should judge to be
+  corrective would be the best way of proceeding. But the fact of
+  alteration should be very distinctly announced on the title of the work
+  itself, not left to a little bit of small type at the end of the preface,
+  in the place where trade advertisements, or directions to the binder, are
+  often found. And the places in which alteration has been made should be
+  pointed out, either by marks of omission, when omission is the
+  alteration, or by putting the altered sentences in brackets, when change
+  has been made. May any one alter the works of the dead at his own
+  discretion? <!-- Page 194 --><span class="pagenum"><a
+  name="page194"></a>[194]</span>We all know that readers in general will
+  take each sentence to be that of the author whose name is on the title;
+  so that a correcting republisher <i>makes use of his author's name to
+  teach his own variation</i>. The tortuous logic of "the trade," which is
+  content when "the world" is satisfied, is not easily answered, any more
+  than an eel is easily caught; but the Religious Tract Society may be
+  <i>convinced</i> [in the old sense] in a sentence. On which course would
+  they feel most safe in giving their account to the God of truth? "In your
+  own conscience, now?"</p>
+
+  <p>I have tracked out a good many of the variations made by the Religious
+  Tract Society in the recently published volume of <i>Repository
+  Tracts</i>. Most of them are doctrinal insertions or amplifications, to
+  the matter of which Hannah More would not have objected&mdash;all that
+  can be brought against them is the want of notice. But I have found two
+  which the respect I have for the Religious Tract Society, in spite of
+  much difference on various points, must not prevent my designating as
+  paltry. In the story of Mary Wood, a kind-hearted clergyman converses
+  with the poor girl who has ruined herself by lying. In the original, he
+  "assisted her in the great work of repentance;" in the reprint it is to
+  be shown in some detail how he did this. He is to begin by pointing out
+  that "the heart is deceitful above all things and desperately wicked."
+  Now the clergyman's name is <i>Heartwell</i>: so to prevent his name from
+  contradicting his doctrine, he is actually cut down to <i>Harwell</i>.
+  Hannah Moore meant this good man for one of those described in Acts xv.
+  8, 9, and his name was appropriate.</p>
+
+  <p>Again, Mr. Flatterwell, in persuasion of Parley the porter to let him
+  into the castle, declares that the worst he will do is to "play an
+  innocent game of cards just to keep you awake, or sing a cheerful song
+  with the maids." Oh fie! Miss Hannah More! and you a single lady too, and
+  a contemporary of the virtuous Bowdler!<a name="NtA_440"
+  href="#Nt_440"><sup>[440]</sup></a> Though Flatterwell be an <!-- Page
+  195 --><span class="pagenum"><a name="page195"></a>[195]</span>allegory
+  of the devil, this is really too indecorous, even for him. Out with the
+  three last words! and out it is.</p>
+
+  <p>The Society cuts a poor figure before a literary tribunal. Nothing was
+  wanted except an admission that the remarks made by me were unanswerable,
+  and this was immediately furnished by the Secretary (<i>N. and Q.</i>, 3d
+  S., vi. 290). In a reply of which six parts out of seven are a very
+  amplified statement that the Society did not intend to reprint <i>all</i>
+  Hannah More's tracts, the remaining seventh is as follows:</p>
+
+  <p>"I am not careful [perhaps this should be <i>careful not</i>] to
+  notice Professor De Morgan's objections to the changes in 'Mary Wood' or
+  'Parley the Porter,' but would merely reiterate that the tracts were
+  neither designed nor announced to be 'reprints' of the originals [design
+  is only known to the designers; as to announcement, the title is ''Tis
+  all for the best, The Shepherd of Salisbury Plain, and other narratives
+  by Hannah More']; and much less [this must be <i>careful not</i>; further
+  removed from answer than <i>not careful</i>] can I occupy your space by a
+  treatise on the Professor's question: 'May any one alter the works of the
+  dead at his own discretion?'"</p>
+
+  <p>To which I say: Thanks for help!</p>
+
+  <p>I predict that Hannah More's <i>Cheap Repository Tracts</i> will
+  somewhat resemble the <i>Pilgrim's Progress</i> in their fate. Written
+  for the cottage, and long remaining in their original position, they will
+  become classical works of their kind. Most assuredly this will happen if
+  my assertion cannot be upset, namely, that they contain the first
+  specimens of fiction addressed to the world at large, and widely
+  circulated, in which dramatic&mdash;as distinguished from
+  puppet&mdash;power is shown, and without indecorum.</p>
+
+<p><!-- Page 196 --><span class="pagenum"><a name="page196"></a>[196]</span></p>
+
+  <p>According to some statements I have seen, but which I have not
+  verified, other publishing bodies, such as the Christian Knowledge
+  Society, have taken the same liberty with the names of the dead as the
+  Religious Tract Society. If it be so, the impropriety is the work of the
+  smaller spirits who have not been sufficiently overlooked. There must be
+  an overwhelming majority in the higher councils to feel that, whenever
+  <i>altered</i> works are published, <i>the fact of alteration should be
+  made as prominent as the name of the author</i>. Everything short of this
+  is suppression of truth, and will ultimately destroy the credit of the
+  Society. Equally necessary is it that the alterations should be noted.
+  When it comes to be known that the author before him is altered, he knows
+  not where nor how nor by whom, the lowest reader will lose his
+  interest.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A TRIBUTE TO WILLIAM FREND.</p>
+
+<blockquote class="b1n">
+
+  <p>The principles of Algebra. By William Frend.<a name="NtA_441"
+  href="#Nt_441"><sup>[441]</sup></a> London, 1796, 8vo. Second Part,
+  1799.</p>
+
+</blockquote>
+
+  <p>This Algebra, says Dr. Peacock,<a name="NtA_442"
+  href="#Nt_442"><sup>[442]</sup></a> shows "great distrust <!-- Page 197
+  --><span class="pagenum"><a name="page197"></a>[197]</span>of the results
+  of algebraical science which were in existence at the time when it was
+  written." Truly it does; for, as Dr. Peacock had shown by full citation,
+  it makes war of extermination upon all that distinguishes algebra from
+  arithmetic. Robert Simson<a name="NtA_443"
+  href="#Nt_443"><sup>[443]</sup></a> and Baron Maseres<a name="NtA_444"
+  href="#Nt_444"><sup>[444]</sup></a> were Mr. Frend's predecessors in this
+  opinion.</p>
+
+  <p>The genuine respect which I entertained for my father-in-law did not
+  prevent my canvassing with perfect freedom his anti-algebraical and
+  anti-Newtonian opinions, in a long obituary memoir read at the
+  Astronomical Society in February 1842, which was written by me. It was
+  copied into the <i>Athenæum</i> of March 19. It must be said that if the
+  manner in which algebra <i>was</i> presented to the learner had been true
+  algebra, he would have been right: and if he had confined himself to
+  protesting against the imposition of attraction as a fundamental part of
+  the existence of matter, he would have been in unity with a great many,
+  including Newton himself. I wish he had preferred amendment to rejection
+  when he was a college tutor: he wrote and spoke English with a clearness
+  which is seldom equaled.</p>
+
+  <p>His anti-Newtonian discussions are confined to the preliminary
+  chapters of his <i>Evening Amusements</i>,<a name="NtA_445"
+  href="#Nt_445"><sup>[445]</sup></a> a series of astronomical lessons in
+  nineteen volumes, following the moon through a period of the golden
+  numbers.</p>
+
+  <p>There is a mistake about him which can never be destroyed. It is
+  constantly said that, at his celebrated trial in 1792, for sedition and
+  opposition to the Liturgy, etc., he was <i>expelled</i> from the
+  University. He was <i>banished</i>. People cannot see the difference; but
+  it made all the difference to <!-- Page 198 --><span class="pagenum"><a
+  name="page198"></a>[198]</span>Mr. Frend. He held his fellowship and its
+  profits till his marriage in 1808, and was a member of the University and
+  of its Senate till his death in 1841, as any Cambridge Calendar up to
+  1841 will show. That they would have expelled him if they could, is
+  perfectly true; and there is a funny story&mdash;also perfectly
+  true&mdash;about their first proceedings being under a statute which
+  would have given the power, had it not been discovered during the
+  proceedings that the statute did not exist. It had come so near to
+  existence as to be entered into the Vice-Chancellor's book for his
+  signature, which it wanted, as was not seen till Mr. Frend exposed it: in
+  fact, the statute had never actually passed.</p>
+
+  <p>There is an absurd mistake in Gunning's<a name="NtA_446"
+  href="#Nt_446"><sup>[446]</sup></a> <i>Reminiscences of Cambridge</i>. In
+  quoting a passage of Mr. Frend's pamphlet, which was very obnoxious to
+  the existing Government, it is printed that the poor market-women
+  complained that they were to be <i>scotched</i> a quarter of their wages
+  by taxation; and attention is called to the word by its being three times
+  printed in italics. In the pamphlet it is "sconced"; that very common old
+  word for fined or mulcted.</p>
+
+  <p>Lord Lyndhurst,<a name="NtA_447" href="#Nt_447"><sup>[447]</sup></a>
+  who has [1863] just passed away under a load of years and honors, was Mr.
+  Frend's private pupil at Cambridge. At the time of the celebrated trial,
+  he and two others amused themselves, and vented the feeling which was
+  very strong among the undergraduates, by chalking the walls of Cambridge
+  with "Frend for ever!" While thus engaged in what, using the term
+  legally, we are probably to call his first publication, he and his
+  friends were surprised by the proctors. Flight and chase followed of
+  course: Copley and one of the others, Serjeant Rough,<a name="NtA_448"
+  href="#Nt_448"><sup>[448]</sup></a> escaped: the <!-- Page 199 --><span
+  class="pagenum"><a name="page199"></a>[199]</span>third, whose name I
+  forget, but who afterwards, I have been told was a bishop,<a
+  name="NtA_449" href="#Nt_449"><sup>[449]</sup></a> being lame, was
+  captured and impositioned. Looking at the Cambridge Calendar to verify
+  the fact that Copley was an undergraduate at the time, I find that there
+  are but two other men in the list of honors of his year whose names are
+  now widely remembered. And they were both celebrated schoolmasters;
+  Butler<a name="NtA_450" href="#Nt_450"><sup>[450]</sup></a> of Harrow,
+  and Tate<a name="NtA_451" href="#Nt_451"><sup>[451]</sup></a> of
+  Richmond.</p>
+
+  <p>But Mr. Frend had another noted pupil. I once had a conversation with
+  a very remarkable man, who was generally called "Place,<a name="NtA_452"
+  href="#Nt_452"><sup>[452]</sup></a> the tailor," but who was politician,
+  political economist, etc., etc. He sat in the room above his
+  shop&mdash;he was then a thriving master tailor at Charing
+  Cross&mdash;surrounded by books enough for nine, to shame a proverb. The
+  blue books alone, cut up into strips, would have measured Great Britain
+  for oh-no-we-never-mention-'ems, the Highlands included. I cannot find a
+  biography of this worthy and able man. I happened to mention William
+  Frend, and he said, "Ah! my old master, as I always call him. Many and
+  many a time, and year after year, did he come in every <!-- Page 200
+  --><span class="pagenum"><a name="page200"></a>[200]</span>now and then
+  to give me instruction, while I was sitting on the board, working for my
+  living, you know."</p>
+
+  <p>Place, who really was a sound economist, is joined with Cobbett,
+  because they were together at one time, and because he was, in 1800,
+  etc., a great Radical. But for Cobbett he had a great contempt. He told
+  me the following story. He and others were advising with Cobbett about
+  the defense he was to make on a trial for seditious libel which was
+  coming on. Said Place, "You must put in the letters you have received
+  from Ministers, members of the Commons from the Speaker downwards, etc.,
+  about your Register, and their wish to have subjects noted. You must then
+  ask the jury whether a person so addressed must be considered as a common
+  sower of sedition, etc. You will be acquitted; nay, if your intention
+  should get about, very likely they will manage to stop proceedings."
+  Cobbett was too much disturbed to listen; he walked about the room
+  ejaculating "D&mdash;&mdash; the prison!" and the like. He had not the
+  sense to follow the advice, and was convicted.</p>
+
+  <p>Cobbett, to go on with the chain, was a political acrobat, ready for
+  any kind of posture. A friend of mine gave me several times an account of
+  a mission to him. A Tory member&mdash;those who know the old Tory world
+  may look for his initials in initials of two consecutive words of "Pay
+  his money with interest"&mdash;who was, of course, a political opponent,
+  thought Cobbett had been hardly used, and determined to subscribe
+  handsomely towards the expenses he was incurring as a candidate. My
+  friend was commissioned to hand over the money&mdash;a bag of sovereigns,
+  that notes might not be traced. He went into Cobbett's committee-room,
+  told the patriot his errand, and put the money on the table. "And to
+  whom, sir, am I indebted?" said Cobbett. "The donor," was the answer, "is
+  Mr. Andrew Theophilus Smith," or some such unlikely pair of baptismals.
+  "Ah!" said Cobbett, "I have known Mr. A.&nbsp;T.&nbsp;S. a long time! he was always
+  a true friend of his country!" <!-- Page 201 --><span class="pagenum"><a
+  name="page201"></a>[201]</span></p>
+
+  <p>To return to Place. He is a noted instance of the advantage of our
+  jury system, which never asks a man's politics, etc. The late King of
+  Hanover, when Duke of Cumberland, being unpopular, was brought under
+  unjust suspicions by the suicide of his valet: he must have seduced the
+  wife and murdered the husband. The charges were as absurd as those
+  brought against the Englishman in the Frenchman's attempt at satirical
+  verses upon him:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"The Englishman is a very bad man;</p>
+      <p>He drink the beer and he steal the can:</p>
+      <p>He kiss the wife and he beat the man;</p>
+      <p>And the Englishman is a very G&mdash;&mdash; d&mdash;&mdash;."</p>
+    </div>
+  </div>
+  <p>The charges were revived in a much later day, and the defense might
+  have given some trouble. But Place, who had been the foreman at the
+  inquest, came forward, and settled the question in a few lines. Every one
+  knew that the old Radical was quite free of all disposition to suppress
+  truth from wish to curry favor with royalty.</p>
+
+  <p>John Speed,<a name="NtA_453" href="#Nt_453"><sup>[453]</sup></a> the
+  author of the <i>English History</i>,<a name="NtA_454"
+  href="#Nt_454"><sup>[454]</sup></a> (1632) which Bishop Nicolson<a
+  name="NtA_455" href="#Nt_455"><sup>[455]</sup></a> calls the best
+  chronicle extant, was a man, like Place, of no education, but what he
+  gave himself. The bishop says he would have done better if he had a
+  better training: but what, he adds, could have been expected from a
+  tailor! This Speed was, as well as Place. But he was <!-- Page 202
+  --><span class="pagenum"><a name="page202"></a>[202]</span>released from
+  manual labor by Sir Fulk Grevil,<a name="NtA_456"
+  href="#Nt_456"><sup>[456]</sup></a> who enabled him to study.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A STORY ON SIMSON.</p>
+
+  <p>I have elsewhere noticed that those who oppose the mysteries of
+  algebra do not ridicule them; this I want the cyclometers to do. Of the
+  three who wrote against the great point, the negative quantity, and the
+  uses of 0 which are connected with it, only one could fire a squib. That
+  Robert Simson<a name="NtA_457" href="#Nt_457"><sup>[457]</sup></a> should
+  do such a thing will be judged impossible by all who admit tradition. I
+  do not vouch for the following; I give it as a proof of the impression
+  which prevailed about him:</p>
+
+  <p>He used to sit at his open window on the ground floor, as deep in
+  geometry as a Robert Simson ought to be. Here he would be accosted by
+  beggars, to whom he generally gave a trifle, he roused himself to hear a
+  few words of the story, made his donation, and instantly dropped down
+  into his depths. Some wags one day stopped a mendicant who was on his way
+  to the window with "Now, my man, do as we tell you, and you will get
+  something from that gentleman, and a shilling from us besides. You will
+  go and say you are in distress, he will ask you who you are, and you will
+  say you are Robert Simson, son of John Simson of Kirktonhill." The man
+  did as he was told; Simson quietly gave him a coin, and dropped off. The
+  wags watched a little, and saw him rouse himself again, and exclaim
+  "Robert Simson, son of John Simson of Kirktonhill! why, that is myself.
+  That man must be an impostor." Lord Brougham tells the same story, with
+  some difference of details.</p>
+
+<p><!-- Page 203 --><span class="pagenum"><a name="page203"></a>[203]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">BARON MASERES.</p>
+
+  <p>Baron Maseres<a name="NtA_458" href="#Nt_458"><sup>[458]</sup></a>
+  was, as a writer, dry; those who knew his writings will feel that he
+  seldom could have taken in a joke or issued a pun. Maseres was the fourth
+  wrangler of 1752, and first Chancellor's medallist (or highest in
+  classics); his second was Porteus<a name="NtA_459"
+  href="#Nt_459"><sup>[459]</sup></a> (afterward Bishop of London).
+  Waring<a name="NtA_460" href="#Nt_460"><sup>[460]</sup></a> came five
+  years after him: he could not get Maseres through the second page of his
+  first book on algebra; a negative quantity stood like a lion in the way.
+  In 1758 he published his <i>Dissertation on the Use of the Negative
+  Sign</i>,<a name="NtA_461" href="#Nt_461"><sup>[461]</sup></a> 4to. There
+  are some who care little about + and -, who would give it house-room for
+  the sake of the four words "Printed by Samuel Richardson."</p>
+
+  <p>Maseres speaks as follows: "A single quantity can never be marked with
+  either of those signs, or considered as either affirmative or negative;
+  for if any single quantity, as <i>b</i>, is marked either with the sign +
+  or with the sign - without assigning some other quantity, as <i>a</i>, to
+  which it is to be added, or from which it is to be subtracted, the mark
+  will have no meaning or signification: thus if it be said that the square
+  of -5, or the product of -5 into -5, is equal to +25, such an assertion
+  must either signify no more than that 5 times 5 is equal to 25 without
+  any regard to the signs, or it must be mere nonsense and unintelligible
+  jargon. I speak according to the foregoing definition, by which the
+  affirmativeness or negativeness of any quantity implies a relation to
+  another quantity of the same kind to which it <!-- Page 204 --><span
+  class="pagenum"><a name="page204"></a>[204]</span>is added, or from which
+  it is subtracted; for it may perhaps be very clear and intelligible to
+  those who have formed to themselves some other idea of affirmative and
+  negative quantities different from that above defined."</p>
+
+  <p>Nothing can be more correct, or more identically logical: +5 and -5,
+  standing alone, are jargon if +5 and -5 are to be understood as without
+  reference to another quantity. But those who have "formed to themselves
+  some other idea" see meaning enough. The great difficulty of the
+  opponents of algebra lay in want of power or will to see extension of
+  terms. Maseres is right when he implies that extension, accompanied by
+  its refusal, makes jargon. One of my paradoxers was present at a meeting
+  of the Royal Society (in 1864, I think) and asked permission to make some
+  remarks upon a paper. He rambled into other things, and, naming me, said
+  that I had written a book in which two sides of a triangle are pronounced
+  <i>equal</i> to the third.<a name="NtA_462"
+  href="#Nt_462"><sup>[462]</sup></a> So they are, in the sense in which
+  the word is used in complete algebra; in which A + B = C makes A, B, C,
+  three sides of a triangle, and declares that going over A and B, one
+  after the other, is equivalent, in change of place, to going over C at
+  once. My critic, who might, if he pleased, have objected to extension,
+  insisted upon reading me in unextended meaning.</p>
+
+  <p>On the other hand, it must be said that those who wrote on the other
+  idea wrote very obscurely about it and justified Des Cartes (<i>De
+  Methodo</i>)<a name="NtA_463" href="#Nt_463"><sup>[463]</sup></a> when he
+  said: "Algebram vero, ut solet doceri, animadverti certis regulis et
+  numerandi formulis ita esse contentam, ut videatur potius ars quædam
+  confusa, cujus usu ingenium quodam modo turbatur et obscuratur, quam
+  scientia qua excolatur et perspicacius <!-- Page 205 --><span
+  class="pagenum"><a name="page205"></a>[205]</span>reddatur."<a
+  name="NtA_464" href="#Nt_464"><sup>[464]</sup></a> Maseres wrote this
+  sentence on the title of his own work, now before me; he would have made
+  it his motto if he had found it earlier.</p>
+
+  <p>There is, I believe, in Cobbett's <i>Annual Register</i>,<a
+  name="NtA_465" href="#Nt_465"><sup>[465]</sup></a> an account of an
+  interview between Maseres and Cobbett when in prison.</p>
+
+  <p>The conversation of Maseres was lively, and full of serious anecdote:
+  but only one attempt at humorous satire is recorded of him; it is an
+  instructive one. He was born in 1731 (Dec. 15), and his father was a
+  refugee. French was the language of the house, with the pronunciation of
+  the time of Louis XIV. He lived until 1824 (May 19), and saw the race of
+  refugees who were driven out by the first Revolution. Their pronunciation
+  differed greatly from his own; and he used to amuse himself by mimicking
+  them. Those who heard him and them had the two schools of pronunciation
+  before them at once; a thing which seldom happens. It might even yet be
+  worth while to examine the Canadian pronunciation.</p>
+
+  <p>Maseres went as Attorney-General to Quebec; and was appointed Cursitor
+  Baron of our Exchequer in 1773. There is a curious story about his
+  mission to Canada, which I have heard as good tradition, but have never
+  seen in print. The reader shall have it as cheap as I; and I confess I
+  rather believe it. Maseres was inveterately honest; he could not, at the
+  bar, bear to see his own client victorious, when he knew his cause was a
+  bad one. On a certain occasion he was in a cause which he knew would go
+  against him if a certain case were quoted. Neither the judge nor the
+  opposite counsel seemed to remember this case, and Maseres could not help
+  dropping an allusion which brought it out. <!-- Page 206 --><span
+  class="pagenum"><a name="page206"></a>[206]</span>His business as a
+  barrister fell off, of course. Some time after, Mr. Pitt (Chatham) wanted
+  a lawyer to send to Canada on a private mission, and wanted a <i>very
+  honest man</i>. Some one mentioned Maseres, and told the above story:
+  Pitt saw that he had got the man he wanted. The mission was
+  satisfactorily performed, and Maseres remained as Attorney-General.</p>
+
+  <p>The <i>Doctrine of Life Annuities</i><a name="NtA_466"
+  href="#Nt_466"><sup>[466]</sup></a> (4to, 726 pages, 1783) is a strange
+  paradox. Its size, the heavy dissertations on the national debt, and the
+  depth of algebra supposed known, put it out of the question as an
+  elementary work, and it is unfitted for the higher student by its
+  elaborate attempt at elementary character, shown in its rejection of
+  forms derived from chances in favor of <i>the average</i>, and its
+  exhibition of the separate values of the years of an annuity, as
+  arithmetical illustrations. It is a climax of unsaleability,
+  unreadability, and inutility. For intrinsic nullity of interest, and
+  dilution of little matter with much ink, I can compare this book to
+  nothing but that of Claude de St. Martin, elsewhere mentioned, or the
+  lectures <i>On the Nature and Properties of Logarithms</i>, by James
+  Little,<a name="NtA_467" href="#Nt_467"><sup>[467]</sup></a> Dublin,
+  1830, 8vo. (254 heavy pages of many words and few symbols), a wonderful
+  weight of weariness.</p>
+
+  <p>The stock of this work on annuities, very little diminished, was given
+  by the author to William Frend, who paid warehouse room for it until
+  about 1835, when he consulted me as to its disposal. As no publisher
+  could be found who would take it as a gift, for any purpose of sale, it
+  was consigned, all but a few copies, to a buyer of waste paper.</p>
+
+  <p>Baron Maseres's republications are well known: the <i>Scriptores
+  Logarithmici</i><a name="NtA_468" href="#Nt_468"><sup>[468]</sup></a> is
+  a set of valuable reprints, mixed <!-- Page 207 --><span
+  class="pagenum"><a name="page207"></a>[207]</span>with much which might
+  better have entered into another collection. It is not so well known that
+  there is a volume of optical reprints, <i>Scriptores Optici</i>, London,
+  1823, 4to, edited for the veteran of ninety-two by Mr. Babbage<a
+  name="NtA_469" href="#Nt_469"><sup>[469]</sup></a> at twenty-nine. This
+  excellent volume contains James Gregory, Des Cartes, Halley, Barrow, and
+  the optical writings of Huyghens, the <i>Principia</i> of the undulatory
+  theory. It also contains, by the sort of whim in which such men as
+  Maseres, myself, and some others are apt to indulge, a reprint of "The
+  great new Art of weighing Vanity,"<a name="NtA_470"
+  href="#Nt_470"><sup>[470]</sup></a> by M. Patrick Mathers, Arch-Bedel to
+  the University of St. Andrews, Glasgow, 1672. Professor Sinclair,<a
+  name="NtA_471" href="#Nt_471"><sup>[471]</sup></a> of Glasgow, a good man
+  at clearing mines of the water which they did not want, and furnishing
+  cities with water which they did want, seems to have written absurdly
+  about hydrostatics, and to have attacked a certain Sanders,<a
+  name="NtA_472" href="#Nt_472"><sup>[472]</sup></a> M.A. So Sanders,
+  assisted by James Gregory, published a heavy bit of jocosity about him.
+  This story of the authorship rested on a note made in his <!-- Page 208
+  --><span class="pagenum"><a name="page208"></a>[208]</span>copy by Robert
+  Gray, M.D.; but it has since been fully confirmed by a letter of James
+  Gregory to Collins, in the Macclesfield Correspondence. "There is one
+  Master Sinclair, who did write the <i>Ars Magna et Nova</i>,<a
+  name="NtA_473" href="#Nt_473"><sup>[473]</sup></a> a pitiful ignorant
+  fellow, who hath lately written horrid nonsense in the hydrostatics, and
+  hath abused a master in the University, one Mr. Sanders, in print. This
+  Mr. Sanders ... is resolved to cause the Bedel of the University to write
+  against him.... We resolve to make excellent sport with him."</p>
+
+  <p>On this I make two remarks: First, I have learned from experience that
+  old notes, made in books by their possessors, are statements of high
+  authority: they are almost always confirmed. I do not receive them
+  without hesitation; but I believe that of all the statements about books
+  which rest on one authority, there is a larger percentage of truth in the
+  written word than in the printed word. Secondly, I mourn to think that
+  when the New Zealander picks up his old copy of this book, and reads it
+  by the associations of his own day, he may, in spite of the many
+  assurances I have received that my <i>Athenæum Budget</i> was amusing,
+  feel me to be as heavy as I feel James Gregory and Sanders. But he will
+  see that I knew what was coming, which Gregory did not.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">MR. FREND'S BURLESQUE.</p>
+
+  <p>It was left for Mr. Frend to prove that an impugner of algebra could
+  attempt ridicule. He was, in 1803, editor of a periodical <i>The
+  Gentleman's Monthly Miscellany</i>, which lasted a few months.<a
+  name="NtA_474" href="#Nt_474"><sup>[474]</sup></a> To this, among other
+  things, he contributed the following, in burlesque of the use made of 0,
+  to which he objected.<a name="NtA_475"
+  href="#Nt_475"><sup>[475]</sup></a> The imitation of Rabelais, a writer
+  <!-- Page 209 --><span class="pagenum"><a
+  name="page209"></a>[209]</span>in whom he delighted, is good: to those
+  who have never dipped, it may give such a notion as they would not easily
+  get elsewhere. The point of the satire is not so good. But in truth it is
+  not easy to make pungent scoffs upon what is common sense to all mankind.
+  Who can laugh with effect at six times nothing is nothing, as false or
+  unintelligible? In an article intended for that undistinguishing know-0
+  the "general reader," there would have been no force of satire, if
+  <i>division</i> by 0 had been separated from multiplication by the
+  same.</p>
+
+  <p>I have followed the above by another squib, by the same author, on the
+  English language. The satire is covertly aimed at theological
+  phraseology; and any one who watches this subject will see that it is a
+  very just observation that the Greek words are not boiled enough.</p>
+
+<p class="cenhead"><span class="sc">Pantagruel's Decision</span> <i>of the</i> <span class="sc">Question</span> <i>about</i> <span class="sc">Nothing</span>.</p>
+
+  <p>"Pantagruel determined to have a snug afternoon with Epistemon and
+  Panurge. Dinner was ordered to be set in a small parlor, and a particular
+  batch of Hermitage with some choice Burgundy to be drawn from a remote
+  corner of the cellar upon the occasion. By way of lunch, about an hour
+  before dinner, Pantagruel was composing his stomach with German sausages,
+  reindeer's tongues, oysters, brawn, and half a dozen different sorts of
+  English beer just come into fashion, when a most thundering knocking was
+  heard at the great gate, and from the noise they expected it to announce
+  the arrival at least of the First Consul, or king Gargantua. Panurge was
+  sent to reconnoiter, and after a quarter of an hour's absence, returned
+  with the news that the University of Pontemaca was waiting his highness's
+  leisure in the great hall, to propound a question which <!-- Page 210
+  --><span class="pagenum"><a name="page210"></a>[210]</span>had turned the
+  brains of thirty-nine students, and had flung twenty-seven more into a
+  high fever. With all my heart, says Pantagruel, and swallowed down three
+  quarts of Burton ale; but remember, it wants but an hour of dinner time,
+  and the question must be asked in as few words as possible; for I cannot
+  deprive myself of the pleasure I expected to enjoy in the company of my
+  good friends for a set of mad-headed masters. I wish brother John was
+  here to settle these matters with the black gentry.</p>
+
+  <p>"Having said or rather growled this, he proceeded to the hall of
+  ceremony, and mounted his throne; Epistemon and Panurge standing on each
+  side, but two steps below him. Then advanced to the throne the three
+  beadles of the University of Pontemaca with their silver staves on their
+  shoulders, and velvet caps on their heads, and they were followed by
+  three times three doctors, and thrice three times three masters of art;
+  for everything was done in Pontemaca by the number three, and on this
+  account the address was written on parchment, one foot in breadth, and
+  thrice three times thrice three feet in length. The beadles struck the
+  ground with their heads and their staves three times in approaching the
+  throne; the doctors struck the ground with their heads thrice three
+  times, and the masters did the same thrice each time, beating the ground
+  with their heads thrice three times. This was the accustomed form of
+  approaching the throne, time out of mind, and it was said to be
+  emblematic of the usual prostration of science to the throne of
+  greatness.</p>
+
+  <p>"The mathematical professor, after having spit, and hawked, and
+  cleared his throat, and blown his nose on a handkerchief lent to him, for
+  he had forgotten to bring his own, began to read the address. In this he
+  was assisted by three masters of arts, one of whom, with a silver pen,
+  pointed out the stops; the second with a small stick rapped his knuckles
+  when he was to raise or lower his voice; and a third pulled his hair
+  behind when he was to look Pantagruel in the face. Pantagruel began to
+  chafe like a lion: <!-- Page 211 --><span class="pagenum"><a
+  name="page211"></a>[211]</span>he turned first on one side, then on the
+  other: he listened and groaned, and groaned and listened, and was in the
+  utmost cogitabundity of cogitation. His countenance began to brighten,
+  when, at the end of an hour, the reader stammered out these words:</p>
+
+  <p>"'It has therefore been most clearly proved that as all matter may be
+  divided into parts infinitely smaller than the infinitely smallest part
+  of the infinitesimal of nothing, so nothing has all the properties of
+  something, and may become, by just and lawful right, susceptible of
+  addition, subtraction, multiplication, division, squaring, and cubing:
+  that it is to all intents and purposes as good as anything that has been,
+  is, or can be taught in the nine universities of the land, and to deprive
+  it of its rights is a most cruel innovation and usurpation, tending to
+  destroy all just subordination in the world, making all universities
+  superfluous, leveling vice-chancellors, doctors, and proctors, masters,
+  bachelors, and scholars, to the mean and contemptible state of butchers
+  and tallow-chandlers, bricklayers and chimney-sweepers, who, if it were
+  not for these learned mysteries, might think that they knew as much as
+  their betters. Every one then, who has the good of science at heart, must
+  pray for the interference of his highness to put a stop to all the
+  disputes about nothing, and by his decision to convince all gainsayers
+  that the science of nothing is taught in the best manner in the
+  universities, to the great edification and improvement of all the youth
+  in the land.'</p>
+
+  <p>"Here Pantagruel whispered in the ear of Panurge, who nodded to
+  Epistemon, and they two left the assembly, and did not return for an
+  hour, till the orator had finished his task. The three beadles had thrice
+  struck the ground with their heads and staves, the <span
+  class="correction" title="text reads `docters'">doctors</span> had
+  finished their compliments, and the masters were making their
+  twenty-seven prostrations. Epistemon and Panurge went up to Pantagruel,
+  whom they found fast asleep and snoring; nor could he be roused but by as
+  many tugs as there had been <!-- Page 212 --><span class="pagenum"><a
+  name="page212"></a>[212]</span>bowings from the corps of learning. At
+  last he opened his eyes, gave a good stretch, made half a dozen yawns,
+  and called for a stoup of wine. I thank you, my masters, says he; so
+  sound a nap I have not had since I came from the island of Priestfolly.
+  Have you dined, my masters? They answered the question by as many bows as
+  at entrance; but his highness left them to the care of Panurge, and
+  retired to the little parlor with Epistemon, where they burst into a fit
+  of laughter, declaring that this learned Baragouin about nothing was just
+  as intelligible as the lawyer's Galimathias. Panurge conducted the
+  learned body into a large saloon, and each in his way hearing a
+  clattering of plates and glasses, congratulated himself on his
+  approaching good cheer. There they were left by Panurge, who took his
+  chair by Pantagruel just as the soup was removed, but he made up for the
+  want of that part of his dinner by a pint of champagne. The learning of
+  the university had whetted their appetites; what they each ate it is
+  needless to recite; good wine, good stories, and hearty laughs went
+  round, and three hours elapsed before one soul of them recollected the
+  hungry students of Pontemaca.</p>
+
+  <p>"Epistemon reminded them of the business in hand, and orders were
+  given for a fresh dozen of hermitage to be put upon table, and the royal
+  attendants to get ready. As soon as the dozen bottles were emptied,
+  Pantagruel rose from table, the royal trumpets sounded, and he was
+  accompanied by the great officers of his court into the large dining
+  hall, where was a table with forty-two covers. Pantagruel sat at the
+  head, Epistemon at the bottom, and Panurge in the middle, opposite an
+  immense silver tureen, which would hold fifty gallons of soup. The wise
+  men of Pontemaca then took their seats according to seniority. Every
+  countenance glistened with delight; the music struck up; the dishes were
+  uncovered. Panurge had enough to do to handle the immense silver ladle:
+  Pantagruel and Epistemon had no time for eating, they were fully employed
+  in carving. The bill <!-- Page 213 --><span class="pagenum"><a
+  name="page213"></a>[213]</span>of fare announced the names of a hundred
+  different dishes. From Panurge's ladle came into the soup plate as much
+  as he took every time out of the tureen; and as it was the rule of the
+  court that every one should appear to eat, as long as he sat at table,
+  there was the clattering of nine and thirty spoons against the silver
+  soup-plates for a quarter of an hour. They were then removed, and knives
+  and forks were in motion for half an hour. Glasses were continually
+  handed round in the mean time, and then everything was removed, except
+  the great tureen of soup. The second course was now served up, in
+  dispatching which half an hour was consumed; and at the conclusion the
+  wise men of Pontemaca had just as much in their stomachs as Pantagruel in
+  his head from their address: for nothing was cooked up for them in every
+  possible shape that Panurge could devise.</p>
+
+  <p>"Wine-glasses, large decanters, fruit dishes, and plates were now set
+  on. Pantagruel and Epistemon alternately gave bumper toasts: the
+  University of Pontemaca, the eye of the world, the mother of taste and
+  good sense and universal learning, the patroness of utility, and the
+  second only to Pantagruel in wisdom and virtue (for these were her
+  titles), was drank standing with thrice three times three, and huzzas and
+  clattering of glasses; but to such wine the wise men of Pontemaca had not
+  been accustomed; and though Pantagruel did not suffer one to rise from
+  table till the eighty-first glass had been emptied, not even the weakest
+  headed master of arts felt his head in the least indisposed. The
+  decanters indeed were often removed, but they were brought back
+  replenished, filled always with nothing.</p>
+
+  <p>"Silence was now proclaimed, and in a trice Panurge leaped into the
+  large silver tureen. Thence he made his bows to Pantagruel and the whole
+  company, and commenced an oration of signs, which lasted an hour and a
+  half, and in which he went over all the matter contained in the Pontemaca
+  address; and though the wise men looked very serious during the whole
+  time, Pantagruel himself and his whole <!-- Page 214 --><span
+  class="pagenum"><a name="page214"></a>[214]</span>court could not help
+  indulging in repeated bursts of laughter. It was universally acknowledged
+  that he excelled himself, and that the arguments by which he beat the
+  English masters of arts at Paris were nothing to the exquisite selection
+  of attitudes which he this day assumed. The greatest shouts of applause
+  were excited when he was running thrice round the tureen on its rim, with
+  his left hand holding his nose, and the other exercising itself nine and
+  thirty times on his back. In this attitude he concluded with his back to
+  the professor of mathematics; and at the instant he gave his last flap,
+  by a sudden jump, and turning heels over head in the air, he presented
+  himself face to face to the professor, and standing on his left leg, with
+  his left hand holding his nose, he presented to him, in a white satin
+  bag, Pantagruel's royal decree. Then advancing his right leg, he fixed it
+  on the professor's head, and after three turns, in which he clapped his
+  sides with both hands thrice three times, down he leaped, and Pantagruel,
+  Epistemon, and himself took their leaves of the wise men of
+  Pontemaca.</p>
+
+  <p>"The wise men now retired, and by royal orders were accompanied by a
+  guard, and according to the etiquette of the court, no one having a royal
+  order could stop at any public house till it was delivered. The
+  procession arrived at Pontemaca at nine o'clock the next morning, and the
+  sound of bells from every church and college announced their arrival. The
+  congregation was assembled; the royal decree was saluted in the same
+  manner as if his highness had been there in person; and after the proper
+  ceremonies had been performed, the satin bag was opened exactly at twelve
+  o'clock. A finely emblazoned roll was drawn forth, and the public orator
+  read to the gaping assembly the following words:</p>
+
+  <p>"'They who can make something out of nothing shall have nothing to eat
+  at the court of&mdash;<span class="sc">Pantagruel</span>.'" <!-- Page 215
+  --><span class="pagenum"><a name="page215"></a>[215]</span></p>
+
+<p class="cenhead"><span class="sc">Origin</span> <i>of the</i> <span class="sc">English Language</span>, <i>related by a</i> <span class="sc">Swede</span>.</p>
+
+  <p>"Some months ago in a party in Holland, consisting of natives of
+  various countries, the merit of their respective languages became a topic
+  of conversation. A Swede, who had been a great traveler, and could
+  converse in most of the modern languages of Europe, laughed very heartily
+  at an Englishman, who had ventured to speak in praise of the tongue of
+  his dear country. I never had any trouble, says he, in learning English.
+  To my very great surprise, the moment I sat foot on shore at Gravesend, I
+  found out, that I could understand, with very little trouble, every word
+  that was said. It was a mere jargon, made up of German, French, and
+  Italian, with now and then a word from the Spanish, Latin or Greek. I had
+  only to bring my mouth to their mode of speaking, which was done with
+  ease in less than a week, and I was everywhere taken for a true-born
+  Englishman; a privilege by the way of no small importance in a country,
+  where each man, God knows why, thinks his foggy island superior to any
+  other part of the world: and though his door is never free from some dun
+  or other coming for a tax, and if he steps out of it he is sure to be
+  knocked down or to have his pocket picked, yet he has the insolence to
+  think every foreigner a miserable slave, and his country the seat of
+  everything wretched. They may talk of liberty as they please, but Spain
+  or Turkey for my money: barring the bowstring and the inquisition, they
+  are the most comfortable countries under heaven, and you need not be
+  afraid of either, if you do not talk of religion and politics. I do not
+  see much difference too in this respect in England, for when I was there,
+  one of their most eminent men for learning was put in prison for a couple
+  of years, and got his death for translating one of Æsop's fables into
+  English, which every child in Spain and Turkey is taught, as soon as he
+  comes out of his leading strings. Here all the company unanimously cried
+  out against the Swede, that it was <!-- Page 216 --><span
+  class="pagenum"><a name="page216"></a>[216]</span>impossible: for in
+  England, the land of liberty, the only thing its worst enemies could say
+  against it, was, that they paid for their liberty a much greater price
+  than it was worth.&mdash;Every man there had a fair trial according to
+  laws, which everybody could understand; and the judges were cool,
+  patient, discerning men, who never took the part of the crown against the
+  prisoner, but gave him every assistance possible for his defense.</p>
+
+  <p>"The Swede was borne down, but not convinced; and he seemed determined
+  to spit out all his venom. Well, says he, at any rate you will not deny
+  that the English have not got a language of their own, and that they came
+  by it in a very odd way. Of this at least I am certain, for the whole
+  history was related to me by a witch in Lapland, whilst I was bargaining
+  for a wind. Here the company were all in unison again for the story.</p>
+
+  <p>"In ancient times, said the old hag, the English occupied a spot in
+  Tartary, where they lived sulkily by themselves, unknowing and unknown.
+  By a great convulsion that took place in China, the inhabitants of that
+  and the adjoining parts of Tartary were driven from their seats, and
+  after various wanderings took up their abode in Germany. During this time
+  nobody could understand the English, for they did not talk, but hissed
+  like so many snakes. The poor people felt uneasy under this circumstance,
+  and in one of their parliaments, or rather hissing meetings, it was
+  determined to seek a remedy: and an embassy was sent to some of our
+  sisterhood then living on Mount Hecla. They were put to a nonplus, and
+  summoned the Devil to their relief. To him the English presented their
+  petitions, and explained their sad case; and he, upon certain conditions,
+  promised to befriend them, and to give them a language. The poor Devil
+  was little aware of what he had promised; but he is, as all the world
+  knows, a man of too much honor to break his word. Up and down the world
+  then he went in quest of this new language: visited all the universities,
+  and all <!-- Page 217 --><span class="pagenum"><a
+  name="page217"></a>[217]</span>the schools, and all the courts of law,
+  and all the play-houses, and all the prisons; never was poor devil so
+  fagged. It would have made your heart bleed to see him. Thrice did he go
+  round the earth in every parallel of latitude; and at last, wearied and
+  jaded out, back came he to Hecla in despair, and would have thrown
+  himself into the volcano, if he had been made of combustible materials.
+  Luckily at that time our sisters were engaged in settling the balance of
+  Europe; and whilst they were looking over projects, and counter-projects,
+  and ultimatums, and post ultimatums, the poor Devil, unable to assist
+  them was groaning in a corner and ruminating over his sad condition.</p>
+
+  <p>"On a sudden, a hellish joy overspread his countenance; up he jumped,
+  and, like Archimedes of old, ran like a madman amongst the throng,
+  turning over tables, and papers, and witches, roaring out for a full hour
+  together nothing else but 'tis found, 'tis found! Away were sent the
+  sisterhood in every direction, some to traverse all the corners of the
+  earth, and others to prepare a larger caldron than had ever yet been set
+  upon Hecla. The affairs of Europe were at a stand: its balance was thrown
+  aside; prime ministers and ambassadors were everywhere in the utmost
+  confusion; and, by the way, they have never been able to find the balance
+  since that time, and all the fine speeches upon the subject, with which
+  your newspapers are every now and then filled, are all mere hocus-pocus
+  and rhodomontade. However, the caldron was soon set on, and the air was
+  darkened by witches riding on broomsticks, bringing a couple of folios
+  under each arm, and across each shoulder. I remember the time exactly: it
+  was just as the council of Nice had broken up, so that they got books and
+  papers there dog cheap; but it was a bad thing for the poor English, as
+  these were the worst materials that entered into the caldron. Besides, as
+  the Devil wanted some amusement, and had not seen an account of the
+  transactions of this famous council, he had all the books brought from it
+  laid before him, and split his sides almost <!-- Page 218 --><span
+  class="pagenum"><a name="page218"></a>[218]</span>with laughing, whilst
+  he was reading the speeches and decrees of so many of his old friends and
+  acquaintances. All this while the witches were depositing their loads in
+  the great caldron. There were books from the Dalai Lama, and from China:
+  there were books from the Hindoos, and tallies from the Caffres: there
+  were paintings from Mexico, and rocks of hieroglyphics from Egypt: the
+  last country supplied besides the swathings of two thousand mummies, and
+  four-fifths of the famed library of Alexandria. Bubble! bubble! toil and
+  trouble! never was a day of more labor and anxiety; and if our good
+  master had but flung in the Greek books at the proper time, they would
+  have made a complete job of it. He was a little too impatient: as the
+  caldron frothed up, he skimmed it off with a great ladle, and filled some
+  thousands of our wind-bags with the froth, which the English with great
+  joy carried back to their own country. These bags were sent to every
+  district: the chiefs first took their fill, and then the common people;
+  hence they now speak a language which no foreigner can understand, unless
+  he has learned half a dozen other languages; and the poor people, not one
+  in ten, understand a third part of what is said to them. The hissing,
+  however, they have not entirely got rid of, and every seven years, when
+  the Devil, according to agreement, pays them a visit, they entertain him
+  at their common halls and county meetings with their original
+  language.</p>
+
+  <p>"The good-natured old hag told me several other circumstances,
+  relative to this curious transaction, which, as there is an Englishman in
+  company, it will be prudent to pass over in silence: but I cannot help
+  mentioning one thing which she told me as a very great secret. You know,
+  says she to me, that the English have more religions among them than any
+  other nation in Europe, and that there is more teaching and sermonizing
+  with them than in any other country. The fact is this; it matters not who
+  gets up to teach them, the hard words of the Greek were not sufficiently
+  <!-- Page 219 --><span class="pagenum"><a
+  name="page219"></a>[219]</span>boiled, and whenever they get into a
+  sentence, the poor people's brains are turned, and they know no more what
+  the preacher is talking about, than if he harangued them in Arabic. Take
+  my word for it if you please; but if not, when you get to England, desire
+  the bettermost sort of people that you are acquainted with to read to you
+  an act of parliament, which of course is written in the clearest and
+  plainest style in which anything can be written, and you will find that
+  not one in ten will be able to make tolerable sense of it. The language
+  would have been an excellent language, if it had not been for the council
+  of Nice, and the words had been well boiled.</p>
+
+  <p>"Here the company burst out into a fit of laughter. The Englishman got
+  up and shook hands with the Swede: <i>si non è vero</i>, said he, <i>è
+  ben trovato</i>.<a name="NtA_476" href="#Nt_476"><sup>[476]</sup></a>
+  But, however I may laugh at it here, I would not advise you to tell this
+  story on the other side of the water. So here's a bumper to Old England
+  for ever, and God save the king."</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON YOUTHFUL PRODIGIES.</p>
+
+  <p>The accounts given of extraordinary children and adolescents
+  frequently defy credence.<a name="NtA_477"
+  href="#Nt_477"><sup>[477]</sup></a> I will give two well-attested
+  instances.</p>
+
+  <p>The celebrated mathematician Alexis Claude Clairault (now Clairaut)<a
+  name="NtA_478" href="#Nt_478"><sup>[478]</sup></a> was certainly born in
+  May, 1713. His treatise on curves of double curvature (printed in 1731)<a
+  name="NtA_479" href="#Nt_479"><sup>[479]</sup></a> received <!-- Page 220
+  --><span class="pagenum"><a name="page220"></a>[220]</span>the
+  approbation of the Academy of Sciences, August 23, 1729. Fontenelle, in
+  his certificate of this, calls the author sixteen years of age, and does
+  not strive to exaggerate the wonder, as he might have done, by reminding
+  his readers that this work, of original and sustained mathematical
+  investigation, must have been coming from the pen at the ages of fourteen
+  and fifteen. The truth was, as attested by De Molières,<a name="NtA_480"
+  href="#Nt_480"><sup>[480]</sup></a> Clairaut had given public proofs of
+  his power at twelve years old. His age being thus publicly certified, all
+  doubt is removed: say he had been&mdash;though great wonder would still
+  have been left&mdash;twenty-one instead of sixteen, his appearance, and
+  the remembrances of his friends, schoolfellows, etc., would have made it
+  utterly hopeless to knock off five years of that age while he was on view
+  in Paris as a young lion. De Molières, who examined the work officially
+  for the <i>Garde des Sceaux</i>, is transported beyond the bounds of
+  official gravity, and says that it "ne mérite pas seulement d'être
+  imprimé, mais d'être admiré comme un prodige d'imagination, de
+  conception, et de capacité."<a name="NtA_481"
+  href="#Nt_481"><sup>[481]</sup></a></p>
+
+  <p>That Blaise Pascal was born in June, 1623, is perfectly well
+  established and uncontested.<a name="NtA_482"
+  href="#Nt_482"><sup>[482]</sup></a> That he wrote his conic sections at
+  the age of sixteen might be difficult to establish, though tolerably well
+  attested, if it were not for <!-- Page 221 --><span class="pagenum"><a
+  name="page221"></a>[221]</span>one circumstance, for the book was not
+  published. The celebrated theorem, "Pascal's hexagram,"<a name="NtA_483"
+  href="#Nt_483"><sup>[483]</sup></a> makes all the rest come very easy.
+  Now Curabelle,<a name="NtA_484" href="#Nt_484"><sup>[484]</sup></a> in a
+  work published in 1644, sneers at Desargues,<a name="NtA_485"
+  href="#Nt_485"><sup>[485]</sup></a> whom he quotes, for having, in 1642,
+  deferred a discussion until "cette grande proposition nommée le Pascale
+  verra le jour."<a name="NtA_486" href="#Nt_486"><sup>[486]</sup></a> That
+  is, by the time Pascal was nineteen, the <i>hexagram</i> was circulating
+  under a name derived from the author. The common story about Pascal,
+  given by his sister,<a name="NtA_487" href="#Nt_487"><sup>[487]</sup></a>
+  is an absurdity which no doubt has prejudiced many against tales of early
+  proficiency. He is made, when quite a boy, to invent geometry <i>in the
+  order of Euclid's propositions</i>: as if that order were natural
+  sequence of investigation. The hexagram at ten years old would be a
+  hundred times less unlikely.</p>
+
+  <p>The instances named are painfully astonishing: I give one which has
+  fallen out of sight, because it will preserve an imperfect biography.
+  John Wilson<a name="NtA_488" href="#Nt_488"><sup>[488]</sup></a> is
+  Wilson of that <!-- Page 222 --><span class="pagenum"><a
+  name="page222"></a>[222]</span>Ilk, that is, of "Wilson's Theorem." It is
+  this: if <i>p</i> be a prime number, the product of all the numbers up to
+  <i>p</i>-1, increased by 1, is divisible without remainder by <i>p</i>.
+  All mathematicians know this as Wilson's theorem, but few know who Wilson
+  was. He was born August 6, 1741, at the Howe in Applethwaite, and he was
+  heir to a small estate at Troutbeck in Westmoreland. He was sent to
+  Peterhouse, at Cambridge, and while an undergraduate was considered
+  stronger in algebra than any one in the University, except Professor
+  Waring, one of the most powerful algebraists of the century.<a
+  name="NtA_489" href="#Nt_489"><sup>[489]</sup></a> He was the senior
+  wrangler of 1761, and was then for some time a private tutor. When
+  Paley,<a name="NtA_490" href="#Nt_490"><sup>[490]</sup></a> then in his
+  third year, determined to make a push for the senior wranglership, which
+  he got, Wilson was recommended to him as a tutor. Both were ardent in
+  their work, except that sometimes Paley, when he came for his lesson,
+  would find "Gone a fishing" written on his tutor's outer door: which was
+  insult added to injury, for Paley was very fond of fishing. Wilson soon
+  left Cambridge, and went to the bar. He practised on the northern circuit
+  with great success; and, one day, while passing his vacation on his
+  little property at Troutbeck, he received information, to his great
+  surprise, that Lord Thurlow,<a name="NtA_491"
+  href="#Nt_491"><sup>[491]</sup></a> with whom he had <!-- Page 223
+  --><span class="pagenum"><a name="page223"></a>[223]</span>no
+  acquaintance, had recommended him to be a Judge of the Court of Common
+  Pleas. He died, Oct. 18, 1793, with a very high reputation as a lawyer
+  and a Judge. These facts are partly from Meadley's <i>Life of
+  Paley</i>,<a name="NtA_492" href="#Nt_492"><sup>[492]</sup></a> no doubt
+  from Paley himself, partly from the <i>Gentleman's Magazine</i>, and from
+  an epitaph written by Bishop Watson.<a name="NtA_493"
+  href="#Nt_493"><sup>[493]</sup></a> Wilson did not publish anything: the
+  theorem by which he has cut his name in the theory of numbers was
+  communicated to Waring, by whom it was published. He married, in 1788, a
+  daughter of Serjeant Adair,<a name="NtA_494"
+  href="#Nt_494"><sup>[494]</sup></a> and left issue. <i>Had a family</i>,
+  many will say: but a man and his wife are a family, even without
+  children. An actuary may be allowed to be accurate in this matter, of
+  which I was reminded by what an actuary wrote of another actuary. William
+  Morgan,<a name="NtA_495" href="#Nt_495"><sup>[495]</sup></a> in the life
+  of his uncle Dr. Richard Price,<a name="NtA_496"
+  href="#Nt_496"><sup>[496]</sup></a> says that the Doctor and his <!--
+  Page 224 --><span class="pagenum"><a name="page224"></a>[224]</span>wife
+  were "never blessed with an addition to their family." I never met with
+  such accuracy elsewhere. Of William Morgan I add that my surname and
+  pursuits have sometimes, to my credit be it said, made a confusion
+  between him and me. Dates are nothing to the mistaken; the last three
+  years of Morgan's life were the first three years of my actuary-life
+  (1830-33). The mistake was to my advantage as well as to my credit. I owe
+  to it the acquaintance of one of the noblest of the human race, I mean
+  Elizabeth Fry,<a name="NtA_497" href="#Nt_497"><sup>[497]</sup></a> who
+  came to me for advice about a philanthropic design, which involved life
+  questions, under a general impression that some Morgan had attended to
+  such things.<a name="NtA_498" href="#Nt_498"><sup>[498]</sup></a></p>
+
+<p><!-- Page 225 --><span class="pagenum"><a name="page225"></a>[225]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">NEWTON AGAIN OVERTHROWN.</p>
+
+<blockquote class="b1n">
+
+  <p>A treatise on the sublime science of heliography, satisfactorily
+  demonstrating our great orb of light, the sun, to be absolutely no other
+  than a body of ice! Overturning all the received systems of the universe
+  hitherto extant; proving the celebrated and indefatigable Sir Isaac
+  Newton, in his theory of the solar system, to be as far distant from the
+  truth, as many of the heathen authors of Greece and Rome. By Charles
+  Palmer,<a name="NtA_499" href="#Nt_499"><sup>[499]</sup></a> Gent.
+  London, 1798, 8vo.</p>
+
+</blockquote>
+
+  <p>Mr. Palmer burned some tobacco with a burning glass, saw that a lens
+  of ice would do as well, and then says:</p>
+
+  <p>"If we admit that the sun could be removed, and a terrestrial body of
+  ice placed in its stead, it would produce the same effect. The sun is a
+  crystaline body receiving the radiance of God, and operates on this earth
+  in a similar manner as the light of the sun does when applied to a convex
+  mirror or glass."</p>
+
+  <p>Nov. 10, 1801. The Rev. Thomas Cormouls,<a name="NtA_500"
+  href="#Nt_500"><sup>[500]</sup></a> minister of Tettenhall, addressed a
+  letter to Sir Wm. Herschel, from which I extract the following:</p>
+
+  <p>"Here it may be asked, then, how came the doctrines of Newton to solve
+  all astronomic Phenomina, and all problems concerning the same, both <i>a
+  parte ante</i> and <i>a parte post</i>.<a name="NtA_501"
+  href="#Nt_501"><sup>[501]</sup></a> It is answered that he certainly
+  wrought the principles he made use of into strickt analogy with the real
+  Phenomina of the heavens, and that the rules and results arizing from
+  them <!-- Page 226 --><span class="pagenum"><a
+  name="page226"></a>[226]</span>agree with them and resolve accurately all
+  questions concerning them. Though they are not fact and true, or nature,
+  but analogous to it, in the manner of the artificial numbers of
+  logarithms, sines, &amp;c. A very important question arises here, Did
+  Newton mean to impose upon the world? By no means: he received and used
+  the doctrines reddy formed; he did a little extend and contract his
+  principles when wanted, and commit a few oversights of consequences. But
+  when he was very much advanced in life, he suspected the fundamental
+  nullity of them: but I have from a certain anecdote strong ground to
+  believe that he knew it before his decease and intended to have retracted
+  his error. But, however, somebody did deceive, if not wilfully,
+  negligently at least. That was a man to whom the world has great
+  obligations too. It was no less a philosopher than Galileo."</p>
+
+  <p>That Newton wanted to retract before his death, is a notion not
+  uncommon among paradoxers. Nevertheless, there is no retraction in the
+  third edition of the <i>Principia</i>, published when Newton was
+  eighty-four years old! The moral of the above is, that a gentleman who
+  prefers instructing William Herschel to learning how to spell, may find a
+  proper niche in a proper place, for warning to others. It seems that
+  gravitation is not truth, but only the logarithm of it.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">BISHOPS AS PARADOXERS.</p>
+
+<blockquote class="b1n">
+
+  <p>The mathematical and philosophical works of the Right Rev. John
+  Wilkins<a name="NtA_502" href="#Nt_502"><sup>[502]</sup></a>.... In two
+  volumes. London, 1802, 8vo.</p>
+
+</blockquote>
+
+  <p>This work, or at least part of the edition&mdash;all for aught I
+  know&mdash;is printed on wood; that is, on paper made from wood-pulp. It
+  has a rough surface; and when held before a candle is of very unequal
+  transparency. There is in it a reprint of the works on the earth and
+  moon. The discourse on the possibility of going to the moon, in this and
+  the edition of 1640, is incorporated: but from the account in the <!--
+  Page 227 --><span class="pagenum"><a name="page227"></a>[227]</span>life
+  prefixed, and a mention by D'Israeli, I should suppose that it had
+  originally a separate title-page, and some circulation as a separate
+  tract. Wilkins treats this subject half seriously, half jocosely; he has
+  evidently not quite made up his mind. He is clear that "arts are not yet
+  come to their solstice," and that posterity will bring hidden things to
+  light. As to the difficulty of carrying food, he thinks, scoffing Puritan
+  that he is, the Papists may be trained to fast the voyage, or may find
+  the bread of their Eucharist "serve well enough for their
+  <i>viaticum</i>."<a name="NtA_503" href="#Nt_503"><sup>[503]</sup></a> He
+  also puts the case that the story of Domingo Gonsales may be realized,
+  namely, that wild geese find their way to the moon. It will be
+  remembered&mdash;to use the usual substitute for, It has been
+  forgotten&mdash;that the posthumous work of Bishop Francis Godwin<a
+  name="NtA_504" href="#Nt_504"><sup>[504]</sup></a> of Llandaff was
+  published in 1638, the very year of Wilkins's first edition, in time for
+  him to mention it at the end. Godwin makes Domingo Gonsales get to the
+  moon in a chariot drawn by wild geese, and, as old books would say,
+  discourses fully on that head. It is not a little amusing that Wilkins
+  should have been seriously accused of plagiarizing Godwin, Wilkins
+  writing in earnest, or nearly so, and Godwin writing fiction. It may
+  serve to show philosophers how very near pure speculation comes to fable.
+  From the sublime to the ridiculous is but a step: which is the sublime,
+  and which the ridiculous, every one must settle for himself. With me,
+  good fiction is the sublime, and bad speculation the ridiculous. The
+  number of bishops in my list is small. I might, had I possessed the book,
+  have opened the list of quadrators with an Archbishop of Canterbury, or
+  at least with a divine who was not wholly not archbishop. Thomas
+  Bradwardine<a name="NtA_505" href="#Nt_505"><sup>[505]</sup></a>
+  (Bragvardinus, Bragadinus) was elected in <!-- Page 228 --><span
+  class="pagenum"><a name="page228"></a>[228]</span>1348; the Pope put in
+  another, who died unconsecrated; and Bradwardine was again elected in
+  1349, and lived five weeks longer, dying, I suppose, unconfirmed and
+  unconsecrated.<a name="NtA_506" href="#Nt_506"><sup>[506]</sup></a>
+  Leland says he held the see a year, <i>unus tantum annulus</i>,<a
+  name="NtA_507" href="#Nt_507"><sup>[507]</sup></a> which seems to be a
+  confusion: the whole business, from the first election, took about a
+  year. He squared the circle, and his performance was printed at Paris in
+  1494. I have never seen it, nor any work of the author, except a tract on
+  proportion.</p>
+
+  <p>As Bradwardine's works are very scarce indeed, I give two titles from
+  one of the Libri catalogues.</p>
+
+<blockquote class="b1n">
+
+  <p>"<span class="sc">Arithmetic. Brauardini</span> (Thomæ) Arithmetica
+  speculativa revisa et correcta a Petro Sanchez Ciruelo Aragonesi, black
+  letter, <i>elegant woodcut title-page</i>, <span class="scac">VERY
+  RARE</span>, <i>folio. Parisiis, per Thomam Anguelast (pro Olivier
+  Senant), s. a. circa 1510</i>.<a name="NtA_508"
+  href="#Nt_508"><sup>[508]</sup></a></p>
+
+</blockquote>
+
+  <p>"This book, by Thomas Bradwardine, Archbishop of Canterbury must be
+  exceedingly scarce as it has escaped the notice of Professor De Morgan,
+  who, in his <i>Arithmetical Books</i>, speaks of a treatise of the same
+  author on proportions,<a name="NtA_509"
+  href="#Nt_509"><sup>[509]</sup></a> printed at Vienna in 1515, but does
+  not mention the present work.</p>
+
+<p><!-- Page 229 --><span class="pagenum"><a name="page229"></a>[229]</span></p>
+
+<blockquote class="b1n">
+
+  <p>"Bradwardine (Archbp. T.). Brauardini (Thomæ) Geometria speculativa,
+  com Tractato de Quadratura Circuli bene revisa a Petro Sanchez Ciruelo,
+  <span class="scac">SCARCE</span>, <i>folio. Parisiis, J. Petit</i>,
+  1511.<a name="NtA_510" href="#Nt_510"><sup>[510]</sup></a></p>
+
+</blockquote>
+
+  <p>"In this work we find the <i>polygones étoilés</i>,<a name="NtA_511"
+  href="#Nt_511"><sup>[511]</sup></a> see Chasles (<i>Aperçu</i>, pp. 480,
+  487, 521, 523, &amp;c.) on the merit of the discoveries of this English
+  mathematician, who was Archbishop of Canterbury in the <span
+  class="scac">XIV</span>th Century (<i>tempore</i> Edward III. <span
+  class="scac">A.D.</span> 1349); and who applied geometry to theology. M.
+  Chasles says that the present work of Bradwardine contains 'Une théorie
+  nouvelle qui doit faire honneur au <span class="scac">XIV</span>e
+  Siècle.'"<a name="NtA_512" href="#Nt_512"><sup>[512]</sup></a></p>
+
+  <p>The titles do not make it quite sure that Bradwardine is the
+  quadrator; it may be Peter Sanchez after all.<a name="NtA_513"
+  href="#Nt_513"><sup>[513]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE QUESTION OF PARALLELS.</p>
+
+<blockquote class="b1n">
+
+  <p>Nouvelle théorie des parallèles. Par Adolphe Kircher<a name="NtA_514"
+  href="#Nt_514"><sup>[514]</sup></a> [so signed at the end of the
+  appendix]. Paris, 1803, 8vo.</p>
+
+</blockquote>
+
+  <p>An alleged emendation of Legendre.<a name="NtA_515"
+  href="#Nt_515"><sup>[515]</sup></a> The author refers <!-- Page 230
+  --><span class="pagenum"><a name="page230"></a>[230]</span>to attempts by
+  Hoffman,<a name="NtA_516" href="#Nt_516"><sup>[516]</sup></a> 1801, by
+  Hauff,<a name="NtA_517" href="#Nt_517"><sup>[517]</sup></a> 1799, and to
+  a work of Karsten,<a name="NtA_518" href="#Nt_518"><sup>[518]</sup></a>
+  or at least a theory of Karsten, contained in "Tentamen novæ parallelarum
+  theoriæ notione situs fundatæ; auctore G. C. Schwal,<a name="NtA_519"
+  href="#Nt_519"><sup>[519]</sup></a> Stuttgardæ, 1801, en 8 volumes."
+  Surely this is a misprint; <i>eight</i> volumes on the theory of
+  parallels? If there be such a work, I trust I and it may never meet,
+  though ever so far produced.</p>
+
+<p><!-- Page 231 --><span class="pagenum"><a name="page231"></a>[231]</span></p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Soluzione ... della quadratura del Circolo. By Gaetano Rossi.<a
+  name="NtA_520" href="#Nt_520"><sup>[520]</sup></a> London, 1804, 8vo.</p>
+
+</blockquote>
+
+  <p>The three remarkable points of this book are, that the household of
+  the Prince of Wales took ten copies, Signora Grassini<a name="NtA_521"
+  href="#Nt_521"><sup>[521]</sup></a> sixteen, and that the circumference
+  is 3-1/5 diameters. That is, the appetite of Grassini for quadrature
+  exceeded that of the whole household (<i>loggia</i>) of the Prince of
+  Wales in the ratio in which the semi-circumference exceeds the diameter.
+  And these are the first two in the list of subscribers. Did the author
+  see this theorem?</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A PATRIOTIC PARADOX.</p>
+
+<blockquote class="b1n">
+
+  <p>Britain independent of commerce; or proofs, deduced from an
+  investigation into the true cause of the wealth of nations, that our
+  riches, prosperity, and power are derived from sources inherent in
+  ourselves, and would not be affected, even though our commerce were
+  annihilated. By Wm. Spence.<a name="NtA_522"
+  href="#Nt_522"><sup>[522]</sup></a> 4th edition, 1808, 8vo.</p>
+
+</blockquote>
+
+  <p>A patriotic paradox, being in alleviation of the Commerce panic which
+  the measures of Napoleon I.&mdash;who <i>felt</i> our Commerce, while Mr.
+  Spence only <i>saw</i> it&mdash;had awakened. In this very month (August,
+  1866), the Pres. Brit. Assoc. has applied a similar salve to the coal
+  panic; it is fit that science, which rubbed the sore, should find a
+  plaster. We ought to have an iron panic and a timber panic; and <!-- Page
+  232 --><span class="pagenum"><a name="page232"></a>[232]</span>a solemn
+  embassy to the Americans, to beg them not to whittle, would be desirable.
+  There was a gold panic beginning, before the new fields were discovered.
+  For myself, I am the unknown and unpitied victim of a chronic
+  gutta-percha panic: I never could get on without it; to me, gutta percha
+  and Rowland Hill are the great discoveries of our day; and not
+  unconnected either, gutta percha being to the submarine post what Rowland
+  Hill is to the superterrene. I should be sorry to lose cow-choke&mdash;I
+  gave up trying to spell it many years ago&mdash;but if gutta percha go, I
+  go too. I think, that perhaps when, five hundred years hence, the people
+  say to the Brit. Assoc. (if it then exist) "Pray gentlemen, is it not
+  time for the coal to be exhausted?" they will be answered out of Molière
+  (who will certainly then exist): "<i>Cela était autrefois ainsi, mais
+  nous avons changé tout cela.</i>"<a name="NtA_523"
+  href="#Nt_523"><sup>[523]</sup></a> A great many people think that if the
+  coal be used up, it will be announced some unexpected morning by all the
+  yards being shut up and written notice outside, "Coal all gone!" just
+  like the "Please, ma'am, there ain't no more sugar," with which the maid
+  servant damps her mistress just at breakfast-time. But these persons
+  should be informed that there is every reason to think that there will be
+  time, as the city gentleman said, to <i>venienti</i> the <i>occurrite
+  morbo</i>.<a name="NtA_524" href="#Nt_524"><sup>[524]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">SOME SCIENTIFIC PARADOXES.</p>
+
+<blockquote class="b1n">
+
+  <p>An appeal to the republic of letters in behalf of injured science,
+  from the opinions and proceedings of some modern authors of elements of
+  geometry. By George Douglas.<a name="NtA_525"
+  href="#Nt_525"><sup>[525]</sup></a> Edinburgh, 1810, 8vo.</p>
+
+</blockquote>
+
+  <p>Mr. Douglas was the author of a very good set of <!-- Page 233
+  --><span class="pagenum"><a name="page233"></a>[233]</span>mathematical
+  tables, and of other works. He criticizes Simson,<a name="NtA_526"
+  href="#Nt_526"><sup>[526]</sup></a> Playfair,<a name="NtA_527"
+  href="#Nt_527"><sup>[527]</sup></a> and others,&mdash;sometimes, I think,
+  very justly. There is a curious phrase which occurs more than once. When
+  he wants to say that something or other was done before Simson or another
+  was born, he says "before he existed, at least as an author." He seems to
+  reserve the possibility of Simson's <i>pre-existence</i>, but at the same
+  time to assume that he never wrote anything in his previous state. Tell
+  me that Simson pre-existed in any other way than as editor of some
+  pre-existent Euclid? Tell Apella!<a name="NtA_528"
+  href="#Nt_528"><sup>[528]</sup></a></p>
+
+  <p>1810. In this year Jean Wood, Professor of Mathematics in the
+  University of Virginia (Richmond),<a name="NtA_529"
+  href="#Nt_529"><sup>[529]</sup></a> addressed a printed circular to "Dr.
+  Herschel, Astronomer, Greenwich Observatory." No mistake was more common
+  than the natural one of imagining that the <i>Private Astronomer</i> of
+  the king was the <i>Astronomer Royal</i>. The letter was on the <!-- Page
+  234 --><span class="pagenum"><a name="page234"></a>[234]</span>difference
+  of velocities of the two sides of the earth, arising from the composition
+  of the rotation and the orbital motion. The <i>paradox</i> is a fair one,
+  and deserving of investigation; but, perhaps it would not be easy to
+  deduce from it tides, trade-winds, aerolithes, &amp;c., as Mr. Wood
+  thought he had done in a work from which he gives an extract, and which
+  he describes as published. The composition of rotations, &amp;c., is not
+  for the world at large: the paradox of the non-rotation of the moon about
+  her axis is an instance. How many persons know that when a wheel rolls on
+  the ground, the lowest point is moving upwards, the highest point
+  forwards, and the intermediate points in all degrees of betwixt and
+  between? This is too short an explanation, with some good
+  difficulties.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>The Elements of Geometry. In 2 vols. [By the Rev. J. Dobson,<a
+  name="NtA_530" href="#Nt_530"><sup>[530]</sup></a> B.D.] Cambridge, 1815.
+  4to.</p>
+
+</blockquote>
+
+  <p>Of this unpunctuating paradoxer I shall give an account in his own
+  way: he would not stop for any one; why should I stop for him? It is
+  worth while to try how unpunctuated sentences will read.</p>
+
+  <p>The reverend J Dobson BD late fellow of saint Johns college Cambridge
+  was rector of Brandesburton in Yorkshire he was seventh wrangler in 1798
+  and died in 1847 he was of that sort of eccentricity which permits
+  account of his private life if we may not rather say that in such cases
+  private life becomes public there is a tradition that he was called Death
+  Dobson on account of his head and aspect of countenance being not very
+  unlike the ordinary pictures of a human skull his mode of life is
+  reported to have been very singular whenever he visited Cambridge he was
+  never known to go twice to the same inn he never would sleep at the
+  rectory with another person in the house some ancient charwoman used to
+  attend to the house but never slept in it he has been known in the time
+  of coach travelling to have <!-- Page 235 --><span class="pagenum"><a
+  name="page235"></a>[235]</span>deferred his return to Yorkshire on
+  account of his disinclination to travel with a lady in the coach he
+  continued his mathematical studies until his death and till his executors
+  sold the type all his tracts to the number of five were kept in type at
+  the university press none of these tracts had any stops except full stops
+  at the end of paragraphs only neither had they capitals except one at the
+  beginning of a paragraph so that a full stop was generally followed by
+  some white as there is not a single proper name in the whole of the book
+  I have I am not able to say whether he would have used capitals before
+  proper names I have inserted them as usual for which I hope his spirit
+  will forgive me if I be wrong he also published the elements of geometry
+  in two volumes quarto Cambridge 1815 this book had also no stops except
+  when a comma was wanted between letters as in the straight lines AB, BC I
+  should also say that though the title is unpunctuated in the author's
+  part it seems the publishers would not stand it in their imprint this
+  imprint is punctuated as usual and Deighton and Sons to prove the
+  completeness of their allegiance have managed that comma semicolon and
+  period shall all appear in it why could they not have contrived
+  interrogation and exclamation this is a good precedent to establish the
+  separate right of the publisher over the imprint it is said that only
+  twenty of the tracts were printed and very few indeed of the book on
+  geometry it is doubtful whether any were sold there is a copy of the
+  geometry in the university library at Cambridge and I have one myself the
+  matter of the geometry differs entirely from Euclid and is so fearfully
+  prolix that I am sure no mortal except the author ever read it the man
+  went on without stops and without stop save for a period at the end of a
+  paragraph this is the unpunctuated account of the unpunctuating geometer
+  <i>suum cuique tribuito</i><a name="NtA_531"
+  href="#Nt_531"><sup>[531]</sup></a> Mrs Thrale<a name="NtA_532"
+  href="#Nt_532"><sup>[532]</sup></a> would have been amused <!-- Page 236
+  --><span class="pagenum"><a name="page236"></a>[236]</span>at a Dobson
+  who managed to come to a full stop without either of the three
+  warnings.</p>
+
+  <p>I do not find any difficulty in reading Dobson's geometry; and I have
+  read more of it to try reading without stops than I should have done had
+  it been printed in the usual way. Those who dip into the middle of my
+  paragraph may be surprised for a moment to see "on account of his
+  disinclination to travel with a lady in the coach he continued his
+  mathematical studies until his death and [further, of course] until his
+  executors sold the type." But a person reading straight through would
+  hardly take it so. I should add that, in order to give a fair trial, I
+  did not compose as I wrote, but copied the words of the correspondent who
+  gave me the facts, so far as they went.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A RELIGIOUS PARADOX.</p>
+
+<blockquote class="b1n">
+
+  <p><i>Philosophia Sacra, or the principles of natural Philosophy.
+  Extracted from Divine Revelation.</i> By the Rev. Samuel Pike.<a
+  name="NtA_533" href="#Nt_533"><sup>[533]</sup></a> Edited by the Rev.
+  Samuel Kittle.<a name="NtA_534" href="#Nt_534"><sup>[534]</sup></a>
+  Edinburgh, 1815, 8vo.</p>
+
+</blockquote>
+
+  <p>This is a work of modified Hutchinsonianism, which I have seen cited
+  by several. Though rather dark on the subject, it seems not to contradict
+  the motion of the earth, or the doctrine of gravitation. Mr. Kittle gives
+  a list of some Hutchinsonians,&mdash;as Bishop Horne;<a name="NtA_535"
+  href="#Nt_535"><sup>[535]</sup></a> Dr. Stukeley;<a name="NtA_536"
+  href="#Nt_536"><sup>[536]</sup></a> the Rev. <!-- Page 237 --><span
+  class="pagenum"><a name="page237"></a>[237]</span>W. Jones,<a
+  name="NtA_537" href="#Nt_537"><sup>[537]</sup></a> author of
+  <i>Physiological Disquisitions</i>; Mr. Spearman,<a name="NtA_538"
+  href="#Nt_538"><sup>[538]</sup></a> author of <i>Letters on the
+  Septuagint</i> and editor of Hutchinson; Mr. Barker,<a name="NtA_539"
+  href="#Nt_539"><sup>[539]</sup></a> author of <i>Reflexions on
+  Learning</i>; Dr. Catcott,<a name="NtA_540"
+  href="#Nt_540"><sup>[540]</sup></a> author of a work on the creation,
+  &amp;c.; Dr. Robertson,<a name="NtA_541"
+  href="#Nt_541"><sup>[541]</sup></a> author of a <i>Treatise on the Hebrew
+  Language</i>; <i>Dr. Holloway</i>,<a name="NtA_542"
+  href="#Nt_542"><sup>[542]</sup></a> author of <i>Originals, Physical and
+  Theological</i>; Dr. Walter Hodges,<a name="NtA_543"
+  href="#Nt_543"><sup>[543]</sup></a> author of a work on <i>Elohim</i>;
+  Lord President Forbes (<i>ob.</i> 1747).<a name="NtA_544"
+  href="#Nt_544"><sup>[544]</sup></a></p>
+
+  <p>The Rev. William Jones, above mentioned (1726-1800), the friend and
+  biographer of Bishop Horne and his stout <!-- Page 238 --><span
+  class="pagenum"><a name="page238"></a>[238]</span>defender, is best known
+  as William Jones of Nayland, who (1757)<a name="NtA_545"
+  href="#Nt_545"><sup>[545]</sup></a> published the <i>Catholic Doctrine of
+  the Trinity</i>; he was also strong for the Hutchinsonian physical
+  trinity of fire, light, and spirit. This well-known work was generally
+  recommended, as the defence of the orthodox system, to those who could
+  not go into the learning of the subject. There is now a work more suited
+  to our time: <i>The Rock of Ages</i>, by the Rev. E.&nbsp;H. Bickersteth,<a
+  name="NtA_546" href="#Nt_546"><sup>[546]</sup></a> now published by the
+  Religious Tract Society, without date, answered by the Rev. Dr. Sadler,<a
+  name="NtA_547" href="#Nt_547"><sup>[547]</sup></a> in a work (1859)
+  entitled <i>Gloria Patri</i>, in which, says Mr. Bickersteth, "the author
+  has not even attempted to grapple with my main propositions." I have read
+  largely on the controversy, and I think I know what this means. Moreover,
+  when I see the note "There are two other passages to which Unitarians
+  sometimes refer, but the deduction they draw from them is, in each case,
+  refuted by the context"&mdash;I think I see why the two texts are not
+  named. Nevertheless, the author is a little more disposed to yield to
+  criticism than his foregoers; he does not insist on texts and readings
+  which the greatest editors have rejected. And he writes with courtesy,
+  both direct and oblique, towards his antagonists; which, on his side of
+  this subject, is like letting in fresh air. So that I suspect the two
+  books will together make a tolerably good introduction to the subject for
+  those who cannot go deep. Mr. Bickersteth's book is well arranged and
+  indexed, which is a point of superiority to Jones of Nayland. There is a
+  point which I should gravely recommend to writers on the orthodox side.
+  The Unitarians in <!-- Page 239 --><span class="pagenum"><a
+  name="page239"></a>[239]</span>England have frequently contended that the
+  method of proving the divinity of Jesus Christ from the New Testament
+  would equally prove the divinity of Moses. I have not fallen in the way
+  of any orthodox answers specially directed at the repeated tracts written
+  by Unitarians in proof of their assertion. If there be any, they should
+  be more known; if there be none, some should be written. Which ever side
+  may be right, the treatment of this point would be indeed coming to close
+  quarters. The heterodox assertion was first supported, it is said, by
+  John Bidle or Biddle (1615-1662) of Magdalen College, Oxford, the
+  earliest of the English Unitarian writers, previously known by a
+  translation of part of Virgil and part of Juvenal.<a name="NtA_548"
+  href="#Nt_548"><sup>[548]</sup></a> But I cannot find that he wrote on
+  it.<a name="NtA_549" href="#Nt_549"><sup>[549]</sup></a> It is the
+  subject of "<span title="haireseôn anastasis" class="grk"
+  >&alpha;&#x1F31;&rho;&epsilon;&sigma;&epsilon;&omega;&nu;
+  &#x1F00;&nu;&alpha;&sigma;&tau;&alpha;&sigma;&iota;&sigmaf;</span>, or a
+  new way of deciding old controversies. By Basanistes. Third edition,
+  enlarged," London, 1815, 8vo.<a name="NtA_550"
+  href="#Nt_550"><sup>[550]</sup></a> It is the appendix to the amusing,
+  "Six more letters to Granville Sharp, Esq., ... By Gregory Blunt, Esq."
+  London, 8vo., 1803.<a name="NtA_551" href="#Nt_551"><sup>[551]</sup></a>
+  This much I can confidently say, that the study of these tracts would
+  prevent orthodox writers from some curious slips, which are slips obvious
+  to all sides of opinion. The lower defenders of orthodoxy frequently vex
+  the spirits of the higher ones.</p>
+
+  <p>Since writing the above I have procured Dr. Sadler's answer. I thought
+  I knew what the challenger meant when he said the respondent had not
+  grappled with his main <!-- Page 240 --><span class="pagenum"><a
+  name="page240"></a>[240]</span>propositions. I should say that he is
+  clung on to from beginning to end. But perhaps Mr. B. has his own meaning
+  of logical terms, such as "proposition": he certainly has his own meaning
+  of "cumulative." He says his evidence is cumulative; not a catena, the
+  strength of which is in its weakest part, but distinct and independent
+  lines, each of which corroborates the other. This is the very opposite of
+  <i>cumulative</i>: it is <i>distributive</i>. When different arguments
+  are each necessary to a conclusion, the evidence is <i>cumulative</i>;
+  when any one will do, even though they strengthen each other, it is
+  <i>distributive</i>. The word "cumulative" is a synonym of the law word
+  "constructive"; a whole which will do made out of parts which separately
+  will not. Lord Strafford <a name="NtA_552"
+  href="#Nt_552"><sup>[552]</sup></a> opens his defence with the use of
+  both words: "They have invented a kind of <i>accumulated</i> or
+  <i>constructive</i> evidence; by which many actions, either totally
+  innocent in themselves, or criminal in a much inferior degree, shall,
+  when united, <i>amount</i> to treason." The conclusion is, that Mr. B. is
+  a Cambridge man; the Oxford men do not confuse the elementary terms of
+  logic. O dear old Cambridge! when the New Zealander comes let him find
+  among the relics of your later sons some proof of attention to the
+  elementary laws of thought. A little-go of logic, please!</p>
+
+  <p>Mr. B., though apparently not a Hutchinsonian, has a nibble at a
+  physical Trinity. "If, as we gaze on the sun shining in the firmament, we
+  see any faint adumbration of the doctrine of the Trinity in the fontal
+  orb, the light ever generated, and the heat proceeding from the sun and
+  its beams&mdash;threefold and yet one, the sun, its light, and its <!--
+  Page 241 --><span class="pagenum"><a
+  name="page241"></a>[241]</span>heat,&mdash;that luminous globe, and the
+  radiance ever flowing from it, are both evident to the eye; but the vital
+  warmth is felt, not seen, and is only manifested in the life it
+  transfuses through creation. The proof of its real existence is
+  self-demonstrating."</p>
+
+  <p>We shall see how Revilo<a name="NtA_553"
+  href="#Nt_553"><sup>[553]</sup></a> illustrates orthodoxy by mathematics.
+  It was my duty to have found one of the many illustrations from physics;
+  but perhaps I should have forgotten it if this instance had not come in
+  my way. It is very bad physics. The sun, apart from its light, evident to
+  the eye! Heat more self-demonstrating than light, because <i>felt</i>!
+  Heat only manifested by the life it diffuses! Light implied not necessary
+  to life! But the theology is worse than Sabellianism<a name="NtA_554"
+  href="#Nt_554"><sup>[554]</sup></a>. To adumbrate&mdash;i.e., make a
+  picture of&mdash;the orthodox doctrine, the sun must be heavenly body,
+  the light heavenly body, the heat heavenly body; and yet, not three
+  heavenly bodies, but one heavenly body. The truth is, that this
+  illustration and many others most strikingly illustrate the Trinity of
+  fundamental doctrine held by the Unitarians, in all its differences from
+  the Trinity of persons held by the Orthodox. Be right which may, the
+  right or wrong of the Unitarians shines out in the comparison. Dr. Sadler
+  confirms me&mdash;by which I mean that I wrote the above before I saw
+  what he says&mdash;in the following words: "The sun is one object with
+  two <i>properties</i>, and these properties have a parallel not in the
+  second and third persons of the Trinity, but in the attributes of
+  Deity."</p>
+
+  <p>The letting light alone, as self-evident, and making heat
+  self-demonstrating, because felt&mdash;i.e., perceptible now and
+  then&mdash;has the character of the Irishman's astronomy:</p>
+
+<p><!-- Page 242 --><span class="pagenum"><a name="page242"></a>[242]</span></p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Long life to the moon, for a dear noble cratur,</p>
+      <p>Which serves us for lamplight all night in the dark,</p>
+      <p>While the sun only shines in the day, which by natur,</p>
+      <p>Wants no light at all, as ye all may remark."</p>
+    </div>
+  </div>
+  <p>&nbsp;</p>
+
+<p class="cenhead">SIR RICHARD PHILLIPS.</p>
+
+  <p><i>Sir Richard Phillips</i><a name="NtA_555"
+  href="#Nt_555"><sup>[555]</sup></a> (born 1768) was conspicuous in 1793,
+  when he was sentenced to a year's imprisonment<a name="NtA_556"
+  href="#Nt_556"><sup>[556]</sup></a> for selling Paine's <i>Rights of
+  Man</i>; and again when, in 1807<a name="NtA_557"
+  href="#Nt_557"><sup>[557]</sup></a>, he was knighted as Sheriff of
+  London. As a bookseller, he was able to enforce his opinions in more ways
+  than others. For instance, in James Mitchell's<a name="NtA_558"
+  href="#Nt_558"><sup>[558]</sup></a> <i>Dictionary of the Mathematical and
+  Physical Sciences</i>, 1823, 12mo, which, though he was not technically a
+  publisher, was printed for him&mdash;a book I should recommend to the
+  collector of works of reference&mdash;there is a temperate description of
+  his doctrines, which one may almost swear was one of his conditions
+  previous to undertaking the work. Phillips himself was not only an
+  anti-Newtonian, but carried to a fearful excess the notion that statesmen
+  and Newtonians were in league to deceive the world. He saw this plot in
+  Mrs. Airy's<a name="NtA_559" href="#Nt_559"><sup>[559]</sup></a> pension,
+  and in Mrs. Somerville's<a name="NtA_560"
+  href="#Nt_560"><sup>[560]</sup></a>. In 1836, he <!-- Page 243 --><span
+  class="pagenum"><a name="page243"></a>[243]</span>did me the honor to
+  attempt my conversion. In his first letter he says:</p>
+
+  <p>"Sir Richard Phillips has an inveterate abhorrence of all the
+  pretended wisdom of philosophy derived from the monks and doctors of the
+  middle ages, and not less of those of higher name who merely sought to
+  make the monkish philosophy more plausible, or so to disguise it as to
+  mystify the mob of small thinkers."</p>
+
+  <p>So little did his writings show any knowledge of antiquity, that I
+  strongly suspect, if required to name one of the monkish doctors, he
+  would have answered&mdash;Aristotle. These schoolmen, and the
+  "philosophical trinity of gravitating force, projectile force, and void
+  space," were the bogies of his life.</p>
+
+  <p>I think he began to publish speculations in the <i>Monthly
+  Magazine</i> (of which he was editor) in July 1817: these he republished
+  separately in 1818. In the Preface, perhaps judging the feelings of
+  others by his own, he says that he "fully expects to be vilified,
+  reviled, and anathematized, for many years to come." Poor man! he was let
+  alone. He appeals with confidence to the "impartial decision of
+  posterity"; but posterity does not appoint a hearing for one per cent. of
+  the appeals which are made; and it is much to be feared that an article
+  in such a work of reference as this will furnish nearly all her materials
+  fifty years hence. The following, addressed to M. Arago,<a name="NtA_561"
+  href="#Nt_561"><sup>[561]</sup></a> in 1835, will give posterity as good
+  a notion as she will probably need:</p>
+
+  <p>"Even the present year has afforded <span
+  class="scac">EVER-MEMORABLE</span> examples, paralleled only by that of
+  the Romish Conclave which persecuted Galileo. Policy has adopted that
+  maxim of Machiavel which teaches that it is <i>more prudent</i> to
+  <i>reward</i> <!-- Page 244 --><span class="pagenum"><a
+  name="page244"></a>[244]</span>partisans than to <i>persecute</i>
+  opponents. Hence, a bigotted party had influence enough with the late
+  short-lived administration [I think he is wrong as to the administration]
+  of Wellington, Peel, &amp;c., to confer munificent royal pensions on
+  three writers whose sole distinction was their advocacy of the Newtonian
+  philosophy. A Cambridge professor last year published an elaborate volume
+  in illustration of <i>Gravitation</i>, and on him has been conferred a
+  pension of 300<i>l.</i> per annum. A lady has written a light popular
+  view of the Newtonian Dogmas, and she has been complimented by a pension
+  of 200<i>l.</i> per annum. And another writer, who has recently published
+  a volume to prove that the only true philosophy is that of Moses, has
+  been endowed with a pension of 200<i>l.</i> per annum. Neither of them
+  were needy persons, and the political and ecclesiastical bearing of the
+  whole was indicated by another pension of 300<i>l.</i> bestowed on a
+  political writer, the advocate of all abuses and prejudices. Whether the
+  conduct of the Romish Conclave was more base for visiting with legal
+  penalties the promulgation of the doctrines that the Earth turns on its
+  axis and revolves around the Sun; or that of the British Court, for its
+  craft in conferring pensions on the opponents of the plain corollary,
+  that all the motions of the Earth are 'part and parcel' of these great
+  motions, and those again and all like them consecutive displays of still
+  greater motions in equality of action and reaction, is <span
+  class="scac">A QUESTION</span> which must be reserved for the casuists of
+  other generations.... I cannot expect that on a sudden you and your
+  friends will come to my conclusion, that the present philosophy of the
+  Schools and Universities of Europe, based on faith in witchcraft, magic,
+  &amp;c., is a system of execrable nonsense, <i>by which quacks live on
+  the faith of fools</i>; but I desire a free and fair examination of my
+  Aphorisms, and if a few are admitted to be true, merely as courteous
+  concessions to arithmetic, my purpose will be effected, for men will thus
+  be led to think; and if they think, then the fabric <!-- Page 245
+  --><span class="pagenum"><a name="page245"></a>[245]</span>of false
+  assumptions, and degrading superstitions will soon tumble in ruins."</p>
+
+  <p>This for posterity. For the present time I ground the fame of Sir R.
+  Phillips on his having squared the circle without knowing it, or
+  intending to do it. In the <i>Protest</i> presently noted he discovered
+  that "the force taken as 1 is equal to the sum of all its fractions ...
+  thus 1 = 1/4 + 1/9 + 1/16 + 1/25, &amp;c., carried to infinity." This the
+  mathematician instantly sees is equivalent to the theorem that the
+  circumference of any circle is double of the diagonal of the cube on its
+  diameter.<a name="NtA_562" href="#Nt_562"><sup>[562]</sup></a></p>
+
+  <p>I have examined the following works of Sir R. Phillips, and heard of
+  many others:</p>
+
+<blockquote class="b1n">
+
+  <p>Essays on the proximate mechanical causes of the general phenomena of
+  the Universe, 1818, 12mo.<a name="NtA_563"
+  href="#Nt_563"><sup>[563]</sup></a></p>
+
+  <p>Protest against the prevailing principles of natural philosophy, with
+  the development of a common sense system (no date, 8vo, pp. 16).<a
+  name="NtA_564" href="#Nt_564"><sup>[564]</sup></a></p>
+
+  <p>Four dialogues between an Oxford Tutor and a disciple of the
+  common-sense philosophy, relative to the proximate causes of material
+  phenomena. 8vo, 1824.</p>
+
+  <p>A century of original aphorisms on the proximate causes of the
+  phenomena of nature, 1835, 12mo.</p>
+
+</blockquote>
+
+  <p>Sir Richard Phillips had four valuable qualities; honesty, zeal,
+  ability, and courage. He applied them all to teaching <!-- Page 246
+  --><span class="pagenum"><a name="page246"></a>[246]</span>matters about
+  which he knew nothing; and gained himself an uncomfortable life and a
+  ridiculous memory.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Astronomy made plain; or only way the true perpendicular distance of
+  the Sun, Moon, or Stars, from this earth, can be obtained. By Wm. Wood.<a
+  name="NtA_565" href="#Nt_565"><sup>[565]</sup></a> Chatham, 1819,
+  12mo.</p>
+
+</blockquote>
+
+  <p>If this theory be true, it will follow, of course, that this earth is
+  the only one God made, and that it does not whirl round the sun, but
+  <i>vice versa</i>, the sun round it.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">WHATELY'S FAMOUS PARADOX.</p>
+
+<blockquote class="b1n">
+
+  <p>Historic doubts relative to Napoleon Buonaparte. London, 1819,
+  8vo.</p>
+
+</blockquote>
+
+  <p>This tract has since been acknowledged by Archbishop Whately<a
+  name="NtA_566" href="#Nt_566"><sup>[566]</sup></a> and reprinted. It is
+  certainly a paradox: but differs from most of those in my list as being a
+  joke, and a satire upon the reasoning of those who cannot receive
+  narrative, no matter what the evidence, which is to them utterly
+  improbable <i>a priori</i>. But had it been serious earnest, it would not
+  have been so absurd as many of those which I have brought forward. The
+  next on the list is not a joke.</p>
+
+  <p>The idea of the satire is not new. Dr. King,<a name="NtA_567"
+  href="#Nt_567"><sup>[567]</sup></a> in the dispute on the genuineness of
+  Phalaris, proved with humor that Bentley did not write his own
+  dissertation. An attempt has lately been made, for the honor of Moses, to
+  prove, <!-- Page 247 --><span class="pagenum"><a
+  name="page247"></a>[247]</span>without humor, that Bishop Colenso did not
+  write his own book. This is intolerable: anybody who tries to use such a
+  weapon without banter, plenty and good, and of form suited to the
+  subject, should get the drubbing which the poor man got in the Oriental
+  tale for striking the dervishes with the wrong hand.</p>
+
+  <p>The excellent and distinguished author of this tract has ceased to
+  live. I call him the Paley of our day: with more learning and more
+  purpose than his predecessor; but perhaps they might have changed places
+  if they had changed centuries. The clever satire above named is not the
+  only work which he published without his name. The following was
+  attributed to him, I believe rightly: "Considerations on the Law of
+  Libel, as relating to Publications on the subject of Religion, by John
+  Search." London, 1833, 8vo. This tract excited little attention: for
+  those who should have answered, could not. Moreover, it wanted a
+  prosecution to call attention to it: the fear of calling such attention
+  may have prevented prosecutions. Those who have read it will have seen
+  why.</p>
+
+  <p>The theological review elsewhere mentioned attributes the pamphlet of
+  John Search on blasphemous libel to Lord Brougham. This is quite absurd:
+  the writer states points of law on credence where the judge must have
+  spoken with authority. Besides which, a hundred points of style are
+  decisive between the two. I think any one who knows Whately's writing
+  will soon arrive at my conclusion. Lord Brougham himself informs me that
+  he has no knowledge whatever of the pamphlet.</p>
+
+  <p>It is stated in <i>Notes and Queries</i> (3 S. xi. 511) that Search
+  was answered by the Bishop of Ferns<a name="NtA_568"
+  href="#Nt_568"><sup>[568]</sup></a> as S.&nbsp;N., with <!-- Page 248 --><span
+  class="pagenum"><a name="page248"></a>[248]</span>a rejoinder by Blanco
+  White.<a name="NtA_569" href="#Nt_569"><sup>[569]</sup></a> These
+  circumstances increase the probability that Whately was written against
+  and for.</p>
+
+<blockquote class="b1n">
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">VOLTAIRE A CHRISTIAN.</p>
+
+  <p>Voltaire Chrétien; preuves tirées de ses ouvrages. Paris, 1820,
+  12mo.</p>
+
+</blockquote>
+
+  <p>If Voltaire have not succeeded in proving himself a strong theist and
+  a strong anti-revelationist, who is to succeed in proving himself one
+  thing or the other in any matter whatsoever? By occasional confusion
+  between theism and Christianity; by taking advantage of the formal
+  phrases of adhesion to the Roman Church, which very often occur, and are
+  often the happiest bits of irony in an ironical production; by citations
+  of his morality, which is decidedly Christian, though often attributed to
+  Brahmins; and so on&mdash;the author makes a fair case for his paradox,
+  in the eyes of those who know no more than he tells them. If he had said
+  that Voltaire was a better Christian than himself knew of, towards all
+  mankind except men of letters, I for one should have agreed with him.</p>
+
+  <p><i>Christian!</i> the word has degenerated into a synonym of
+  <i>man</i>, in what are called Christian countries. So we have the parrot
+  who "swore for all the world like a Christian," and the two dogs who
+  "hated each other just like Christians." When the Irish duellist of the
+  last century, whose name may be spared in consideration of its historic
+  fame <!-- Page 249 --><span class="pagenum"><a
+  name="page249"></a>[249]</span>and the worthy people who bear it, was
+  (June 12, 1786) about to take the consequence of his last brutal murder,
+  the rope broke, and the criminal got up, and exclaimed, "By
+  &mdash;&mdash; Mr. Sheriff, you ought to be ashamed of yourself! this
+  rope is not strong enough to hang a dog, far less a Christian!" But such
+  things as this are far from the worst depravations. As to a word so
+  defiled by usage, it is well to know that there is a way of escape from
+  it, without renouncing the New Testament. I suppose any one may assume
+  for himself what I have sometimes heard contended for, that no New
+  Testament word is to be used in religion in any sense except that of the
+  New Testament. This granted, the question is settled. The word
+  <i>Christian</i>, which occurs three times, is never recognized as
+  anything but a term of contempt from those without the pale to those
+  within. Thus, Herod Agrippa, who was deep in Jewish literature, and a
+  correspondent of Josephus, says to Paul (Acts xxvi. 28), "Almost thou
+  persuadest me to be (what I and other followers of the state religion
+  despise under the name) a Christian." Again (Acts xi. 26), "The disciples
+  (as they called <i>themselves</i>) were called (by the surrounding
+  heathens) Christians first in Antioch." Thirdly (1 Peter iv. 16), "Let
+  none of you suffer as a <i>murderer</i>.... But if as a <i>Christian</i>
+  (as the heathen call it by whom the suffering comes), let him not be
+  ashamed." That is to say, no <i>disciple</i> ever called <i>himself</i> a
+  Christian, or applied the name, as from himself, to another disciple,
+  from one end of the New Testament to the other; and no disciple need
+  apply that name to himself in our day, if he dislike the associations
+  with which the conduct of Christians has clothed it.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">WRONSKI ON THE LONGITUDE PROBLEM.</p>
+
+<blockquote class="b1n">
+
+  <p>Address of M. Hoene Wronski to the British Board of Longitude, upon
+  the actual state of the mathematics, their reform, <!-- Page 250 --><span
+  class="pagenum"><a name="page250"></a>[250]</span>and upon the new
+  celestial mechanics, giving the definitive solution of the problem of
+  longitude.<a name="NtA_570" href="#Nt_570"><sup>[570]</sup></a> London,
+  1820, 8vo.</p>
+
+</blockquote>
+
+  <p>M. Wronski<a name="NtA_571" href="#Nt_571"><sup>[571]</sup></a> was
+  the author of seven quartos on mathematics, showing very great power of
+  generalization. He was also deep in the transcendental philosophy,<a
+  name="NtA_572" href="#Nt_572"><sup>[572]</sup></a> and had the Absolute
+  at his fingers' ends. All this knowledge was rendered useless by a
+  persuasion that he had greatly advanced beyond the whole world, with many
+  hints that the Absolute would not be forthcoming, unless prepaid. He was
+  a man of the widest extremes. At one time he desired people to see all
+  possible mathematics in</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>F<i>x</i> = A<sub>0</sub><span class="grk">&Omega;</span><sub>0</sub> + A<sub>1</sub><span class="grk">&Omega;</span><sub>1</sub> + A<sub>2</sub><span class="grk">&Omega;</span><sub>2</sub> + A<sub>3</sub><span class="grk">&Omega;</span><sub>3</sub> + &amp;c.</p>
+    </div>
+  </div>
+  <p>which he did not explain, though there is meaning to it in the
+  quartos. At another time he was proposing the general solution of the<a
+  name="NtA_573" href="#Nt_573"><sup>[573]</sup></a> fifth degree by help
+  of 625 independent equations of one form and 125 of another. The first
+  separate memoir from any Transactions that I ever possessed was given to
+  me when at Cambridge; the refutation (1819) of this asserted solution,
+  presented to the Academy of Lisbon by Evangelista Torriano. I cannot say
+  I read it. The tract above is an attack on modern mathematicians in
+  general, and on the Board of Longitude, and Dr. Young.<a name="NtA_574"
+  href="#Nt_574"><sup>[574]</sup></a></p>
+
+<p><!-- Page 251 --><span class="pagenum"><a name="page251"></a>[251]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">DR. MILNER'S PARADOXES.</p>
+
+  <p>1820. In this year died Dr. Isaac Milner,<a name="NtA_575"
+  href="#Nt_575"><sup>[575]</sup></a> President of Queens' College,
+  Cambridge, one of the class of rational paradoxers. Under this name I
+  include all who, in private life, and in matters which concern
+  themselves, take their own course, and suit their own notions, no matter
+  what other people may think of them. These men will put things to uses
+  they were never intended for, to the great distress and disgust of their
+  gregarious friends. I am one of the class, and I could write a little
+  book of cases in which I have incurred absolute reproach for not "doing
+  as other people do." I will name two of my atrocities: I took one of
+  those butter-dishes which have for a top a dome with holes in it, which
+  is turned inward, out of reach of accident, when not in use. Turning the
+  dome inwards, I filled the dish with water, and put a sponge in the dome:
+  the holes let it fill with water, and I had a penwiper, always moist, and
+  worth its price five times over. "Why! what do you mean? It was made to
+  hold butter. You are always at some queer thing or other!" I bought a
+  leaden comb, intended to dye the hair, it being supposed that the
+  application of lead will have this effect. I did not try: but I divided
+  the comb into two, separated the part of closed prongs from the other;
+  and thus I had two ruling machines. The lead marks paper, and by drawing
+  the end of one of the machines along a ruler, I could rule twenty lines
+  at a time, quite fit to write on. I thought I should have killed a friend
+  to whom I explained it: he could not for the life of him understand how
+  leaden <i>lines</i> on paper would dye the hair.</p>
+
+  <p>But Dr. Milner went beyond me. He wanted a seat suited to his shape,
+  and he defied opinion to a fearful point. <!-- Page 252 --><span
+  class="pagenum"><a name="page252"></a>[252]</span>He spread a thick block
+  of putty over a wooden chair and sat in it until it had taken a ceroplast
+  copy of the proper seat. This he gave to a carpenter to be imitated in
+  wood. One of the few now living who knew him&mdash;my friend, General
+  Perronet Thompson<a name="NtA_576"
+  href="#Nt_576"><sup>[576]</sup></a>&mdash;answers for the wood, which was
+  shown him by Milner himself; but he does not vouch for the material being
+  putty, which was in the story told me at Cambridge; William Frend<a
+  name="NtA_577" href="#Nt_577"><sup>[577]</sup></a> also remembered it.
+  Perhaps the Doctor took off his great seal in green wax, like the Crown;
+  but some soft material he certainly adopted; and very comfortable he
+  found the wooden copy.</p>
+
+  <div class="figleft" style="width:10%;">
+      <a href="images/adem_260.png"><img style="width:100%" src="images/adem_260.png"
+      alt="Milner's lamp" title="Milner's lamp" /></a>
+  </div>
+  <p>The same gentleman vouches for Milner's lamp: but this had visible
+  <i>science</i> in it; the vulgar see no science in the construction of
+  the chair. A hollow semi-cylinder, but not with a circular curve,
+  revolved on pivots. The curve was calculated on the law that, whatever
+  quantity of oil might be in the lamp, the position of equilibrium just
+  brought the oil up to the edge of the cylinder, at which a bit of wick
+  was placed. As the wick exhausted the oil, the cylinder slowly revolved
+  about the pivots so as to keep the oil always touching the wick.</p>
+
+  <p>Great discoveries are always laughed at; but it is very often not the
+  laugh of incredulity; it is a mode of distorting the sense of inferiority
+  into a sense of superiority, or a mimicry of superiority interposed
+  between the laugher and his feeling of inferiority. Two persons in
+  conversation <!-- Page 253 --><span class="pagenum"><a
+  name="page253"></a>[253]</span>agreed that it was often a nuisance not to
+  be able to lay hands on a bit of paper to mark the place in a book, every
+  bit of paper on the table was sure to contain something not to be spared.
+  I very quietly said that I always had a stock of bookmarkers ready cut,
+  with a proper place for them: my readers owe many of my anecdotes to this
+  absurd practice. My two colloquials burst into a fit of laughter; about
+  what? Incredulity was out of the question; and there could be nothing
+  foolish in my taking measures to avoid what they knew was an
+  inconvenience. I was in this matter obviously their superior, and so they
+  laughed at me. Much more candid was the Royal Duke of the last century,
+  who was noted for slow ideas. "The rain comes into my mouth," said he,
+  while riding. "Had not your Royal Highness better shut your mouth?" said
+  the equerry. The Prince did so, and ought, by rule, to have laughed
+  heartily at his adviser; instead of this, he said quietly, "It doesn't
+  come in now."</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">HERBART'S MATHEMATICAL PSYCHOLOGY.</p>
+
+<blockquote class="b1n">
+
+  <p>De Attentionis mensura causisque primariis. By J.&nbsp;F. Herbart.<a
+  name="NtA_578" href="#Nt_578"><sup>[578]</sup></a> K&oelig;nigsberg,
+  1822, 4to.</p>
+
+</blockquote>
+
+<p><!-- Page 254 --><span class="pagenum"><a name="page254"></a>[254]</span></p>
+
+  <p>This celebrated philosopher maintained that mathematics ought to be
+  applied to psychology, in a separate tract, published also in 1822: the
+  one above seems, therefore, to be his challenge on the subject. It is on
+  <i>attention</i>, and I think it will hardly support Herbart's thesis. As
+  a specimen of his formula, let <i>t</i> be the time elapsed since the
+  consideration began, <span class="grk">&beta;</span> the whole perceptive
+  intensity of the individual, <span class="grk">&phi;</span> the whole of
+  his mental force, and <i>z</i> the force given to a notion by attention
+  during the time <i>t</i>. Then,</p>
+
+<p class="cenhead"><i>z</i> = <span class="grk">&phi;</span> (1 - <span class="grk">&epsilon;</span><sup>-<span class="grk">&beta;</span><i>t</i></sup>)</p>
+
+  <p>Now for a test. There is a <i>jactura</i>, <i>v</i>, the meaning of
+  which I do not comprehend. If there be anything in it, my mathematical
+  readers ought to interpret it from the formula</p>
+
+<p class="cenhead"><i>v</i> = <span class="grk">&pi;</span><span class="grk">&phi;</span><span class="grk">&beta;</span>/(1 - <span class="grk">&beta;</span>)<span class="grk">&epsilon;</span><sup>-<span class="grk">&beta;</span><i>t</i></sup> + C<span class="grk">&epsilon;</span><sup>-t</sup></p>
+
+  <p>and to this task I leave them, wishing them better luck than mine. The
+  time may come when other manifestations of mind, besides <i>belief</i>,
+  shall be submitted to calculation: at that time, should it arrive, a
+  final decision may be passed upon Herbart.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON THE WHIZGIG.</p>
+
+<blockquote class="b1n">
+
+  <p>The theory of the Whizgig considered; in as much as it mechanically
+  exemplifies the three working properties of nature; which are now set
+  forth under the guise of this toy, for children of all ages. London,
+  1822, 12mo (pp. 24, B. McMillan, Bow Street, Covent Garden).</p>
+
+</blockquote>
+
+  <p>The toy called the <i>whizgig</i> will be remembered by many. The
+  writer is a follower of Jacob Behmen,<a name="NtA_579"
+  href="#Nt_579"><sup>[579]</sup></a> William Law,<a name="NtA_580"
+  href="#Nt_580"><sup>[580]</sup></a> <!-- Page 255 --><span
+  class="pagenum"><a name="page255"></a>[255]</span>Richard Clarke,<a
+  name="NtA_581" href="#Nt_581"><sup>[581]</sup></a> and Eugenius
+  Philalethes.<a name="NtA_582" href="#Nt_582"><sup>[582]</sup></a> Jacob
+  Behmen first announced the three working properties of nature, which
+  Newton stole, as described in the <i>Gentleman's Magazine</i>, July,
+  1782, p. 329. These laws are illustrated in the whizgig. There is the
+  harsh astringent, attractive compression; the bitter compunction,
+  repulsive expansion; and the stinging anguish, duplex motion. The author
+  hints that he has written other works, to which he gives no clue. I have
+  heard that Behmen was pillaged by Newton, and Swedenborg<a name="NtA_583"
+  href="#Nt_583"><sup>[583]</sup></a> by Laplace,<a name="NtA_584"
+  href="#Nt_584"><sup>[584]</sup></a> and Pythagoras by Copernicus,<a
+  name="NtA_585" href="#Nt_585"><sup>[585]</sup></a> and Epicurus by
+  Dalton,<a name="NtA_586" href="#Nt_586"><sup>[586]</sup></a> &amp;c. I do
+  not think this mention will revive Behmen; but it may the whizgig, a very
+  pretty toy, and philosophical withal, for few of those who used it could
+  explain it.</p>
+
+<p><!-- Page 256 --><span class="pagenum"><a name="page256"></a>[256]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">SOME MYTHOLOGICAL PARADOXES.</p>
+
+<blockquote class="b1n">
+
+  <p>A Grammar of infinite forms; or the mathematical elements of ancient
+  philosophy and mythology. By Wm. Howison.<a name="NtA_587"
+  href="#Nt_587"><sup>[587]</sup></a> Edinburgh, 1823, 8vo.</p>
+
+</blockquote>
+
+  <p>A curius combination of geometry and mythology. Perseus, for instance,
+  is treated under the head, "the evolution of diminishing hyperbolic
+  branches."</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>The Mythological Astronomy of the Ancients; part the second: or the
+  key of Urania, the words of which will unlock all the mysteries of
+  antiquity. Norwich, 1823, 12mo.</p>
+
+  <p>A Companion to the Mythological Astronomy, &amp;c., containing remarks
+  on recent publications.... Norwich, 1824, 12mo.</p>
+
+  <p>A new Theory of the Earth and of planetary motion; in which it is
+  demonstrated that the Sun is vicegerent of his own system. Norwich, 1825,
+  12mo.</p>
+
+  <p>The analyzation of the writings of the Jews, so far as they are found
+  to have any connection with the sublime science of astronomy. [This is
+  pp. 97-180 of some other work, being all I have seen.]</p>
+
+</blockquote>
+
+  <p>These works are all by Sampson Arnold Mackey,<a name="NtA_588"
+  href="#Nt_588"><sup>[588]</sup></a> for whom see <i>Notes and
+  Queries</i>, 1st S. viii. 468, 565, ix. 89, 179. Had it not been for
+  actual quotations given by one correspondent only (1st S. viii. 565),
+  that journal would have handed him down as a man of some real learning.
+  An extraordinary man he certainly was: it is not one illiterate shoemaker
+  in a thousand who could work upon such a singular mass of Sanskrit and
+  Greek words, without showing <!-- Page 257 --><span class="pagenum"><a
+  name="page257"></a>[257]</span>evidence of being able to read a line in
+  any language but his own, or to spell that correctly. He was an
+  uneducated Godfrey Higgins.<a name="NtA_589"
+  href="#Nt_589"><sup>[589]</sup></a> A few extracts will put this in a
+  strong light: one for history of science, one for astronomy, and one for
+  philology:</p>
+
+  <p>"Sir Isaac Newton was of opinion that 'the atmosphere of the earth was
+  the sensory of God; by which he was enabled to see quite round the
+  earth:' which proves that Sir Isaac had no idea that God could see
+  through the earth.</p>
+
+  <p>"Sir Richard [Phillips] has given the most rational explanation of the
+  cause of the earth's elliptical orbit that I have ever seen in print. It
+  is because the earth presents its watery hemisphere to the sun at one
+  time and that of solid land the other; but why has he made his Oxonian
+  astonished at the coincidence? It is what I taught in my attic twelve
+  years before.</p>
+
+  <p>"Again, admitting that the Eloim were powerful and intelligent beings
+  that managed these things, we would accuse <i>them</i> of being the
+  authors of all the sufferings of Chrisna. And as they and the
+  constellation of Leo were below the horizon, and consequently cut off
+  from the end of the zodiac, there were but eleven constellations of the
+  zodiac to be seen; the three at the end were wanted, but those three
+  would be accused of bringing Chrisna into the troubles which at last
+  ended in his death. All this would be expressed in the Eastern language
+  by saying that Chrisna was persecuted by those Judoth Ishcarioth!!!!!
+  [the five notes of exclamation are the author's]. But the astronomy of
+  those distant ages, when the sun was at the south pole in winter, would
+  leave five of those Decans cut off from our view, in the latitude of
+  twenty-eight degrees; hence Chrisna died of <!-- Page 258 --><span
+  class="pagenum"><a name="page258"></a>[258]</span>wounds from five
+  Decans, but the whole five may be included in Judoth Ishcarioth! for the
+  phrase means 'the men that are wanted at the extreme parts.' Ishcarioth
+  is a compound of <i>ish</i>, a man, and <i>carat</i> wanted or taken
+  away, and oth the plural termination, more ancient than
+  <i>im</i>...."</p>
+
+  <p>I might show at length how Michael is the sun, and the D'-ev-'l in
+  French Di-ob-al, also 'L-evi-ath-an&mdash;the evi being the radical part
+  both of d<i>evi</i>l and l<i>evi</i>athan&mdash;is the Nile, which the
+  sun dried up for Moses to pass: a battle celebrated by Jude. Also how
+  <i>Moses</i>, the same name as <i>Muses</i>, is from <i>mesha</i>, drawn
+  out of the water, "and hence we called our land which is saved from the
+  water by the name of <i>marsh</i>." But it will be of more use to collect
+  the character of S.&nbsp;A.&nbsp;M. from such correspondents of <i>Notes and
+  Queries</i> as have written after superficial examination. Great
+  astronomical and philological attainments, much ability and learning; had
+  evidently read and studied deeply; remarkable for the originality of his
+  views upon the very abstruse subject of mythological astronomy, in which
+  he exhibited great sagacity. Certainly his views were <i>original</i>;
+  but their sagacity, if it be allowable to copy his own mode of
+  etymologizing, is of an <i>ori-gin-ale</i> cast, resembling that of a
+  person who puts to his mouth liquors both distilled and fermented.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A KANTESIAN JEWELER.</p>
+
+<blockquote class="b1n">
+
+  <p>Principles of the Kantesian, or transcendental philosophy. By Thomas
+  Wirgman.<a name="NtA_590" href="#Nt_590"><sup>[590]</sup></a> London,
+  1824, 8vo.</p>
+
+</blockquote>
+
+  <p>Mr. Wirgman's mind was somewhat attuned to psychology; but he was
+  cracky and vagarious. He had been a fashionable jeweler in St. James's
+  Street, no doubt the son or grandson of Wirgman at "the well-known
+  toy-shop in <!-- Page 259 --><span class="pagenum"><a
+  name="page259"></a>[259]</span>St. James's Street," where Sam Johnson
+  smartened himself with silver buckles. (Boswell, <i>æt.</i> 69). He would
+  not have the ridiculous large ones in fashion; and he would give no more
+  than a guinea a pair; such, says Boswell, in Italics, were the
+  <i>principles</i> of the business: and I think this may be the first
+  place in which the philosophical word was brought down from heaven to mix
+  with men. However this may be, <i>my</i> Wirgman sold snuff-boxes, among
+  other things, and fifty years ago a fashionable snuff-boxer would be
+  under inducement, if not positively obliged, to have a stock with very
+  objectionable pictures. So it happened that Wirgman&mdash;by reason of a
+  trifle too much candor&mdash;came under the notice of the
+  <i>Suppression</i> Society, and ran considerable risk. Mr. Brougham was
+  his counsel; and managed to get him acquitted. Years and years after
+  this, when Mr. Brougham was deep in the formation of the London
+  University (now University College), Mr. Wirgman called on him. "What
+  now?" said Mr. B. with his most sarcastic look&mdash;a very perfect thing
+  of its kind&mdash;"you're in a scrape again, I suppose!" "No! indeed!"
+  said W., "my present object is to ask your interest for the chair of
+  Moral Philosophy in the new University!" He had taken up Kant!</p>
+
+  <p>Mr. Wirgman, an itinerant paradoxer, called on me in 1831: he came to
+  convert me. "I assure you," said he, "I am nothing but an old brute of a
+  jeweler;" and his eye and manner were of the extreme of jocosity, as good
+  in their way, as the satire of his former counsel. I mention him as one
+  of that class who go away quite satisfied that they have wrought
+  conviction. "Now," said he, "I'll make it clear to you! Suppose a number
+  of gold-fishes in a glass bowl,&mdash;you understand? Well! I come with
+  my cigar and go puff, puff, puff, over the bowl, until there is a little
+  cloud of smoke: now, tell me, what will the gold-fishes say to that?" "I
+  should imagine," said I, "That they would not know what to make of it."
+  "By Jove! you're a Kantian;" said he, and with this and the like, he left
+  me, vowing that <!-- Page 260 --><span class="pagenum"><a
+  name="page260"></a>[260]</span>it was delightful to talk to so
+  intelligent a person. The greatest compliment Wirgman ever received was
+  from James Mill, who used to say he did not <i>understand</i> Kant. That
+  such a man as Mill should think this worth saying is a feather in the cap
+  of the jocose jeweler.</p>
+
+  <p>Some of my readers will stare at my supposing that Boswell may have
+  been the first down-bringer of the word <i>principles</i> into common
+  life; the best answer will be a prior instance of the word as true
+  vernacular; it has never happened to me to notice one. Many words have
+  very common uses which are not old. Take the following from Nichols
+  (<i>Anecd.</i> ix. 263): "Lord Thurlow presents his best respects to Mr.
+  and Mrs. Thicknesse, and assures them that he knows of no cause to
+  complain of any part of Mr. Thicknesse's carriage; least of all the
+  circumstance of sending the head to Ormond Street." Surely Mr. T. had
+  lent Lord T. a satisfactory carriage with a movable head, and the above
+  is a polite answer to inquiries. Not a bit of it! <i>carriage</i> is here
+  <i>conduct</i>, and the <i>head</i> is a <i>bust</i>. The vehicles of the
+  rich, at the time, were coaches, chariots, chaises, etc., never
+  carriages, which were rather <i>carts</i>. Gibbon has the word for
+  baggage-wagons. In Jane Austen's novels the word carriage is
+  established.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">WALSH'S DELUSIONS.</p>
+
+  <p><i>John Walsh</i>,<a name="NtA_591"
+  href="#Nt_591"><sup>[591]</sup></a> of Cork (1786-1847). This discoverer
+  has had the honor of a biography from Professor Boole, who, at my
+  request, collected information about him on the scene of his labors. It
+  is in the <i>Philosophical Magazine</i> for November, 1851, and will, I
+  hope, be transferred to some biographical collection where it may find a
+  larger class of readers. It is the best biography of a single hero of the
+  kind that I know. Mr. Walsh introduced himself to me, <!-- Page 261
+  --><span class="pagenum"><a name="page261"></a>[261]</span>as he did to
+  many others, in the anterowlandian days of the Post-office; his unpaid
+  letters were double, treble, &amp;c. They contained his pamphlets, and
+  cost their weight in silver: all have the name of the author, and all are
+  in octavo or in quarto letter-form: most are in four pages, and all dated
+  from Cork. I have the following by me:</p>
+
+<blockquote class="b1n">
+
+  <p>The Geometric Base, 1825.&mdash;The theory of plane angles.
+  1827.&mdash;Three Letters to Dr. Francis Sadleir. 1838.&mdash;The
+  invention of polar geometry. By Irelandus. 1839.&mdash;The theory of
+  partial functions. Letter to Lord Brougham. 1839.&mdash;On the invention
+  of polar geometry. 1839.&mdash;Letter to the Editor of the Edinburgh
+  Review. 1840.&mdash;Irish Manufacture. A new method of tangents.
+  1841.&mdash;The normal diameter in curves. 1843.&mdash;Letter to Sir R.
+  Peel. 1845.&mdash;[Hints that Government should compel the introduction
+  of Walsh's Geometry into Universities.]&mdash;Solution of Equations of
+  the higher orders. 1845.</p>
+
+</blockquote>
+
+  <p>Besides these, there is a <i>Metalogia</i>, and I know not how many
+  others.</p>
+
+  <p>Mr. Boole,<a name="NtA_592" href="#Nt_592"><sup>[592]</sup></a> who
+  has taken the moral and social features of Walsh's delusions from the
+  commiserating point of view, which makes ridicule out of place, has been
+  obliged to treat Walsh as Scott's Alan Fairford treated his client Peter
+  Peebles; namely, keep the scarecrow out of court while the case was
+  argued. My plan requires me to bring him in: and when he comes in at the
+  door, pity and sympathy fly out at the window. Let the reader remember
+  that he was not an ignoramus in mathematics: he might have won his spurs
+  if he could have first served as an esquire. Though so illiterate that
+  even in Ireland he never picked up anything more Latin than
+  <i>Irelandus</i>, he was a very pretty mathematician spoiled in the
+  making by intense self-opinion.</p>
+
+  <p>This is part of a private letter to me at the back of a page of print:
+  I had never addressed a word to him:</p>
+
+<p><!-- Page 262 --><span class="pagenum"><a name="page262"></a>[262]</span></p>
+
+  <p>"There are no limits in mathematics, and those that assert there are,
+  are infinite ruffians, ignorant, lying blackguards. There is no
+  differential calculus, no Taylor's theorem, no calculus of variations,
+  &amp;c. in mathematics. There is no quackery whatever in mathematics; no
+  % equal to anything. What sheer ignorant blackguardism that!</p>
+
+  <p>"In mechanics the parallelogram of forces is quackery, and is
+  dangerous; for nothing is at rest, or in uniform, or in rectilinear
+  motion, in the universe. Variable motion is an essential property of
+  matter. Laplace's demonstration of the parallelogram of forces is a
+  begging of the question; and the attempts of them all to show that the
+  difference of twenty minutes between the sidereal and actual revolution
+  of the earth round the sun arises from the tugging of the Sun and Moon at
+  the pot-belly of the earth, without being sure even that the earth has a
+  pot-belly at all, is perfect quackery. The said difference arising from
+  and demonstrating the revolution of the Sun itself round some distant
+  center."</p>
+
+  <p>In the letter to Lord Brougham we read as follows:</p>
+
+  <p>"I ask the Royal Society of London, I ask the Saxon crew of that crazy
+  hulk, where is the dogma of their philosophic god now?... When the Royal
+  Society of London, and the Academy of Sciences of Paris, shall have read
+  this memorandum, how will they appear? Like two cur dogs in the paws of
+  the noblest beast of the forest.... Just as this note was going to press,
+  a volume lately published by you was put into my hands, wherein you
+  attempt to defend the fluxions and <i>Principia</i> of Newton. Man! what
+  are you about? You come forward now with your special pleading, and
+  fraught with national prejudice, to defend, like the philosopher
+  Grassi,<a name="NtA_593" href="#Nt_593"><sup>[593]</sup></a> the
+  persecutor of Galileo, principles <!-- Page 263 --><span
+  class="pagenum"><a name="page263"></a>[263]</span>and reasoning which,
+  unless you are actually insane, or an ignorant quack in mathematics, you
+  know are mathematically false. What a moral lesson this for the students
+  of the University of London from its head! Man! demonstrate corollary 3,
+  in this note, by the lying dogma of Newton, or turn your thoughts to
+  something you understand.</p>
+
+  <p class="author">"<span class="sc">Walsh Irelandus.</span>"
+
+  <p>Mr. Walsh&mdash;honor to his memory&mdash;once had the consideration
+  to save me postage by addressing a pamphlet under cover to a Member of
+  Parliament, with an explanatory letter. In that letter he gives a candid
+  opinion of himself:</p>
+
+  <p>(1838.) "Mr. Walsh takes leave to send the enclosed corrected copy to
+  Mr. Hutton as one of the Council of the University of London, and to save
+  postage for the Professor of Mathematics there. He will find in it
+  geometry more deep and subtle, and at the same time more simple and
+  elegant, than it was ever contemplated human genius could invent."</p>
+
+  <p>He then proceeds to set forth that a certain "tomfoolery lemma," with
+  its "tomfoolery" superstructure, "never had existence outside the shallow
+  brains of its inventor," Euclid. He then proceeds thus:</p>
+
+  <p>"The same spirit that animated those philosophers who sent Galileo to
+  the Inquisition animates all the philosophers of the present day without
+  exception. If anything can free them from the yoke of error, it is the
+  [Walsh] problem of double tangence. But free them it will, how deeply
+  soever they may be sunk into mental slavery&mdash;and God knows that is
+  deeply enough; and they bear it with an admirable grace; for none bear
+  slavery with a better grace than tyrants. The lads must adopt my
+  theory.... It will be a sad reverse for all our great professors to be
+  compelled to become schoolboys in their gray years. But the sore scratch
+  is to be compelled, as they had before been compelled one thousand years
+  ago, to have recourse to Ireland for instruction." <!-- Page 264 --><span
+  class="pagenum"><a name="page264"></a>[264]</span></p>
+
+  <p>The following "Impromptu" is no doubt by Walsh himself: he was more of
+  a poet than of an astronomer:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="i2hg3">"Through ages unfriended,</p>
+      <p class="i2">With sophistry blended,</p>
+      <p>Deep science in Chaos had slept;</p>
+      <p class="i2">Its limits were fettered,</p>
+      <p class="i2">Its voters unlettered,</p>
+      <p>Its students in movements but crept.</p>
+      <p class="i2">Till, despite of great foes,</p>
+      <p class="i2">Great <span class="sc">Walsh</span> first arose,</p>
+      <p>And with logical might did unravel</p>
+      <p class="i2">Those mazes of knowledge,</p>
+      <p class="i2">Ne'er known in a college,</p>
+      <p>Though sought for with unceasing travail.</p>
+      <p class="i2">With cheers we now hail him,</p>
+      <p class="i2">May success never fail him,</p>
+      <p>In Polar Geometrical mining;</p>
+      <p class="i2">Till his foes be as tamed</p>
+      <p class="i2">As his works are far-famed</p>
+      <p>For true philosophic refining."</p>
+    </div>
+  </div>
+  <p>Walsh's system is, that all mathematics and physics are wrong: there
+  is hardly one proposition in Euclid which is demonstrated. His example
+  ought to warn all who rely on their own evidence to their own success. He
+  was not, properly speaking, insane; he only spoke his mind more freely
+  than many others of his class. The poor fellow died in the Cork union,
+  during the famine. He had lived a happy life, contemplating his own
+  perfections, like Brahma on the lotus-leaf.<a name="NtA_594"
+  href="#Nt_594"><sup>[594]</sup></a></p>
+
+<p><!-- Page 265 --><span class="pagenum"><a name="page265"></a>[265]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">GROWTH OF FREEDOM OF OPINION.</p>
+
+  <p>The year 1825 brings me to about the middle of my <i>Athenæum</i>
+  list: that is, so far as mere number of names mentioned is concerned.
+  Freedom of opinion, beyond a doubt, is gaining ground, for good or for
+  evil, according to what the speaker happens to think: admission of
+  authority is no longer made in the old way. If we take soul-cure and
+  body-cure, divinity and medicine, it is manifest that a change has come
+  over us. Time was when it was enough that dose or dogma should be
+  certified by "Il a été ordonné, Monsieur, il a été ordonné,"<a
+  name="NtA_595" href="#Nt_595"><sup>[595]</sup></a> as the apothecary said
+  when he wanted to operate upon poor de Porceaugnac. Very much changed:
+  but whether for good or for evil does not now matter; the question is,
+  whether contempt of <i>demonstration</i> such as our paradoxers show has
+  augmented with the rejection of <i>dogmatic authority</i>. It ought to be
+  just the other way: for the worship of reason is the system on which, if
+  we trust them, the deniers of guidance ground their plan of life. The
+  following attempt at an experiment on this point is the best which I can
+  make; and, so far as I know, the first that ever was made.</p>
+
+  <p>Say that my list of paradoxers divides in 1825: this of itself proves
+  nothing, because so many of the earlier books are lost, or not likely to
+  be come at. It would be a fearful rate of increase which would make the
+  number of paradoxes since 1825 equal to the whole number before that
+  date. Let us turn now to another collection of mine, arithmetical books,
+  of which I have published a list. The two collections are similarly
+  circumstanced as to new and old books; the paradoxes had no care given to
+  the collection of either; the arithmetical books equal care to both. The
+  list of arithmetical books, published in 1847, divides at 1735; the
+  paradoxes, up to 1863, divide at 1825. If we take the process which is
+  most against the distinction, and allow every year <!-- Page 266 --><span
+  class="pagenum"><a name="page266"></a>[266]</span>from 1847 to 1863 to
+  add a year to 1735, we should say that the arithmetical writers divide at
+  1751. This rough process may serve, with sufficient certainty, to show
+  that the proportion of paradoxes to books of sober demonstration is on
+  the increase; and probably, quite as much as the proportion of
+  heterodoxes to books of orthodox adherence. So that divinity and medicine
+  may say to geometry, Don't <i>you</i> sneer: if rationalism,
+  hom&oelig;opathy, and their congeners are on the rise among us, your
+  enemies are increasing quite as fast. But geometry replies&mdash;Dear
+  friends, content yourselves with the rational inference that the rise of
+  heterodoxy within your pales is not conclusive against you, taken alone;
+  for it rises at the same time within mine. Store within your garners the
+  precious argument that you are not proved wrong by increase of dissent;
+  because there is increase of dissent against exact science. But do not
+  therefore <i>even</i> yourselves to me: remember that you, Dame Divinity,
+  have inflicted every kind of penalty, from the stake to the stocks, in
+  aid of your reasoning; remember that you, Mother Medicine, have not many
+  years ago applied to Parliament for increase of forcible hindrance of
+  antipharmacop&oelig;al drenches, pills, and powders. Who ever heard of my
+  asking the legislature to fine blundering circle-squarers? Remember that
+  the D in dogma is the D in decay; but the D in demonstration is the D in
+  durability.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE STATUS OF MEDICINE.</p>
+
+  <p>I have known a medical man&mdash;a young one&mdash;who was seriously
+  of the opinion that the country ought to be divided into medical
+  parishes, with a practitioner appointed to each, and a penalty for
+  calling in any but the incumbent curer. How should people know how to
+  choose? The hair-dressers once petitioned Parliament for an act to compel
+  people to wear wigs. My own opinion is of the opposite extreme, as in the
+  following letter (<i>Examiner</i>, April 5, 1856); which, to my surprise,
+  I saw reprinted in a medical journal, as a <!-- Page 267 --><span
+  class="pagenum"><a name="page267"></a>[267]</span>plan not absolutely to
+  be rejected. I am perfectly satisfied that it would greatly promote true
+  medical orthodoxy, the predominance of well educated thinkers, and the
+  development of their desirable differences.</p>
+
+  <p>&nbsp;</p>
+
+  <p>"<span class="sc">Sir.</span> The Medical Bill and the medical
+  question generally is one on which experience would teach, if people
+  would be taught.</p>
+
+  <p>"The great soul question took three hundred years to settle: the
+  little body question might be settled in thirty years, if the decisions
+  in the former question were studied.</p>
+
+  <p>"Time was when the State believed, as honestly as ever it believed
+  anything, that it <i>might</i>, <i>could</i>, and <i>should</i> find out
+  the true doctrine for the poor ignorant community; to which, like a
+  worthy honest state, it added <i>would</i>. Accordingly, by the
+  assistance of the Church, which undertook the physic, the surgery, and
+  the pharmacy of sound doctrine all by itself, it sent forth its legally
+  qualified teachers into every parish, and woe to the man who called in
+  any other. They burnt that man, they whipped him, they imprisoned him,
+  they did everything but what was Christian to him, all for his soul's
+  health and the amendment of his excesses.</p>
+
+  <p>"But men would not submit. To the argument that the State was a father
+  to the ignorant, they replied that it was at best the ignorant father of
+  an ignorant son, and that a blind man could find his way into a ditch
+  without another blind man to help him. And when the State said&mdash;But
+  here we have the Church, which knows all about it, the ignorant community
+  declared that it had a right to judge that question, and that it would
+  judge it. It also said that the Church was never one thing long, and that
+  it progressed, on the whole, rather more slowly than the ignorant
+  community.</p>
+
+  <p>"The end of it was, in this country, that every one who chose taught
+  all who chose to let him teach, on condition only of an open and true
+  registration. The State was <!-- Page 268 --><span class="pagenum"><a
+  name="page268"></a>[268]</span>allowed to patronize one particular
+  Church, so that no one need trouble himself to choose a pastor from the
+  mere necessity of choosing. But every church is allowed its colleges, its
+  studies, its diplomas; and every man is allowed his choice. There is no
+  proof that our souls are worse off than in the sixteenth century; and,
+  judging by fruits, there is much reason to hope they are better off.</p>
+
+  <p>"Now the little body question is a perfect parallel to the great soul
+  question in all its circumstances. The only things in which the parallel
+  fails are the following: Every one who believes in a future state sees
+  that the soul question is incomparably more important than the body
+  question, and every one can try the body question by experiment to a
+  larger extent than the soul question. The proverb, which always has a
+  spark of truth at the bottom, says that every man of forty is either a
+  fool or a physician; but did even the proverb maker ever dare to say that
+  every man is at any age either a fool or a fit teacher of religion?</p>
+
+  <p>"Common sense points out the following settlement of the medical
+  question: and to this it will come sooner or later.</p>
+
+  <p>"Let every man who chooses&mdash;subject to one common law of
+  manslaughter for all the <i>crass</i> cases&mdash;doctor the bodies of
+  all who choose to trust him, and recover payment according to agreement
+  in the courts of law. Provided always that every person practising should
+  be registered at a moderate fee in a register to be republished every six
+  months.</p>
+
+  <p>"Let the register give the name, address, and asserted qualification
+  of each candidate&mdash;as licentiate, or doctor, or what not, of this or
+  that college, hall, university, &amp;c., home or foreign. Let it be
+  competent to any man to describe himself as qualified by study in public
+  schools without a diploma, or by private study, or even by intuition or
+  divine inspiration, if he please. But whatever he holds his qualification
+  to be, that let him declare. Let all qualification <!-- Page 269 --><span
+  class="pagenum"><a name="page269"></a>[269]</span>which of its own nature
+  admits of proof be proved, as by the diploma or certificate, &amp;c.,
+  leaving things which cannot be proved, as asserted private study,
+  intuition, inspiration, &amp;c., to work their own way.</p>
+
+  <p>"Let it be highly penal to assert to the patient any qualification
+  which is not in the register, and let the register be sold very cheap.
+  Let the registrar give each registered practitioner a copy of the
+  register in his own case; let any patient have the power to demand a
+  sight of this copy; and let no money for attendance be recoverable in any
+  case in which there has been false representation.</p>
+
+  <p>"Let any party in any suit have a right to produce what medical
+  testimony he pleases. Let the medical witness produce his register, and
+  let his evidence be for the jury, as is that of an engineer or a
+  practitioner of any art which is not attested by diplomas.</p>
+
+  <p>"Let any man who practises without venturing to put his name on the
+  register be liable to fine and imprisonment.</p>
+
+  <p>"The consequence would be that, as now, anybody who pleases might
+  practise; for the medical world is well aware that there is no power of
+  preventing what they call quacks from practising. But very different from
+  what is now, every man who practises would be obliged to tell the whole
+  world what his claim is, and would run a great risk if he dared to tell
+  his patient in private anything different from what he had told the whole
+  world.</p>
+
+  <p>"The consequence would be that a real education in anatomy,
+  physiology, chemistry, surgery, and what is known of the thing called
+  medicine, would acquire more importance than it now has.</p>
+
+  <p>"It is curious to see how completely the medical man of the nineteenth
+  century squares with the priest of the sixteenth century. The clergy of
+  all sects are now better divines and better men than they ever were. They
+  have lost Bacon's reproach that they took a smaller measure of things
+  than any other educated men; and the physicians are now <!-- Page 270
+  --><span class="pagenum"><a name="page270"></a>[270]</span>in this
+  particular the rearguard of the learned world; though it may be true that
+  the rear in our day is further on in the march than the van of Bacon's
+  day. Nor will they ever recover the lost position until medicine is as
+  free as religion.</p>
+
+  <p>"To this it must come. To this the public, which will decide for
+  itself, has determined it shall come. To this the public has, in fact,
+  brought it, but on a plan which it is not desirable to make permanent. We
+  will be as free to take care of our bodies as of our souls and of our
+  goods. This is the profession of all who sign as I do, and the practice
+  of most of those who would not like the name</p>
+
+  <p class="author">"<span class="sc">Heteropath</span>."
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>The motion of the Sun in the Ecliptic, proved to be uniform in a
+  circular orbit ... with preliminary observations on the fallacy of the
+  Solar System. By Bartholomew Prescott,<a name="NtA_596"
+  href="#Nt_596"><sup>[596]</sup></a> 1825, 8vo.</p>
+
+</blockquote>
+
+  <p>The author had published, in 1803, a <i>Defence of the Divine
+  System</i>, which I never saw; also, <i>On the inverted scheme of
+  Copernicus</i>. The above work is clever in its satire.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE CHRISTIAN EVIDENCE SOCIETY.</p>
+
+<blockquote class="b1n">
+
+  <p>Manifesto of the Christian Evidence Society, established Nov. 12,
+  1824. Twenty-four plain questions to honest men.</p>
+
+</blockquote>
+
+  <p>These are two broadsides of August and November, 1826, signed by
+  Robert Taylor,<a name="NtA_597" href="#Nt_597"><sup>[597]</sup></a> A.B.,
+  Orator of the Christian Evidence Society. This gentleman was a clergyman,
+  <!-- Page 271 --><span class="pagenum"><a
+  name="page271"></a>[271]</span>and was convicted of blasphemy in 1827,
+  for which he suffered imprisonment, and got the name of the <i>Devil's
+  Chaplain</i>. The following are quotations:</p>
+
+  <p>"For the book of Revelation, there was no original Greek at all, but
+  <i>Erasmus</i> wrote it himself in Switzerland, in the year 1516. Bishop
+  Marsh,<a name="NtA_598" href="#Nt_598"><sup>[598]</sup></a> vol. i. p.
+  320."&mdash;"Is not God the author of your reason? Can he then be the
+  author of anything which is contrary to your reason? If reason be a
+  sufficient guide, why should God give you any other? if it be not a
+  sufficient guide, why has he given you <i>that</i>?"</p>
+
+  <p>I remember a votary of the Society being asked to substitute for
+  <i>reason</i> "the right leg," and for <i>guide</i> "support," and to
+  answer the two last questions: he said there must be a quibble, but he
+  did not see what. It is pleasant to reflect that the <i>argumentum à
+  carcere</i><a name="NtA_599" href="#Nt_599"><sup>[599]</sup></a> is
+  obsolete. One great defect of it was that it did not go far enough: there
+  should have been laws against subscriptions for blasphemers, against
+  dealing at their shops, and against rich widows marrying them.</p>
+
+  <p>Had I taken in theology, I must have entered books against
+  Christianity. I mention the above, and Paine's <i>Age of Reason</i>,
+  simply because they are the only English modern works that ever came in
+  my way without my asking for them. The three parts of the <i>Age of
+  Reason</i> were published in Paris 1793, Paris 1795, and New York 1807.
+  Carlile's<a name="NtA_600" href="#Nt_600"><sup>[600]</sup></a> edition is
+  of London, 1818, 8vo. It must be republished when the time comes, to show
+  what stuff governments and clergy were afraid of at the beginning of this
+  century. I should never have seen the book, if it <!-- Page 272 --><span
+  class="pagenum"><a name="page272"></a>[272]</span>had not been
+  prohibited: a bookseller put it under my nose with a fearful look round
+  him; and I could do no less, in common curiosity, than buy a work which
+  had been so complimented by church and state. And when I had read it, I
+  said in my mind to church and state,&mdash;Confound you! you have taken
+  me in worse than any reviewer I ever met with. I forget what I gave for
+  the book, but I ought to have been able to claim compensation
+  somewhere.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE CABBALA.</p>
+
+<blockquote class="b1n">
+
+  <p>Cabbala Algebraica. Auctore Gul. Lud. Christmann.<a name="NtA_601"
+  href="#Nt_601"><sup>[601]</sup></a> Stuttgard, 1827, 4to.</p>
+
+</blockquote>
+
+  <p>Eighty closely printed pages of an attempt to solve equations of every
+  degree, which has a process called by the author <i>cabbala</i>. An
+  anonymous correspondent spells <i>cabbala</i> as follows, <span
+  title="chabball" class="grk"
+  >&chi;&alpha;&beta;&beta;&alpha;&lambda;&lambda;</span>, and makes 666
+  out of its letters. This gentleman has sent me since my Budget commenced,
+  a little heap of satirical communications, each having a 666 or two; for
+  instance, alluding to my remarks on the spelling of <i>chemistry</i>, he
+  finds the fated number in <span title="chimeia" class="grk"
+  >&chi;&iota;&mu;&epsilon;&iota;&alpha;</span>. With these are challenges
+  to explain them, and hints about the end of the world. All these letters
+  have different fantastic seals; one of them with the legend "keep your
+  temper,"&mdash;another bearing "bank token five pence." The only
+  signature is a triangle with a little circle in it, which I interpret to
+  mean that the writer confesses himself to be the round man stuck in the
+  three-cornered hole, to be explained as in Sydney Smith's joke.</p>
+
+<p><!-- Page 273 --><span class="pagenum"><a name="page273"></a>[273]</span></p>
+
+  <p>There is a kind of Cabbala Alphabetica which the investigators of the
+  numerals in words would do well to take up: it is the formation of
+  sentences which contain all the letters of the alphabet, and each only
+  once. No one has done it with <i>v</i> and <i>j</i> treated as
+  consonants; but you and I can do it. Dr. Whewell<a name="NtA_602"
+  href="#Nt_602"><sup>[602]</sup></a> and I amused ourselves, some years
+  ago, with attempts. He could not make sense, though he joined words: he
+  gave me</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>Phiz, styx, wrong, buck, flame, quid.</p>
+    </div>
+  </div>
+  <p>I gave him the following, which he agreed was "admirable sense": I
+  certainly think the words would never have come together except in this
+  way:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>I, quartz pyx, who fling muck beds.</p>
+    </div>
+  </div>
+  <p>I long thought that no human being could say this under any
+  circumstances. At last I happened to be reading a religious
+  writer&mdash;as he thought himself&mdash;who threw aspersions on his
+  opponents thick and threefold. Heyday! came into my head, this fellow
+  flings muck beds; he must be a quartz pyx. And then I remembered that a
+  pyx is a sacred vessel, and quartz is a hard stone, as hard as the heart
+  of a religious foe-curser. So that the line is the motto of the ferocious
+  sectarian, who turns his religious vessels into mudholders, for the
+  benefit of those who will not see what he sees.</p>
+
+  <p>I can find no circumstances for the following, which I received from
+  another:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>Fritz! quick! land! hew gypsum box.</p>
+    </div>
+  </div>
+  <p>From other quarters I have the following:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>Dumpy quiz! whirl back fogs next.</p>
+    </div>
+  </div>
+  <p>This might be said in time of haze to the queer little figure in the
+  Dutch weather-toy, which comes out or goes in with the change in the
+  atmosphere. Again,</p>
+
+<p><!-- Page 274 --><span class="pagenum"><a name="page274"></a>[274]</span></p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>Export my fund!  Quiz black whigs.</p>
+    </div>
+  </div>
+  <p>This Squire Western might have said, who was always afraid of the
+  whigs sending the sinking-fund over to Hanover. But the following is the
+  best: it is good advice to a young man, very well expressed under the
+  circumstances:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>Get nymph; quiz sad brow; fix luck.</p>
+    </div>
+  </div>
+  <p>Which in more sober English would be, Marry; be cheerful; watch your
+  business. There is more edification, more religion in this than in all
+  the 666-interpretations put together.</p>
+
+  <p>Such things would make excellent writing copies, for they secure
+  attention to every letter; <i>v</i> and <i>j</i> might be placed at the
+  end.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON GODFREY HIGGINS.</p>
+
+<blockquote class="b1n">
+
+  <p>The Celtic Druids. By Godfrey Higgins,<a name="NtA_603"
+  href="#Nt_603"><sup>[603]</sup></a> Esq. of Skellow Grange, near
+  Doncaster. London, 1827, 4to.</p>
+
+  <p>Anacalypsis, or an attempt to draw aside the veil of the Saitic Isis:
+  or an inquiry into the origin of languages, nations, and religions. By
+  Godfrey Higgins, &amp;c..., London, 1836, 2 vols. 4to.</p>
+
+</blockquote>
+
+  <p>The first work had an additional preface and a new index in 1829.
+  Possibly, in future time, will be found bound up with copies of the
+  second work two sheets which Mr. Higgins circulated among his friends in
+  1831: the first a "Recapitulation," the second "Book vi. ch. 1."</p>
+
+  <p>The system of these works is that&mdash;</p>
+
+  <p>"The Buddhists of Upper India (of whom the Phenician Canaanite,
+  Melchizedek, was a priest), who built the Pyramids, Stonehenge, Carnac,
+  &amp;c. will be shown to have founded all the ancient mythologies of the
+  world, which, however varied and corrupted in recent times, were
+  originally one, and that one founded on principles sublime, beautiful,
+  and true."</p>
+
+<p><!-- Page 275 --><span class="pagenum"><a name="page275"></a>[275]</span></p>
+
+  <p>These works contain an immense quantity of learning, very honestly put
+  together. I presume the enormous number of facts, and the goodness of the
+  index, to be the reasons why the <i>Anacalypsis</i> found a permanent
+  place in the <i>old</i> reading-room of the British Museum, even before
+  the change which greatly increased the number of books left free to the
+  reader in that room.</p>
+
+  <p>Mr. Higgins, whom I knew well in the last six years of his life, and
+  respected as a good, learned, and (in his own way) <i>pious</i> man, was
+  thoroughly and completely the man of a system. He had that sort of mental
+  connection with his theory that made his statements of his authorities
+  trustworthy: for, besides perfect integrity, he had no bias towards
+  alteration of facts: he saw his system in the way the fact was presented
+  to him by his authority, be that what it might.</p>
+
+  <p>He was very sure of a fact which he got from any of his authorities:
+  nothing could shake him. Imagine a conversation between him and an Indian
+  officer who had paid long attention to Hindoo antiquities and their
+  remains: a third person was present, <i>ego qui scribo</i>. <i>G. H.</i>
+  "You know that in the temples of I-forget-who the Ceres is always
+  sculptured precisely as in Greece." <i>Col.</i> &mdash;&mdash;, "I really
+  do not remember it, and I have seen most of these temples." <i>G. H.</i>
+  "It is so, I assure you, especially at I-forget-where." <i>Col.</i>
+  &mdash;&mdash;, "Well, I am sure! I was encamped for six weeks at the
+  gate of that very temple, and, except a little shooting, had nothing to
+  do but to examine its details, which I did, day after day, and I found
+  nothing of the kind." It was of no use at all.</p>
+
+  <p>Godfrey Higgins began life by exposing and conquering, at the expense
+  of two years of his studies, some shocking abuses which existed in the
+  York Lunatic Asylum. This was a proceeding which called much attention to
+  the treatment of the insane, and produced much good effect. He was very
+  resolute and energetic. The magistracy of his <!-- Page 276 --><span
+  class="pagenum"><a name="page276"></a>[276]</span>time had such scruples
+  about using the severity of law to people of such station as well-to-do
+  farmers, &amp;c.: they would allow a great deal of resistance, and
+  endeavor to mollify the rebels into obedience. A young farmer flatly
+  refused to pay under an order of affiliation made upon him by Godfrey
+  Higgins. He was duly warned; and persisted: he shortly found himself in
+  gaol. He went there sure to conquer the Justice, and the first thing he
+  did was to demand to see his lawyer. He was told, to his horror, that as
+  soon as he had been cropped and prison-dressed, he might see as many
+  lawyers as he pleased, to be looked at, laughed at, and advised that
+  there was but one way out of the scrape. Higgins was, in his
+  speculations, a regular counterpart of Bailly; but the celebrated Mayor
+  of Paris had not his nerve. It was impossible to say, if their characters
+  had been changed, whether the unfortunate crisis in which Bailly was not
+  equal to the occasion would have led to very different results if Higgins
+  had been in his place: but assuredly constitutional liberty would have
+  had one chance more. There are two works of his by which he was known,
+  apart from his paradoxes. First, <i>An apology for the life and character
+  of the celebrated prophet of Arabia, called Mohamed, or the
+  Illustrious</i>. London, 8vo. 1829. The reader will look at this writing
+  of our English Buddhist with suspicious eye, but he will not be able to
+  avoid confessing that the Arabian prophet has some reparation to demand
+  at the hands of Christians. Next, <i>Horæ Sabaticæ; or an attempt to
+  correct certain superstitions and vulgar errors respecting the
+  Sabbath</i>. Second edition, with a large appendix. London, 12mo. 1833.
+  This book was very heterodox at the time, but it has furnished material
+  for some of the clergy of our day.</p>
+
+  <p>I never could quite make out whether Godfrey Higgins took that system
+  which he traced to the Buddhists to have a Divine origin, or to be the
+  result of good men's meditations. Himself a strong theist, and believer
+  in a future <!-- Page 277 --><span class="pagenum"><a
+  name="page277"></a>[277]</span>state, one would suppose that he would
+  refer a <i>universal</i> religion, spread in different forms over the
+  whole earth from one source, directly to the universal Parent. And this I
+  suspect he did, whether he knew it or not. The external evidence is
+  balanced. In his preface he says:</p>
+
+  <p>"I cannot help smiling when I consider that the priests have objected
+  to admit my former book, <i>The Celtic Druids</i>, into libraries,
+  because it was antichristian; and it has been attacked by Deists, because
+  it was superfluously religious. The learned Deist, the Rev. R. Taylor
+  [already mentioned], has designated me as the <i>religious</i> Mr.
+  Higgins."</p>
+
+  <p>The time will come when some profound historian of literature will
+  make himself much clearer on the point than I am.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON POPE'S DIPPING NEEDLE.</p>
+
+<blockquote class="b1n">
+
+  <p>The triumphal Chariot of Friction: or a familiar elucidation of the
+  origin of magnetic attraction, &amp;c. &amp;c. By William Pope.<a
+  name="NtA_604" href="#Nt_604"><sup>[604]</sup></a> London, 1829, 4to.</p>
+
+</blockquote>
+
+  <p>Part of this work is on a dipping-needle of the author's construction.
+  It must have been under the impression that a book of naval magnetism was
+  proposed, that a great many officers, the Royal Naval Club, etc. lent
+  their names to the subscription list. How must they have been surprised
+  to find, right opposite to the list of subscribers, the plate presenting
+  "the three emphatic letters, J.&nbsp;A.&nbsp;O." And how much more when they saw it
+  set forth that if a square be inscribed in a circle, a circle within
+  that, then a square again, &amp;c., it is impossible to have more than
+  fourteen circles, let the first circle be as large as you please. From
+  this the seven attributes of God are unfolded; and further, that all
+  matter was <i>moral</i>, until Lucifer <i>churned</i> it into
+  <i>physical</i> "as far as the third circle in Deity": this Lucifer,
+  called Leviathan in Job, being thus the moving cause of <!-- Page 278
+  --><span class="pagenum"><a name="page278"></a>[278]</span>chaos. I shall
+  say no more, except that the friction of the air is the cause of
+  magnetism.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Remarks on the Architecture, Sculpture, and Zodiac of Palmyra; with a
+  Key to the Inscriptions. By B. Prescot.<a name="NtA_605"
+  href="#Nt_605"><sup>[605]</sup></a> London, 1830, 8vo.</p>
+
+</blockquote>
+
+  <p>Mr. Prescot gives the signs of the zodiac a Hebrew origin.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE JACOTOT METHOD.</p>
+
+<blockquote class="b1n">
+
+  <p>Epitomé de mathématiques. Par F. Jacotot,<a name="NtA_606"
+  href="#Nt_606"><sup>[606]</sup></a> Avocat. 3ième edition, Paris, 1830,
+  8vo. (pp. 18).</p>
+
+  <p>Méthode Jacotot. Choix de propositions mathématiques. Par P. Y.
+  Séprés.<a name="NtA_607" href="#Nt_607"><sup>[607]</sup></a> 2nde
+  édition. Paris, 1830, 8vo. (pp. 82).</p>
+
+</blockquote>
+
+  <p>Of Jacotot's method, which had some vogue in Paris, the principle was
+  <i>Tout est dans tout</i>,<a name="NtA_608"
+  href="#Nt_608"><sup>[608]</sup></a> and the process <i>Apprendre quelque
+  chose, et à y rapporter tout le reste</i>.<a name="NtA_609"
+  href="#Nt_609"><sup>[609]</sup></a> The first tract has a proposition in
+  conic sections and its preliminaries: the second has twenty exercises, of
+  which the first is finding the greatest common measure of two numbers,
+  and the last is the motion of a point on a surface, acted on by given
+  forces. This is topped up with the problem of sound in a tube, and a
+  slice of Laplace's theory of the tides. All to be studied until known by
+  heart, and all the rest will come, or at least join on easily when it
+  comes. There is much truth in the assertion that new knowledge <!-- Page
+  279 --><span class="pagenum"><a name="page279"></a>[279]</span>hooks on
+  easily to a little of the old, thoroughly mastered. The day is coming
+  when it will be found out that crammed erudition, got up for
+  examinations, does not cast out any hooks for more.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Lettre à MM. les Membres de l'Académie Royale des Sciences, contenant
+  un développement de la réfutation du système de la gravitation
+  universelle, qui leur a été présentée le 30 août, 1830. Par Félix
+  Passot.<a name="NtA_610" href="#Nt_610"><sup>[610]</sup></a> Paris, 1830,
+  8vo.</p>
+
+</blockquote>
+
+  <p>Works of this sort are less common in France than in England. In
+  France there is only the Academy of Sciences to go to: in England there
+  is a reading public out of the Royal Society, &amp;c.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A DISCOURSE ON PROBABILITY.</p>
+
+  <p>About 1830 was published, in the <i>Library of Useful Knowledge</i>,
+  the tract on <i>Probability</i>, the joint work of the late Sir John
+  Lubbock<a name="NtA_611" href="#Nt_611"><sup>[611]</sup></a> and Mr.
+  Drinkwater (Bethune).<a name="NtA_612"
+  href="#Nt_612"><sup>[612]</sup></a> It is one of the best elementary
+  openings of the subject. A binder put my name on the outside (the work
+  was anonymous) and the consequence was that nothing could drive out of
+  people's heads that it was written by me. I do not know how many denials
+  I have made, from a passage in one of my own works to a letter in the
+  <i>Times</i>: and I am not sure that I have succeeded in establishing the
+  truth, even now. I accordingly note the fact once more. But as a book has
+  no right here unless it contain a paradox&mdash;or thing counter to
+  general opinion or practice&mdash;I will produce two small ones. Sir John
+  Lubbock, with whom lay the executive arrangement, had a strong objection
+  to the last word in "Theory of Probabilities," he maintained that the
+  singular <i>probability</i>, should be used; and I hold him quite
+  right.</p>
+
+<p><!-- Page 280 --><span class="pagenum"><a name="page280"></a>[280]</span></p>
+
+  <p>The second case was this: My friend Sir J.&nbsp;L., with a large cluster of
+  intellectual qualities, and another of social qualities, had one point of
+  character which I will not call bad and cannot call good; he never used a
+  slang expression. To such a length did he carry his dislike, that he
+  could not bear <i>head</i> and <i>tail</i>, even in a work on games of
+  chance: so he used <i>obverse</i> and <i>reverse</i>. I stared when I
+  first saw this: but, to my delight, I found that the force of
+  circumstances beat him at last. He was obliged to take an example from
+  the race-course, and the name of one of the horses was <i>Bessy
+  Bedlam</i>! And he did not put her down as <i>Elizabeth Bethlehem</i>,
+  but forced himself to follow the jockeys.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>[Almanach Romain sur la Loterie Royale de France, ou les Etrennes
+  nécessaires aux Actionnaires et Receveurs de la dite Loterie. Par M.
+  Menut de St.-Mesmin. Paris, 1830. 12mo.</p>
+
+</blockquote>
+
+  <p>This book contains all the drawings of the French lottery (two or
+  three, each month) from 1758 to 1830. It is intended for those who
+  thought they could predict the future drawings from the past: and various
+  sets of <i>sympathetic</i> numbers are given to help them. The principle
+  is, that anything which has not happened for a long time must be soon to
+  come. At <i>rouge et noir</i>, for example, when the red has won five
+  times running, sagacious gamblers stake on the black, for they think the
+  turn which must come at last is nearer than it was. So it is: but
+  observation would have shown that if a large number of those cases had
+  been registered which show a run of five for the red, the next game would
+  just as often have made the run into six as have turned in favor of the
+  black. But the gambling reasoner is incorrigible: if he would but take to
+  squaring the circle, what a load of misery would be saved. A writer of
+  1823, who appeared to be thoroughly acquainted with the gambling of Paris
+  and London, says that the gamesters by <!-- Page 281 --><span
+  class="pagenum"><a name="page281"></a>[281]</span>profession are haunted
+  by a secret foreboding of their future destruction, and seem as if they
+  said to the banker at the table, as the gladiators said to the emperor,
+  <i>Morituri te salutant</i>.<a name="NtA_613"
+  href="#Nt_613"><sup>[613]</sup></a></p>
+
+  <p>In the French lottery, five numbers out of ninety were drawn at a
+  time. Any person, in any part of the country, might stake any sum upon
+  any event he pleased, as that 27 should be drawn; that 42 and 81 should
+  be drawn; that 42 and 81 should be drawn, and 42 first; and so on up to a
+  <i>quine déterminé</i>, if he chose, which is betting on five given
+  numbers in a given order. Thus, in July, 1821, one of the drawings
+  was</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>8 &nbsp; 46 &nbsp; 16 &nbsp; 64 &nbsp; 13.</p>
+    </div>
+  </div>
+  <p>A gambler had actually predicted the five numbers (but not their
+  order), and won 131,350 francs on a trifling stake. M. Menut seems to
+  insinuate that the hint what numbers to choose was given at his own
+  office. Another won 20,852 francs on the quaterne, 8, 16, 46, 64, in this
+  very drawing. These gains, of course, were widely advertised: of the
+  multitudes who lost nothing was said. The enormous number of those who
+  played is proved to all who have studied chances arithmetically by the
+  numbers of simple quaternes which were gained: in 1822, fourteen; in
+  1823, six; in 1824, sixteen; in 1825, nine, &amp;c.</p>
+
+  <p>The paradoxes of what is called chance, or hazard, might themselves
+  make a small volume. All the world understands that there is a long run,
+  a general average; but great part of the world is surprised that this
+  general average should be computed and predicted. There are many
+  remarkable cases of verification; and one of them relates to the
+  quadrature of the circle. I give some account of this and another. Throw
+  a penny time after time until <i>head</i> arrives, which it will do
+  before long: let this be called a <i>set</i>. Accordingly, H is the
+  smallest set, TH the next smallest, then TTH, &amp;c. For abbreviation,
+  let a set in which seven <i>tails</i> <!-- Page 282 --><span
+  class="pagenum"><a name="page282"></a>[282]</span>occur before
+  <i>head</i> turns up be T<sup>7</sup>H. In an immense number of trials of
+  sets, about half will be H; about a quarter TH; about an eighth,
+  T<sup>2</sup>H. Buffon<a name="NtA_614"
+  href="#Nt_614"><sup>[614]</sup></a> tried 2,048 sets; and several have
+  followed him. It will tend to illustrate the principle if I give all the
+  results; namely, that many trials will with moral certainty show an
+  approach&mdash;and the greater the greater the number of trials&mdash;to
+  that average which sober reasoning predicts. In the first column is the
+  most likely number of the theory: the next column gives Buffon's result;
+  the three next are results obtained from trial by correspondents of mine.
+  In each case the number of trials is 2,048.</p>
+
+<table class="nobctr" summary="Coin tossing trials" title="Coin tossing trials">
+<tr><td>H</td><td align="right">1,024</td><td align="right">1,061</td><td align="right">1,048</td><td align="right">1,017</td><td align="right">1,039</td></tr>
+<tr><td>TH</td><td align="right">512</td><td align="right">494</td><td align="right">507</td><td align="right">547</td><td align="right">480</td></tr>
+<tr><td>T<sup>2</sup>H</td><td align="right">256</td><td align="right">232</td><td align="right">248</td><td align="right">235</td><td align="right">267</td></tr>
+<tr><td>T<sup>3</sup>H</td><td align="right">128</td><td align="right">137</td><td align="right">99</td><td align="right">118</td><td align="right">126</td></tr>
+<tr><td>T<sup>4</sup>H</td><td align="right">64</td><td align="right">56</td><td align="right">71</td><td align="right">72</td><td align="right">67</td></tr>
+<tr><td>T<sup>5</sup>H</td><td align="right">32</td><td align="right">29</td><td align="right">38</td><td align="right">32</td><td align="right">33</td></tr>
+<tr><td>T<sup>6</sup>H</td><td align="right">16</td><td align="right">25</td><td align="right">17</td><td align="right">10</td><td align="right">19</td></tr>
+<tr><td>T<sup>7</sup>H</td><td align="right">8</td><td align="right">8</td><td align="right">9</td><td align="right">9</td><td align="right">10</td></tr>
+<tr><td>T<sup>8</sup>H</td><td align="right">4</td><td align="right">6</td><td align="right">5</td><td align="right">3</td><td align="right">3</td></tr>
+<tr><td>T<sup>9</sup>H</td><td align="right">2</td><td align="right">&nbsp;</td><td align="right">3</td><td align="right">2</td><td align="right">4</td></tr>
+<tr><td>T<sup>10</sup>H</td><td align="right">1</td><td align="right">&nbsp;</td><td align="right">1</td><td align="right">1</td></tr>
+<tr><td>T<sup>11</sup>H</td><td align="right">&nbsp;</td><td align="right">&nbsp;</td><td align="right">0</td><td align="right">1</td></tr>
+<tr><td>T<sup>12</sup>H</td><td align="right">&nbsp;</td><td align="right">&nbsp;</td><td align="right">0</td><td align="right">0</td></tr>
+<tr><td>T<sup>13</sup>H</td><td align="right">1</td><td align="right">&nbsp;</td><td align="right">1</td><td align="right">0</td></tr>
+<tr><td>T<sup>14</sup>H</td><td align="right">&nbsp;</td><td align="right">&nbsp;</td><td align="right">0</td><td align="right">0</td></tr>
+<tr><td>T<sup>15</sup>H</td><td align="right">&nbsp;</td><td align="right">&nbsp;</td><td align="right">1</td><td align="right">1</td></tr>
+<tr><td>&amp;c.</td><td align="right">&nbsp;</td><td align="right">&nbsp;</td><td align="right">0</td><td align="right">0</td></tr>
+<tr><td>&nbsp;</td><td align="right">&mdash;&mdash;</td><td align="right">&mdash;&mdash;</td><td align="right">&mdash;&mdash;</td><td align="right">&mdash;&mdash;</td><td align="right">&mdash;&mdash;</td></tr>
+<tr><td>&nbsp;</td><td align="right"> &nbsp; 2,048</td><td align="right"> &nbsp; 2,048</td><td align="right"> &nbsp; 2,048</td><td align="right"> &nbsp; 2,048</td><td align="right"> &nbsp; 2,048</td></tr>
+</table>
+
+<p><!-- Page 283 --><span class="pagenum"><a name="page283"></a>[283]</span></p>
+
+  <p>In very many trials, then, we may depend upon something like the
+  predicted average. Conversely, from many trials we may form a guess at
+  what the average will be. Thus, in Buffon's experiment the 2,048 first
+  throws of the sets gave <i>head</i> in 1,061 cases: we have a right to
+  infer that in the long run something like 1,061 out of 2,048 is the
+  proportion of heads, even before we know the reasons for the equality of
+  chance, which tell us that 1,024 out of 2,048 is the real truth. I now
+  come to the way in which such considerations have led to a mode in which
+  mere pitch-and-toss has given a more accurate approach to the quadrature
+  of the circle than has been reached by some of my paradoxers. What would
+  my friend<a name="NtA_615" href="#Nt_615"><sup>[615]</sup></a> in No. 14
+  have said to this? The method is as follows: Suppose a planked floor of
+  the usual kind, with thin visible seams between the planks. Let there be
+  a thin straight rod, or wire, not so long as the breadth of the plank.
+  This rod, being tossed up at hazard, will either fall quite clear of the
+  seams, or will lay across one seam. Now Buffon, and after him Laplace,
+  proved the following: That in the long run the fraction of the whole
+  number of trials in which a seam is intersected will be the fraction
+  which twice the length of the rod is of the circumference of the circle
+  having the breadth of a plank for its diameter. In 1855 Mr.
+  <i>Ambrose</i> Smith, of Aberdeen, made 3,204 trials with a rod
+  three-fifths of the distance between the planks: there were 1,213 clear
+  intersections, and 11 contacts on which it was difficult to decide.
+  Divide these contacts equally, and we have 1,218½ to 3,204 for the ratio
+  of 6 to 5<span class="grk">&pi;</span>, presuming that the greatness of
+  the number of trials gives something near to the final average, or result
+  in the long run: this gives <span class="grk">&pi;</span> = 3.1553. If
+  all the 11 contacts had been treated as intersections, the result would
+  have been <!-- Page 284 --><span class="pagenum"><a
+  name="page284"></a>[284]</span><span class="grk">&pi;</span> = 3.1412,
+  exceedingly near. A pupil of mine made 600 trials with a rod of the
+  length between the seams, and got <span class="grk">&pi;</span> =
+  3.137.</p>
+
+  <p>This method will hardly be believed until it has been repeated so
+  often that "there never could have been any doubt about it."</p>
+
+  <p>The first experiment strongly illustrates a truth of the theory, well
+  confirmed by practice: whatever can happen will happen if we make trials
+  enough. Who would undertake to throw tail eight times running?
+  Nevertheless, in the 8,192 sets tail 8 times running occurred 17 times; 9
+  times running, 9 times; 10 times running, twice; 11 times and 13 times,
+  each once; and 15 times twice.]</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON CURIOSITIES OF <span class="grk">&pi;</span>.</p>
+
+  <p>1830. The celebrated interminable fraction 3.14159..., which the
+  mathematician calls <span class="grk">&pi;</span>, is the ratio of the
+  circumference to the diameter. But it is thousands of things besides. It
+  is constantly turning up in mathematics: and if arithmetic and algebra
+  had been studied without geometry, <span class="grk">&pi;</span> must
+  have come in somehow, though at what stage or under what name must have
+  depended upon the casualties of algebraical invention. This will readily
+  be seen when it is stated that <span class="grk">&pi;</span> is nothing
+  but four times the series</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...</p>
+    </div>
+  </div>
+  <p><i>ad infinitum</i>.<a name="NtA_616"
+  href="#Nt_616"><sup>[616]</sup></a> It would be wonderful if so simple a
+  series <!-- Page 285 --><span class="pagenum"><a
+  name="page285"></a>[285]</span>had but one kind of occurrence. As it is,
+  our trigonometry being founded on the circle, <span
+  class="grk">&pi;</span> first appears as the ratio stated. If, for
+  instance, a deep study of probable fluctuation from average had preceded,
+  <span class="grk">&pi;</span> might have emerged as a number perfectly
+  indispensable in such problems as: What is the chance of the number of
+  aces lying between a million + <i>x</i> and a million - <i>x</i>, when
+  six million of throws are made with a die? I have not gone into any
+  detail of all those cases in which the paradoxer finds out, by his
+  unassisted acumen, that results of mathematical investigation <i>cannot
+  be</i>: in fact, this discovery is only an accompaniment, though a
+  necessary one, of his paradoxical statement of that which <i>must be</i>.
+  Logicians are beginning to see that the notion of <i>horse</i> is
+  inseparably connected with that of <i>non-horse</i>: that the first
+  without the second would be no notion at all. And it is clear that the
+  positive affirmation of that which contradicts mathematical demonstration
+  cannot but be accompanied by a declaration, mostly overtly made, that
+  demonstration is false. If the mathematician were interested in punishing
+  this indiscretion, he could make his denier ridiculous by inventing
+  asserted results which would completely take him in.</p>
+
+  <p>More than thirty years ago I had a friend, now long gone, who was a
+  mathematician, but not of the higher branches: he was, <i>inter alia</i>,
+  thoroughly up in all that relates to mortality, life assurance, &amp;c.
+  One day, explaining to him how it should be ascertained what the chance
+  is of the survivors of a large number of persons now alive lying between
+  given limits of number at the end of a certain time, I came, of course
+  upon the introduction of <span class="grk">&pi;</span>, which I could
+  only describe as the ratio of the circumference of a circle to its
+  diameter. "Oh, my dear friend! that must be a delusion; what can the
+  circle have to do with the numbers alive at the end of a given
+  time?"&mdash;"I cannot demonstrate it to you; but it is
+  demonstrated."&mdash;"Oh! stuff! I think you can prove anything with your
+  differential calculus: figment, <!-- Page 286 --><span class="pagenum"><a
+  name="page286"></a>[286]</span>depend upon it." I said no more; but, a
+  few days afterwards, I went to him and very gravely told him that I had
+  discovered the law of human mortality in the Carlisle Table, of which he
+  thought very highly. I told him that the law was involved in this
+  circumstance. Take the table of expectation of life, choose any age, take
+  its expectation and make the nearest integer a new age, do the same with
+  that, and so on; begin at what age you like, you are sure to end at the
+  place where the age past is equal, or most nearly equal, to the
+  expectation to come. "You don't mean that this always
+  happens?"&mdash;"Try it." He did try, again and again; and found it as I
+  said. "This is, indeed, a curious thing; this <i>is</i> a discovery." I
+  might have sent him about trumpeting the law of life: but I contented
+  myself with informing him that the same thing would happen with any table
+  whatsoever in which the first column goes up and the second goes down;
+  and that if a proficient in the higher mathematics chose to palm a
+  figment upon him, he could do without the circle: <i>à corsaire, corsaire
+  et demi</i>,<a name="NtA_617" href="#Nt_617"><sup>[617]</sup></a> the
+  French proverb says. "Oh!" it was remarked, "I see, this was Milne!"<a
+  name="NtA_618" href="#Nt_618"><sup>[618]</sup></a> It was <i>not</i>
+  Milne: I remember well showing the formula to him some time afterwards.
+  He raised no difficulty about <span class="grk">&pi;</span>; he knew the
+  forms of Laplace's results, and he was much interested. Besides, Milne
+  never said stuff! and figment! And he would not have been taken in: he
+  would have quietly tried it with the Northampton and all the other
+  tables, and would have got at the truth.</p>
+
+<p><!-- Page 287 --><span class="pagenum"><a name="page287"></a>[287]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">EUCLID WITHOUT AXIOMS.</p>
+
+<blockquote class="b1n">
+
+  <p>The first book of Euclid's Elements. With alterations and familiar
+  notes. Being an attempt to get rid of axioms altogether; and to establish
+  the theory of parallel lines, without the introduction of any principle
+  not common to other parts of the elements. By a member of the University
+  of Cambridge. Third edition. In usum serenissimæ filiolæ. London,
+  1830.</p>
+
+</blockquote>
+
+  <p>The author was Lieut. Col. (now General) Perronet Thompson,<a
+  name="NtA_619" href="#Nt_619"><sup>[619]</sup></a> the author of the
+  "Catechism on the Corn Laws." I reviewed the fourth edition&mdash;which
+  had the name of "Geometry without Axioms," 1833&mdash;in the quarterly
+  <i>Journal of Education</i> for January, 1834. Col. Thompson, who then
+  was a contributor to&mdash;if not editor of&mdash;the <i>Westminster
+  Review</i>, replied in an article the authorship of which could not be
+  mistaken.</p>
+
+  <p>Some more attempts upon the problem, by the same author, will be found
+  in the sequel. They are all of acute and legitimate speculation; but they
+  do not conquer the difficulty in the manner demanded by the conditions of
+  the problem. The paradox of parallels does not contribute much to my
+  pages: its cases are to be found for the most part in geometrical
+  systems, or in notes to them. Most of them consist in the proposal of
+  additional postulates; some are attempts to do without any new postulate.
+  Gen. Perronet Thompson, whose paradoxes are always constructed on much
+  study of previous writers, has collected in the work above named, a
+  budget of attempts, the heads of which are in the <i>Penny</i> and
+  <i>English Cyclopædias</i>, at "Parallels." He has given thirty
+  instances, selected from what he had found.<a name="NtA_620"
+  href="#Nt_620"><sup>[620]</sup></a></p>
+
+<p><!-- Page 288 --><span class="pagenum"><a name="page288"></a>[288]</span></p>
+
+  <p>Lagrange,<a name="NtA_621" href="#Nt_621"><sup>[621]</sup></a> in one
+  of the later years of his life, imagined that he had overcome the
+  difficulty. He went so far as to write a paper, which he took with him to
+  the Institute, and began to read it. But in the first paragraph something
+  struck him which he had not observed: he muttered <i>Il faut que j'y
+  songe encore</i>,<a name="NtA_622" href="#Nt_622"><sup>[622]</sup></a>
+  and put the paper in his pocket.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE LUNAR CAUSTIC JOKE.</p>
+
+  <p>The following paragraph appeared in the <i>Morning Post</i>, May 4,
+  1831:</p>
+
+  <p>"We understand that although, owing to circumstances with which the
+  public are not concerned, Mr. Goulburn<a name="NtA_623"
+  href="#Nt_623"><sup>[623]</sup></a> declined becoming a candidate for
+  University honors, that his scientific attainments are far from
+  inconsiderable. He is well known to be the author of an essay in the
+  Philosophical Transactions on the accurate rectification of a circular
+  arc, and of an investigation of the equation of a lunar caustic&mdash;a
+  problem likely to become of great use in nautical astronomy."</p>
+
+<p><!-- Page 289 --><span class="pagenum"><a name="page289"></a>[289]</span></p>
+
+  <p>This hoax&mdash;which would probably have succeeded with any
+  journal&mdash;was palmed upon the <i>Morning Post</i>, which supported
+  Mr. Goulburn, by some Cambridge wags who supported Mr. Lubbock, the other
+  candidate for the University of Cambridge. Putting on the usual
+  concealment, I may say that I always suspected Dr-nkw-t-r B-th-n-<a
+  name="NtA_624" href="#Nt_624"><sup>[624]</sup></a> of having a share in
+  the matter. The skill of the hoax lies in avoiding the words "quadrature
+  of the circle," which all know, and speaking of "the accurate
+  rectification of a circular arc," which all do not know for its synonyme.
+  The <i>Morning Post</i> next day gave a reproof to hoaxers in general,
+  without referring to any particular case. It must be added, that although
+  there are <i>caustics</i> in mathematics, there is no <i>lunar</i>
+  caustic.</p>
+
+  <p>So far as Mr. Goulburn was concerned, the above was poetic justice. He
+  was the minister who, in old time, told a deputation from the
+  Astronomical Society that the Government "did not care twopence for all
+  the science in the country." There may be some still alive who remember
+  this: I heard it from more than one of those who were present, and are
+  now gone. Matters are much changed. I was thirty years in office at the
+  Astronomical Society; and, to my certain knowledge, every Government of
+  that period, Whig and Tory, showed itself ready to help with influence
+  when wanted, and with money whenever there was an answer for the House of
+  Commons. The following correction subsequently appeared. Referring to the
+  hoax about Mr. Goulburn, Messrs. C.&nbsp;H. and Thompson Cooper<a
+  name="NtA_625" href="#Nt_625"><sup>[625]</sup></a> have corrected an
+  error, by stating that the election which gave rise to the hoax was that
+  in which Messrs. Goulburn <!-- Page 290 --><span class="pagenum"><a
+  name="page290"></a>[290]</span>and Yates Peel<a name="NtA_626"
+  href="#Nt_626"><sup>[626]</sup></a> defeated Lord Palmerston<a
+  name="NtA_627" href="#Nt_627"><sup>[627]</sup></a> and Mr. Cavendish.<a
+  name="NtA_628" href="#Nt_628"><sup>[628]</sup></a> They add that Mr.
+  Gunning, the well-known Esquire Bedell of the University, attributed the
+  hoax to the late Rev. R. Sheepshanks, to whom, they state, are also
+  attributed certain clever fictitious biographies&mdash;of public men, as
+  I understand it&mdash;which were palmed upon the editor of the
+  <i>Cambridge Chronicle</i>, who never suspected their genuineness to the
+  day of his death. Being in most confidential intercourse with Mr.
+  Sheepshanks,<a name="NtA_629" href="#Nt_629"><sup>[629]</sup></a> both at
+  the time and all the rest of his life (twenty-five years), and never
+  heard him allude to any such things&mdash;which were not in his line,
+  though he had satirical power of quite another <!-- Page 291 --><span
+  class="pagenum"><a name="page291"></a>[291]</span>kind&mdash;I feel
+  satisfied he had nothing to do with them. I may add that others, his
+  nearest friends, and also members of his family, never heard him allude
+  to these hoaxes as their author, and disbelieve his authorship as much as
+  I do myself. I say this not as imputing any blame to the true author,
+  such hoaxes being fair election jokes in all time, but merely to put the
+  saddle off the wrong horse, and to give one more instance of the
+  insecurity of imputed authorship. Had Mr. Sheepshanks ever told me that
+  he had perpetrated the hoax, I should have had no hesitation in giving it
+  to him. I consider all clever election squibs, free from bitterness and
+  personal imputation, as giving the multitude good channels for the vent
+  of feelings which but for them would certainly find bad ones.</p>
+
+  <p>[But I now suspect that Mr. Babbage<a name="NtA_630"
+  href="#Nt_630"><sup>[630]</sup></a> had some hand in the hoax. He gives
+  it in his "Passages, &amp;c." and is evidently writing from memory, for
+  he gives the wrong year. But he has given the paragraph, though not
+  accurately, yet with such a recollection of the points as brings
+  suspicion of the authorship upon him, perhaps in conjunction with D.&nbsp;B.<a
+  name="NtA_631" href="#Nt_631"><sup>[631]</sup></a> Both were on
+  Cavendish's committee. Mr. Babbage adds, that "late one evening a cab
+  drove up in hot haste to the office of the <i>Morning Post</i>, delivered
+  the copy as coming from Mr. Goulburn's committee, and at the same time
+  ordered fifty extra copies of the <i>Post</i> to be sent next morning to
+  their committee-room." I think the man&mdash;the only one I ever heard
+  of&mdash;who knew all about the cab and the extra copies must have known
+  more.]</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON M. DEMONVILLE.</p>
+
+  <p><i>Demonville.</i>&mdash;A Frenchman's Christian name is his own
+  secret, unless there be two of the surname. M. Demonville is a very good
+  instance of the difference between a <!-- Page 292 --><span
+  class="pagenum"><a name="page292"></a>[292]</span>French and English
+  discoverer. In England there is a public to listen to discoveries in
+  mathematical subjects made without mathematics: a public which will hear,
+  and wonder, and think it possible that the pretensions of the discoverer
+  have some foundation. The unnoticed man may possibly be right: and the
+  old country-town reputation which I once heard of, attaching to a man who
+  "had written a book about the signs of the zodiac which all the
+  philosophers in London could not answer," is fame as far as it goes.
+  Accordingly, we have plenty of discoverers who, even in astronomy,
+  pronounce the learned in error because of mathematics. In France, beyond
+  the sphere of influence of the Academy of Sciences, there is no one to
+  cast a thought upon the matter: all who take the least interest repose
+  entire faith in the Institute. Hence the French discoverer turns all his
+  thoughts to the Institute, and looks for his only hearing in that
+  quarter. He therefore throws no slur upon the means of knowledge, but
+  would say, with M. Demonville: "A l'égard de M. Poisson,<a name="NtA_632"
+  href="#Nt_632"><sup>[632]</sup></a> j'envie loyalement la millième partie
+  de ses connaissances mathématiques, pour prouver mon systême d'astronomie
+  aux plus incrédules."<a name="NtA_633"
+  href="#Nt_633"><sup>[633]</sup></a> This system is that the only bodies
+  of our system are the earth, the sun, and the moon; all the others being
+  illusions, caused by reflection of the sun and moon from the ice of the
+  polar regions. In mathematics, addition and subtraction are for men;
+  multiplication and division, which are in truth creation and destruction,
+  are prerogatives of deity. But <i>nothing</i> multiplied by
+  <i>nothing</i> is <i>one</i>. M. Demonville obtained an introduction to
+  William the Fourth, who desired the opinion of the Royal Society upon his
+  system: the <!-- Page 293 --><span class="pagenum"><a
+  name="page293"></a>[293]</span>answer was very brief. The King was quite
+  right; so was the Society: the fault lay with those who advised His
+  Majesty on a matter they knew nothing about. The writings of M.
+  Demonville in my possession are as follows.<a name="NtA_634"
+  href="#Nt_634"><sup>[634]</sup></a> The dates&mdash;which were only on
+  covers torn off in binding&mdash;were about 1831-34:</p>
+
+  <p><i>Petit cours d'astronomie</i><a name="NtA_635"
+  href="#Nt_635"><sup>[635]</sup></a> followed by <i>Sur l'unité
+  mathématique.</i>&mdash;<i>Principes de la physique de la création
+  implicitement admis dans la notice sur le tonnerre par M.
+  Arago.</i>&mdash;<i>Question de longitude sur mer.</i><a name="NtA_636"
+  href="#Nt_636"><sup>[636]</sup></a>&mdash;<i>Vrai système du monde</i><a
+  name="NtA_637" href="#Nt_637"><sup>[637]</sup></a> (pp. 92). Same title,
+  four pages, small type. Same title, four pages, addressed to the British
+  Association. Same title, four pages, addressed to M. Mathieu. Same title,
+  four pages, on M. Bouvard's report.&mdash;<i>Résumé de la physique de la
+  création; troisième partie du vrai système du monde.</i><a name="NtA_638"
+  href="#Nt_638"><sup>[638]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">PARSEY'S PARADOX.</p>
+
+<blockquote class="b1n">
+
+  <p>The quadrature of the circle discovered, by Arthur Parsey,<a
+  name="NtA_639" href="#Nt_639"><sup>[639]</sup></a> author of the 'art of
+  miniature painting.' Submitted to the consideration of the Royal Society,
+  on whose protection the author humbly throws himself. London, 1832,
+  8vo.</p>
+
+</blockquote>
+
+  <p>Mr. Parsey was an artist, who also made himself conspicuous by a new
+  view of perspective. Seeing that the sides of a tower, for instance,
+  would appear to meet in a point if the tower were high enough, he thought
+  that these sides ought to slope to one another in the picture. On this
+  <!-- Page 294 --><span class="pagenum"><a
+  name="page294"></a>[294]</span>theory he published a small work, of which
+  I have not the title, with a Grecian temple in the frontispiece, stated,
+  if I remember rightly, to be the first picture which had ever been drawn
+  in true perspective. Of course the building looked very Egyptian, with
+  its sloping sides. The answer to his notion is easy enough. What is
+  called the picture is not the picture from which the mind takes its
+  perception; that picture is on the retina. The <i>intermediate</i>
+  picture, as it may be called&mdash;the human artist's work&mdash;is
+  itself seen perspectively. If the tower were so high that the sides,
+  though parallel, appeared to meet in a point, the picture must also be so
+  high that the <i>picture-sides</i>, though parallel, would appear to meet
+  in a point. I never saw this answer given, though I have seen and heard
+  the remarks of artists on Mr. Parsey's work. I am inclined to think it is
+  commonly supposed that the artist's picture is the representation which
+  comes before the mind: this is not true; we might as well say the same of
+  the object itself. In July 1831, reading an article on squaring the
+  circle, and finding that there was a difficulty, he set to work, got a
+  light denied to all mathematicians in&mdash;some would say
+  through&mdash;a crack, and advertised in the <i>Times</i> that he had
+  done the trick. He then prepared this work, in which, those who read it
+  will see how, he showed that 3.14159... should be 3.0625. He might have
+  found out his error by <i>stepping</i> a draughtsman's circle with the
+  compasses.</p>
+
+  <p>Perspective has not had many paradoxes. The only other one I remember
+  is that of a writer on perspective, whose name I forget, and whose four
+  pages I do not possess. He circulated remarks on my notes on the subject,
+  published in the <i>Athenæum</i>, in which he denies that the
+  stereographic projection is a case of perspective, the reason being that
+  the whole hemisphere makes too large a picture for the eye conveniently
+  to grasp at once. That is to say, it is no perspective because there is
+  too much perspective. <!-- Page 295 --><span class="pagenum"><a
+  name="page295"></a>[295]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON A COUPLE OF GEOMETRIES.</p>
+
+<blockquote class="b1n">
+
+  <p>Principles of Geometry familiarly illustrated. By the Rev. W.
+  Ritchie,<a name="NtA_640" href="#Nt_640"><sup>[640]</sup></a> LL.D.
+  London, 1833, 12mo.</p>
+
+  <p>A new Exposition of the system of Euclid's Elements, being an attempt
+  to establish his work on a different basis. By Alfred Day,<a
+  name="NtA_641" href="#Nt_641"><sup>[641]</sup></a> LL.D. London, 1839,
+  12mo.</p>
+
+</blockquote>
+
+  <p>These works belong to a small class which have the peculiarity of
+  insisting that in the general propositions of geometry a proposition
+  gives its converse: that "Every B is A" follows from "Every A is B." Dr.
+  Ritchie says, "If it be proved that the equality of two of the angles of
+  a triangle depends <i>essentially</i> upon the equality of the opposite
+  sides, it follows that the equality of opposite sides depends
+  <i>essentially</i> on the equality of the angles." Dr. Day puts it as
+  follows:</p>
+
+  <p>"That the converses of Euclid, so called, where no particular
+  limitation is specified or implied in the leading proposition, more than
+  in the converse, must be necessarily true; for as by the nature of the
+  reasoning the leading proposition must be universally true, should the
+  converse be not so, it cannot be so universally, but has at least all the
+  exceptions conveyed in the leading proposition, and the case is therefore
+  unadapted to geometric reasoning; or, what is the same thing, by the very
+  nature of geometric reasoning, the particular exceptions to the extended
+  converse must be identical with some one or other of the cases under the
+  universal affirmative proposition with which we set forth, which is
+  absurd."</p>
+
+<p><!-- Page 296 --><span class="pagenum"><a name="page296"></a>[296]</span></p>
+
+  <p>On this I cannot help transferring to my reader the words of the Pacha
+  when he orders the bastinado,&mdash;May it do you good! A rational study
+  of logic is much wanted to show many mathematicians, of all degrees of
+  proficiency, that there is nothing in the <i>reasoning</i> of mathematics
+  which differs from other reasoning. Dr. Day repeated his argument in <i>A
+  Treatise on Proportion</i>, London, 1840, 8vo. Dr. Ritchie was a very
+  clear-headed man. He published, in 1818, a work on arithmetic, with
+  rational explanations. This was too early for such an improvement, and
+  nearly the whole of his excellent work was sold as waste paper. His
+  elementary introduction to the Differential Calculus was drawn up while
+  he was learning the subject late in life. Books of this sort are often
+  very effective on points of difficulty.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">NEWTON AGAIN OBLITERATED.</p>
+
+<blockquote class="b1n">
+
+  <p>Letter to the Royal Astronomical Society in refutation of Mistaken
+  Notions held in common, by the Society, and by all the Newtonian
+  philosophers. By Capt. Forman,<a name="NtA_642"
+  href="#Nt_642"><sup>[642]</sup></a> R.N. Shepton-Mallet, 1833, 8vo.</p>
+
+</blockquote>
+
+  <p>Capt. Forman wrote against the whole system of gravitation, and got no
+  notice. He then wrote to Lord Brougham, Sir J. Herschel, and others I
+  suppose, desiring them to procure notice of his books in the reviews:
+  this not being acceded to, he wrote (in print) to Lord John Russell<a
+  name="NtA_643" href="#Nt_643"><sup>[643]</sup></a> to complain of their
+  "dishonest" conduct. He then sent a manuscript letter to the Astronomical
+  Society, inviting controversy: he was answered by a recommendation to
+  study <!-- Page 297 --><span class="pagenum"><a
+  name="page297"></a>[297]</span>dynamics. The above pamphlet was the
+  consequence, in which, calling the Council of the Society "craven
+  dunghill cocks," he set them right about their doctrines. From all I can
+  learn, the life of a worthy man and a creditable officer was completely
+  embittered by his want of power to see that no person is bound in reason
+  to enter into controversy with every one who chooses to invite him to the
+  field. This mistake is not peculiar to philosophers, whether of orthodoxy
+  or paradoxy; a majority of educated persons imply, by their modes of
+  proceeding, that no one has a right to any opinion which he is not
+  prepared to defend against all comers.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>David and Goliath, or an attempt to prove that the Newtonian system of
+  Astronomy is directly opposed to the Scriptures. By Wm. Lauder,<a
+  name="NtA_644" href="#Nt_644"><sup>[644]</sup></a> Sen., Mere, Wilts.
+  Mere, 1833, 12mo.</p>
+
+</blockquote>
+
+  <p>Newton is Goliath; Mr. Lauder is David. David took five pebbles; Mr.
+  Lauder takes five arguments. He expects opposition; for Paul and Jesus
+  both met with it.</p>
+
+  <p>Mr. Lauder, in his comparison, seems to put himself in the divinely
+  inspired class. This would not be a fair inference in every case; but we
+  know not what to think when we remember that a tolerable number of
+  cyclometers have attributed their knowledge to direct revelation. The
+  works of this class are very scarce; I can only mention one or two from
+  Montucla.<a name="NtA_645" href="#Nt_645"><sup>[645]</sup></a> Alphonso
+  Cano de Molina,<a name="NtA_646" href="#Nt_646"><sup>[646]</sup></a> in
+  the last century, upset all Euclid, and squared the circle upon the
+  ruins; he found a follower, Janson, who translated him from Spanish into
+  Latin. He declared that he believed in Euclid, until God, who humbles the
+  proud, taught him better. One Paul Yvon, called from his estate de la
+  Leu, a merchant at Rochelle, supported by his book-keeper, M. Pujos, and
+  a <!-- Page 298 --><span class="pagenum"><a
+  name="page298"></a>[298]</span>Scotchman, John Dunbar, solved the problem
+  by divine grace, in a manner which was to convert all Jews, Infidels,
+  etc. There seem to have been editions of his work in 1619 and 1628, and a
+  controversial "Examen" in 1630, by Robert Sara. There was a noted
+  discussion, in which Mydorge,<a name="NtA_647"
+  href="#Nt_647"><sup>[647]</sup></a> Hardy,<a name="NtA_648"
+  href="#Nt_648"><sup>[648]</sup></a> and others took part against de la
+  Leu. I cannot find this name either in Lipenius<a name="NtA_649"
+  href="#Nt_649"><sup>[649]</sup></a> or Murhard,<a name="NtA_650"
+  href="#Nt_650"><sup>[650]</sup></a> and I should not have known the dates
+  if it had not been for one of the keenest bibliographers of any time, my
+  friend Prince Balthasar Boncompagni,<a name="NtA_651"
+  href="#Nt_651"><sup>[651]</sup></a> who is trying to find copies of the
+  works, and has managed to find copies of the titles. In 1750, Henry
+  Sullamar, an Englishman, squared the circle by the number of the Beast:
+  he published a pamphlet every two or three years; but I cannot find any
+  mention of him in English works.<a name="NtA_652"
+  href="#Nt_652"><sup>[652]</sup></a> In France, in 1753, M. de Causans,<a
+  name="NtA_653" href="#Nt_653"><sup>[653]</sup></a> of the Guards, cut a
+  circular piece of turf, squared it, and <!-- Page 299 --><span
+  class="pagenum"><a name="page299"></a>[299]</span>deduced original sin
+  and the Trinity. He found out that the circle was equal to the square in
+  which it is inscribed; and he offered a reward for detection of any
+  error, and actually deposited 10,000 francs as earnest of 300,000. But
+  the courts would not allow any one to recover.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">SIR JOHN HERSCHEL.</p>
+
+  <p>1834. In this year Sir John Herschel<a name="NtA_654"
+  href="#Nt_654"><sup>[654]</sup></a> set up his telescope at Feldhausen,
+  Cape of Good Hope. He did much for astronomy, but not much for the
+  <i>Budget of Paradoxes</i>. He gives me, however, the following story. He
+  showed a resident a remarkable blood-red star, and some little time after
+  he heard of a sermon preached in those parts in which it was asserted
+  that the statements of the Bible must be true, for that Sir J.&nbsp;H. had
+  seen in his telescope "the very place where wicked people go."</p>
+
+  <p>But red is not always the color. Sir J. Herschel has in his possession
+  a letter written to his father, Sir W.&nbsp;H.,<a name="NtA_655"
+  href="#Nt_655"><sup>[655]</sup></a> dated April 3, 1787, and signed
+  "Eliza Cumyns," begging to know if any of the stars be <i>indigo</i> in
+  color, "because, if there be, I think it may be deemed a strong
+  conjectural illustration of the expression, so often used by our Saviour
+  in the Holy Gospels, that 'the disobedient shall be cast into outer
+  darkness'; for as the Almighty Being can doubtless confine any of his
+  creatures, whether corporeal or spiritual, to what part of his creation
+  He pleases, if therefore any of the stars (which are beyond all doubt so
+  many suns to other systems) be of so dark a color as that above
+  mentioned, they may be calculated to give the most insufferable heat to
+  those dolorous systems dependent upon them (and to reprobate spirits
+  placed there), without one ray of cheerful light; and may therefore be
+  the scenes of future punishments." This letter is addressed to Dr.
+  Heirschel at Slow. Some have placed the infernal regions inside the
+  earth, but <!-- Page 300 --><span class="pagenum"><a
+  name="page300"></a>[300]</span>others have filled this internal
+  cavity&mdash;for cavity they will have&mdash;with refulgent light, and
+  made it the abode of the blessed. It is difficult to build without
+  knowing the number to be provided for. A friend of mine heard the
+  following (part) dialogue between two strong Scotch Calvinists: "Noo! hoo
+  manny d'ye thank there are of the alact on the arth at this
+  moment?&mdash;Eh! mabbee a doozen&mdash;Hoot! mon! nae so mony as
+  thot!"</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE NAUTICAL ALMANAC.</p>
+
+  <p>1834. From 1769 to 1834 the <i>Nautical Almanac</i> was published on a
+  plan which gradually fell behind what was wanted. In 1834 the new series
+  began, under a new superintendent (Lieut. W.&nbsp;S. Stratford).<a
+  name="NtA_656" href="#Nt_656"><sup>[656]</sup></a> There had been a long
+  scientific controversy, which would not be generally intelligible. To set
+  some of the points before the reader, I reprint a cutting which I have by
+  me. It is from the Nautical <i>Magazine</i>, but I did hear that some had
+  an idea that it was in the Nautical <i>Almanac</i> itself. It certainly
+  was not, and I feel satisfied the Lords of the Admiralty would not have
+  permitted the insertion; they are never in advance of their age. The
+  Almanac for 1834 was published in July 1833.</p>
+
+<blockquote class="b1n">
+
+  <p><span class="sc">The New Nautical Almanac</span>&mdash;Extract from
+  the 'Primum Mobile,' and 'Milky Way Gazette.' Communicated by <span
+  class="sc">Aerolith</span>.</p>
+
+</blockquote>
+
+  <p>A meeting of the different bodies composing the Solar System was this
+  day held at the Dragon's Tail, for the purpose of taking into
+  consideration the alterations and amendments introduced into the New
+  Nautical Almanac. The honorable luminaries had been individually summoned
+  <!-- Page 301 --><span class="pagenum"><a
+  name="page301"></a>[301]</span>by fast-sailing comets, and there was a
+  remarkably full attendance. Among the visitors we <i>observed</i> several
+  nebulæ, and almost all the stars whose proper motions would admit of
+  their being present.</p>
+
+  <p>The <span class="sc">Sun</span> was unanimously called to the focus.
+  The small planets took the oaths, and their places, after a short
+  discussion, in which it was decided that the places should be those of
+  the Almanac itself, with leave reserved to move for corrections.</p>
+
+  <p>Petitions were presented from <span class="grk">&alpha;</span> and
+  <span class="grk">&delta;</span> Ursæ Minoris, complaining of being put
+  on daily duty, and praying for an increase of salary.&mdash;Laid on the
+  plane of the ecliptic.</p>
+
+  <p>The trustees of the eccentricity<a name="NtA_657"
+  href="#Nt_657"><sup>[657]</sup></a> and inclination funds reported a
+  balance of .00001 in the former, and a deficit of 0".009 in the latter.
+  This announcement caused considerable surprise, and a committee was moved
+  for, to ascertain which of the bodies had more or less than his share.
+  After some discussion, in which the small planets offered to consent to a
+  reduction, if necessary, the motion was carried.</p>
+
+  <p>The <span class="sc">Focal Body</span> then rose to address the
+  meeting. He remarked that the subject on which they were assembled was
+  one of great importance to the routes and revolutions of the heavenly
+  bodies. For himself, though a private arrangement between two of his
+  honourable neighbours (here he looked hard at the Earth and Venus) had
+  prevented his hitherto paying that close attention to the predictions of
+  the Nautical Almanac which he declared he always had wished to do; yet he
+  felt consoled by knowing that the conductors of that work had every
+  disposition to take his peculiar circumstances into consideration. He
+  declared that he had never passed the wires of a transit without deeply
+  feeling his inability to adapt himself to the present state of his
+  theory; a feeling which he was afraid had sometimes caused a slight
+  tremor in his limb. Before <!-- Page 302 --><span class="pagenum"><a
+  name="page302"></a>[302]</span>he sat down, he expressed a hope that
+  honourable luminaries would refrain as much as possible from eclipsing
+  each other, or causing mutual <span class="correction" title="text reads `peturbations'"
+  >perturbations</span>. Indeed, he should be very sorry to see any
+  interruption of the harmony of the spheres. (Applause.)</p>
+
+  <p>The several articles of the New Nautical Almanac were then read over
+  without any comment; only we observed that Saturn shook his ring at every
+  novelty, and Jupiter gave his belt a hitch, and winked at the satellites
+  at page 21 of each month.</p>
+
+  <p>The <span class="sc">Moon</span> rose to propose a resolution. No one,
+  he said, would be surprised at his bringing this matter forward in the
+  way he did, when it was considered in how complete and satisfactory a
+  manner his motions were now represented. He must own he had trembled when
+  the Lords of the Admiralty dissolved the Board of Longitude, but his
+  tranquillity was more than reestablished by the adoption of the new
+  system. He did not know but that any little assistance he could give in
+  Nautical Astronomy was becoming of less and less value every day, owing
+  to the improvement of chronometers. But there was one thing, of which
+  nothing could deprive him&mdash;he meant the regulation of the tides.
+  And, perhaps, when his attention was not occupied by more than the
+  latter, he should be able to introduce a little more regularity into the
+  phenomena. (Here the honourable luminary gave a sort of modest libration,
+  which convulsed the meeting with laughter.) They might laugh at his
+  natural infirmity if they pleased, but he could assure them it arose only
+  from the necessity he was under, when young, of watching the motions of
+  his worthy primary. He then moved a resolution highly laudatory of the
+  alterations which appeared in the New Nautical Almanac.</p>
+
+  <p>The <span class="sc">Earth</span> rose, to second the motion. His
+  honourable satellite had fully expressed his opinions on the subject. He
+  joined his honourable friend in the focus in wishing to pay every
+  attention to the Nautical Almanac, but, <!-- Page 303 --><span
+  class="pagenum"><a name="page303"></a>[303]</span>really, when so
+  important an alteration had taken place in his magnetic pole<a
+  name="NtA_658" href="#Nt_658"><sup>[658]</sup></a> (hear) and there
+  might, for aught he knew, be a successful attempt to reach his pole of
+  rotation, he thought he could not answer for the preservation of the
+  precession in its present state. (Here the hon. luminary, scratching his
+  side, exclaimed, as he sat down, "More steamboats&mdash;confound
+  'em!")</p>
+
+  <p>An honourable satellite (whose name we could not learn) proposed that
+  the resolution should be immediately despatched, corrected for
+  refraction, when he was called to order by the Focal Body, who reminded
+  him that it was contrary to the moving orders of the system to take
+  cognizance of what passed inside the atmosphere of any planet.</p>
+
+  <p><span class="sc">Saturn</span> and <span class="sc">Pallas</span> rose
+  together. (Cries of "New member!" and the former gave way.) The latter,
+  in a long and eloquent speech, praised the liberality with which he and
+  his colleagues had at length been relieved from astronomical
+  disqualifications. He thought that it was contrary to the spirit of the
+  laws of gravitation to exclude any planet from office on account of the
+  eccentricity or inclination of his orbit. Honourable luminaries need not
+  talk of the want of convergency of his series. What had they to do with
+  any private arrangements between him and the general equations of the
+  system? (Murmurs from the opposition.) So long as he obeyed the laws of
+  motion, to which he had that day taken a solemn oath, he would ask, were
+  old planets, which were now so well known that nobody trusted them,
+  to....</p>
+
+  <p>The <span class="sc">Focal Body</span> said he was sorry to break the
+  continuity of the proceedings, but he thought that remarks upon
+  character, with a negative sign, would introduce <!-- Page 304 --><span
+  class="pagenum"><a name="page304"></a>[304]</span>differences of too high
+  an order. The honourable luminary must eliminate the expression which he
+  had brought out, in finite terms, and use smaller inequalities in future.
+  (Hear, hear.)</p>
+
+  <p><span class="sc">Pallas</span> explained, that he was far from meaning
+  to reflect upon the orbital character of any planet present. He only
+  meant to protest against being judged by any laws but those of
+  gravitation, and the differential calculus: he thought it most unjust
+  that astronomers should prevent the small planets from being observed,
+  and then reproach them with the imperfections of the tables, which were
+  the result of their own narrow-minded policy. (Cheers.)</p>
+
+  <p><span class="sc">Saturn</span> thought that, as an old planet, he had
+  not been treated with due respect. (Hear, from his satellites.) He had
+  long foretold the wreck of the system from the friends of innovation.
+  Why, he might ask, were his satellites to be excluded, when small
+  planets, trumpery comets, which could not keep their mean distances
+  (cries of oh! oh!), double stars, with graphical approximations, and such
+  obscure riff-raff of the heavens (great uproar) found room enough. So
+  help him Arithmetic, nothing could come of it, but a stoppage of all
+  revolution. His hon. friend in the focus might smile, for he would be a
+  gainer by such an event; but as for him (Saturn), he had something to
+  lose, and hon. luminaries well knew that, whatever they might think
+  <i>under</i> an atmosphere, <i>above</i> it continual revolution was the
+  only way of preventing perpetual anarchy. As to the hon. luminary who had
+  risen before him, he was not surprised at his remarks, for he had
+  invariably observed that he and his colleagues allowed themselves <i>too
+  much latitude</i>. The stability of the system required that they should
+  be brought down, and he, for one, would exert all his powers of
+  attraction to accomplish that end. If other bodies would cordially unite
+  with him, particularly his noble friend next him, than whom no luminary
+  possessed greater weight&mdash;</p>
+
+  <p><span class="sc">Jupiter</span> rose to order. He conceived his noble
+  friend <!-- Page 305 --><span class="pagenum"><a
+  name="page305"></a>[305]</span>had no right to allude to him in that
+  manner, and was much surprised at his proposal, considering the matters
+  which remained in dispute between them. In the present state of affairs,
+  he would take care never to be in conjunction with his hon. neighbour one
+  moment longer than he could help. (Cries of "Order, order, no long
+  inequalities," during which he sat down.)</p>
+
+  <p><span class="sc">Saturn</span> proceeded to say, that he did not know
+  till then that a planet with a ring could affront one who had only a
+  belt, by proposing mutual co-operation. He would now come to the subject
+  under discussion. He should think meanly of his hon. colleagues if they
+  consented to bestow their approbation upon a mere astronomical
+  production. Had they forgotten that they once were considered the
+  arbiters of fate, and the prognosticators of man's destiny? What had lost
+  them that proud position? Was it not the infernal march of intellect,
+  which, after having turned the earth topsy-turvy, was now disturbing the
+  very universe? For himself (others might do as they pleased), but he
+  stuck to the venerable Partridge,<a name="NtA_659"
+  href="#Nt_659"><sup>[659]</sup></a> and the Stationers' Company, and
+  trusted that they would outlive infidels and anarchists, whether of
+  Astronomical or Diffusion of Knowledge Societies. (Cries of oh! oh!)</p>
+
+  <p><span class="sc">Mars</span> said he had been told, for he must
+  confess he had not seen the work, that the places of the planets were
+  given for Sundays. This, he must be allowed to say, was an indecorum he
+  had not expected; and he was convinced the Lords of the Admiralty had
+  given no orders to that effect. He hoped this point would be considered
+  in the measure which had been introduced in another place, and that some
+  <!-- Page 306 --><span class="pagenum"><a
+  name="page306"></a>[306]</span>one would move that the prohibition
+  against travelling on Sundays extend to the heavenly as well as earthly
+  bodies.</p>
+
+  <p>Several of the stars here declared, that they had been much annoyed by
+  being observed on Sunday evenings, during the hours of divine
+  service.</p>
+
+  <p>The room was then cleared for a division, but we are unable to state
+  what took place. Several comets-at-arms were sent for, and we heard
+  rumors of a personal collision having taken place between two luminaries
+  in opposition. We were afterwards told that the resolution was carried by
+  a majority, and the luminaries elongated at 2 h. 15 m. 33,41 s. sidereal
+  time.</p>
+
+  <p>* * * It is reported, but we hope without foundation, that Saturn, and
+  several other discontented planets, have accepted an invitation from
+  Sirius to join his system, on the most liberal appointments. We believe
+  the report to have originated in nothing more than the discovery of the
+  annual parallax of Sirius from the orbit of Saturn; but we may safely
+  assure our readers that no steps have as yet been taken to open any
+  communication.</p>
+
+  <p>We are also happy to state, that there is no truth in the rumor of the
+  laws of gravitation being about to be repealed. We have traced this
+  report, and find it originated with a gentleman living near Bath (Captain
+  Forman, R.N),<a name="NtA_660" href="#Nt_660"><sup>[660]</sup></a> whose
+  name we forbear to mention.</p>
+
+  <p>A great excitement has been observed among the nebulæ, visible to the
+  earth's southern hemisphere, particularly among those which have not yet
+  been discovered from thence. We are at a loss to conjecture the cause,
+  but we shall not fail to report to our readers the news of any movement
+  which may take place. (Sir J. Herschel's visit. He could just see this
+  before he went out.)</p>
+
+<p><!-- Page 307 --><span class="pagenum"><a name="page307"></a>[307]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">WOODLEY'S DIVINE SYSTEM.</p>
+
+<blockquote class="b1n">
+
+  <p>A Treatise on the Divine System of the Universe, by Captain Woodley,
+  R.N.,<a name="NtA_661" href="#Nt_661"><sup>[661]</sup></a> and as
+  demonstrated by his Universal Time-piece, and universal method of
+  determining a ship's longitude by the apparent true place of the moon;
+  with an introduction refuting the solar system of Copernicus, the
+  Newtonian philosophy, and mathematics. 1834.<a name="NtA_662"
+  href="#Nt_662"><sup>[662]</sup></a> 8vo.</p>
+
+  <p>Description of the Universal Time-piece. (4pp. 12mo.)</p>
+
+</blockquote>
+
+  <p>I think this divine system was published several years before, and was
+  republished with an introduction in 1834.<a name="NtA_663"
+  href="#Nt_663"><sup>[663]</sup></a> Capt. Woodley was very sure that the
+  earth does not move: he pointed out to me, in a conversation I had with
+  him, something&mdash;I forget what&mdash;in the motion of the Great Bear,
+  visible to any eye, which could not possibly be if the earth moved. He
+  was exceedingly ignorant, as the following quotation from his account of
+  the usual opinion will show:</p>
+
+  <p>"The north pole of the Earth's axis deserts, they say, the north star
+  or pole of the Heavens, at the rate of 1° in 71¾ years.... The fact is,
+  nothing can be more certain than that the Stars have not changed their
+  latitudes or declinations <i>one degree</i> in the last 71¾ years."</p>
+
+  <p>This is a strong specimen of a class of men by whom all accessible
+  persons who have made any name in science are hunted. It is a pity that
+  they cannot be admitted into scientific societies, and allowed fairly to
+  state their cases, and stand quiet cross-examination, being kept in their
+  answers very close to the questions, and the answers written down. I am
+  perfectly satisfied that if one meeting in the year were devoted to the
+  hearing of those who chose to come forward on such conditions, much good
+  would be done. But I strongly suspect few would come forward <!-- Page
+  308 --><span class="pagenum"><a name="page308"></a>[308]</span>at first,
+  and none in a little while: and I have had some experience of the method
+  I recommend, privately tried. Capt. Woodley was proposed, a little after
+  1834, as a Fellow of the Astronomical Society; and, not caring whether he
+  moved the sun or the earth, or both&mdash;I could not have stood
+  <i>neither</i>&mdash;I signed the proposal. I always had a sneaking
+  kindness for paradoxers, such a one, perhaps, as Petit André had for his
+  <i>lambs</i>, as he called them. There was so little feeling against his
+  opinions, that he only failed by a fraction of a ball. Had I myself
+  voted, he would have been elected; but being engaged in conversation, and
+  not having heard the slightest objection to him, I did not think it worth
+  while to cross the room for the purpose. I regretted this at the time,
+  but had I known how ignorant he was I should not have supported him.
+  Probably those who voted against him knew more of his book than I
+  did.</p>
+
+  <p>I remember no other instance of exclusion from a scientific society on
+  the ground of opinion, even if this be one; of which it may be that
+  ignorance had more to do with it than paradoxy. Mr. Frend,<a
+  name="NtA_664" href="#Nt_664"><sup>[664]</sup></a> a strong
+  anti-Newtonian, was a Fellow of the Astronomical Society, and for some
+  years in the Council. Lieut. Kerigan<a name="NtA_665"
+  href="#Nt_665"><sup>[665]</sup></a> was elected to the Royal Society at a
+  time when his proposers must have known that his immediate object was to
+  put F.R.S. on the title-page of a work against the tides. To give all I
+  know, I may add that the editor of some very ignorant bombast about the
+  "forehead of the solar sky," who did not know the difference between
+  <i>Bailly</i><a name="NtA_666" href="#Nt_666"><sup>[666]</sup></a> and
+  <i>Baily</i>,<a name="NtA_667" href="#Nt_667"><sup>[667]</sup></a>
+  received hints which induced him to withdraw his proposal for election
+  into the Astronomical Society. But this was an act of kindness; <!-- Page
+  309 --><span class="pagenum"><a name="page309"></a>[309]</span>for if he
+  had seen Mr. Baily in the chair, with his head on, he might have been
+  political historian enough to faint away.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>De la formation des Corps. Par Paul Laurent.<a name="NtA_668"
+  href="#Nt_668"><sup>[668]</sup></a> Nancy, 1834, 8vo.</p>
+
+</blockquote>
+
+  <p>Atoms, and ether, and ovules or eggs, which are planets, and their
+  eggs, which are satellites. These speculators can create worlds, in which
+  they cannot be refuted; but none of them dare attack the problem of a
+  grain of wheat, and its passage from a seed to a plant, bearing scores of
+  seeds like what it was itself.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON JOHN FLAMSTEED.</p>
+
+<blockquote class="b1n">
+
+  <p>An account of the Rev. John Flamsteed,<a name="NtA_669"
+  href="#Nt_669"><sup>[669]</sup></a> the First Astronomer-Royal.... By
+  Francis Baily,<a name="NtA_670" href="#Nt_670"><sup>[670]</sup></a> Esq.
+  London, 1835, 4to. Supplement, London, 1837, 4to.</p>
+
+</blockquote>
+
+  <p>My friend Francis Baily was a paradoxer: he brought forward things
+  counter to universal opinion. That Newton was impeccable in every point
+  was the national creed; and failings of temper and conduct would have
+  been utterly disbelieved, if the paradox had not come supported by very
+  unusual evidence. Anybody who impeached Newton on existing evidence might
+  as well have been squaring the circle, for any attention he would have
+  got. About this book I will tell a story. It was published by the
+  Admiralty for distribution; and the distribution was entrusted to Mr.
+  Baily. On the eve of its appearance, rumors of its extraordinary
+  revelations got about, and persons of influence applied to the Admiralty
+  for copies. The Lords were in a difficulty: but on looking at the list
+  they saw names, as they <!-- Page 310 --><span class="pagenum"><a
+  name="page310"></a>[310]</span>thought, which were so obscure that they
+  had a right to assume Mr. Baily had included persons who had no claim to
+  such a compliment as presentation from the Admiralty. The Secretary
+  requested Mr. Baily to call upon him. "Mr. Baily, my Lords are inclined
+  to think that some of the persons in this list are perhaps not of that
+  note which would justify their Lordships in presenting this
+  work."&mdash;"To whom does your observation apply, Mr.
+  Secretary?"&mdash;"Well, now, let us examine the list; let me see;
+  now,&mdash;now,&mdash;now,&mdash;come!&mdash;here's Gauss<a
+  name="NtA_671" href="#Nt_671"><sup>[671]</sup></a>&mdash;<i>who's
+  Gauss</i>?"&mdash;"Gauss, Mr. Secretary, is the oldest mathematician now
+  living, and is generally thought to be the greatest."&mdash;"O-o-oh!
+  Well, Mr. Baily, we will see about it, and I will write you a letter."
+  The letter expressed their Lordships' perfect satisfaction with the
+  list.</p>
+
+  <p>There was a controversy about the revelations made in this work; but
+  as the eccentric anomalies took no part in it, there is nothing for my
+  purpose. The following valentine from Mrs. Flamsteed,<a name="NtA_672"
+  href="#Nt_672"><sup>[672]</sup></a> which I found among Baily's papers,
+  illustrates some of the points:</p>
+
+  <p class="author">"3 Astronomers' Row, Paradise: February 14, 1836.
+
+  <p>"Dear Sir,&mdash;I suppose you hardly expected to receive a letter
+  from me, dated from this place; but the truth is, a gentleman from our
+  street was appointed guardian angel to the American Treaty, in which
+  there is some astronomical question about boundaries. He has got leave to
+  go back to fetch some instruments which he left behind, and I take this
+  opportunity of making your acquaintance. That America has become a
+  wonderful place since I was down among you; you have no idea how grand
+  the fire at New York <!-- Page 311 --><span class="pagenum"><a
+  name="page311"></a>[311]</span>looked up here. Poor dear Mr. Flamsteed
+  does not know I am writing a letter to a gentleman on Valentine's day; he
+  is walked out with Sir Isaac Newton (they are pretty good friends now,
+  though they do squabble a little sometimes) and Sir William Herschel, to
+  see a new nebula. Sir Isaac says he can't make out at all how it is
+  managed; and I am sure I cannot help him. I never bothered my head about
+  those things down below, and I don't intend to begin here.</p>
+
+  <p>"I have just received the news of your having written a book about my
+  poor dear man. It's a chance that I heard it at all; for the truth is,
+  the scientific gentlemen are somehow or other become so wicked, and go so
+  little to church, that very few of them are considered fit company for
+  this place. If it had not been for Dr. Brinkley,<a name="NtA_673"
+  href="#Nt_673"><sup>[673]</sup></a> who came here of course, I should not
+  have heard about it. He seems a nice man, but is not yet used to our
+  ways. As to Mr. Halley,<a name="NtA_674"
+  href="#Nt_674"><sup>[674]</sup></a> he is of course not here; which is
+  lucky for him, for Mr. Flamsteed swore the moment he caught him in a
+  place where there are no magistrates, he would make a sacrifice of him to
+  heavenly truth. It was very generous in Mr. F. not appearing against Sir
+  Isaac when he came up, for I am told that if he had, Sir Isaac would not
+  have been allowed to come in at all. I should have been sorry for that,
+  for he is a companionable man enough, only holds his head rather higher
+  than he should do. I met him the other day walking with Mr. Whiston,<a
+  name="NtA_675" href="#Nt_675"><sup>[675]</sup></a> and disputing about
+  the deluge. 'Well, Mrs. Flamsteed,' says he, 'does old Poke-the-Stars
+  understand gravitation yet?' Now you must know that is rather a sore
+  point with poor dear Mr. Flamsteed. He says that Sir Isaac is as
+  crochetty about the moon as ever; and as to <!-- Page 312 --><span
+  class="pagenum"><a name="page312"></a>[312]</span>what some people say
+  about what has been done since his time, he says he should like to see
+  somebody who knows something about it of himself. For it is very singular
+  that none of the people who have carried on Sir Isaac's notions have been
+  allowed to come here.</p>
+
+  <p>"I hope you have not forgotten to tell how badly Sir Isaac used Mr.
+  Flamsteed about that book. I have never quite forgiven him; as for Mr.
+  Flamsteed, he says that as long as he does not come for observations, he
+  does not care about it, and that he will never trust him with any papers
+  again as long as he lives. I shall never forget what a rage he came home
+  in when Sir Isaac had called him a puppy. He struck the stairs all the
+  way up with his crutch, and said puppy at every step, and all the
+  evening, as soon as ever a star appeared in the telescope, he called it
+  puppy. I could not think what was the matter, and when I asked, he only
+  called me puppy.</p>
+
+  <p>"I shall be very glad to see you if you come our way. Pray keep up
+  some appearances, and go to church a little. St. Peter is always
+  uncommonly civil to astronomers, and indeed to all scientific persons,
+  and never bothers them with many questions. If they can make anything out
+  of the case, he is sure to let them in. Indeed, he says, it is perfectly
+  out of the question expecting a mathematician to be as religious as an
+  apostle, but that it is as much as his place is worth to let in the
+  greater number of those who come. So try if you cannot manage it, for I
+  am very curious to know whether you found all the letters. I remain, dear
+  sir, your faithful servant,</p>
+
+  <p class="author">"<span class="sc">Margaret Flamsteed.</span>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>Francis Baily, Esq.</p>
+    </div>
+  </div>
+  <p>"P.S. Mr. Flamsteed has come in, and says he left Sir Isaac riding
+  cockhorse upon the nebula, and poring over it as if it were a book. He
+  has brought in his old acquaintance Ozanam,<a name="NtA_676"
+  href="#Nt_676"><sup>[676]</sup></a> who says that it was always his maxim
+  on <!-- Page 313 --><span class="pagenum"><a
+  name="page313"></a>[313]</span>earth, that 'il appartient aux docteurs de
+  Sorbonne de disputer, au Pape de prononcer, et au mathématicien d'aller
+  en Paradis en ligne perpendiculaire.'"<a name="NtA_677"
+  href="#Nt_677"><sup>[677]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON STEVIN.</p>
+
+  <p>The Secretary of the Admiralty was completely extinguished. I can
+  recall but two instances of demolition as complete, though no doubt there
+  are many others. The first is in</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>Simon Stevin<a name="NtA_678" href="#Nt_678"><sup>[678]</sup></a> and M. Dumortier. Nieuport, 1845, 12mo.</p>
+    </div>
+  </div>
+  <p>M. Dumortier was a member of the Academy of Brussels: there was a
+  discussion, I believe, about a national Pantheon for Belgium. The name of
+  Stevinus suggested itself as naturally as that of Newton to an
+  Englishman; probably no Belgian is better known to foreigners as
+  illustrious in science. Stevinus is great in the <i>Mécanique
+  Analytique</i> of Lagrange;<a name="NtA_679"
+  href="#Nt_679"><sup>[679]</sup></a> Stevinus is great in the <i>Tristram
+  Shandy</i> of Sterne. M. Dumortier, who believed that not one Belgian in
+  a thousand knew Stevinus, and who confesses with ironical shame that he
+  was not the odd man, protested against placing the statue of an obscure
+  man in the Pantheon, to give foreigners the notion that Belgium could
+  show nothing greater. The work above named is a slashing retort: any one
+  who knows the history of science ever so little may imagine what a
+  dressing was given, by mere extract from foreign writers. The tract is a
+  letter signed J. du Fan, but this is a pseudonym of Mr. Van de Weyer.<a
+  name="NtA_680" href="#Nt_680"><sup>[680]</sup></a> The Academician says
+  Stevinus was a man who was not <!-- Page 314 --><span class="pagenum"><a
+  name="page314"></a>[314]</span>without merit for the time at which he
+  lived: Sir! is the answer, he was as much before his own time as you are
+  behind yours. How came a man who had never heard of Stevinus to be a
+  member of the Brussels Academy?</p>
+
+  <p>The second story was told me by Mr. Crabb Robinson,<a name="NtA_681"
+  href="#Nt_681"><sup>[681]</sup></a> who was long connected with the
+  <i>Times</i>, and intimately acquainted with Mr. W***.<a name="NtA_682"
+  href="#Nt_682"><sup>[682]</sup></a> When W*** was an undergraduate at
+  Cambridge, taking a walk, he came to a stile, on which sat a bumpkin who
+  did not make way for him: the gown in that day looked down on the town.
+  "Why do you not make way for a gentleman?"&mdash;"Eh?"&mdash;"Yes, why do
+  you not move? You deserve a good hiding, and you shall get it if you
+  don't take care!" The bumpkin raised his muscular figure on its feet,
+  patted his menacer on the head, and said, very quietly,&mdash;"Young man!
+  I'm Cribb."<a name="NtA_683" href="#Nt_683"><sup>[683]</sup></a> W***
+  seized the great pugilist's hand, and shook it warmly, got him to his own
+  rooms in college, collected some friends, and had a symposium which
+  lasted until the large end of the small hours.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">FINLEYSON AS A PARADOXER.</p>
+
+<blockquote class="b1n">
+
+  <p>God's Creation of the Universe as it is, in support of the Scriptures.
+  By Mr. Finleyson.<a name="NtA_684" href="#Nt_684"><sup>[684]</sup></a>
+  Sixth Edition, 1835, 8vo.</p>
+
+</blockquote>
+
+<p><!-- Page 315 --><span class="pagenum"><a name="page315"></a>[315]</span></p>
+
+  <p>This writer, by his own account, succeeded in delivering the famous
+  Lieut. Richard Brothers<a name="NtA_685"
+  href="#Nt_685"><sup>[685]</sup></a> from the lunatic asylum, and tending
+  him, not as a keeper but as a disciple, till he died. Brothers was, by
+  his own account, the nephew of the Almighty, and Finleyson ought to have
+  been the nephew of Brothers. For Napoleon came to him in a vision, with a
+  broken sword and an arrow in his side, beseeching help: Finleyson pulled
+  out the arrow, but refused to give a new sword; whereby poor Napoleon,
+  though he got off with life, lost the battle of Waterloo. This story was
+  written to the Duke of Wellington, ending with "I pulled out the arrow,
+  but left the broken sword. Your Grace can supply the rest, and what
+  followed is amply recorded in history." The book contains a long account
+  of applications to Government to do three things: to pay 2,000<i>l.</i>
+  for care taken of Brothers, to pay 10,000<i>l.</i> for discovery of the
+  longitude, and to prohibit the teaching of the Newtonian system, which
+  makes God a liar. The successive administrations were threatened that
+  they would have to turn out if they refused, which, it is remarked, came
+  to pass in every case. I have heard of a joke of Lord Macaulay, that the
+  House of Commons must be the Beast of the Revelations, since 658 members,
+  with the officers necessary for the action of the House, make 666.
+  Macaulay read most things, and the greater part of the rest: so that he
+  might be suspected of having appropriated as a joke one of Finleyson's
+  serious points&mdash;"I wrote Earl Grey<a name="NtA_686"
+  href="#Nt_686"><sup>[686]</sup></a> upon the 13th of July, 1831,
+  informing him that his Reform <!-- Page 316 --><span class="pagenum"><a
+  name="page316"></a>[316]</span>Bill could not be carried, as it reduced
+  the members below the present amount of 658, which, with the eight
+  principal clerks or officers of the House, make the number 666." But a
+  witness has informed me that Macaulay's joke was made in his hearing a
+  great many years before the Reform Bill was proposed; in fact, when both
+  were students at Cambridge. Earl Grey was, according to Finleyson, a
+  descendant of Uriah the Hittite. For a specimen of Lieut. Brothers, this
+  book would be worth picking up. Perhaps a specimen of the Lieutenant's
+  poetry may be acceptable: Brothers <i>loquitur</i>, remember:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Jerusalem ! Jerusalem! shall be built again!</p>
+      <p class="i2">More rich, more grand then ever;</p>
+      <p>And through it shall Jordan flow!(!)</p>
+      <p class="i2">My people's favourite river.</p>
+      <p>There I'll erect a splendid throne,</p>
+      <p class="i2">And build on the wasted place;</p>
+      <p>To fulfil my ancient covenant</p>
+      <p class="i2">To King David and his race.</p>
+      <p>&nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; *</p>
+      <p class="hg3">"Euphrates' stream shall flow with ships,</p>
+      <p class="i2">And also my wedded Nile;</p>
+      <p>And on my coast shall cities rise,</p>
+      <p class="i2">Each one distant but a mile.</p>
+      <p>&nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; *</p>
+      <p class="hg3">"My friends the Russians on the north</p>
+      <p class="i2">With Persees and Arabs round,</p>
+      <p>Do show the limits of my land,</p>
+      <p class="i2">Here! Here! then I mark the ground."</p>
+    </div>
+  </div>
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON THEOLOGICAL PARADOXERS.</p>
+
+  <p>Among the paradoxers are some of the theologians who in their own
+  organs of the press venture to criticise science. These may hold their
+  ground when they confine themselves to the geology of long past periods
+  and to general cosmogony: for it is the tug of Greek against Greek; and
+  both sides deal much in what is grand when called <i>hypothesis</i>,
+  petty when called <i>supposition</i>. And very often they are not
+  conspicuous when they venture upon things within knowledge; <!-- Page 317
+  --><span class="pagenum"><a name="page317"></a>[317]</span>wrong, but not
+  quite wrong enough for a Budget of Paradoxes. One case, however, is
+  destined to live, as an instance of a school which finds writers,
+  editors, and readers. The double stars have been seen from the
+  seventeenth century, and diligently observed by many from the time of Wm.
+  Herschel, who first devoted continuous attention to them. The year 1836
+  was that of a remarkable triumph of astronomical prediction. The theory
+  of gravitation had been applied to the motion of binary stars about each
+  other, in elliptic orbits, and in that year the two stars of <span
+  class="grk">&gamma;</span> Virginis, as had been predicted should happen
+  within a few years of that time&mdash;for years are small quantities in
+  such long revolutions&mdash;the two stars came to their nearest: in fact,
+  they appeared to be one as much with the telescope as without it. This
+  remarkable turning-point of the history of a long and widely-known branch
+  of astronomy was followed by an article in the <i>Church of England
+  Quarterly Review</i> for April 1837, written against the Useful Knowledge
+  Society. The notion that there are any such things as double stars is (p.
+  460) implied to be imposture or delusion, as in the following extract. I
+  suspect that I myself am the <i>Sidrophel</i>, and that my companion to
+  the maps of the stars, written for the Society and published in 1836, is
+  the work to which the writer refers:</p>
+
+  <p>"We have forgotten the name of that Sidrophel who lately discovered
+  that the fixed stars were not single stars, but appear in the heavens
+  like soles at Billingsgate, in pairs; while a second astronomer, under
+  the influence of that competition in trade which the political economists
+  tell us is so advantageous to the public, professes to show us, through
+  his superior telescope, that the apparently single stars are really
+  three. Before such wondrous mandarins of science, how continually must
+  <i>homunculi</i> like ourselves keep in the background, lest we come
+  between the wind and their nobility."</p>
+
+  <p>If the <i>homunculus</i> who wrote this be still above ground, <!--
+  Page 318 --><span class="pagenum"><a name="page318"></a>[318]</span>how
+  devoutly must he hope he may be able to keep in the background! But the
+  chief blame falls on the editor. The title of the article is:</p>
+
+  <p>"The new school of superficial pantology; a speech intended to be
+  delivered before a defunct Mechanics' Institute. By Swallow Swift, late
+  M.P. for the Borough of Cockney-Cloud, Witsbury: reprinted Balloon
+  Island, Bubble year, month <i>Ventose</i>. Long live Charlatan!"</p>
+
+  <p>As a rule, orthodox theologians should avoid humor, a weapon which all
+  history shows to be very difficult to employ in favor of establishment,
+  and which, nine times out of ten, leaves its wielder fighting on the side
+  of heterodoxy. Theological argument, when not enlivened by bigotry, is
+  seldom worse than narcotic: but theological fun, when not covert heresy,
+  is almost always sialagogue. The article in question is a craze, which no
+  editor should have admitted, except after severe inspection by qualified
+  persons. The author of this wit committed a mistake which occurs now and
+  then in old satire, the confusion between himself and the party aimed at.
+  He ought to be reviewing this fictitious book, but every now and then the
+  article becomes the book itself; not by quotation, but by the writer
+  forgetting that <i>he</i> is not Mr. Swallow Swift, but his reviewer. In
+  fact he and Mr. S. Swift had each had a dose of the <i>Devil's
+  Elixir</i>. A novel so called, published about forty years ago, proceeds
+  upon a legend of this kind. If two parties both drink of the elixir,
+  their identities get curiously intermingled; each turns up in the
+  character of the other throughout the three volumes, without having his
+  ideas clear as to whether he be himself or the other. There is a similar
+  confusion in the answer made to the famous <i>Epistolæ Obscurorum
+  Virorum</i>:<a name="NtA_687" href="#Nt_687"><sup>[687]</sup></a> it is
+  headed <i>Lamentationes Obscurorum Virorum</i>.<a name="NtA_688"
+  href="#Nt_688"><sup>[688]</sup></a> <!-- Page 319 --><span
+  class="pagenum"><a name="page319"></a>[319]</span>This is not a retort of
+  the writer, throwing back the imputation: the obscure men who had been
+  satirized are themselves made, by name, to wince under the disapprobation
+  which the Pope had expressed at the satire upon themselves.</p>
+
+  <p>Of course the book here reviewed is a transparent forgery. But I do
+  not know how often it may have happened that the book, in the journals
+  which always put a title at the head, may have been written after the
+  review. About the year 1830 a friend showed me the proof of an article of
+  his on the malt tax, for the next number of the <i>Edinburgh Review</i>.
+  Nothing was wanting except the title of the book reviewed; I asked what
+  it was. He sat down, and wrote as follows at the head, "The Maltster's
+  Guide (pp. 124)," and said that would do as well as anything.</p>
+
+  <p>But I myself, it will be remarked, have employed such humor as I can
+  command "in favor of establishment." What it is worth I am not to judge;
+  as usual in such cases, those who are of my cabal pronounce it good, but
+  cyclometers and other paradoxers either call it very poor, or commend it
+  as sheer buffoonery. Be it one or the other, I observe that all the
+  effective ridicule is, in this subject, on the side of establishment.
+  This is partly due to the difficulty of quizzing plain and sober
+  demonstration; but so much, if not more, to the ignorance of the
+  paradoxers. For that which cannot be <i>ridiculed</i>, can be <i>turned
+  into ridicule</i> by those who know how. But by the time a person is deep
+  enough in <i>negative</i> quantities, and <i>impossible</i> quantities,
+  to be able to satirize them, he is caught, and being inclined to become a
+  <i>user</i>, shrinks from being an <i>abuser</i>. Imagine a person with a
+  gift of ridicule, and knowledge enough, trying his hand on the junction
+  of the assertions which he will find in various books of algebra. First,
+  that a negative quantity has no logarithm; secondly, that a <!-- Page 320
+  --><span class="pagenum"><a name="page320"></a>[320]</span>negative
+  quantity has no square root; thirdly, that the first non-existent is to
+  the second as the circumference of a circle to its diameter. One great
+  reason of the allowance of such unsound modes of expression is the
+  confidence felt by the writers that &radic;-1 and log(-1) will make their
+  way, however inaccurately described. I heartily wish that the cyclometers
+  had knowledge enough to attack the weak points of algebraical diction:
+  they would soon work a beneficial change.<a name="NtA_689"
+  href="#Nt_689"><sup>[689]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">AN EARLY METEOROLOGIST.</p>
+
+<blockquote class="b1n">
+
+  <p>Recueil de ma vie, mes ouvrages et mes pensées. Par Thomas Ignace
+  Marie Forster.<a name="NtA_690" href="#Nt_690"><sup>[690]</sup></a>
+  Brussels, 1836, 12mo.</p>
+
+</blockquote>
+
+  <p>Mr. Forster, an Englishman settled at Bruges, was an observer in many
+  subjects, but especially in meteorology. He communicated to the
+  Astronomical Society, in 1848, the information that, in the registers
+  kept by his grandfather, his father, and himself, beginning in 1767, new
+  moon on Saturday was followed, nineteen times out of twenty, by twenty
+  days of rain and wind. This statement being published in the
+  <i>Athenæum</i>, a cluster of correspondents averred that the belief is
+  common among seamen, in all parts of the world, and among landsmen too.
+  Some one quoted a distich:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Saturday's moon and Sunday's full</p>
+      <p>Never were fine and never <i>wull</i>."</p>
+    </div>
+  </div>
+<p><!-- Page 321 --><span class="pagenum"><a name="page321"></a>[321]</span></p>
+
+  <p>Another brought forward:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"If a Saturday's moon</p>
+      <p>Comes once in seven years it comes too soon."</p>
+    </div>
+  </div>
+  <p>Mr. Forster did not say he was aware of the proverbial character of
+  the phenomenon. He was a very eccentric man. He treated his dogs as
+  friends, and buried them with ceremony. He quarrelled with the
+  <i>curé</i> of his parish, who remarked that he could not take his dogs
+  to heaven with him. I will go nowhere, said he, where I cannot take my
+  dog. He was a sincere Catholic: but there is a point beyond which even
+  churches have no influence.</p>
+
+  <p>The following is some account of the announcement of 1849. The
+  <i>Athenæum</i> (Feb. 17), giving an account of the meeting of the
+  Astronomical Society in December, 1858, says:</p>
+
+  <p>"Dr. Forster of Bruges, who is well known as a meteorologist, made a
+  communication at which our readers will stare: he declares that by
+  journals of the weather kept by his grandfather, father, and himself,
+  ever since 1767, to the present time, <i>whenever the new moon has fallen
+  on a Saturday, the following twenty days have been wet and windy</i>, in
+  nineteen cases out of twenty. In spite of our friend Zadkiel<a
+  name="NtA_691" href="#Nt_691"><sup>[691]</sup></a> and the others who
+  declare that we would smother every truth that does not happen to agree
+  with us, we are glad to see that the Society had the sense to publish
+  this communication, coming, as it does, from a veteran observer, and one
+  whose love of truth is undoubted. It must be that the fact is so set down
+  in the journals, because Dr. Forster says it: and whether it be only a
+  fact of the journals, or one of the heavens, can soon be tried. The new
+  moon of March next, falls on <i>Saturday</i> the 24th, at 2 in the
+  afternoon. We shall certainly look out."</p>
+
+<p><!-- Page 322 --><span class="pagenum"><a name="page322"></a>[322]</span></p>
+
+  <p>The following appeared in the number of March 31:</p>
+
+  <p>"The first <i>Saturday Moon</i> since Dr. Forster's announcement came
+  off a week ago. We had previously received a number of letters from
+  different correspondents&mdash;all to the effect that the notion of new
+  moon on Saturday bringing wet weather is one of widely extended currency.
+  One correspondent (who gives his name) states that he has constantly
+  heard it at sea, and among the farmers and peasantry in Scotland,
+  Ireland, and the North of England. He proceeds thus: 'Since 1826,
+  nineteen years of the time I have spent in a seafaring life. I have
+  constantly observed, though unable to account for, the phenomenon. I have
+  also heard the stormy qualities of a Saturday's moon remarked by
+  American, French, and Spanish seamen; and, still more distant, a Chinese
+  pilot, who was once doing duty on board my vessel seemed to be perfectly
+  cognizant of the fact.' So that it seems we have, in giving currency to
+  what we only knew as a very curious communication from an earnest
+  meteorologist, been repeating what is common enough among sailors and
+  farmers. Another correspondent affirms that the thing is most devoutly
+  believed in by seamen; who would as soon sail on a Friday as be in the
+  Channel after a Saturday moon.&mdash;After a tolerable course of dry
+  weather, there was some snow, accompanied by wind on Saturday last, here
+  in London; there were also heavy louring clouds. Sunday was cloudy and
+  cold, with a little rain; Monday was louring, Tuesday unsettled;
+  Wednesday quite overclouded, with rain in the morning. The present
+  occasion shows only a general change of weather with a tendency towards
+  rain. If Dr. Forster's theory be true, it is decidedly one of the minor
+  instances, as far as London weather is concerned.&mdash;It will take a
+  good deal of evidence to make us believe in the omen of a Saturday Moon.
+  But, as we have said of the Poughkeepsie Seer, the thing is very curious
+  whether true or false. Whence comes this universal proverb&mdash;and a
+  hundred others&mdash;while the meteorological observer <!-- Page 323
+  --><span class="pagenum"><a name="page323"></a>[323]</span>cannot, when
+  he puts down a long series of results, detect any weather cycles at all?
+  One of our correspondents wrote us something of a lecture for
+  encouraging, he said, the notion that <i>names</i> could influence the
+  weather. He mistakes the question. If there be any weather cycles
+  depending on the moon, it is possible that one of them may be so related
+  to the week cycle of seven days, as to show recurrences which are of the
+  kind stated, or any other. For example, we know that if the new moon of
+  March fall on a Saturday in this year, it will most probably fall on a
+  Saturday nineteen years hence. This is not connected with the spelling of
+  Saturday&mdash;but with the connection between the motions of the sun and
+  moon. Nothing but the Moon can settle the question&mdash;and we are
+  willing to wait on her for further information. If the adage be true,
+  then the philosopher has missed what lies before his eyes; if false, then
+  the world can be led by the nose in spite of the eyes. Both these things
+  happen sometimes; and we are willing to take whichever of the two
+  solutions is borne out by future facts. In the mean time, we announce the
+  next Saturday Moon for the 18th of August."</p>
+
+  <p>How many coincidences are required to establish a law of connection?
+  It depends on the way in which the mind views the matter in question.
+  Many of the paradoxers are quite set up by a very few instances. I will
+  now tell a story about myself, and then ask them a question.</p>
+
+  <p>So far as instances can prove a law, the following is proved: no
+  failure has occurred. Let a clergyman be known to me, whether by personal
+  acquaintance or correspondence, or by being frequently brought before me
+  by those with whom I am connected in private life: that clergyman does
+  not, except in few cases, become a bishop; but <i>if</i> he become a
+  bishop, he is sure, first or last, to become an arch-bishop. This has
+  happened in every case. As follows:</p>
+
+  <p>1. My last schoolmaster, a former Fellow of Oriel, was <!-- Page 324
+  --><span class="pagenum"><a name="page324"></a>[324]</span>a very
+  intimate college friend of Richard Whately<a name="NtA_692"
+  href="#Nt_692"><sup>[692]</sup></a>, a younger man. Struck by his
+  friend's talents, he used to talk of him perpetually, and predict his
+  future eminence. Before I was sixteen, and before Whately had even given
+  his Bampton Lectures, I was very familiar with his name, and some of his
+  sayings. I need not say that he became Archbishop of Dublin.</p>
+
+  <p>2. When I was a child, a first cousin of John Bird Sumner<a
+  name="NtA_693" href="#Nt_693"><sup>[693]</sup></a> married a sister of my
+  mother. I cannot remember the time when I first heard his name, but it
+  was made very familiar to me. In time he became Bishop of Chester, and
+  then, Archbishop of Canterbury. My reader may say that Dr. C.&nbsp;R.
+  Sumner,<a name="NtA_694" href="#Nt_694"><sup>[694]</sup></a> Bishop of
+  Winchester, has just as good a claim: but it is not so: those connected
+  with me had more knowledge of Dr. J.&nbsp;B. Sumner;<a name="NtA_695"
+  href="#Nt_695"><sup>[695]</sup></a> and said nothing, or next to nothing,
+  of the other. Rumor says that the Bishop of Winchester has
+  <i>declined</i> an Archbishopric: if so, my rule is a rule of
+  gradations.</p>
+
+  <p>3. Thomas Musgrave,<a name="NtA_696"
+  href="#Nt_696"><sup>[696]</sup></a> Fellow of Trinity College, Cambridge,
+  was <i>Dean</i> of the college when I was an undergraduate: this brought
+  me into connection with him, he giving impositions for not going to
+  chapel, I writing them out according. We had also friendly intercourse in
+  after life; I forgiving, he probably forgetting. Honest Tom <!-- Page 325
+  --><span class="pagenum"><a name="page325"></a>[325]</span>Musgrave, as
+  he used to be called, became Bishop of Hereford, and Archbishop of
+  York.</p>
+
+  <p>4. About the time when I went to Cambridge, I heard a great deal about
+  Mr. C.&nbsp;T. Longley,<a name="NtA_697" href="#Nt_697"><sup>[697]</sup></a>
+  of Christchurch, from a cousin of my own of the same college, long since
+  deceased, who spoke of him much, and most affectionately. Dr. Longley
+  passed from Durham to York, and thence to Canterbury. I cannot quite make
+  out the two Archbishoprics; I do not remember any other private channel
+  through which the name came to me: perhaps Dr. Longley, having two
+  strings to his bow, would have been one archbishop if I had never heard
+  of him.</p>
+
+  <p>5. When Dr. Wm. Thomson<a name="NtA_698"
+  href="#Nt_698"><sup>[698]</sup></a> was appointed to the see of
+  Gloucester in 1861, he and I had been correspondents on the subject of
+  logic&mdash;on which we had both written&mdash;for about fourteen years.
+  On his elevation I wrote to him, giving the preceding instances, and
+  informing him that he would certainly be an Archbishop. The case was a
+  strong one, and the law acted rapidly; for Dr. Thomson's elevation to the
+  see of York took place in 1862.</p>
+
+  <p>Here are five cases; and there is no opposing instance. I have
+  searched the almanacs since 1828, and can find no instance of a Bishop
+  not finally Archbishop of whom I had known through private sources,
+  direct or indirect. Now what do my paradoxers say? Is this a
+  pre-established harmony, or a chain of coincidences? And how many
+  instances will it require to establish a law?<a name="NtA_699"
+  href="#Nt_699"><sup>[699]</sup></a></p>
+
+<p><!-- Page 326 --><span class="pagenum"><a name="page326"></a>[326]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE HERSCHEL HOAX.</p>
+
+<blockquote class="b1n">
+
+  <p>Some account of the great astronomical discoveries lately made by Sir
+  John Herschel at the Cape of Good Hope. Second Edition. London, 12mo.
+  1836.</p>
+
+</blockquote>
+
+  <p>This is a curious hoax, evidently written by a person versed in
+  astronomy and clever at introducing probable circumstances and undesigned
+  coincidences.<a name="NtA_700" href="#Nt_700"><sup>[700]</sup></a> It
+  first appeared in a newspaper. It makes Sir J. Herschel discover men,
+  animals, etc. in the moon, of which much detail is given. There seems to
+  have been a French edition, the original, and English editions in
+  America, whence the work came into Britain: but whether the French was
+  published in America or at Paris I do not know. There is no doubt that it
+  was produced in the United States, by M. Nicollet,<a name="NtA_701"
+  href="#Nt_701"><sup>[701]</sup></a> an astronomer, once of Paris, and a
+  fugitive of some kind. About him I have heard two stories. First that he
+  fled to America with funds not his own, and that this book was a mere
+  device to raise the wind. Secondly, that he was a protégé of Laplace, and
+  of the Polignac party, and also an outspoken man. That after the
+  revolution he was so obnoxious to the republican party that he judged it
+  prudent to quit France; which he did in debt, leaving money for his
+  creditors, but not enough, with M. Bouvard. In America he connected
+  himself with an assurance office. <!-- Page 327 --><span
+  class="pagenum"><a name="page327"></a>[327]</span>The moon-story was
+  written, and sent to France, chiefly with the intention of entrapping M.
+  Arago, Nicollet's especial foe, into the belief of it. And those who
+  narrate this version of the story wind up by saying that M. Arago
+  <i>was</i> entrapped, and circulated the wonders through Paris, until a
+  letter from Nicollet to M. Bouvard<a name="NtA_702"
+  href="#Nt_702"><sup>[702]</sup></a> explained the hoax. I have no
+  personal knowledge of either story: but as the poor man had to endure the
+  first, it is but right that the second should be told with it.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">SOME MORE METEOROLOGY.</p>
+
+<blockquote class="b1n">
+
+  <p>The Weather Almanac for the Year 1838. By P. Murphy,<a name="NtA_703"
+  href="#Nt_703"><sup>[703]</sup></a> Esq., M.N.S.</p>
+
+</blockquote>
+
+  <p>By M. N. S. is meant <i>member of no society.</i>. This almanac bears
+  on the title-page two recommendations. The <i>Morning Post</i> calls it
+  one of the most important-if-true publications of our generation. The
+  <i>Times</i> says: "If the basis of his theory prove sound, and its
+  principles be sanctioned by a more extended experience, it is not too
+  much to say that the importance of the discovery is equal to that of the
+  longitude." Cautious journalist! Three times that of the longitude would
+  have been too little to say. That the landsman might predict the weather
+  of all the year, at its beginning, Jack would cheerfully give up
+  astronomical longitude&mdash;<i>the</i> problem&mdash;altogether, and
+  fall back on chronometers with the older Ls, lead, latitude, and
+  look-out, applied to dead-reckoning. Mr. Murphy attempted to give the
+  weather day by day: thus the first seven days of March <!-- Page 328
+  --><span class="pagenum"><a name="page328"></a>[328]</span>bore
+  Changeable; Rain; Rain; Rain-<i>wind</i>; Changeable; Fair; Changeable.
+  To aim at such precision as to put a fair day between two changeable ones
+  by weather theory was going very near the wind and weather too. Murphy
+  opened the year with cold and frost; and the weather did the same. But
+  Murphy, opposite to Saturday, January 20, put down "Fair, Probable lowest
+  degree of winter temperature." When this Saturday came, it was not merely
+  the probably coldest of 1838, but certainly the coldest of many
+  consecutive years. Without knowing anything of Murphy, I felt it prudent
+  to cover my nose with my glove as I walked the street at eight in the
+  morning. The fortune of the Almanac was made. Nobody waited to see
+  whether the future would dement the prophecy: the shop was beset in a
+  manner which brought the police to keep order; and it was said that the
+  Almanac for 1838 was a gain of 5,000<i>l.</i> to the owners. It very soon
+  appeared that this was only a lucky hit: the weather-prophet had a
+  modified reputation for a few years; and is now no more heard of. A work
+  of his will presently appear in the list.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE GREAT PYRAMIDS.</p>
+
+<blockquote class="b1n">
+
+  <p>Letter from Alexandria on the evidence of the practical application of
+  the quadrature of the circle in the great pyramids of Gizeh. By H.&nbsp;C.
+  Agnew,<a name="NtA_704" href="#Nt_704"><sup>[704]</sup></a> Esq. London,
+  1838, 4to.</p>
+
+</blockquote>
+
+<p><!-- Page 329 --><span class="pagenum"><a name="page329"></a>[329]</span></p>
+
+  <p>Mr. Agnew detects proportions which he thinks were suggested by those
+  of the circumference and diameter of a circle.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE MATHEMATICS OF A CREED.</p>
+
+<blockquote class="b1n">
+
+  <p>The creed of St. Athanasius proved by a mathematical parallel. Before
+  you censure, condemn, or approve; read, examine, and understand. <span
+  class="sc">E. B. Revilo</span>.<a name="NtA_705"
+  href="#Nt_705"><sup>[705]</sup></a> London, 1839, 8vo.</p>
+
+</blockquote>
+
+  <p>This author really believed himself, and was in earnest. He is not the
+  only person who has written nonsense by confounding the mathematical
+  infinite (of quantity) with what speculators now more correctly express
+  by the unlimited, the unconditioned, or the absolute. This tract is worth
+  preserving, as the extreme case of a particular kind. The following is a
+  specimen. Infinity being represented by &infin;, as usual, and <i>f</i>,
+  <i>s</i>, <i>g</i>, being finite integers, the three Persons are denoted
+  by &infin;<sup><i>f</i></sup>, (<i>m</i> &infin;)<sup><i>s</i></sup>,
+  &infin;<sup><i>g</i></sup>, the finite fraction <i>m</i> representing
+  human nature, as opposed to &infin;. The clauses of the Creed are then
+  given with their mathematical parallels. I extract a couple:</p>
+
+<table class="nobctr" width="80%" summary="Credal Mathematics" title="Credal Mathematics"><tr><td valign="top" style="width:50%" class="spac">
+"But the Godhead of the
+Father, of the Son, and of
+the Holy Ghost, is all one:
+the glory equal, the Majesty
+co-eternal.
+</td><td valign="top" style="width:50%" class="spac">
+"It has been shown that
+&infin;<sup><i>f</i></sup>, &infin;<sup><i>g</i></sup>, and (<i>m</i> &infin;)<sup><i>s</i></sup>, together,
+are but &infin;, and that
+each is &infin;, and any magnitude
+in existence represented
+by &infin; always was and always
+will be: for it cannot
+be made, or destroyed, and
+yet exists.
+</td></tr></table>
+
+<p><!-- Page 330 --><span class="pagenum"><a name="page330"></a>[330]</span></p>
+
+<table class="nobctr" width="80%" summary="Credal Mathematics" title="Credal Mathematics"><tr><td valign="top" style="width:50%" class="spac">
+"Equal to the Father, as
+touching his Godhead: and
+inferior to the Father,
+touching his Manhood."
+</td><td valign="top" style="width:50%" class="spac">
+"(<i>m</i> &infin;)<sup><i>s</i></sup> is equal to &infin;<sup><i>f</i></sup> as
+touching &infin;, but inferior to
+&infin;<sup><i>f</i></sup> as touching <i>m</i>: because
+<i>m</i> is not infinite."
+</td></tr></table>
+
+  <p>I might have passed this over, as beneath even my present subject, but
+  for the way in which I became acquainted with it. A bookseller, <i>not
+  the publisher</i>, handed it to me over his counter: one who had
+  published mathematical works. He said, with an air of important
+  communication, Have you seen <i>this</i>, Sir! In reply, I recommended
+  him to show it to my friend Mr.&mdash;&mdash;, for whom he had published
+  mathematics. Educated men, used to books and to the converse of learned
+  men, look with mysterious wonder on such productions as this: for which
+  reason I have made a quotation which many will judge had better have been
+  omitted. But it would have been an imposition on the public if I were,
+  omitting this and some other uses of the Bible and Common Prayer, to
+  pretend that I had given a true picture of my school.</p>
+
+  <p>[Since the publication of the above, it has been stated that the
+  author is Mr. Oliver Byrne, the author of the <i>Dual Arithmetic</i>
+  mentioned further on: E. B. Revilo seems to be obviously a reversal.]</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">LOGIC HAS NO PARADOXERS.</p>
+
+<blockquote class="b1n">
+
+  <p>Old and new logic contrasted: being an attempt to elucidate, for
+  ordinary comprehension, how Lord Bacon delivered the human mind from its
+  2,000 years' enslavement under Aristotle. By Justin Brenan.<a
+  name="NtA_706" href="#Nt_706"><sup>[706]</sup></a> London, 1839,
+  12mo.</p>
+
+</blockquote>
+
+  <p>Logic, though the other exact science, has not had the sort of
+  assailants who have clustered about mathematics. There is a sect which
+  disputes the utility of logic, but there are no special points, like the
+  quadrature of the circle, which <!-- Page 331 --><span class="pagenum"><a
+  name="page331"></a>[331]</span>excite dispute among those who admit other
+  things. The old story about Aristotle having one logic to trammel us, and
+  Bacon another to set us free,&mdash;always laughed at by those who really
+  knew either Aristotle or Bacon,&mdash;now begins to be understood by a
+  large section of the educated world. The author of this tract connects
+  the old logic with the indecencies of the classical writers, and the new
+  with moral purity: he appeals to women, who, "when they see plainly the
+  demoralizing tendency of syllogistic logic, they will no doubt exert
+  their powerful influence against it, and support the Baconian method."
+  This is the only work against logic which I can introduce, but it is a
+  rare one, I mean in contents. I quote the author's idea of a
+  syllogism:</p>
+
+  <p>"The basis of this system is the syllogism. This is a form of couching
+  the substance of your argument or investigation into one short line or
+  sentence&mdash;then corroborating or supporting it in another, and
+  drawing your conclusion or proof in a third."</p>
+
+  <p>On this definition he gives an example, as follows: "Every sin
+  deserves death," the substance of the "argument or investigation." Then
+  comes, "Every unlawful wish is a sin," which "corroborates or supports"
+  the preceding: and, lastly, "therefore every unlawful wish deserves
+  death," which is the "conclusion or proof." We learn, also, that
+  "sometimes the first is called the premises (<i>sic</i>), and sometimes
+  the first premiss"; as also that "the first is sometimes called the
+  proposition, or subject, or affirmative, and the next the predicate, and
+  sometimes the middle term." To which is added, with a mark of exclamation
+  at the end, "but in analyzing the syllogism, there is a middle term, and
+  a predicate too, in each of the lines!" It is clear that Aristotle never
+  enslaved this mind.</p>
+
+  <p>I have said that logic has no paradoxers, but I was speaking of old
+  time. This science has slept until our own day: Hamilton<a name="NtA_707"
+  href="#Nt_707"><sup>[707]</sup></a> says there has been "no progress made
+  in <!-- Page 332 --><span class="pagenum"><a
+  name="page332"></a>[332]</span>the <i>general</i> development of the
+  syllogism since the time of Aristotle; and in regard to the few
+  <i>partial</i> improvements, the professed historians seem altogether
+  ignorant." But in our time, the paradoxer, the opponent of common
+  opinion, has appeared in this field. I do not refer to Prof. Boole,<a
+  name="NtA_708" href="#Nt_708"><sup>[708]</sup></a> who is not a
+  <i>paradoxer</i>, but a <i>discoverer</i>: his system could neither
+  oppose nor support common opinion, for its grounds were not in the
+  conception of any one. I speak especially of two others, who fought like
+  cat and dog: one was dogmatical, the other categorical. The first was
+  Hamilton himself&mdash;Sir William Hamilton of Edinburgh, the
+  metaphysician, not Sir William <i>Rowan</i> Hamilton<a name="NtA_709"
+  href="#Nt_709"><sup>[709]</sup></a> of Dublin, the mathematician, a
+  combination of peculiar genius with unprecedented learning, erudite in
+  all he could want except mathematics, for which he had no turn, and in
+  which he had not even a schoolboy's knowledge, thanks to the Oxford of
+  his younger day. The other was the author of this work, so fully
+  described in Hamilton's writings that there is no occasion to describe
+  him here. I shall try to say a few words in common language about the
+  paradoxers.</p>
+
+  <p>Hamilton's great paradox was the <i>quantification of the
+  predicate</i>; a fearful phrase, easily explained. We all know that when
+  we say "Men are animals," a form wholly unquantified in phrase, we speak
+  of <i>all</i> men, but not of all animals: it is <i>some or all</i>, some
+  may be all for aught the proposition says. This
+  some-may-be-all-for-aught-we-say, or <i>not-none,</i> is the logician's
+  <i>some</i>. One would suppose <!-- Page 333 --><span class="pagenum"><a
+  name="page333"></a>[333]</span>that "all men are some animals," would
+  have been the logical phrase in all time: but the predicate never was
+  quantified. The few who alluded to the possibility of such a thing found
+  reasons for not adopting it over and above the great reason, that
+  Aristotle did not adopt it. For Aristotle never ruled in physics or
+  metaphysics <i>in the old time</i> with near so much of absolute sway as
+  he has ruled in logic <i>down to our own time</i>. The logicians knew
+  that in the proposition "all men are animals" the "animal" is not
+  <i>universal</i>, but <i>particular</i> yet no one dared to say that
+  <i>all</i> men are <i>some</i> animals, and to invent the phrase,
+  "<i>some</i> animals are <i>all</i> men" until Hamilton leaped the ditch,
+  and not only completed a system of enunciation, but applied it to
+  syllogism.</p>
+
+  <p>My own case is as peculiar as his: I have proposed to introduce
+  mathematical <i>thought</i> into logic to an extent which makes the old
+  stagers cry:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"St. Aristotle! what wild notions!</p>
+      <p>Serve a <i>ne exeat regno</i><a name="NtA_710" href="#Nt_710"><sup>[710]</sup></a> on him!"</p>
+    </div>
+  </div>
+  <p>Hard upon twenty years ago, a friend and opponent who stands high in
+  these matters, and who is not nearly such a sectary of Aristotle and
+  establishment as most, wrote to me as follows: "It is said that next to
+  the man who forms the taste of the nation, the greatest genius is the man
+  who corrupts it. I mean therefore no disrespect, but very much the
+  reverse, when I say that I have hitherto always considered you as a great
+  logical heresiarch." Coleridge says he thinks that it was Sir Joshua
+  Reynolds who made the remark: which, to copy a bull I once heard, I
+  cannot deny, because I was not there when he said it. My friend did not
+  call me to repentance and reconciliation with the church: I think he had
+  a guess that I was a reprobate sinner. My offences at that time were but
+  small: I went on spinning syllogism systems, all alien from the common
+  logic, until I had six, the initial letters of which, put together, from
+  the <!-- Page 334 --><span class="pagenum"><a
+  name="page334"></a>[334]</span>names I gave before I saw what they would
+  make, bar all repentance by the words</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>RUE NOT!</p>
+    </div>
+  </div>
+  <p>leaving to the followers of the old school the comfortable option of
+  placing the letters thus:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>TRUE? NO!</p>
+    </div>
+  </div>
+  <p>It should however be stated that the question is not about absolute
+  truth or falsehood. No one denies that anything I call an inference is an
+  inference: they say that my alterations are <i>extra-logical</i>; that
+  they are <i>material</i>, not <i>formal</i>; and that logic is a
+  <i>formal</i> science.</p>
+
+  <p>The distinction between material and formal is easily made, where the
+  usual perversions are not required. A <i>form</i> is an empty machine,
+  such as "Every X is Y"; it may be supplied with <i>matter</i>, as in
+  "Every <i>man</i> is <i>animal</i>." The logicians will not see that
+  their <i>formal</i> proposition, "Every X is Y," is material in three
+  points, the degree of assertion, the quantity of the proposition, and the
+  copula. The purely formal proposition is "There is the probability <span
+  class="grk">&alpha;</span> that X stands in the relation L to Y." The
+  time will come when it will be regretted that logic went without
+  paradoxers for two thousand years: and when much that has been said on
+  the distinction of form and matter will breed jokes.</p>
+
+  <p>I give one instance of one mood of each of the systems, in the order
+  of the letters first written above.</p>
+
+  <p><i>Relative.</i>&mdash;In this system the formal relation is taken,
+  that is, the copula may be any whatever. As a material instance, in which
+  the <i>relations</i> are those of consanguinity (of men understood), take
+  the following: X is the brother of Y; X is not the uncle of Z; therefore,
+  Z is not the child of Y. The discussion of relation, and of the
+  objections to the extension, is in the <i>Cambridge Transactions</i>,
+  Vol. X, Part 2; a crabbed conglomerate.</p>
+
+  <p><i>Undecided.</i>&mdash;In this system one premise, and want of power
+  over another, infer want of power over a conclusion. <!-- Page 335
+  --><span class="pagenum"><a name="page335"></a>[335]</span>As "Some men
+  are not capable of tracing consequences; we cannot be sure that there are
+  beings responsible for consequences who are incapable of tracing
+  consequences; therefore, we cannot be sure that all men are responsible
+  for the consequences of their actions."</p>
+
+  <p><i>Exemplar.</i>&mdash;This, long after it suggested itself to me as a
+  means of correcting a defect in Hamilton's system, I saw to be the very
+  system of Aristotle himself, though his followers have drifted into
+  another. It makes its subject and predicate examples, thus: Any one man
+  is an animal; any one animal is a mortal; therefore, any one man is a
+  mortal.</p>
+
+  <p><i>Numerical.</i>&mdash;Suppose 100 Ys to exist: then if 70 Xs be Ys,
+  and 40 Zs be Ys, it follows that 10 Xs (at least) are Zs. Hamilton, whose
+  mind could not generalize on symbols, saw that the word <i>most</i> would
+  come under this system, and admitted, as valid, such a syllogism as "most
+  Ys are Xs; most Ys are Zs; therefore, some Xs are Zs."</p>
+
+  <p><i>Onymatic.</i>&mdash;This is the ordinary system much enlarged in
+  propositional forms. It is fully discussed in my <i>Syllabus of
+  Logic</i>.</p>
+
+  <p><i>Transposed.</i>&mdash;In this syllogism the quantity in one premise
+  is transposed into the other. As, some Xs are not Ys; for every X there
+  is a Y which is Z; therefore, some Zs are not Xs.</p>
+
+  <p>Sir William Hamilton of Edinburgh was one of the best friends and
+  allies I ever had. When I first began to publish speculation on this
+  subject, he introduced me to the logical world as having plagiarized from
+  him. This drew their attention: a mathematician might have written about
+  logic under forms which had something of mathematical look long enough
+  before the Aristotelians would have troubled themselves with him: as was
+  done by John Bernoulli,<a name="NtA_711"
+  href="#Nt_711"><sup>[711]</sup></a> <!-- Page 336 --><span
+  class="pagenum"><a name="page336"></a>[336]</span>James Bernoulli,<a
+  name="NtA_712" href="#Nt_712"><sup>[712]</sup></a> Lambert,<a
+  name="NtA_713" href="#Nt_713"><sup>[713]</sup></a> and Gergonne;<a
+  name="NtA_714" href="#Nt_714"><sup>[714]</sup></a> who, when our
+  discussion began, were not known even to omnilegent Hamilton. He
+  retracted his accusation of <i>wilful</i> theft in a manly way when he
+  found it untenable; but on this point he wavered a little, and was
+  convinced to the last that I had taken his principle unconsciously. He
+  thought I had done the same with Ploucquet<a name="NtA_715"
+  href="#Nt_715"><sup>[715]</sup></a> and Lambert. It was his pet notion
+  that I did not understand the commonest principles of logic, that I did
+  not always know the difference between the middle term of a syllogism and
+  its conclusion. It went against his grain to imagine that a mathematician
+  could be a logician. So long as he took me to be riding my own hobby, he
+  laughed consumedly: but when he thought he could make out that I was
+  mounted behind Ploucquet or Lambert, the current ran thus: "It would
+  indeed have been little short of a miracle had he, ignorant even of the
+  common principles of logic, been able of himself to rise to
+  generalization so lofty and so accurate as are supposed in the peculiar
+  doctrines of both the rival logicians, Lambert and Ploucquet&mdash;how
+  useless soever these may in practice prove to be." All this has been
+  sufficiently discussed elsewhere: "but, masters, remember that I am an
+  ass."</p>
+
+  <p>I know that I never saw Lambert's work until after all Hamilton
+  supposed me to have taken was written: he himself, who read almost
+  everything, knew nothing about it until after I did. I cannot prove what
+  I say about my knowledge of Lambert: but the means of doing it may turn
+  up. For, by the casual turning up of an old letter, I <i>have</i> <!--
+  Page 337 --><span class="pagenum"><a name="page337"></a>[337]</span>found
+  the means of clearing myself as to Ploucquet. Hamilton assumed that
+  (unconsciously) I took from Ploucquet the notion of a logical notation in
+  which the symbol of the conclusion is seen in the joint symbols of the
+  premises. For example, in my own fashion I write down ( . ) ( . ), two
+  symbols of premises. By these symbols I see that there is a valid
+  conclusion, and that it may be written in symbol by striking out the two
+  middle parentheses, which gives ( . . ) and reading the two negative dots
+  as an affirmative. And so I see in ( . ) ( . ) that ( ) is the
+  conclusion. This, in full, is the perception that "all are either Xs or
+  Ys" and "all are either Ys or Zs" necessitates "some Xs are Zs." Now in
+  Ploucquet's book of 1763, is found, "Deleatur in præmissis medius; id
+  quod restat indicat conclusionem."<a name="NtA_716"
+  href="#Nt_716"><sup>[716]</sup></a> In the paper in which I explain my
+  symbols&mdash;which are altogether different from Ploucquet's&mdash;there
+  is found "Erase the symbols of the middle term; the remaining symbols
+  show the inference." There is very great likeness: and I would have
+  excused Hamilton for his notion if he had fairly given reference to the
+  part of the book in which his quotation was found. For I had shown in my
+  <i>Formal Logic</i> what part of Ploucquet's book I had used: and a fair
+  disputant would either have strengthened his point by showing that I had
+  been at his part of the book, or allowed me the advantage of it being
+  apparent that I had not given evidence of having seen that part of the
+  book. My good friend, though an honest man, was sometimes unwilling to
+  allow due advantage to controversial opponents.</p>
+
+  <p>But to my point. The only work of Ploucquet I ever saw was lent me by
+  my friend Dr. Logan,<a name="NtA_717" href="#Nt_717"><sup>[717]</sup></a>
+  with whom I have often corresponded on logic, etc. I chanced (in 1865)
+  <!-- Page 338 --><span class="pagenum"><a
+  name="page338"></a>[338]</span>to turn up the letter which he sent me
+  (Sept. 12, 1847) <i>with the book</i>. Part of it runs thus: "I
+  congratulate you on your success in your logical researches [that is, in
+  asking for the book, I had described some results]. Since the reading of
+  your first paper I have been satisfied as to the possibility of inventing
+  a logical notation in which the rationale of the inference is contained
+  in the symbol, though I never attempted to verify it [what I
+  communicated, then, satisfied the writer that I had done and communicated
+  what he, from my previous paper, suspected to be practicable]. I send you
+  Ploucquet's dissertation....'</p>
+
+  <p>It now being manifest that I cannot be souring grapes which have been
+  taken from me, I will say what I never said in print before. There is not
+  the slightest merit in making the symbols of the premises yield that of
+  the conclusion by erasure: <i>the thing must do itself in every system
+  which symbolises quantities</i>. For in every syllogism (except the
+  inverted <i>Bramantip</i> of the Aristotelians) the conclusion is
+  manifest in this way without symbols. This <i>Bramantip</i> destroys
+  system in the Aristotelian lot: and circumstances which I have pointed
+  out destroy it in Hamilton's own collection. But in that enlargement of
+  the reputed Aristotelian system which I have called <i>onymatic</i>, and
+  in that correction of Hamilton's system which I have called
+  <i>exemplar</i>, the rule of erasure is universal, and may be seen
+  without symbols.</p>
+
+  <p>Our first controversy was in 1846. In 1847, in my <i>Formal Logic</i>,
+  I gave him back a little satire for satire, just to show, as I stated,
+  that I could employ ridicule if I pleased. He was so offended with the
+  appendix in which this was contained, that he would not accept the copy
+  of the book I sent him, but returned it. Copies of controversial works,
+  sent from opponent to opponent, are not <i>presents</i>, in the usual
+  sense: it was a marked success to make him angry enough to forget this.
+  It had some effect however: during the rest of his life I wished to avoid
+  provocation; for I <!-- Page 339 --><span class="pagenum"><a
+  name="page339"></a>[339]</span>could not feel sure that excitement might
+  not produce consequences. I allowed his slashing account of me in the
+  <i>Discussions</i> to pass unanswered: and before that, when he proposed
+  to open a controversy in the <i>Athenæum</i> upon my second Cambridge
+  paper, I merely deferred the dispute until the next edition of my
+  <i>Formal Logic</i>. I cannot expect the account in the
+  <i>Discussions</i> to amuse an unconcerned reader as much as it amused
+  myself: but for a cut-and-thrust, might-and-main, tooth-and-nail,
+  hammer-and-tongs assault, I can particularly recommend it. I never knew,
+  until I read it, how much I should enjoy a thundering onslought on
+  myself, done with racy insolence by a master hand, to whom my good genius
+  had whispered <i>Ita feri ut se sentiat emori</i>.<a name="NtA_718"
+  href="#Nt_718"><sup>[718]</sup></a> Since that time I have, as the
+  Irishman said, become "dry moulded for want of a bating." Some of my
+  paradoxers have done their best: but theirs is mere twopenny&mdash;"small
+  swipes," as Peter Peebles said. Brandy for heroes! I hope a reviewer or
+  two will have mercy on me, and will give me as good discipline as
+  Strafford would have given Hampden and his set: "much beholden," said he,
+  "should they be to any one that should thoroughly take pains with them in
+  that kind"&mdash;meaning <i>objective</i> flagellation. And I shall be
+  the same to any one who will serve me so&mdash;but in a literary and
+  periodical sense: my corporeal cuticle is as thin as my neighbors'.</p>
+
+  <p>Sir W. H. was suffering under local paralysis before our controversy
+  commenced: and though his mind was quite unaffected, a retort of as
+  downright a character as the attack might have produced serious effect
+  upon a person who had shown himself sensible of ridicule. Had a second
+  attack of his disorder followed an answer from me, I should have been
+  held to have caused it: though, looking at Hamilton's genial love of
+  combat, I strongly suspected that a retort in kind</p>
+
+<p><!-- Page 340 --><span class="pagenum"><a name="page340"></a>[340]</span></p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Would cheer his heart, and warm his blood,</p>
+      <p>And make him fight, and do him good."</p>
+    </div>
+  </div>
+  <p>But I could not venture to risk it. So all I did, in reply to the
+  article in the <i>Discussions</i>, was to write to him the following
+  note: which, as illustrating an etiquette of controversy, I insert.</p>
+
+  <p>"I beg to acknowledge and thank you for.... It is necessary that I
+  should say a word on my retention of this work, with reference to your
+  return of the copy of my <i>Formal Logic</i>, which I presented to you on
+  its publication: a return made on the ground of your disapproval of the
+  account of our controversy which that work contained. According to my
+  view of the subject, any one whose dealing with the author of a book is
+  specially attacked in it, has a right to expect from the author that part
+  of the book in which the attack is made, together with so much of the
+  remaining part as is fairly context. And I hold that the acceptance by
+  the party assailed of such work or part of a work does not imply any
+  amount of approval of the contents, or of want of disapproval. On this
+  principle (though I am not prepared to add the word <i>alone</i>) I
+  forwarded to you the whole of my work on <i>Formal Logic</i> and my
+  second Cambridge Memoir. And on this principle I should have held you
+  wanting in due regard to my literary rights if you had not forwarded to
+  me your asterisked pages, with all else that was necessary to a full
+  understanding of their scope and meaning, so far as the contents of the
+  book would furnish it. For the remaining portion, which it would be a
+  hundred pities to separate from the pages in which I am directly
+  concerned, I am your debtor on another principle; and shall be glad to
+  remain so if you will allow me to make a feint of balancing the account
+  by the offer of two small works on subjects as little connected with our
+  discussion as the <i>Epistolæ Obscurorum Virorum</i>, or the Lutheran
+  dispute. I trust that by accepting my <i>Opuscula</i> you will enable me
+  to avoid the <!-- Page 341 --><span class="pagenum"><a
+  name="page341"></a>[341]</span>use of the knife, and leave me to cut you
+  up with the pen as occasion shall serve, I remain, etc. (April 21,
+  1852)."</p>
+
+  <p>I received polite thanks, but not a word about the body of the letter:
+  my argument, I suppose, was admitted.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">SOME DOGGEREL AND COUNTER DOGGEREL.</p>
+
+  <p>I find among my miscellaneous papers the following <i>jeu
+  d'esprit</i>, or <i>jeu de bêtise</i>,<a name="NtA_719"
+  href="#Nt_719"><sup>[719]</sup></a> whichever the reader pleases&mdash;I
+  care not&mdash;intended, before I saw ground for abstaining, to have, as
+  the phrase is, come in somehow. I think I could manage to bring anything
+  into anything: certainly into a Budget of Paradoxes. Sir W.&nbsp;H. rather
+  piqued himself upon some caniculars, or doggerel verses, which he had put
+  together <i>in memoriam</i> [<i>technicam</i>] of the way in which
+  A&nbsp;E&nbsp;I&nbsp;O are used in logic: he added U, Y, for the addition of
+  <i>meet</i>, etc., to the system. I took the liberty of concocting some
+  counter-doggerel, just to show that a mathematician may have
+  architectonic power as well as a metaphysician.</p>
+
+  <p>&nbsp;</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="i8">DOGGEREL.</p>
+      <p class="i4"><span class="scac">BY SIR W.  HAMILTON.</span></p>
+      <p>A it affirms of <i>this</i>, <i>these</i>, <i>all</i>,</p>
+      <p class="i2">Whilst E denies of <i>any</i>;</p>
+      <p>I it affirms (whilst O denies)</p>
+      <p class="i2">Of some (or few, or many).</p>
+    </div>
+
+    <div class="stanza">
+      <p>Thus A affirms, as E denies,</p>
+      <p class="i2">And definitely either;</p>
+      <p>Thus I affirms, as O denies,</p>
+      <p class="i2">And definitely neither.</p>
+    </div>
+
+    <div class="stanza">
+      <p>A half, left semidefinite,</p>
+      <p class="i2">Is worthy of its score;</p>
+      <p>U, then, affirms, as Y denies,</p>
+      <p class="i2">This, neither less nor more.</p>
+    </div>
+
+    <div class="stanza">
+      <p>Indefinito-definites,</p>
+      <p class="i2">I, UI, YO, last we come;</p>
+<!-- Page 342 --><span class="pagenum"><a name="page342"></a>[342]</span>
+      <p>And this affirms, as that denies</p>
+      <p class="i2">Of <i>more</i>, <i>most</i> (<i>half</i>, <i>plus</i>, <i>some</i>).</p>
+    </div>
+
+    <div class="stanza">
+      <p class="i2">COUNTER DOGGEREL.</p>
+      <p class="i4"><span class="scac">BY PROF. DE MORGAN.</span></p>
+      <p class="i8">(1847.)</p>
+      <p>Great A affirms of all;</p>
+      <p class="i2">Sir William does so too:</p>
+      <p>When the subject is "my suspicion,"</p>
+      <p class="i2">And the predicate "must be true."</p>
+    </div>
+
+    <div class="stanza">
+      <p>Great E denies of all;</p>
+      <p class="i2">Sir William of all but one:</p>
+      <p>When he speaks about this present time,</p>
+      <p class="i2">And of those who in logic have done.</p>
+    </div>
+
+    <div class="stanza">
+      <p>Great I takes up but <i>some</i>;</p>
+      <p class="i2">Sir William! my dear soul!</p>
+      <p>Why then in all your writings,</p>
+      <p class="i2">Does "Great I" fill<a name="NtA_720" href="#Nt_720"><sup>[720]</sup></a> the whole!</p>
+    </div>
+
+    <div class="stanza">
+      <p>Great O says some are not;</p>
+      <p class="i2">Sir William's readers catch,</p>
+      <p>That some (modern) Athens is not without</p>
+      <p class="i2">An Aristotle to match.</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"A half, left semi-definite,</p>
+      <p class="i2">Is worthy of its score:"</p>
+      <p>This looked very much like balderdash,</p>
+      <p class="i2">And neither less nor more.</p>
+    </div>
+
+    <div class="stanza">
+      <p>It puzzled me like anything;</p>
+      <p class="i2">In fact, it puzzled me worse:</p>
+      <p>Isn't schoolman's logic hard enough,</p>
+      <p class="i2">Without being in Sibyl's verse?</p>
+    </div>
+
+    <div class="stanza">
+<!-- Page 343 --><span class="pagenum"><a name="page343"></a>[343]</span>
+      <p>At last, thinks I, 'tis German;</p>
+      <p class="i2">And I'll try it with some beer!</p>
+      <p>The landlord asked what bothered me so,</p>
+      <p class="i2">And at once he made it clear.</p>
+    </div>
+
+    <div class="stanza">
+      <p>It's <i>half-and-half</i>, the gentleman means;</p>
+      <p class="i2">Don't you see he talks of <i>score</i>?</p>
+      <p>That's the bit of memorandum</p>
+      <p class="i2">That we chalk behind the door.</p>
+    </div>
+
+    <div class="stanza">
+      <p><i>Semi-definite</i>'s outlandish;</p>
+      <p class="i2">But I see, in half a squint,</p>
+      <p>That he speaks of the lubbers who call for a quart,</p>
+      <p class="i2">When they can't manage more than a pint.</p>
+    </div>
+
+    <div class="stanza">
+      <p>Now I'll read it into English,</p>
+      <p class="i2">And then you'll answer me this:</p>
+      <p>If it isn't good logic all the world round,</p>
+      <p class="i2">I should like to know what is?</p>
+    </div>
+
+    <div class="stanza">
+      <p>When you call for a pot of half-and-half,</p>
+      <p class="i2">If you're lost to sense of shame,</p>
+      <p>You may leave it <i>semi-definite</i>,</p>
+      <p class="i2">But you pay for it all just the same.</p>
+      <p>&nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; * &nbsp; &nbsp; &nbsp; *</p>
+    </div>
+  </div>
+  <p>I am unspeakably comforted when I look over the above in remembering
+  that the question is not whether it be Pindaric or Horatian, but whether
+  the copy be as good as the original. And I say it is: and will take no
+  denial.</p>
+
+  <p>Long live&mdash;long will live&mdash;the glad memory of William
+  Hamilton, Good, Learned, Acute, and Disputatious! He fought upon
+  principle: the motto of his book is:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Truth, like a torch, the more it's shook it shines."</p>
+    </div>
+  </div>
+  <p>There is something in this; but metaphors, like puddings, quarrels,
+  rivers, and arguments, always have two sides to them. For instance,</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Truth, like a torch, the more it's shook it shines;</p>
+      <p class="i2">But those who want to use it, hold it steady.</p>
+      <p>They shake the flame who like a glare to gaze at,</p>
+      <p class="i2">They keep it still who want a light to see by."</p>
+    </div>
+  </div>
+<p><!-- Page 344 --><span class="pagenum"><a name="page344"></a>[344]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ANOTHER THEORY OF PARALLELS.</p>
+
+<blockquote class="b1n">
+
+  <p>Theory of Parallels. The proof of Euclid's axiom looked for in the
+  properties of the Equiangular Spiral. By Lieut-Col. G. Perronet
+  Thompson.<a name="NtA_721" href="#Nt_721"><sup>[721]</sup></a> The same,
+  second edition, revised and corrected. The same, third edition,
+  shortened, and freed from dependence on the theory of limits. The same,
+  fourth edition, ditto, ditto. All London, 1840, 8vo.</p>
+
+</blockquote>
+
+  <p>To explain these editions it should be noted that General Thompson
+  rapidly modified his notions, and republished his tracts accordingly.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">SOME PRIMITIVE DARWINISM.</p>
+
+<blockquote class="b1n">
+
+  <p>Vestiges of the Natural History of Creation.<a name="NtA_722"
+  href="#Nt_722"><sup>[722]</sup></a> London, 1840, 12mo.</p>
+
+</blockquote>
+
+  <p>This is the first edition of this celebrated work. Its form is a case
+  of the theory: the book is an undeniable duodecimo, but the size of its
+  paper gives it the look of not the smallest of octavos. Does not this
+  illustrate the law of development, the gradation of families, the
+  transference of species, and so on? If so, I claim the discovery of this
+  esoteric testimony of the book to its own contents; I defy any one to
+  point out the reviewer who has mentioned it. The work itself is <span
+  class="correction" title="text reads `decribed'">described</span> by its
+  author as "the first attempt to connect the natural sciences into a
+  history of creation." The attempt was commenced, and has been carried on,
+  both with marked talent, and will be continued. Great advantage will
+  result: at the worst we are but in the alchemy of some new chemistry, or
+  the astrology of some new astronomy. Perhaps it would be as well not to
+  be too sure on the matter, until we have an antidote to possible
+  consequences as exhibited under another theory, on which <!-- Page 345
+  --><span class="pagenum"><a name="page345"></a>[345]</span>it is as
+  reasonable to speculate as on that of the <i>Vestiges</i>. I met long ago
+  with a splendid player on the guitar, who assured me, and was confirmed
+  by his friends, that he <i>never practised</i>, except in thought, and
+  did not possess an instrument: he kept his fingers acting in his mind,
+  until they got their habits; and thus he learnt the most difficult
+  novelties of execution. Now what if this should be a minor segment of a
+  higher law? What if, by constantly thinking of ourselves as descended
+  from primeval monkeys, we should&mdash;if it be true&mdash;actually
+  <i>get our tails again</i>? What if the first man who was detected with
+  such an appendage should be obliged to confess himself the author of the
+  <i>Vestiges</i>&mdash;a person yet unknown&mdash;who would naturally get
+  the start of his species by having had the earliest habit of thinking on
+  the matter? I confess I never hear a man of note talk fluently about it
+  without a curious glance at his proportions, to see whether there may be
+  ground to conjecture that he may have more of "mortal coil" than others,
+  in anaxyridical concealment. I do not feel sure that even a paternal love
+  for his theory would induce him, in the case I am supposing, to exhibit
+  himself at the British Association,</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>With a hole behind which his tail peeped through.</p>
+    </div>
+  </div>
+  <p>The first sentence of this book (1840) is a cast of the log, which
+  shows our rate of progress. "It is familiar knowledge that the earth
+  which we inhabit is a globe of somewhat less than 8,000 miles in
+  diameter, being one of a series of eleven which revolve at different
+  distances around the sun." The <i>eleven</i>! Not to mention the Iscariot
+  which Le Verrier and Adams calculated into existence, there is more than
+  a septuagint of <i>new</i> planetoids.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ON RELIGIOUS INSURANCE.</p>
+
+<blockquote class="b1n">
+
+  <p>The Constitution and Rules of the Ancient and Universal 'Benefit
+  Society' established by Jesus Christ, exhibited, and its advantages and
+  claims maintained, against all Modern and <!-- Page 346 --><span
+  class="pagenum"><a name="page346"></a>[346]</span>merely Human
+  Institutions of the kind: A Letter very respectfully addressed to the
+  Rev. James Everett,<a name="NtA_723" href="#Nt_723"><sup>[723]</sup></a>
+  and occasioned by certain remarks made by him, in a speech to the Members
+  of the 'Wesleyan Centenary Institute' Benefit Society. Dated York, Dec.
+  7, 1840. By Thomas Smith.<a name="NtA_724"
+  href="#Nt_724"><sup>[724]</sup></a> 12mo, (pp. 8.)</p>
+
+</blockquote>
+
+  <p>The Wesleyan minister addressed had advocated provision against old
+  age, etc.: the writer declares all <i>private</i> provision un-Christian.
+  After decent maintenance and relief of family claims of indigence, he
+  holds that all the rest is to go to the "Benefit Society," of which he
+  draws up the rules, in technical form, with chapters of "Officers,"
+  "Contributors" etc., from the Acts of the Apostles, etc., and some of the
+  early Fathers. He holds that a Christian may not "make a <i>private</i>
+  provision against the contingencies of the future": and that the great
+  "Benefit Society" is the divinely-ordained recipient of all the surplus
+  of his income; capital, beyond what is necessary for business, he is to
+  have none. A real good speculator shuts his eyes by instinct, when
+  opening them would not serve the purpose: he has the vizor of the Irish
+  fairy tale, which fell of itself over the eyes of the wearer the moment
+  he turned them upon the enchanted light which would have destroyed him if
+  he had caught sight of it. "Whiles it remained, was it not thine own? and
+  after it was sold, was it (the purchase-money) not in thine own power?"
+  would have been awkward to quote, and accordingly nothing is stated
+  except the well-known result, which is rule 3, cap. 5, "Prevention of
+  Abuses." By putting his principles together, the author can be made,
+  logically, to mean that the successors of the apostles should put to
+  death all contributors who are detected in not paying their full
+  premiums.</p>
+
+<p><!-- Page 347 --><span class="pagenum"><a name="page347"></a>[347]</span></p>
+
+  <p>I have known one or two cases in which policy-holders have surrendered
+  their policies through having arrived at a conviction that direct
+  provision is unlawful. So far as I could make it out, these parties did
+  not think it unlawful to lay by out of income, except when this was done
+  in a manner which involved calculation of death-chances. It is singular
+  they did not see that the entrance of chance of death was the entrance of
+  the very principle of the benefit society described in the Acts of the
+  Apostles. The family of the one who died young received more in
+  proportion to <i>premiums</i> paid than the family of one who died old.
+  Every one who understands life assurance sees that&mdash;<i>bonus</i>
+  apart&mdash;the difference between an assurance office and a savings bank
+  consists in the adoption, <i>pro tanto</i>, of the principle of community
+  of goods. In the original constitution of the oldest assurance office,
+  the <i>Amicable Society</i>, the plan with which they started was nothing
+  but this: persons of all ages under forty-five paid one common premium,
+  and the proceeds were divided among the representatives of those who died
+  within the year.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE TWO OLD PARADOXES AGAIN.</p>
+
+  <p>[I omitted from its proper place a manuscript quadrature (3.1416
+  exactly) addressed to an eminent mathematician, dated in 1842 from the
+  debtor's ward of a country gaol. The unfortunate speculator says, "I have
+  labored many years to find the precise ratio." I have heard of several
+  cases in which squaring the circle has produced an inability to square
+  accounts. I remind those who feel a kind of inspiration to employ native
+  genius upon difficulties, without gradual progression from elements, that
+  the call is one which becomes stronger and stronger, and may lead, as it
+  has led, to abandonment of the duties of life, and all the consequences.]
+  <!-- Page 348 --><span class="pagenum"><a
+  name="page348"></a>[348]</span></p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>1842. Provisional Prospectus of the Double Acting Rotary Engine
+  Company. Also Mechanic's Magazine, March 26, 1842.</p>
+
+</blockquote>
+
+  <p>Perpetual motion by a drum with one vertical half in mercury, the
+  other in a vacuum: the drum, I suppose, working round forever to find an
+  easy position. Steam to be superseded: steam and electricity convulsions
+  of nature never intended by Providence for the use of man. The price of
+  the present engines, as old iron, will buy new engines that will work
+  without fuel and at no expense. Guaranteed by the Count de Predaval,<a
+  name="NtA_725" href="#Nt_725"><sup>[725]</sup></a> the discoverer. I was
+  to have been a Director, but my name got no further than ink, and not so
+  far as official notification of the honor, partly owing to my having
+  communicated to the <i>Mechanic's Magazine</i> information privately
+  given to me, which gave premature publicity, and knocked up the plan.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>An Exposition of the Nature, Force, Action, and other properties of
+  Gravitation on the Planets. London, 1842, 12mo.</p>
+
+  <p>An Investigation of the principles of the Rules for determining the
+  Measures of the Areas and Circumferences of Circular Plane Surfaces ...
+  London, 1844, 8vo.</p>
+
+</blockquote>
+
+  <p>These are anonymous; but the author (whom I believe to be Mr.
+  Denison,<a name="NtA_726" href="#Nt_726"><sup>[726]</sup></a> presently
+  noted) is described as author of a new system of mathematics, and also of
+  mechanics. He had need have both, for he shows that the line which has a
+  square equal to a given circle, has a cube equal to the sphere on the
+  same diameter: that is, in old mathematics, the diameter is to the
+  circumference as 9 to 16! Again, admitting that the velocities of planets
+  in circular orbits are inversely as the square roots of their distances,
+  that is, admitting Kepler's law, he manages to prove that gravitation is
+  inversely as the square <i>root</i> of the distance: and suspects
+  magnetism of doing the difference between this and Newton's law. <!--
+  Page 349 --><span class="pagenum"><a
+  name="page349"></a>[349]</span>Magnetism and electricity are, in physics,
+  the member of parliament and the cabman&mdash;at every man's bidding, as
+  Henry Warburton<a name="NtA_727" href="#Nt_727"><sup>[727]</sup></a>
+  said.</p>
+
+  <p>The above is an outrageous quadrature. In the preceding year, 1841,
+  was published what I suppose at first to be a Maori quadrature, by
+  Maccook. But I get it from a cutting out of some French periodical, and I
+  incline to think that it must be by a Mr. M<sup>c</sup>Cook. He makes
+  <span class="grk">&pi;</span> to be 2 + 2&radic;(8&radic;2 - 11).</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE DUPLICATION PROBLEM.</p>
+
+<blockquote class="b1n">
+
+  <p>Refutation of a Pamphlet written by the Rev. John Mackey, R.C.P.,<a
+  name="NtA_728" href="#Nt_728"><sup>[728]</sup></a> entitled "A method of
+  making a cube double of a cube, founded on the principles of elementary
+  geometry," wherein his principles are proved erroneous, and the required
+  solution not yet obtained. By Robert Murphy.<a name="NtA_729"
+  href="#Nt_729"><sup>[729]</sup></a> Mallow, 1824, 12mo.</p>
+
+</blockquote>
+
+  <p>This refutation was the production of an Irish boy of eighteen years
+  old, self-educated in mathematics, the son of a shoemaker at Mallow. He
+  died in 1843, leaving a name which is well known among mathematicians.
+  His works on the theory of equations and on electricity, and his papers
+  in the <i>Cambridge Transactions</i>, are all of high genius. The only
+  account of him which I know of is that which I wrote for the
+  <i>Supplement</i> of the <i>Penny Cyclopædia</i>. He was thrown by his
+  talents into a good income at Cambridge, with no social training except
+  penury, and very little intellectual training except mathematics. He fell
+  into dissipation, and his scientific career was almost arrested: but he
+  had great good in him, to my knowledge. A sentence in <!-- Page 350
+  --><span class="pagenum"><a name="page350"></a>[350]</span>a letter from
+  the late Dean Peacock<a name="NtA_730"
+  href="#Nt_730"><sup>[730]</sup></a> to me&mdash;giving some advice about
+  the means of serving Murphy&mdash;sets out the old case: "Murphy is a man
+  whose <i>special</i> education is in advance of his <i>general</i>; and
+  such men are almost always difficult subjects to manage." This article
+  having been omitted in its proper place, I put it at 1843, the date of
+  Murphy's death.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A NEW VALUE OF <span class="grk">&pi;</span>.</p>
+
+<blockquote class="b1n">
+
+  <p>The Invisible Universe disclosed; or, the real Plan and Government of
+  the Universe. By Henry Coleman Johnson, Esq. London, 1843, 8vo.</p>
+
+</blockquote>
+
+  <p>The book opens abruptly with:</p>
+
+  <p>"First demonstration. Concerning the centre: showing that, because the
+  centre is an innermost point at an equal distance between two extreme
+  points of a right line, and from every two relative and opposite
+  intermediate points, it is composed of the two extreme internal points of
+  each half of the line; each extreme internal point attracting towards
+  itself all parts of that half to which it belongs...."</p>
+
+  <p>Of course the circle is squared: and the circumference is 3-1/21
+  diameters.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">SOME MODERN ASTROLOGY.</p>
+
+<blockquote class="b1n">
+
+  <p>Combination of the Zodiacal and Cometical Systems. Printed for the
+  London Society, Exeter Hall. Price Sixpence. (n. d. 1843.)</p>
+
+</blockquote>
+
+  <p>What this London Society was, or the "combination," did not appear.
+  There was a remarkable comet in 1843, the tail of which was at first
+  confounded with what is called the <i>zodiacal light</i>. This
+  nicely-printed little tract, evidently got up with less care for expense
+  than is usual in such works, brings together all the announcements of the
+  astronomers, and adds a short head and tail piece, which I shall quote
+  entire. As the announcements are very ordinary <!-- Page 351 --><span
+  class="pagenum"><a name="page351"></a>[351]</span>astronomy, the reader
+  will be able to detect, if detection be possible, what is the meaning and
+  force of the "Combination of the Zodiacal and Cometical Systems":</p>
+
+  <p>"<i>Premonition.</i> It has pleased the <span class="sc">Author</span>
+  <i>of</i> <span class="sc">Creation</span> to cause (to His <i>human and
+  reasoning</i> Creatures of this generation, by a '<i>combined</i>'
+  appearance in His <i>Zodiacal</i> and <i>Cometical</i> system) a
+  '<i>warning Crisis</i>' of universal concernment to this our <span
+  class="sc">Globe</span>. It is this '<i>Crisis</i>' that has so generally
+  '<span class="scac">ROUSED</span>' at this moment the '<i>nations
+  throughout the Earth</i>' that no equal interest has ever before been
+  excited by <span class="sc">Man</span>; unless it be in that caused by
+  the '<span class="sc">Pagan-Temple in Rome</span>,' which is recorded by
+  the elder Pliny, '<i>Nat. Hist.</i>' i. 23. iii. 3. <span
+  class="sc">Hardouin</span>."</p>
+
+  <p>After the accounts given by the unperceiving astronomers, comes what
+  follows:</p>
+
+  <p>"Such has been (<i>hitherto</i>) the only object discerned by the
+  '<i>Wise of this World</i>,' in this <i>twofold union</i> of the
+  '<i>Zodiacal</i>' and '<i>Cometical</i>' systems: yet it is nevertheless
+  a most '<i>Thrilling Warning</i>,' to <i>all</i> the inhabitants of this
+  precarious and transitory <span class="sc">Earth</span>. We have no
+  authorized intimation or reasonable prospective contemplation, of
+  '<i>current time</i>' beyond a year 1860, of the present century; or
+  rather, except '<i>the interval which may now remain from the present
+  year 1843, to a year 1860</i>' (<span title="hêmeras HEXÊKONTA" class="grk"
+  >&#x1F21;&mu;&#x1F73;&rho;&alpha;&sigmaf;
+  &#x1F19;&Xi;&Eta;&Kappa;&Omicron;&Nu;&Tau;&Alpha;</span>&mdash;'<i>threescore
+  or sixty days</i>'&mdash;'<i>I have appointed each</i> "<span
+  class="sc">Day</span>" <i>for a</i> "<span class="sc">Year</span>,"'
+  <i>Ezek.</i> iv. 6): and we know, from our '<i>common experience</i>,'
+  how speedily such a measure of time will pass away.</p>
+
+  <p>"No words can be '<i>more explicit</i>' than these of <span
+  class="sc">our blessed Lord</span>: viz. '<span class="sc">This
+  Gospel</span> <i>of the Kingdom shall be preached in</i> <span
+  class="scac">ALL</span> the <span class="sc">Earth</span>, <i>for a
+  Witness to</i> <span class="sc">all Nations; and then</span>, <i>shall
+  the</i> <span class="sc">End come</span>.' The '<i>next 18 years</i>'
+  must therefore supply the interval of the '<i>special Episcopal
+  forerunners</i>.'</p>
+
+<p class="cenhead">(Matt. xxiv. 14.)</p>
+
+  <p>"See the '<span class="sc">Jewish Intelligencer</span>' of the present
+  month (<i>April</i>), p. 153, for the '<i>Debates in Parliament</i>,'
+  respecting <!-- Page 352 --><span class="pagenum"><a
+  name="page352"></a>[352]</span>the <span class="sc">Bishop of
+  Jerusalem</span>, <i>viz.</i> Dr. Bowring,<a name="NtA_731"
+  href="#Nt_731"><sup>[731]</sup></a> Mr. Hume,<a name="NtA_732"
+  href="#Nt_732"><sup>[732]</sup></a> Sir R. Inglis,<a name="NtA_733"
+  href="#Nt_733"><sup>[733]</sup></a> Sir R. Peel,<a name="NtA_734"
+  href="#Nt_734"><sup>[734]</sup></a> Viscount Palmerston.<a name="NtA_735"
+  href="#Nt_735"><sup>[735]</sup></a>"</p>
+
+  <p>I have quoted this at length, to show the awful threats which were
+  published at a time of some little excitement about the phenomenon, under
+  the name of the <i>London Society</i>. The assumption of a corporate
+  appearance is a very unfair trick: and there are junctures at which harm
+  might be done by it.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE NUMBER OF THE BEAST.</p>
+
+<blockquote class="b1n">
+
+  <p><i>Wealth</i> the name and number of the Beast, 666, in the Book of
+  Revelation. [by John Taylor.<a name="NtA_736"
+  href="#Nt_736"><sup>[736]</sup></a>] London, 1844, 8vo.</p>
+
+</blockquote>
+
+  <p>Whether Junius or the Beast be the more difficult to identify, must be
+  referred to Mr. Taylor, the only person who has attempted both. His
+  cogent argument on the political secret is not unworthily matched in his
+  treatment of the theological riddle. He sees the solution in <span
+  title="euporia" class="grk"
+  >&epsilon;&#x1F50;&pi;&omicron;&rho;&#x1F77;&alpha;</span>, which occurs
+  in the Acts of the Apostles as the word for wealth in one of its most
+  disgusting forms, and makes 666 in the most straightforward way. This
+  explanation has as good a chance as any other. The work contains a
+  general <!-- Page 353 --><span class="pagenum"><a
+  name="page353"></a>[353]</span>attempt at explanation of the Apocalypse,
+  and some history of opinion on the subject. It has not the prolixity
+  which is so common a fault of apocalyptic commentators.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>A practical Treatise on Eclipses ... with remarks on the anomalies of
+  the present Theory of the Tides. By T. Kerigan,<a name="NtA_737"
+  href="#Nt_737"><sup>[737]</sup></a> F.R.S. 1844, 8vo.</p>
+
+</blockquote>
+
+  <p>Containing also a refutation of the theory of the tides, and
+  afterwards increased by a supplement, "Additional facts and arguments
+  against the theory of the tides," in answer to a short notice in the
+  <i>Athenæum</i> journal. Mr. Kerigan was a lieutenant in the Navy: he
+  obtained admission to the Royal Society just before the publication of
+  his book.</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>A new theory of Gravitation. By Joseph Denison,<a name="NtA_738"
+  href="#Nt_738"><sup>[738]</sup></a> Esq. London, 1844, 12mo.</p>
+
+  <p>Commentaries on the Principia. By the author of 'A new theory of
+  Gravitation.' London, 1846, 8vo.</p>
+
+</blockquote>
+
+  <p>Honor to the speculator who can be put in his proper place by one
+  sentence, be that place where it may.</p>
+
+  <p>"But we have shown that the velocities are inversely as the square
+  roots of the mean distances from the sun; wherefore, by equality of
+  ratios, the forces of the sun's gravitation upon them are also inversely
+  as the square roots of their distances from the sun."</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">EASTER DAY PARADOXERS.</p>
+
+  <p>In the years 1818 and 1845 the full moon fell on Easter Day, having
+  been particularly directed to fall before it in the act for the change of
+  style and in the English missals and prayer-books of all time: perhaps it
+  would be more correct to say that Easter Day was directed to fall after
+  the full moon; "but the principle is the same." No explanation was given
+  in 1818, but Easter was kept by the tables, <!-- Page 354 --><span
+  class="pagenum"><a name="page354"></a>[354]</span>in defiance of the
+  rule, and of several protests. A chronological panic was beginning in
+  December 1844, which was stopped by the <i>Times</i> newspaper printing
+  extracts from an article of mine in the <i>Companion to the Almanac</i>
+  for 1845, which had then just appeared. No one had guessed the true
+  reason, which is that the thing called the moon in the Gregorian Calendar
+  is not the moon of the heavens, but a fictitious imitation put wrong on
+  purpose, as will presently appear, partly to keep Easter out of the way
+  of the Jews' Passover, partly for convenience of calculation. The
+  apparent error happens but rarely; and all the work will perhaps have to
+  be gone over next time. I now give two bits of paradox.</p>
+
+  <p>Some theologians were angry at this explanation. A review called the
+  <i>Christian Observer</i> (of which Christianity I do not know) got up a
+  crushing article against me. I did not look at it, feeling sure that an
+  article on such a subject which appeared on January 1, 1845, against a
+  publication made in December 1844, must be a second-hand job. But some
+  years afterwards (Sept. 10, 1850), the reviews, etc. having been just
+  placed at the disposal of readers in the <i>old</i> reading-room of the
+  Museum, I made a tour of inspection, came upon my critic on his perch,
+  and took a look at him. I was very glad to remember this, for, though
+  expecting only second-hand, yet even of this there is good and bad; and I
+  expected to find some hints in the good second-hand of a respectable
+  clerical publication. I read on, therefore, attentively, but not long: I
+  soon came to the information that some additions to Delambre's<a
+  name="NtA_739" href="#Nt_739"><sup>[739]</sup></a> statement of the rule
+  for finding Easter, belonging to distant years, had been made by Sir
+  Harris Nicolas!<a name="NtA_740" href="#Nt_740"><sup>[740]</sup></a> Now
+  as I myself furnished my friend Sir H.&nbsp;N. with Delambre's digest of <!--
+  Page 355 --><span class="pagenum"><a
+  name="page355"></a>[355]</span>Clavius's<a name="NtA_741"
+  href="#Nt_741"><sup>[741]</sup></a> rule, which I translated out of
+  algebra into common language for the purpose, I was pretty sure this was
+  the ignorant reading of a person to whom Sir H.&nbsp;N. was the highest
+  <i>arithmetical</i> authority on the subject. A person pretending to
+  chronology, without being able to distinguish the historical
+  points&mdash;so clearly as they stand out&mdash;in which Sir H.&nbsp;N. speaks
+  with authority, from the arithmetical points of pure reckoning on which
+  he does not pretend to do more than directly repeat others, must be as
+  fit to talk about the construction of Easter Tables as the Spanish are to
+  talk French. I need hardly say that the additions for distant years are
+  as much from Clavius as the rest: my reviewer was not deep enough in his
+  subject to know that Clavius made and published, from his rules, the full
+  table up to A.D. 5000, for all the movable feasts of every year! I gave
+  only a glance at the rest: I found I was either knave or fool, with a
+  leaning to the second opinion; and I came away satisfied that my critic
+  was either ignoramus or novice, with a leaning to the first. I afterwards
+  found an ambiguity of expression in Sir H.&nbsp;N.'s account&mdash;whether his
+  or mine I could not tell&mdash;which might mislead a novice or content an
+  ignoramus, but would have been properly read or further inquired into by
+  a competent person.</p>
+
+  <p>The second case is this. Shortly after the publication of my article,
+  a gentleman called at my house, and, finding I was not at home, sent up
+  his card&mdash;with a stylish west-end club on it&mdash;to my wife,
+  begging for a few words on pressing business. With many well-expressed
+  apologies, he stated that he had been alarmed by hearing that Prof. De M.
+  had an intention of altering Easter next year. Mrs. De M. kept her
+  countenance, and assured him that I had no such intention, and further,
+  that she greatly doubted my having the power to do it. Was she quite
+  sure? his authority was very good: fresh assurances given. He was greatly
+  relieved, for he had some horses training for after Easter, which <!--
+  Page 356 --><span class="pagenum"><a name="page356"></a>[356]</span>would
+  not be ready to run if it were altered the wrong way. A doubt comes over
+  him: would Mrs. De M., in the event of her being mistaken, give him the
+  very earliest information? Promise given; profusion of thanks; more
+  apologies; and departure.</p>
+
+  <p>Now, candid reader!&mdash;or uncandid either!&mdash;which most
+  deserves to be laughed at? A public instructor, who undertakes to settle
+  for the world whether a reader of Clavius, the constructor of the
+  Gregorian Calendar, is fool or knave, upon information derived from a
+  compiler&mdash;in this matter&mdash;of his own day; or a gentleman of
+  horse and dog associations, who, misapprehending something which he heard
+  about a current topic, infers that the reader of Clavius had the ear of
+  the Government on a proposed alteration. I suppose the querist had heard
+  some one say, perhaps, that the day ought to be set right, and some one
+  else remark that I might be consulted, as the only person who had
+  discussed the matter from the original source of the Calendar.</p>
+
+  <p>To give a better chance of the explanation being at once produced,
+  next time the real full moon and Easter Day shall fall together, I insert
+  here a summary which was printed in the Irish Prayer-book of the
+  Ecclesiastical Society. If the amusement given by paradoxers should
+  prevent a useless discussion some years hence, I and the paradoxers shall
+  have done a little good between us&mdash;at any rate, I have done my best
+  to keep the heavy weight afloat by tying bladders to it. I think the next
+  occurrence will be in 1875.</p>
+
+<p class="cenhead"><span class="scac">EASTER DAY.</span></p>
+
+  <p>In the years 1818 and 1845, Easter Day, as given by the <i>rules
+  in</i> 24 Geo. II cap. 23. (known as the act for the <i>change of
+  style</i>) contradicted the <i>precept</i> given in the preliminary
+  explanations. The precept is as follows:</p>
+
+  <p>"<i>Easter Day</i>, on which the rest" of the moveable feasts "depend,
+  is always the First Sunday after the Full Moon, which happens upon or
+  next after the Twenty-first Day of <!-- Page 357 --><span
+  class="pagenum"><a name="page357"></a>[357]</span><i>March</i>; and if
+  the Full Moon happens upon a Sunday, <i>Easter Day</i> is the Sunday
+  after."</p>
+
+  <p>But in 1818 and 1845, the full moon fell on a Sunday, and yet the
+  rules gave <i>that same Sunday</i> for Easter Day. Much discussion was
+  produced by this circumstance in 1818: but a repetition of it in 1845 was
+  nearly altogether prevented by a timely<a name="NtA_742"
+  href="#Nt_742"><sup>[742]</sup></a> reference to the intention of those
+  who conducted the Gregorian reformation of the Calendar. Nevertheless,
+  seeing that the apparent error of the Calendar is due to the precept in
+  the Act of Parliament, which is both erroneous and insufficient, and that
+  the difficulty will recur so often as Easter Day falls on the day of full
+  moon, it may be advisable to select from the two articles cited in the
+  note such of their conclusions and rules, without proof or controversy,
+  as will enable the reader to understand the main points of the Easter
+  question, and, should he desire it, to calculate for himself the Easter
+  of the old or new style, for any given year.</p>
+
+  <p>1. In the very earliest age of Christianity, a controversy arose as to
+  the mode of keeping Easter, some desiring to perpetuate the
+  <i>Passover</i>, others to keep the <i>festival of the Resurrection</i>.
+  The first afterwards obtained the name of <i>Quartadecimans</i>, from
+  their Easter being always kept on the <i>fourteenth day</i> of the moon
+  (Exod. xii. 18, Levit. xxiii. 5.). But though it is unquestionable that a
+  Judaizing party existed, it is also likely that many dissented on
+  chronological grounds. It is clear that no <i>perfect</i> anniversary can
+  take place, except when the fourteenth of the moon, and with it the
+  passover, falls on a Friday. Suppose, for instance, it falls on a
+  Tuesday: one of three things must be <!-- Page 358 --><span
+  class="pagenum"><a name="page358"></a>[358]</span>done. Either (which
+  seems never to have been proposed) the crucifixion and resurrection must
+  be celebrated on Tuesday and Sunday, with a wrong interval; or the former
+  on Tuesday, the latter on Thursday, abandoning the first day of the week;
+  or the former on Friday, and the latter on Sunday, abandoning the paschal
+  commemoration of the crucifixion.</p>
+
+  <p>The last mode has been, as every one knows, finally adopted. The
+  disputes of the first three centuries did not turn on any <i>calendar</i>
+  questions. The Easter question was merely the symbol of the struggle
+  between what we may call the Jewish and Gentile sects of Christians: and
+  it nearly divided the Christian world, the Easterns, for the most part,
+  being <i>Quartadecimans</i>. It is very important to note that there is
+  no recorded dispute about a method of predicting the new moon, that is,
+  no general dispute leading to formation of sects: there may have been
+  difficulties, and discussions about them. The Metonic cycle, presently
+  mentioned, must have been used by many, perhaps most, churches.</p>
+
+  <p>2. The question came before the Nicene Council (A.D. 325) not as an
+  astronomical, but as a doctrinal, question: it was, in fact, this, Shall
+  the <i>passover</i><a name="NtA_743" href="#Nt_743"><sup>[743]</sup></a>
+  be treated as a part of Christianity? The Council resolved this question
+  in the negative, and the only information on its premises and conclusion,
+  or either, which comes from itself, is contained in the following
+  sentence of the synodical epistle, which epistle is preserved by
+  Socrates<a name="NtA_744" href="#Nt_744"><sup>[744]</sup></a> and
+  Theodoret.<a name="NtA_745" href="#Nt_745"><sup>[745]</sup></a> "We also
+  send <!-- Page 359 --><span class="pagenum"><a
+  name="page359"></a>[359]</span>you the good news concerning the unanimous
+  consent of all in reference to the celebration of the most solemn feast
+  of Easter, for this difference also has been made up by the assistance of
+  your prayers: so that all the brethren in the East, who formerly
+  celebrated this festival <i>at the same time as the Jews</i>, will in
+  future conform <i>to the Romans and to us</i>, and to all who have of old
+  observed <i>our manner</i> of celebrating Easter." This is all that can
+  be found on the subject: none of the stories about the Council ordaining
+  the astronomical mode of finding Easter, and introducing the Metonic
+  cycle into ecclesiastical reckoning, have any contemporary evidence: the
+  canons which purport to be those of the Nicene Council do not contain a
+  word about Easter; and this is evidence, whether we suppose those canons
+  to be genuine or spurious.</p>
+
+  <p>3. The astronomical dispute about a lunar cycle for the prediction of
+  Easter either commenced, or became prominent, by the extinction of
+  greater ones, soon after the time of the Nicene Council. Pope Innocent
+  I<a name="NtA_746" href="#Nt_746"><sup>[746]</sup></a> met with
+  difficulty in 414. S. Leo,<a name="NtA_747"
+  href="#Nt_747"><sup>[747]</sup></a> in 454, ordained that Easter of 455
+  should be April 24; which is right. It is useless to record details of
+  these disputes in a summary: the result was, that in the year 463, Pope
+  Hilarius<a name="NtA_748" href="#Nt_748"><sup>[748]</sup></a> employed
+  Victorinus<a name="NtA_749" href="#Nt_749"><sup>[749]</sup></a> of
+  Aquitaine to correct the Calendar, and Victorinus formed a rule which
+  lasted until the sixteenth century. He combined the Metonic cycle and the
+  solar cycle presently described. But <!-- Page 360 --><span
+  class="pagenum"><a name="page360"></a>[360]</span>this cycle bears the
+  name of Dionysius Exiguus,<a name="NtA_750"
+  href="#Nt_750"><sup>[750]</sup></a> a Scythian settled at Rome, about
+  A.D. 530, who adapted it to his new yearly reckoning, when he abandoned
+  the era of Diocletian as a commencement, and constructed that which is
+  now in common use.</p>
+
+  <p>4. With Dionysius, if not before, terminated all difference as to the
+  mode of keeping Easter which is of historical note: the increasing
+  defects of the Easter Cycle produced in time the remonstrance of persons
+  versed in astronomy, among whom may be mentioned Roger Bacon,<a
+  name="NtA_751" href="#Nt_751"><sup>[751]</sup></a> Sacrobosco,<a
+  name="NtA_752" href="#Nt_752"><sup>[752]</sup></a> Cardinal Cusa,<a
+  name="NtA_753" href="#Nt_753"><sup>[753]</sup></a> Regiomontanus,<a
+  name="NtA_754" href="#Nt_754"><sup>[754]</sup></a> etc. From the middle
+  of the sixth to that of the sixteenth century, one rule was observed.</p>
+
+  <p>5. The mode of applying astronomy to chronology has always involved
+  these two principles. First, the actual position of the heavenly body is
+  not the object of consideration, but what astronomers call its <i>mean
+  place</i>, which may be described thus. Let a fictitious sun or moon move
+  in the heavens, in such manner as to revolve among the fixed stars at an
+  average rate, avoiding the alternate accelerations and retardations which
+  take place in every planetary motion. Thus the fictitious (say
+  <i>mean</i>) sun and moon are always very near to the real sun and moon.
+  The ordinary clocks show time by the mean, not the real, sun: and it was
+  always laid down that Easter depends on the opposition (or full moon) of
+  the mean sun and moon, not of the real ones. Thus we see that, were the
+  Calendar ever so correct <!-- Page 361 --><span class="pagenum"><a
+  name="page361"></a>[361]</span>as to the <i>mean</i> moon, it would be
+  occasionally false as to the <i>true</i> one: if, for instance, the
+  opposition of the mean sun and moon took place at one second before
+  midnight, and that of the real bodies only two seconds afterwards, the
+  calendar day of full moon would be one day before that of the common
+  almanacs. Here is a way in which the discussions of 1818 and 1845 might
+  have arisen: the British legislature has defined <i>the moon</i> as the
+  regulator of the paschal calendar. But this was only a part of the
+  mistake.</p>
+
+  <p>6. Secondly, in the absence of perfectly accurate knowledge of the
+  solar and lunar motion (and for convenience, even if such knowledge
+  existed), cycles are, and always have been taken, which serve to
+  represent those motions nearly. The famous Metonic cycle, which is
+  introduced into ecclesiastical chronology under the name of the cycle of
+  the golden numbers, is a period of 19 Julian<a name="NtA_755"
+  href="#Nt_755"><sup>[755]</sup></a> years. This period, in the old
+  Calendar, was taken to contain exactly 235 <i>lunations</i>, or intervals
+  between new moons, of the mean moon. Now the state of the case is:</p>
+
+  <p>19 average Julian years make 6939 days 18 hours.</p>
+
+  <p>235 average lunations make 6939 days 16 hours 31 minutes.</p>
+
+  <p>So that successive cycles of golden numbers, supposing the first to
+  start right, amount to making the new moons fall too late, gradually, so
+  that the mean moon <i>of this cycle</i> gains 1 hour 29 minutes in 19
+  years upon the mean moon of the heavens, or about a day in 300 years.
+  When the Calendar was reformed, the calendar new moons were four days in
+  advance of the mean moon of the heavens: so that, for instance, calendar
+  full moon on the 18th usually meant real full moon on the 14th.</p>
+
+  <p>7. If the difference above had not existed, the moon of the heavens
+  (the mean moon at least), would have returned <!-- Page 362 --><span
+  class="pagenum"><a name="page362"></a>[362]</span>permanently to the same
+  days of the month in 19 years; with an occasional slip arising from the
+  unequal distribution of the leap years, of which a period contains
+  sometimes five and sometimes four. As a general rule, the days of new and
+  full moon in any one year would have been also the days of new and full
+  moon of a year having 19 more units in its date. Again, if there had been
+  no leap years, the days of the month would have returned to the same days
+  of the week every seven years. The introduction of occasional 29ths of
+  February disturbs this, and makes the permanent return of month days to
+  week days occur only after 28 years. If all had been true, the lapse of
+  28 times 19, or 532 years, would have restored the year in every point:
+  that is, A.D. 1, for instance, and A.D. 533, would have had the same
+  almanac in every matter relating to week days, month days, sun, and moon
+  (mean sun and moon at least). And on the supposition of its truth, the
+  old system of Dionysius was framed. Its errors, are, first, that the
+  moments of mean new moon advance too much by 1 h. 29 m. in 19 average
+  Julian years; secondly, that the average Julian year of 365¼ days is too
+  long by 11 m. 10 s.</p>
+
+  <p>8. The Council of Trent, moved by the representations made on the
+  state of the Calendar, referred the consideration of it to the Pope. In
+  1577, Gregory XIII<a name="NtA_756" href="#Nt_756"><sup>[756]</sup></a>
+  submitted to the Roman Catholic Princes and Universities a plan presented
+  to him by the representatives of Aloysius Lilius,<a name="NtA_757"
+  href="#Nt_757"><sup>[757]</sup></a> then deceased. This plan being
+  approved of, the Pope nominated a commission to consider its details, the
+  working member of which was the Jesuit Clavius. A short work was prepared
+  by Clavius, descriptive of the new Calendar: this <!-- Page 363 --><span
+  class="pagenum"><a name="page363"></a>[363]</span>was published<a
+  name="NtA_758" href="#Nt_758"><sup>[758]</sup></a> in 1582, with the
+  Pope's bull (dated February 24, 1581) prefixed. A larger work was
+  prepared by Clavius, containing fuller explanation, and entitled
+  <i>Romani Calendarii a Gregorio XIII. Pontifice Maximo restituti
+  Explicatio</i>. This was published at Rome in 1603, and again in the
+  collection of the works of Clavius in 1612.</p>
+
+  <p>9. The following extracts from Clavius settle the question of the
+  meaning of the term <i>moon</i>, as used in the Calendar:</p>
+
+  <p>"Who, except a few who think they are very sharp-sighted in this
+  matter, is so blind as not to see that the 14th of the moon and the full
+  moon are not the same things in the Church of God?... Although the
+  Church, in finding the new moon, and from it the 14th day, <i>uses
+  neither the true nor the mean motion of the moon</i>, but measures only
+  according to the order of a cycle, it is nevertheless undeniable that the
+  mean full moons found from astronomical tables are of the greatest use in
+  determining the cycle which is to be preferred ... the new moons of which
+  cycle, in order to the due celebration of Easter, should be so arranged
+  that the 14th days of those moons, reckoning from the day of new moon
+  <i>inclusive</i>, should not fall two or more days before the mean full
+  moon, but only one day, or else on the very day itself, or not long
+  after. And even thus far the Church need not take very great pains ...
+  for it is sufficient that all should reckon by the 14th day of the moon
+  in the cycle, even though sometimes it <i>should be more than one day
+  before or after</i> the mean full moon.... We have taken pains that in
+  our cycle the new moons should <i>follow</i> the real new moons, so that
+  the 14th of the moon should fall either the day before the mean full
+  moon, or on that day, or not long after; and this was done on purpose,
+  for if the new moon of the cycle fell on the same day as the mean new
+  moon of the <!-- Page 364 --><span class="pagenum"><a
+  name="page364"></a>[364]</span>astronomers, it might chance that we
+  should celebrate Easter on the same day as the Jews or the Quartadeciman
+  heretics, which would be absurd, or else before them, which would be
+  still more absurd."</p>
+
+  <p>From this it appears that Clavius continued the Calendar of his
+  predecessors in the choice of the <i>fourteenth</i> day of the moon. Our
+  legislature lays down the day of the <i>full moon</i>: and this mistake
+  appears to be rather English than Protestant; for it occurs in missals
+  published in the reign of Queen Mary. The calendar lunation being 29½
+  days, the middle day is the <i>fifteenth</i> day, and this is and was
+  reckoned as the day of the full moon. There is every right to presume
+  that the original passover was a feast of the <i>real full moon</i>: but
+  it is most probable that the moons were then reckoned, not from the
+  astronomical conjunction with the sun, which nobody sees except at an
+  eclipse, but from the day of <i>first visibility</i> of the new moon. In
+  fine climates this would be the day or two days after conjunction; and
+  the fourteenth day from that of first visibility inclusive, would very
+  often be the day of full moon. The following is then the proper
+  correction of the precept in the Act of Parliament:</p>
+
+  <p>Easter Day, on which the rest depend, is always the First Sunday after
+  the <i>fourteenth day</i> of the <i>calendar</i> moon which happens upon
+  or next after the Twenty-first day of March, <i>according to the rules
+  laid down for the construction of the Calendar</i>; and if the
+  <i>fourteenth day</i> happens upon a Sunday, Easter Day is the Sunday
+  after.</p>
+
+  <p>10. Further, it appears that Clavius valued the celebration of the
+  festival after the Jews, etc., more than astronomical correctness. He
+  gives comparison tables which would startle a believer in the
+  astronomical intention of his Calendar: they are to show that a calendar
+  in which the moon is always made a day older than by him, <i>represents
+  the heavens better than he has done, or meant to do</i>. But it must be
+  observed that this diminution of the real moon's age has <!-- Page 365
+  --><span class="pagenum"><a name="page365"></a>[365]</span>a tendency to
+  make the English explanation often practically accordant with the
+  Calendar. For the fourteenth day of Clavius <i>is</i> generally the
+  fifteenth day of the mean moon of the heavens, and therefore most often
+  that of the real moon. But for this, 1818 and 1845 would not have been
+  the only instances of our day in which the English precept would have
+  contradicted the Calendar.</p>
+
+  <p>11. In the construction of the Calendar, Clavius adopted the ancient
+  cycle of 532 years, but, we may say, without ever allowing it to run out.
+  At certain periods, a shift is made from one part of the cycle into
+  another. This is done whenever what should be Julian leap year is made a
+  common year, as in 1700, 1800, 1900, 2100, etc. It is also done at
+  certain times to correct the error of 1 h. 19 m., before referred to, in
+  each cycle of golden numbers: Clavius, to meet his view of the amount of
+  that error, put forward the moon's age a day 8 times in 2,500 years. As
+  we cannot enter at full length into the explanation, we must content
+  ourselves with giving a set of rules, independent of tables, by which the
+  reader may find Easter for himself in any year, either by the old
+  Calendar or the new. Any one who has much occasion to find Easters and
+  movable feasts should procure Franc&oelig;ur's<a name="NtA_759"
+  href="#Nt_759"><sup>[759]</sup></a> tables.</p>
+
+  <p>12. <i>Rule for determining Easter Day of the Gregorian Calendar in
+  any year of the new style.</i> To the several parts <!-- Page 366
+  --><span class="pagenum"><a name="page366"></a>[366]</span>of the rule
+  are annexed, by way of example, the results for the year 1849.</p>
+
+  <p>I. Add 1 to the given year. (1850).</p>
+
+  <p>II. Take the quotient of the given year divided by 4, neglecting the
+  remainder. (462).</p>
+
+  <p>III. Take 16 from the centurial figures of the given year, if it can
+  be done, and take the remainder. (2).</p>
+
+  <p>IV. Take the quotient of III. divided by 4, neglecting the remainder.
+  (0).</p>
+
+  <p>V. From the sum of I, II, and IV., subtract III. (2310).</p>
+
+  <p>VI. Find the remainder of V. divided by 7. (0).</p>
+
+  <p>VII. Subtract VI. from 7; this is the number of the dominical
+  letter</p>
+
+<table class="nob" summary="Dominical letters" title="Dominical letters">
+<tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td valign="middle">(7; dominical letter G).</td></tr>
+<tr><td>A</td><td>B</td><td>C</td><td>D</td><td>E</td><td>F</td><td>G</td></tr>
+</table>
+
+  <p>VIII. Divide I. by 19, the remainder (or 19, if no remainder) is the
+  <i>golden number</i>. (7).</p>
+
+  <p>IX. From the centurial figures of the year subtract 17, divide by 25,
+  and keep the quotient. (0).</p>
+
+  <p>X. Subtract IX. and 15 from the centurial figures, divide by 3, and
+  keep the quotient. (1).</p>
+
+  <p>XI. To VIII. add ten times the next less number, divide by 30, and
+  keep the remainder. (7).</p>
+
+  <p>XII. To XI. add X. and IV., and take away III., throwing out thirties,
+  if any. If this give 24, change it into 25. If 25, change it into 26,
+  whenever the golden number is greater than 11. If 0, change it into 30.
+  Thus we have the epact, or age of the <i>Calendar</i> moon at the
+  beginning of the year. (6).</p>
+
+<table width="100%" summary="Epacts" title="Epacts"><tr><td valign="top" class="spac" style="width:50%">
+<i>When the Epact is 23, or less.</i>
+
+  <p>XIII. Subtract XII., the epact, from 45. (39).</p>
+
+  <p>XIV. Subtract the epact from 27, divide by 7, and keep the remainder,
+  or 7, if there be no remainder. (7)</p>
+
+</td><td valign="top" class="spac" style="width:50%">
+<i>When the Epact is greater than 23.</i>
+
+  <p>XIII. Subtract XII., the epact, from 75.</p>
+
+  <p>XIV. Subtract the epact from 57, divide by 7, and keep the remainder,
+  or 7, if there be no remainder.</p>
+
+</td></tr></table>
+
+  <p>XV. To XIII. add VII., the dominical number, (and 7 besides, if XIV.
+  be greater than VII.,) and subtract XIV., the result is the day of March,
+  or if more than 31, subtract 31, and <!-- Page 367 --><span
+  class="pagenum"><a name="page367"></a>[367]</span>the result is the day
+  of April, on which Easter Sunday falls. (39; Easter Day is April 8).</p>
+
+  <p>In the following examples, the several results leading to the final
+  conclusion are tabulated.</p>
+
+<table class="allbctr" summary="Easter calculations" title="Easter calculations">
+<tr><td class="allb"><span class="sc">Given Year</span></td><td class="allb" align="right">1592</td><td class="allb" align="right">1637</td><td class="allb" align="right">1723</td><td class="allb" align="right">1853</td><td class="allb" align="right">2018</td><td class="allb" align="right">4686</td></tr>
+<tr><td class="vertb" align="right">I.</td><td class="vertb" align="right">1593</td><td class="vertb" align="right">1638</td><td class="vertb" align="right">1724</td><td class="vertb" align="right">1854</td><td class="vertb" align="right">2019</td><td class="vertb" align="right">4687</td></tr>
+<tr><td class="vertb" align="right">II.</td><td class="vertb" align="right">398</td><td class="vertb" align="right">409</td><td class="vertb" align="right">430</td><td class="vertb" align="right">463</td><td class="vertb" align="right">504</td><td class="vertb" align="right">1171</td></tr>
+<tr><td class="vertb" align="right">III.</td><td class="vertb" align="right">&mdash;</td><td class="vertb" align="right">0</td><td class="vertb" align="right">1</td><td class="vertb" align="right">2</td><td class="vertb" align="right">4</td><td class="vertb" align="right">30</td></tr>
+<tr><td class="vertb" align="right">IV.</td><td class="vertb" align="right">&mdash;</td><td class="vertb" align="right">0</td><td class="vertb" align="right">0</td><td class="vertb" align="right">0</td><td class="vertb" align="right">1</td><td class="vertb" align="right">7</td></tr>
+<tr><td class="vertb" align="right">V.</td><td class="vertb" align="right">1991</td><td class="vertb" align="right">2047</td><td class="vertb" align="right">2153</td><td class="vertb" align="right">2315</td><td class="vertb" align="right">2520</td><td class="vertb" align="right">5835</td></tr>
+<tr><td class="vertb" align="right">VI.</td><td class="vertb" align="right">3</td><td class="vertb" align="right">3</td><td class="vertb" align="right">4</td><td class="vertb" align="right">5</td><td class="vertb" align="right">0</td><td class="vertb" align="right">4</td></tr>
+<tr><td class="vertb" align="right">VII.</td><td class="vertb" align="right">4</td><td class="vertb" align="right">4</td><td class="vertb" align="right">3</td><td class="vertb" align="right">2</td><td class="vertb" align="right">7</td><td class="vertb" align="right">3</td></tr>
+<tr><td class="vertb" align="right">VIII.</td><td class="vertb" align="right">16</td><td class="vertb" align="right">4</td><td class="vertb" align="right">14</td><td class="vertb" align="right">11</td><td class="vertb" align="right">5</td><td class="vertb" align="right">13</td></tr>
+<tr><td class="vertb" align="right">IX.</td><td class="vertb" align="right">&mdash;</td><td class="vertb" align="right">&mdash;</td><td class="vertb" align="right">0</td><td class="vertb" align="right">0</td><td class="vertb" align="right">0</td><td class="vertb" align="right">1</td></tr>
+<tr><td class="vertb" align="right">X.</td><td class="vertb" align="right">0</td><td class="vertb" align="right">0</td><td class="vertb" align="right">0</td><td class="vertb" align="right">1</td><td class="vertb" align="right">1</td><td class="vertb" align="right">10</td></tr>
+<tr><td class="vertb" align="right">XI.</td><td class="vertb" align="right">16</td><td class="vertb" align="right">4</td><td class="vertb" align="right">24</td><td class="vertb" align="right">21</td><td class="vertb" align="right">15</td><td class="vertb" align="right">13</td></tr>
+<tr><td class="vertb" align="right">XII.</td><td class="vertb" align="right">16</td><td class="vertb" align="right">4</td><td class="vertb" align="right">23</td><td class="vertb" align="right">20</td><td class="vertb" align="right">13</td><td class="vertb" align="right">0 say 30</td></tr>
+<tr><td class="vertb" align="right">XIII.</td><td class="vertb" align="right">29</td><td class="vertb" align="right">41</td><td class="vertb" align="right">22</td><td class="vertb" align="right">25</td><td class="vertb" align="right">32</td><td class="vertb" align="right">45</td></tr>
+<tr><td class="vertb" align="right">XIV.</td><td class="vertb" align="right">4</td><td class="vertb" align="right">2</td><td class="vertb" align="right">4</td><td class="vertb" align="right">7</td><td class="vertb" align="right">7</td><td class="vertb" align="right">6</td></tr>
+<tr><td class="vertb" align="right">XV.</td><td class="vertb" align="right">29</td><td class="vertb" align="right">43</td><td class="vertb" align="right">28</td><td class="vertb" align="right">27</td><td class="vertb" align="right">32</td><td class="vertb" align="right">49</td></tr>
+<tr><td class="vertb" align="right">Easter Day</td><td class="vertb" align="right">Mar.29</td><td class="vertb" align="right">Apr.12</td><td class="vertb" align="right">Mar.28</td><td class="vertb" align="right">Mar.27</td><td class="vertb" align="right">Apr.1</td><td class="vertb" align="right">Apr.18</td></tr>
+</table>
+
+  <p>13. <i>Rule for determining Easter Day of the Antegregorian Calendar
+  in any year of the old style.</i> To the several parts of the rule are
+  annexed, by way of example, the results for the year 1287. The steps are
+  numbered to correspond with the steps of the Gregorian rule, so that it
+  can be seen what augmentations the latter requires.</p>
+
+  <p>I. Set down the given year. (1287).</p>
+
+  <p>II. Take the quotient of the given year divided by 4, neglecting the
+  remainder (321).</p>
+
+  <p>V. Take 4 more than the sum of I. and II. (1612).</p>
+
+  <p>VI. Find the remainder of V. divided by 7. (2).</p>
+
+  <p>VII. Subtract VI. from 7; this is the number of the dominical
+  letter</p>
+
+<table class="nob" summary="Dominical letters" title="Dominical letters">
+<tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td valign="middle">(5; dominical letter E).</td></tr>
+<tr><td>A</td><td>B</td><td>C</td><td>D</td><td>E</td><td>F</td><td>G</td></tr>
+</table>
+
+  <p>VIII. Divide one more than the given year by 19, the remainder (or 19
+  if no remainder) is the golden number. (15).</p>
+
+  <p>XII. Divide 3 less than 11 times VIII. by 30; the remainder (or 30 if
+  there be no remainder) is the epact. (12).</p>
+
+<p><!-- Page 368 --><span class="pagenum"><a name="page368"></a>[368]</span></p>
+
+<table width="100%" summary="Epacts" title="Epacts"><tr><td valign="top" class="spac" style="width:50%">
+<i>When the Epact is 23, or less.</i>
+
+  <p>XIII. Subtract XII., the epact, from 45. (33).</p>
+
+  <p>XIV. Subtract the epact from 27, divide by 7, and keep the remainder,
+  or 7, if there be no remainder, (1).</p>
+
+</td><td valign="top" class="spac" style="width:50%">
+<i>When the Epact is greater than 23.</i>
+
+  <p>XIII. Subtract XII., the epact, from 75.</p>
+
+  <p>XIV. Subtract the epact from 57, divide by 7, and keep the remainder,
+  or 7, if there be no remainder.</p>
+
+</td></tr></table>
+
+  <p>XV. To XIII. add VII., the dominical number, (and 7 besides if XIV. be
+  greater than VII.,) and subtract XIV., the result is the day of March, or
+  if more than 31, subtract 31, and the result is the day of April, on
+  which Easter Sunday (old style) falls. (37; Easter Day is April 6).</p>
+
+  <p>These rules completely represent the old and new Calendars, so far as
+  Easter is concerned. For further explanation we must refer to the
+  articles cited at the commencement.</p>
+
+  <p>The annexed is the table of new and full moons of the Gregorian
+  Calendar, cleared of the errors made for the purpose of preventing Easter
+  from coinciding with the Jewish Passover.</p>
+
+  <p>The second table (page <a href="#page370">370</a>) contains
+  <i>epacts</i>, or ages of the moon at the beginning of the year: thus in
+  1913, the epact is 22, in 1868 it is 6. This table goes from 1850 to
+  1999: should the New Zealander not have arrived by that time, and should
+  the churches of England and Rome then survive, the epact table may be
+  continued from their liturgy-books. The way of using the table is as
+  follows: Take the epact of the required year, and find it in the first or
+  last column of the first table, in line with it are seen the calendar
+  days of new and full moon. Thus, when the epact is 17, the new and full
+  moons of March fall on the 13th and 28th. The result is, for the most
+  part, correct: but in a minority of cases there is an error of a day.
+  When this happens, the error is almost always a fraction of a day much
+  less than twelve hours. Thus, when the table gives full moon on the 27th,
+  and the real truth is the 28th, we may be sure it is early on the
+  28th.</p>
+
+<p><!-- Page 369 --><span class="pagenum"><a name="page369"></a>[369]</span></p>
+
+<table class="allbctr" summary="True table of moons" title="True table of moons">
+<tr><td class="allb" align="center">&nbsp;</td><td class="allb" align="center">Jan.</td><td class="allb" align="center">Feb.</td><td class="allb" align="center">Mar.</td><td class="allb" align="center">Apr.</td><td class="allb" align="center">May </td><td class="allb" align="center">June</td><td class="allb" align="center">July</td><td class="allb" align="center">Aug.</td><td class="allb" align="center">Sep.</td><td class="allb" align="center">Oct.</td><td class="allb" align="center">Nov.</td><td class="allb" align="center">Dec.</td><td class="allb" align="center">&nbsp;</td></tr>
+<tr><td class="vertb" align="center">1</td><td class="vertb" align="center">29</td><td class="vertb" align="center">27</td><td class="vertb" align="center">29</td><td class="vertb" align="center">27</td><td class="vertb" align="center">27</td><td class="vertb" align="center">25</td><td class="vertb" align="center">25</td><td class="vertb" align="center">23</td><td class="vertb" align="center">22</td><td class="vertb" align="center">21</td><td class="vertb" align="center">20</td><td class="vertb" align="center">19</td><td class="vertb" align="center">1</td></tr>
+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">14</td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">14</td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="vertb" align="center">2</td><td class="vertb" align="center">28</td><td class="vertb" align="center">26</td><td class="vertb" align="center">28</td><td class="vertb" align="center">26</td><td class="vertb" align="center">26</td><td class="vertb" align="center">24</td><td class="vertb" align="center">24</td><td class="vertb" align="center">22</td><td class="vertb" align="center">21</td><td class="vertb" align="center">20</td><td class="vertb" align="center">19</td><td class="vertb" align="center">18</td><td class="vertb" align="center">2</td></tr>
+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="vertb" align="center">3</td><td class="vertb" align="center">27</td><td class="vertb" align="center">25</td><td class="vertb" align="center">27</td><td class="vertb" align="center">25</td><td class="vertb" align="center">25</td><td class="vertb" align="center">23</td><td class="vertb" align="center">23</td><td class="vertb" align="center">21</td><td class="vertb" align="center">20</td><td class="vertb" align="center">19</td><td class="vertb" align="center">18</td><td class="vertb" align="center">17</td><td class="vertb" align="center">3</td></tr>
+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="vertb" align="center">4</td><td class="vertb" align="center">26</td><td class="vertb" align="center">24</td><td class="vertb" align="center">26</td><td class="vertb" align="center">24</td><td class="vertb" align="center">24</td><td class="vertb" align="center">22</td><td class="vertb" align="center">22</td><td class="vertb" align="center">20</td><td class="vertb" align="center">19</td><td class="vertb" align="center">18</td><td class="vertb" align="center">17</td><td class="vertb" align="center">16</td><td class="vertb" align="center">4</td></tr>
+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">2</td><td class="vertbotb" align="center">2,31</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="vertb" align="center">5</td><td class="vertb" align="center">25</td><td class="vertb" align="center">23</td><td class="vertb" align="center">25</td><td class="vertb" align="center">23</td><td class="vertb" align="center">23</td><td class="vertb" align="center">21</td><td class="vertb" align="center">21</td><td class="vertb" align="center">19</td><td class="vertb" align="center">18</td><td class="vertb" align="center">17</td><td class="vertb" align="center">16</td><td class="vertb" align="center">15</td><td class="vertb" align="center">5</td></tr>
+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">1</td><td class="vertbotb" align="center">1,30</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="vertb" align="center">6</td><td class="vertb" align="center">24</td><td class="vertb" align="center">22</td><td class="vertb" align="center">24</td><td class="vertb" align="center">22</td><td class="vertb" align="center">22</td><td class="vertb" align="center">20</td><td class="vertb" align="center">20</td><td class="vertb" align="center">18</td><td class="vertb" align="center">17</td><td class="vertb" align="center">16</td><td class="vertb" align="center">15</td><td class="vertb" align="center">14</td><td class="vertb" align="center">6</td></tr>
+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">2</td><td class="vertbotb" align="center">2,31</td><td class="vertbotb" align="center">30</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="vertb" align="center">7</td><td class="vertb" align="center">23</td><td class="vertb" align="center">21</td><td class="vertb" align="center">23</td><td class="vertb" align="center">21</td><td class="vertb" align="center">21</td><td class="vertb" align="center">19</td><td class="vertb" align="center">19</td><td class="vertb" align="center">17</td><td class="vertb" align="center">16</td><td class="vertb" align="center">15</td><td class="vertb" align="center">14</td><td class="vertb" align="center">13</td><td class="vertb" align="center">7</td></tr>
+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">1</td><td class="vertbotb" align="center">1,30</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="vertb" align="center">8</td><td class="vertb" align="center">22</td><td class="vertb" align="center">20</td><td class="vertb" align="center">22</td><td class="vertb" align="center">20</td><td class="vertb" align="center">20</td><td class="vertb" align="center">18</td><td class="vertb" align="center">18</td><td class="vertb" align="center">16</td><td class="vertb" align="center">15</td><td class="vertb" align="center">14</td><td class="vertb" align="center">13</td><td class="vertb" align="center">12</td><td class="vertb" align="center">8</td></tr>
+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">2,31</td><td class="vertbotb" align="center">30</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="vertb" align="center">9</td><td class="vertb" align="center">21</td><td class="vertb" align="center">19</td><td class="vertb" align="center">21</td><td class="vertb" align="center">19</td><td class="vertb" align="center">19</td><td class="vertb" align="center">17</td><td class="vertb" align="center">17</td><td class="vertb" align="center">15</td><td class="vertb" align="center">14</td><td class="vertb" align="center">13</td><td class="vertb" align="center">12</td><td class="vertb" align="center">11</td><td class="vertb" align="center">9</td></tr>
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+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">19</td><td class="vertbotb" align="center">18</td><td class="vertbotb" align="center">19</td><td class="vertbotb" align="center">18</td><td class="vertbotb" align="center">17</td><td class="vertbotb" align="center">16</td><td class="vertbotb" align="center">15</td><td class="vertbotb" align="center">14</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="vertb" align="center">27</td><td class="vertb" align="center">3</td><td class="vertb" align="center">2</td><td class="vertb" align="center">3</td><td class="vertb" align="center">2</td><td class="vertb" align="center">1,31</td><td class="vertb" align="center">29</td><td class="vertb" align="center">29</td><td class="vertb" align="center">27</td><td class="vertb" align="center">26</td><td class="vertb" align="center">25</td><td class="vertb" align="center">24</td><td class="vertb" align="center">23</td><td class="vertb" align="center">27</td></tr>
+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">18</td><td class="vertbotb" align="center">17</td><td class="vertbotb" align="center">18</td><td class="vertbotb" align="center">17</td><td class="vertbotb" align="center">16</td><td class="vertbotb" align="center">15</td><td class="vertbotb" align="center">14</td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="vertb" align="center">28</td><td class="vertb" align="center">2</td><td class="vertb" align="center">1</td><td class="vertb" align="center">2</td><td class="vertb" align="center">1,30</td><td class="vertb" align="center">30</td><td class="vertb" align="center">28</td><td class="vertb" align="center">28</td><td class="vertb" align="center">26</td><td class="vertb" align="center">25</td><td class="vertb" align="center">24</td><td class="vertb" align="center">23</td><td class="vertb" align="center">22</td><td class="vertb" align="center">28</td></tr>
+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">17</td><td class="vertbotb" align="center">16</td><td class="vertbotb" align="center">17</td><td class="vertbotb" align="center">16</td><td class="vertbotb" align="center">15</td><td class="vertbotb" align="center">14</td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="vertb" align="center">29</td><td class="vertb" align="center">1,31</td><td class="vertb" align="center">&mdash;</td><td class="vertb" align="center">1,31</td><td class="vertb" align="center">29</td><td class="vertb" align="center">29</td><td class="vertb" align="center">27</td><td class="vertb" align="center">27</td><td class="vertb" align="center">25</td><td class="vertb" align="center">24</td><td class="vertb" align="center">23</td><td class="vertb" align="center">22</td><td class="vertb" align="center">21</td><td class="vertb" align="center">29</td></tr>
+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">16</td><td class="vertbotb" align="center">15</td><td class="vertbotb" align="center">16</td><td class="vertbotb" align="center">15</td><td class="vertbotb" align="center">14</td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="vertb" align="center">30</td><td class="vertb" align="center">30</td><td class="vertb" align="center">28</td><td class="vertb" align="center">30</td><td class="vertb" align="center">28</td><td class="vertb" align="center">28</td><td class="vertb" align="center">26</td><td class="vertb" align="center">26</td><td class="vertb" align="center">24</td><td class="vertb" align="center">23</td><td class="vertb" align="center">22</td><td class="vertb" align="center">21</td><td class="vertb" align="center">20</td><td class="vertb" align="center">30</td></tr>
+<tr><td class="vertbotb" align="center">&nbsp;</td><td class="vertbotb" align="center">15</td><td class="vertbotb" align="center">14</td><td class="vertbotb" align="center">15</td><td class="vertbotb" align="center">14</td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center"></td></tr>
+<tr><td class="allb" align="center">&nbsp;</td><td class="allb" align="center">Jan.</td><td class="allb" align="center">Feb.</td><td class="allb" align="center">Mar.</td><td class="allb" align="center">Apr.</td><td class="allb" align="center">May</td><td class="allb" align="center">June</td><td class="allb" align="center">July</td><td class="allb" align="center">Aug.</td><td class="allb" align="center">Sep.</td><td class="allb" align="center">Oct.</td><td class="allb" align="center">Nov.</td><td class="allb" align="center">Dec.</td><td class="allb" align="center">&nbsp;</td></tr>
+</table>
+
+<p><!-- Page 370 --><span class="pagenum"><a name="page370"></a>[370]</span></p>
+
+<table class="allbctr" summary="True table of epacts" title="True table of epacts">
+<tr><td class="allb" align="center">&nbsp;</td><td class="allb" align="center">0</td><td class="allb" align="center">1</td><td class="allb" align="center">2</td><td class="allb" align="center">3</td><td class="allb" align="center">4</td><td class="allb" align="center">5</td><td class="allb" align="center">6</td><td class="allb" align="center">7</td><td class="allb" align="center">8</td><td class="allb" align="center">9</td></tr>
+<tr><td class="allb" align="center">185</td><td class="allb" align="center">17</td><td class="allb" align="center">28</td><td class="allb" align="center"><span class="correction" title="text reads `19'">9</span></td><td class="allb" align="center">20</td><td class="allb" align="center">2</td><td class="allb" align="center">12</td><td class="allb" align="center">23</td><td class="allb" align="center">4</td><td class="allb" align="center">15</td><td class="allb" align="center">26</td></tr>
+<tr><td class="allb" align="center">186</td><td class="allb" align="center">7</td><td class="allb" align="center">18</td><td class="allb" align="center">30</td><td class="allb" align="center">11</td><td class="allb" align="center">22</td><td class="allb" align="center">3</td><td class="allb" align="center">14</td><td class="allb" align="center">25</td><td class="allb" align="center">6</td><td class="allb" align="center">17</td></tr>
+<tr><td class="allb" align="center">187</td><td class="allb" align="center">28</td><td class="allb" align="center">9</td><td class="allb" align="center">20</td><td class="allb" align="center">1</td><td class="allb" align="center">12</td><td class="allb" align="center">23</td><td class="allb" align="center">4</td><td class="allb" align="center">15</td><td class="allb" align="center">26</td><td class="allb" align="center">7</td></tr>
+<tr><td class="allb" align="center">188</td><td class="allb" align="center">18</td><td class="allb" align="center">30</td><td class="allb" align="center">11</td><td class="allb" align="center">22</td><td class="allb" align="center">3</td><td class="allb" align="center">14</td><td class="allb" align="center">25</td><td class="allb" align="center">6</td><td class="allb" align="center">17</td><td class="allb" align="center">28</td></tr>
+<tr><td class="allb" align="center">189</td><td class="allb" align="center">9</td><td class="allb" align="center">21</td><td class="allb" align="center">1</td><td class="allb" align="center">12</td><td class="allb" align="center">23</td><td class="allb" align="center">4</td><td class="allb" align="center">15</td><td class="allb" align="center">26</td><td class="allb" align="center">7</td><td class="allb" align="center">18</td></tr>
+<tr><td class="allb" align="center">190</td><td class="allb" align="center">29</td><td class="allb" align="center">10</td><td class="allb" align="center">21</td><td class="allb" align="center">2</td><td class="allb" align="center">13</td><td class="allb" align="center">24</td><td class="allb" align="center">5</td><td class="allb" align="center">16</td><td class="allb" align="center">27</td><td class="allb" align="center">8</td></tr>
+<tr><td class="allb" align="center">191</td><td class="allb" align="center">19</td><td class="allb" align="center">30</td><td class="allb" align="center">11</td><td class="allb" align="center">22</td><td class="allb" align="center">3</td><td class="allb" align="center">14</td><td class="allb" align="center">26</td><td class="allb" align="center">6</td><td class="allb" align="center">17</td><td class="allb" align="center">29</td></tr>
+<tr><td class="allb" align="center">192</td><td class="allb" align="center">10</td><td class="allb" align="center">21</td><td class="allb" align="center">2</td><td class="allb" align="center">13</td><td class="allb" align="center">24</td><td class="allb" align="center">5</td><td class="allb" align="center">16</td><td class="allb" align="center">27</td><td class="allb" align="center">8</td><td class="allb" align="center">19</td></tr>
+<tr><td class="allb" align="center">193</td><td class="allb" align="center">30</td><td class="allb" align="center">11</td><td class="allb" align="center">22</td><td class="allb" align="center">3</td><td class="allb" align="center">14</td><td class="allb" align="center">26</td><td class="allb" align="center">6</td><td class="allb" align="center">17</td><td class="allb" align="center">29</td><td class="allb" align="center">10</td></tr>
+<tr><td class="allb" align="center">194</td><td class="allb" align="center">21</td><td class="allb" align="center">2</td><td class="allb" align="center">13</td><td class="allb" align="center">24</td><td class="allb" align="center">5</td><td class="allb" align="center">16</td><td class="allb" align="center">27</td><td class="allb" align="center">8</td><td class="allb" align="center">19</td><td class="allb" align="center">30</td></tr>
+<tr><td class="allb" align="center">195</td><td class="allb" align="center">11</td><td class="allb" align="center">22</td><td class="allb" align="center">3</td><td class="allb" align="center">14</td><td class="allb" align="center">26</td><td class="allb" align="center">6</td><td class="allb" align="center">17</td><td class="allb" align="center">29</td><td class="allb" align="center">10</td><td class="allb" align="center">21</td></tr>
+<tr><td class="allb" align="center">196</td><td class="allb" align="center">2</td><td class="allb" align="center">13</td><td class="allb" align="center">24</td><td class="allb" align="center">5</td><td class="allb" align="center">16</td><td class="allb" align="center">27</td><td class="allb" align="center">8</td><td class="allb" align="center">19</td><td class="allb" align="center">30</td><td class="allb" align="center">11</td></tr>
+<tr><td class="allb" align="center">197</td><td class="allb" align="center">22</td><td class="allb" align="center">3</td><td class="allb" align="center">14</td><td class="allb" align="center">26</td><td class="allb" align="center">6</td><td class="allb" align="center">17</td><td class="allb" align="center">29</td><td class="allb" align="center">10</td><td class="allb" align="center">21</td><td class="allb" align="center">2</td></tr>
+<tr><td class="allb" align="center">198</td><td class="allb" align="center">13</td><td class="allb" align="center">24</td><td class="allb" align="center">5</td><td class="allb" align="center">16</td><td class="allb" align="center">27</td><td class="allb" align="center">8</td><td class="allb" align="center">19</td><td class="allb" align="center">30</td><td class="allb" align="center">11</td><td class="allb" align="center">22</td></tr>
+<tr><td class="allb" align="center">199</td><td class="allb" align="center">3</td><td class="allb" align="center">14</td><td class="allb" align="center">26</td><td class="allb" align="center">6</td><td class="allb" align="center">17</td><td class="allb" align="center">29</td><td class="allb" align="center">10</td><td class="allb" align="center">21</td><td class="allb" align="center">2</td><td class="allb" align="center">13</td></tr>
+</table>
+
+  <p>For example, the year 1867. The epact is 25, and we find in the
+  table:</p>
+
+<table class="nobctr" summary="Moons for 1867" title="Moons for 1867">
+<tr><td class="spac">&nbsp;</td><td class="spac" align="center">J.</td><td class="spac" align="center">F.</td><td class="spac" align="center">M.</td><td class="spac" align="center">AP.</td><td class="spac" align="center">M.</td><td class="spac" align="center">JU.</td><td class="spac" align="center">JL.</td><td class="spac" align="center">AU.</td><td class="spac" align="center">S.</td><td class="spac" align="center">O.</td><td class="spac" align="center">N.</td><td class="spac" align="center">D.</td></tr>
+<tr><td class="spac">New</td><td class="spac" align="center">5+</td><td class="spac" align="center">4</td><td class="spac" align="center">5+</td><td class="spac" align="center">4</td><td class="spac" align="center">3+</td><td class="spac" align="center">2</td><td class="spac" align="center">1,31</td><td class="spac" align="center">29</td><td class="spac" align="center">28-</td><td class="spac" align="center">27</td><td class="spac" align="center">26</td><td class="spac" align="center">25</td></tr>
+<tr><td class="spac">Full</td><td class="spac" align="center">20</td><td class="spac" align="center">19-</td><td class="spac" align="center">20</td><td class="spac" align="center">19-</td><td class="spac" align="center">18</td><td class="spac" align="center">17</td><td class="spac" align="center">16</td><td class="spac" align="center">15</td><td class="spac" align="center">13-</td><td class="spac" align="center">13</td><td class="spac" align="center">11+</td><td class="spac" align="center">11</td></tr>
+</table>
+
+  <p>When the truth is the day after + is written after the date; when the
+  day before, -. Thus, the new moon of March is on the 6th; the full moon
+  of April is on the 18th. <!-- Page 371 --><span class="pagenum"><a
+  name="page371"></a>[371]</span></p>
+
+  <p>I now introduce a small paradox of my own; and as I am not able to
+  prove it, I am compelled to declare that any one who shall dissent must
+  be either very foolish or very dishonest, and will make me quite
+  uncomfortable about the state of his soul. This being settled once for
+  all, I proceed to say that the necessity of arriving at the truth about
+  the assertions that the Nicene Council laid down astronomical tests led
+  me to look at Fathers, Church histories, etc. to an extent which I never
+  dreamed of before. One conclusion which I arrived at was, that the Nicene
+  Fathers had a knack of sticking to the question which many later councils
+  could not acquire. In our own day, it is not permitted to Convocation
+  seriously to discuss any one of the points which are bearing so hard upon
+  their resources of defence&mdash;the cursing clauses of the Athanasian
+  Creed, for example. And it may be collected that the prohibition arises
+  partly from fear that there is no saying where a beginning, if allowed,
+  would end. There seems to be a suspicion that debate, once let loose,
+  would play up old Trent with the liturgy, and bring the whole book to
+  book. But if any one will examine the real Nicene Creed, without the
+  augmentation, he will admire the way in which the framers stuck to the
+  point, and settled what they had to decide, according to their view of
+  it. With such a presumption of good sense in their favor, it becomes
+  easier to believe in any claim which may be made on their behalf to tact
+  or sagacity in settling any other matter. And I strongly suspect such a
+  claim may be made for them on the Easter question.</p>
+
+  <p>I collect from many little indications, both before and after the
+  Council, that the division of the Christian world into Judaical and
+  Gentile, though not giving rise to a sectarian distinction expressed by
+  names, was of far greater force and meaning than historians prominently
+  admit. I took <i>note</i> of many indications of this, but not
+  <i>notes</i>, as it was not to my purpose. If it were so, we must admire
+  the discretion of the Council. The Easter question was the <!-- Page 372
+  --><span class="pagenum"><a name="page372"></a>[372]</span>fighting
+  ground of the struggle: the Eastern or Judaical Christians, with some
+  varieties of usage and meaning, would have the Passover itself to be the
+  great feast, but taken in a Christian sense; the Western or Gentile
+  Christians, would have the commemoration of the Resurrection, connected
+  with the Passover only by chronology. To shift the Passover in time,
+  under its name, <i>Pascha</i>, without allusion to any of the force of
+  the change, was gently cutting away the ground from under the feet of the
+  Conservatives. And it was done in a very quiet way: no allusion to the
+  precise character of the change; no hint that the question was about two
+  different festivals: "all the brethren in the East, who formerly
+  celebrated this festival at the same time as the Jews, will in future
+  conform to the Romans and to us." The Judaizers meant to be keeping the
+  Passover <i>as</i> a Christian feast: they are gently assumed to be
+  keeping, <i>not</i> the Passover, <i>but</i> a Christian feast; and a
+  doctrinal decision is quietly, but efficiently, announced under the form
+  of a chronological ordinance. Had the Council issued theses of doctrine,
+  and excommunicated all dissentients, the rupture of the East and West
+  would have taken place earlier by centuries than it did. The only place
+  in which I ever saw any part of my paradox advanced, was in an article in
+  the <i>Examiner</i> newspaper, towards the end of 1866, after the above
+  was written.</p>
+
+  <p>A story about Christopher Clavius, the workman of the new Calendar. I
+  chanced to pick up "Albertus Pighius Campensis de æquinoctiorum
+  solsticiorumque inventione... Ejusdem de ratione Paschalis celebrationis,
+  De que Restitutione ecclesiastici Kalendarii," Paris, 1520, folio.<a
+  name="NtA_760" href="#Nt_760"><sup>[760]</sup></a> On the title-page were
+  decayed words followed by "..<i>hristophor.. C..ii</i>, 1556 (or 8)," the
+  last blank not entirely erased by time, but showing the lower halves of
+  an <i>l</i> and of an <i>a</i>, and <!-- Page 373 --><span
+  class="pagenum"><a name="page373"></a>[373]</span>rather too much room
+  for a <i>v</i>. It looked very like <i>E Libris Christophori Clavii</i>
+  1556. By the courtesy of some members of the Jesuit body in London, I
+  procured a tracing of the signature of Clavius from Rome, and the shapes
+  of the letters, and the modes of junction and disjunction, put the matter
+  beyond question. Even the extra space was explained; he wrote himself
+  Cla<i>u</i>ius. Now in 1556, Clavius was nineteen years old: it thus
+  appears probable that the framer of the Gregorian Calendar was selected,
+  not merely as a learned astronomer, but as one who had attended to the
+  calendar, and to works on its reformation, from early youth. When on the
+  subject I found reason to think that Clavius had really read this work,
+  and taken from it a phrase or two and a notion or two. Observe the
+  advantage of writing the baptismal name at full length.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A COUPLE OF MINOR PARADOXES.</p>
+
+<blockquote class="b1n">
+
+  <p>The discovery of a general resolution of all superior finite
+  equations, of every numerical both algebraick and transcendent form. By
+  A.&nbsp;P. Vogel,<a name="NtA_761" href="#Nt_761"><sup>[761]</sup></a>
+  mathematician at Leipzick. Leipzick and London, 1845, 8vo.</p>
+
+</blockquote>
+
+  <p>This work is written in the English of a German who has not mastered
+  the idiom: but it is always intelligible. It professes to solve equations
+  of every degree "in a more extent sense, and till to every degree of
+  exactness." The general solution of equations of <i>all</i> degrees is a
+  vexed question, which cannot have the mysterious interest of the circle
+  problem, and is of a comparatively modern date.<a name="NtA_762"
+  href="#Nt_762"><sup>[762]</sup></a> Mr. Vogel <!-- Page 374 --><span
+  class="pagenum"><a name="page374"></a>[374]</span>announces a forthcoming
+  treatise in which are resolved the "last impossibilities of pure
+  mathematics."</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Elective Polarity the Universal Agent. By Frances Barbara Burton,
+  authoress of 'Astronomy familiarized,' 'Physical Astronomy,' &amp;c.
+  London, 1845, 8vo.<a name="NtA_763"
+  href="#Nt_763"><sup>[763]</sup></a></p>
+
+</blockquote>
+
+  <p>The title gives a notion of the theory. The first sentence states,
+  that 12,500 years ago <span class="grk">&alpha;</span> Lyræ was the
+  pole-star, and attributes the immense magnitude of the now fossil animals
+  to a star of such "polaric intensity as Vega pouring its magnetic streams
+  through our planet." Miss Burton was a lady of property, and of very
+  respectable acquirements, especially in Hebrew; she was eccentric in all
+  things.</p>
+
+  <p>1867.&mdash;Miss Burton is revived by the writer of a book on
+  meteorology which makes use of the planets: she is one of his leading
+  minds.<a name="NtA_764" href="#Nt_764"><sup>[764]</sup></a></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">SPECULATIVE THOUGHT IN ENGLAND.</p>
+
+  <p>In the year 1845 the old <i>Mathematical Society</i> was merged in the
+  Astronomical Society. The circle-squarers, etc., thrive more in England
+  than in any other country: there are most weeds where there is the
+  largest crop. Speculation, though not encouraged by our Government so
+  much as by those of the Continent, has had, not indeed such forcing, but
+  much wider diffusion: few tanks, but many rivulets. On this point I quote
+  from the preface to the reprint of the work of Ramchundra,<a
+  name="NtA_765" href="#Nt_765"><sup>[765]</sup></a> which I superintended
+  for the late Court of Directors of the East India Company.</p>
+
+<p><!-- Page 375 --><span class="pagenum"><a name="page375"></a>[375]</span></p>
+
+  <p>"That sound judgment which gives men well to know what is best for
+  them, as well as that faculty of invention which leads to development of
+  resources and to the increase of wealth and comfort, are both materially
+  advanced, perhaps cannot rapidly be advanced without, a great taste for
+  pure speculation among the general mass of the people, down to the lowest
+  of those who can read and write. England is a marked example. Many
+  persons will be surprised at this assertion. They imagine that our
+  country is the great instance of the refusal of all <i>unpractical</i>
+  knowledge in favor of what is <i>useful</i>. I affirm, on the contrary,
+  that there is no country in Europe in which there has been so wide a
+  diffusion of speculation, theory, or what other unpractical word the
+  reader pleases. In our country, the scientific <i>society</i> is always
+  formed and maintained by the people; in every other, the scientific
+  <i>academy</i>&mdash;most aptly named&mdash;has been the creation of the
+  government, of which it has never ceased to be the nursling. In all the
+  parts of England in which manufacturing pursuits have given the artisan
+  some command of time, the cultivation of mathematics and other
+  speculative studies has been, as is well known, a very frequent
+  occupation. In no other country has the weaver at his loom bent over the
+  <i>Principia</i> of Newton; in no other country has the man of weekly
+  wages maintained his own scientific periodical. With us, since the
+  beginning of the last century, scores upon scores&mdash;perhaps hundreds,
+  for I am far from knowing all&mdash;of annuals have run, some their ten
+  years, some their half-century, some their century and a half, containing
+  questions to be answered, from which many of our examiners in the
+  universities have culled materials for the academical contests. And these
+  questions have always been answered, and in cases without number by the
+  lower order of purchasers, the mechanics, the weavers, and the printers'
+  workmen. I cannot here digress to point out the manner in which the
+  concentration of manufactures, and the general diffusion of education,
+  have affected the <!-- Page 376 --><span class="pagenum"><a
+  name="page376"></a>[376]</span>state of things; I speak of the time
+  during which the present system took its rise, and of the circumstances
+  under which many of its most effective promoters were trained. In all
+  this there is nothing which stands out, like the state-nourished academy,
+  with its few great names and brilliant single achievements. This country
+  has differed from all others in the wide diffusion of the disposition to
+  speculate, which disposition has found its place among the ordinary
+  habits of life, moderate in its action, healthy in its amount."</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE OLD MATHEMATICAL SOCIETY.</p>
+
+  <p>Among the most remarkable proofs of the diffusion of speculation was
+  the Mathematical Society, which flourished from 1717 to 1845. Its habitat
+  was Spitalfields, and I think most of its existence was passed in Crispin
+  Street. It was originally a plain society, belonging to the studious
+  artisan. The members met for discussion once a week; and I believe I am
+  correct in saying that each man had his pipe, his pot, and his problem.
+  One of their old rules was that, "If any member shall so far forget
+  himself and the respect due to the Society as in the warmth of debate to
+  threaten or offer personal violence to any other member, he shall be
+  liable to immediate expulsion, or to pay such fine as the majority of the
+  members present shall decide." But their great rule, printed large on the
+  back of the title page of their last book of regulations, was "By the
+  constitution of the Society, it is the duty of every member, if he be
+  asked any mathematical or philosophical question by another member, to
+  instruct him in the plainest and easiest manner he is able." We shall
+  presently see that, in old time, the rule had a more homely form.</p>
+
+  <p>I have been told that De Moivre<a name="NtA_766"
+  href="#Nt_766"><sup>[766]</sup></a> was a member of this <!-- Page 377
+  --><span class="pagenum"><a name="page377"></a>[377]</span>Society. This
+  I cannot verify: circumstances render it unlikely; even though the French
+  refugees clustered in Spitalfields; many of them were of the Society,
+  which there is some reason to think was founded by them. But Dolland,<a
+  name="NtA_767" href="#Nt_767"><sup>[767]</sup></a> Thomas Simpson,<a
+  name="NtA_768" href="#Nt_768"><sup>[768]</sup></a> Saunderson,<a
+  name="NtA_769" href="#Nt_769"><sup>[769]</sup></a> Crossley,<a
+  name="NtA_770" href="#Nt_770"><sup>[770]</sup></a> and others of known
+  name, were certainly members. The Society gradually declined, and in 1845
+  was reduced to nineteen members. An arrangement was made by which sixteen
+  of these members, who where not already in the Astronomical Society
+  became Fellows without contribution, all the books and other property of
+  the old Society being transferred to the new one. I was one of the
+  committee which made the preliminary inquiries, and the reason of the
+  decline was soon manifest. The only question which could arise was
+  whether the members of the society of working men&mdash;for this repute
+  still continued&mdash;were of that class of educated men who could
+  associate with the Fellows of the Astronomical Society on terms agreeable
+  to all parties. We found that the artisan element had been extinct for
+  many years; there was not a man but might, as to education, manners, and
+  position, have become a Fellow in the usual way. The fact was that life
+  in Spitalfields had become harder: and the weaver could <!-- Page 378
+  --><span class="pagenum"><a name="page378"></a>[378]</span>only live from
+  hand to mouth, and not up to the brain. The material of the old Society
+  no longer existed.</p>
+
+  <p>In 1798, experimental lectures were given, a small charge for
+  admission being taken at the door: by this hangs a tale&mdash;and a song.
+  Many years ago, I found among papers of a deceased friend, who certainly
+  never had anything to do with the Society, and who passed all his life
+  far from London, a song, headed "Song sung by the Mathematical Society in
+  London, at a dinner given Mr. Fletcher,<a name="NtA_771"
+  href="#Nt_771"><sup>[771]</sup></a> a solicitor, who had defended the
+  Society gratis." Mr. Williams,<a name="NtA_772"
+  href="#Nt_772"><sup>[772]</sup></a> the Assistant Secretary of the
+  Astronomical Society, formerly Secretary of the Mathematical Society,
+  remembered that the Society had had a solicitor named Fletcher among the
+  members. Some years elapsed before it struck me that my old friend
+  Benjamin Gompertz,<a name="NtA_773" href="#Nt_773"><sup>[773]</sup></a>
+  who had long been a member, might have some recollection of the matter.
+  The following is an extract of a letter from him (July 9, 1861):</p>
+
+  <p>"As to the Mathematical Society, of which I was a member when only 18
+  years of age, [Mr. G. was born in 1779], having been, contrary to the
+  rules, elected under the age of 21. How I came to be a member of that
+  Society&mdash;and continued so until it joined the Astronomical Society,
+  and was then the President&mdash;was: I happened to pass a bookseller's
+  small shop, of second-hand books, kept by a poor taylor, but a good
+  mathematician, John Griffiths. I was very pleased to meet a
+  mathematician, and I asked him if he would give me some lessons; and his
+  reply was that I was more capable to teach him, but he belonged to a
+  society of mathematicians, and he would introduce me. I accepted the
+  offer, and I was elected, and had many scholars then to teach, as <!--
+  Page 379 --><span class="pagenum"><a name="page379"></a>[379]</span>one
+  of the rules was, if a member asked for information, and applied to any
+  one who could give it, he was obliged to give it, or fine one penny.
+  Though I might say much with respect to the Society which would be
+  interesting, I will for the present reply only to your question. I well
+  knew Mr. Fletcher, who was a very clever and very scientific person. He
+  did, as solicitor, defend an action brought by an informer against the
+  Society&mdash;I think for 5,000<i>l.</i>&mdash;for giving lectures to the
+  public in philosophical subjects [i.e., for unlicensed public exhibition
+  with money taken at the doors]. I think the price for admission was one
+  shilling, and we used to have, if I rightly recollect, from two to three
+  hundred visitors. Mr. Fletcher was successful in his defence, and we got
+  out of our trouble. There was a collection made to reward his services,
+  but he did not accept of any reward: and I think we gave him a dinner, as
+  you state, and enjoyed ourselves; no doubt with astronomical songs and
+  other songs; but my recollection does not enable me to say if the
+  astronomical song was a drinking song. I think the anxiety caused by that
+  action was the cause of some of the members' death. [They had, no doubt,
+  broken the law in ignorance; and by the sum named, the informer must have
+  been present, and sued for a penalty on every shilling he could prove to
+  have been taken]."</p>
+
+  <p>I by no means guarantee that the whole song I proceed to give is what
+  was sung at the dinner: I suspect, by the completeness of the chain, that
+  augmentations have been made. My deceased friend was just the man to add
+  some verses, or the addition may have been made before it came into his
+  hands, or since his decease, for the scraps containing the verses passed
+  through several hands before they came into mine. We may, however, be
+  pretty sure that the original is substantially contained in what is
+  given, and that the character is therefore preserved. I have had myself
+  to repair damages every now and then, in the way of conjectural
+  restoration of defects caused by ill-usage. <!-- Page 380 --><span
+  class="pagenum"><a name="page380"></a>[380]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE ASTRONOMER'S DRINKING SONG.</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"Whoe'er would search the starry sky,</p>
+      <p class="i2">Its secrets to divine, sir,</p>
+      <p>Should take his glass&mdash;I mean, should try</p>
+      <p class="i2">A glass or two of wine, sir!</p>
+      <p>True virtue lies in golden mean,</p>
+      <p class="i2">And man must wet his clay, sir;</p>
+      <p>Join these two maxims, and 'tis seen</p>
+      <p class="i2">He should drink his bottle a day, sir!</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"Old Archimedes, reverend sage!</p>
+      <p class="i2">By trump of fame renowned, sir,</p>
+      <p>Deep problems solved in every page,</p>
+      <p class="i2">And the sphere's curved surface found,<a name="NtA_774" href="#Nt_774"><sup>[774]</sup></a> sir:</p>
+      <p>Himself he would have far outshone,</p>
+      <p class="i2">And borne a wider sway, sir,</p>
+      <p>Had he our modern secret known,</p>
+      <p class="i2">And drank a bottle a day, sir!</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"When Ptolemy,<a name="NtA_775" href="#Nt_775"><sup>[775]</sup></a> now long ago,</p>
+      <p class="i2">Believed the earth stood still, sir,</p>
+      <p>He never would have blundered so,</p>
+      <p class="i2">Had he but drunk his fill, sir:</p>
+      <p>He'd then have felt<a name="NtA_776" href="#Nt_776"><sup>[776]</sup></a> it circulate,</p>
+      <p class="i2">And would have learnt to say, sir,</p>
+      <p>The true way to investigate</p>
+      <p class="i2">Is to drink your bottle a day, sir!</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"Copernicus,<a name="NtA_777" href="#Nt_777"><sup>[777]</sup></a> that learned wight,</p>
+      <p class="i2">The glory of his nation,</p>
+      <p>With draughts of wine refreshed his sight,</p>
+      <p class="i2">And saw the earth's rotation;</p>
+<!-- Page 381 --><span class="pagenum"><a name="page381"></a>[381]</span>
+      <p>Each planet then its orb described,</p>
+      <p class="i2">The moon got under way, sir;</p>
+      <p>These truths from nature he imbibed</p>
+      <p class="i2">For he drank his bottle a day, sir!</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"The noble<a name="NtA_778" href="#Nt_778"><sup>[778]</sup></a> Tycho placed the stars,</p>
+      <p class="i2">Each in its due location;</p>
+      <p>He lost his nose<a name="NtA_779" href="#Nt_779"><sup>[779]</sup></a> by spite of Mars,</p>
+      <p class="i2">But that was no privation:</p>
+      <p>Had he but lost his mouth, I grant</p>
+      <p class="i2">He would have felt dismay, sir,</p>
+      <p>Bless you! <i>he</i> knew what he should want</p>
+      <p class="i2">To drink his bottle a day, sir!</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"Cold water makes no lucky hits;</p>
+      <p class="i2">On mysteries the head runs:</p>
+      <p>Small drink let Kepler<a name="NtA_780" href="#Nt_780"><sup>[780]</sup></a> time his wits</p>
+      <p class="i2">On the regular polyhedrons:</p>
+      <p>He took to wine, and it changed the chime,</p>
+      <p class="i2">His genius swept away, sir,</p>
+      <p>Through area varying<a name="NtA_781" href="#Nt_781"><sup>[781]</sup></a> as the time</p>
+      <p class="i2">At the rate of a bottle a day, sir!</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"Poor Galileo,<a name="NtA_782" href="#Nt_782"><sup>[782]</sup></a> forced to rat</p>
+      <p class="i2">Before the Inquisition,</p>
+      <p><i>E pur si muove</i><a name="NtA_783" href="#Nt_783"><sup>[783]</sup></a> was the pat</p>
+      <p class="i2">He gave them in addition:</p>
+<!-- Page 382 --><span class="pagenum"><a name="page382"></a>[382]</span>
+      <p>He meant, whate'er you think you prove,</p>
+      <p class="i2">The earth must go its way, sirs;</p>
+      <p>Spite of your teeth I'll make it move,</p>
+      <p class="i2">For I'll drink my bottle a day, sirs!</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"Great Newton, who was never beat</p>
+      <p class="i2">Whatever fools may think, sir;</p>
+      <p>Though sometimes he forgot to eat,</p>
+      <p class="i2">He never forgot to drink, sir:</p>
+      <p>Descartes<a name="NtA_784" href="#Nt_784"><sup>[784]</sup></a> took nought but lemonade,</p>
+      <p class="i2">To conquer him was play, sir;</p>
+      <p>The first advance that Newton made</p>
+      <p class="i2">Was to drink his bottle a day, sir!</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"D'Alembert,<a name="NtA_785" href="#Nt_785"><sup>[785]</sup></a> Euler,<a name="NtA_786" href="#Nt_786"><sup>[786]</sup></a> and Clairaut,<a name="NtA_787" href="#Nt_787"><sup>[787]</sup></a></p>
+      <p class="i2">Though they increased our store, sir,</p>
+      <p>Much further had been seen to go</p>
+      <p class="i2">Had they tippled a little more, sir!</p>
+      <p>Lagrange<a name="NtA_788" href="#Nt_788"><sup>[788]</sup></a> gets mellow with Laplace,<a name="NtA_789" href="#Nt_789"><sup>[789]</sup></a></p>
+      <p class="i2">And both are wont to say, sir,</p>
+      <p>The <i>philosophe</i> who's not an ass</p>
+      <p class="i2">Will drink his bottle a day, sir!</p>
+    </div>
+
+    <div class="stanza">
+      <p class="hg3">"Astronomers! what can avail</p>
+      <p class="i2">Those who calumniate us;</p>
+      <p>Experiment can never fail</p>
+      <p class="i2">With such an apparatus:</p>
+      <p>Let him who'd have his merits known</p>
+      <p class="i2">Remember what I say, sir;</p>
+      <p>Fair science shines on him alone</p>
+      <p class="i2">Who drinks his bottle a day, sir!</p>
+    </div>
+
+    <div class="stanza">
+<!-- Page 383 --><span class="pagenum"><a name="page383"></a>[383]</span>
+      <p class="hg3">"How light we reck of those who mock</p>
+      <p class="i2">By this we'll make to appear, sir,</p>
+      <p>We'll dine by the sidereal<a name="NtA_790" href="#Nt_790"><sup>[790]</sup></a> clock</p>
+      <p class="i2">For one more bottle a year, sir:</p>
+      <p>But choose which pendulum you will,</p>
+      <p class="i2">You'll never make your way, sir,</p>
+      <p>Unless you drink&mdash;and drink your fill,&mdash;</p>
+      <p class="i2">At least a bottle a day, sir!"</p>
+    </div>
+  </div>
+  <p>Old times are changed, old manners gone!</p>
+
+  <p>There is a new Mathematical Society,<a name="NtA_791"
+  href="#Nt_791"><sup>[791]</sup></a> and I am, at this present writing
+  (1866), its first President. We are very high in the newest developments,
+  and bid fair to take a place among the scientific establishments.
+  Benjamin Gompertz, who was President of the old Society when it expired,
+  was the link between the old and new body: he was a member of <i>ours</i>
+  at his death. But not a drop of liquor is seen at our meetings, except a
+  decanter of water: all our heavy is a fermentation of symbols; and we do
+  not draw it mild. There is no penny fine for reticence or occult science;
+  and as to a song! not the ghost of a chance.</p>
+
+  <p>&nbsp;</p>
+
+  <p>1826. The time may have come when the original documents connected
+  with the discovery of Neptune may be worth revising. The following are
+  extracts from the <i>Athenæum</i> of October 3 and October 17:</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">LE VERRIER'S<a name="NtA_792" href="#Nt_792"><sup>[792]</sup></a> PLANET.</p>
+
+  <p>We have received, at the last moment before making up for press, the
+  following letter from Sir John Herschel,<a name="NtA_793"
+  href="#Nt_793"><sup>[793]</sup></a> <!-- Page 384 --><span
+  class="pagenum"><a name="page384"></a>[384]</span>in reference to the
+  matter referred to in the communication from Mr. Hind<a name="NtA_794"
+  href="#Nt_794"><sup>[794]</sup></a> given below:</p>
+
+  <p class="author">"Collingwood, Oct. 1.
+
+  <p>"In my address to the British Association assembled at Southampton, on
+  the occasion of my resigning the chair to Sir R. Murchison,<a
+  name="NtA_795" href="#Nt_795"><sup>[795]</sup></a> I stated, among the
+  remarkable astronomical events of the last twelvemonth, that it had added
+  a new planet to our list,&mdash;adding, 'it has done more,&mdash;it has
+  given us the probable prospect of the discovery of another. We see it as
+  Columbus saw America from the shores of Spain. Its movements have been
+  felt, trembling along the far-reaching line of our analysis, with a
+  certainty hardly inferior to that of ocular demonstration.'&mdash;These
+  expressions are not reported in any of the papers which profess to give
+  an account of the proceedings, but I appeal to all present whether they
+  were not used.</p>
+
+  <p>"Give me leave to state my reasons for this confidence; and, in so
+  doing, to call attention to some facts which deserve to be put on record
+  in the history of this noble discovery. On July 12, 1842, the late
+  illustrious astronomer, Bessel,<a name="NtA_796"
+  href="#Nt_796"><sup>[796]</sup></a> honored me with a visit at my present
+  residence. On the evening of that day, conversing on the great work of
+  the planetary reductions undertaken by the Astronomer Royal<a
+  name="NtA_797" href="#Nt_797"><sup>[797]</sup></a>&mdash;then in
+  progress, and since published,<a name="NtA_798"
+  href="#Nt_798"><sup>[798]</sup></a>&mdash;M. Bessel remarked that the
+  motions of Uranus, as he had satisfied <!-- Page 385 --><span
+  class="pagenum"><a name="page385"></a>[385]</span>himself by careful
+  examination of the recorded observations, could not be accounted for by
+  the perturbations of the known planets; and that the deviations far
+  exceeded any possible limits of error of observation. In reply to the
+  question, Whether the deviations in question might not be due to the
+  action of an unknown planet?&mdash;he stated that he considered it highly
+  probable that such was the case,&mdash;being systematic, and such as
+  might be produced by an exterior planet. I then inquired whether he had
+  attempted, from the indications afforded by these perturbations, to
+  discover the position of the unknown body,&mdash;in order that 'a hue and
+  cry' might be raised for it. From his reply, the words of which I do not
+  call to mind, I collected that he had not then gone into that inquiry;
+  but proposed to do so, having now completed certain works which had
+  occupied too much of his time. And, accordingly, in a letter which I
+  received from him after his return to Königsberg, dated November 14,
+  1842, he says,&mdash;'In reference to our conversation at Collingwood, I
+  <i>announce</i> to you (<i>melde</i> ich Ihnen) that Uranus is not
+  forgotten.' Doubtless, therefore, among his papers will be found some
+  researches on the subject.</p>
+
+  <p>"The remarkable calculations of M. Le Verrier&mdash;which have pointed
+  out, as now appears, nearly the true situation of the new planet, by
+  resolving the inverse problem of the perturbations&mdash;if
+  uncorroborated by repetition of the numerical calculations by another
+  hand, or by independent investigation from another quarter, would hardly
+  justify so strong an assurance as that conveyed by my expressions above
+  alluded to. But it was known to me, at that time, (I will take the
+  liberty to cite the Astronomer Royal as my authority) that a similar
+  investigation had been independently entered into, and a conclusion as to
+  the situation of the new planet very nearly coincident with M. Le
+  Verrier's arrived at (in entire ignorance of his conclusions), by a young
+  Cambridge mathematician, Mr. Adams;<a name="NtA_799"
+  href="#Nt_799"><sup>[799]</sup></a>&mdash;who will, I hope, <!-- Page 386
+  --><span class="pagenum"><a name="page386"></a>[386]</span>pardon this
+  mention of his name (the matter being one of great historical
+  moment),&mdash;and who will, doubtless, in his own good time and manner,
+  place his calculations before the public.</p>
+
+  <p class="author">"J. F. W. HERSCHEL."
+
+<p class="cenhead"><i>Discovery of Le Verrier's Planet.</i></p>
+
+  <p>Mr. Hind announces to the <i>Times</i> that he has received a letter
+  from Dr. Brünnow, of the Royal Observatory at Berlin, giving the very
+  important information that Le Verrier's planet was found by M. Galle, on
+  the night of September 23. "In announcing this grand discovery," he says,
+  "I think it better to copy Dr. Brünnow's<a name="NtA_800"
+  href="#Nt_800"><sup>[800]</sup></a> letter."</p>
+
+  <p>&nbsp;</p>
+
+  <p class="author">"Berlin, Sept. 25.
+
+  <p>"My dear Sir&mdash;M. Le Verrier's planet was discovered here the 23d
+  of September, by M. Galle.<a name="NtA_801"
+  href="#Nt_801"><sup>[801]</sup></a> It is a star of the 8th magnitude,
+  but with a diameter of two or three seconds. Here are its places:</p>
+
+<table class="nobctr" summary="Locations of Neptune" title="Locations of Neptune">
+<tr><td>&nbsp;</td><td>h.</td><td>m.</td><td>s.</td><td>&nbsp;</td><td align="center" colspan="4">R. A.</td><td>&nbsp;</td><td align="center" colspan="4">Declination.</td></tr>
+<tr><td>Sept. 23,</td><td align="right">12</td><td align="right">0</td><td align="right">14.6 M.T.</td><td>&nbsp;</td><td align="right">328°</td><td align="right">19'</td><td align="right">16.0"</td><td>&nbsp;</td><td align="right">-13°</td><td align="right">24'</td><td align="right">8.2"</td></tr>
+<tr><td>Sept. 24,</td><td align="right">8</td><td align="right">54</td><td align="right">40.9 M.T.</td><td>&nbsp;</td><td align="right">328°</td><td align="right">18'</td><td align="right">14.3"</td><td>&nbsp;</td><td align="right">-13°</td><td align="right">24'</td><td align="right">29.7"</td></tr>
+</table>
+
+  <p>The planet is now retrograde, its motion amounting daily to four
+  seconds of time.</p>
+
+<p class="cenhead">"Yours most respectfully, <span class="sc">Brünnow</span>."</p>
+
+  <p>"This discovery," Mr. Hind says, "may be justly considered one of the
+  greatest triumphs of theoretical astronomy;" and he adds, in a
+  postscript, that the planet was observed at Mr. Bishop's<a name="NtA_802"
+  href="#Nt_802"><sup>[802]</sup></a> Observatory, in the Regent's Park,
+  <!-- Page 387 --><span class="pagenum"><a
+  name="page387"></a>[387]</span>on Wednesday night, notwithstanding the
+  moonlight and hazy sky. "It appears bright," he says, "and with a power
+  of 320 I can see the disc. The following position is the result of
+  instrumental comparisons with 33 Aquarii:</p>
+
+  <p>Sept. 30, at 8h. 16m. 21s. Greenwich mean time&mdash;</p>
+
+<table class="nob" summary="Location of Neptune" title="Location of Neptune">
+<tr><td class="spac">Right ascension of planet</td><td>21h.</td><td>52m.</td><td>47.15s.</td></tr>
+<tr><td class="spac">South declination</td><td>13°</td><td>27'</td><td>20"."</td></tr>
+</table>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THE NEW PLANET.</p>
+
+  <p class="author">"Cambridge Observatory, Oct. 15.
+
+  <p>"The allusion made by Sir John Herschel, in his letter contained in
+  the <i>Athenæum</i> of October 3, to the theoretical researches of Mr.
+  Adams, respecting the newly-discovered planet, has induced me to request
+  that you would make the following communication public. It is right that
+  I should first say that I have Mr. Adams's permission to make the
+  statements that follow, so far as they relate to his labors. I do not
+  propose to enter into a detail of the steps by which Mr. Adams was led,
+  by his spontaneous and independent researches, to a conclusion that a
+  planet must exist more distant than Uranus. The matter is of too great
+  historical moment not to receive a more formal record than it would be
+  proper to give here. My immediate object is to show, while the attention
+  of the scientific public is more particularly directed to the subject,
+  that, with respect to this remarkable discovery, English astronomers may
+  lay claim to some merit.</p>
+
+  <p>"Mr. Adams formed the resolution of trying, by calculation, to account
+  for the anomalies in the motion of Uranus on the hypothesis of a more
+  distant planet, when he was an undergraduate in this university, and when
+  his exertions for the academical distinction, which he obtained in
+  January 1843, left him no time for pursuing the research. In the course
+  of that year, he arrived at an approximation to the position of the
+  supposed planet; which, however, he did not consider to be worthy of
+  confidence, on account of his not <!-- Page 388 --><span
+  class="pagenum"><a name="page388"></a>[388]</span>having employed a
+  sufficient number of observations of Uranus. Accordingly, he requested my
+  intervention to obtain for him the early Greenwich observations, then in
+  course of reduction;&mdash;which the Astronomer Royal immediately
+  supplied, in the kindest possible manner. This was in February, 1844. In
+  September, 1845, Mr. Adams communicated to me values which he had
+  obtained for the heliocentric longitude, excentricity of orbit, longitude
+  of perihelion, and mass, of an assumed exterior planet,&mdash;deduced
+  entirely from unaccounted-for perturbations of Uranus. The same results,
+  somewhat corrected, he communicated, in October, to the Astronomer Royal.
+  M. Le Verrier, in an investigation which was published in June of 1846,
+  assigned very nearly the same heliocentric longitude for the probable
+  position of the planet as Mr. Adams had arrived at, but gave no results
+  respecting its mass and the form of its orbit. The coincidence as to
+  position from two entirely independent investigations naturally inspired
+  confidence; and the Astronomer Royal shortly after suggested the
+  employing of the Northumberland telescope of this observatory in a
+  systematic search after the hypothetical planet; recommending, at the
+  same time, a definite plan of operations. I undertook to make the
+  search,&mdash;and commenced observing on July 29. The observations were
+  directed, in the first instance, to the part of the heavens which theory
+  had pointed out as the most probable place of the planet; in selecting
+  which I was guided by a paper drawn up for me by Mr. Adams. Not having
+  hour xxi. of the Berlin star-maps&mdash;of the publication of which I was
+  not aware&mdash;I had to proceed on the principle of comparison of
+  observations made at intervals. On July 30, I went over a zone 9' broad,
+  in such a manner as to include all stars to the eleventh magnitude. On
+  August 4, I took a broader zone and recorded a place of the planet. My
+  next observations were on August 12; when I met with a star of the eighth
+  magnitude in the zone which I had gone over on July 30,&mdash;and which
+  did not then <!-- Page 389 --><span class="pagenum"><a
+  name="page389"></a>[389]</span>contain this star. Of course, this was the
+  planet;&mdash;the place of which was, thus, recorded a second time in
+  four days of observing. A comparison of the observations of July 30 and
+  August 12 would, according to the principle of search which I employed,
+  have shown me the planet. I did not make the comparison till after the
+  detection of it at Berlin&mdash;partly because I had an impression that a
+  much more extensive search was required to give any probability of
+  discovery&mdash;and partly from the press of other occupation. The
+  planet, however, was <i>secured</i>, and two positions of it recorded six
+  weeks earlier here than in any other observatory,&mdash;and in a
+  systematic search expressly undertaken for that purpose. I give now the
+  positions of the planet on August 4 and August 12.</p>
+
+<table class="nob" summary="Locations of Neptune" title="Locations of Neptune">
+<tr><td>Greenwich mean time.</td></tr>
+<tr><td rowspan="2" valign="middle">Aug. 4, 13h. 36m. 25s. ...</td><td rowspan="2" valign="middle"><img src="images/$lbrace.png" style="height:4ex; width:0.5em" alt="left brace" /></td><td>R.A.</td><td>21h.</td><td>58m.</td><td>14.70s.</td></tr>
+<tr><td>N.P.D.</td><td>102°</td><td>57'</td><td>32.2"</td></tr>
+<tr><td rowspan="2" valign="middle">Aug. 12, 13h. 3m. 26s. ...</td><td rowspan="2" valign="middle"><img src="images/$lbrace.png" style="height:4ex; width:0.5em" alt="left brace" /></td><td>R.A.</td><td>21h.</td><td>57m.</td><td>26.13s.</td></tr>
+<tr><td>N.P.D.</td><td>103°</td><td>2'</td><td>&nbsp;0.2"</td></tr>
+</table>
+
+  <p>"From these places compared with recent observations Mr. Adams has
+  obtained the following results:</p>
+
+<table class="nob" summary="Orbital elements of Neptune" title="Orbital elements of Neptune">
+<tr><td>Distance of the planet from the sun ...</td><td align="right">30.05</td></tr>
+<tr><td>Inclination of the orbit ...</td><td align="right">1° 45'</td></tr>
+<tr><td>Longitude of the descending node ...</td><td align="right">309° 43'</td></tr>
+<tr><td>Heliocentric longitude, Aug. 4 ...</td><td align="right">326° 39'</td></tr>
+</table>
+
+  <p>"The present distance from the sun is, therefore, thirty times the
+  earth's mean distance;&mdash;which is somewhat less than the theory had
+  indicated. The other elements of the orbit cannot be approximated to till
+  the observations shall have been continued for a longer period.</p>
+
+  <p>"The part taken by Mr. Adams in the theoretical search after this
+  planet will, perhaps, be considered to justify the suggesting of a name.
+  With his consent, I mention <i>Oceanus</i> as one which may possibly
+  receive the votes of astronomers.&mdash;I <!-- Page 390 --><span
+  class="pagenum"><a name="page390"></a>[390]</span>have authority to state
+  that Mr. Adams's investigations will in a short time, be published in
+  detail.</p>
+
+  <p class="author">"<span class="sc">J. Challis</span>."<a name="NtA_803" href="#Nt_803"><sup>[803]</sup></a>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">ASTRONOMICAL POLICE REPORT.</p>
+
+  <p>"An ill-looking kind of a body, who declined to give any name, was
+  brought before the Academy of Sciences, charged with having assaulted a
+  gentleman of the name of Uranus in the public highway. The prosecutor was
+  a youngish looking person, wrapped up in two or three great coats; and
+  looked chillier than anything imaginable, except the
+  prisoner,&mdash;whose teeth absolutely shook, all the time.</p>
+
+  <p>Policeman Le Verrier<a name="NtA_804"
+  href="#Nt_804"><sup>[804]</sup></a> stated that he saw the prosecutor
+  walking along the pavement,&mdash;and sometimes turning sideways, and
+  sometimes running up to the railings and jerking about in a strange way.
+  Calculated that somebody must be pulling his coat, or otherwise
+  assaulting him. It was so dark that he could not see; but thought, if he
+  watched the direction in which the next odd move was made, he might find
+  out something. When the time came, he set Brünnow, a constable in another
+  division of the same force, to watch where he told him; and Brünnow
+  caught the prisoner lurking about in the very spot,&mdash;trying to look
+  as if he was minding his own business. Had suspected for a long time that
+  somebody was lurking about in the neighborhood. Brünnow was then called,
+  and deposed to his catching the prisoner as described.</p>
+
+  <p><i>M. Arago.</i>&mdash;Was the prosecutor sober?</p>
+
+  <p><i>Le Verrier.</i>&mdash;Lord, yes, your worship; no man who had a
+  drop in him ever looks so cold as he did.</p>
+
+  <p><i>M. Arago.</i>&mdash;Did you see the assault?</p>
+
+  <p><i>Le Verrier.</i>&mdash;I can't say I did; but I told Brünnow exactly
+  how he'd be crouched down;&mdash;just as he was.</p>
+
+<p><!-- Page 391 --><span class="pagenum"><a name="page391"></a>[391]</span></p>
+
+  <p><i>M. Arago (to Brünnow).</i>&mdash;Did <i>you</i> see the
+  assault?</p>
+
+  <p><i>Brünnow.</i>&mdash;No, your worship; but I caught the prisoner.</p>
+
+  <p><i>M. Arago.</i>&mdash;How did you know there was any assault at
+  all?</p>
+
+  <p><i>Le Verrier.</i>&mdash;I reckoned it couldn't be otherwise, when I
+  saw the prosecutor making those odd turns on the pavement.</p>
+
+  <p><i>M. Arago.</i>&mdash;You reckon and you calculate! Why, you'll tell
+  me, next, that you policemen may sit at home and find out all that's
+  going on in the streets by arithmetic. Did you ever bring a case of this
+  kind before me till now?</p>
+
+  <p><i>Le Verrier.</i>&mdash;Why, you see, your worship, the police are
+  growing cleverer and cleverer every day. We can't help it:&mdash;it grows
+  upon us.</p>
+
+  <p><i>M. Arago.</i>&mdash;You're getting too clever for me. What does the
+  prosecutor know about the matter?</p>
+
+  <p>The prosecutor said, all he knew was that he was pulled behind by
+  somebody several times. On being further examined, he said that he had
+  seen the prisoner often, but did not know his name, nor how he got his
+  living; but had understood he was called Neptune. He himself had paid
+  rates and taxes a good many years now. Had a family of six,&mdash;two of
+  whom got their own living.</p>
+
+  <p>The prisoner being called on for his defence, said that it was a
+  quarrel. He had pushed the prosecutor&mdash;and the prosecutor had pushed
+  him. They had known each other a long time, and were always
+  quarreling;&mdash;he did not know why. It was their nature, he supposed.
+  He further said, that the prosecutor had given a false account of
+  himself;&mdash;that he went about under different names. Sometimes he was
+  called Uranus, sometimes Herschel, and sometimes Georgium Sidus; and he
+  had no character for regularity in the neighborhood. Indeed, he was
+  sometimes not to be seen for a long time at once.</p>
+
+  <p>The prosecutor, on being asked, admitted, after a little hesitation,
+  that he had pushed and pulled the prisoner too. <!-- Page 392 --><span
+  class="pagenum"><a name="page392"></a>[392]</span>In the altercation
+  which followed, it was found very difficult to make out which
+  began:&mdash;and the worthy magistrate seemed to think they must have
+  begun together.</p>
+
+  <p><i>M. Arago.</i>&mdash;Prisoner, have you any family?</p>
+
+  <p>The prisoner declined answering that question at present. He said he
+  thought the police might as well reckon it out whether he had or not.</p>
+
+  <p><i>M. Arago</i> said he didn't much differ from that opinion.&mdash;He
+  then addressed both prosecutor and prisoner; and told them that if they
+  couldn't settle their differences without quarreling in the streets, he
+  should certainly commit them both next time. In the meantime, he called
+  upon both to enter into their own recognizances; and directed the police
+  to have an eye upon both,&mdash;observing that the prisoner would be
+  likely to want it a long time, and the prosecutor would be not a hair the
+  worse for it."</p>
+
+  <p>&nbsp;</p>
+
+  <p>This quib was written by a person who was among the astronomers: and
+  it illustrates the fact that Le Verrier had sole possession of the field
+  until Mr. Challis's letter appeared. Sir John Herschel's <span
+  class="correction" title="text reads `pervious'">previous</span>
+  communication should have paved the way: but the wonder of the discovery
+  drove it out of many heads. There is an excellent account of the whole
+  matter in Professor Grant's<a name="NtA_805"
+  href="#Nt_805"><sup>[805]</sup></a> <i>History of Physical Astronomy</i>.
+  The squib scandalized some grave people, who wrote severe admonitions to
+  the editor. There are formalists who spend much time in writing propriety
+  to journals, to which they serve as foolometers. In a letter to the
+  <i>Athenæum</i>, speaking of the way in which people hawk fine terms for
+  common things, I said that these people ought to have a new translation
+  of the Bible, which should contain the verse "gentleman and lady, created
+  He them." The editor was handsomely fired and brimstoned!</p>
+
+<p><!-- Page 393 --><span class="pagenum"><a name="page393"></a>[393]</span></p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">A NEW THEORY OF TIDES.</p>
+
+<blockquote class="b1n">
+
+  <p>A new theory of the tides: in which the errors of the usual theory are
+  demonstrated; and proof shewn that the full moon is not the cause of a
+  concomitant spring tide, but actually the cause of the neaps.... By
+  Comm<sup>r</sup>. Debenham,<a name="NtA_806"
+  href="#Nt_806"><sup>[806]</sup></a> R.N. London, 1846, 8vo.</p>
+
+</blockquote>
+
+  <p>The author replied to a criticism in the <i>Athenæum</i>, and I
+  remember how, in a very few words, he showed that he had read nothing on
+  the subject. The reviewer spoke of the forces of the planets (i.e., the
+  Sun and Moon) on the ocean, on which the author remarks, "But N.B. the
+  Sun is no planet, Mr. Critic." Had he read any of the actual
+  investigations on the usual theory, he would have known that to this day
+  the sun and moon continue to be called <i>planets</i>&mdash;though the
+  phrase is disappearing&mdash;in speaking of the tides; the sense, of
+  course, being the old one, wandering bodies.</p>
+
+  <p>A large class of the paradoxers, when they meet with something which
+  taken in their sense is absurd, do not take the trouble to find out the
+  intended meaning, but walk off with the words laden with their own first
+  construction. Such men are hardly fit to walk the streets without an
+  interpreter. I was startled for a moment, at the time when a recent
+  happy&mdash;and more recently happier&mdash;marriage occupied the public
+  thoughts, by seeing in a haberdasher's window, in staring large letters,
+  an unpunctuated sentence which read itself to me as "Princess Alexandra!
+  collar and cuff!" It immediately occurred to me that had I been any one
+  of some scores of my paradoxers, I should, no doubt, have proceeded to
+  raise the mob against the unscrupulous person who dared to hint to a
+  young bride such maleficent&mdash;or at least immellificent&mdash;conduct
+  towards her new lord. But, as it was, certain material contexts in the
+  shop window suggested a less <!-- Page 394 --><span class="pagenum"><a
+  name="page394"></a>[394]</span>savage explanation. A paradoxer should not
+  stop at reading the advertisements of Newton or Laplace; he should learn
+  to look at the stock of goods.</p>
+
+  <p>I think I must have an eye for double readings, when presented: though
+  I never guess riddles. On the day on which I first walked into the
+  <i>Panizzi</i> reading room<a name="NtA_807"
+  href="#Nt_807"><sup>[807]</sup></a>&mdash;as it ought to be
+  called&mdash;at the Museum, I began my circuit of the wall-shelves at the
+  ladies' end: and perfectly coincided in the propriety of the Bibles and
+  theological works being placed there. But the very first book I looked on
+  the back of had, in flaming gold letters, the following
+  inscription&mdash;"Blast the Antinomians!"<a name="NtA_808"
+  href="#Nt_808"><sup>[808]</sup></a> If a line had been drawn below the
+  first word, Dr. Blast's history of the Antinomians would not have been so
+  fearfully misinterpreted. It seems that neither the binder nor the
+  arranger of the room had caught my reading. The book was removed before
+  the catalogue of books of reference was printed.</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">AN ASTRONOMICAL PARADOXER.</p>
+
+<blockquote class="b1n">
+
+  <p>Two systems of astronomy: first, the Newtonian system, showing the
+  rise and progress thereof, with a short historical account; the general
+  theory with a variety of remarks thereon: second, the system in
+  accordance with the Holy Scriptures, showing the rise and progress from
+  Enoch, the seventh from Adam, the prophets, Moses, and others, in the
+  first Testament; our Lord Jesus Christ, and his apostles, in the new or
+  second Testament; Reeve and Muggleton, in the third and last Testament;
+  with a variety of remarks thereon. By Isaac Frost.<a name="NtA_809"
+  href="#Nt_809"><sup>[809]</sup></a> London, 1846, 4to.</p>
+
+</blockquote>
+
+<p><!-- Page 395 --><span class="pagenum"><a name="page395"></a>[395]</span></p>
+
+  <p>A very handsomely printed volume, with beautiful plates. Many readers
+  who have heard of Muggletonians have never had any distinct idea of
+  Lodowick Muggleton,<a name="NtA_810" href="#Nt_810"><sup>[810]</sup></a>
+  the inspired tailor, (1608-1698) who about 1650 received his commission
+  from heaven, wrote a Testament, founded a sect, and descended to
+  posterity. Of Reeve<a name="NtA_811" href="#Nt_811"><sup>[811]</sup></a>
+  less is usually said; according to Mr. Frost, he and Muggleton are the
+  two "witnesses." I shall content myself with one specimen of Mr. Frost's
+  science:</p>
+
+  <p>"I was once invited to hear read over 'Guthrie<a name="NtA_812"
+  href="#Nt_812"><sup>[812]</sup></a> on Astronomy,' and when the reading
+  was concluded I was asked my opinion thereon; when I said, 'Doctor, it
+  appears to me that Sir I. Newton has only given two proofs in support of
+  his theory of the earth revolving round the sun: all the rest is
+  assertion without any proofs.'&mdash;'What are they?' inquired the
+  Doctor.&mdash;'Well,' I said, 'they are, first, the power of <!-- Page
+  396 --><span class="pagenum"><a name="page396"></a>[396]</span>attraction
+  to keep the earth to the sun; the second is the power of repulsion, by
+  virtue of the centrifugal motion of the earth: all the rest appears to me
+  assertion without proof.' The Doctor considered a short time and then
+  said, 'It certainly did appear so.' I said, 'Sir Isaac has certainly
+  obtained the credit of completing the system, but really he has only half
+  done his work.'&mdash;'How is that,' inquired my friend the Doctor. My
+  reply was this: 'You will observe his system shows the earth traverses
+  round the sun on an inclined plane; the consequence is, there are four
+  powers required to make his system complete:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>1st. The power of <i>attraction</i>.</p>
+      <p>2ndly. The power of <i>repulsion</i>.</p>
+      <p>3rdly. The power of <i>ascending</i> the inclined plane.</p>
+      <p>4thly. The power of <i>descending</i> the inclined plane.</p>
+    </div>
+  </div>
+  <p>You will thus easily see the <i>four</i> powers required, and Newton
+  has only accounted for <i>two</i>; the work is therefore only half done.'
+  Upon due reflection the Doctor said, 'It certainly was necessary to have
+  these <i>four</i> points cleared up before the system could be said to be
+  complete.'"</p>
+
+  <p>&nbsp;</p>
+
+  <p>I have no doubt that Mr. Frost, and many others on my list, have
+  really encountered doctors who could be puzzled by such stuff as this, or
+  nearly as bad, among the votaries of existing systems, and have been
+  encouraged thereby to print their objections. But justice requires me to
+  say that from the words "power of repulsion by virtue of the centrifugal
+  motion of the earth," Mr. Frost may be suspected of having something more
+  like a notion of the much-mistaken term "centrifugal force" than many
+  paradoxers of greater fame. The Muggletonian sect is not altogether
+  friendless: over and above this handsome volume, the works of Reeve and
+  Muggleton were printed, in 1832, in three quarto volumes. See <i>Notes
+  and Queries, 1st Series</i>, v, 80; 3d Series, iii, 303. <!-- Page 397
+  --><span class="pagenum"><a name="page397"></a>[397]</span></p>
+
+  <p>[The system laid down by Mr. Frost, though intended to be
+  substantially that of Lodowick Muggleton, is not so vagarious. It is
+  worthy of note how very different have been the fates of two contemporary
+  paradoxers, Muggleton and George Fox.<a name="NtA_813"
+  href="#Nt_813"><sup>[813]</sup></a> They were friends and associates,<a
+  name="NtA_814" href="#Nt_814"><sup>[814]</sup></a> and commenced their
+  careers about the same time, 1647-1650. The followers of Fox have made
+  their sect an institution, and deserve to be called the pioneers of
+  philanthropy. But though there must still be Muggletonians, since
+  expensive books are published by men who take the name, no sect of that
+  name is known to the world. Nevertheless, Fox and Muggleton are men of
+  one type, developed by the same circumstances: it is for those who
+  investigate such men to point out why their teachings have had fates so
+  different. Macaulay says it was because Fox found followers of more sense
+  than himself. True enough: but why did Fox find such followers and not
+  Muggleton? The two were equally crazy, to all appearance: and the
+  difference required must be sought in the doctrines themselves.</p>
+
+  <p>Fox was not a <i>rational</i> man: but the success of his sect and
+  doctrines entitles him to a letter of alteration of the phrase which I am
+  surprised has not become current. When Conduitt,<a name="NtA_815"
+  href="#Nt_815"><sup>[815]</sup></a> the husband of Newton's half-niece,
+  wrote a circular to Newton's friends, just after his death, inviting them
+  to bear their parts in a proper biography, he said, "As Sir I. Newton was
+  a <i>national</i> man, I think every one ought to contribute to a work
+  intended to do him justice." Here is the very phrase which is often
+  wanted to signify that <!-- Page 398 --><span class="pagenum"><a
+  name="page398"></a>[398]</span>celebrity which puts its mark, good or
+  bad, on the national history, in a manner which cannot be asserted of
+  many notorious or famous historical characters. Thus George Fox and
+  Newton are both <i>national</i> men. Dr. Roget's<a name="NtA_816"
+  href="#Nt_816"><sup>[816]</sup></a> <i>Thesaurus</i> gives more than
+  fifty synonyms&mdash;<i>colleagues</i> would be the better word&mdash;of
+  "<i>celebrated</i>," any one of which might be applied, either in prose
+  or poetry, to Newton or to his works, no one of which comes near to the
+  meaning which Conduitt's adjective immediately suggests.</p>
+
+  <p>The truth is, that we are too <i>monarchical</i> to be
+  <i>national</i>. We have the Queen's army, the Queen's navy, the Queen's
+  highway, the Queen's English, etc.; nothing is national except the
+  <i>debt</i>. That this remark is not new is an addition to its force; it
+  has hardly been repeated since it was first made. It is some excuse that
+  <i>nation</i> is not vernacular English: the <i>country</i> is our word,
+  and <i>country man</i> is appropriated.]</p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>Astronomical Aphorisms, or Theory of Nature; founded on the immutable
+  basis of Meteoric Action. By P. Murphy,<a name="NtA_817"
+  href="#Nt_817"><sup>[817]</sup></a> Esq. London, 1847, 12mo.</p>
+
+</blockquote>
+
+  <p>This is by the framer of the Weather Almanac, who appeals to that work
+  as corroborative of his theory of planetary temperature, years after all
+  the world knew by experience that this meteorological theory was just as
+  good as the others.</p>
+
+<p><!-- Page 399 --><span class="pagenum"><a name="page399"></a>[399]</span></p>
+
+  <p>&nbsp;</p>
+
+<blockquote class="b1n">
+
+  <p>The conspiracy of the Bullionists as it affects the present system of
+  the money laws. By Caleb Quotem. Birmingham, 1847, 8vo. (pp. 16).</p>
+
+</blockquote>
+
+  <p>This pamphlet is one of a class of which I know very little, in which
+  the effects of the laws relating to this or that political bone of
+  contention are imputed to deliberate conspiracy of one class to rob
+  another of what the one knew ought to belong to the other. The success of
+  such writers in believing what they have a bias to believe, would, if
+  they knew themselves, make them think it equally likely that the
+  inculpated classes might really believe what it is <i>their</i> interest
+  to believe. The idea of a <i>guilty</i> understanding existing among
+  fundholders, or landholders, or any holders, all the country over, and
+  never detected except by bouncing pamphleteers, is a theory which should
+  have been left for Cobbett<a name="NtA_818"
+  href="#Nt_818"><sup>[818]</sup></a> to propose, and for Apella to
+  believe.<a name="NtA_819" href="#Nt_819"><sup>[819]</sup></a></p>
+
+  <p>[<i>August</i>, 1866. A pamphlet shows how to pay the National Debt.
+  Advance paper to railways, etc., receivable in payment of taxes. The
+  railways pay interest and principal in money, with which you pay your
+  national debt, and redeem your notes. Twenty-five years of interest
+  redeems the notes, and then the principal pays the debt. Notes to be kept
+  up to value by penalties.]</p>
+
+  <p>&nbsp;</p>
+
+<p class="cenhead">THEISM INDEPENDENT OF REVELATION.</p>
+
+<blockquote class="b1n">
+
+  <p>The Reasoner. No. 45. Edited by G.J. Holyoake.<a name="NtA_820"
+  href="#Nt_820"><sup>[820]</sup></a> Price <i>2d.</i> Is there sufficient
+  proof of the existence of God? 8vo. 1847.</p>
+
+</blockquote>
+
+  <p>This acorn of the holy oak was forwarded to me with a manuscript note,
+  signed by the editor, on the part of the <!-- Page 400 --><span
+  class="pagenum"><a name="page400"></a>[400]</span>"London Society of
+  Theological Utilitarians," who say, "they trust you may be induced to
+  give this momentous subject your consideration." The supposition that a
+  middle-aged person, known as a student of thought on more subjects than
+  one, had that particular subject yet to begin, is a specimen of what I
+  will call the <i>assumption-trick</i> of controversy, a habit which
+  pervades all sides of all subjects. The tract is a proof of the good
+  policy of letting opinions find their level, without any assistance from
+  the Court of Queen's Bench. Twenty years earlier the thesis would have
+  been positive, "There is sufficient proof of the non-existence of God,"
+  and bitter in its tone. As it stands, we have a moderate and respectful
+  treatment&mdash;wrong only in making the opponent argue absurdly, as
+  usually happens when one side invents the other&mdash;of a question in
+  which a great many Christians have agreed with the atheist: that question
+  being&mdash;Can the existence of God be proved independently of
+  revelation? Many very religious persons answer this question in the
+  negative, as well as Mr. Holyoake. And, this point being settled, all who
+  agree in the negative separate into those who can endure scepticism, and
+  those who cannot: the second class find their way to Christianity. This
+  very number of <i>The Reasoner</i> announces the secession of one of its
+  correspondents, and his adoption of the Christian faith. This would not
+  have happened twenty years before: nor, had it happened, would it have
+  been respectfully announced.</p>
+
+  <p>There are people who are very unfortunate in the expression of their
+  meaning. Mr. Holyoake, in the name of the "London Society" etc.,
+  forwarded a pamphlet on the existence of God, and said that the Society
+  trusted I "may be induced to give" the subject my "consideration." How
+  could I know the Society was one person, who supposed I had arrived at a
+  conclusion and wanted a "<i>guiding word</i>"? But so it seems it was:
+  Mr. Holyoake, in the <i>English <!-- Page 401 --><span class="pagenum"><a
+  name="page401"></a>[401]</span>Leader</i> of October 15, 1864, and in a
+  private letter to me, writes as follows:</p>
+
+  <p>"The gentleman who was the author of the argument, and who asked me to
+  send it to Mr. De Morgan, never assumed that that gentleman had 'that
+  particular subject to begin'&mdash;on the contrary, he supposed that one
+  whom we all knew to be eminent as a thinker <i>had</i> come to a
+  conclusion upon it, and would perhaps vouchsafe a guiding word to one who
+  was, as yet, seeking the solution of the Great Problem of Theology. I
+  told my friend that 'Mr. De Morgan was doubtless preoccupied, and that he
+  must be content to wait. On some day of courtesy and leisure he might
+  have the kindness to write.' Nor was I wrong&mdash;the answer appears in
+  your pages at the lapse of seventeen years."</p>
+
+  <p>I suppose Mr. Holyoake's way of putting his request was the <i>stylus
+  curiæ</i> of the Society. A worthy Quaker who was sued for debt in the
+  King's Bench was horrified to find himself charged in the declaration
+  with detaining his creditor's money by force and arms, contrary to the
+  peace of our Lord the King, etc. It's only the <i>stylus curiæ</i>, said
+  a friend: I don't know <i>curiæ</i>, said the Quaker, but he shouldn't
+  style us peace-breakers.</p>
+
+  <p>The notion that the <i>non</i>-existence of God can be <i>proved</i>,
+  has died out under the light of discussion: had the only lights shone
+  from the pulpit and the prison, so great a step would never have been
+  made. The question now is as above. The dictum that Christianity is "part
+  and parcel of the law of the land" is also abrogated: at the same time,
+  and the coincidence is not an accident, it is becoming somewhat nearer
+  the truth that the law of the land is part and parcel of Christianity. It
+  must also be noticed that <i>Christianity</i> was part and parcel of the
+  articles of <i>war</i>; and so was <i>duelling</i>. Any officer speaking
+  against religion was to be cashiered; and any officer receiving an
+  affront without, in the last resort, attempting to kill his opponent, was
+  also to be cashiered. Though somewhat of a book-hunter, I <!-- Page 402
+  --><span class="pagenum"><a name="page402"></a>[402]</span>have never
+  been able to ascertain the date of the collected remonstrances of the
+  prelates in the House of Lords against this overt inculcation of murder,
+  under the soft name of <i>satisfaction</i>: it is neither in Watt,<a
+  name="NtA_821" href="#Nt_821"><sup>[821]</sup></a> nor in Lowndes,<a
+  name="NtA_822" href="#Nt_822"><sup>[822]</sup></a> nor in any edition of
+  Brunet;<a name="NtA_823" href="#Nt_823"><sup>[823]</sup></a> and there is
+  no copy in the British Museum. Was the collected edition really
+  published?</p>
+
+  <p>[The publication of the above in the <i>Athenæum</i> has not produced
+  reference to a single copy. The collected edition seems to be doubted. I
+  have even met one or two persons who doubt the fact of the Bishops having
+  remonstrated at all: but their doubt was founded on an absurd
+  supposition, namely, that it was <i>no business of theirs</i>; that it
+  was not the business of the prelates of the church in union with the
+  state to remonstrate against the Crown commanding murder! Some say that
+  the edition was published, but under an irrelevant title, which prevented
+  people from knowing what it was about. Such things have happened: for
+  example, arranged extracts from Wellington's general orders, which would
+  have attracted attention, fell dead under the title of "Principles of
+  War." It is surmised that the book I am looking for also contains the
+  protests of the Reverend bench against other things besides the
+  Thou-shalt-do-murder of the Articles (of war), and is called "First
+  Elements of Religion" or some similar title. Time clears up all
+  things.]</p>
+
+<hr class="full" >
+
+<h3>Notes</h3>
+
+<div class="note">
+  <p><a name="Nt_1" href="#NtA_1">[1]</a> See Mrs. De Morgan's <i>Memoir of
+  Augustus De Morgan</i>, London, 1882, p 61.</p>
+
+  <p><a name="Nt_2" href="#NtA_2">[2]</a> In the first edition this
+  reference was to page 11.</p>
+
+  <p><a name="Nt_3" href="#NtA_3">[3]</a> In the first edition this read
+  "at page 438," the work then appearing in a single volume.</p>
+
+  <p><a name="Nt_4" href="#NtA_4">[4]</a> "Just as it would surely have
+  been better not to have considered it (i.e., the trinity) as a mystery,
+  and with Cl. Kleckermann to have investigated by the aid of philosophy
+  according to the teaching of true logic what it might be, before they
+  determined what it was; just so would it have been better to withdraw
+  zealously and industriously into the deepest caverns and darkest recesses
+  of metaphysical speculations and suppositions in order to establish their
+  opinion beyond danger from the weapons of their adversaries.... Indeed
+  that great man so explains and demonstrates this dogma (although to
+  theologians the word has not much charm) from the immovable foundations
+  of philosophy, that with but few changes and additions a mind sincerely
+  devoted to truth can desire nothing more."</p>
+
+  <p><a name="Nt_5" href="#NtA_5">[5]</a> Mrs. Wititterly, in <i>Nicholas
+  Nickleby</i>.&mdash;A. De M.</p>
+
+  <p><a name="Nt_6" href="#NtA_6">[6]</a> The brackets mean that the
+  paragraph is substantially from some one of the <i>Athenæum
+  Supplements</i>.&mdash;S.&nbsp;E. De M.</p>
+
+  <p><a name="Nt_7" href="#NtA_7">[7]</a> "It is annoying that this
+  ingenious naturalist who has already given us more useful works and has
+  still others in preparation, uses for this odious task, a pen dipped in
+  gall and wormwood. It is true that many of his remarks have some
+  foundation, and that to each error that he points out he at the same time
+  adds its correction. But he is not always just and never fails to insult.
+  After all, what does his book prove except that a forty-fifth part of a
+  very useful review is not free from mistakes? Must we confuse him with
+  those superficial writers whose liberty of body does not permit them to
+  restrain their fruitfulness, that crowd of savants of the highest rank
+  whose writings have adorned and still adorn the <i>Transactions</i>? Has
+  he forgotten that the names of the Boyles, Newtons, Halleys, De Moivres,
+  Hans Sloanes, etc. have been seen frequently? and that still are found
+  those of the Wards, Bradleys, Grahams, Ellicots, Watsons, and of an
+  author whom Mr. Hill prefers to all others, I mean Mr. Hill himself?"</p>
+
+  <p><a name="Nt_8" href="#NtA_8">[8]</a> "Let no free man be seized or
+  imprisoned or in any way harmed except by trial of his peers."</p>
+
+  <p><a name="Nt_9" href="#NtA_9">[9]</a> "The master can rob, wreck and
+  punish his slave according to his pleasure save only that he may not maim
+  him."</p>
+
+  <p><a name="Nt_10" href="#NtA_10">[10]</a> An Irish antiquary informs me
+  that Virgil is mentioned in annals at A.D. 784, as "Verghil, i.e., the
+  geometer, Abbot of Achadhbo [and Bishop of Saltzburg] died in Germany in
+  the thirteenth year of his bishoprick." No allusion is made to his
+  opinions; but it seems he was, by tradition, a mathematician. The Abbot
+  of Aghabo (Queen's County) was canonized by Gregory IX, in 1233. The
+  story of the second, or scapegoat, Virgil would be much damaged by the
+  character given to the real bishop, if there were anything in it to
+  dilapidate.&mdash;A. De M.</p>
+
+  <p><a name="Nt_11" href="#NtA_11">[11]</a> "He performed many acts
+  befitting the Papal dignity, and likewise many excellent (to be sure!)
+  works."</p>
+
+  <p><a name="Nt_12" href="#NtA_12">[12]</a> "After having been on the
+  throne during ten years of pestilence."</p>
+
+  <p><a name="Nt_13" href="#NtA_13">[13]</a> The work is the <i>Questiones
+  Joannis Buridani super X libros Aristotelis ad Nicomachum, curante Egidio
+  Delfo</i> ... Parisiis, 1489, folio. It also appeared at Paris in
+  editions of 1499, 1513, and 1518, and at Oxford in 1637.</p>
+
+  <p><a name="Nt_14" href="#NtA_14">[14]</a> Jean Buridan was born at
+  Béthune about 1298, and died at Paris about 1358. He was professor of
+  philosophy at the University of Paris and several times held the office
+  of Rector. As a philosopher he was classed among the nominalists.</p>
+
+  <p><a name="Nt_15" href="#NtA_15">[15]</a> So in the original.</p>
+
+  <p><a name="Nt_16" href="#NtA_16">[16]</a> Baruch Spinoza, or Benedict de
+  Spinoza as he later called himself, the pantheistic philosopher,
+  excommunicated from the Jewish faith for heresy, was born at Amsterdam in
+  1632 and died there in 1677.</p>
+
+  <p><a name="Nt_17" href="#NtA_17">[17]</a> Michael Scott, or Scot, was
+  born about 1190, probably in Fifeshire, Scotland, and died about 1291. He
+  was one of the best known savants of the court of Emperor Frederick II,
+  and wrote upon astrology, alchemy, and the occult sciences. He was looked
+  upon as a great magician and is mentioned among the wizards in Dante's
+  <i>Inferno</i>.</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="i12hg3">"That other, round the loins</p>
+      <p>So slender of his shape, was Michael Scot,</p>
+      <p>Practised in every slight of magic wile." <i>Inferno</i>, XX.</p>
+    </div>
+  </div>
+  <p>Boccaccio also speaks of him: "It is not long since there was in this
+  city (Florence) a great master in necromancy, who was called Michele
+  Scotto, because he was a Scot." <i>Decameron</i>, Dec. Giorno.</p>
+
+  <p>Scott's mention of him in Canto Second of his <i>Lay of the Last
+  Minstrel</i>, is well known:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="hg3">"In these fair climes, it was my lot</p>
+      <p>To meet the wondrous Michael Scott;</p>
+      <p class="i2">A wizard of such dreaded fame,</p>
+      <p>That when, in Salamanca's cave,</p>
+      <p>Him listed his magic wand to wave,</p>
+      <p class="i2">The bells would ring in Notre Dame!"</p>
+    </div>
+  </div>
+  <p>Sir Walter's notes upon him are of interest.</p>
+
+  <p><a name="Nt_18" href="#NtA_18">[18]</a> These were some of the
+  forgeries which Michel Chasles (1793-1880) was duped into buying. They
+  purported to be a correspondence between Pascal and Newton and to show
+  that the former had anticipated some of the discoveries of the great
+  English physicist and mathematician. That they were forgeries was shown
+  by Sir David Brewster in 1855.</p>
+
+  <p><a name="Nt_19" href="#NtA_19">[19]</a> "Let the serpent also break
+  from its appointed path."</p>
+
+  <p><a name="Nt_20" href="#NtA_20">[20]</a> Guglielmo Brutus Icilius
+  Timoleon Libri-Carucci della Sommaja, born at Florence in 1803; died at
+  Fiesole in 1869. His <i>Histoire des Sciences Mathématiques</i> appeared
+  at Paris in 1838, the entire first edition of volume I, save some half
+  dozen that he had carried home, being burned on the day that the printing
+  was completed. He was a great collector of early printed works on
+  mathematics, and was accused of having stolen large numbers of them from
+  other libraries. This accusation took him to London, where he bitterly
+  attacked his accusers. There were two auction sales of his library, and a
+  number of his books found their way into De Morgan's collection.</p>
+
+  <p><a name="Nt_21" href="#NtA_21">[21]</a> Philo of Gadara lived in the
+  second century B.C. He was a pupil of Sporus, who worked on the problem
+  of the two mean proportionals.</p>
+
+  <p><a name="Nt_22" href="#NtA_22">[22]</a> In his <i>Histoire des
+  Mathématiques</i>, the first edition of which appeared in 1758. Jean
+  Etienne Montucla was born at Lyons in 1725 and died at Versailles in
+  1799. He was therefore only thirty-three years old when his great work
+  appeared. The second edition, with additions by D'Alembert, appeared in
+  1799-1802. He also wrote a work on the quadrature of the circle,
+  <i>Histoire des recherches sur la Quadrature du Cercle</i>, which
+  appeared in 1754.</p>
+
+  <p><a name="Nt_23" href="#NtA_23">[23]</a> Eutocius of Ascalon was born
+  in 480 A.D. He wrote commentaries on the first four books of the conics
+  of Apollonius of Perga (247-222 B.C.). He also wrote on the Sphere and
+  Cylinder and the Quadrature of the Circle, and on the two books on
+  Equilibrium of Archimedes (287-212 B.C.)</p>
+
+  <p><a name="Nt_24" href="#NtA_24">[24]</a> Edward Cocker was born in 1631
+  and died between 1671 and 1677. His famous arithmetic appeared in 1677
+  and went through many editions. It was written in a style that appealed
+  to teachers, and was so popular that the expression "According to Cocker"
+  became a household phrase. Early in the nineteenth century there was a
+  similar saying in America, "According to Daboll," whose arithmetic had
+  some points of analogy to that of Cocker. Each had a well-known prototype
+  in the ancient saying, "He reckons like Nicomachus of Gerasa."</p>
+
+  <p><a name="Nt_25" href="#NtA_25">[25]</a> So in the original, for
+  Barrême. François Barrême was to France what Cocker was to England. He
+  was born at Lyons in 1640, and died at Paris in 1703. He published
+  several arithmetics, dedicating them to his patron, Colbert. One of the
+  best known of his works is <i>L'arithmétique, ou le livre facile pour
+  apprendre l'arithmétique soi-mème</i>, 1677. The French word
+  <i>barême</i> or <i>barrême</i>, a ready-reckoner, is derived from his
+  name.</p>
+
+  <p><a name="Nt_26" href="#NtA_26">[26]</a> Born at Rome, about 480 A.D.;
+  died at Pavia, 524. Gibbon speaks of him as "the last of the Romans whom
+  Cato or Tully could have acknowledged for their countryman." His works on
+  arithmetic, music, and geometry were classics in the medieval
+  schools.</p>
+
+  <p><a name="Nt_27" href="#NtA_27">[27]</a> Johannes Campanus, of Novarra,
+  was chaplain to Pope Urban IV (1261-1264). He was one of the early
+  medieval translators of Euclid from the Arabic into Latin, and the first
+  printed edition of the <i>Elements</i> (Venice, 1482) was from his
+  translation. In this work he probably depended not a little upon at least
+  two or three earlier scholars. He also wrote <i>De computo ecclesiastico
+  Calendarium</i>, and <i>De quadratura circuli</i>.</p>
+
+  <p><a name="Nt_28" href="#NtA_28">[28]</a> Archimedes gave 3-1/7, and
+  3-10/71 as the limits of the ratio of the circumference to the diameter
+  of a circle.</p>
+
+  <p><a name="Nt_29" href="#NtA_29">[29]</a> Friedrich W. A. Murhard was
+  born at Cassel in 1779 and died there in 1853. His <i>Bibliotheca
+  Mathematica</i>, Leipsic, 1797-1805, is ill arranged and inaccurate, but
+  it is still a helpful bibliography. De Morgan speaks somewhere of his
+  indebtedness to it.</p>
+
+  <p><a name="Nt_30" href="#NtA_30">[30]</a> Abraham Gotthelf Kästner was
+  born at Leipsic in 1719, and died at Göttingen in 1800. He was professor
+  of mathematics and physics at Göttingen. His <i>Geschichte der
+  Mathematik</i> (1796-1800) was a work of considerable merit. In the text
+  of the <i>Budget of Paradoxes</i> the name appears throughout as Kastner
+  instead of Kästner.</p>
+
+  <p><a name="Nt_31" href="#NtA_31">[31]</a> Lucas Gauricus, or Luca
+  Gaurico, born at Giffoni, near Naples, in 1476; died at Rome in 1558. He
+  was an astrologer and mathematician, and was professor of mathematics at
+  Ferrara in 1531. In 1545 he became bishop of Cività Ducale.</p>
+
+  <p><a name="Nt_32" href="#NtA_32">[32]</a> John Couch Adams was born at
+  Lidcot, Cornwall, in 1819, and died in 1892. He and Leverrier predicted
+  the discovery of Neptune from the perturbations in Uranus.</p>
+
+  <p><a name="Nt_33" href="#NtA_33">[33]</a> Urbain-Jean-Joseph Leverrier
+  was born at Saint-Lô, Manche, in 1811, and died at Paris in 1877. It was
+  his data respecting the perturbations of Uranus that were used by Adams
+  and himself in locating Neptune.</p>
+
+  <p><a name="Nt_34" href="#NtA_34">[34]</a> Joseph-Juste Scaliger, the
+  celebrated philologist, was born at Agen in 1540, and died at Leyden in
+  1609. His <i>Cyclometrica elementa</i>, to which De Morgan refers,
+  appeared at Leyden in 1594.</p>
+
+  <p><a name="Nt_35" href="#NtA_35">[35]</a> The title is: <i>In hoc libra
+  contenta.... Introductio i geometri&#x101;.... Liber de quadratura
+  circuli. Liber de cubicatione sphere. Perspectiva introductio</i>.
+  Carolus Bovillus, or Charles Bouvelles (Boüelles, Bouilles, Bouvel), was
+  born at Saucourt, Picardy, about 1470, and died at Noyon about 1533. He
+  was canon and professor of theology at Noyon. His <i>Introductio</i>
+  contains considerable work on star polygons, a favorite study in the
+  Middle Ages and early Renaissance. His work <i>Que hoc volumine
+  contin&#x113;tur. Liber de intellectu. Liber de sensu</i>, etc., appeared
+  at Paris in 1509-10.</p>
+
+  <p><a name="Nt_36" href="#NtA_36">[36]</a> Nicolaus Cusanus, Nicolaus
+  Chrypffs or Krebs, was born at Kues on the Mosel in 1401, and died at
+  Todi, Umbria, August 11, 1464. He held positions of honor in the church,
+  including the bishopric of Brescia. He was made a cardinal in 1448. He
+  wrote several works on mathematics, his <i>Opuscula varia</i> appearing
+  about 1490, probably at Strasburg, but published without date or place.
+  His <i>Opera</i> appeared at Paris in 1511 and again in 1514, and at
+  Basel in 1565.</p>
+
+  <p><a name="Nt_37" href="#NtA_37">[37]</a> Henry Stephens (born at Paris
+  about 1528, died at Lyons in 1598) was one of the most successful
+  printers of his day. He was known as <i>Typographus Parisiensis</i>, and
+  to his press we owe some of the best works of the period.</p>
+
+  <p><a name="Nt_38" href="#NtA_38">[38]</a> Jacobus Faber Stapulensis
+  (Jacques le Fèvre d'Estaples) was born at Estaples, near Amiens, in 1455,
+  and died at Nérac in 1536. He was a priest, vicar of the bishop of Meaux,
+  lecturer on philosophy at the Collège Lemoine in Paris, and tutor to
+  Charles, son of Francois I. He wrote on philosophy, theology, and
+  mathematics.</p>
+
+  <p><a name="Nt_39" href="#NtA_39">[39]</a> Claude-François Milliet de
+  Challes was born at Chambéry in 1621, and died at Turin in 1678. He
+  edited <i>Euclidis Elementorum libri octo</i> in 1660, and published a
+  <i>Cursus seu mundus mathematicus</i>, which included a short history of
+  mathematics, in 1674. He also wrote on mathematical geography.</p>
+
+  <p><a name="Nt_40" href="#NtA_40">[40]</a> This date should be 1503, if
+  he refers to the first edition. It is well known that this is the first
+  encyclopedia worthy the name to appear in print. It was written by
+  Gregorius Reisch (born at Balingen, and died at Freiburg in 1487), prior
+  of the cloister at Freiburg and confessor to Maximilian I. The first
+  edition appeared at Freiburg in 1503, and it passed through many editions
+  in the sixteenth and seventeenth centuries. The title of the 1504 edition
+  reads: <i>Aepitoma omnis phylosophiae. alias Margarita phylosophica
+  tractans de omni genere scibili: Cum additionibus: Quae in alijs non
+  habentur</i>.</p>
+
+  <p><a name="Nt_41" href="#NtA_41">[41]</a> This is the <i>Introductio in
+  arithmeticam Divi S. Boetii.... Epitome rerum geometricarum ex geometrica
+  introductio C. Bovilli. De quadratura circuli demonstratio ex
+  Campano</i>, that appeared without date about 1507.</p>
+
+  <p><a name="Nt_42" href="#NtA_42">[42]</a> Born at Liverpool in 1805, and
+  died there about 1872. He was a merchant, and in 1865 he published, at
+  Liverpool, a work entitled <i>The Quadrature of the Circle, or the True
+  Ratio between the Diameter and Circumference geometrically and
+  mathematically demonstrated</i>. In this he gives the ratio as exactly
+  3&#x215B;.</p>
+
+  <p><a name="Nt_43" href="#NtA_43">[43]</a> "That it would be impossible
+  to tell him exactly, since no one had yet been able to find precisely the
+  ratio of the circumference to the diameter."</p>
+
+  <p><a name="Nt_44" href="#NtA_44">[44]</a> This is the Paris edition:
+  "Parisiis: ex officina Ascensiana anno Christi ... MDXIIII," as appears
+  by the colophon of the second volume to which De Morgan refers.</p>
+
+  <p><a name="Nt_45" href="#NtA_45">[45]</a> Regiomontanus, or Johann
+  Müller of Königsberg (Regiomontanus), was born at Königsberg in
+  Franconia, June 5, 1436, and died at Rome July 6, 1476. He studied at
+  Vienna under the great astronomer Peuerbach, and was his most famous
+  pupil. He wrote numerous works, chiefly on astronomy. He is also known by
+  the names Ioannes de Monte Regio, de Regiomonte, Ioannes Germanus de
+  Regiomonte, etc.</p>
+
+  <p><a name="Nt_46" href="#NtA_46">[46]</a> Henry Cornelius Agrippa was
+  born at Cologne in 1486 and died either at Lyons in 1534 or at Grenoble
+  in 1535. He was professor of theology at Cologne and also at Turin. After
+  the publication of his <i>De Occulta Philosophia</i> he was imprisoned
+  for sorcery. Both works appeared at Antwerp in 1530, and each passed
+  through a large number of editions. A French translation appeared in
+  Paris in 1582, and an English one in London in 1651.</p>
+
+  <p><a name="Nt_47" href="#NtA_47">[47]</a> Nicolaus Remegius was born in
+  Lorraine in 1554, and died at Nancy in 1600. He was a jurist and
+  historian, and held the office of procurator general to the Duke of
+  Lorraine.</p>
+
+  <p><a name="Nt_48" href="#NtA_48">[48]</a> This was at the storming of
+  the city by the British on May 4, 1799. From his having been born in
+  India, all this appealed strongly to the interests of De Morgan.</p>
+
+  <p><a name="Nt_49" href="#NtA_49">[49]</a> Orontius Finaeus, or Oronce
+  Finé, was born at Briançon in 1494 and died at Paris, October 6, 1555. He
+  was imprisoned by François I for refusing to recognize the concordat
+  (1517). He was made professor of mathematics in the Collège Royal (later
+  called the Collège de France) in 1532. He wrote extensively on astronomy
+  and geometry, but was by no means a great scholar. He was a pretentious
+  man, and his works went through several editions. His
+  <i>Protomathesis</i> appeared at Paris in 1530-32. The work referred to
+  by De Morgan is the <i>Quadratura circuli tandem inventa &amp; clarissime
+  demonstrata</i> ... Lutetiae Parisiorum, 1544, fol. In the 1556 edition
+  of his <i>De rebus mathematicis, hactenus desideratis, Libri IIII</i>,
+  published at Paris, the subtitle is: <i>Quibus inter cætera, Circuli
+  quadratura Centum modis, &amp; suprà, per eundem Orontium recenter
+  excogitatis, demonstratus</i>, so that he kept up his efforts until his
+  death.</p>
+
+  <p><a name="Nt_50" href="#NtA_50">[50]</a> Johannes Buteo (Boteo, Butéon,
+  Bateon) was born in Dauphiné c. 1485-1489, and died in a cloister in 1560
+  or 1564. Some writers give Charpey as the place and 1492 as the date of
+  his birth, and state that he died at Canar in 1572. He belonged to the
+  order of St. Anthony, and wrote chiefly on geometry, exposing the
+  pretenses of Finaeus. His <i>Opera geometrica</i> appeared at Lyons in
+  1554, and his <i>Logistica</i> and <i>De quadratura circuli libri duo</i>
+  at Lyons in 1559.</p>
+
+  <p><a name="Nt_51" href="#NtA_51">[51]</a> This is the great French
+  algebraist, François Viète (Vieta), who was born at Fontenay-le-Comte in
+  1540, and died at Paris, December 13, 1603. His well-known <i>Isagoge in
+  artem analyticam</i> appeared at Tours in 1591. His <i>Opera
+  mathematica</i> was edited by Van Schooten in 1646.</p>
+
+  <p><a name="Nt_52" href="#NtA_52">[52]</a> This is the <i>De Rebus
+  mathematicis hactenus desideratis, Libri IIII</i>, that appeared in Paris
+  in 1556. For the title page see Smith, D. E., <i>Rara Arithmetica</i>,
+  Boston, 1908, p. 280.</p>
+
+  <p><a name="Nt_53" href="#NtA_53">[53]</a> The title is correct except
+  for a colon after <i>Astronomicum</i>. Nicolaus Raimarus Ursus was born
+  in Henstede or Hattstede, in Dithmarschen, and died at Prague in 1599 or
+  1600. He was a pupil of Tycho Brahe. He also wrote <i>De astronomis
+  hypothesibus</i> (1597) and <i>Arithmetica analytica vulgo Cosa oder
+  Algebra</i> (1601).</p>
+
+  <p><a name="Nt_54" href="#NtA_54">[54]</a> Born at Dôle, Franche-Comté,
+  about 1550, died in Holland about 1600. The work to which reference is
+  made is the <i>Quadrature du cercle, ou manière de trouver un quarré égal
+  au cercle donné</i>, which appeared at Delft in 1584. Duchesne had the
+  courage of his convictions, not only on circle-squaring but on religion
+  as well, for he was obliged to leave France because of his conversion to
+  Calvinism. De Morgan's statement that his real name is Van der Eycke is
+  curious, since he was French born. The Dutch may have translated his name
+  when he became professor at Delft, but we might equally well say, that
+  his real name was Quercetanus or à Quercu.</p>
+
+  <p><a name="Nt_55" href="#NtA_55">[55]</a> This was the father of Adriaan
+  Metius (1571-1635). He was a mathematician and military engineer, and
+  suggested the ratio 355/113 for <span class="grk">&pi;</span>, a ratio
+  afterwards published by his son. The ratio, then new to Europe, had long
+  been known and used in China, having been found by Tsu Ch'ung-chih
+  (428-499 A.D.).</p>
+
+  <p><a name="Nt_56" href="#NtA_56">[56]</a> This was Jost Bürgi, or Justus
+  Byrgius, the Swiss mathematician of whom Kepler wrote in 1627: "Apices
+  logistici Justo Byrgio multis annis ante editionem Neperianam viam
+  præiverunt ad hos ipsissimos logarithmos." He constructed a table of
+  antilogarithms (<i>Arithmetische und geometrische Progress-Tabulen</i>),
+  but it was not published until after Napier's work appeared.</p>
+
+  <p><a name="Nt_57" href="#NtA_57">[57]</a> Ludolphus Van Ceulen, born at
+  Hildesheim, and died at Leyden in 1610. It was he who first carried the
+  computation of <span class="grk">&pi;</span> to 35 decimal places.</p>
+
+  <p><a name="Nt_58" href="#NtA_58">[58]</a> Jens Jenssen Dodt, van
+  Flensburg, a Dutch historian, who died in 1847.</p>
+
+  <p><a name="Nt_59" href="#NtA_59">[59]</a> I do not know this edition.
+  There was one "Antverpiae apud Petrum Bellerum sub scuto Burgundiae,"
+  4to, in 1591.</p>
+
+  <p><a name="Nt_60" href="#NtA_60">[60]</a> Archytas of Tarentum (430-365
+  B.C.) who wrote on proportions, irrationals, and the duplication of the
+  cube.</p>
+
+  <p><a name="Nt_61" href="#NtA_61">[61]</a> &nbsp;</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p class="i4"><i>The Circle Speaks.</i></p>
+      <p class="hg3">"At first a circle I was called,</p>
+      <p>And was a curve around about</p>
+      <p>Like lofty orbit of the sun</p>
+      <p>Or rainbow arch among the clouds.</p>
+      <p>A noble figure then was I&mdash;</p>
+      <p>And lacking nothing but a start,</p>
+      <p>And lacking nothing but an end.</p>
+      <p>But now unlovely do I seem</p>
+      <p>Polluted by some angles new.</p>
+      <p>This thing Archytas hath not done</p>
+      <p>Nor noble sire of Icarus</p>
+      <p>Nor son of thine, Iapetus.</p>
+      <p>What accident or god can then</p>
+      <p>Have quadrated mine area?"</p>
+    </div>
+
+    <div class="stanza">
+      <p class="i4"><i>The Author Replies.</i></p>
+      <p class="hg3">"By deepest mouth of Turia</p>
+      <p>And lake of limpid clearness, lies</p>
+      <p>A happy state not far removed</p>
+      <p>From old Saguntus; farther yet</p>
+      <p>A little way from Sucro town.</p>
+      <p>In this place doth a poet dwell,</p>
+      <p>Who oft the stars will closely scan,</p>
+      <p>And always for himself doth claim</p>
+      <p>What is denied to wiser men;&mdash;</p>
+      <p>An old man musing here and there</p>
+      <p>And oft forgetful of himself,</p>
+      <p>Not knowing how to rightly place</p>
+      <p>The compasses, nor draw a line,</p>
+      <p>As he doth of himself relate.</p>
+      <p>This craftsman fine, in sooth it is</p>
+      <p>Hath quadrated thine area."</p>
+    </div>
+  </div>
+  <p><a name="Nt_62" href="#NtA_62">[62]</a> Pietro Bongo, or Petrus
+  Bungus, was born at Bergamo, and died there in 1601. His work on the
+  Mystery of Numbers is one of the most exhaustive and erudite ones of the
+  mystic writers. The first edition appeared at Bergamo in 1583-84; the
+  second, at Bergamo in 1584-85; the third, at Venice in 1585; the fourth,
+  at Bergamo in 1590; and the fifth, which De Morgan calls the second, in
+  1591. Other editions, before the Paris edition to which he refers,
+  appeared in 1599 and 1614; and the colophon of the Paris edition is dated
+  1617. See the editor's <i>Rara Arithmetica</i>, pp. 380-383.</p>
+
+  <p><a name="Nt_63" href="#NtA_63">[63]</a> William Warburton (1698-1779),
+  Bishop of Gloucester, whose works got him into numerous literary
+  quarrels, being the subject of frequent satire.</p>
+
+  <p><a name="Nt_64" href="#NtA_64">[64]</a> Thomas Galloway (1796-1851),
+  who was professor of mathematics at Sandhurst for a time, and was later
+  the actuary of the Amicable Life Assurance Company of London. In the
+  latter capacity he naturally came to be associated with De Morgan.</p>
+
+  <p><a name="Nt_65" href="#NtA_65">[65]</a> Giordano Bruno was born near
+  Naples about 1550. He left the Dominican order to take up Calvinism, and
+  among his publications was <i>L'expulsion de la bête triomphante</i>. He
+  taught philosophy at Paris and Wittenberg, and some of his works were
+  published in England in 1583-86. Whether or not he was roasted alive "for
+  the maintenance and defence of the holy Church," as De Morgan states,
+  depends upon one's religious point of view. At any rate, he was roasted
+  as a heretic.</p>
+
+  <p><a name="Nt_66" href="#NtA_66">[66]</a> Referring to part of his
+  <i>Discours de la méthode</i>, Leyden, 1637.</p>
+
+  <p><a name="Nt_67" href="#NtA_67">[67]</a> Bartholomew Legate, who was
+  born in Essex about 1575. He denied the divinity of Christ and was the
+  last heretic burned at Smithfield.</p>
+
+  <p><a name="Nt_68" href="#NtA_68">[68]</a> Edward Wightman, born probably
+  in Staffordshire. He was anti-Trinitarian, and claimed to be the Messiah.
+  He was the last man burned for heresy in England.</p>
+
+  <p><a name="Nt_69" href="#NtA_69">[69]</a> Gaspar Schopp, born at
+  Neumarck in 1576, died at Padua in 1649; grammarian, philologist, and
+  satirist.</p>
+
+  <p><a name="Nt_70" href="#NtA_70">[70]</a> Konrad Ritterhusius, born at
+  Brunswick in 1560; died at Altdorf in 1613. He was a jurist of some
+  power.</p>
+
+  <p><a name="Nt_71" href="#NtA_71">[71]</a> Johann Jakob Brucker, born at
+  Augsburg in 1696, died there in 1770. He wrote on the history of
+  philosophy (1731-36, and 1742-44).</p>
+
+  <p><a name="Nt_72" href="#NtA_72">[72]</a> Daniel Georg Morhof, born at
+  Wismar in 1639, died at Lübeck in 1691. He was rector of the University
+  of Kiel, and professor of eloquence, poetry, and history.</p>
+
+  <p><a name="Nt_73" href="#NtA_73">[73]</a> In the <i>Histoire des
+  Sciences Mathématiques</i>, vol. IV, note X, pp. 416-435 of the 1841
+  edition.</p>
+
+  <p><a name="Nt_74" href="#NtA_74">[74]</a> Colenso (1814-1883),
+  missionary bishop of Natal, was one of the leaders of his day in the
+  field of higher biblical criticism. De Morgan must have admired his
+  mathematical works, which were not without merit.</p>
+
+  <p><a name="Nt_75" href="#NtA_75">[75]</a> Samuel Roffey Maitland, born
+  at London in 1792; died at Gloucester in 1866. He was an excellent
+  linguist and a critical student of the Bible. He became librarian at
+  Lambeth in 1838.</p>
+
+  <p><a name="Nt_76" href="#NtA_76">[76]</a> Archbishop Howley (1766-1848)
+  was a thorough Tory. He was one of the opponents of the Roman Catholic
+  Relief bill, the Reform bill, and the Jewish Civil Disabilities Relief
+  bill.</p>
+
+  <p><a name="Nt_77" href="#NtA_77">[77]</a> We have, in America at least,
+  almost forgotten the great stir made by Edward B. Pusey (1800-1882) in
+  the great Oxford movement in the middle of the nineteenth century. He was
+  professor of Hebrew at Oxford, and canon of Christ Church.</p>
+
+  <p><a name="Nt_78" href="#NtA_78">[78]</a> That is, his <i>Magia
+  universalis naturae et artis sive recondita naturalium et artificialium
+  rerum scientia</i>, Würzburg, 1657, 4to, with editions at Bamberg in
+  1671, and at Frankfort in 1677. Gaspard Schott (Königshofen 1608,
+  Würzburg 1666) was a physicist and mathematician, devoting most of his
+  attention to the curiosities of his sciences. His type of mind must have
+  appealed to De Morgan.</p>
+
+  <p><a name="Nt_79" href="#NtA_79">[79]</a> <i>Salicetti Quadratura
+  circuli nova, perspicua, expedita, veraque tum naturalis, tum
+  geometrica</i>, etc., 1608.&mdash;<i>Consideratio nova in opusculum
+  Archimedis de circuli dimensione</i>, etc., 1609.</p>
+
+  <p><a name="Nt_80" href="#NtA_80">[80]</a> Melchior Adam, who died at
+  Heidelberg in 1622, wrote a collection of biographies which was published
+  at Heidelberg and Frankfort from 1615 to 1620.</p>
+
+  <p><a name="Nt_81" href="#NtA_81">[81]</a> Born at Baden in 1524; died at
+  Basel in 1583. The Erastians were related to the Zwinglians, and opposed
+  all power of excommunication and the infliction of penalties by a
+  church.</p>
+
+  <p><a name="Nt_82" href="#NtA_82">[82]</a> See Acts xii. 20.</p>
+
+  <p><a name="Nt_83" href="#NtA_83">[83]</a> Theodore de Bèse, a French
+  theologian; born at Vezelay, in Burgundy, in 1519; died at Geneva, in
+  1605.</p>
+
+  <p><a name="Nt_84" href="#NtA_84">[84]</a> Dr. Robert Lee (1804-1868) had
+  some celebrity in De Morgan's time through his attempt to introduce music
+  and written prayers into the service of the Scotch Presbyterian
+  church.</p>
+
+  <p><a name="Nt_85" href="#NtA_85">[85]</a> Born at Veringen,
+  Hohenzollern, in 1512; died at Röteln in 1564.</p>
+
+  <p><a name="Nt_86" href="#NtA_86">[86]</a> Born at Kinnairdie,
+  Bannfshire, in 1661; died at London in 1708. His <i>Astronomiae Physicae
+  et Geometriae Elementa</i>, Oxford, 1702, was an influential work.</p>
+
+  <p><a name="Nt_87" href="#NtA_87">[87]</a> The title was carelessly
+  copied by De Morgan, not an unusual thing in his case. The original
+  reads: A Plaine Discovery, of the whole Revelation of S. Iohn: set downe
+  in two treatises ... set foorth by John Napier L. of Marchiston ...
+  whereunto are annexed, certaine Oracles of Sibylla ... London ...
+  1611.</p>
+
+  <p><a name="Nt_88" href="#NtA_88">[88]</a> I have not seen the first
+  edition, but it seems to have appeared in Edinburgh, in 1593, with a
+  second edition there in 1594. The 1611 edition was the third.</p>
+
+  <p><a name="Nt_89" href="#NtA_89">[89]</a> It seems rather certain that
+  Napier felt his theological work of greater importance than that in
+  logarithms. He was born at Merchiston, near (now a part of) Edinburgh, in
+  1550, and died there in 1617, three years after the appearance of his
+  <i>Mirifici logarithmorum canonis descriptio</i>.</p>
+
+  <p><a name="Nt_90" href="#NtA_90">[90]</a> Followed, in the third
+  edition, from which he quotes, by a comma.</p>
+
+  <p><a name="Nt_91" href="#NtA_91">[91]</a> There was an edition published
+  at Stettin in 1633. An English translation by P.&nbsp;F. Mottelay appeared at
+  London in 1893. Gilbert (1540-1603) was physician to Queen Elizabeth and
+  President of the College of Physicians at London. His <i>De Magnete</i>
+  was the first noteworthy treatise on physics printed in England. He
+  treated of the earth as a spherical magnet and suggested the variation
+  and declination of the needle as a means of finding latitude at sea.</p>
+
+  <p><a name="Nt_92" href="#NtA_92">[92]</a> The title says "ab authoris
+  fratre collectum," although it was edited by J. Gruterus.</p>
+
+  <p><a name="Nt_93" href="#NtA_93">[93]</a> Porta was born at Naples in
+  1550 and died there in 1615. He studied the subject of lenses and the
+  theory of sight, did some work in hydraulics and agriculture, and was
+  well known as an astrologer. His <i>Magiae naturalis libri XX</i> was
+  published at Naples in 1589. The above title should read
+  <i>curvilineorum</i>.</p>
+
+  <p><a name="Nt_94" href="#NtA_94">[94]</a> Cataldi was born in 1548 and
+  died at Bologna in 1626. He was professor of mathematics at Perugia,
+  Florence, and Bologna, and is known in mathematics chiefly for his work
+  in continued fractions. He was one of the scholarly men of his day.</p>
+
+  <p><a name="Nt_95" href="#NtA_95">[95]</a> Georg Joachim Rheticus was
+  born at Feldkirch in 1514 and died at Caschau, Hungary, in 1576. He was
+  one of the most prominent pupils of Copernicus, his <i>Narratio de libris
+  revolutionum Copernici</i> (Dantzig, 1540) having done much to make the
+  theory of his master known.</p>
+
+  <p><a name="Nt_96" href="#NtA_96">[96]</a> Henry Briggs, who did so much
+  to make logarithms known, and who used the base 10, was born at Warley
+  Wood, in Yorkshire, in 1560, and died at Oxford in 1630. He was Savilian
+  professor of mathematics at Oxford, and his grave may still be seen
+  there.</p>
+
+  <p><a name="Nt_97" href="#NtA_97">[97]</a> He lived at "Reggio nella
+  Emilia" in the 16th and 17th centuries. His <i>Regola e modo facilissimo
+  di quadrare il cerchio</i> was published at Reggio in 1609.</p>
+
+  <p><a name="Nt_98" href="#NtA_98">[98]</a> Christoph Klau (Clavius) was
+  born at Bamberg in 1537, and died at Rome in 1612. He was a Jesuit priest
+  and taught mathematics in the Jesuit College at Rome. He wrote a number
+  of works on mathematics, including excellent text-books on arithmetic and
+  algebra.</p>
+
+  <p><a name="Nt_99" href="#NtA_99">[99]</a> Christopher Gruenberger, or
+  Grienberger, was born at Halle in Tyrol in 1561, and died at Rome in
+  1636. He was, like Clavius, a Jesuit and a mathematician, and he wrote a
+  little upon the subject of projections. His <i>Prospectiva nova
+  coelestis</i> appeared at Rome in 1612.</p>
+
+  <p><a name="Nt_100" href="#NtA_100">[100]</a> The name should, of course,
+  be Lansbergii in the genitive, and is so in the original title. Philippus
+  Lansbergius was born at Ghent in 1560, and died at Middelburg in 1632. He
+  was a Protestant theologian, and was also a physician and astronomer. He
+  was a well-known supporter of Galileo and Copernicus. His
+  <i>Commentationes in motum terrae diurnum et annuum</i> appeared at
+  Middelburg in 1630 and did much to help the new theory.</p>
+
+  <p><a name="Nt_101" href="#NtA_101">[101]</a> I have never seen the work.
+  It is rare.</p>
+
+  <p><a name="Nt_102" href="#NtA_102">[102]</a> The African explorer, born
+  in Somersetshire in 1827, died at Bath in 1864. He was the first European
+  to cross Central Africa from north to south. He investigated the sources
+  of the Nile.</p>
+
+  <p><a name="Nt_103" href="#NtA_103">[103]</a> Prester (Presbyter, priest)
+  John, the legendary Christian king whose realm, in the Middle Ages, was
+  placed both in Asia and in Africa, is first mentioned in the chronicles
+  of Otto of Freisingen in the 12th century. In the 14th century his
+  kingdom was supposed to be Abyssinia.</p>
+
+  <p><a name="Nt_104" href="#NtA_104">[104]</a> "It is a profane and
+  barbarous nation, dirty and slovenly, who eat their meat half raw and
+  drink mare's milk, and who use table-cloths and napkins only to wipe
+  their hands and mouths."</p>
+
+  <p><a name="Nt_105" href="#NtA_105">[105]</a> "The great Prester John,
+  who is the fourth in rank, is emperor of Ethiopia and of the Abyssinians,
+  and boasts of his descent from the race of David, as having descended
+  from the Queen of Sheba, Queen of Ethiopia. She, having gone to Jerusalem
+  to see the wisdom of Solomon, about the year of the world 2952, returned
+  pregnant with a son whom they called Moylech, from whom they claim
+  descent in a direct line. And so he glories in being the most ancient
+  monarch in the world, saying that his empire has endured for more than
+  three thousand years, which no other empire is able to assert. He also
+  puts into his titles the following: 'We, the sovereign in my realms,
+  uniquely beloved of God, pillar of the faith, sprung from the race of
+  Judah, etc.' The boundaries of this empire touch the Red Sea and the
+  mountains of Azuma on the east, and on the western side it is bordered by
+  the River Nile which separates it from Nubia. To the north lies Egypt,
+  and to the south the kingdoms of Congo and Mozambique. It extends forty
+  degrees in length, or one thousand twenty-five leagues, from Congo or
+  Mozambique on the south to Egypt on the north; and in width it reaches
+  from the Nile on the west to the mountains of Azuma on the east, seven
+  hundred twenty-five leagues, or twenty-nine degrees. This empire contains
+  thirty large provinces, namely Medra, Gaga, Alchy, Cedalon, Mantro,
+  Finazam, Barnaquez, Ambiam, Fungy, Angoté, Cigremaon, Gorga, Cafatez,
+  Zastanla, Zeth, Barly, Belangana, Tygra, Gorgany, Barganaza, d'Ancut,
+  Dargaly, Ambiacatina, Caracogly, Amara, Maon (<i>sic</i>), Guegiera,
+  Bally, Dobora, and Macheda. All of these provinces are situated directly
+  under the equinoctial line between the tropics of Capricorn and Cancer;
+  but they are two hundred fifty leagues nearer our tropic than the other.
+  The name of Prester John signifies Great Lord, and is not Priest
+  [Presbyter] as many think. He has always been a Christian, but often
+  schismatic. At the present time he is a Catholic and recognizes the Pope
+  as sovereign pontiff. I met one of his bishops in Jerusalem, and often
+  conversed with him through the medium of our guide. He was of grave and
+  serious bearing, pleasant of speech, but wonderfully subtle in everything
+  he said. He took great delight in what I had to relate concerning our
+  beautiful ceremonies and the dignity of our prelates in their pontifical
+  vestments. As to other matters I will only say that the Ethiopian is
+  joyous and merry, not at all like the Tartar in the matter of filth, nor
+  like the wretched Arab. They are refined and subtle, trusting no one,
+  wonderfully suspicious, and very devout. They are not at all black as is
+  commonly supposed, by which I refer to those who do not live under the
+  equator or too near to it, for these are Moors as we shall see."</p>
+
+  <p>With respect to this translation it should be said that the original
+  forms of the proper names have been preserved, although they are not
+  those found in modern works. It should also be stated that the meaning of
+  Prester is not the one that was generally accepted by scholars at the
+  time the work was written, nor is it the one accepted to-day. There seems
+  to be no doubt that the word is derived from Presbyter as stated in note
+  <a href="#Nt_103">103</a> on page <a href="#page71">71</a>, since the
+  above-mentioned chronicles of Otto, bishop of Freisingen about the middle
+  of the twelfth century, states this fact clearly. Otto received his
+  information from the bishop of Gabala (the Syrian Jibal) who told him the
+  story of John, <i>rex et sacerdos</i>, or Presbyter John as he liked to
+  be called. He goes on to say "Should it be asked why, with all this power
+  and splendor, he calls himself merely 'presbyter,' this is because of his
+  humility, and because it was not fitting for one whose server was a
+  primate and king, whose butler an archbishop and king, whose chamberlain
+  a bishop and king, whose master of the horse an archimandrite and king,
+  whose chief cook an abbot and king, to be called by such titles as
+  these."</p>
+
+  <p><a name="Nt_106" href="#NtA_106">[106]</a> Thomas Fienus (Fyens) was
+  born at Antwerp in 1567 and died in 1631. He was professor of medicine at
+  Louvain. Besides the editions mentioned below, his <i>De cometis anni
+  1618</i> appeared at Leipsic in 1656. He also wrote a <i>Disputatio an
+  coelum moveatur et terra quiescat</i>, which appeared at Antwerp in 1619,
+  and again at Leipsic in 1656.</p>
+
+  <p><a name="Nt_107" href="#NtA_107">[107]</a> Libertus Fromondus (1587-c
+  1653), a Belgian theologian, dean of the College Church at Harcourt, and
+  professor at Louvain. The name also appears as Froidmont and
+  Froimont.</p>
+
+  <p><a name="Nt_108" href="#NtA_108">[108]</a> <i>L. Fromondi ...
+  meteorologicorum libri sex.... Cui accessit T. Fieni et L. Fromondi
+  dissertationes de cometa anni 1618....</i> This is from the 1670 edition.
+  The 1619 edition was published at Antwerp. The <i>Meteorologicorum libri
+  VI</i>, appeared at Antwerp in 1627. He also wrote <i>Anti-Aristarchus
+  sive orbis terrae immobilis liber unicus</i> (Antwerp, 1631);
+  <i>Labyrrinthus sive de compositione continui liber unus, Philosophis,
+  Mathematicis, Theologis utilis et jucundus</i> (Antwerp, 1631) and
+  <i>Vesta sive Anti-Aristarchi vindex adversus Jac. Lansbergium (Philippi
+  filium) et copernicanos</i> (Antwerp, 1634).</p>
+
+  <p><a name="Nt_109" href="#NtA_109">[109]</a> Snell was born at Leyden in
+  1591, and died there in 1626. He studied under Tycho Brahe and Kepler,
+  and is known for Snell's law of the refraction of light. He was the first
+  to determine the size of the earth by measuring the arc of a meridian
+  with any fair degree of accuracy. The title should read: <i>Willebrordi
+  Snellii R.&nbsp;F. Cyclometricus, de circuli dimensione secundum Logistarum
+  abacos, et ad Mechanicem accuratissima....</i></p>
+
+  <p><a name="Nt_110" href="#NtA_110">[110]</a> Bacon was born at York
+  House, London, in 1561, and died near Highgate, London, in 1626. His
+  <i>Novum Organum Scientiarum or New Method of employing the reasoning
+  faculties in the pursuits of Truth</i> appeared at London in 1620. He had
+  previously published a work entitled <i>Of the Proficience and
+  Advancement of Learning, divine and humane</i> (London, 1605), which
+  again appeared in 1621. His <i>De augmentis scientiarum Libri IX</i>
+  appeared at Paris in 1624, and his <i>Historia naturalis et
+  experimentalis de ventis</i> at Leyden in 1638. He was successively
+  solicitor general, attorney general, lord chancellor (1619), Baron
+  Verulam and Viscount St. Albans. He was deprived of office and was
+  imprisoned in the Tower of London in 1621, but was later pardoned.</p>
+
+  <p><a name="Nt_111" href="#NtA_111">[111]</a> The Greek form,
+  <i>Organon</i>, is sometimes used.</p>
+
+  <p><a name="Nt_112" href="#NtA_112">[112]</a> James Spedding (1808-1881),
+  fellow of Cambridge, who devoted his life to his edition of Bacon.</p>
+
+  <p><a name="Nt_113" href="#NtA_113">[113]</a> R. Leslie Ellis
+  (1817-1859), editor of the <i>Cambridge Mathematical Journal</i>. He also
+  wrote on Roman aqueducts, on Boole's Laws of Thought, and on the
+  formation of a Chinese dictionary.</p>
+
+  <p><a name="Nt_114" href="#NtA_114">[114]</a> Douglas Derion Heath
+  (1811-1897), a classical and mathematical scholar.</p>
+
+  <p><a name="Nt_115" href="#NtA_115">[115]</a> There have been numerous
+  editions of Bacon's complete works, including the following: Frankfort,
+  1665; London, 1730, 1740, 1764, 1765, 1778, 1803, 1807, 1818, 1819, 1824,
+  1825-36, 1857-74, 1877. The edition to which De Morgan refers is that of
+  1857-74, 14 vols., of which five were apparently out at the time he
+  wrote. There were also French editions in 1800 and 1835.</p>
+
+  <p><a name="Nt_116" href="#NtA_116">[116]</a> So in the original for
+  Tycho Brahe.</p>
+
+  <p><a name="Nt_117" href="#NtA_117">[117]</a> In general these men acted
+  before Baron wrote, or at any rate, before he wrote the <i>Novum
+  Organum</i>, but the statement must not be taken too literally. The dates
+  are as follows: Copernicus, 1473-1543; Tycho Brahe, 1546-1601; Gilbert,
+  1540-1603; Kepler, 1571-1630; Galileo, 1564-1642; Harvey, 1578-1657. For
+  example, Harvey's <i>Exercitatio Anatomica de Motu Cordis et
+  Sanguinis</i> did not appear until 1628, and his <i>Exercitationes de
+  Generatione</i> until 1651.</p>
+
+  <p><a name="Nt_118" href="#NtA_118">[118]</a> Robert Hooke (1635-1703)
+  studied under Robert Boyle at Oxford. He was "Curator of Experiments" to
+  the Royal Society and its secretary, and was professor of geometry at
+  Gresham College, London. It is true that he was "very little of a
+  mathematician" although he wrote on the motion of the earth (1674), on
+  helioscopes and other instruments (1675), on the rotation of Jupiter
+  (1666), and on barometers and sails.</p>
+
+  <p><a name="Nt_119" href="#NtA_119">[119]</a> The son of the Sir William
+  mentioned below. He was born in 1792 and died in 1871. He wrote a
+  treatise on light (1831) and one on astronomy (1836), and established an
+  observatory at the Cape of Good Hope where he made observations during
+  1834-1838, publishing them in 1847. On his return to England he was
+  knighted, and in 1848 was made president of the Royal Society. The title
+  of the work to which reference is made is: <i>A preliminary discourse on
+  the Study of Natural Philosophy</i>. It appeared at London in 1831.</p>
+
+  <p><a name="Nt_120" href="#NtA_120">[120]</a> Sir William was horn at
+  Hanover in 1738 and died at Slough, near Windsor in 1822. He discovered
+  the planet Uranus and six satellites, besides two satellites of Saturn.
+  He was knighted by George III.</p>
+
+  <p><a name="Nt_121" href="#NtA_121">[121]</a> This was the work of 1836.
+  He also published a work entitled <i>Outlines of Astronomy</i> in
+  1849.</p>
+
+  <p><a name="Nt_122" href="#NtA_122">[122]</a> While Newton does not tell
+  the story, he refers in the <i>Principia</i> (1714 edition, p. 293) to
+  the accident caused by his cat.</p>
+
+  <p><a name="Nt_123" href="#NtA_123">[123]</a> Marino Ghetaldi
+  (1566-1627), whose <i>Promotus Archimedes</i> appeared at Rome in 1603,
+  <i>Nonnullae propositiones de parabola</i> at Rome in 1603. and
+  <i>Apollonius redivivus</i> at Venice in 1607. He was a nobleman and was
+  ambassador from Venice to Rome.</p>
+
+  <p><a name="Nt_124" href="#NtA_124">[124]</a> Simon Stevin (born at
+  Bruges, 1548; died at the Hague, 1620). He was an engineer and a soldier,
+  and his <i>La Disme</i> (1585) was the first separate treatise on the
+  decimal fraction. The contribution referred to above is probably that on
+  the center of gravity of three bodies (1586).</p>
+
+  <p><a name="Nt_125" href="#NtA_125">[125]</a> Habakuk Guldin (1577-1643),
+  who took the name Paul on his conversion to Catholicism. He became a
+  Jesuit, and was professor of mathematics at Vienna and later at Gratz. In
+  his <i>Centrobaryca seu de centro gravitatis trium specierum quantitatis
+  continuae</i> (1635), of the edition of 1641, appears the Pappus rule for
+  the volume of a solid formed by the revolution of a plane figure about an
+  axis, often spoken of as Guldin's Theorem.</p>
+
+  <p><a name="Nt_126" href="#NtA_126">[126]</a> Edward Wright was born at
+  Graveston, Norfolkshire, in 1560, and died at London in 1615. He was a
+  fellow of Caius College, Cambridge, and in his work entitled <i>The
+  correction of certain errors in Navigation</i> (1599) he gives the
+  principle of Mercator's projection. He translated the <i>Portuum
+  investigandorum ratio</i> of Stevin in 1599.</p>
+
+  <p><a name="Nt_127" href="#NtA_127">[127]</a> De Morgan never wrote a
+  more suggestive sentence. Its message is not for his generation
+  alone.</p>
+
+  <p><a name="Nt_128" href="#NtA_128">[128]</a> The eminent French
+  physicist, Jean Baptiste Biot (1779-1862), professor in the Collège de
+  France. His work <i>Sur les observatoires météorologiques</i> appeared in
+  1855.</p>
+
+  <p><a name="Nt_129" href="#NtA_129">[129]</a> George Biddell Airy
+  (1801-1892), professor of astronomy and physics at Cambridge, and
+  afterwards director of the Observatory at Greenwich.</p>
+
+  <p><a name="Nt_130" href="#NtA_130">[130]</a> De Morgan would have
+  rejoiced in the rôle played by Intuition in the mathematics of to-day,
+  notably among the followers of Professor Klein.</p>
+
+  <p><a name="Nt_131" href="#NtA_131">[131]</a> Colburn was the best known
+  of the calculating boys produced in America. He was born at Cabot,
+  Vermont, in 1804, and died at Norwich, Vermont, in 1840. Having shown
+  remarkable skill in numbers as early as 1810, he was taken to London in
+  1812, whence he toured through Great Britain and to Paris. The Earl of
+  Bristol placed him in Westminster School (1816-1819). On his return to
+  America he became a preacher, and later a teacher of languages.</p>
+
+  <p><a name="Nt_132" href="#NtA_132">[132]</a> The history of calculating
+  boys is interesting. Mathieu le Coc (about 1664), a boy of Lorraine,
+  could extract cube roots at sight at the age of eight. Tom Fuller, a
+  Virginian slave of the eighteenth century, although illiterate, gave the
+  number of seconds in 7 years 17 days 12 hours after only a minute and a
+  half of thought. Jedediah Buxton, an Englishman of the eighteenth
+  century, was studied by the Royal Society because of his remarkable
+  powers. Ampère, the physicist, made long calculations with pebbles at the
+  age of four. Gauss, one of the few infant prodigies to become an adult
+  prodigy, corrected his father's payroll at the age of three. One of the
+  most remarkable of the French calculating boys was Henri Mondeux. He was
+  investigated by Arago, Sturm, Cauchy, and Liouville, for the Académie des
+  Sciences, and a report was written by Cauchy. His specialty was the
+  solution of algebraic problems mentally. He seems to have calculated
+  squares and cubes by a binomial formula of his own invention. He died in
+  obscurity, but was the subject of a <i>Biographie</i> by Jacoby (1846).
+  George P. Bidder, the Scotch engineer (1806-1878), was exhibited as an
+  arithmetical prodigy at the age of ten, and did not attend school until
+  he was twelve. Of the recent cases two deserve special mention, Inaudi
+  and Diamandi. Jacques Inaudi (born in 1867) was investigated for the
+  Académie in 1892 by a commission including Poincaré, Charcot, and Binet.
+  (See the <i>Revue des Deux Mondes</i>, June 15, 1892, and the laboratory
+  bulletins of the Sorbonne). He has frequently exhibited his remarkable
+  powers in America. Périclès Diamandi was investigated by the same
+  commission in 1893. See Alfred Binet, <i>Psychologie des Grands
+  Calculateurs et Joueurs d'Echecs</i>, Paris, 1894.</p>
+
+  <p><a name="Nt_133" href="#NtA_133">[133]</a> John Flamsteed's
+  (1646-1719) "old white house" was the first Greenwich observatory. He was
+  the Astronomer Royal and first head of this observatory.</p>
+
+  <p><a name="Nt_134" href="#NtA_134">[134]</a> It seems a pity that De
+  Morgan should not have lived to lash those of our time who are demanding
+  only the immediately practical in mathematics. His satire would have been
+  worth the reading against those who seek to stifle the science they
+  pretend to foster.</p>
+
+  <p><a name="Nt_135" href="#NtA_135">[135]</a> Ismael Bouillaud, or
+  Boulliau, was born in 1605 and died at Paris in 1694. He was well known
+  as an astronomer, mathematician, and jurist. He lived with De Thou at
+  Paris, and accompanied him to Holland. He traveled extensively, and was
+  versed in the astronomical work of the Persians and Arabs. It was in his
+  <i>Astronomia philolaica, opus novum</i> (Paris, 1645) that he attacked
+  Kepler's laws. His tables were shown to be erroneous by the fact that the
+  solar eclipse did not take place as predicted by him in 1645.</p>
+
+  <p><a name="Nt_136" href="#NtA_136">[136]</a> As it did, until 1892, when
+  Airy had reached the ripe age of ninety-one.</p>
+
+  <p><a name="Nt_137" href="#NtA_137">[137]</a> <i>Didaci a Stunica ... In
+  Job commentaria</i> appeared at Toledo in 1584.</p>
+
+  <p><a name="Nt_138" href="#NtA_138">[138]</a> "The false Pythagorean
+  doctrine, absolutely opposed to the Holy Scriptures, concerning the
+  mobility of the earth and the immobility of the sun."</p>
+
+  <p><a name="Nt_139" href="#NtA_139">[139]</a> Paolo Antonio Foscarini
+  (1580-1616), who taught theology and philosophy at Naples and Messina,
+  was one of the first to champion the theories of Copernicus. This was in
+  his <i>Lettera sopra l'opinione de' Pittagorici e del Copernico, della
+  mobilità della Terra e stabilità del Sole, e il nuovo pittagorico sistema
+  del mondo</i>, 4to, Naples, 1615. The condemnation of the Congregation
+  was published in the following spring, and in the year of Foscarini's
+  death at the early age of thirty-six.</p>
+
+  <p><a name="Nt_140" href="#NtA_140">[140]</a> "To be wholly prohibited
+  and condemned," because "it seeks to show that the aforesaid doctrine is
+  consonant with truth and is not opposed to the Holy Scriptures."</p>
+
+  <p><a name="Nt_141" href="#NtA_141">[141]</a> "As repugnant to the Holy
+  Scriptures and to its true and Catholic interpretation (which in a
+  Christian man cannot be tolerated in the least), he does not hesitate to
+  treat (of his subject) '<i>by hypothesis</i>', but he even adds '<i>as
+  most true</i>'!"</p>
+
+  <p><a name="Nt_142" href="#NtA_142">[142]</a> "To the places in which he
+  discusses not by hypothesis but by making assertions concerning the
+  position and motion of the earth."</p>
+
+  <p><a name="Nt_143" href="#NtA_143">[143]</a> "<i>Copernicus.</i> If by
+  chance there shall be vain talkers who, although ignorant of all
+  mathematics, yet taking it upon themselves to sit in judgment upon the
+  subject on account of a certain passage of Scripture badly distorted for
+  their purposes, shall have dared to criticize and censure this teaching
+  of mine, I pay no attention to them, even to the extent of despising
+  their judgment as rash. For it is not unknown that Lactantius, a writer
+  of prominence in other lines although but little versed in mathematics,
+  spoke very childishly about the form of the earth when he ridiculed those
+  who declared that it was spherical. Hence it should not seem strange to
+  the learned if some shall look upon us in the same way. Mathematics is
+  written for mathematicians, to whom these labors of ours will seem, if I
+  mistake not, to add something even to the republic of the Church....
+  <i>Emend.</i> Here strike out everything from 'if by chance' to the words
+  'these labors of ours,' and adapt it thus: 'But these labors of
+  ours.'"</p>
+
+  <p><a name="Nt_144" href="#NtA_144">[144]</a> "<i>Copernicus.</i> However
+  if we consider the matter more carefully it will be seen that the
+  investigation is not yet completed, and therefore ought by no means to be
+  condemned. <i>Emend.</i> However, if we consider the matter more
+  carefully it is of no consequence whether we regard the earth as existing
+  in the center of the universe or outside of the center, so far as the
+  solution of the phenomena of celestial movements is concerned."</p>
+
+  <p><a name="Nt_145" href="#NtA_145">[145]</a> "The whole of this chapter
+  may be cut out, since it avowedly treats of the earth's motion, while it
+  refutes the reasons of the ancients proving its immobility. Nevertheless,
+  since it seems to speak problematically, in order that it may satisfy the
+  learned and keep intact the sequence and unity of the book let it be
+  emended as below."</p>
+
+  <p><a name="Nt_146" href="#NtA_146">[146]</a> "<i>Copernicus.</i>
+  Therefore why do we still hesitate to concede to it motion which is by
+  nature consistent with its form, the more so because the whole universe
+  is moving, whose end is not and cannot be known, and not confess that
+  there is in the sky an appearance of daily revolution, while on the earth
+  there is the truth of it? And in like manner these things are as if
+  Virgil's Æneas should say, 'We are borne from the harbor' ...
+  <i>Emend.</i> Hence I cannot concede motion to this form, the more so
+  because the universe would fall, whose end is not and cannot be known,
+  and what appears in the heavens is just as if ..."</p>
+
+  <p><a name="Nt_147" href="#NtA_147">[147]</a> "<i>Copernicus</i>. I also
+  add that it would seem very absurd that motion should be ascribed to that
+  which contains and locates, and not rather to that which is contained and
+  located, that is the earth. <i>Emend.</i> I also add that it is not more
+  difficult to ascribe motion to the contained and located, which is the
+  earth, than to that which contains it."</p>
+
+  <p><a name="Nt_148" href="#NtA_148">[148]</a> "<i>Copernicus.</i> You
+  see, therefore, that from all these things the motion of the earth is
+  more probable than its immobility, especially in the daily revolution
+  which is as it were a particular property of it. <i>Emend.</i> Omit from
+  'You see' to the end of the chapter."</p>
+
+  <p><a name="Nt_149" href="#NtA_149">[149]</a> "<i>Copernicus.</i>
+  Therefore, since there is nothing to hinder the motion of the earth, it
+  seems to me that we should consider whether it has several motions, to
+  the end that it may be looked upon as one of the moving stars.
+  <i>Emend.</i> Therefore, since I have assumed that the earth moves, it
+  seems to me that we should consider whether it has several motions."</p>
+
+  <p><a name="Nt_150" href="#NtA_150">[150]</a> "<i>Copernicus.</i> We are
+  not ashamed to acknowledge ... that this is preferably verified in the
+  motion of the earth. <i>Emend.</i> We are not ashamed to assume ... that
+  this is consequently verified in the motion."</p>
+
+  <p><a name="Nt_151" href="#NtA_151">[151]</a> "<i>Copernicus.</i> So
+  divine is surely this work of the Best and Greatest. <i>Emend.</i> Strike
+  out these last words."</p>
+
+  <p><a name="Nt_152" href="#NtA_152">[152]</a> This should be Cap. 11,
+  lib. i, p. 10.</p>
+
+  <p><a name="Nt_153" href="#NtA_153">[153]</a> "<i>Copernicus.</i>
+  Demonstration of the threefold motion of the earth. <i>Emend.</i> On the
+  hypothesis of the threefold motion of the earth and its
+  demonstration."</p>
+
+  <p><a name="Nt_154" href="#NtA_154">[154]</a> This should be Cap. 20,
+  lib. iv, p. 122.</p>
+
+  <p><a name="Nt_155" href="#NtA_155">[155]</a> "<i>Copernicus.</i>
+  Concerning the size of these three stars, the sun, the moon and the
+  earth. <i>Emend.</i> Strike out the words 'these three stars,' because
+  the earth is not a star as Copernicus would make it."</p>
+
+  <p><a name="Nt_156" href="#NtA_156">[156]</a> He seems to speak
+  problematically in order to satisfy the learned.</p>
+
+  <p><a name="Nt_157" href="#NtA_157">[157]</a> One of the Church Fathers,
+  born about 250 A.D., and died about 330, probably at Trèves. He wrote
+  <i>Divinarum Institutionum Libri VII.</i> and other controversial and
+  didactic works against the learning and philosophy of the Greeks.</p>
+
+  <p><a name="Nt_158" href="#NtA_158">[158]</a> Giovanni Battista Riccioli
+  (1598-1671) taught philosophy and theology at Parma and Bologna, and was
+  later professor of astronomy. His <i>Almagestum novum</i> appeared in
+  1651, and his <i>Argomento fisico-matematico contro il moto diurno della
+  terra</i> in 1668.</p>
+
+  <p><a name="Nt_159" href="#NtA_159">[159]</a> He was a native of
+  Arlington, Sussex, and a pensioner of Christ's College, Cambridge. In
+  1603 he became a master of arts at Oxford.</p>
+
+  <p><a name="Nt_160" href="#NtA_160">[160]</a> Straying, i.e., from the
+  right way.</p>
+
+  <p><a name="Nt_161" href="#NtA_161">[161]</a> "Private subjects may, in
+  the presence of danger, defend themselves or their families against a
+  monarch as against any malefactor, if the monarch assaults them like a
+  bandit or a ravisher, and provided they are unable to summon the usual
+  protection and cannot in any way escape the danger."</p>
+
+  <p><a name="Nt_162" href="#NtA_162">[162]</a> Daniel Neal (1678-1743), an
+  independent minister, wrote a <i>History of the Puritans</i> that
+  appeared in 1732. The account may be found in the New York edition of
+  1843-44, vol. I, p. 271.</p>
+
+  <p><a name="Nt_163" href="#NtA_163">[163]</a> Anthony Wood (1632-1695),
+  whose <i>Historia et Antiquitates Universitatis Oxoniensis</i> (1674) and
+  <i>Athenae Oxoniensis</i> (1691) are among the classics on Oxford.</p>
+
+  <p><a name="Nt_164" href="#NtA_164">[164]</a> Part of the title, not here
+  quoted, shows the nature of the work more clearly: "liber unicus, in quo
+  decretum S. Congregationis S.&nbsp;R.&nbsp;E. Cardinal. an. 1616, adversus
+  Pythagorico-Copernicanos editum defenditur."</p>
+
+  <p><a name="Nt_165" href="#NtA_165">[165]</a> This was John Elliot
+  Drinkwater Bethune (1801-1851), the statesman who did so much for
+  legislative and educational reform in India. His father, John Drinkwater
+  Bethune, wrote a history of the siege of Gibraltar.</p>
+
+  <p><a name="Nt_166" href="#NtA_166">[166]</a> The article referred to is
+  about thirty years old; since it appeared another has been given
+  (<i>Dubl. Rev.</i>, Sept. 1865) which is of much greater depth. In it
+  will also be found the Roman view of Bishop Virgil (<i>ante</i>, p.
+  32).&mdash;A. De M.</p>
+
+  <p><a name="Nt_167" href="#NtA_167">[167]</a> Jean Baptiste Morin
+  (1583-1656), in his younger days physician to the Bishop of Boulogne and
+  the Duke of Luxemburg, became in 1630 professor of mathematics at the
+  Collège Royale. His chief contribution to the problem of the
+  determination of longitude is his <i>Longitudinum terrestrium et
+  coelestium nova et hactenus optata scientia</i> (1634). He also wrote
+  against Copernicus in his <i>Famosi problematis de telluris motu vel
+  quiete hactenus optata solutio</i> (1631), and against Lansberg in his
+  <i>Responsio pro telluris quiete</i> (1634).</p>
+
+  <p><a name="Nt_168" href="#NtA_168">[168]</a> The work appeared at Leyden
+  in 1626, at Amsterdam in 1634, at Copenhagen in 1640 and again at Leyden
+  in 1650. The title of the 1640 edition is <i>Arithmeticae Libri II et
+  Geometriae Libri VI</i>. The work on which it is based is the
+  <i>Arithmeticae et Geometriae Practica</i>, which appeared in 1611.</p>
+
+  <p><a name="Nt_169" href="#NtA_169">[169]</a> The father's name was
+  Adriaan, and Lalande says that it was Montucla who first made the mistake
+  of calling him Peter, thinking that the initials P. M. stood for Petrus
+  Metius, when in reality they stood for <i>piae memoriae</i>! The ratio
+  355/113 was known in China hundreds of years before his time. See note <a
+  href="#Nt_55">55</a>, page <a href="#page52">52</a>.</p>
+
+  <p><a name="Nt_170" href="#NtA_170">[170]</a> Adrian Metius (1571-1635)
+  was professor of medicine at the University of Franeker. His work was,
+  however, in the domain of astronomy, and in this domain he published
+  several treatises.</p>
+
+  <p><a name="Nt_171" href="#NtA_171">[171]</a> The first edition was
+  entitled: <i>The Discovery of a World in the Moone. Or, a Discourse
+  Tending to prove that 'tis probable there may be another habitable World
+  in that Planet</i>. 1638, 8vo. The fourth edition appeared in 1684. John
+  Wilkins (1614-1672) was Warden of Wadham College, Oxford; master of
+  Trinity, Cambridge; and, later, Bishop of Chester. He was influential in
+  founding the Royal Society.</p>
+
+  <p><a name="Nt_172" href="#NtA_172">[172]</a> The first edition was
+  entitled: <i>C. Hugenii</i> <span title="Kosmotheôros" class="grk"
+  >&Kappa;&omicron;&sigma;&mu;&omicron;&theta;&epsilon;&omega;&rho;&omicron;&sigmaf;</span>,
+  <i>sive de Terris coelestibus, earumque ornatu, conjecturae</i>, The
+  Hague, 1698, 4to. There were several editions. It was also translated
+  into French (1718), and there was another English edition (1722).
+  Huyghens (1629-1695) was one of the best mathematical physicists of his
+  time.</p>
+
+  <p><a name="Nt_173" href="#NtA_173">[173]</a> It is hardly necessary to
+  say that science has made enormous advance in the chemistry of the
+  universe since these words were written.</p>
+
+  <p><a name="Nt_174" href="#NtA_174">[174]</a> William Whewell (1794-1866)
+  is best known through his <i>History of the Inductive Sciences</i> (1837)
+  and <i>Philosophy of the Inductive Sciences</i> (1840).</p>
+
+  <p><a name="Nt_175" href="#NtA_175">[175]</a> Thomas Chalmers
+  (1780-1847), the celebrated Scotch preacher. These discourses were
+  delivered while he was minister in a large parish in the poorest part of
+  Glasgow, and in them he attempted to bring science into harmony with the
+  Bible. He was afterwards professor of moral philosophy at St. Andrew's
+  (1823-28), and professor of theology at Edinburgh (1828). He became the
+  leader of a schism from the Scotch Presbyterian Church,&mdash;the Free
+  Church.</p>
+
+  <p><a name="Nt_176" href="#NtA_176">[176]</a> That is, in Robert Watt's
+  (1774-1819) <i>Bibliotheca Britannica</i> (posthumous, 1824). Nor is it
+  given in the <i>Dictionary of National Biography</i>.</p>
+
+  <p><a name="Nt_177" href="#NtA_177">[177]</a> The late Greek satirist and
+  poet, c. 120-c. 200 A.D.</p>
+
+  <p><a name="Nt_178" href="#NtA_178">[178]</a> François Rabelais (c.
+  1490-1553) the humorist who created Pantagruel (1533) and Gargantua
+  (1532). His work as a physician and as editor of the works of Galen and
+  Hippocrates is less popularly known.</p>
+
+  <p><a name="Nt_179" href="#NtA_179">[179]</a> Francis Godwin (1562-1633)
+  bishop of Llandaff and Hereford. Besides some valuable historical works
+  he wrote <i>The Man in the Moone, or a Discourse of a voyage thither by
+  Domingo Gonsales, the Speed Messenger of London</i>, 1638.</p>
+
+  <p><a name="Nt_180" href="#NtA_180">[180]</a> Bernard Le Bovier de
+  Fontenelle (1657-1757), historian, critic, mathematician, Secretary of
+  the Académie des Sciences, and member of the Académie Française. His
+  <i>Entretien sur la pluralité des mondes</i> appeared at Paris in
+  1686.</p>
+
+  <p><a name="Nt_181" href="#NtA_181">[181]</a> Athanasius Kircher
+  (1602-1680), Jesuit, professor of mathematics and philosophy, and later
+  of Hebrew and Syriac, at Wurzburg; still later professor of mathematics
+  and Hebrew at Rome. He wrote several works on physics. His collection of
+  mathematical instruments and other antiquities became the basis of the
+  Kircherian Museum at Rome.</p>
+
+  <p><a name="Nt_182" href="#NtA_182">[182]</a> "Both belief and non-belief
+  are dangerous. Hippolitus died because his stepmother was believed. Troy
+  fell because Cassandra was not believed. Therefore the truth should be
+  investigated long before foolish opinion can properly judge." (Prove =
+  probe?).</p>
+
+  <p><a name="Nt_183" href="#NtA_183">[183]</a> Jacobus Grandamicus
+  (Jacques Grandami) was born at Nantes in 1588 and died at Paris in 1672.
+  He was professor of theology and philosophy in the Jesuit colleges at
+  Rennes, Tours, Rouen, and other places. He wrote several works on
+  astronomy.</p>
+
+  <p><a name="Nt_184" href="#NtA_184">[184]</a> "And I, if I be lifted up
+  from the earth, will draw all men unto me." John xii. 32.</p>
+
+  <p><a name="Nt_185" href="#NtA_185">[185]</a> Andrea Argoli (1568-1657)
+  wrote a number of works on astronomy, and computed ephemerides from 1621
+  to 1700.</p>
+
+  <p><a name="Nt_186" href="#NtA_186">[186]</a> So in the original edition
+  of the <i>Budget</i>. It is Johannem Pellum in the original title. John
+  Pell (1610 or 1611-1685) studied at Cambridge and Oxford, and was
+  professor of mathematics at Amsterdam (1643-46) and Breda (1646-52). He
+  left many manuscripts but published little. His name attaches by accident
+  to an interesting equation recently studied with care by Dr. E.&nbsp;E.
+  Whitford (New York, 1912).</p>
+
+  <p><a name="Nt_187" href="#NtA_187">[187]</a> Christianus Longomontanus
+  (Christen Longberg or Lumborg) was born in 1569 at Longberg, Jutland, and
+  died in 1647 at Copenhagen. He was an assistant of Tycho Brahe and
+  accepted the diurnal while denying the orbital motion of the earth. His
+  <i>Cyclometria e lunulis reciproce demonstrata</i> appeared in 1612 under
+  the name of Christen Severin, the latter being his family name. He wrote
+  several other works on the quadrature problem, and some treatises on
+  astronomy.</p>
+
+  <p><a name="Nt_188" href="#NtA_188">[188]</a> The names are really pretty
+  well known. Giles Persone de Roberval was born at Roberval near Beauvais
+  in 1602, and died at Paris in 1675. He was professor of philosophy at the
+  Collège Gervais at Paris, and later at the Collège Royal. He claimed to
+  have discovered the theory of indivisibles before Cavalieri, and his work
+  is set forth in his <i>Traité des indivisibles</i> which appeared
+  posthumously in 1693.</p>
+
+  <p>Hobbes (1588-1679), the political and social philosopher, lived a good
+  part of his time (1610-41) in France where he was tutor to several young
+  noblemen, including the Cavendishes. His <i>Leviathan</i> (1651) is said
+  to have influenced Spinoza, Leibnitz, and Rousseau. His <i>Quadratura
+  circuli, cubatio sphaerae, duplicatio cubi ...</i> (London, 1669),
+  <i>Rosetum geometricum ...</i> (London, 1671), and <i>Lux Mathematica,
+  censura doctrinae Wallisianae contra Rosetum Hobbesii</i> (London, 1674)
+  are entirely forgotten to-day. (See a further note, <i>infra</i>.)</p>
+
+  <p>Pierre de Carcavi, a native of Lyons, died at Paris in 1684. He was a
+  member of parliament, royal librarian, and member of the Académie des
+  Sciences. His attempt to prove the impossibility of the quadrature
+  appeared in 1645. He was a frequent correspondent of Descartes.</p>
+
+  <p>Cavendish (1591-1654) was Sir (not Lord) Charles. He was, like De
+  Morgan himself, a bibliophile in the domain of mathematics. His life was
+  one of struggle, his term as member of parliament under Charles I being
+  followed by gallant service in the royal army. After the war he sought
+  refuge on the continent where he met most of the mathematicians of his
+  day. He left a number of manuscripts on mathematics, which his widow
+  promptly disposed of for waste paper. If De Morgan's manuscripts had been
+  so treated we should not have had his revision of his <i>Budget of
+  Paradoxes</i>.</p>
+
+  <p>Marin Mersenne (1588-1648), a minorite, living in the cloisters at
+  Nevers and Paris, was one of the greatest Franciscan scholars. He edited
+  Euclid, Apollonius, Archimedes, Theodosius, and Menelaus (Paris, 1626),
+  translated the Mechanics of Galileo into French (1634), wrote
+  <i>Harmonicorum Libri XII</i> (1636), and <i>Cogitata
+  physico-mathematica</i> (1644), and taught theology and philosophy at
+  Nevers.</p>
+
+  <p>Johann Adolph Tasse (Tassius) was born in 1585 and died at Hamburg in
+  1654. He was professor of mathematics in the Gymnasium at Hamburg, and
+  wrote numerous works on astronomy, chronology, statics, and elementary
+  mathematics.</p>
+
+  <p>Johann Ludwig, Baron von Wolzogen, seems to have been one of the early
+  unitarians, called <i>Fratres Polonorum</i> because they took refuge in
+  Poland. Some of his works appear in the <i>Bibliotheca Fratrum
+  Polonorum</i> (Amsterdam, 1656). I find no one by the name who was
+  contributing to mathematics at this time.</p>
+
+  <p>Descartes is too well known to need mention in this connection.</p>
+
+  <p>Bonaventura Cavalieri (1598-1647) was a Jesuit, a pupil of Galileo,
+  and professor of mathematics at Bologna. His greatest work, <i>Geometria
+  indivisibilibus continuorum nova quadam ratione promota</i>, in which he
+  makes a noteworthy step towards the calculus, appeared in 1635.</p>
+
+  <p>Jacob (Jacques) Golius was born at the Hague in 1596 and died at
+  Leyden in 1667. His travels in Morocco and Asia Minor (1622-1629) gave
+  him such knowledge of Arabic that he became professor of that language at
+  Leyden. After Snell's death he became professor of mathematics there. He
+  translated Arabic works on mathematics and astronomy into Latin.</p>
+
+  <p><a name="Nt_189" href="#NtA_189">[189]</a> It would be interesting to
+  follow up these rumors, beginning perhaps with the tomb of Archimedes.
+  The Ludolph van Ceulen story is very likely a myth. The one about Fagnano
+  may be such. The Bernoulli tomb does have the spiral, however (such as it
+  is), as any one may see in the cloisters at Basel to-day.</p>
+
+  <p><a name="Nt_190" href="#NtA_190">[190]</a> Collins (1625-1683) was
+  secretary of the Royal Society, and was "a kind of register of all new
+  improvements in mathematics." His office brought him into correspondence
+  with all of the English scientists, and he was influential in the
+  publication of various important works, including Branker's translation
+  of the algebra by Rhonius, with notes by Pell, which was the first work
+  to contain the present English-American symbol of division. He also
+  helped in the publication of editions of Archimedes and Apollonius, of
+  Kersey's Algebra, and of the works of Wallis. His profession was that of
+  accountant and civil engineer, and he wrote three unimportant works on
+  mathematics (one published posthumously, and the others in 1652 and
+  1658).</p>
+
+  <p>Heinrich Christian Schumacher (1780-1850) was professor of astronomy
+  at Copenhagen and director of the observatory at Altona. His translation
+  of Carnot's <i>Géométrie de position</i> (1807) brought him into personal
+  relations with Gauss, and the friendship was helpful to Schumacher. He
+  was a member of many learned societies and had a large circle of
+  acquaintances. He published numerous monographs and works on
+  astronomy.</p>
+
+  <p>Gassendi (1592-1655) might well have been included by De Morgan in the
+  group, since he knew and was a friend of most of the important
+  mathematicians of his day. Like Mersenne, he was a minorite, but he was a
+  friend of Galileo and Kepler, and wrote a work under the title
+  <i>Institutio astronomica, juxta hypotheses Copernici, Tychonis-Brahaei
+  et Ptolemaei</i> (1645). He taught philosophy at Aix, and was later
+  professor of mathematics at the College Royal at Paris.</p>
+
+  <p>Burnet is the Bishop Gilbert Burnet (1643-1715) who was so strongly
+  anti-Romanistic that he left England during the reign of James II and
+  joined the ranks of the Prince of Orange. William made him bishop of
+  Salisbury.</p>
+
+  <p><a name="Nt_191" href="#NtA_191">[191]</a> There is some substantial
+  basis for De Morgan's doubts as to the connection of that
+  <i>mirandula</i> of his age, Sir Kenelm Digby (1603-1665), with the
+  famous <i>poudre de sympathie</i>. It is true that he was just the one to
+  prepare such a powder. A dilletante in everything,&mdash;learning, war,
+  diplomacy, religion, letters, and science&mdash;he was the one to exploit
+  a fraud of this nature. He was an astrologer, an alchemist, and a
+  fabricator of tales, and well did Henry Stubbes characterize him as "the
+  very Pliny of our age for lying." He first speaks of the powder in a
+  lecture given at Montpellier in 1658, and in the same year he published
+  the address at Paris under the title: <i>Discours fait en une célèbre
+  assemblée par le chevalier Digby .... touchant la guérison de playes par
+  la poudre de sympathie</i>. The London edition referred to by De Morgan
+  also came out in 1658, and several editions followed it in England,
+  France and Germany. But Nathaniel Highmore in his <i>History of
+  Generation</i> (1651) referred to the concoction as "Talbot's Powder"
+  some years before Digby took it up. The basis seems to have been vitriol,
+  and it was claimed that it would heal a wound by simply being applied to
+  a bandage taken from it.</p>
+
+  <p><a name="Nt_192" href="#NtA_192">[192]</a> This work by Thomas Birch
+  (1705-1766) came out in 1756-57. Birch was a voluminous writer on English
+  history. He was a friend of Dr. Johnson and of Walpole, and he wrote a
+  life of Robert Boyle.</p>
+
+  <p><a name="Nt_193" href="#NtA_193">[193]</a> We know so much about John
+  Evelyn (1620-1706) through the diary which he began at the age of eleven,
+  that we forget his works on navigation and architecture.</p>
+
+  <p><a name="Nt_194" href="#NtA_194">[194]</a> I suppose this was the
+  seventh Earl of Shrewsbury (1553-1616).</p>
+
+  <p><a name="Nt_195" href="#NtA_195">[195]</a> This is interesting in view
+  of the modern aseptic practice of surgery and the antiseptic treatment of
+  wounds inaugurated by the late Lord Lister.</p>
+
+  <p><a name="Nt_196" href="#NtA_196">[196]</a> Perhaps De Morgan had not
+  heard the <i>bon mot</i> of Dr. Holmes: "I firmly believe that if the
+  whole <i>materia medica</i> could be sunk to the bottom of the sea, it
+  would be all the better for mankind and all the worse for the
+  fishes."</p>
+
+  <p><a name="Nt_197" href="#NtA_197">[197]</a> The full title is worth
+  giving, because it shows the mathematical interests of Hobbes, and the
+  nature of the six dialogues: <i>Examinatio et emendatio mathematicae
+  hodiernae qualis explicatur in libris Johannis Wallisii geometriae
+  professoris Saviliani in Academia Oxoniensi: distributa in sex dialogos
+  (1. De mathematicae origine ...; 2. De principiis traditis ab Euclide; 3.
+  De demonstratione operationum arithmeticarum ...; 4. De rationibus; 5. De
+  angula contactus, de sectionibus coni, et arithmetica infinitorum; 6.
+  Dimensio circuli tribus methodis demonstrata ... item cycloidis verae
+  descriptio et proprietates aliquot.)</i> Londini, 1660 (not 1666). For a
+  full discussion of the controversy over the circle, see George Croom
+  Robertson's biography of Hobbes in the eleventh edition of the
+  <i>Encyclopaedia Britannica</i>.</p>
+
+  <p><a name="Nt_198" href="#NtA_198">[198]</a> This is his
+  <i>Animadversions upon Mr. Hobbes' late book De principiis et
+  ratiocinatione geometrarum</i>, 1666, or his <i>Hobbianae quadraturae
+  circuli, cubationis sphaerae et duplicationis cubi confutatio</i>, also
+  of 1669.</p>
+
+  <p><a name="Nt_199" href="#NtA_199">[199]</a> This is the work of 1669
+  referred to above.</p>
+
+  <p><a name="Nt_200" href="#NtA_200">[200]</a> Gregoire de St. Vincent
+  (1584-1667) published his <i>Opus geometricum quadraturae circuli et
+  sectionum coni</i> at Antwerp in 1647.</p>
+
+  <p><a name="Nt_201" href="#NtA_201">[201]</a> This appears in <i>J.
+  Scaligeri cyclometrica elementa duo</i>, Lugduni Batav., 1594.</p>
+
+  <p><a name="Nt_202" href="#NtA_202">[202]</a> Adriaen van Roomen
+  (1561-1615) gave the value of <span class="grk">&pi;</span> to sixteen
+  decimal places in his <i>Ideae mathematicae pars prima</i> (1593), and
+  wrote his <i>In Archimedis circuli dimensionem expositio &amp;
+  analysis</i> in 1597.</p>
+
+  <p><a name="Nt_203" href="#NtA_203">[203]</a> Kästner. See note <a
+  href="#Nt_30">30</a> on page <a href="#page43">43</a>.</p>
+
+  <p><a name="Nt_204" href="#NtA_204">[204]</a> Bentley (1662-1742) might
+  have done it, for as the head of Trinity College, Cambridge, and a
+  follower of Newton, he knew some mathematics. Erasmus (1466-1536) lived a
+  little too early to attempt it, although his brilliant satire might have
+  been used to good advantage against those who did try.</p>
+
+  <p><a name="Nt_205" href="#NtA_205">[205]</a> "In grammar, to give the
+  winds to the ships and to give the ships to the winds mean the same
+  thing. But in geometry it is one thing to assume the circle BCD not
+  greater than thirty-six segments BCDF, and another (to assume) the
+  thirty-six segments BCDF not greater than the circle. The one assumption
+  is true, the other false."</p>
+
+  <p><a name="Nt_206" href="#NtA_206">[206]</a> The Greek scholar
+  (1559-1614) who edited a Greek and Latin edition of Aristotle in
+  1590.</p>
+
+  <p><a name="Nt_207" href="#NtA_207">[207]</a> Jacques Auguste de Thou
+  (1553-1617), the historian and statesman.</p>
+
+  <p><a name="Nt_208" href="#NtA_208">[208]</a> "To value Scaliger higher
+  even when wrong, than the multitude when right."</p>
+
+  <p><a name="Nt_209" href="#NtA_209">[209]</a> "I would rather err with
+  Scaliger than be right with Clavius."</p>
+
+  <p><a name="Nt_210" href="#NtA_210">[210]</a> "The perimeter of the
+  dodecagon to be inscribed in a circle is greater than the perimeter of
+  the circle. And the more sides a polygon to be inscribed in a circle
+  successively has, so much the greater will the perimeter of the polygon
+  be than the perimeter of the circle."</p>
+
+  <p><a name="Nt_211" href="#NtA_211">[211]</a> De Morgan took, perhaps,
+  the more delight in speaking thus of Sir William Hamilton (1788-1856)
+  because of a spirited controversy that they had in 1847 over the theory
+  of logic. Possibly, too, Sir William's low opinion of mathematics had its
+  influence.</p>
+
+  <p><a name="Nt_212" href="#NtA_212">[212]</a> Edwards (1699-1757) wrote
+  <i>The canons of criticism</i> (1747) in which he gave a scathing
+  burlesque on Warburton's Shakespeare. It went through six editions.</p>
+
+  <p><a name="Nt_213" href="#NtA_213">[213]</a> Antoine Teissier (born in
+  1632) published his <i>Eloges des hommes savants, tirés de l'histoire de
+  M. de Thou</i> in 1683.</p>
+
+  <p><a name="Nt_214" href="#NtA_214">[214]</a> "He boasted without reason
+  of having found the quadrature of the circle. The glory of this admirable
+  discovery was reserved for Joseph Scaliger, as Scévole de St. Marthe has
+  written."</p>
+
+  <p><a name="Nt_215" href="#NtA_215">[215]</a> <i>Natural and political
+  observations mentioned in the following Index, and made upon the Bills of
+  Mortality.... With reference to the government, religion, trade, growth,
+  ayre, and diseases of the said city.</i> London, 1662, 4to. The book went
+  through several editions.</p>
+
+  <p><a name="Nt_216" href="#NtA_216">[216]</a> <i>Ne sutor ultra
+  crepidam</i>, "Let the cobbler stick to his last," as we now say.</p>
+
+  <p><a name="Nt_217" href="#NtA_217">[217]</a> The author (1632-1695) of
+  the <i>Historia et Antiquitates Universitatis Oxoniensis</i> (1674). See
+  note <a href="#Nt_163">163</a>, page <a href="#page98">98</a>.</p>
+
+  <p><a name="Nt_218" href="#NtA_218">[218]</a> The mathematical guild owes
+  Samuel Pepys (1633-1703) for something besides his famous diary
+  (1659-1669). Not only was he president of the Royal Society (1684), but
+  he was interested in establishing Sir William Boreman's mathematical
+  school at Greenwich.</p>
+
+  <p><a name="Nt_219" href="#NtA_219">[219]</a> John Graunt (1620-1674) was
+  a draper by trade, and was a member of the Common Council of London until
+  he lost office by turning Romanist. Although a shopkeeper, he was elected
+  to the Royal Society on the special recommendation of Charles II. Petty
+  edited the fifth edition of his work, adding much to its size and value,
+  and this may be the basis of Burnet's account of the authorship.</p>
+
+  <p><a name="Nt_220" href="#NtA_220">[220]</a> Petty (1623-1687) was a
+  mathematician and economist, and a friend of Pell and Sir Charles
+  Cavendish. His survey of Ireland, made for Cromwell, was one of the first
+  to be made on a large scale in a scientific manner. He was one of the
+  founders of the Royal Society.</p>
+
+  <p><a name="Nt_221" href="#NtA_221">[221]</a> The story probably arose
+  from Graunt's recent conversion to the Roman Catholic faith.</p>
+
+  <p><a name="Nt_222" href="#NtA_222">[222]</a> He was born in 1627 and
+  died in 1704. He published a series of ephemerides, beginning in 1659. He
+  was imprisoned in 1679, at the time of the "Popish Plot," and again for
+  treason in 1690. His important astrological works are the <i>Animal
+  Cornatum, or the Horn'd Beast</i> (1654) and <i>The Nativity of the late
+  King Charls</i> (1659).</p>
+
+  <p><a name="Nt_223" href="#NtA_223">[223]</a> Isaac D'Israeli
+  (1766-1848), in his <i>Curiosities of Literature</i> (1791), speaking of
+  Lilly, says: "I shall observe of this egregious astronomer, that there is
+  in this work, so much artless narrative, and at the same time so much
+  palpable imposture, that it is difficult to know when he is speaking what
+  he really believes to be the truth." He goes on to say that Lilly relates
+  that "those adepts whose characters he has drawn were the lowest
+  miscreants of the town. Most of them had taken the air in the pillory,
+  and others had conjured themselves up to the gallows. This seems a true
+  statement of facts."</p>
+
+  <p><a name="Nt_224" href="#NtA_224">[224]</a> It is difficult to estimate
+  William Lilly (1602-1681) fairly. His <i>Merlini Anglici ephemeris</i>,
+  issued annually from 1642 to 1681, brought him a great deal of money. Sir
+  George Wharton (1617-1681) also published an almanac annually from 1641
+  to 1666. He tried to expose John Booker (1603-1677) by a work entitled
+  <i>Mercurio-Coelicio-Mastix; or, an Anti-caveat to all such, as have
+  (heretofore) had the misfortune to be Cheated and Deluded by that Grand
+  and Traiterous Impostor of this Rebellious Age, John Booker</i>, 1644.
+  Booker was "licenser of mathematical [astrological] publications," and as
+  such he had quarrels with Lilly, Wharton, and others.</p>
+
+  <p><a name="Nt_225" href="#NtA_225">[225]</a> See note <a
+  href="#Nt_171">171</a> on page <a href="#page100">100</a>.</p>
+
+  <p><a name="Nt_226" href="#NtA_226">[226]</a> This is the <i>Ars
+  Signorum, vulgo character universalis et lingua philosophica</i>, that
+  appeared at London in 1661, 8vo. George Dalgarno anticipated modern
+  methods in the teaching of the deaf and dumb.</p>
+
+  <p><a name="Nt_227" href="#NtA_227">[227]</a> See note <a
+  href="#Nt_200">200</a> on page <a href="#page110">110</a>.</p>
+
+  <p><a name="Nt_228" href="#NtA_228">[228]</a> If the hyperbola is
+  referred to the asymptotes as axes, the area between two ordinates
+  (<i>x</i> = <i>a</i>, <i>x</i> = <i>b</i>) is the difference of the
+  logarithms of <i>a</i> and <i>b</i> to the base <i>e</i>. E.g., in the
+  case of the hyperbola <i>xy</i> = 1, the area between <i>x</i> = <i>a</i>
+  and <i>x</i> = 1 is log <i>a</i>.</p>
+
+  <p><a name="Nt_229" href="#NtA_229">[229]</a> "On ne peut lui refuser la
+  justice de remarquer que personne avant lui ne s'est porté dans cette
+  recherche avec autant de génie, &amp; même, si nous en exceptons son
+  objet principal, avec autant de succès." <i>Quadrature du Cercle</i>, p.
+  66.</p>
+
+  <p><a name="Nt_230" href="#NtA_230">[230]</a> The title proceeds: <i>Seu
+  duae mediae proportionales inter extremas datas per circulum et per
+  infinitas hyperbolas, vel ellipses et per quamlibet exhibitae</i>....
+  René Francois, Baron de Sluse (1622-1685) was canon and chancellor of
+  Liège, and a member of the Royal Society. He also published a work on
+  tangents (1672). The word <i>mesolabium</i> is from the Greek <span
+  title="mesolabion" class="grk"
+  >&mu;&epsilon;&sigma;&omicron;&lambda;&#x1F71;&beta;&iota;&omicron;&nu;</span>
+  or <span title="mesolabon" class="grk"
+  >&mu;&epsilon;&sigma;&#x1F79;&lambda;&alpha;&beta;&omicron;&nu;</span>,
+  an instrument invented by Eratosthenes for finding two mean
+  proportionals.</p>
+
+  <p><a name="Nt_231" href="#NtA_231">[231]</a> The full title has some
+  interest: <i>Vera circuli et hyperbolae quadratura cui accedit geometriae
+  pars universalis inserviens quantitatum curvarum transmutationi et
+  mensurae. Authore Jacobo Gregorio Abredonensi Scoto ... Patavii</i>,
+  1667. That is, James Gregory (1638-1675) of Aberdeen (he was really born
+  near but not in the city), a good Scot, was publishing his work down in
+  Padua. The reason was that he had been studying in Italy, and that this
+  was a product of his youth. He had already (1663) published his <i>Optica
+  promota</i>, and it is not remarkable that his brilliancy brought him a
+  wide circle of friends on the continent and the offer of a pension from
+  Louis XIV. He became professor of mathematics at St Andrews and later at
+  Edinburgh, and invented the first successful reflecting telescope. The
+  distinctive feature of his <i>Vera quadratura</i> is his use of an
+  infinite converging series, a plan that Archimedes used with the
+  parabola.</p>
+
+  <p><a name="Nt_232" href="#NtA_232">[232]</a> Jean de Beaulieu wrote
+  several works on mathematics, including <i>La lumière de
+  l'arithmétique</i> (n.d.), <i>La lumière des mathématiques</i> (1673),
+  <i>Nouvelle invention d'arithmétique</i> (1677), and some mathematical
+  tables.</p>
+
+  <p><a name="Nt_233" href="#NtA_233">[233]</a> A just estimate. There were
+  several works published by Gérard Desargues (1593-1661), of which the
+  greatest was the <i>Brouillon Proiect</i> (Paris, 1639). There is an
+  excellent edition of the <i>&OElig;uvres de Desargues</i> by M. Poudra,
+  Paris, 1864.</p>
+
+  <p><a name="Nt_234" href="#NtA_234">[234]</a> "A certain M. de Beaugrand,
+  a mathematician, very badly treated by Descartes, and, as it appears,
+  rightly so."</p>
+
+  <p><a name="Nt_235" href="#NtA_235">[235]</a> This is a very old
+  approximation for <span class="grk">&pi;</span>. One of the latest
+  pretended geometric proofs resulting in this value appeared in New York
+  in 1910, entitled <i>Quadrimetry</i> (privately printed).</p>
+
+  <p><a name="Nt_236" href="#NtA_236">[236]</a> "Copernicus, a German, made
+  himself no less illustrious by his learned writings; and we might say of
+  him that he stood alone and unique in the strength of his problems, if
+  his excessive presumption had not led him to set forth in this science a
+  proposition so absurd that it is contrary to faith and reason, namely
+  that the circumference of a circle is fixed and immovable while the
+  center is movable: on which geometrical principle he has declared in his
+  astrological treatise that the sun is fixed and the earth is in
+  motion."</p>
+
+  <p><a name="Nt_237" href="#NtA_237">[237]</a> So in the original.</p>
+
+  <p><a name="Nt_238" href="#NtA_238">[238]</a> Franciscus Maurolycus
+  (1494-1575) was really the best mathematician produced by Sicily for a
+  long period. He made Latin translations of Theodosius, Menelaus, Euclid,
+  Apollonius, and Archimedes, and wrote on cosmography and other
+  mathematical subjects.</p>
+
+  <p><a name="Nt_239" href="#NtA_239">[239]</a> "Nicolaus Copernicus is
+  also tolerated who asserted that the sun is fixed and that the earth
+  whirls about it; and he rather deserves a whip or a lash than a
+  reproof."</p>
+
+  <p><a name="Nt_240" href="#NtA_240">[240]</a> "Algebra is the curious
+  science of scholars, and particularly for a general of an army, or a
+  captain, in order quickly to draw up an army in battle array and to
+  number the musketeers and pikemen who compose it, without the figures of
+  arithmetic. This science has five special figures of this kind: P means
+  <i>plus</i> in commerce and <i>pikemen</i> in the army; M means
+  <i>minus</i>, and <i>musketeer</i> in the art of war;... R signifies
+  <i>root</i> in the measurement of a cube, and <i>rank</i> in <i>the
+  army</i>; Q means <i>square</i> (French <i>quarè</i>, as then spelled) in
+  both cases; C means <i>cube</i> in mensuration, and <i>cavalry</i> in
+  arranging batallions and squadrons. As for the operations of this
+  science, they are as follows: to add a <i>plus</i> and a <i>plus</i>, the
+  sum will be <i>plus</i>; to add <i>minus</i> with <i>plus</i>, take the
+  less from the greater and the remainder will be the sum required or the
+  number to be found. I say this only in passing, for the benefit of those
+  who are wholly ignorant of it."</p>
+
+  <p><a name="Nt_241" href="#NtA_241">[241]</a> He refers to the <i>Joannis
+  de Beaugrand ... Geostatice, seu de vario pondere gravium secundum varia
+  a terrae (centro) intervalla dissertatio mathematica</i>, Paris, 1636.
+  Pascal relates that de Beaugrand sent all of Roberval's theorems on the
+  cycloid and Fermat's on maxima and minima to Galileo in 1638, pretending
+  that they were his own.</p>
+
+  <p><a name="Nt_242" href="#NtA_242">[242]</a> More (1614-1687) was a
+  theologian, a fellow of Christ College, Cambridge, and a Christian
+  Platonist.</p>
+
+  <p><a name="Nt_243" href="#NtA_243">[243]</a> Matthew Hale (1609-1676)
+  the famous jurist, wrote a number of tracts on scientific, moral, and
+  religious subjects. These were collected and published in 1805.</p>
+
+  <p><a name="Nt_244" href="#NtA_244">[244]</a> They might have been
+  attributed to many a worse man than Dr. Hales (1677-1761), who was a
+  member of the Royal Society and of the Paris Academy, and whose scheme
+  for the ventilation of prisons reduced the mortality at the Savoy prison
+  from one hundred to only four a year. The book to which reference is made
+  is <i>Vegetable Staticks or an Account of some statical experiments on
+  the sap in Vegetables</i>, 1727.</p>
+
+  <p><a name="Nt_245" href="#NtA_245">[245]</a> <i>Pleas of the Crown; or a
+  Methodical Summary of the Principal Matters relating to the subject</i>,
+  1678.</p>
+
+  <p><a name="Nt_246" href="#NtA_246">[246]</a> <i>Thomae Streete
+  Astronomia Carolina, a new theory of the celestial motions</i>, 1661. It
+  also appeared at Nuremberg in 1705, and at London in 1710 and 1716
+  (Halley's editions). He wrote other works on astronomy.</p>
+
+  <p><a name="Nt_247" href="#NtA_247">[247]</a> This was the Sir Thomas
+  Street (1626-1696) who passed sentence of death on a Roman Catholic
+  priest for saying mass. The priest was reprieved by the king, but in the
+  light of the present day one would think the justice more in need of
+  pardon. He took part in the trial of the Rye House Conspirators in
+  1683.</p>
+
+  <p><a name="Nt_248" href="#NtA_248">[248]</a> Edmund Halley (1656-1742),
+  who succeeded Wallis (1703) as Savilian professor of mathematics at
+  Oxford, and Flamsteed (1720) as head of the Greenwich observatory. It is
+  of interest to note that he was instrumental in getting Newton's
+  <i>Principia</i> printed.</p>
+
+  <p><a name="Nt_249" href="#NtA_249">[249]</a> Shepherd (born in 1760) was
+  one of the most famous lawyers of his day. He was knighted in 1814 and
+  became Attorney General in 1817.</p>
+
+  <p><a name="Nt_250" href="#NtA_250">[250]</a> This was William Hone
+  (1780-1842), a book publisher, who wrote satires against the government,
+  and who was tried three times because of his parodies on the catechism,
+  creed, and litany (illustrated by Cruikshank). He was acquitted on all of
+  the charges.</p>
+
+  <p><a name="Nt_251" href="#NtA_251">[251]</a> Valentinus was a
+  Benedictine monk and was still living at Erfurt in 1413. His <i>Currus
+  triumphalis antimonii</i> appeared in 1624. Synesius was Bishop of
+  Ptolemaide, who died about 430. His works were printed at Paris in 1605.
+  Theodor Kirckring (1640-1693) was a fellow-student of Spinoza's. Besides
+  the commentary on Valentine he left several works on anatomy. His
+  commentary appeared at Amsterdam in 1671. There were several editions of
+  the <i>Chariot</i>.</p>
+
+  <p><a name="Nt_252" href="#NtA_252">[252]</a> The chief difficulty with
+  this curious "monk-bane" etymology is its absurdity. The real origin of
+  the word has given etymologists a good deal of trouble.</p>
+
+  <p><a name="Nt_253" href="#NtA_253">[253]</a> Robert Boyle (1627-1691),
+  son of "the Great Earl" (of Cork). Perhaps his best-known discovery is
+  the law concerning the volume of gases.</p>
+
+  <p><a name="Nt_254" href="#NtA_254">[254]</a> The real name of Eirenaeus
+  Philalethes (born in 1622) is unknown. It may have been Childe. He
+  claimed to have discovered the philosopher's stone in 1645. His tract in
+  this work is <i>The Secret of the Immortal Liquor Alkahest or
+  Ignis-Aqua</i>. See note <a href="#Nt_260">260</a>, <i>infra</i>.</p>
+
+  <p><a name="Nt_255" href="#NtA_255">[255]</a> Johann Baptist van Helmont,
+  Herr von Merode, Royenborg etc. (1577-1644). His chemical discoveries
+  appeared in his <i>Ortus medicinae</i> (1648), which went through many
+  editions.</p>
+
+  <p><a name="Nt_256" href="#NtA_256">[256]</a> De Morgan should have
+  written up Francis Anthony (1550-1623), whose <i>Panacea aurea sive
+  tractatus duo de auro potabili</i> (Hamburg, 1619) described a panacea
+  that he gave for every ill. He was repeatedly imprisoned for practicing
+  medicine without a license from the Royal College of Physicians.</p>
+
+  <p><a name="Nt_257" href="#NtA_257">[257]</a> Bernardus Trevisanus
+  (1406-1490), who traveled even through Barbary, Egypt, Palestine, and
+  Persia in search of the philosopher's stone. He wrote several works on
+  alchemy,&mdash;<i>De Chemica</i> (1567), <i>De Chemico Miraculo</i>
+  (1583), <i>Traité de la nature de l'oeuf des philosophes</i> (1659),
+  etc., all published long after his death.</p>
+
+  <p><a name="Nt_258" href="#NtA_258">[258]</a> George Ripley (1415-1490)
+  was an Augustinian monk, later a chamberlain of Innocent VIII, and still
+  later a Carmelite monk. His <i>Liber de mercuris philosophico</i> and
+  other tracts first appeared in <i>Opuscula quaedam chymica</i>
+  (Frankfort, 1614).</p>
+
+  <p><a name="Nt_259" href="#NtA_259">[259]</a> Besides the <i>Opus
+  majus</i>, and other of the better known works of this celebrated
+  Franciscan (1214-1294), there are numerous tracts on alchemy that
+  appeared in the <i>Thesaurus chymicus</i> (Frankfort, 1603).</p>
+
+  <p><a name="Nt_260" href="#NtA_260">[260]</a> George Starkey (1606-1665
+  or 1666) has special interest for American readers. He seems to have been
+  born in the Bermudas and to have obtained the bachelor's degree in
+  England. He then went to America and in 1646 obtained the master's degree
+  at Harvard, apparently under the name of Stirk. He met Eirenaeus
+  Philalethes (see note <a href="#Nt_254">254</a> above) in America and
+  learned alchemy from him. Returning to England, he sold quack medicines
+  there, and died in 1666 from the plague after dissecting a patient who
+  had died of the disease. Among his works was the <i>Liquor Alcahest, or a
+  Discourse of that Immortal Dissolvent of Paracelsus and Helmont</i>,
+  which appeared (1675) some nine years after his death.</p>
+
+  <p><a name="Nt_261" href="#NtA_261">[261]</a> Platt (1552-1611) was the
+  son of a London brewer. Although he left a manuscript on alchemy, and
+  wrote a book entitled <i>Delights for Ladies to adorne their Persons</i>
+  (1607), he was knighted for some serious work on the chemistry of
+  agriculture, fertilizing, brewing, and the preserving of foods, published
+  in <i>The Jewell House of Art and Nature</i> (1594).</p>
+
+  <p><a name="Nt_262" href="#NtA_262">[262]</a> "Those who wish to call a
+  man a liar and deceiver speak of him a writer of almanacs; but those who
+  (would call him) a scoundrel and an imposter (speak of him as) a
+  chemist."</p>
+
+  <p><a name="Nt_263" href="#NtA_263">[263]</a> "Trust your barque to the
+  winds but not your body to a chemist; any breeze is safer than the faith
+  of a chemist."</p>
+
+  <p><a name="Nt_264" href="#NtA_264">[264]</a> Probably the Jesuit, Père
+  Claude François Menestrier (1631-1705), a well known historian.</p>
+
+  <p><a name="Nt_265" href="#NtA_265">[265]</a> The author was Christopher
+  Nesse (1621-1705), a belligerent Calvinist, who wrote many controversial
+  works and succeeded in getting excommunicated four times. One of his most
+  virulent works was <i>A Protestant Antidote against the Poison of
+  Popery</i>.</p>
+
+  <p><a name="Nt_266" href="#NtA_266">[266]</a> John Case (c. 1660-1700)
+  was a famous astrologer and physician. He succeeded to Lilly's practice
+  in London. In a darkened room, wherein he kept an array of mystical
+  apparatus, he pretended to show the credulous the ghosts of their
+  departed relatives. Besides his astrological works he wrote one serious
+  treatise, the <i>Compendium Anatomicum nova methodo institutum</i>
+  (1695), in which he defends Harvey's theories of embryology.</p>
+
+  <p><a name="Nt_267" href="#NtA_267">[267]</a> Marcelis (1636-after 1714)
+  was a soap maker of Amsterdam. It is to be hoped that he made better soap
+  than values of <span class="grk">&pi;</span>.</p>
+
+  <p><a name="Nt_268" href="#NtA_268">[268]</a> John Craig (died in 1731)
+  was a Scotchman, but most of his life was spent at Cambridge reading and
+  writing on mathematics. He endeavored to introduce the Leibnitz
+  differential calculus into England. His mathematical works include the
+  <i>Methodus Figurarum ... Quadraturas determinandi</i> (1685),
+  <i>Tractatus ... de Figurarum Curvilinearum Quadraturis et locis
+  Geometricis</i> (1693), and <i>De Calculo Fluentium libri duo</i>
+  (1718).</p>
+
+  <p><a name="Nt_269" href="#NtA_269">[269]</a> As is well known, this
+  subject owes much to the Bernoullis. Craig's works on the calculus
+  brought him into controversy with them. He also wrote on other subjects
+  in which they were interested, as in his memoir <i>On the Curve of the
+  quickest descent</i> (1700), <i>On the Solid of least resistance</i>
+  (1700), and the <i>Solution of Bernoulli's problem on Curves</i>
+  (1704).</p>
+
+  <p><a name="Nt_270" href="#NtA_270">[270]</a> This is Samuel Lee
+  (1783-1852), the young prodigy in languages. He was apprenticed to a
+  carpenter at twelve and learned Greek while working at the trade. Before
+  he was twenty-five he knew Hebrew, Chaldee, Syriac, Samaritan, Persian,
+  and Hindustani. He later became Regius professor of Hebrew at
+  Cambridge.</p>
+
+  <p><a name="Nt_271" href="#NtA_271">[271]</a> "Where the devil, Master
+  Ludovico, did you pick up such a collection?"</p>
+
+  <p><a name="Nt_272" href="#NtA_272">[272]</a> Lord William Brounker (c.
+  1620-1684), the first president of the Royal Society, is best known in
+  mathematics for his contributions to continued fractions.</p>
+
+  <p><a name="Nt_273" href="#NtA_273">[273]</a> Horace Walpole (1717-1797)
+  published his <i>Catalogue of the Royal and Noble Authors of England</i>
+  in 1758. Since his time a number of worthy names in the domain of science
+  in general and of mathematics in particular might be added from the
+  peerage of England.</p>
+
+  <p><a name="Nt_274" href="#NtA_274">[274]</a> It was written by Charles
+  Hayes (1678-1760), a mathematician and scholar of no mean attainments. He
+  travelled extensively, and was deputy governor of the Royal African
+  Company. His <i>Treatise on Fluxions</i> (London, 1704) was the first
+  work in English to explain Newton's calculus. He wrote a work entitled
+  <i>The Moon</i> (1723) to prove that our satellite shines by its own as
+  well as by reflected light. His <i>Chronographia Asiatica &amp;
+  Aegyptica</i> (1758) gives the results of his travels.</p>
+
+  <p><a name="Nt_275" href="#NtA_275">[275]</a> <i>Publick</i> in the
+  original.</p>
+
+  <p><a name="Nt_276" href="#NtA_276">[276]</a> Whiston (1667-1752)
+  succeeded Newton as Lucasian professor of mathematics at Cambridge. In
+  1710 he turned Arian and was expelled from the university. His work on
+  <i>Primitive Christianity</i> appeared the following year. He wrote many
+  works on astronomy and religion.</p>
+
+  <p><a name="Nt_277" href="#NtA_277">[277]</a> Ditton (1675-1715) was, on
+  Newton's recommendation, made Head of the mathematical school at Christ's
+  Hospital, London. He wrote a work on fluxions (1706). His idea for
+  finding longitude at sea was to place stations in the Atlantic to fire
+  off bombs at regular intervals, the time between the sound and the flash
+  giving the distance. He also corresponded with Huyghens concerning the
+  use of chronometers for the purpose.</p>
+
+  <p><a name="Nt_278" href="#NtA_278">[278]</a> This was John Arbuthnot (c.
+  1658-1735), the mathematician, physician and wit. He was intimate with
+  Pope and Swift, and was Royal physician to Queen Anne. Besides various
+  satires he published a translation of Huyghens's work on probabilities
+  (1692) and a well-known treatise on ancient coins, weights, and measures
+  (1727).</p>
+
+  <p><a name="Nt_279" href="#NtA_279">[279]</a> Greene (1678-1730) was a
+  very eccentric individual and was generally ridiculed by his
+  contemporaries. In his will he directed that his body be dissected and
+  his skeleton hung in the library of King's College, Cambridge.
+  Unfortunately for his fame, this wish was never carried out.</p>
+
+  <p><a name="Nt_280" href="#NtA_280">[280]</a> This was the historian,
+  Robert Sanderson (1660-1741), who spent most of his life at
+  Cambridge.</p>
+
+  <p><a name="Nt_281" href="#NtA_281">[281]</a> I presume this was William
+  Jones (1675-1749) the friend of Newton and Halley, vice-president of the
+  Royal Society, in whose <i>Synopsis Palmariorum Matheseos</i> (1706) the
+  symbol <span class="grk">&pi;</span> is first used for the circle
+  ratio.</p>
+
+  <p><a name="Nt_282" href="#NtA_282">[282]</a> This was the <i>Geometrica
+  solidorum, sive materiae, seu de varia compositione, progressione,
+  rationeque velocitatum</i>, Cambridge, 1712. The work was parodied in
+  <i>A Taste of Philosophical Fanaticism ... by a gentleman of the
+  University of Gratz</i>.</p>
+
+  <p><a name="Nt_283" href="#NtA_283">[283]</a> The antiquary and scientist
+  (1690-1754), president of the Royal Society, member of the Académie,
+  friend of Newton, and authority on numismatics.</p>
+
+  <p><a name="Nt_284" href="#NtA_284">[284]</a> She was Catherine Barton,
+  Newton's step-niece. She married John Conduitt, master of the mint, who
+  collected materials for a life of Newton.</p>
+
+  <p><i>A propos</i> of Mrs. Conduitt's life of her illustrious uncle, Sir
+  George Greenhill tells a very good story on Poincaré, the well-known
+  French mathematician. At an address given by the latter at the
+  International Congress of Mathematicians held in Rome in 1908 he spoke of
+  the story of Newton and the apple as a mere fable. After the address Sir
+  George asked him why he had done so, saying that the story was first
+  published by Voltaire, who had heard it from Newton's niece, Mrs.
+  Conduitt. Poincaré looked blank and said, "Newton, et la nièce de Newton,
+  et Voltaire,&mdash;non! je ne vous comprends pas!" He had thought Sir
+  George meant Professor Volterra of Rome, whose name in French is
+  Voltaire, and who could not possibly have known a niece of Newton without
+  bridging a century or so.</p>
+
+  <p><a name="Nt_285" href="#NtA_285">[285]</a> This was the Edmund Turnor
+  (1755-1829) who wrote the <i>Collections for the Town and Soke of
+  Grantham, containing authentic Memoirs of Sir Isaac Newton, from Lord
+  Portsmouth's Manuscripts</i>, London, 1806.</p>
+
+  <p><a name="Nt_286" href="#NtA_286">[286]</a> It may be recalled to mind
+  that Sir David (1781-1868) wrote a life of Newton (1855).</p>
+
+  <p><a name="Nt_287" href="#NtA_287">[287]</a> "They are in the country.
+  We rejoice."</p>
+
+  <p><a name="Nt_288" href="#NtA_288">[288]</a> "I am here, chatterbox,
+  suck!"</p>
+
+  <p><a name="Nt_289" href="#NtA_289">[289]</a> "I have been graduated! I
+  decline!"</p>
+
+  <p><a name="Nt_290" href="#NtA_290">[290]</a> Giovanni Castiglioni
+  (Castillon, Castiglione), was born at Castiglione, in Tuscany, in 1708,
+  and died at Berlin in 1791. He was professor of mathematics at Utrecht
+  and at Berlin. He wrote on De Moivre's equations (1762), Cardan's rule
+  (1783), and Euclid's treatment of parallels (1788-89).</p>
+
+  <p><a name="Nt_291" href="#NtA_291">[291]</a> This was the <i>Isaaci
+  Newtoni, equitis aurati, opuscula mathematica, philosophica et
+  philologica</i>, Lausannae &amp; Genevae, 1744.</p>
+
+  <p><a name="Nt_292" href="#NtA_292">[292]</a> At London, 4to.</p>
+
+  <p><a name="Nt_293" href="#NtA_293">[293]</a> "All the English attribute
+  it to Newton."</p>
+
+  <p><a name="Nt_294" href="#NtA_294">[294]</a> Stephen Peter Rigaud
+  (1774-1839), Savilian professor of geometry at Oxford (1810-27) and later
+  professor of astronomy and head of the Radcliffe Observatory. He wrote
+  <i>An historical Essay on first publication of Sir Isaac Newton's
+  Principia</i>, Oxford, 1838, and a two-volume work entitled
+  <i>Correspondence of Scientific Men of the 17th Century</i>, 1841.</p>
+
+  <p><a name="Nt_295" href="#NtA_295">[295]</a> It is no longer considered
+  by scholars as the work of Newton.</p>
+
+  <p><a name="Nt_296" href="#NtA_296">[296]</a> J. Edleston, the author of
+  the <i>Correspondence of Sir Isaac Newton and Professor Cotes</i>,
+  London, 1850.</p>
+
+  <p><a name="Nt_297" href="#NtA_297">[297]</a> Palmer (1601-1647) was
+  Master of Queen's College, Cambridge, a Puritan but not a separatist. His
+  work, <i>The Characters of a believing Christian, in Paradoxes and
+  seeming contradictions</i>, appeared in 1645.</p>
+
+  <p><a name="Nt_298" href="#NtA_298">[298]</a> Grosart (1827-1899) was a
+  Presbyterian clergyman. He was a great bibliophile, and issued numerous
+  reprints of rare books.</p>
+
+  <p><a name="Nt_299" href="#NtA_299">[299]</a> This was the year after
+  Palmer's death. The title was, <i>The Remaines of ... Francis Lord
+  Verulam....; being Essays and severall Letters to severall great
+  personages, and other pieces of various and high concernment not
+  heretofore published</i>, London, 1648, 4to.</p>
+
+  <p><a name="Nt_300" href="#NtA_300">[300]</a> Shaw (1694-1763) was
+  physician extraordinary to George II. He wrote on chemistry and medicine,
+  and his edition of the <i>Philosophical Works of Francis Bacon</i>
+  appeared at London in 1733.</p>
+
+  <p><a name="Nt_301" href="#NtA_301">[301]</a> John Locke (1632-1704), the
+  philosopher. This particular work appeared in 1695. There was an edition
+  in 1834 (vol. 25 of the <i>Sacred Classics</i>) and one in 1836 (vol. 2
+  of the <i>Christian Library</i>).</p>
+
+  <p><a name="Nt_302" href="#NtA_302">[302]</a> I use the word
+  <i>Socinian</i> because it was so much used in Locke's time: it is used
+  in our own day by the small fry, the unlearned clergy and their immediate
+  followers, as a term of reproach for <i>all</i> Unitarians. I suspect
+  they have a kind of liking for the <i>word</i>; it sounds like <i>so
+  sinful</i>. The learned clergy and the higher laity know better: they
+  know that the bulk of the modern Unitarians go farther than Socinus, and
+  are not correctly named as his followers. The Unitarians themselves
+  neither desire nor deserve a name which puts them one point nearer to
+  orthodoxy than they put themselves. That point is the doctrine that
+  direct prayer to Jesus Christ is lawful and desirable: this Socinus held,
+  and the modern Unitarians do not hold. Socinus, in treating the subject
+  in his own <i>Institutio</i>, an imperfect catechism which he left, lays
+  much more stress on John xiv. 13 than on xv. 16 and xvi. 23. He is not
+  disinclined to think that <i>Patrem</i> should be in the first citation,
+  where some put it; but he says that to ask the Father in the name of the
+  Son is nothing but praying to the Son in prayer to the Father. He labors
+  the point with obvious wish to secure a conclusive sanction. In the
+  Racovian Catechism, of which Faustus Socinus probably drew the first
+  sketch, a clearer light is arrived at. The translation says: "But wherein
+  consists the divine honor due to Christ? In adoration likewise and
+  invocation. For we ought at all times to adore Christ, and may in our
+  necessities address our prayers to him as often as we please; and there
+  are many reasons to induce us to do this freely." There are some who like
+  accuracy, even in aspersion&mdash;A.&nbsp;De&nbsp;M.</p>
+
+  <p>Socinus, or Fausto Paolo Sozzini (1539-1604), was an antitrinitarian
+  who believed in prayer and homage to Christ. Leaving Italy after his
+  views became known, he repaired to Basel, but his opinions were too
+  extreme even for the Calvinists. He then tried Transylvania, attempting
+  to convert to his views the antitrinitarian Bishop Dávid. The only result
+  of his efforts was the imprisonment of Dávid and his own flight to
+  Poland, in which country he spent the rest of his life (1579-1604). His
+  complete works appeared first at Amsterdam in 1668, in the <i>Bibliotheca
+  Fratres Polonorum</i>. The <i>Racovian Catechism</i> (1605) appeared
+  after his death, but it seems to have been planned by him.</p>
+
+  <p><a name="Nt_303" href="#NtA_303">[303]</a> "As much of faith as is
+  necessary to salvation is contained in this article, Jesus is the
+  Christ."</p>
+
+  <p><a name="Nt_304" href="#NtA_304">[304]</a> Edwards (1637-1716) was a
+  Cambridge fellow, strongly Calvinistic. He published many theological
+  works, attacking the Arminians and Socinians. Locke and Whiston were
+  special objects of attack.</p>
+
+  <p><a name="Nt_305" href="#NtA_305">[305]</a> <i>Sir I. Newton's views on
+  points of Trinitarian Doctrine; his Articles of Faith, and the General
+  Coincidence of his Opinions with those of J. Locke; a Selection of
+  Authorities, with Observations</i>, London, 1856.</p>
+
+  <p><a name="Nt_306" href="#NtA_306">[306]</a> <i>A Confession of the
+  Faith</i>, Bristol, 1752, 8vo.</p>
+
+  <p><a name="Nt_307" href="#NtA_307">[307]</a> This was really very
+  strange, because Laud (1573-1644), while he was Archbishop of Canterbury,
+  forced a good deal of High Church ritual on the Puritan clergy, and even
+  wished to compel the use of a prayer book in Scotland. It was this
+  intolerance that led to his impeachment and execution.</p>
+
+  <p><a name="Nt_308" href="#NtA_308">[308]</a> The name is Jonchère. He
+  was a man of some merit, proposing (1718) an important canal in Burgundy,
+  and publishing a work on the <i>Découverte des longitudes estimées
+  généralement impossible à trouver</i>, 1734 (or 1735).</p>
+
+  <p><a name="Nt_309" href="#NtA_309">[309]</a> Locke invented a kind of an
+  instrument for finding longitude, and it is described in the appendix,
+  but I can find nothing about the man. There was published some years
+  later (London, 1751) another work of his, <i>A new Problem to discover
+  the longitude at sea</i>.</p>
+
+  <p><a name="Nt_310" href="#NtA_310">[310]</a> Baxter, concerning whom I
+  know merely that he was a schoolmaster, starts with the assumption of
+  this value, and deduces from it some fourteen properties relating to the
+  circle.</p>
+
+  <p><a name="Nt_311" href="#NtA_311">[311]</a> John, who died in 1780, was
+  a well-known character in his way. He was a bookseller on Fleet Street,
+  and his shop was a general rendezvous for the literary men of his time.
+  He wrote the <i>Memoirs of the Life and Writings of Mr. William
+  Whiston</i> (1749, with another edition in 1753). He was one of the first
+  to issue regular catalogues of books with prices affixed.</p>
+
+  <p><a name="Nt_312" href="#NtA_312">[312]</a> The name appears both as
+  Hulls and as Hull. He was born in Gloucestershire in 1699. In 1754 he
+  published <i>The Art of Measuring made Easy by the help of a new Sliding
+  Scale</i>.</p>
+
+  <p><a name="Nt_313" href="#NtA_313">[313]</a> Thomas Newcomen (1663-1729)
+  invented the first practical steam engine about 1710. It was of about
+  five and a half horse power, and was used for pumping water from coal
+  mines. Savery had described such an engine in 1702, but Newcomen improved
+  upon it and made it practical.</p>
+
+  <p><a name="Nt_314" href="#NtA_314">[314]</a> The well-known benefactor
+  of art (1787-1863).</p>
+
+  <p><a name="Nt_315" href="#NtA_315">[315]</a> The tract was again
+  reprinted in 1860.</p>
+
+  <p><a name="Nt_316" href="#NtA_316">[316]</a> Hulls made his experiment
+  on the Avon, at Evesham, in 1737, having patented his machine in 1736. He
+  had a Newcomen engine connected with six paddles. This was placed in the
+  front of a small tow boat. The experiment was a failure.</p>
+
+  <p><a name="Nt_317" href="#NtA_317">[317]</a> William Symington
+  (1763-1831). In 1786 he <span class="correction" title="text reads `contructed'"
+  >constructed</span> a working model of a steam road carriage. The
+  machinery was applied to a small boat in 1788, and with such success as
+  to be tried on a larger boat in 1789. The machinery was clumsy, however,
+  and in 1801 he took out a new patent for the style of engine still used
+  on paddle wheel steamers. This engine was successfully used in 1802, on
+  the Charlotte Dundas. Fulton (1765-1815) was on board, and so impressed
+  Robert Livingston with the idea that the latter furnished the money to
+  build the Clermont (1807), the beginning of successful river
+  navigation.</p>
+
+  <p><a name="Nt_318" href="#NtA_318">[318]</a> Louis Bertrand Castel
+  (1688-1757), most of whose life was spent in trying to perfect his
+  <i>Clavecin oculaire</i>, an instrument on the order of the harpsichord,
+  intended to produce melodies and harmonies of color. He also wrote
+  <i>L'Optique des couleurs</i> (1740) and <i>Sur le fond de la Musique</i>
+  (1754).</p>
+
+  <p><a name="Nt_319" href="#NtA_319">[319]</a> Dr. Robinson (1680-1754)
+  was professor of physic at Trinity College, Dublin, and three times
+  president of King and Queen's College of Physicians. In his <i>Treatise
+  on the Animal Economy</i> (1732-3, with a third edition in 1738) he
+  anticipated the discoveries of Lavoisier and Priestley on the nature of
+  oxygen.</p>
+
+  <p><a name="Nt_320" href="#NtA_320">[320]</a> There was another edition,
+  published at London in 1747, 8vo.</p>
+
+  <p><a name="Nt_321" href="#NtA_321">[321]</a> The author seems to have
+  shot his only bolt in this work. I can find nothing about him.</p>
+
+  <p><a name="Nt_322" href="#NtA_322">[322]</a> <i>Quod Deus sit, mundusque
+  ab ipso creatus fuerit in tempore, ejusque providentia gubernetur.
+  Selecta aliquot theoremata adversos atheos</i>, etc., Paris, 1635,
+  4to.</p>
+
+  <p><a name="Nt_323" href="#NtA_323">[323]</a> The British Museum
+  Catalogue mentions a copy of 1740, but this is possibly a misprint.</p>
+
+  <p><a name="Nt_324" href="#NtA_324">[324]</a> This was Johann II
+  (1710-1790), son of Johann I, who succeeded his father as professor of
+  mathematics at Basel.</p>
+
+  <p><a name="Nt_325" href="#NtA_325">[325]</a> Samuel Koenig (1712-1757),
+  who studied under Johann Bernoulli I. He became professor of mathematics
+  at Franeker (1747) and professor of philosophy at the Hague (1749).</p>
+
+  <p><a name="Nt_326" href="#NtA_326">[326]</a> "In accordance with the
+  hypotheses laid down in this memoir it is so evident that <i>t</i> must =
+  34, <i>y</i> = 1, and <i>z</i> = 1, that there is no need of proof or
+  authority for it to be recognized by every one."</p>
+
+  <p><a name="Nt_327" href="#NtA_327">[327]</a> "I subscribe to the
+  judgment of Mr. Bernoulli as a result of these hypotheses."</p>
+
+  <p><a name="Nt_328" href="#NtA_328">[328]</a> "It clearly appears from my
+  present analysis and demonstration that they have already recognized and
+  perfectly agreed to the fact that the quadrature of the circle is
+  mathematically demonstrated."</p>
+
+  <p><a name="Nt_329" href="#NtA_329">[329]</a> Dr. Knight (died in 1772)
+  made some worthy contributions to the literature of the mariner's
+  compass. As De Morgan states, he was librarian of the British Museum.</p>
+
+  <p><a name="Nt_330" href="#NtA_330">[330]</a> Sir Anthony Panizzi
+  (1797-1879) fled from Italy under sentence of death (1822). He became
+  assistant (1831) and chief (1856) librarian of the British Museum, and
+  was knighted in 1869. He began the catalogue of printed books of the
+  Museum.</p>
+
+  <p><a name="Nt_331" href="#NtA_331">[331]</a> Wright (1711-1786) was a
+  physicist. He was offered the professorship of mathematics at the
+  Imperial Academy of St. Petersburg but declined to accept it. This work
+  is devoted chiefly to the theory of the Milky Way, the <i>via lactea</i>
+  as he calls it after the manner of the older writers.</p>
+
+  <p><a name="Nt_332" href="#NtA_332">[332]</a> Troughton (1753-1835) was
+  one of the world's greatest instrument makers. He was apprenticed to his
+  brother John, and the two succeeded (1770) Wright and Cole in Fleet
+  Street. Airy called his method of graduating circles the greatest
+  improvement ever made in instrument making. He constructed (1800) the
+  first modern transit circle, and his instruments were used in many of the
+  chief observatories of the world.</p>
+
+  <p><a name="Nt_333" href="#NtA_333">[333]</a> William Simms (1793-1860)
+  was taken into partnership by Troughton (1826) after the death of the
+  latter's brother. The firm manufactured some well-known instruments.</p>
+
+  <p><a name="Nt_334" href="#NtA_334">[334]</a> This was George Horne
+  (1730-1792), fellow of Magdalen College, Oxford, vice-Chancellor of the
+  University (1776), Dean of Canterbury (1781), and Bishop of Norwich
+  (1790). He was a great satirist, but most of his pamphlets against men
+  like Adam Smith, Swedenborg, and Hume, were anonymous, as in the case of
+  this one against Newton. He was so liberal in his attitude towards the
+  Methodists that he would not have John Wesley forbidden to preach in his
+  diocese. He was twenty-one when this tract appeared.</p>
+
+  <p><a name="Nt_335" href="#NtA_335">[335]</a> Martin (1704-1782) was by
+  no means "old Benjamin Martin" when Horne wrote this pamphlet in 1749. In
+  fact he was then only forty-five. He was a physicist and a well-known
+  writer on scientific instruments. He also wrote <i>Philosophia Britannica
+  or a new and comprehensive system of the Newtonian Philosophy</i>
+  (1759).</p>
+
+  <p><a name="Nt_336" href="#NtA_336">[336]</a> Jean Théophile Desaguliers,
+  or Des Aguliers (1683-1744) was the son of a Protestant who left France
+  after the revocation of the Edict of Nantes. He became professor of
+  physics at Oxford, and afterwards gave lectures in London. Later he
+  became chaplain to the Prince of Wales. He published several works on
+  physics.</p>
+
+  <p><a name="Nt_337" href="#NtA_337">[337]</a> Charles Hutton (1737-1823),
+  professor of mathematics at Woolwich (1772-1807). His <i>Mathematical
+  Tables</i> (1785) and <i>Mathematical and Philosophical Dictionary</i>
+  (1795-1796) are well known.</p>
+
+  <p><a name="Nt_338" href="#NtA_338">[338]</a> James Epps (1773-1839)
+  contributed a number of memoirs on the use and corrections of
+  instruments. He was assistant secretary of the Astronomical Society.</p>
+
+  <p><a name="Nt_339" href="#NtA_339">[339]</a> John Hutchinson (1674-1737)
+  was one of the first to try to reconcile the new science of geology with
+  Genesis. He denied the Newtonian hypothesis as dangerous to religion, and
+  because it necessitated a vacuum. He was a mystic in his interpretation
+  of the Scriptures, and created a sect that went under the name of
+  Hutchinsonians.</p>
+
+  <p><a name="Nt_340" href="#NtA_340">[340]</a> John Rowning, a
+  Lincolnshire rector, died in 1771. He wrote on physics, and published a
+  memoir on <i>A machine for finding the roots of equations universally</i>
+  (1770).</p>
+
+  <p><a name="Nt_341" href="#NtA_341">[341]</a> It is always difficult to
+  sanction this spelling of the name of this Jesuit father who is so often
+  mentioned in the analytic treatment of conics. He was born in Ragusa in
+  1711, and the original spelling was Ru&#x111;er Josip
+  Bo&#x161;kovi&#x107;. When he went to live in Italy, as professor of
+  mathematics at Rome (1740) and at Pavia, the name was spelled Ruggiero
+  Giuseppe Boscovich, although Boscovicci would seem to a foreigner more
+  natural. His astronomical work was notable, and in his <i>De maculis
+  solaribus</i> (1736) there is the first determination of the equator of a
+  planet by observing the motion of spots on its surface. Boscovich came
+  near having some contact with America, for he was delegated to observe in
+  California the transit of Venus in 1755, being prevented by the
+  dissolution of his order just at that time. He died in 1787, at
+  Milan.</p>
+
+  <p><a name="Nt_342" href="#NtA_342">[342]</a> James Granger (1723-1776)
+  who wrote the <i>Biographical History of England</i>, London, 1769. His
+  collection of prints was remarkable, numbering some fourteen
+  thousand.</p>
+
+  <p><a name="Nt_343" href="#NtA_343">[343]</a> He was curator of
+  experiments for the Royal Society. He wrote a large number of books and
+  monographs on physics. He died about 1713.</p>
+
+  <p><a name="Nt_344" href="#NtA_344">[344]</a> Lee seems to have made no
+  impression on biographers.</p>
+
+  <p><a name="Nt_345" href="#NtA_345">[345]</a> This work appeared at
+  London in 1852.</p>
+
+  <p><a name="Nt_346" href="#NtA_346">[346]</a> Of course this is no longer
+  true. The most scholarly work to-day is that of Rudio, <i>Archimedes,
+  Huygens, Lambert, Legendre, vier Abhandlungen über die Kreismessung ...
+  mit einer Uebersicht über die Geschichte des Problems von der Quadratur
+  des Zirkels, von den ältesten Zeiten bis auf unsere Tage</i>, Leipsic,
+  1892.</p>
+
+  <p><a name="Nt_347" href="#NtA_347">[347]</a> Joseph Jérome le François
+  de Lalande (1732-1807), professor of astronomy in the Collège de France
+  (1753) and director of the Paris Observatory (1761). His writings on
+  astronomy and his <i>Bibliographie astronomique, avec l'histoire de
+  l'astronomie depuis 1781 jusqu'en 1802</i> (Paris, 1803) are well
+  known.</p>
+
+  <p><a name="Nt_348" href="#NtA_348">[348]</a> De Morgan refers to his
+  <i>Histoire de l'Astronomie au 18e siècle</i>, which appeared in 1827,
+  five years after Delambre's death. Jean Baptiste Joseph Delambre
+  (1749-1822) was a pupil of and a collaborator with Lalande, following his
+  master as professor of astronomy in the Collège de France. His work on
+  the measurements for the metric system is well known, and his four
+  histories of astronomy, <i>ancienne</i> (1817), <i>au moyen âge</i>
+  (1819), <i>moderne</i> (1821), and <i>au 18e siècle</i> (posthumous,
+  1827) are highly esteemed.</p>
+
+  <p><a name="Nt_349" href="#NtA_349">[349]</a> Jean-Joseph Rive
+  (1730-1792), a priest who left his cure under grave charges, and a
+  quarrelsome character. His attack on Montucla was a case of the pot
+  calling the kettle black; for while he was a brilliant writer he was a
+  careless bibliographer.</p>
+
+  <p><a name="Nt_350" href="#NtA_350">[350]</a> Isaac Barrow (1630-1677)
+  was quite as well known as a theologian as he was from his Lucasian
+  professorship of mathematics at Cambridge.</p>
+
+  <p><a name="Nt_351" href="#NtA_351">[351]</a> "Besides we can see by this
+  that Barrow was a poor philosopher; for he believed in the immortality of
+  the soul and in a Divinity other than universal nature."</p>
+
+  <p><a name="Nt_352" href="#NtA_352">[352]</a> The <i>Récréations
+  mathématiques et physiques</i> (Paris, 1694) of Jacques Ozanam
+  (1640-1717) is a work that is still highly esteemed. Among various other
+  works he wrote a <i>Dictionnaire mathématique ou Idée générale des
+  mathématiques</i> (1690) that was not without merit. The
+  <i>Récréations</i> went through numerous editions (Paris, 1694, 1696,
+  1741, 1750, 1770, 1778, and the Montucla edition of 1790; London, 1708,
+  the Montucla-Hutton edition of 1803 and the Riddle edition of 1840;
+  Dublin, 1790).</p>
+
+  <p><a name="Nt_353" href="#NtA_353">[353]</a> Hendryk van Etten, the
+  <i>nom de plume</i> of Jean Leurechon (1591-1670), rector of the Jesuit
+  college at Bar, and professor of philosophy and mathematics. He wrote on
+  astronomy (1619) and horology (1616), and is known for his <i>Selecta
+  Propositiones in tota sparsim mathematica pulcherrime propositae in
+  solemni festo SS. Ignatii et Francesci Xaverii</i>, 1622. The book to
+  which De Morgan refers is his <i>Récréation mathématicque, composée de
+  plusieurs problèmes plaisants et facetieux</i>, Lyons, 1627, with an
+  edition at Pont-à-Mousson, 1629. There were English editions published at
+  London in 1633, 1653, and 1674, and Dutch editions in 1662 and 1672.</p>
+
+  <p>I do not understand how De Morgan happened to miss owning the work by
+  Claude Gaspar Bachet de Meziriac (1581-1638), <i>Problèmes plaisans et
+  délectables</i>, which appeared at Lyons in 1612, 8vo, with a second
+  edition in 1624. There was a fifth edition published at Paris in
+  1884.</p>
+
+  <p><a name="Nt_354" href="#NtA_354">[354]</a> His title page closes with
+  "Paris, Chez Ch. Ant. Jombert.... M DCC LIV."</p>
+
+  <p>This was Charles-Antoine Jombert (1712-1784), a printer and bookseller
+  with some taste for painting and architecture. He wrote several works and
+  edited a number of early treatises.</p>
+
+  <p><a name="Nt_355" href="#NtA_355">[355]</a> The late Professor Newcomb
+  made the matter plain even to the non-mathematical mind, when he said
+  that "ten decimal places are sufficient to give the circumference of the
+  earth to the fraction of an inch, and thirty decimal places would give
+  the circumference of the whole visible universe to a quantity
+  imperceptible with the most powerful microscope."</p>
+
+  <p><a name="Nt_356" href="#NtA_356">[356]</a> <i>Antinewtonianismi pars
+  prima, in qua Newtoni de coloribus systema ex propriis principiis
+  geometrice evertitur, et nova de coloribus theoria luculentissimis
+  experimentis demonstrantur</i>.... Naples, 1754; <i>pars secunda</i>,
+  Naples, 1756.</p>
+
+  <p><a name="Nt_357" href="#NtA_357">[357]</a> Celestino Cominale
+  (1722-1785) was professor of medicine at the University of Naples.</p>
+
+  <p><a name="Nt_358" href="#NtA_358">[358]</a> The work appeared in the
+  years from 1844 to 1849.</p>
+
+  <p><a name="Nt_359" href="#NtA_359">[359]</a> There was a Vienna edition
+  in 1758, 4to, and another in 1759, 4to. This edition is described on the
+  title page as <i>Editio Veneta prima ipso auctore praesente, et
+  corrigente</i>.</p>
+
+  <p><a name="Nt_360" href="#NtA_360">[360]</a> The first edition was
+  entitled <i>De solis ac lunae defectibus libri V.&nbsp;P. Rogerii Josephi
+  Boscovich ... cum ejusdem auctoris adnotationibus</i>, London, 1760. It
+  also appeared in Venice in 1761, and in French translation by the Abbé de
+  Baruel in 1779, and was a work of considerable influence.</p>
+
+  <p><a name="Nt_361" href="#NtA_361">[361]</a> Paulian (1722-1802) was
+  professor of physics at the Jesuit college at Avignon. He wrote several
+  works, the most popular of which, the <i>Dictionnaire de physique</i>
+  (Avignon, 1761), went through nine editions by 1789.</p>
+
+  <p><a name="Nt_362" href="#NtA_362">[362]</a> This is correct.</p>
+
+  <p><a name="Nt_363" href="#NtA_363">[363]</a> Probably referring to the
+  fact that Hill (1795-1879), who had done so much for postal reform, was
+  secretary to the postmaster general (1846), and his name was a synonym
+  for the post office directory.</p>
+
+  <p><a name="Nt_364" href="#NtA_364">[364]</a> Richard Lovett (1692-1780)
+  was a good deal of a charlatan. He claimed to have studied electrical
+  phenomena, and in 1758 advertised that he could effect marvelous cures,
+  especially of sore throat, by means of electricity. Before publishing the
+  works mentioned by De Morgan he had issued others of similar character,
+  including <i>The Subtile Medium proved</i> (London, 1756) and <i>The
+  Reviewers Reviewed</i> (London, 1760).</p>
+
+  <p><a name="Nt_365" href="#NtA_365">[365]</a> Jean Sylvain Bailly
+  (1736-1793), member of the <i>Académie française</i> and of the
+  <i>Académie des sciences</i>, first deputy elected to represent Paris in
+  the <i>Etats-généraux</i> (1789), president of the first National
+  Assembly, and mayor of Paris (1789-1791). For his vigor as mayor in
+  keeping the peace, and for his manly defence of the Queen, he was
+  guillotined. He was an astronomer of ability, but is best known for his
+  histories of the science.</p>
+
+  <p><a name="Nt_366" href="#NtA_366">[366]</a> These were the <i>Histoire
+  de l'Astronomie ancienne</i> (1775), <i>Histoire de l'Astronomie
+  moderne</i> (1778-1783), <i>Histoire de l'Astronomie indienne et
+  orientale</i> (1787), and <i>Lettres sur l'origine des peuples de
+  l'Asie</i> (1775).</p>
+
+  <p><a name="Nt_367" href="#NtA_367">[367]</a> "The sick old man of
+  Ferney, V., a boy of a hundred years." Voltaire was born in 1694, and
+  hence was eighty-three at this time.</p>
+
+  <p><a name="Nt_368" href="#NtA_368">[368]</a> In Palmézeaux's <i>Vie de
+  Bailly</i>, in Bailly's <i>Ouvrage Posthume</i> (1810), M. de Sales is
+  quoted as saying that the <i>Lettres sur l'Atlantide</i> were sent to
+  Voltaire and that the latter did not approve of the theory set forth.</p>
+
+  <p><a name="Nt_369" href="#NtA_369">[369]</a> The British Museum
+  catalogue gives two editions, 1781 and 1782.</p>
+
+  <p><a name="Nt_370" href="#NtA_370">[370]</a> A mystic and a
+  spiritualist. His chief work was the one mentioned here.</p>
+
+  <p><a name="Nt_371" href="#NtA_371">[371]</a> Jacob Behmen, or Böhme
+  (1575-1624), known as "the German theosophist," was founder of the sect
+  of Boehmists, a cult allied to the Swedenborgians. He was given to the
+  study of alchemy, and brought the vocabulary of the science into his
+  mystic writings. His sect was revived in England in the eighteenth
+  century through the efforts of William Law. Saint-Martin translated into
+  French two of his Latin works under the titles <i>L'Aurore naissante, ou
+  la Racine de la philosophie</i> (1800), and <i>Les trois principes de
+  l'essence divine</i> (1802). The originals had appeared nearly two
+  hundred years earlier,&mdash;<i>Aurora</i> in 1612, and <i>De tribus
+  principiis</i> in 1619.</p>
+
+  <p><a name="Nt_372" href="#NtA_372">[372]</a> "Unknown."</p>
+
+  <p><a name="Nt_373" href="#NtA_373">[373]</a> "Skeptical."</p>
+
+  <p><a name="Nt_374" href="#NtA_374">[374]</a> "Man, man, man."</p>
+
+  <p><a name="Nt_375" href="#NtA_375">[375]</a> "Men, men, men."</p>
+
+  <p><a name="Nt_376" href="#NtA_376">[376]</a> It is interesting to read
+  De Morgan's argument against Saint-Martin's authorship of this work. It
+  is attributed to Saint-Martin both by the <i>Biographie Universelle</i>
+  and by the <i>British Museum Catalogue</i>, and De Morgan says by
+  "various catalogues and biographies."</p>
+
+  <p><a name="Nt_377" href="#NtA_377">[377]</a> "To explain things by man
+  and not man by things. <i>On Errors and Truth</i>, by a Ph....
+  Inc...."</p>
+
+  <p><a name="Nt_378" href="#NtA_378">[378]</a> "If we would preserve
+  ourselves from all illusions, and above all from the allurements of
+  pride, by which man is so often seduced, we should never take man, but
+  always God, for our term of comparison."</p>
+
+  <p><a name="Nt_379" href="#NtA_379">[379]</a> "And here is found already
+  an explanation of the numbers four and nine which caused some perplexity
+  in the work cited above. Man is lost in passing from four to nine."</p>
+
+  <p><a name="Nt_380" href="#NtA_380">[380]</a> Williams also took part in
+  the preparation of some tables for the government to assist in the
+  determination of longitude. He had published a work two years before the
+  one here cited, on the same subject,&mdash;<i>An entire new work and
+  method to discover the variation of the Earth's <span class="correction"
+  title="text reads `Diaameters'">Diameters</span></i>, London, 1786.</p>
+
+  <p><a name="Nt_381" href="#NtA_381">[381]</a> This is Gabriel Mouton
+  (1618-1694), a vicar at Lyons, who suggested as a basis for a natural
+  system of measures the <i>mille</i>, a minute of a degree of the
+  meridian. This appeared in his <i>Observationes diametrorum solis et
+  lunae apparentium, meridianarumque aliquot altitudinum cum tabula
+  declinationum solis</i>.... Lyons, 1670.</p>
+
+  <p><a name="Nt_382" href="#NtA_382">[382]</a> Jacques Cassini
+  (1677-1756), one of the celebrated Cassini family of astronomers. After
+  the death of his father he became director of the observatory at Paris.
+  The basis for a metric unit was set forth by him in his <i>Traité de la
+  grandeur et de la figure de la terre</i>, Paris, 1720. He was a prolific
+  writer on astronomy.</p>
+
+  <p><a name="Nt_383" href="#NtA_383">[383]</a> Alexis Jean Pierre Paucton
+  (1732-1798). He was, for a time, professor of mathematics at Strassburg,
+  but later (1796) held office in Paris. His leading contribution to
+  metrology was his <i>Métrologie ou Traité des mesures</i>, Paris,
+  1780.</p>
+
+  <p><a name="Nt_384" href="#NtA_384">[384]</a> He was an obscure writer,
+  born at Deptford.</p>
+
+  <p><a name="Nt_385" href="#NtA_385">[385]</a> He was also a writer of no
+  scientific merit, his chief contributions being religious tracts. One of
+  his productions, however, went through many editions, even being
+  translated into French; <i>Three dialogues between a Minister and one of
+  his Parishioners; on the true principles of Religion and salvation for
+  sinners by Jesus Christ</i>. The twentieth edition appeared at Cambridge
+  in 1786.</p>
+
+  <p><a name="Nt_386" href="#NtA_386">[386]</a> This was the <i>Reflections
+  on the Revolution in France, and on the proceedings in certain societies
+  in London relative to that event</i> (London, 1790) by Edmund Burke
+  (1729-1797). Eleven editions of the work appeared the first year.</p>
+
+  <p><a name="Nt_387" href="#NtA_387">[387]</a> Paine (1736-1809) was born
+  in Norfolkshire, of Quaker parents. He went to America at the beginning
+  of the Revolution and published, in January 1776, a violent pamphlet
+  entitled <i>Common Sense</i>. He was a private soldier under Washington,
+  and on his return to England after the war he published <i>The Rights of
+  Man</i>. He was indicted for treason and was outlawed to France. He was
+  elected to represent Calais at the French convention, but his plea for
+  moderation led him perilously near the guillotine. His <i>Age of
+  Reason</i> (1794) was dedicated to Washington. He returned to America in
+  1802 and remained there until his death.</p>
+
+  <p><a name="Nt_388" href="#NtA_388">[388]</a> Part I appeared in 1791 and
+  was so popular that eight editions appeared in that year. It was followed
+  in 1792 by Part II, of which nine editions appeared in that year. Both
+  parts were immediately republished in Paris, and there have been several
+  subsequent editions.</p>
+
+  <p><a name="Nt_389" href="#NtA_389">[389]</a> Mary Wollstonecraft
+  (1759-1797) was only thirty-three when this work came out. She had
+  already published <i>An historical and moral View of the Origin and
+  Progress of the French Revolution</i> (1790), and <i>Original Stories
+  from Real Life</i> (1791). She went to Paris in 1792 and remained during
+  the Reign of Terror.</p>
+
+  <p><a name="Nt_390" href="#NtA_390">[390]</a> Samuel Parr (1747-1827) was
+  for a time head assistant at Harrow (1767-1771), afterwards headmaster in
+  other schools. At the time this book was written he was vicar of Hatton,
+  where he took private pupils (1785-1798) to the strictly limited number
+  of seven. He was a violent Whig and a caustic writer.</p>
+
+  <p><a name="Nt_391" href="#NtA_391">[391]</a> On Mary Wollstonecraft's
+  return from France she married (1797) William Godwin (1756-1836). He had
+  started as a strong Calvinistic Nonconformist minister, but had become
+  what would now be called an anarchist, at least by conservatives. He had
+  written an <i>Inquiry concerning Political Justice</i> (1793) and a novel
+  entitled <i>Caleb Williams, or Things as they are</i> (1794), both of
+  which were of a nature to attract his future wife.</p>
+
+  <p><a name="Nt_392" href="#NtA_392">[392]</a> This child was a daughter.
+  She became Shelley's wife, and Godwin's influence on Shelley was very
+  marked.</p>
+
+  <p><a name="Nt_393" href="#NtA_393">[393]</a> This was John Nichols
+  (1745-1826), the publisher and antiquary. He edited the <i>Gentleman's
+  Magazine</i> (1792-1826) and his works include the <i>Literary Anecdotes
+  of the Eighteenth Century</i> (1812-1815), to which De Morgan here
+  refers.</p>
+
+  <p><a name="Nt_394" href="#NtA_394">[394]</a> William Bellenden, a Scotch
+  professor at the University of Paris, who died about 1633. His textbooks
+  are now forgotten, but Parr edited an edition of his works in 1787. The
+  Latin preface, <i>Praefatio ad Bellendum de Statu</i>, was addressed to
+  Burke, North, and Fox, and was a satire on their political opponents.</p>
+
+  <p><a name="Nt_395" href="#NtA_395">[395]</a> As we have seen, he had
+  been head-master before he began taking "his handful of private
+  pupils."</p>
+
+  <p><a name="Nt_396" href="#NtA_396">[396]</a> The story has evidently got
+  mixed up in the telling, for Tom Sheridan (1721-1788), the great actor,
+  was old enough to have been Dr. Parr's father. It was his son, Richard
+  Brinsley Sheridan (1751-1816), the dramatist and politician, who was the
+  pupil of Parr. He wrote <i>The Rivals</i> (1775) and <i>The School for
+  Scandal</i> (1777) soon after Parr left Harrow.</p>
+
+  <p><a name="Nt_397" href="#NtA_397">[397]</a> Horner (1785-1864) was a
+  geologist and social reformer. He was very influential in improving the
+  conditions of child labor.</p>
+
+  <p><a name="Nt_398" href="#NtA_398">[398]</a> William Cobbett
+  (1762-1835), the journalist, was a character not without interest to
+  Americans. Born in Surrey, he went to America at the age of thirty and
+  remained there eight years. Most of this time he was occupied as a
+  bookseller in Philadelphia, and while thus engaged he was fined for libel
+  against the celebrated Dr. Rush. On his return to England he edited the
+  <i>Weekly Political Register</i> (1802-1835), a popular journal among the
+  working classes. He was fined and imprisoned for two years because of his
+  attack (1810) on military flogging, and was also (1831) prosecuted for
+  sedition. He further showed his paradox nature by his <i>History of the
+  Protestant Reformation</i> (1824-1827), an attack on the prevailing
+  Protestant opinion. He also wrote a <i>Life of Andrew Jackson</i> (1834).
+  After repeated attempts he succeeded in entering parliament, a result of
+  the Reform Bill.</p>
+
+  <p><a name="Nt_399" href="#NtA_399">[399]</a> Robinson (1735-1790) was a
+  Baptist minister who wrote several theological works and a number of
+  hymns. His work at Cambridge so offended the students that they at one
+  time broke up the services.</p>
+
+  <p><a name="Nt_400" href="#NtA_400">[400]</a> This work had passed
+  through twelve editions by 1823.</p>
+
+  <p><a name="Nt_401" href="#NtA_401">[401]</a> Dyer (1755-1841), the poet
+  and reformer, edited Robinson's <i>Ecclesiastical Researches</i> (1790).
+  He was a life-long friend of Charles Lamb, and in their boyhood they were
+  schoolmates at Christ's Hospital. His <i>Complaints of the Poor People of
+  England</i> (1793) made him a worthy companion of the paradoxers above
+  mentioned.</p>
+
+  <p><a name="Nt_402" href="#NtA_402">[402]</a> These were John Thelwall
+  (1764-1834) whose <i>Politics for the People or Hogswash</i> (1794) took
+  its title from the fact that Burke called the people the "swinish
+  multitude." The book resulted in sending the author to the Tower for
+  sedition. In 1798 he gave up politics and started a school of elocution
+  which became very famous. Thomas Hardy (1752-1832), who kept a
+  bootmaker's shop in Piccadilly, was a fellow prisoner with Thelwall,
+  being arrested for high treason. He was founder (1792) of The London
+  Corresponding Society, a kind of clearing house for radical associations
+  throughout the country. Horne Tooke was really John Horne (1736-1812), he
+  having taken the name of his friend William Tooke in 1782. He was a
+  radical of the radicals, and organized a number of reform societies.
+  Among these was the Constitutional Society that voted money (1775) to
+  assist the American revolutionists, appointing him to give the
+  contribution to Franklin. For this he was imprisoned for a year. With his
+  fellow rebels in the Tower in 1794, however, he was acquitted. As a
+  philologist he is known for his early advocacy of the study of
+  Anglo-Saxon and Gothic, and his <i>Diversions of Purley</i> (1786) is
+  still known to readers.</p>
+
+  <p><a name="Nt_403" href="#NtA_403">[403]</a> This was the admiral, Adam
+  Viscount Duncan (1731-1804), who defeated the Dutch off Camperdown in
+  1797.</p>
+
+  <p><a name="Nt_404" href="#NtA_404">[404]</a> He was created Duke of
+  Clarence and St. Andrews in 1789 and was Admiral of the Fleet escorting
+  Louis XVIII on his return to France in 1814. He became Lord High Admiral
+  in 1827, and reigned as William IV from 1830 to 1837.</p>
+
+  <p><a name="Nt_405" href="#NtA_405">[405]</a> This was Charles Abbott
+  (1762-1832) first Lord Tenterden. He succeeded Lord Ellenborough as Chief
+  Justice (1818) and was raised to the peerage in 1827. He was a strong
+  Tory and opposed the Catholic Relief Bill, the Reform Bill, and the
+  abolition of the death penalty for forgery. </p>
+
+  <p><a name="Nt_406" href="#NtA_406">[406]</a> Edward Law (1750-1818),
+  first Baron Ellenborough. He was chief counsel for Warren Hastings, and
+  his famous speech in defense of his client is well known. He became Chief
+  Justice and was raised to the peerage in 1802. He opposed all efforts to
+  modernize the criminal code, insisting upon the reactionary principle of
+  new death penalties. </p>
+
+  <p><a name="Nt_407" href="#NtA_407">[407]</a> Edmund Law (1703-1787),
+  Bishop of Carlisle (1768), was a good deal more liberal than his son. His
+  <i>Considerations on the Propriety of requiring subscription to the
+  Articles of Faith</i> (1774) was published anonymously. In it he asserts
+  that not even the clergy should be required to subscribe to the
+  thirty-nine articles.</p>
+
+  <p><a name="Nt_408" href="#NtA_408">[408]</a> Joe Miller (1684-1738), the
+  famous Drury Lane comedian, was so illiterate that he could not have
+  written the <i>Joe Miller's Jests, or the Wit's Vade-Mecum</i> that
+  appeared the year after his death. It was often reprinted and probably
+  contained more or less of Miller's own jokes.</p>
+
+  <p><a name="Nt_409" href="#NtA_409">[409]</a> The sixth duke (1766-1839)
+  was much interested in parliamentary reform. He was a member of the
+  Society of Friends of the People. He was for fourteen years a member of
+  parliament (1788-1802) and was later Lord Lieutenant of Ireland
+  (1806-1807). He afterwards gave up politics and became interested in
+  agricultural matters.</p>
+
+  <p><a name="Nt_410" href="#NtA_410">[410]</a> George Jeffreys (c.
+  1648-1689), the favorite of James II, who was active in prosecuting the
+  Rye House conspirators. He was raised to the peerage in 1684 and held the
+  famous "bloody assize" in the following year, being made Lord Chancellor
+  as a result. He was imprisoned in the Tower by William III and died
+  there.</p>
+
+  <p><a name="Nt_411" href="#NtA_411">[411]</a> <i>The Every Day Book,
+  forming a Complete History of the Year, Months, and Seasons, and a
+  perpetual Key to the Almanack</i>, 1826-1827.</p>
+
+  <p><a name="Nt_412" href="#NtA_412">[412]</a> The first and second
+  editions appeared in 1820. Two others followed in 1821.</p>
+
+  <p><a name="Nt_413" href="#NtA_413">[413]</a> <i>The three trials of W.
+  H., for publishing three parodies; viz the late John Wilkes' Catechism,
+  the Political Litany, and the Sinecurists Creed; on three ex-officio
+  informations, at Guildhall, London, ... Dec. 18, 19, &amp; 20,
+  1817</i>,... London, 1818.</p>
+
+  <p><a name="Nt_414" href="#NtA_414">[414]</a> The <i>Political Litany</i>
+  appeared in 1817.</p>
+
+  <p><a name="Nt_415" href="#NtA_415">[415]</a> That is, Castlereagh's.</p>
+
+  <p><a name="Nt_416" href="#NtA_416">[416]</a> The well-known caricaturist
+  (1792-1878), then only twenty-nine years old.</p>
+
+  <p><a name="Nt_417" href="#NtA_417">[417]</a> Robert Stewart (1769-1822)
+  was second Marquis of Londonderry and Viscount Castlereagh. As Chief
+  Secretary for Ireland he was largely instrumental in bringing about the
+  union of Ireland and Great Britain. He was at the head of the war
+  department during most of the Napoleonic wars, and was to a great extent
+  responsible for the European coalition against the Emperor. He suicided
+  in 1822.</p>
+
+  <p><a name="Nt_418" href="#NtA_418">[418]</a> John Murray (1778-1843),
+  the well-known London publisher. He refused to finish the publication of
+  Don Juan, after the first five cantos, because of his Tory
+  principles.</p>
+
+  <p><a name="Nt_419" href="#NtA_419">[419]</a> Only the first two cantos
+  appeared in 1819.</p>
+
+  <p><a name="Nt_420" href="#NtA_420">[420]</a> Proclus (412-485), one of
+  the greatest of the neo-Platonists, studied at Alexandria and taught
+  philosophy at Athens. He left commentaries on Plato and on part of
+  Euclid's <i>Elements</i>.</p>
+
+  <p><a name="Nt_421" href="#NtA_421">[421]</a> Thomas Taylor (1758-1835),
+  called "the Platonist," had a liking for mathematics, and was probably
+  led by his interest in number mysticism to a study of neo-Platonism. He
+  translated a number of works from the Latin and Greek, and wrote two
+  works on theoretical arithmetic (1816, 1823).</p>
+
+  <p><a name="Nt_422" href="#NtA_422">[422]</a> There was an earlier
+  edition, 1788-89.</p>
+
+  <p><a name="Nt_423" href="#NtA_423">[423]</a> Georgius Gemistus, or
+  Georgius Pletho (Plethon), lived in the fourteenth and fifteenth
+  centuries. He was a native of Constantinople, but spent most of his time
+  in Greece. He devoted much time to the propagation of the Platonic
+  philosophy, but also wrote on divinity, geography, and history.</p>
+
+  <p><a name="Nt_424" href="#NtA_424">[424]</a> Hannah More (1745-1833),
+  was, in her younger days, a friend of Burke, Reynolds, Dr. Johnson, and
+  Garrick. At this time she wrote a number of poems and aspired to become a
+  dramatist. Her <i>Percy</i> (1777), with a prologue and epilogue by
+  Garrick, had a long run at Covent Garden. Somewhat later she came to
+  believe that the playhouse was a grave public evil, and refused to attend
+  the revival of her own play with Mrs. Siddons in the leading part. After
+  1789 she and her sisters devoted themselves to starting schools for poor
+  children, teaching them religion and housework, but leaving them
+  illiterate.</p>
+
+  <p><a name="Nt_425" href="#NtA_425">[425]</a> These were issued at the
+  rate of three each month,&mdash;a story, a ballad, and a Sunday tract.
+  They were collected and published in one volume in 1795. It is said that
+  two million copies were sold the first year. There were also editions in
+  1798, 1819, 1827, and 1836-37.</p>
+
+  <p><a name="Nt_426" href="#NtA_426">[426]</a> That is, Dr. Johnson
+  (1709-1784). The <i>Rambler</i> was published in 1750-1752, and was an
+  imitation of Addison's <i>Spectator</i>.</p>
+
+  <p><a name="Nt_427" href="#NtA_427">[427]</a> Dr. Moore, referred to
+  below.</p>
+
+  <p><a name="Nt_428" href="#NtA_428">[428]</a> Dr. John Moore (1729-1802),
+  physician and novelist, is now best known for his <i>Journal during a
+  Residence in France from the beginning of August to the middle of
+  December, 1792</i>, a work quoted frequently by Carlyle in his <i>French
+  Revolution</i>.</p>
+
+  <p><a name="Nt_429" href="#NtA_429">[429]</a> Sir John Moore (1761-1809),
+  Lieutenant General in the Napoleonic wars. He was killed in the battle of
+  Corunna. The poem by Charles Wolfe (1791-1823), <i>The Burial of Sir John
+  Moore</i> (1817), is well known.</p>
+
+  <p><a name="Nt_430" href="#NtA_430">[430]</a> Referring to the novels of
+  Thomas Love Peacock (1785-1866), who succeeded James Mill as chief
+  examiner of the East India Company, and was in turn succeeded by John
+  Stuart Mill.</p>
+
+  <p><a name="Nt_431" href="#NtA_431">[431]</a> Frances Burney, Madame
+  d'Arblay (1752-1840), married General d'Arblay, a French officer and
+  companion of Lafayette, in 1793. She was only twenty-five when she
+  acquired fame by her <i>Evelina, or a Young Lady's Entrance into the
+  World</i>. Her <i>Letters and Diaries</i> appeared posthumously
+  (1842-45).</p>
+
+  <p><a name="Nt_432" href="#NtA_432">[432]</a> Henry Peter, Baron Brougham
+  and Vaux (1778-1868), well known in politics, science, and letters. He
+  was one of the founders of the <i>Edinburgh Review</i>, became Lord
+  Chancellor in 1830, and took part with men like William Frend, De
+  Morgan's father-in-law, in the establishing of London University. He was
+  also one of the founders of the Society for the Diffusion of Useful
+  Knowledge. He was always friendly to De Morgan, who entered the faculty
+  of London University, whose work on geometry was published by the Society
+  mentioned, and who was offered the degree of doctor of laws by the
+  University of Edinburgh while Lord Brougham was Lord Rector. The
+  Edinburgh honor was refused by De Morgan who said he "did not feel like
+  an LL.D."</p>
+
+  <p><a name="Nt_433" href="#NtA_433">[433]</a> Maria Edgeworth
+  (1767-1849).</p>
+
+  <p><a name="Nt_434" href="#NtA_434">[434]</a> Sydney Owenson (c.
+  1783-1859) married Sir Thomas Morgan, a well-known surgeon, in 1812. Her
+  Irish stories were very popular with the patriots but were attacked by
+  the <i>Quarterly Review</i>. <i>The Wild Irish Girl</i> (1806) went
+  through seven editions in two years.</p>
+
+  <p><a name="Nt_435" href="#NtA_435">[435]</a> 1775-1817.</p>
+
+  <p><a name="Nt_436" href="#NtA_436">[436]</a> 1771-1832.</p>
+
+  <p><a name="Nt_437" href="#NtA_437">[437]</a> The famous preacher
+  (1732-1808). He was the first chairman of the Religious Tract Society. He
+  is also known as one of the earliest advocates of vaccination, in his
+  <i>Cow-pock Inoculation vindicated and recommended from matters of
+  fact</i>, 1806.</p>
+
+  <p><a name="Nt_438" href="#NtA_438">[438]</a> Sir Rowland Hill
+  (1795-1879), the father of penny postage.</p>
+
+  <p><a name="Nt_439" href="#NtA_439">[439]</a> Beilby Porteus (1731-1808),
+  Bishop of Chester (1776) and Bishop of London (1787). He encouraged the
+  Sunday-school movement and the dissemination of Hannah More's tracts. He
+  was an active opponent of slavery, but also of Catholic emancipation.</p>
+
+  <p><a name="Nt_440" href="#NtA_440">[440]</a> Henrietta Maria Bowdler
+  (1754-1830), generally known as Mrs. Harriet Bowdler. She was the author
+  of many religious tracts and poems. Her <i>Poems and Essays</i> (1786)
+  were often reprinted. The story goes that on the appearance of her
+  <i>Sermons on the Doctrines and duties of Christianity</i> (published
+  anonymously), Bishop Porteus offered the author a living under the
+  impression that it was written by a man.</p>
+
+  <p><a name="Nt_441" href="#NtA_441">[441]</a> William Frend (1757-1841),
+  whose daughter Sophia Elizabeth became De Morgan's wife (1837), was at
+  one time a clergyman of the Established Church, but was converted to
+  Unitarianism (1787). He came under De Morgan's definition of a true
+  paradoxer, carrying on a zealous warfare for what he thought right. As a
+  result of his <i>Address to the Inhabitants of Cambridge</i> (1787), and
+  his efforts to have abrogated the requirement that candidates for the
+  M.A. must subscribe to the thirty-nine articles, he was deprived of his
+  tutorship in 1788. A little later he was banished (see De Morgan's
+  statement in the text) from Cambridge because of his denunciation of the
+  abuses of the Church and his condemnation of the liturgy. His
+  eccentricity is seen in his declining to use negative quantities in the
+  operations of algebra. He finally became an actuary at London and was
+  prominent in radical associations. He was a mathematician of ability,
+  having been second wrangler and having nearly attained the first place,
+  and he was also an excellent scholar in Latin, Greek, and Hebrew.</p>
+
+  <p><a name="Nt_442" href="#NtA_442">[442]</a> George Peacock (1791-1858),
+  Fellow of Trinity College, Cambridge, Lowndean professor of astronomy,
+  and Dean of Ely Cathedral (1839). His tomb may be seen at Ely where he
+  spent the latter part of his life. He was one of the group that
+  introduced the modern continental notation of the calculus into England,
+  replacing the cumbersome notation of Newton, passing from "the
+  <i>dot</i>age of fluxions to the <i>de</i>ism of the calculus."</p>
+
+  <p><a name="Nt_443" href="#NtA_443">[443]</a> Robert Simson (1687-1768);
+  professor of mathematics at Glasgow. His restoration of Apollonius (1749)
+  and his translation and restoration of Euclid (1756, and
+  1776&mdash;posthumous) are well known.</p>
+
+  <p><a name="Nt_444" href="#NtA_444">[444]</a> Francis Maseres
+  (1731-1824), a prominent lawyer. His mathematical works had some
+  merit.</p>
+
+  <p><a name="Nt_445" href="#NtA_445">[445]</a> These appeared annually
+  from 1804 to 1822.</p>
+
+  <p><a name="Nt_446" href="#NtA_446">[446]</a> Henry Gunning (1768-1854)
+  was senior esquire bedell of Cambridge. The <i>Reminiscences</i> appeared
+  in two volumes in 1854.</p>
+
+  <p><a name="Nt_447" href="#NtA_447">[447]</a> John Singleton Copley,
+  Baron Lyndhurst (1772-1863), the son of John Singleton Copley the
+  portrait painter, was born in Boston. He was educated at Trinity College,
+  Cambridge, and became a lawyer. He was made Lord Chancellor in 1827.</p>
+
+  <p><a name="Nt_448" href="#NtA_448">[448]</a> Sir William Rough (c.
+  1772-1838), a lawyer and poet, became Chief Justice of Ceylon in 1836. He
+  was knighted in 1837.</p>
+
+  <p><a name="Nt_449" href="#NtA_449">[449]</a> Herbert Marsh, afterwards
+  Bishop of Peterborough, a relation of my father.&mdash;S.&nbsp;E. De M.</p>
+
+  <p>He was born in 1757 and died in 1839. On the trial of Frend he
+  publicly protested against testifying against a personal confidant, and
+  was excused. He was one of the first of the English clergy to study
+  modern higher criticism of the Bible, and amid much opposition he wrote
+  numerous works on the subject. He was professor of theology at Cambridge
+  (1707), Bishop of Llandaff (1816), and Bishop of Peterborough.</p>
+
+  <p><a name="Nt_450" href="#NtA_450">[450]</a> George Butler (1774-1853),
+  Headmaster of Harrow (1805-1829), Chancellor of Peterborough (1836), and
+  Dean of Peterborough (1842).</p>
+
+  <p><a name="Nt_451" href="#NtA_451">[451]</a> James Tate (1771-1843),
+  Headmaster of Richmond School (1796-1833) and Canon of St. Paul's
+  Cathedral (1833). He left several works on the classics.</p>
+
+  <p><a name="Nt_452" href="#NtA_452">[452]</a> Francis Place (1771-1854),
+  at first a journeyman breeches maker, and later a master tailor. He was a
+  hundred years ahead of his time as a strike leader, but was not so
+  successful as an agitator as he was as a tailor, since his shop in
+  Charing Cross made him wealthy. He was a well-known radical, and it was
+  largely due to his efforts that the law against the combinations of
+  workmen was repealed in 1824. His chief work was <i>The Principles of
+  Population</i> (1822).</p>
+
+  <p><a name="Nt_453" href="#NtA_453">[453]</a> Speed (1552-1629) was a
+  tailor until Grevil (Greville) made him independent of his trade. He was
+  not only an historian of some merit, but a skilful cartographer. His maps
+  of the counties were collected in the <i>Theatre of the Empire of Great
+  Britaine</i>, 1611. About this same time he also published <i>Genealogies
+  recorded in Sacred Scripture</i>, a work that had passed through
+  thirty-two editions by 1640.</p>
+
+  <p><a name="Nt_454" href="#NtA_454">[454]</a> <i>The history of Great
+  Britaine under the conquests of ye Romans, Saxons, Danes, and
+  Normans....</i> London, 1611, folio. The second edition appeared in 1623;
+  the third, to which De Morgan here refers, posthumously in 1632; and the
+  fourth in 1650.</p>
+
+  <p><a name="Nt_455" href="#NtA_455">[455]</a> William Nicolson
+  (1655-1727) became Bishop of Carlisle in 1702, and Bishop of Derry in
+  1718. His chief work was the <i>Historical Library</i> (1696-1724), in
+  the form of a collection of documents and chronicles. It was reprinted in
+  1736 and in 1776.</p>
+
+  <p><a name="Nt_456" href="#NtA_456">[456]</a> Sir Fulk Grevil, or Fulke
+  Greville (1554-1628), was a favorite of Queen Elizabeth, Chancellor of
+  the Exchequer under James I, a patron of literature, and a friend of Sir
+  Philip Sidney.</p>
+
+  <p><a name="Nt_457" href="#NtA_457">[457]</a> See note <a
+  href="#Nt_443">443</a> on page <a href="#page197">197</a>.</p>
+
+  <p><a name="Nt_458" href="#NtA_458">[458]</a> See note <a
+  href="#Nt_444">444</a> on page <a href="#page197">197</a>.</p>
+
+  <p><a name="Nt_459" href="#NtA_459">[459]</a> See note <a
+  href="#Nt_439">439</a> on page <a href="#page193">193</a>.</p>
+
+  <p><a name="Nt_460" href="#NtA_460">[460]</a> Edward Waring (1736-1796)
+  was Lucasian professor of mathematics at Cambridge. He published several
+  works on analysis and curves. The work referred to was the <i>Miscellanea
+  Analytica de aequationibus algebraicis et curvarum proprietatibus</i>,
+  Cambridge, 1762.</p>
+
+  <p><a name="Nt_461" href="#NtA_461">[461]</a> <i>A Dissertation on the
+  use of the Negative Sign in Algebra...; to which is added, Machin's
+  Quadrature of the Circle</i>, London, 1758.</p>
+
+  <p><a name="Nt_462" href="#NtA_462">[462]</a> The paper was probably one
+  on complex numbers, or possibly one on quaternions, in which direction as
+  well as absolute value is involved.</p>
+
+  <p><a name="Nt_463" href="#NtA_463">[463]</a> De Morgan quotes from one
+  of the Latin editions. Descartes wrote in French, the title of his first
+  edition being: <i>Discours de la méthode pour bien conduire sa raison et
+  chercher la vérité dans les sciences, plus la dioptrique, les météores et
+  la géométrie qui sont des essais de cette méthode</i>, Leyden, 1637,
+  4to.</p>
+
+  <p><a name="Nt_464" href="#NtA_464">[464]</a> "I have observed that
+  algebra indeed, as it is usually taught, is so restricted by definite
+  rules and formulas of calculation, that it seems rather a confused kind
+  of an art, by the practice of which the mind is in a certain manner
+  disturbed and obscured, than a science by which it is cultivated and made
+  acute."</p>
+
+  <p><a name="Nt_465" href="#NtA_465">[465]</a> It appeared in 93 volumes,
+  from 1758 to 1851.</p>
+
+  <p><a name="Nt_466" href="#NtA_466">[466]</a> <i>The principles of the
+  doctrine of life-annuities; explained in a familiar manner ... with a
+  variety of new tables</i> ..., London, 1783.</p>
+
+  <p><a name="Nt_467" href="#NtA_467">[467]</a> I suppose the one who wrote
+  <i>Conjectures on the physical causes of Earthquakes and Volcanoes</i>,
+  Dublin, 1820.</p>
+
+  <p><a name="Nt_468" href="#NtA_468">[468]</a> <i>Scriptores Logarithmici;
+  or, a Collection of several curious</i> <i>tracts on the nature and
+  construction of Logarithms ... together with same tracts on the Binomial
+  Theorem</i> ..., 6 vols., London, 1791-1807.</p>
+
+  <p><a name="Nt_469" href="#NtA_469">[469]</a> Charles Babbage
+  (1792-1871), whose work on the calculating machine is well known. Maseres
+  was, it is true, ninety-two at this time, but Babbage was thirty-one
+  instead of twenty-nine. He had already translated Lacroix's <i>Treatise
+  on the differential and integral calculus</i> (1816), in collaboration
+  with Herschel and Peacock. He was Lucasian professor of mathematics at
+  Cambridge from 1828 to 1839.</p>
+
+  <p><a name="Nt_470" href="#NtA_470">[470]</a> <i>The great and new Art of
+  weighing Vanity, or a discovery of the ignorance of the great and new
+  artist in his pseudo-philosophical writings.</i> The "great and new
+  artist" was Sinclair.</p>
+
+  <p><a name="Nt_471" href="#NtA_471">[471]</a> George Sinclair, probably a
+  native of East Lothian, who died in 1696. He was professor of philosophy
+  and mathematics at Glasgow, and was one of the first to use the barometer
+  in measuring altitudes. The work to which De Morgan refers is his
+  <i>Hydrostaticks</i> (1672). He was a firm believer in evil spirits, his
+  work on the subject going through four editions: <i>Satan's Invisible
+  World Discovered; or, a choice collection of modern relations, proving
+  evidently against the Saducees and Athiests of this present age, that
+  there are Devils, Spirits, Witches, and Apparitions</i>, Edinburgh,
+  1685.</p>
+
+  <p><a name="Nt_472" href="#NtA_472">[472]</a> This was probably William
+  Sanders, Regent of St. Leonard's College, whose <i>Theses
+  philosophicae</i> appeared in 1674, and whose <i>Elementa geometriae</i>
+  came out a dozen years later.</p>
+
+  <p><a name="Nt_473" href="#NtA_473">[473]</a> <i>Ars nova et magna
+  gravitatis et levitatis; sive dialogorum philosophicorum libri sex de
+  aeris vera ac reali gravitate</i>, Rotterdam, 1669, 4to.</p>
+
+  <p><a name="Nt_474" href="#NtA_474">[474]</a> Volume I, Nos. 1 and 2,
+  appeared in 1803.</p>
+
+  <p><a name="Nt_475" href="#NtA_475">[475]</a> His daughter, Mrs. De
+  Morgan, says in her <i>Memoir</i> of her husband: "My father had been
+  second wrangler in a year in which the two highest were close together,
+  and was, as his son-in-law afterwards described him, an exceedingly clear
+  thinker. It is possible, as Mr. De Morgan said, that this mental
+  clearness and directness may have caused his mathematical heresy, the
+  rejection of the use of negative quantities in algebraical operations;
+  and it is probable that he thus deprived himself of an instrument of
+  work, the use of which might have led him to greater eminence in the
+  higher branches." <i>Memoir of Augustus De Morgan</i>, London, 1882, p.
+  19.</p>
+
+  <p><a name="Nt_476" href="#NtA_476">[476]</a> "If it is not true it is a
+  good invention." A well-known Italian proverb.</p>
+
+  <p><a name="Nt_477" href="#NtA_477">[477]</a> See page <a
+  href="#page86">86</a>, note <a href="#Nt_132">132</a>.</p>
+
+  <p><a name="Nt_478" href="#NtA_478">[478]</a> He was born at Paris in
+  1713, and died there in 1765.</p>
+
+  <p><a name="Nt_479" href="#NtA_479">[479]</a> <i>Recherches sur les
+  courbes à double courbure</i>, Paris, 1731. Clairaut was then only
+  eighteen, and was in the same year made a member of the Académie des
+  sciences. His <i>Elémens de géométrie</i> appeared in 1741. Meantime he
+  had taken part in the measurement of a degree in Lapland (1736-1737). His
+  <i>Traité de la figure de la terre</i> was published in 1741. The Academy
+  of St. Petersburg awarded him a prize for his <i>Théorie de la lune</i>
+  (1750). His various works on comets are well known, particularly his
+  <i>Théorie du mouvement des comètes</i> (1760) in which he applied the
+  "problem of three bodies" to Halley's comet as retarded by Jupiter and
+  Saturn.</p>
+
+  <p><a name="Nt_480" href="#NtA_480">[480]</a> Joseph Privat, Abbé de
+  Molières (1677-1742), was a priest of the Congregation of the Oratorium.
+  In 1723 he became a professor in the Collège de France. He was well known
+  as an astronomer and a mathematician, and wrote in defense of Descartes's
+  theory of vortices (1728, 1729). He also contributed to the methods of
+  finding prime numbers (1705).</p>
+
+  <p><a name="Nt_481" href="#NtA_481">[481]</a> "Deserves not only to be
+  printed, but to be admired as a marvel of imagination, of understanding,
+  and of ability."</p>
+
+  <p><a name="Nt_482" href="#NtA_482">[482]</a> Blaise Pascal (1623-1662),
+  the well-known French philosopher and mathematician. He lived for some
+  time with the Port Royalists, and defended them against the Jesuits in
+  his <i>Provincial Letters</i>. Among his works are the following:
+  <i>Essai pour les coniques</i> (1640); <i>Recit de la grande expérience
+  de l'équilibre des liqueurs</i> (1648), describing his experiment in
+  finding altitudes by barometric readings; <i>Histoire de la roulette</i>
+  (1658); <i>Traité du triangle arithmétique</i> (1665); <i>Aleae
+  geometria</i> (1654).</p>
+
+  <p><a name="Nt_483" href="#NtA_483">[483]</a> This proposition shows that
+  if a hexagon is inscribed in a conic (in particular a circle) and the
+  opposite sides are produced to meet, the three points determined by their
+  intersections will be in the same straight line.</p>
+
+  <p><a name="Nt_484" href="#NtA_484">[484]</a> Jacques Curabelle,
+  <i>Examen des &OElig;uvres du Sr. Desargues</i>, Paris, 1644. He also
+  published without date a work entitled: <i>Foiblesse pitoyable du Sr. G.
+  Desargues employée contre l'examen fait de ses &oelig;uvres</i>.</p>
+
+  <p><a name="Nt_485" href="#NtA_485">[485]</a> See page <a
+  href="#page119">119</a>, note <a href="#Nt_233">233</a>.</p>
+
+  <p><a name="Nt_486" href="#NtA_486">[486]</a> Until "this great
+  proposition called Pascal's should see the light."</p>
+
+  <p><a name="Nt_487" href="#NtA_487">[487]</a> The story is that his
+  father, Etienne Pascal, did not wish him to study geometry until he was
+  thoroughly grounded in Latin and Greek. Having heard the nature of the
+  subject, however, he began at the age of twelve to construct figures by
+  himself, drawing them on the floor with a piece of charcoal. When his
+  father discovered what he was doing he was attempting to demonstrate that
+  the sum of the angles of a triangle equals two right angles. The story is
+  given by his sister, Mme. Perier.</p>
+
+  <p><a name="Nt_488" href="#NtA_488">[488]</a> Sir John Wilson (1741-1793)
+  was knighted in 1786 and became Commissioner of the Great Seal in 1792.
+  He was a lawyer and jurist of recognized merit. He stated his theorem
+  without proof, the first demonstration having been given by Lagrange in
+  the Memoirs of the Berlin Academy for 1771,&mdash;<i>Demonstration d'un
+  théorème nouveau concernant les nombres premiers</i>. Euler also gave a
+  proof in his <i>Miscellanea Analytica</i> (1773). Fermat's works should
+  be consulted in connection with the early history of this theorem.</p>
+
+  <p><a name="Nt_489" href="#NtA_489">[489]</a> He wrote, in 1760, a tract
+  in defense of Waring, a point of whose algebra had been assailed by a Dr.
+  Powell. Waring wrote another tract of the same date.&mdash;A. De M.</p>
+
+  <p>William Samuel Powell (1717-1775) was at this time a fellow of St.
+  John's College, Cambridge. In 1765 he became Vice Chancellor of the
+  University. Waring was a Magdalene man, and while candidate for the
+  Lucasian professorship he circulated privately his <i>Miscellanea
+  Analytica</i>. Powell attacked this in his <i>Observations on the First
+  Chapter of a Book called Miscellanea</i> (1760). This attack was probably
+  in the interest of another candidate, a man of his own college (St.
+  John's), William Ludlam.</p>
+
+  <p><a name="Nt_490" href="#NtA_490">[490]</a> William Paley (1743-1805)
+  was afterwards a tutor at Christ's College, Cambridge. He never
+  contributed anything to mathematics, but his <i>Evidences of
+  Christianity</i> (1794) was long considered somewhat of a classic. He
+  also wrote <i>Principles of Morality and Politics</i> (1785), and
+  <i>Natural Theology</i> (1802).</p>
+
+  <p><a name="Nt_491" href="#NtA_491">[491]</a> Edward, first Baron Thurlow
+  (1731-1806) is known to Americans because of his strong support of the
+  Royal prerogative during the Revolution. He was a favorite of George III,
+  and became Lord Chancellor in 1778.</p>
+
+  <p><a name="Nt_492" href="#NtA_492">[492]</a> George Wilson Meadley
+  (1774-1818) published his <i>Memoirs of ... Paley</i> in 1809. He also
+  published <i>Memoirs of Algernon Sidney</i> in 1813. He was a merchant
+  and banker, and had traveled extensively in Europe and the East. He was a
+  convert to unitarianism, to which sect Paley had a strong leaning.</p>
+
+  <p><a name="Nt_493" href="#NtA_493">[493]</a> Watson (1737-1816) was a
+  strange kind of man for a bishopric. He was professor of chemistry at
+  Cambridge (1764) at the age of twenty-seven. It was his experiments that
+  led to the invention of the black-bulb thermometer. He is said to have
+  saved the government £100,000 a year by his advice on the manufacture of
+  gunpowder. Even after he became professor of divinity at Cambridge (1771)
+  he published four volumes of <i>Chemical Essays</i> (vol. I, 1781). He
+  became Bishop of Llandaff in 1782.</p>
+
+  <p><a name="Nt_494" href="#NtA_494">[494]</a> James Adair (died in 1798)
+  was counsel for the defense in the trial of the publishers of the
+  <i>Letters of Junius</i> (1771). As King's Serjeant he assisted in
+  prosecuting Hardy and Horne Tooke.</p>
+
+  <p><a name="Nt_495" href="#NtA_495">[495]</a> Morgan (1750-1833) was
+  actuary of the Equitable Assurance Society of London (1774-1830), and it
+  was to his great abilities that the success of that company was due at a
+  time when other corporations of similar kind were meeting with disaster.
+  The Royal Society awarded him a medal (1783) for a paper on
+  <i>Probability of Survivorship</i>. He wrote several important works on
+  insurance and finance.</p>
+
+  <p><a name="Nt_496" href="#NtA_496">[496]</a> Dr. Price (1723-1791) was a
+  non-conformist minister and a writer on ethics, economics, politics, and
+  insurance. He was a defender of the American Revolution and a personal
+  friend of Franklin. In 1778 Congress invited him to America to assist in
+  the financial administration of the new republic, but he declined. His
+  famous sermon on the French Revolution is said to have inspired Burke's
+  <i>Reflections on the Revolution in France</i>.</p>
+
+  <p><a name="Nt_497" href="#NtA_497">[497]</a> Elizabeth Gurney
+  (1780-1845), a Quaker, who married Joseph Fry (1800), a London merchant.
+  She was the prime mover in the Association for the Improvement of the
+  Female Prisoners in Newgate, founded in 1817. Her influence in prison
+  reform extended throughout Europe, and she visited the prisons of many
+  countries in her efforts to improve the conditions of penal servitude.
+  The friendship of Mrs. Fry with the De Morgans began in 1837. Her scheme
+  for a female benefit society proved worthless from the actuarial
+  standpoint, and would have been disastrous to all concerned if it had
+  been carried out, and it was therefore fortunate that De Morgan was
+  consulted in time. Mrs. De Morgan speaks of the consultation in these
+  words: "My husband, who was very sensitive on such points, was charmed
+  with Mrs. Fry's voice and manner as much as by the simple
+  self-forgetfulness with which she entered into this business; her own
+  very uncomfortable share of it not being felt as an element in the
+  question, as long as she could be useful in promoting good or preventing
+  mischief. I can see her now as she came into our room, took off her
+  little round Quaker cap, and laying it down, went at once into the
+  matter. 'I have followed thy advice, and I think nothing further can be
+  done in this case; but all harm is prevented.' In the following year I
+  had an opportunity of seeing the effect of her most musical tones. I
+  visited her at Stratford, taking my little baby and nurse with me, to
+  consult her on some articles on prison discipline, which I had written
+  for a periodical. The baby&mdash;three months old&mdash;was restless, and
+  the nurse could not quiet her, neither could I entirely, until Mrs. Fry
+  began to read something connected with the subject of my visit, when the
+  infant, fixing her large eyes on the reader, lay listening till she fell
+  asleep." <i>Memoirs</i>, p. 91.</p>
+
+  <p><a name="Nt_498" href="#NtA_498">[498]</a> Mrs. Fry certainly believed
+  that the writer was the old actuary of the Equitable, when she first
+  consulted him upon the benevolent Assurance project; but we were
+  introduced to her by our old and dear friend Lady Noel Byron, by whom she
+  had been long known and venerated, and who referred her to Mr. De Morgan
+  for advice. An unusual degree of confidence in, and appreciation of each
+  other, arose on their first meeting between the two, who had so much that
+  was externally different, and so much that was essentially alike, in
+  their natures.&mdash;S.&nbsp;E. De M.</p>
+
+  <p>Anne Isabella Milbanke (1792-1860) married Lord Byron in 1815, when
+  both took the additional name of Noel, her mother's name. They were
+  separated in 1816.</p>
+
+  <p><a name="Nt_499" href="#NtA_499">[499]</a> An obscure writer not
+  mentioned in the ordinary biographies.</p>
+
+  <p><a name="Nt_500" href="#NtA_500">[500]</a> Not mentioned in the
+  ordinary biographies, and for obvious reasons.</p>
+
+  <p><a name="Nt_501" href="#NtA_501">[501]</a> "Before" and "after."</p>
+
+  <p><a name="Nt_502" href="#NtA_502">[502]</a> On Bishop Wilkins see note
+  <a href="#Nt_171">171</a> on page <a href="#page100">100</a>.</p>
+
+  <p><a name="Nt_503" href="#NtA_503">[503]</a> Provision for a
+  journey.</p>
+
+  <p><a name="Nt_504" href="#NtA_504">[504]</a> See note <a
+  href="#Nt_179">179</a> on page <a href="#page103">103</a>.</p>
+
+  <p><a name="Nt_505" href="#NtA_505">[505]</a> Thomas Bradwardine
+  (1290-1349), known as <i>Doctor Profundus</i>, proctor and professor of
+  theology at Oxford, and afterwards Chancellor of St. Paul's and confessor
+  to Edward III. The English ascribed their success at Crécy to his
+  prayers.</p>
+
+  <p><a name="Nt_506" href="#NtA_506">[506]</a> He was consecrated
+  Archbishop of Canterbury by the Pope at Avignon, July 13, 1349, and died
+  of the plague at London in the same year.</p>
+
+  <p><a name="Nt_507" href="#NtA_507">[507]</a> "One paltry little
+  year."</p>
+
+  <p><a name="Nt_508" href="#NtA_508">[508]</a> The title is carelessly
+  copied, as is so frequently the case in catalogues, even of the Libri
+  class. It should read: <i>Arithmetica thome brauardini</i> || <i>Olivier
+  Senant</i> || <i>Venum exponuntur ab Oliuiario senant in vico diui Jacobi
+  sub signo beate Barbare sedente</i>. The colophon reads: <i>Explicit
+  arithmetica speculatiua th&#x14D;e brauardini b<span
+  class="over">n</span> reuisa et correcta a Petro sanchez Ciruelo
+  aragonensi mathematicas leg&#x113;te Parisius, &#x12B;pressa per
+  Thom&#x101; anguelart</i>. There were Paris editions of 1495, 1496, 1498,
+  s. a. (c. 1500), 1502, 1504, 1505, s. a. (c. 1510), 1512, 1530, a
+  Valencia edition of 1503, two Wittenberg editions of 1534 and 1536, and
+  doubtless several others. The work is not "very rare," although of course
+  no works of that period are common. See the editor's <i>Rara
+  Arithmetica</i>, page 61.</p>
+
+  <p><a name="Nt_509" href="#NtA_509">[509]</a> This is his <i>Tractatus de
+  proportionibus</i>, Paris, 1495; Venice, 1505; Vienna, 1515, with other
+  editions.</p>
+
+  <p><a name="Nt_510" href="#NtA_510">[510]</a> The colophon of the 1495
+  edition reads: <i>Et sic explicit Geometria Thome brauardini c&#x16B;
+  tractatulo de quadratura circuli bene reuisa a Petro sanchez ciruelo:
+  operaqz Guidonis mercatoris dilig&#x113;tissime impresse
+  parisi<sup>o</sup> in c&#x101;po gaillardi. Anno d<span
+  class="over">n</span>i. 1495. die. 20, maij.</i></p>
+
+  <p>This Petro Ciruelo was born in Arragon, and died in 1560 at Salamanca.
+  He studied mathematics and philosophy at Paris, and took the doctor's
+  degree there. He taught at the University of Alcalà and became canon of
+  the Cathedral at Salamanca. Besides his editions of Bradwardine he wrote
+  several works, among them the <i>Liber arithmeticae practicae qui dicitur
+  algorithmus</i> (Paris, 1495) and the <i>Cursus quatuor mathematicarum
+  artium liberalium</i> (Alcalà, 1516).</p>
+
+  <p><a name="Nt_511" href="#NtA_511">[511]</a> Star polygons, a subject of
+  considerable study in the later Middle Ages. See note <a
+  href="#Nt_35">35</a> on page <a href="#page44">44</a>.</p>
+
+  <p><a name="Nt_512" href="#NtA_512">[512]</a> "A new theory that adds
+  lustre to the fourteenth century."</p>
+
+  <p><a name="Nt_513" href="#NtA_513">[513]</a> There is nothing in the
+  edition of 1495 that leads to this conclusion.</p>
+
+  <p><a name="Nt_514" href="#NtA_514">[514]</a> The full title is:
+  <i>Nouvelle théorie des parallèles, avec un appendice contenant la
+  manière de perfectionner la théorie des parallèles de A.&nbsp;M. Legendre</i>.
+  The author had no standing as a scientist.</p>
+
+  <p><a name="Nt_515" href="#NtA_515">[515]</a> Adrien Marie Legendre
+  (1752-1833) was one of the great mathematicians of the opening of the
+  nineteenth century. His <i>Eléments de géométrie</i> (1794) had great
+  influence on the geometry of the United States. His <i>Essai sur la
+  théorie des nombres</i> (1798) is one of the classics upon the subject.
+  The work to which Kircher refers is the <i>Nouvelle théorie des
+  parallèles</i> (1803), in which the attempt is made to avoid using
+  Euclid's postulate of parallels, the result being merely the substitution
+  of another assumption that was even more unsatisfactory. The best
+  presentations of the general theory are W.&nbsp;B. Frankland's <i>Theories of
+  Parallelism</i>, Cambridge, 1910, and Engel and Stäckel's <i>Die Theorie
+  der Parallellinien von Euclid bis auf Gauss</i>, Leipsic, 1895. Legendre
+  published a second work on the theory the year of his death,
+  <i>Réflexions sur ... la théorie des parallèles</i> (1833). His other
+  works include the <i>Nouvelles méthodes pour la détermination des orbites
+  des comètes</i> (1805), in which he uses the method of least squares; the
+  <i>Traité des fonctions elliptiques et des intégrales</i> (1827-1832),
+  and the <i>Exercises de calcul intégral</i> (1811, 1816, 1817).</p>
+
+  <p><a name="Nt_516" href="#NtA_516">[516]</a> Johann Joseph Ignatz von
+  Hoffmann (1777-1866), professor of mathematics at Aschaffenburg,
+  published his <i>Theorie der Parallellinien</i> in 1801. He supplemented
+  this by his <i>Kritik der Parallelen-Theorie</i> in 1807, and his <i>Das
+  eilfte Axiom der Elemente des Euclidis neu bewiesen</i> in 1859. He wrote
+  other works on mathematics, but none of his contributions was of any
+  importance.</p>
+
+  <p><a name="Nt_517" href="#NtA_517">[517]</a> Johann Karl Friedrich Hauff
+  (1766-1846) was successively professor of mathematics at Marburg,
+  director of the polytechnic school at Augsburg, professor at the
+  Gymnasium at Cologne, and professor of mathematics and physics at Ghent.
+  The work to which Kircher refers is his memoirs on the Euclidean
+  <i>Theorie der Parallelen</i> in Hindenburg's <i>Archiv</i>, vol. III
+  (1799), an article of no merit in the general theory.</p>
+
+  <p><a name="Nt_518" href="#NtA_518">[518]</a> Wenceslaus Johann Gustav
+  Karsten (1732-1787) was professor of logic at Rostock (1758) and Butzow
+  (1760), and later became professor of mathematics and physics at Halle.
+  His work on parallels is the <i>Versuch einer völlig berichtigten Theorie
+  der Parallellinien</i> (1779). He also wrote a work entitled
+  <i>Anfangsgründe der mathematischen Wissenschaften</i> (1780), but
+  neither of these works was more than mediocre.</p>
+
+  <p><a name="Nt_519" href="#NtA_519">[519]</a> Johann Christoph Schwab
+  (not Schwal) was born in 1743 and died in 1821. He was professor at the
+  Karlsschule at Stuttgart. De Morgan's wish was met, for the catalogues
+  give "c. fig. 8," so that it evidently had eight illustrations instead of
+  eight volumes. He wrote several other works on the principles of
+  geometry, none of any importance.</p>
+
+  <p><a name="Nt_520" href="#NtA_520">[520]</a> Gaetano Rossi of Catanzaro.
+  This was the libretto writer (1772-1855), and hence the imperfections of
+  the work can better be condoned. De Morgan should have given a little
+  more of the title: <i>Solusione esatta e regolare ... del ... problema
+  della quadratura del circolo</i>. There was a second edition, London,
+  1805.</p>
+
+  <p><a name="Nt_521" href="#NtA_521">[521]</a> This identifies Rossi, for
+  Joséphine Grassini (1773-1850) was a well-known contralto, <i>prima
+  donna</i> at Napoleon's court opera.</p>
+
+  <p><a name="Nt_522" href="#NtA_522">[522]</a> William Spence (1783-1860)
+  was an entomologist and economist of some standing, a fellow of the Royal
+  Society, and one of the founders of the Entomological Society of London.
+  The work here mentioned was a popular one, the first edition appearing in
+  1807, and four editions being justified in a single year. He also wrote
+  <i>Agriculture the Source of Britain's Wealth</i> (1808) and
+  <i>Objections against the Corn Bill refuted</i> (1815), besides a work in
+  four volumes on entomology (1815-1826) in collaboration with William
+  Kirby.</p>
+
+  <p><a name="Nt_523" href="#NtA_523">[523]</a> "That used to be so, but we
+  have changed all that."</p>
+
+  <p><a name="Nt_524" href="#NtA_524">[524]</a> "Meet the coming
+  disease."</p>
+
+  <p><a name="Nt_525" href="#NtA_525">[525]</a> George Douglas (or
+  Douglass) was a Scotch writer. He got out an edition of the <i>Elements
+  of Euclid</i> in 1776, with an appendix on trigonometry and a set of
+  tables. His work on <i>Mathematical Tables</i> appeared in 1809, and his
+  <i>Art of Drawing in Perspective, from mathematical principles</i>, in
+  1810.</p>
+
+  <p><a name="Nt_526" href="#NtA_526">[526]</a> See note <a
+  href="#Nt_443">443</a>, on page <a href="#page197">197</a>.</p>
+
+  <p><a name="Nt_527" href="#NtA_527">[527]</a> John Playfair (1748-1848)
+  was professor of mathematics (1785) and natural philosophy (1805) at the
+  University of Edinburgh. His <i>Elements of Geometry</i> went through
+  many editions.</p>
+
+  <p><a name="Nt_528" href="#NtA_528">[528]</a> "Tell Apella" was an
+  expression current in classical Rome to indicate incredulity and to show
+  the contempt in which the Jew was held. Horace says: <i>Credat Judæus
+  Apella</i>, "Let Apella the Jew believe it." Our "Tell it to the
+  marines," is a similar phrase.</p>
+
+  <p><a name="Nt_529" href="#NtA_529">[529]</a> As De Morgan says two lines
+  later, "No mistake is more common than the natural one of imagining that
+  the"&mdash;University of Virginia is at Richmond. The fact is that it is
+  not there, and that it did not exist in 1810. It was not chartered until
+  1819, and was not opened until 1825, and then at Charlottesville. The act
+  establishing the Central College, from which the University of Virginia
+  developed, was passed in 1816. The Jean Wood to whom De Morgan refers was
+  one John Wood who was born about 1775 in Scotland and who emigrated to
+  the United States in 1800. He published a <i>History of the
+  Administration of J. Adams</i> (New York, 1802) that was suppressed by
+  Aaron Burr. This act called forth two works, a <i>Narrative of the
+  Suppression, by Col. Burr, of the 'History of the Administration of John
+  Adams'</i> (1802), in which Wood was sustained; and the <i>Antidote to
+  John Wood's Poison</i> (1802), in which he was attacked. The work
+  referred to in the "printed circular" may have been the <i>New theory of
+  the diurnal rotation of the earth</i> (Richmond, Va., 1809). Wood spent
+  the last years of his life in Richmond, Va., making county maps. He died
+  there in 1822. A careful search through works relating to the University
+  of Virginia fails to show that Wood had any connection with it.</p>
+
+  <p><a name="Nt_530" href="#NtA_530">[530]</a> There seems to be nothing
+  to add to Dobson's biography beyond what De Morgan has so deliciously set
+  forth.</p>
+
+  <p><a name="Nt_531" href="#NtA_531">[531]</a> "Give to each man his
+  due."</p>
+
+  <p><a name="Nt_532" href="#NtA_532">[532]</a> Hester Lynch Salusbury
+  (1741-1821), the friend of Dr. Johnson, married Henry Thrale (1763), a
+  brewer, who died in 1781. She then married Gabriel Piozzi (1784), an
+  Italian musician. Her <i>Anecdotes of the late Samuel Johnson</i> (1786)
+  and <i>Letters to and from Samuel Johnson</i> (1788) are well known. She
+  also wrote numerous essays and poems.</p>
+
+  <p><a name="Nt_533" href="#NtA_533">[533]</a> Samuel Pike (c. 1717-1773)
+  was an independent minister, with a chapel in London and a theological
+  school in his house. He later became a disciple of Robert Sandeman and
+  left the Independents for the Sandemanian church (1765). The
+  <i>Philosophia Sacra</i> was first published at London in 1753. De Morgan
+  here cites the second edition.</p>
+
+  <p><a name="Nt_534" href="#NtA_534">[534]</a> Pike had been dead over
+  forty years when Kittle published this second edition. Kittle had already
+  published a couple of works: <i>King Solomon's portraiture of Old Age</i>
+  (Edinburgh, 1813), and <i>Critical and Practical Lectures on the
+  Apocalyptical Epistles to the Seven Churches of Asia Minor</i> (London,
+  1814).</p>
+
+  <p><a name="Nt_535" href="#NtA_535">[535]</a> See note <a
+  href="#Nt_334">334</a>, on page <a href="#page152">152</a>.</p>
+
+  <p><a name="Nt_536" href="#NtA_536">[536]</a> William Stukely (1687-1765)
+  was a fellow of the Royal Society and of the College of Physicians and
+  Surgeons. He afterwards (1729) entered the Church. He was prominent as an
+  antiquary, especially in the study of the Roman and Druidic remains of
+  Great Britain. He was the author of numerous works, chiefly on
+  paleography.</p>
+
+  <p><a name="Nt_537" href="#NtA_537">[537]</a> William Jones (1726-1800),
+  who should not be confused with his namesake who is mentioned in note <a
+  href="#Nt_281">281</a> on page <a href="#page135">135</a>. He was a
+  lifelong friend of Bishop Horne, and his vicarage at Nayland was a
+  meeting place of an influential group of High Churchmen. Besides the
+  <i>Physiological Disquisitions</i> (1781) he wrote <i>The Catholic
+  Doctrine of the Trinity</i> (1756) and <i>The Grand Analogy</i>
+  (1793).</p>
+
+  <p><a name="Nt_538" href="#NtA_538">[538]</a> Robert Spearman (1703-1761)
+  was a pupil of John Hutchinson, and not only edited his works but wrote
+  his life. He wrote a work against the Newtonian physics, entitled <i>An
+  Enquiry after Philosophy and Theology</i> (Edinburgh, 1755), besides the
+  <i>Letters to a Friend concerning the Septuagint Translation</i>
+  (Edinburgh, 1759) to which De Morgan refers.</p>
+
+  <p><a name="Nt_539" href="#NtA_539">[539]</a> A writer of no importance,
+  at least in the minds of British biographers.</p>
+
+  <p><a name="Nt_540" href="#NtA_540">[540]</a> Alexander Catcott
+  (1725-1779), a theologian and geologist, wrote not only a work on the
+  creation (1756) but a <i>Treatise on the Deluge</i> (1761, with a second
+  edition in 1768). Sir Charles Lyell considered the latter work a valuable
+  contribution to geology.</p>
+
+  <p><a name="Nt_541" href="#NtA_541">[541]</a> James Robertson
+  (1714-1795), professor of Hebrew at the University of Edinburgh. Probably
+  De Morgan refers to his <i>Grammatica Linguae Hebrææ</i> (Edinburgh,
+  1758; with a second edition in 1783). He also wrote <i>Clavis
+  Pentateuchi</i> (1770).</p>
+
+  <p><a name="Nt_542" href="#NtA_542">[542]</a> Benjamin Holloway (c.
+  1691-1759), a geologist and theologian. He translated Woodward's
+  <i>Naturalis Historia Telluris</i>, and was introduced by Woodward to
+  Hutchinson. The work referred to by De Morgan appeared at Oxford in two
+  volumes in 1754.</p>
+
+  <p><a name="Nt_543" href="#NtA_543">[543]</a> His work was <i>The
+  Christian plan exhibited in the interpretation of Elohim: with
+  observations upon a few other matters relative to the same subject</i>,
+  Oxford, 1752, with a second edition in 1755.</p>
+
+  <p><a name="Nt_544" href="#NtA_544">[544]</a> Duncan Forbes (1685-1747)
+  studied Oriental languages and Civil law at Leyden. He was Lord President
+  of the Court of Sessions (1737). He wrote a number of theological
+  works.</p>
+
+  <p><a name="Nt_545" href="#NtA_545">[545]</a> Should be 1756.</p>
+
+  <p><a name="Nt_546" href="#NtA_546">[546]</a> Edward Henry Bickersteth
+  (1825-1906), bishop of Exeter (1885-1900); published <i>The Rock of Ages;
+  or scripture testimony to the one Eternal Godhead of the Father, and of
+  the Son, and of the Holy Ghost</i> at Hampstead in 1859. A second edition
+  appeared at London in 1860.</p>
+
+  <p><a name="Nt_547" href="#NtA_547">[547]</a> Thomas Sadler (1822-1891)
+  took his Ph.D. at Erlangen in 1844, and became a Unitarian minister at
+  Hampstead, where Bickersteth's work was published. Besides writing the
+  <i>Gloria Patri</i> (1859), he edited Crabb Robinson's Diaries.</p>
+
+  <p><a name="Nt_548" href="#NtA_548">[548]</a> This was his <i>Virgil's
+  Bucolics and the two first Satyrs of Juvenal</i>, 1634.</p>
+
+  <p><a name="Nt_549" href="#NtA_549">[549]</a> Possibly in his <i>Twelve
+  Questions or Arguments drawn out of Scripture, wherein the commonly
+  received Opinion touching the Deity of the Holy Spirit is clearly and
+  fully refuted</i>, 1647. This was his first heretical work, and it was
+  followed by a number of others that were written during the intervals in
+  which the Puritan parliament allowed him out of prison. It was burned by
+  the hangman as blasphemous. Biddle finally died in prison, unrepentant to
+  the last.</p>
+
+  <p><a name="Nt_550" href="#NtA_550">[550]</a> The first edition of the
+  <span class="correction" title="text reads `anonynous'">anonymous</span>
+  <span title="Haireseôn anastasis" class="grk"
+  >&#x1F09;&iota;&rho;&epsilon;&sigma;&epsilon;&omega;&nu;
+  &#x1F00;&nu;&alpha;&sigma;&tau;&alpha;&sigma;&iota;&sigmaf;</span> (by
+  Vicars?) appeared in 1805.</p>
+
+  <p><a name="Nt_551" href="#NtA_551">[551]</a> Possibly by Thomas Pearne
+  (c. 1753-1827), a fellow of St. Peter's College, Cambridge, and a
+  Unitarian minister.</p>
+
+  <p><a name="Nt_552" href="#NtA_552">[552]</a> Thomas Wentworth, Earl of
+  Strafford, was borne in London in 1593, and was executed there in 1641.
+  He was privy councilor to Charles I, and was Lord Deputy of Ireland. On
+  account of his repressive measures to uphold the absolute power of the
+  king he was impeached by the Long Parliament and was executed for
+  treason. The essence of his defence is in the sentence quoted by De
+  Morgan, to which Pym replied that taken as a whole, the acts tended to
+  show an intention to change the government, and this was in itself
+  treason.</p>
+
+  <p><a name="Nt_553" href="#NtA_553">[553]</a> The name assumed by a
+  writer who professed to give a mathematical explanation of the Trinity,
+  see farther on.&mdash;S.&nbsp;E. De M.</p>
+
+  <p><a name="Nt_554" href="#NtA_554">[554]</a> Sabellius (fl. 230 A.D.)
+  was an early Christian of Libyan origin. He taught that Father, Son, and
+  Holy Spirit were different names for the same person.</p>
+
+  <p><a name="Nt_555" href="#NtA_555">[555]</a> Sir Richard Phillips was
+  born in London in 1767 (not 1768 as stated above), and died there in
+  1840. He was a bookseller and printer in Leicester, where he also edited
+  a radical newspaper. He went to London to live in 1795 and started the
+  <i>Monthly Magazine</i> there in 1796. Besides the works mentioned by De
+  Morgan he wrote on law and economics.</p>
+
+  <p><a name="Nt_556" href="#NtA_556">[556]</a> It was really eighteen
+  months.</p>
+
+  <p><a name="Nt_557" href="#NtA_557">[557]</a> While he was made sheriff
+  in 1807 he was not knighted until the following year.</p>
+
+  <p><a name="Nt_558" href="#NtA_558">[558]</a> James Mitchell (c.
+  1786-1844) was a London actuary, or rather a Scotch actuary living a good
+  part of his life in London. Besides the work mentioned he compiled a
+  <i>Dictionary of Chemistry, Mineralogy, and Geology</i> (1823), and wrote
+  <i>On the Plurality of Worlds</i> (1813) and <i>The Elements of
+  Astronomy</i> (1820).</p>
+
+  <p><a name="Nt_559" href="#NtA_559">[559]</a> Richarda Smith, wife of Sir
+  George Biddell Airy (see note <a href="#Nt_129">129</a>, page <a
+  href="#page85">85</a>) the astronomer. In 1835 Sir Robert Peel offered a
+  pension of £300 a year to Airy, who requested that it be settled on his
+  wife.</p>
+
+  <p><a name="Nt_560" href="#NtA_560">[560]</a> Mary Fairfax (1780-1872)
+  married as her second husband Dr. William Somerville. In 1826 she
+  presented to the Royal Society a paper on <i>The Magnetic Properties of
+  the Violet Rays of the Solar Spectrum</i>, which attracted much
+  attention. It was for her <i>Mechanism of the Heavens</i> (1831), a
+  popular translation of Laplace's <i>Mécanique Céleste</i>, that she was
+  pensioned.</p>
+
+  <p><a name="Nt_561" href="#NtA_561">[561]</a> Dominique François Jean
+  Arago (1786-1853) the celebrated French astronomer and physicist.</p>
+
+  <p><a name="Nt_562" href="#NtA_562">[562]</a> For there is a well-known
+  series</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>1 + 1/2<sup>2</sup> + 1/3<sup>2</sup> + ... = <span class="grk">&pi;</span><sup>2</sup>/6.</p>
+    </div>
+  </div>
+  <p>If, therefore, the given series equals 1, we have</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p>2 = 1/6 <span class="grk">&pi;</span><sup>2</sup></p>
+    </div>
+
+    <div class="stanza">
+      <p>or <span class="grk">&pi;</span><sup>2</sup> = 12,</p>
+    </div>
+
+    <div class="stanza">
+      <p>whence <span class="grk">&pi;</span> = 2 &radic;3.</p>
+    </div>
+  </div>
+  <p>But c = <span class="grk">&pi;</span>d, and twice the diagonal of a
+  cube on the diameter is 2d &radic;3.</p>
+
+  <p><a name="Nt_563" href="#NtA_563">[563]</a> There was a second edition
+  in 1821.</p>
+
+  <p><a name="Nt_564" href="#NtA_564">[564]</a> London, 1830.</p>
+
+  <p><a name="Nt_565" href="#NtA_565">[565]</a> He was a resident of
+  Chatham, and seems to have published no other works.</p>
+
+  <p><a name="Nt_566" href="#NtA_566">[566]</a> Richard Whately (1787-1863)
+  was, as a child, a calculating prodigy (see note <a
+  href="#Nt_132">132</a>, page <a href="#page86">86</a>), but lost the
+  power as is usually the case with well-balanced minds. He was a fellow of
+  Oriel College, Oxford, and in 1825 became principal of St. Alban Hall. He
+  was a friend of Newman, Keble, and others who were interested in the
+  religious questions of the day. He became archbishop of Dublin in 1831.
+  He was for a long time known to students through his <i>Logic</i> (1826)
+  and <i>Rhetoric</i> (1828).</p>
+
+  <p><a name="Nt_567" href="#NtA_567">[567]</a> William King, D.C.L.
+  (1663-1712), student at Christ Church, Oxford, and celebrated as a wit
+  and scholar. His <i>Dialogues of the Dead</i> (1699) is a satirical
+  attack on Bentley.</p>
+
+  <p><a name="Nt_568" href="#NtA_568">[568]</a> Thomas Ebrington
+  (1760-1835) was a fellow of Trinity College, Dublin, and taught divinity,
+  mathematics, and natural philosophy there. He became provost of the
+  college in 1811, bishop of Limerick in 1820, and bishop of Leighlin and
+  Ferns in 1822. His edition of Euclid was reprinted a dozen times. The
+  <i>Reply to John Search's Considerations on the Law of Libel</i> appeared
+  at Dublin in 1834.</p>
+
+  <p><a name="Nt_569" href="#NtA_569">[569]</a> Joseph Blanco White
+  (1775-1841) was the son of an Irishman living in Spain. He was born at
+  Seville and studied for orders there, being ordained priest in 1800. He
+  lost his faith in the Roman Catholic Church, and gave up the ministry,
+  escaping to England at the time of the French invasion. At London he
+  edited <i>Español</i>, a patriotic journal extensively circulated in
+  Spain, and for this service he was pensioned after the expulsion of the
+  French. He then studied at Oriel College, Oxford, and became intimate
+  with men like Whately, Newman, and Keble. In 1835 he became a Unitarian.
+  Among his theological writings is his <i>Evidences against
+  Catholicism</i> (1825). The "rejoinder" to which De Morgan refers
+  consisted of two letters: <i>The law of anti-religious Libel
+  reconsidered</i> (Dublin, 1834) and <i>An Answer to some Friendly Remarks
+  on "The Law of Anti-Religious Libel Reconsidered"</i> (Dublin, 1834).</p>
+
+  <p><a name="Nt_570" href="#NtA_570">[570]</a> The work was translated
+  from the French.</p>
+
+  <p><a name="Nt_571" href="#NtA_571">[571]</a> J. Hoëné Wronski
+  (1778-1853) served, while yet a mere boy, as an artillery officer in
+  Kosciusko's army (1791-1794). He was imprisoned after the battle of
+  Maciejowice. He afterwards lived in Germany, and (after 1810) in Paris.
+  For the bibliography of his works see S. Dickstein's article in the
+  <i>Bibliotheca Mathematica</i>, vol. VI (2), page 48.</p>
+
+  <p><a name="Nt_572" href="#NtA_572">[572]</a> Perhaps referring to his
+  <i>Introduction à la philosophie des mathématiques</i> (1811).</p>
+
+  <p><a name="Nt_573" href="#NtA_573">[573]</a> Read "equation of the."</p>
+
+  <p><a name="Nt_574" href="#NtA_574">[574]</a> Thomas Young (1773-1829),
+  physician and physicist, sometimes called the founder of physiological
+  optics. He seems to have initiated the theory of color blindness that was
+  later developed by Helmholtz. The attack referred to was because of his
+  connection with the Board of Longitude, he having been made (1818)
+  superintendent of the Nautical Almanac and secretary of the Board. He
+  opposed introducing into the Nautical Almanac anything not immediately
+  useful to navigation, and this antagonized many scientists.</p>
+
+  <p><a name="Nt_575" href="#NtA_575">[575]</a> Isaac Milner (1750-1820)
+  was professor of natural philosophy at Cambridge (1783) and later became,
+  as De Morgan states, president of Queens' College (1788). In 1791 he
+  became dean of Carlisle, and in 1798 Lucasian professor of mathematics.
+  His chief interest was in chemistry and physics, but he contributed
+  nothing of importance to these sciences or to mathematics.</p>
+
+  <p><a name="Nt_576" href="#NtA_576">[576]</a> Thomas Perronet Thompson
+  (1783-1869), fellow of Queens' College, Cambridge, saw service in Spain
+  and India, but after 1822 lived in England. He became major general in
+  1854, and general in 1868. Besides some works on economics and politics
+  he wrote a <i>Geometry without Axioms</i> (1830) that De Morgan includes
+  later on in his <i>Budget</i>. In it Thompson endeavored to prove the
+  parallel postulate.</p>
+
+  <p><a name="Nt_577" href="#NtA_577">[577]</a> De Morgan's father-in-law.
+  See note <a href="#Nt_441">441</a>, page <a href="#page196">196</a>.</p>
+
+  <p><a name="Nt_578" href="#NtA_578">[578]</a> Johann Friedrich Herbart
+  (1776-1841), successor of Kant as professor of philosophy at Königsberg
+  (1809-1833), where he established a school of pedagogy. From 1833 until
+  his death he was professor of philosophy at Göttingen. The title of the
+  pamphlet is: <i>De Attentionis mensura causisque primariis. Psychologiae
+  principia statica et mechanica exemplo illustraturus.... Regiomonti,...
+  1822</i>. The formulas in question are given on pages 15 and 17, and De
+  Morgan has omitted the preliminary steps, which are, for the first
+  one:</p>
+
+  <div class="poem">
+    <div class="stanza">
+      <p><span class="grk">&beta;</span> (<span class="grk">&phi;</span> - <i>z</i>) <span class="grk">&delta;</span><i>t</i> = <span class="grk">&delta;</span><i>z</i></p>
+    </div>
+
+    <div class="stanza">
+      <p>unde <span class="grk">&beta;</span><i>t</i>= Const / (<span class="grk">&phi;</span> - <i>z</i>).</p>
+    </div>
+
+    <div class="stanza">
+      <p>Pro <i>t</i> = 0 etiam <i>z</i> = 0; hinc <span class="grk">&beta;</span><i>t</i> = log <span class="grk">&phi;</span>/(<span class="grk">&phi;</span> - <i>z</i>).</p>
+    </div>
+
+    <div class="stanza">
+      <p><i>z</i> = <span class="grk">&phi;</span> (1 - <span class="grk">&epsilon;</span><sup>-<span class="grk">&beta;</span><i>t</i></sup>);</p>
+    </div>
+
+    <div class="stanza">
+      <p>et &nbsp; <span class="grk">&delta;</span><i>z</i>/<span class="grk">&delta;</span><i>t</i> = <span class="grk">&beta;</span><span class="grk">&phi;</span><span class="grk">&epsilon;</span><sup>-<span class="grk">&beta;</span><i>t</i></sup></p>
+    </div>
+  </div>
+  <p>These are, however, quite elementary as compared with other portions
+  of the theory.</p>
+
+  <p><a name="Nt_579" href="#NtA_579">[579]</a> See note <a
+  href="#Nt_371">371</a>, page <a href="#page168">168</a>.</p>
+
+  <p><a name="Nt_580" href="#NtA_580">[580]</a> William Law (1686-1761) was
+  a clergyman, a fellow of Emanuel College, Cambridge, and in later life a
+  convert to Behmen's philosophy. He was so free in his charities that the
+  village in which he lived became so infested by beggars that he was urged
+  by the citizens to leave. He wrote <i>A serious call to a devout and holy
+  life</i> (1728).</p>
+
+  <p><a name="Nt_581" href="#NtA_581">[581]</a> He was a curate at
+  Cheshunt, and wrote the <i>Spiritual voice to the Christian Church and to
+  the Jews</i> (London, 1760), <i>A second warning to the world by the
+  Spirit of Prophecy</i> (London, 1760), and <i>Signs of the Times; or a
+  Voice to Babylon</i> (London, 1773).</p>
+
+  <p><a name="Nt_582" href="#NtA_582">[582]</a> His real name was Thomas
+  Vaughan (1622-1666). He was a fellow of Jesus College, Oxford, taking
+  orders, but was deprived of his living on account of drunkenness. He
+  became a mystic philosopher and gave attention to alchemy. His works had
+  a large circulation, particularly on the continent. He wrote <i>Magia
+  Adamica</i> (London, 1650), <i>Euphrates; or the Waters of the East</i>
+  (London, 1655), and <i>The Chymist's key to shut, and to open; or the
+  True Doctrine of Corruption and Generation</i> (London, 1657).</p>
+
+  <p><a name="Nt_583" href="#NtA_583">[583]</a> Emanuel Swedenborg, or
+  Svedberg (1688-1772) the mystic. It is not commonly known to
+  mathematicians that he was one of their guild, but he wrote on both
+  mathematics and chemistry. Among his works are the <i>Regelkonst eller
+  algebra</i> (Upsala, 1718) and the <i>Methodus nova inveniendi
+  longitudines locorum, terra marique, ope lunae</i> (Amsterdam, 1721,
+  1727, and 1766). After 1747 he devoted his attention to mystic
+  philosophy.</p>
+
+  <p><a name="Nt_584" href="#NtA_584">[584]</a> Pierre Simon Laplace
+  (1749-1827), whose <i>Exposition du système du monde</i> (1796) and
+  <i>Traité de mécanique celeste</i> (1799) are well known.</p>
+
+  <p><a name="Nt_585" href="#NtA_585">[585]</a> See note <a
+  href="#Nt_117">117</a>, page <a href="#page76">76</a>.</p>
+
+  <p><a name="Nt_586" href="#NtA_586">[586]</a> John Dalton (1766-1844),
+  who taught mathematics and physics at New College, Manchester (1793-1799)
+  and was the first to state the law of the expansion of gases known by his
+  name and that of Gay-Lussac. His <i>New system of Chemical Philosophy</i>
+  (Vol. I, pt. i, 1808; pt. ii, 1810; vol. II, 1827) sets forth his atomic
+  theory.</p>
+
+  <p><a name="Nt_587" href="#NtA_587">[587]</a> Howison was a poet and
+  philosopher. He lived in Edinburgh and was a friend of Sir Walter Scott.
+  This work appeared in 1822.</p>
+
+  <p><a name="Nt_588" href="#NtA_588">[588]</a> He was a shoemaker, born
+  about 1765 at Haddiscoe, and his "astro-historical" lectures at Norwich
+  attracted a good deal of attention at one time. He traced all geologic
+  changes to differences in the inclination of the earth's axis to the
+  plane of its orbit. Of the works mentioned by De Morgan the first
+  appeared at Norwich in 1822-1823, and there was a second edition in 1824.
+  The second appeared in 1824-1825. The fourth was <i>Urania's Key to the
+  Revelation; or the analyzation of the writings of the Jews...</i>, and
+  was first published at Norwich in 1823, there being a second edition at
+  London in 1833. His books were evidently not a financial success, for
+  Mackey died in an almshouse at Norwich.</p>
+
+  <p><a name="Nt_589" href="#NtA_589">[589]</a> Godfrey Higgins
+  (1773-1833), the archeologist, was interested in the history of religious
+  beliefs and in practical sociology. He wrote <i>Horae Sabbaticae</i>
+  (1826), <i>The Celtic Druids</i> (1827 and 1829), and <i>Anacalypsis, an
+  attempt to draw aside the veil of the Saitic Isis; or an Inquiry into the
+  Origin of Languages, Nations, and Religions</i> (posthumously published,
+  1836), and other works. See also page <a href="#page274">274</a>,
+  <i>infra</i>.</p>
+
+  <p><a name="Nt_590" href="#NtA_590">[590]</a> The work also appeared in
+  French. Wirgman wrote, or at least began, two other works:
+  <i>Divarication of the New Testament into Doctrine and History; part I,
+  The Four Gospels</i> (London, 1830), and <i>Mental Philosophy; part I,
+  Grammar of the five senses; being the first step to infant education</i>
+  (London, 1838).</p>
+
+  <p><a name="Nt_591" href="#NtA_591">[591]</a> He was born at Shandrum,
+  County Limerick, and supported himself by teaching writing and
+  arithmetic. He died in an almshouse at Cork.</p>
+
+  <p><a name="Nt_592" href="#NtA_592">[592]</a> George Boole (1815-1864),
+  professor of mathematics at Queens' College, Cork. His <i>Laws of
+  Thought</i> (1854) was the first work on the algebra of logic.</p>
+
+  <p><a name="Nt_593" href="#NtA_593">[593]</a> Oratio Grassi (1582-1654),
+  the Jesuit who became famous for his controversy with Galileo over the
+  theory of comets. Galileo ridiculed him in <i>Il Saggiatore</i>, although
+  according to the modern view Grassi was the more nearly right. It is said
+  that the latter's resentment led to the persecution of Galileo.</p>
+
+  <p><a name="Nt_594" href="#NtA_594">[594]</a> De Morgan might have found
+  much else for his satire in the letters of Walsh. He sought, in his
+  <i>Theory of Partial Functions</i>, to substitute "partial equations" for
+  the differential calculus. In his diary there is an entry: "Discovered
+  the general solution of numerical equations of the fifth degree at 114
+  Evergreen Street, at the Cross of Evergreen, Cork, at nine o'clock in the
+  forenoon of July 7th, 1844; exactly twenty-two years after the invention
+  of the Geometry of Partial Equations, and the expulsion of the
+  differential calculus from Mathematical Science."</p>
+
+  <p><a name="Nt_595" href="#NtA_595">[595]</a> "It has been ordered, sir,
+  it has been ordered."</p>
+
+  <p><a name="Nt_596" href="#NtA_596">[596]</a> Bartholomew Prescot was a
+  Liverpool accountant. De Morgan gives this correct spelling on page <a
+  href="#page278">278</a>. He died after 1849. His <i>Inverted Scheme of
+  Copernicus</i> appeared in Liverpool in 1822.</p>
+
+  <p><a name="Nt_597" href="#NtA_597">[597]</a> Robert Taylor (1784-1844)
+  had many more ups and downs than De Morgan mentions. He was a priest of
+  the Church of England, but resigned his parish in 1818 after preaching
+  against Christianity. He soon recanted and took another parish, but was
+  dismissed by the Bishop almost immediately on the ground of heresy. As
+  stated in the text, he was convicted of blasphemy in 1827 and was
+  sentenced to a year's imprisonment, and again for two years on the same
+  charge in 1831. He then married a woman who was rich in money and in
+  years, and was thereupon sued for breach of promise by another woman. To
+  escape paying the judgment that was rendered against him he fled to Tours
+  where he took up surgery.</p>
+
+  <p><a name="Nt_598" href="#NtA_598">[598]</a> Herbert Marsh, Bishop of
+  Peterborough. See note <a href="#Nt_449">449</a> on page <a
+  href="#page199">199</a>.</p>
+
+  <p><a name="Nt_599" href="#NtA_599">[599]</a> "Argument from the
+  prison."</p>
+
+  <p><a name="Nt_600" href="#NtA_600">[600]</a> Richard Carlile
+  (1790-1843), one of the leading radicals of his time. He published Hone's
+  parodies (see note <a href="#Nt_250">250</a>, page <a
+  href="#page124">124</a>) after they had been suppressed, and an edition
+  of Thomas Paine (1818). He was repeatedly imprisoned, serving nine years
+  in all. His continued conflict with the authorities proved a good
+  advertisement for his bookshop.</p>
+
+  <p><a name="Nt_601" href="#NtA_601">[601]</a> Wilhelm Ludwig Christmann
+  (1780-1835) was a protestant clergyman and teacher of mathematics. For a
+  while he taught under Pestalozzi. Disappointed in his ambition to be
+  professor of mathematics at Tubingen, he became a confirmed misanthrope
+  and is said never to have left his house during the last ten years of his
+  life. He wrote several works: <i>Ein Wort über Pestalozzi und
+  Pestalozzismus</i> (1812); <i>Ars cossae promota</i> (1814);
+  <i>Philosophia cossica</i> (1815); <i>Aetas argentea cossae</i> (1819);
+  <i>Ueber Tradition und Schrift, Logos und Kabbala</i> (1829), besides the
+  one mentioned above. The word <i>coss</i> in the above titles was a
+  German name for algebra, from the Italian <i>cosa</i> (thing), the name
+  for the unknown quantity. It appears in English in the early name for
+  algebra, "the cossic art."</p>
+
+  <p><a name="Nt_602" href="#NtA_602">[602]</a> See note <a
+  href="#Nt_174">174</a>, page <a href="#page101">101</a>.</p>
+
+  <p><a name="Nt_603" href="#NtA_603">[603]</a> See note <a
+  href="#Nt_589">589</a>, page <a href="#page257">257</a>.</p>
+
+  <p><a name="Nt_604" href="#NtA_604">[604]</a> He seems to have written
+  nothing else.</p>
+
+  <p><a name="Nt_605" href="#NtA_605">[605]</a> See note <a
+  href="#Nt_596">596</a> on page <a href="#page270">270</a>. The name is
+  here spelled correctly.</p>
+
+  <p><a name="Nt_606" href="#NtA_606">[606]</a> Joseph Jacotot (1770-1840),
+  the father of this Fortuné Jacotot, was an infant prodigy. At nineteen he
+  was made professor of the humanities at Dijon. He served in the army, and
+  then became professor of mathematics at Dijon. He continued in his chair
+  until the restoration of the Bourbons, and then fled to Louvain. It was
+  here that he developed the method with which his name is usually
+  connected. He wrote a <i>Mathématiques</i> in 1827, which went through
+  four editions. The <i>Epitomé</i> is by his son, Fortuné.</p>
+
+  <p><a name="Nt_607" href="#NtA_607">[607]</a> He wrote on educational
+  topics and a <i>Sacred History</i> that went through several
+  editions.</p>
+
+  <p><a name="Nt_608" href="#NtA_608">[608]</a> "All is in all."</p>
+
+  <p><a name="Nt_609" href="#NtA_609">[609]</a> "Know one thing and refer
+  everything else to it," as it is often translated.</p>
+
+  <p><a name="Nt_610" href="#NtA_610">[610]</a> A writer of no
+  reputation.</p>
+
+  <p><a name="Nt_611" href="#NtA_611">[611]</a> Sir John Lubbock
+  (1803-1865), banker, scientist, publicist, astronomer, one of the
+  versatile men of his time.</p>
+
+  <p><a name="Nt_612" href="#NtA_612">[612]</a> See note <a
+  href="#Nt_165">165</a>, page <a href="#page99">99</a>.</p>
+
+  <p><a name="Nt_613" href="#NtA_613">[613]</a> "Those about to die salute
+  you."</p>
+
+  <p><a name="Nt_614" href="#NtA_614">[614]</a> Georges Louis Leclerc
+  Buffon (1707-1788), the well-known biologist. He also experimented with
+  burning mirrors, his results appearing in his <i>Invention des miroirs
+  ardens pour brûler à une grande distance</i> (1747). The reference here
+  may be to his <i>Resolution des problèmes qui regardent le jeu du franc
+  carreau</i> (1733). The prominence of his <i>Histoire naturelle</i> (36
+  volumes, 1749-1788) has overshadowed the credit due to him for his
+  translation of Newton's work on Fluxions.</p>
+
+  <p><a name="Nt_615" href="#NtA_615">[615]</a> See page <a
+  href="#page285">285</a>. This article was a supplement to No. 14 in the
+  <i>Athenæum</i> Budget.&mdash;A. De M.</p>
+
+  <p><a name="Nt_616" href="#NtA_616">[616]</a> There are many similar
+  series and products. Among the more interesting are the following:</p>
+
+<table class="math"><tr><td>
+<span class="grk">&pi;</span><br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />2</td><td>=</td><td>2·2·4·4·6·6·8...<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />1·3·3·5·5·7·7...</td><td>,
+</td></tr></table>
+
+<table class="math"><tr><td>
+<span class="grk">&pi;</span>-3<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />4</td><td>=</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />2·3·4</td><td>-</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />4·5·6</td><td>+</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />6·7·8</td><td>-...,
+</td></tr></table>
+
+<table class="math"><tr><td>
+<span class="grk">&pi;</span><br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />6</td><td>=</td><td><img src="images/$sqrt.png" style="height:4ex; width:0.5em" alt="square root" /></td><td></td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3</td><td>·</td><td><img src="images/$lbracket.png" style="height:4ex; width:0.5em" alt="left bracket" /></td><td>1 -</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3·3</td><td>+</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3<sup>2</sup>·5</td><td>-</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3<sup>3</sup>·7</td><td>+</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3<sup>4</sup>·9</td><td>- ...</td><td><img src="images/$rbracket.png" style="height:4ex; width:0.5em" alt="right bracket" /></td><td>,
+</td></tr></table>
+
+<table class="math"><tr><td>
+<span class="grk">&pi;</span><br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />4</td><td>= 4</td><td><img src="images/$lbracket.png" style="height:4ex; width:0.5em" alt="left bracket" /></td><td></td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />5</td><td>-</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3·5<sup>3</sup></td><td>+</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />5·5<sup>5</sup></td><td>-</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />7·5<sup>7</sup></td><td>+ ...</td><td><img src="images/$rbracket.png" style="height:4ex; width:0.5em" alt="right bracket" /></td><td> - </td><td><img src="images/$lbracket.png" style="height:4ex; width:0.5em" alt="left bracket" /></td><td></td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />239</td><td>-</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3·239<sup>3</sup></td><td>+</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />5·239<sup>5</sup></td><td>- ...</td><td><img src="images/$rbracket.png" style="height:4ex; width:0.5em" alt="right bracket" /></td><td>.
+</td></tr></table>
+
+  <p><a name="Nt_617" href="#NtA_617">[617]</a> "To a privateer, a
+  privateer and a half."</p>
+
+  <p><a name="Nt_618" href="#NtA_618">[618]</a> Joshua Milne (1776-1851)
+  was actuary of the Sun Life Assurance Society. He wrote <i>A Treatise on
+  the Valuation of Annuities and Assurances on Lives and Survivorships; on
+  the Construction of tables of mortality; and on the Probabilities and
+  Expectations of Life</i>, London, 1815. Upon the basis of the Carlisle
+  bills of mortality of Dr. Heysham he reconstructed the mortality tables
+  then in use and which were based upon the Northampton table of Dr. Price.
+  His work revolutionized the actuarial science of the time. In later years
+  he devoted his attention to natural history.</p>
+
+  <p><a name="Nt_619" href="#NtA_619">[619]</a> See note <a
+  href="#Nt_576">576</a>, page <a href="#page252">252</a>. He also wrote
+  the <i>Theory of Parallels. The proof of Euclid's axiom looked for in the
+  properties of the equiangular spiral</i> (London, 1840), which went
+  through four editions, and the <i>Theory of Parallels. The proof that the
+  three angles of a triangle are equal to two right angles looked for in
+  the inflation of the sphere</i> (London, 1853), of which there were three
+  editions.</p>
+
+  <p><a name="Nt_620" href="#NtA_620">[620]</a> For the latest summary, see
+  W. B. Frankland, <i>Theories of Parallelism, an historical critique</i>,
+  Cambridge, 1910.</p>
+
+  <p><a name="Nt_621" href="#NtA_621">[621]</a> Joseph Louis Lagrange
+  (1736-1813), author of the <i>Mécanique analytique</i> (1788), <i>Théorie
+  des functions analytiques</i> (1797), <i>Traité de la résolution des
+  équations numériques de tous degrés</i> (1798), <i>Leçons sur le calcul
+  des fonctions</i> (1806), and many memoirs. Although born in Turin and
+  spending twenty of his best years in Germany, he is commonly looked upon
+  as the great leader of French mathematicians. The last twenty-seven years
+  of his life were spent in Paris, and his remarkable productivity
+  continued to the time of his death. His genius in the theory of numbers
+  was probably never excelled except by Fermat. He received very high
+  honors at the hands of Napoleon and was on the first staff of the Ecole
+  polytechnique (1797).</p>
+
+  <p><a name="Nt_622" href="#NtA_622">[622]</a> "I shall have to think it
+  over again."</p>
+
+  <p><a name="Nt_623" href="#NtA_623">[623]</a> Henry Goulburn (1784-1856)
+  held various government posts. He was under-secretary for war and the
+  colonies (1813), commissioner to negotiate peace with America (1814),
+  chief secretary to the Lord Lieutenant of Ireland (1821), and several
+  times Chancellor of the Exchequer. On the occasion mentioned by De Morgan
+  he was standing for parliament, and was successful.</p>
+
+  <p><a name="Nt_624" href="#NtA_624">[624]</a> On Drinkwater Bethune see
+  note <a href="#Nt_165">165</a>, page <a href="#page99">99</a>.</p>
+
+  <p><a name="Nt_625" href="#NtA_625">[625]</a> Charles Henry Cooper
+  (1808-1866) was a biographer and antiquary. He was town clerk of
+  Cambridge (1849-1866) and wrote the <i>Annals of Cambridge</i>
+  (1842-1853). His <i>Memorials of Cambridge</i> (1874) appeared after his
+  death. Thompson Cooper was his son, and the two collaborated in the
+  <i>Athenae Cantabrigiensis</i> (1858).</p>
+
+  <p><a name="Nt_626" href="#NtA_626">[626]</a> William Yates Peel
+  (1789-1858) was a brother of Sir Robert Peel, he whose name degenerated
+  into the familiar title of the London "Bobby" or "Peeler." Yates Peel was
+  a member of parliament almost continuously from 1817 to 1852. He
+  represented Cambridge at Westminster from 1831 to 1835.</p>
+
+  <p><a name="Nt_627" href="#NtA_627">[627]</a> Henry John Temple, third
+  Viscount of Palmerston (1784-1865), was member for Cambridge in 1811,
+  1818, 1820, 1826 (defeating Goulburn), and 1830. He failed of reelection
+  in 1831 because of his advocacy of reform. This must have been the time
+  when Goulburn defeated him. He was Foreign Secretary (1827) and Secretary
+  of State for Foreign Affairs (1830-1841, and 1846-1851). It is said of
+  him that he "created Belgium, saved Portugal and Spain from absolutism,
+  rescued Turkey from Russia and the highway to India from France." He was
+  Prime Minister almost continuously from 1855 to 1865, a period covering
+  the Indian Mutiny and the American Civil War.</p>
+
+  <p><a name="Nt_628" href="#NtA_628">[628]</a> William Cavendish, seventh
+  Duke of Devonshire (1808-1891). He was member for Cambridge from 1829 to
+  1831, but was defeated in 1831 because he had favored parliamentary
+  reform. He became Earl of Burlington in 1834, and Duke of Devonshire in
+  1858. He was much interested in the promotion of railroads and in the
+  iron and steel industries.</p>
+
+  <p><a name="Nt_629" href="#NtA_629">[629]</a> Richard Sheepshanks
+  (1794-1855) was a brother of John Sheepshanks the benefactor of art. (See
+  note <a href="#Nt_314">314</a>, p. <a href="#page147">147</a>.) He was a
+  fellow of Trinity College, Cambridge, a fellow of the Royal Society and
+  secretary of the Astronomical Society. Babbage (See note <a
+  href="#Nt_469">469</a>, p. <a href="#page207">207</a>) suspected him of
+  advising against the government support of his calculating machine and
+  attacked him severely in his <i>Exposition of 1851</i>, in the chapter on
+  <i>The Intrigues of Science</i>. Babbage also showed that Sheepshanks got
+  an astronomical instrument of French make through the custom house by
+  having Troughton's (See note <a href="#Nt_332">332</a>, page <a
+  href="#page152">152</a>) name engraved on it. Sheepshanks admitted this
+  second charge, but wrote a <i>Letter in Reply to the Calumnies of Mr.
+  Babbage</i>, which was published in 1854. He had a highly controversial
+  nature.</p>
+
+  <p><a name="Nt_630" href="#NtA_630">[630]</a> See note <a
+  href="#Nt_469">469</a>, page <a href="#page207">207</a>. The work
+  referred to is <i>Passages from the Life of a Philosopher</i>, London,
+  1864.</p>
+
+  <p><a name="Nt_631" href="#NtA_631">[631]</a> Drinkwater Bethune. See
+  note <a href="#Nt_165">165</a>, page <a href="#page99">99</a>.</p>
+
+  <p><a name="Nt_632" href="#NtA_632">[632]</a> Siméon-Denis Poisson
+  (1781-1840) was professor of calculus and mechanics at the Ecole
+  polytechnique. He was made a baron by Napoleon, and was raised to the
+  peerage in 1837. His chief works are the <i>Traité de mécanìque</i>
+  (1811) and the <i>Traité mathématique de la chaleur</i> (1835).</p>
+
+  <p><a name="Nt_633" href="#NtA_633">[633]</a> "As to M. Poisson, I really
+  wish I had a thousandth part of his mathematical knowledge that I might
+  prove my system to the incredulous."</p>
+
+  <p><a name="Nt_634" href="#NtA_634">[634]</a> This list includes most of
+  the works of Antoine-Louis-Guénard Demonville. There was also the
+  <i>Nouveau système du monde ... et hypothèses conformes aux expériences
+  sur les vents, sur la lumière et sur le fluide électro-magnétique</i>,
+  Paris, 1830.</p>
+
+  <p><a name="Nt_635" href="#NtA_635">[635]</a> Paris, 1835.</p>
+
+  <p><a name="Nt_636" href="#NtA_636">[636]</a> Paris, 1833.</p>
+
+  <p><a name="Nt_637" href="#NtA_637">[637]</a> The second part appeared in
+  1837. There were also editions in 1850 and 1852, and one edition appeared
+  without date.</p>
+
+  <p><a name="Nt_638" href="#NtA_638">[638]</a> Paris, 1842.</p>
+
+  <p><a name="Nt_639" href="#NtA_639">[639]</a> Parsey also wrote <i>The
+  Art of Miniature Painting on Ivory</i> (1831), <i>Perspective
+  Rectified</i> (1836), and <i>The Science of Vision</i> (1840), the third
+  being a revision of the second.</p>
+
+  <p><a name="Nt_640" href="#NtA_640">[640]</a> William Ritchie (1790-1837)
+  was a physicist who had studied at Paris under Biot and Gay-Lussac. He
+  contributed several papers on electricity, heat, and elasticity, and was
+  looked upon as a good experimenter. Besides the geometry he wrote the
+  <i>Principles of the Differential and Integral Calculus</i> (1836).</p>
+
+  <p><a name="Nt_641" href="#NtA_641">[641]</a> Alfred Day (1810-1849) was
+  a man who was about fifty years ahead of his time in his attempt to get
+  at the logical foundations of geometry. It is true that he laid himself
+  open to criticism, but his work was by no means bad. He also wrote <i>A
+  Treatise on Harmony</i> (1849, second edition 1885), <i>The Rotation of
+  the Pendulum</i> (1851), and several works on Greek and Latin
+  Grammar.</p>
+
+  <p><a name="Nt_642" href="#NtA_642">[642]</a> Walter Forman wrote a
+  number of controversial tracts. His first seems to have been <i>A plan
+  for improving the Revenue without adding to the burdens of the
+  people</i>, a letter to Canning in 1813. He also wrote <i>A New Theory of
+  the Tides</i> (1822). His <i>Letter to Lord John Russell, on Lord
+  Brougham's most extraordinary conduct; and another to Sir J. Herschel, on
+  the application of Kepler's third law</i> appeared in 1832.</p>
+
+  <p><a name="Nt_643" href="#NtA_643">[643]</a> Lord John Russell
+  (1792-1878) first Earl Russell, was one of the strongest supporters of
+  the reform measures of the early Victorian period. He became prime
+  minister in 1847, and again in 1865.</p>
+
+  <p><a name="Nt_644" href="#NtA_644">[644]</a> Lauder seems never to have
+  written anything else.</p>
+
+  <p><a name="Nt_645" href="#NtA_645">[645]</a> See note <a
+  href="#Nt_22">22</a>, page <a href="#page40">40</a>.</p>
+
+  <p><a name="Nt_646" href="#NtA_646">[646]</a> The names of Alphonso Cano
+  de Molina, Yvon, and Robert Sara have no standing in the history of the
+  subject beyond what would be inferred from De Morgan's remark.</p>
+
+  <p><a name="Nt_647" href="#NtA_647">[647]</a> Claude Mydorge (1585-1647),
+  an intimate friend of Descartes, was a dilletante in mathematics who read
+  much but accomplished little. His <i>Récréations mathématiques</i> is his
+  chief work. Boncompagni published the "Problèmes de Mydorge" in his
+  <i>Bulletino</i>.</p>
+
+  <p><a name="Nt_648" href="#NtA_648">[648]</a> Claude Hardy was born
+  towards the end of the 16th century and died at Paris in 1678. In 1625 he
+  edited the <i>Data Euclidis</i>, publishing the Greek text with a Latin
+  translation. He was a friend of Mydorge and Descartes, but an opponent of
+  Fermat.</p>
+
+  <p><a name="Nt_649" href="#NtA_649">[649]</a> That is, in the
+  <i>Bibliotheca Realis</i> of Martin Lipen, or Lipenius (1630-1692), which
+  appeared in six folio volumes, at Frankfort, 1675-1685.</p>
+
+  <p><a name="Nt_650" href="#NtA_650">[650]</a> See note <a
+  href="#Nt_29">29</a>, page <a href="#page43">43</a>.</p>
+
+  <p><a name="Nt_651" href="#NtA_651">[651]</a> Baldassare Boncompagni
+  (1821-1894) was the greatest general collector of mathematical works that
+  ever lived, possibly excepting Libri. His magnificent library was
+  dispersed at his death. His <i>Bulletino</i> (1868-1887) is one of the
+  greatest source books on the history of mathematics that we have. He also
+  edited the works of Leonardo of Pisa.</p>
+
+  <p><a name="Nt_652" href="#NtA_652">[652]</a> He seems to have attracted
+  no attention since De Morgan's search, for he is not mentioned in recent
+  bibliographies.</p>
+
+  <p><a name="Nt_653" href="#NtA_653">[653]</a> Joseph-Louis Vincens de
+  Mouléon de Causans was born about the beginning of the l8th century. He
+  was a Knight of Malta, colonel in the infantry, prince of Conti, and
+  governor of the principality of Orange. His works on geometry are the
+  <i>Prospectus apologétique pour la quadrature du cercle</i> (1753), and
+  <i>La vraie géométrie transcendante</i> (1754).</p>
+
+  <p><a name="Nt_654" href="#NtA_654">[654]</a> See note <a
+  href="#Nt_119">119</a>, page <a href="#page80">80</a>.</p>
+
+  <p><a name="Nt_655" href="#NtA_655">[655]</a> See note <a
+  href="#Nt_120">120</a>, page <a href="#page81">81</a>.</p>
+
+  <p><a name="Nt_656" href="#NtA_656">[656]</a> Lieut. William Samuel
+  Stratford (1791-1853), was in active service during the Napoleonic wars
+  but retired from the army in 1815. He was first secretary of the
+  Astronomical Society (1820) and became superintendent of the Nautical
+  Almanac in 1831. With Francis Baily he compiled a star catalogue, and
+  wrote on Halley's (1835-1836) and Encke's (1838) comets.</p>
+
+  <p><a name="Nt_657" href="#NtA_657">[657]</a> See Sir J. Herschel's
+  <i>Astronomy</i>, p. 369.&mdash;A. De M.</p>
+
+  <p><a name="Nt_658" href="#NtA_658">[658]</a> Captain Ross had just stuck
+  a bit of brass there.&mdash;A. De M.</p>
+
+  <p>Sir James Clark Ross (1800-1862) was a rear admiral in the British
+  navy and an arctic and antarctic explorer of prominence. De Morgan's
+  reference is to Ross's discovery of the magnetic pole on June 1, 1831. In
+  1838 he was employed by the Admiralty on a magnetic survey of the United
+  Kingdom. He was awarded the gold medal of the geographical societies of
+  London and Paris in 1842.</p>
+
+  <p><a name="Nt_659" href="#NtA_659">[659]</a> John Partridge (1644-1715),
+  the well-known astrologer and almanac maker. Although bound to a
+  shoemaker in his early boyhood, he had acquired enough Latin at the age
+  of eighteen to read the works of the astrologers. He then mastered Greek
+  and Hebrew and studied medicine. In 1680 he began the publication of his
+  almanac, the <i>Merlinus Liberatus</i>, a book that acquired literary
+  celebrity largely through the witty comments upon it by such writers as
+  Swift and Steele.</p>
+
+  <p><a name="Nt_660" href="#NtA_660">[660]</a> See note <a
+  href="#Nt_642">642</a> on page <a href="#page296">296</a>.</p>
+
+  <p><a name="Nt_661" href="#NtA_661">[661]</a> William Woodley also
+  published several almanacs (1838, 1839, 1840) after his rejection by the
+  Astronomical Society in 1834.</p>
+
+  <p><a name="Nt_662" href="#NtA_662">[662]</a> It appeared at London.</p>
+
+  <p><a name="Nt_663" href="#NtA_663">[663]</a> The first edition appeared
+  in 1830, also at London.</p>
+
+  <p><a name="Nt_664" href="#NtA_664">[664]</a> See note <a
+  href="#Nt_441">441</a>, page <a href="#page196">196</a>.</p>
+
+  <p><a name="Nt_665" href="#NtA_665">[665]</a> Thomas Kerigan wrote <i>The
+  Young Navigator's Guide to the siderial and planetary parts of Nautical
+  Astronomy</i> (London, 1821, second edition 1828), a work on eclipses
+  (London, 1844), and the work on tides (London, 1847) to which De Morgan
+  refers.</p>
+
+  <p><a name="Nt_666" href="#NtA_666">[666]</a> Jean Sylvain Bailly, who
+  was guillotined. See note <a href="#Nt_365">365</a>, page <a
+  href="#page166">166</a>.</p>
+
+  <p><a name="Nt_667" href="#NtA_667">[667]</a> See note <a
+  href="#Nt_670">670</a>, page <a href="#page309">309</a>.</p>
+
+  <p><a name="Nt_668" href="#NtA_668">[668]</a> Laurent seems to have had
+  faint glimpses of the modern theory of matter. He is, however,
+  unknown.</p>
+
+  <p><a name="Nt_669" href="#NtA_669">[669]</a> See note <a
+  href="#Nt_133">133</a>, page <a href="#page87">87</a>.</p>
+
+  <p><a name="Nt_670" href="#NtA_670">[670]</a> Francis Baily (1774-1844)
+  was a London stockbroker. His interest in science in general and in
+  astronomy in particular led to his membership in the Royal Society and to
+  his presidency of the Astronomical Society. He wrote on interest and
+  annuities (1808), but his chief works were on astronomy.</p>
+
+  <p><a name="Nt_671" href="#NtA_671">[671]</a> If the story is correctly
+  told Baily must have enjoyed his statement that Gauss was "the oldest
+  mathematician now living." As a matter of fact he was then only 58, three
+  years the junior of Baily himself. Gauss was born in 1777 and died in
+  1855, and Baily was quite right in saying that he was "generally thought
+  to be the greatest" mathematician then living.</p>
+
+  <p><a name="Nt_672" href="#NtA_672">[672]</a> Margaret Cooke, who married
+  Flamsteed in 1692.</p>
+
+  <p><a name="Nt_673" href="#NtA_673">[673]</a> John Brinkley (1763-1835),
+  senior wrangler, first Smith's prize-man (1788), Andrews professor of
+  astronomy at Dublin, first Astronomer Royal for Ireland (1792), F.R.S.
+  (1803), Copley medallist, president of the Royal Society and Bishop of
+  Cloyne. His <i>Elements of Astronomy</i> appeared in 1808.</p>
+
+  <p><a name="Nt_674" href="#NtA_674">[674]</a> See note <a
+  href="#Nt_248">248</a>, page <a href="#page124">124</a>.</p>
+
+  <p><a name="Nt_675" href="#NtA_675">[675]</a> See note <a
+  href="#Nt_276">276</a>, page <a href="#page133">133</a>.</p>
+
+  <p><a name="Nt_676" href="#NtA_676">[676]</a> See note <a
+  href="#Nt_352">352</a>, page <a href="#page161">161</a>.</p>
+
+  <p><a name="Nt_677" href="#NtA_677">[677]</a> "It becomes the doctors of
+  the Sorbonne to dispute, the Pope to decree, and the mathematician to go
+  to Paradise on a perpendicular line."</p>
+
+  <p><a name="Nt_678" href="#NtA_678">[678]</a> See note <a
+  href="#Nt_124">124</a>, page <a href="#page83">83</a>.</p>
+
+  <p><a name="Nt_679" href="#NtA_679">[679]</a> See note <a
+  href="#Nt_621">621</a>, page <a href="#page288">288</a>.</p>
+
+  <p><a name="Nt_680" href="#NtA_680">[680]</a> Sylvain van de Weyer, who
+  was born at Louvain in 1802. He was a jurist and statesman, holding the
+  portfolio for foreign affairs (1831-1833), and being at one time
+  ambassador to England.</p>
+
+  <p><a name="Nt_681" href="#NtA_681">[681]</a> Henry Crabb Robinson
+  (1775-1867), correspondent of the <i>Times</i> at Altona and in the
+  Peninsula, and later foreign editor. He was one of the founders of the
+  Athenæum Club and of University College, London. He seems to have known
+  pretty much every one of his day, and his posthumous <i>Diary</i>
+  attracted attention when it appeared.</p>
+
+  <p><a name="Nt_682" href="#NtA_682">[682]</a> Was this Whewell, who was
+  at Trinity from 1812 to 1816 and became a fellow in 1817?</p>
+
+  <p><a name="Nt_683" href="#NtA_683">[683]</a> Tom Cribb (1781-1848) the
+  champion pugilist. He had worked as a coal porter and hence received his
+  nickname, the Black Diamond.</p>
+
+  <p><a name="Nt_684" href="#NtA_684">[684]</a> John Finleyson, or
+  Finlayson, was born in Scotland in 1770 and died in London in 1854. He
+  published a number of pamphlets that made a pretense to being scientific.
+  Among his striking phrases and sentences are the statements that the
+  stars were made "to amuse us in observing them"; that the earth is "not
+  shaped like a garden turnip as the Newtonians make it," and that the
+  stars are "oval-shaped immense masses of frozen water." The first edition
+  of the work here mentioned appeared at London in 1830.</p>
+
+  <p><a name="Nt_685" href="#NtA_685">[685]</a> Richard Brothers
+  (1757-1824) was a native of Newfoundland. He went to London when he was
+  about 30, and a little later set forth his claim to being a descendant of
+  David, prince of the Hebrews, and ruler of the world. He was confined as
+  a criminal lunatic in 1795 but was released in 1806.</p>
+
+  <p><a name="Nt_686" href="#NtA_686">[686]</a> Charles Grey (1764-1845),
+  second Earl Grey, Viscount Howick, was then Prime Minister. The Reform
+  Bill was introduced and defeated in 1831. The following year, with the
+  Royal guarantees to allow him to create peers, he finally carried the
+  bill in spite of "the number of the beast."</p>
+
+  <p><a name="Nt_687" href="#NtA_687">[687]</a> The letters of obscure men,
+  the <i>Epistolæ obscurorum virorum ad venerabilem virum Magistrum
+  Ortuinum Gratium Dauentriensem</i>, by Joannes Crotus, Ulrich von Hutten,
+  and others appeared at Venice about 1516.</p>
+
+  <p><a name="Nt_688" href="#NtA_688">[688]</a> The lamentations of obscure
+  men, the <i>Lamentationes obscurorum virorum, non prohibete per sedem
+  Apostolicam. Epistola D. Erasmi Roterodami: quid de obscuris sentiat</i>,
+  by G. Ortwinus, appeared at Cologne in 1518.</p>
+
+  <p><a name="Nt_689" href="#NtA_689">[689]</a> The criticism was timely
+  when De Morgan wrote it. At present it would have but little force with
+  respect to the better class of algebras.</p>
+
+  <p><a name="Nt_690" href="#NtA_690">[690]</a> Thomas Ignatius Maria
+  Forster (1789-1860) was more of a man than one would infer from this
+  satire upon his theory. He was a naturalist, astronomer, and
+  physiologist. In 1812 he published his <i>Researches about Atmospheric
+  Phenomena</i>, and seven years later (July 3, 1819) he discovered a
+  comet. With Sir Richard Phillips he founded a Meteorological Society, but
+  it was short lived. He declined a fellowship in the Royal Society because
+  he disapproved of certain of its rules, so that he had a recognized
+  standing in his day. The work mentioned by De Morgan is the second
+  edition, the first having appeared at Frankfort on the Main in 1835 under
+  the title, <i>Recueil des ouvrages et des pensées d'un physicien et
+  metaphysicien</i>.</p>
+
+  <p><a name="Nt_691" href="#NtA_691">[691]</a> Zadkiel, whose real name
+  was Richard James Morrison (1795-1874), was in his early years an officer
+  in the navy. In 1831 he began the publication of the <i>Herald of
+  Astrology</i>, which was continued as <i>Zadkiel's Almanac</i>. His name
+  became familiar throughout Great Britain as a result.</p>
+
+  <p><a name="Nt_692" href="#NtA_692">[692]</a> See note <a
+  href="#Nt_566">566</a>, page <a href="#page246">246</a>.</p>
+
+  <p><a name="Nt_693" href="#NtA_693">[693]</a> Sumner (1780-1862) was an
+  Eton boy. He went to King's College, Cambridge, and was elected fellow in
+  1801. He took many honors, and in 1807 became M.A. He was successively
+  Canon of Durham (1820), Bishop of Chester (1828), and Archbishop of
+  Canterbury (1848). Although he voted for the Catholic Relief Bill (1829)
+  and the Reform Bill (1832), he opposed the removal of Jewish
+  disabilities.</p>
+
+  <p><a name="Nt_694" href="#NtA_694">[694]</a> Charles Richard Sumner
+  (1790-1874) was not only Bishop of Winchester (1827), but also Bishop of
+  Llandaff and Dean of St. Paul's, London (1826). He lost the king's favor
+  by voting for the Catholic Relief Bill.</p>
+
+  <p><a name="Nt_695" href="#NtA_695">[695]</a> John Bird Sumner, brother
+  of Charles Richard.</p>
+
+  <p><a name="Nt_696" href="#NtA_696">[696]</a> Thomas Musgrave (1788-1860)
+  became Fellow of Trinity in 1812, and senior proctor in 1831. He was also
+  Dean of Bristol.</p>
+
+  <p><a name="Nt_697" href="#NtA_697">[697]</a> Charles Thomas Longley
+  (1794-1868) was educated at Westminster School and at Christ Church,
+  Oxford. He became M.A. in 1818 and D.D. in 1829. Besides the bishoprics
+  mentioned he was Bishop of Ripon (1836-1856), and before that was
+  headmaster of Harrow (1829-1836).</p>
+
+  <p><a name="Nt_698" href="#NtA_698">[698]</a> Thomson (1819-1890) was
+  scholar and fellow of Queen's College, Oxford. He became chaplain to the
+  Queen in 1859.</p>
+
+  <p><a name="Nt_699" href="#NtA_699">[699]</a> This is worthy of the
+  statistical psychologists of the present day.</p>
+
+  <p><a name="Nt_700" href="#NtA_700">[700]</a> The famous Moon Hoax was
+  written by Richard Adams Locke, who was born in New York in 1800 and died
+  in Staten Island in 1871. He was at one time editor of the <i>Sun</i>,
+  and the Hoax appeared in that journal in 1835. It was reprinted in London
+  (1836) and Germany, and was accepted seriously by most readers. It was
+  published in book form in New York in 1852 under the title <i>The Moon
+  Hoax</i>. Locke also wrote another hoax, the <i>Lost Manuscript of Mungo
+  Park</i>, but it attracted relatively little attention.</p>
+
+  <p><a name="Nt_701" href="#NtA_701">[701]</a> It is true that
+  Jean-Nicolas Nicollet (1756-1843) was at that time in the United States,
+  but there does not seem to be any very tangible evidence to connect him
+  with the story. He was secretary and librarian of the Paris observatory
+  (1817), member of the Bureau of Longitudes (1822), and teacher of
+  mathematics in the Lycée Louis-le-Grand. Having lost his money through
+  speculations he left France for the United States in 1831 and became
+  connected with the government survey of the Mississippi Valley.</p>
+
+  <p><a name="Nt_702" href="#NtA_702">[702]</a> This was Alexis Bouvard
+  (1767-1843), who made most of the computations for Laplace's <i>Mécanique
+  céleste</i> (1793). He discovered eight new comets and calculated their
+  orbits. In his tables of Uranus (1821) he attributed certain
+  perturbations to the presence of an undiscovered planet, but unlike
+  Leverrier and Adams he did not follow up this clue and thus discover
+  Neptune.</p>
+
+  <p><a name="Nt_703" href="#NtA_703">[703]</a> Patrick Murphy (1782-1847)
+  awoke to find himself famous because of his natural guess that there
+  would be very cold weather on January 20, although that is generally the
+  season of lowest temperature. It turned out that his forecasts were
+  partly right on 168 days and very wrong on 197 days.</p>
+
+  <p><a name="Nt_704" href="#NtA_704">[704]</a> He seems to have written
+  nothing else. If one wishes to enter into the subject of the mathematics
+  of the Great Pyramid there is an extensive literature awaiting him.
+  Richard William Howard Vyse (1784-1853) published in 1840 his
+  <i>Operations carried on at the Pyramids of Gizeh in 1837</i>, and in
+  this he made a beginning of a scientific metrical study of the subject.
+  Charles Piazzi Smyth (1819-1900), astronomer Royal for Scotland
+  (1845-1888) was much carried away with the number mysticism of the Great
+  Pyramid, so much so that he published in 1864 a work entitled <i>Our
+  Inheritance in the Great Pyramid</i>, in which his vagaries were set
+  forth. Although he was then a Fellow of the Royal Society (1857), his
+  work was so ill received that when he offered a paper on the subject it
+  was rejected (1874) and he resigned in consequence of this action. The
+  latest and perhaps the most scholarly of all investigators of the subject
+  is William Matthew Flinders Petrie (born in 1853), Edwards professor of
+  Egyptology at University College, London, whose <i>Pyramids and Temples
+  of Gizeh</i> (1883) and subsequent works are justly esteemed as
+  authorities.</p>
+
+  <p><a name="Nt_705" href="#NtA_705">[705]</a> As De Morgan subsequently
+  found, this name reversed becomes Oliver B...e, for Oliver Byrne, one of
+  the odd characters among the minor mathematical writers of the middle of
+  the last century. One of his most curious works is <i>The first six Books
+  of the Elements of Euclid; in which coloured diagrams and symbols are
+  used instead of letters</i> (1847). There is some merit in speaking of
+  the red triangle instead of the triangle ABC, but not enough to give the
+  method any standing. His <i>Dual Arithmetic</i> (1863-1867) was also a
+  curious work.</p>
+
+  <p><a name="Nt_706" href="#NtA_706">[706]</a> Brenan also wrote on
+  English composition (1829), a work that went through fourteen editions by
+  1865; a work entitled <i>The Foreigner's English Conjugator</i> (1831),
+  and a work on the national debt.</p>
+
+  <p><a name="Nt_707" href="#NtA_707">[707]</a> See note <a
+  href="#Nt_211">211</a>, page <a href="#page112">112</a>.</p>
+
+  <p><a name="Nt_708" href="#NtA_708">[708]</a> See note <a
+  href="#Nt_592">592</a>, page <a href="#page261">261</a>.</p>
+
+  <p><a name="Nt_709" href="#NtA_709">[709]</a> Sir William Rowan Hamilton
+  (1805-1865), the discoverer of quaternions (1852), was an infant prodigy,
+  competing with Zerah Colburn as a child. He was a linguist of remarkable
+  powers, being able, at thirteen years of age, to boast that he knew as
+  many languages as he had lived years. When only sixteen he found an error
+  in Laplace's <i>Mécanique céleste</i>. When only twenty-two he was
+  appointed Andrews professor of astronomy, and he soon after became
+  Astronomer Royal of Ireland. He was knighted in 1835. His earlier work
+  was on optics, his <i>Theory of Systems of Rays</i> appearing in 1823. In
+  1827 he published a paper on the principle of <i>Varying Action</i>. He
+  also wrote on dynamics.</p>
+
+  <p><a name="Nt_710" href="#NtA_710">[710]</a> "Let him not leave the
+  kingdom,"&mdash;a legal phrase.</p>
+
+  <p><a name="Nt_711" href="#NtA_711">[711]</a> Probably De Morgan is
+  referring to Johann Bernoulli III (1744-1807), who edited Lambert's
+  <i>Logische und philosophische Abhandlungen</i>, Berlin, 1782. He was
+  astronomer of the Academy of Sciences at Berlin.</p>
+
+  <p><a name="Nt_712" href="#NtA_712">[712]</a> Jacob Bernoulli (1654-1705)
+  was one of the two brothers who founded the famous Bernoulli family of
+  mathematicians, the other being Johann I. His <i>Ars conjectandi</i>
+  (1713), published posthumously, was the first distinct treatise on
+  probabilities.</p>
+
+  <p><a name="Nt_713" href="#NtA_713">[713]</a> Johann Heinrich Lambert
+  (1728-1777) was one of the most learned men of his time. Although
+  interested chiefly in mathematics, he wrote also on science, logic, and
+  philosophy.</p>
+
+  <p><a name="Nt_714" href="#NtA_714">[714]</a> Joseph Diez Gergonne
+  (1771-1859), a soldier under Napoleon, and founder of the <i>Annales de
+  mathématiques</i> (1810).</p>
+
+  <p><a name="Nt_715" href="#NtA_715">[715]</a> Gottfried Ploucquet
+  (1716-1790) was at first a clergyman, but afterwards became professor of
+  logic at Tübingen.</p>
+
+  <p><a name="Nt_716" href="#NtA_716">[716]</a> "In the premises let the
+  middle term be omitted; what remains indicates the conclusion."</p>
+
+  <p><a name="Nt_717" href="#NtA_717">[717]</a> Probably Sir William Edmond
+  Logan (1789-1875), who became so interested in geology as to be placed at
+  the head of the geological survey of Canada (1842). The University of
+  Montreal conferred the title LL.D. upon him, and Napoleon III gave him
+  the cross of the Legion of Honor.</p>
+
+  <p><a name="Nt_718" href="#NtA_718">[718]</a> "So strike that he may
+  think himself to die."</p>
+
+  <p><a name="Nt_719" href="#NtA_719">[719]</a> "Witticism or piece of
+  stupidity."</p>
+
+  <p><a name="Nt_720" href="#NtA_720">[720]</a> A very truculently unjust
+  assertion: for Sir W. was as great a setter up of some as he was a puller
+  down of others. His writings are a congeries of praises and blames, both
+  <i>cruel smart</i>, as they say in the States. But the combined
+  instigation of prose, rhyme, and retort would send Aristides himself to
+  Tartarus, if it were not pretty certain that Minos would grant a <i>stet
+  processus</i> under the circumstances. The first two verses are
+  exaggerations standing on a basis of truth. The fourth verse is quite
+  true: Sir W.&nbsp;H. was an Edinburgh Aristotle, with the difference of
+  ancient and modern Athens well marked, especially the <i>perfervidum
+  ingenium Scotorum</i>.&mdash;A. De M.</p>
+
+  <p><a name="Nt_721" href="#NtA_721">[721]</a> See note <a
+  href="#Nt_576">576</a>, p. <a href="#page252">252</a>. There was also a
+  <i>Theory of Parallels</i> that differed from these, London, 1853, second
+  edition 1856, third edition 1856.</p>
+
+  <p><a name="Nt_722" href="#NtA_722">[722]</a> The work was written by
+  Robert Chambers (1802-1871), the Edinburgh publisher, a friend of Scott
+  and of many of his contemporaries in the literary field. He published the
+  <i>Vestiges of the Natural History of Creation</i> in 1844, not 1840.</p>
+
+  <p><a name="Nt_723" href="#NtA_723">[723]</a> Everett (1784-1872) was at
+  that time a good Wesleyan, but was expelled from the ministry in 1849 for
+  having written <i>Wesleyan Takings</i> and as under suspicion for having
+  started the <i>Fly Sheets</i> in 1845. In 1857 he established the United
+  Methodist Free Church.</p>
+
+  <p><a name="Nt_724" href="#NtA_724">[724]</a> Smith was a Primitive
+  Methodist preacher. He also wrote an <i>Earnest Address to the
+  Methodists</i> (1841) and <i>The Wealth Question</i> (1840?).</p>
+
+  <p><a name="Nt_725" href="#NtA_725">[725]</a> He wrote the <i>Nouveau
+  traité de Balistique</i>, Paris, 1837.</p>
+
+  <p><a name="Nt_726" href="#NtA_726">[726]</a> Joseph Denison, known to
+  fame only through De Morgan. See also page <a
+  href="#page353">353</a>.</p>
+
+  <p><a name="Nt_727" href="#NtA_727">[727]</a> The radical (1784?-1858),
+  advocate of the founding of London university (1826), of medical reform
+  (1827-1834), and of the repeal of the duties on newspapers and corn, and
+  an ardent champion of penny postage.</p>
+
+  <p><a name="Nt_728" href="#NtA_728">[728]</a> I. e., Roman Catholic
+  Priest.</p>
+
+  <p><a name="Nt_729" href="#NtA_729">[729]</a> Murphy (1806-1843) showed
+  extraordinary powers in mathematics even before the age of thirteen. He
+  became a fellow of Caius College, Cambridge, in 1829, dean in 1831, and
+  examiner in mathematics in London University in 1838.</p>
+
+  <p><a name="Nt_730" href="#NtA_730">[730]</a> See note <a
+  href="#Nt_442">442</a>, page <a href="#page196">196</a>.</p>
+
+  <p><a name="Nt_731" href="#NtA_731">[731]</a> Sir John Bowring
+  (1792-1872), the linguist, writer, and traveler, member of many learned
+  societies and a writer of high reputation in his time. His works were
+  not, however, of genuine merit.</p>
+
+  <p><a name="Nt_732" href="#NtA_732">[732]</a> Joseph Hume (1777-1855)
+  served as a surgeon with the British army in India early in the
+  nineteenth century. He returned to England in 1808 and entered parliament
+  as a radical in 1812. He was much interested in all reform movements.</p>
+
+  <p><a name="Nt_733" href="#NtA_733">[733]</a> Sir Robert Harry Inglis
+  (1786-1855), a strong Tory, known for his numerous addresses in the House
+  of Commons rather than for any real ability.</p>
+
+  <p><a name="Nt_734" href="#NtA_734">[734]</a> Sir Robert Peel (1788-1850)
+  began his parliamentary career in 1809 and was twice prime minister. He
+  was prominent in most of the great reforms of his time.</p>
+
+  <p><a name="Nt_735" href="#NtA_735">[735]</a> See note <a
+  href="#Nt_627">627</a>, page <a href="#page290">290</a>.</p>
+
+  <p><a name="Nt_736" href="#NtA_736">[736]</a> John Taylor (1781-1864) was
+  a publisher, and published several pamphlets opposed to Peel's currency
+  measures. De Morgan refers to his work on the Junius question. This was
+  done early in his career, and resulted in <i>A Discovery of the author of
+  the Letters of Junius</i> (1813), and <i>The Identity of Junius with a
+  distinguished living character established</i> (1816), this being Sir
+  Philip Francis.</p>
+
+  <p><a name="Nt_737" href="#NtA_737">[737]</a> See note <a
+  href="#Nt_665">665</a>, page <a href="#page308">308</a>.</p>
+
+  <p><a name="Nt_738" href="#NtA_738">[738]</a> See page <a
+  href="#page348">348</a>.</p>
+
+  <p><a name="Nt_739" href="#NtA_739">[739]</a> See note <a
+  href="#Nt_348">348</a>, page <a href="#page160">160</a>.</p>
+
+  <p><a name="Nt_740" href="#NtA_740">[740]</a> Sir Nicholas Harris Nicolas
+  (1799-1848) was a reformer in various lines,&mdash;the Record Commission,
+  the Society of Antiquaries, and the British Museum,&mdash;and his work
+  was not without good results.</p>
+
+  <p><a name="Nt_741" href="#NtA_741">[741]</a> See note <a
+  href="#Nt_98">98</a>, page <a href="#page69">69</a>.</p>
+
+  <p><a name="Nt_742" href="#NtA_742">[742]</a> In the <i>Companion to the
+  Almanac</i> for 1845 is a paper by Prof. De Morgan, "On the
+  Ecclesiastical Calendar," the statements of which, so far as concerns the
+  Gregorian Calendar, are taken direct from the work of Clavius, the
+  principal agent in the arrangement of the reformed reckoning. This was
+  followed, in the <i>Companion to the Almanac</i> for 1846, by a second
+  paper, by the same author, headed "On the Earliest Printed Almanacs,"
+  much of which is written in direct supplement to the former
+  article.&mdash;S.&nbsp;E. De Morgan.</p>
+
+  <p><a name="Nt_743" href="#NtA_743">[743]</a> It may be necessary to
+  remind some English readers that in Latin and its derived European
+  languages, what we call Easter is called the passover (<i>pascha</i>).
+  The Quartadecimans had the <i>name</i> on their side: a possession which
+  often is, in this world, nine points of the law.&mdash;A. De M.</p>
+
+  <p><a name="Nt_744" href="#NtA_744">[744]</a> Socrates Scholasticus was
+  born at Constantinople c. 379, and died after 439. His <i>Historia
+  Ecclesiastica</i> (in Greek) covers the period from Constantine the Great
+  to about 439, and includes the Council of Nicæa. The work was printed in
+  Paris 1544.</p>
+
+  <p><a name="Nt_745" href="#NtA_745">[745]</a> Theodoretus or Theodoritus
+  was born at Antioch and died about 457. He was one of the greatest
+  divines of the fifth century, a man of learning, piety, and judicial
+  mind, and a champion of freedom of opinion in all religious matters.</p>
+
+  <p><a name="Nt_746" href="#NtA_746">[746]</a> He died in 417. He was a
+  man of great energy and of high attainments.</p>
+
+  <p><a name="Nt_747" href="#NtA_747">[747]</a> He died in 461, having
+  reigned as pope for twenty-one years. It was he who induced Attila to
+  spare Rome in 452.</p>
+
+  <p><a name="Nt_748" href="#NtA_748">[748]</a> He succeeded Leo as pope in
+  461, and reigned for seven years.</p>
+
+  <p><a name="Nt_749" href="#NtA_749">[749]</a> Victorinus or Victorius
+  Marianus seems to have been born at Limoges. He was a mathematician and
+  astronomer, and the cycle mentioned by De Morgan is one of 532 years, a
+  combination of the Metonic cycle of 19 years with the solar cycle of 28
+  years. His canon was published at Antwerp in 1633 or 1634, <i>De doctrina
+  temporum sive commentarius in Victorii Aquitani et aliorum canones
+  paschales</i>.</p>
+
+  <p><a name="Nt_750" href="#NtA_750">[750]</a> He went to Rome about 497,
+  and died there in 540. He wrote his <i>Liber de paschate</i> in 525, and
+  it was in this work that the Christian era was first used for calendar
+  purposes.</p>
+
+  <p><a name="Nt_751" href="#NtA_751">[751]</a> See note <a
+  href="#Nt_259">259</a>, page <a href="#page126">126</a>.</p>
+
+  <p><a name="Nt_752" href="#NtA_752">[752]</a> Johannes de Sacrobosco
+  (Holy wood), or John of Holywood. The name was often written, without
+  regard to its etymology, Sacrobusto. He was educated at Oxford and taught
+  in Paris until his death (1256). He did much to make the Hindu-Arabic
+  numerals known to European scholars.</p>
+
+  <p><a name="Nt_753" href="#NtA_753">[753]</a> See note <a
+  href="#Nt_36">36</a>, page <a href="#page44">44</a>.</p>
+
+  <p><a name="Nt_754" href="#NtA_754">[754]</a> See note <a
+  href="#Nt_45">45</a>, page <a href="#page48">48</a>.</p>
+
+  <p><a name="Nt_755" href="#NtA_755">[755]</a> The Julian year is a year
+  of the Julian Calendar, in which there is leap year every fourth year.
+  Its average length is therefore 365 days and a quarter.&mdash;A. De
+  M.</p>
+
+  <p><a name="Nt_756" href="#NtA_756">[756]</a> Ugo Buoncompagno
+  (1502-1585) was elected pope in 1572.</p>
+
+  <p><a name="Nt_757" href="#NtA_757">[757]</a> He was a Calabrian, and as
+  early as 1552 was professor of medicine at Perugia. In 1576 his
+  manuscript on the reform of the calendar was presented to the Roman Curia
+  by his brother, Antonius. The manuscript was not printed and it has not
+  been preserved.</p>
+
+  <p><a name="Nt_758" href="#NtA_758">[758]</a> The title of this work,
+  which is the authority on all points of the new Calendar, is
+  <i>Kalendarium Gregorianum Perpetuum. Cum Privilegio Summi Pontificis Et
+  Aliorum Principum. Romæ, Ex Officina Dominici Basæ. MDLXXXII. Cum
+  Licentia Superiorum</i> (quarto, pp. 60).&mdash;A. De M.</p>
+
+  <p><a name="Nt_759" href="#NtA_759">[759]</a> <i>Manuels-Roret. Théorie
+  du Calendrier et collection de tous les Calendriers des Années passées et
+  futures</i>.... Par L.&nbsp;B. Franc&oelig;ur,... Paris, à la librairie
+  encyclopédique de Roret, rue Hautefeuille, 10 bis. 1842. (12mo.) In this
+  valuable manual, the 35 possible almanacs are given at length, with such
+  preliminary tables as will enable any one to find, by mere inspection,
+  which almanac he is to choose for any year, whether of old or new style.
+  [1866. I may now refer to my own <i>Book of Almanacs</i>, for the same
+  purpose].&mdash;A. De M.</p>
+
+  <p>Louis Benjamin Franc&oelig;ur (1773-1849), after holding positions in
+  the Ecole polytechnique (1804) and the Lycée Charlemagne (1805), became
+  professor of higher algebra in the University of Paris (1809). His
+  <i>Cours complet des mathématiques pures</i> was well received, and he
+  also wrote on mechanics, astronomy, and geodesy.</p>
+
+  <p><a name="Nt_760" href="#NtA_760">[760]</a> Albertus Pighius, or Albert
+  Pigghe, was born at Kempen c. 1490 and died at Utrecht in 1542. He was a
+  mathematician and a firm defender of the faith, asserting the supremacy
+  of the Pope and attacking both Luther and Calvin. He spent some time in
+  Rome. His greatest work was his <i>Hierarchiæ ecclesiasticæ assertio</i>
+  (1538).</p>
+
+  <p><a name="Nt_761" href="#NtA_761">[761]</a> This was A. F. Vogel. The
+  work was his translation from the German edition which appeared at
+  Leipsic the same year, <i>Entdeckung einer numerischen General-Auflösung
+  aller höheren endlichen Gleichungen von jeder beliebigen algebraischen
+  und transcendenten Form</i>.</p>
+
+  <p><a name="Nt_762" href="#NtA_762">[762]</a> The latest edition of
+  Burnside and Panton's <i>Theory of Equations</i> has this brief summary
+  of the present status of the problem: "Demonstrations have been given by
+  Abel and Wantzel (see Serret's <i>Cours d'Algèbre Supérieure</i>, Art.
+  516) of the impossibility of resolving algebraically equations
+  unrestricted in form, of a degree higher than the fourth. A
+  transcendental solution, however, of the quintic has been given by M.
+  Hermite, in a form involving elliptic integrals."</p>
+
+  <p><a name="Nt_763" href="#NtA_763">[763]</a> There was a second edition
+  of this work in 1846. The author's <i>Astronomy Simplified</i> was
+  published in 1838, and the <i>Thoughts on Physical Astronomy</i> in 1840,
+  with a second edition in 1842.</p>
+
+  <p><a name="Nt_764" href="#NtA_764">[764]</a> This was <i>The Science of
+  the Weather, by several authors... edited by B.</i>, Glasgow, 1867.</p>
+
+  <p><a name="Nt_765" href="#NtA_765">[765]</a> This was Y. Ramachandra,
+  son of Sundara L&#x101;la. He was a teacher of science in Delhi College,
+  and the work to which De Morgan refers is <i>A Treatise on problems of
+  Maxima and Minima solved by Algebra</i>, which appeared at Calcutta in
+  1850. De Morgan's edition was published at London nine years later.</p>
+
+  <p><a name="Nt_766" href="#NtA_766">[766]</a> Abraham de Moivre
+  (1667-1754), French refugee in London, poor, studying under difficulties,
+  was a man with tastes in some respects like those of De Morgan. For one
+  thing, he was a lover of books, and he had a good deal of interest in the
+  theory of probabilities to which De Morgan also gave much thought. His
+  introduction of imaginary quantities into trigonometry was an event of
+  importance in the history of mathematics, and the theorem that bears his
+  name, (cos <span class="grk">&phi;</span> + <i>i</i> sin <span
+  class="grk">&phi;</span>)<sup><i>n</i></sup> = cos <i>n</i><span
+  class="grk">&phi;</span> + <i>i</i> sin <i>n</i><span
+  class="grk">&phi;</span>, is one of the most important ones in all
+  analysis.</p>
+
+  <p><a name="Nt_767" href="#NtA_767">[767]</a> John Dolland (1706-1761),
+  the silk weaver who became the greatest maker of optical instruments in
+  his time.</p>
+
+  <p><a name="Nt_768" href="#NtA_768">[768]</a> Thomas Simpson (1710-1761),
+  also a weaver, taking his leisure from his loom at Spitalfields to teach
+  mathematics. His <i>New Treatise on Fluxions</i> (1737) was written only
+  two years after he began working in London, and six years later he was
+  appointed professor of mathematics at Woolwich. He wrote many works on
+  mathematics and Simpson's Formulas for computing trigonometric tables are
+  still given in the text-books.</p>
+
+  <p><a name="Nt_769" href="#NtA_769">[769]</a> Nicholas Saunderson
+  (1682-1739), the blind mathematician. He lost his eyesight through
+  smallpox when only a year old. At the age of 25 he began lecturing at
+  Cambridge on the principles of the Newtonian philosophy. His
+  <i>Algebra</i>, in two large volumes, was long the standard treatise on
+  the subject.</p>
+
+  <p><a name="Nt_770" href="#NtA_770">[770]</a> He was not in the class
+  with the others mentioned.</p>
+
+  <p><a name="Nt_771" href="#NtA_771">[771]</a> Not known in the literature
+  of mathematics.</p>
+
+  <p><a name="Nt_772" href="#NtA_772">[772]</a> Probably J. Butler Williams
+  whose <i>Practical Geodesy</i> appeared in 1842, with a third edition in
+  1855.</p>
+
+  <p><a name="Nt_773" href="#NtA_773">[773]</a> Benjamin Gompertz
+  (1779-1865) was debarred as a Jew from a university education. He studied
+  mathematics privately and became president of the Mathematical Society.
+  De Morgan knew him professionally through the fact that he was prominent
+  in actuarial work.</p>
+
+  <p><a name="Nt_774" href="#NtA_774">[774]</a> Referring to the
+  contributions of Archimedes (287-212 B.C.) to the mensuration of the
+  sphere.</p>
+
+  <p><a name="Nt_775" href="#NtA_775">[775]</a> The famous Alexandrian
+  astronomer (c. 87-c. 165 A.D.), author of the <i>Almagest</i>, a treatise
+  founded on the works of Hipparchus.</p>
+
+  <p><a name="Nt_776" href="#NtA_776">[776]</a> Dr. Whewell, when I
+  communicated this song to him, started the opinion, which I had before
+  him, that this was a very good idea, of which too little was
+  made.&mdash;A. De M.</p>
+
+  <p><a name="Nt_777" href="#NtA_777">[777]</a> See note <a
+  href="#Nt_117">117</a>, page <a href="#page76">76</a>.</p>
+
+  <p><a name="Nt_778" href="#NtA_778">[778]</a> The common epithet of rank:
+  <i>nobilis Tycho</i>, as he was a nobleman. The writer had been at
+  history.&mdash;A. De M.</p>
+
+  <p>See note <a href="#Nt_117">117</a>, page <a href="#page76">76</a>.</p>
+
+  <p><a name="Nt_779" href="#NtA_779">[779]</a> He lost it in a duel, with
+  Manderupius Pasbergius. A contemporary, T.&nbsp;B. Laurus, insinuates that
+  they fought to settle which was the best mathematician! This seems odd,
+  but it must be remembered they fought in the dark, "<i>in tenebris
+  densis</i>"; and it is a nice problem to shave off a nose in the dark,
+  without any other harm.&mdash;A. De M.</p>
+
+  <p>Was this T. B. Laurus Joannes Baptista Laurus or Giovanni Battista
+  Lauro (1581-1621), the poet and writer?</p>
+
+  <p><a name="Nt_780" href="#NtA_780">[780]</a> See note <a
+  href="#Nt_117">117</a>, page <a href="#page76">76</a>.</p>
+
+  <p><a name="Nt_781" href="#NtA_781">[781]</a> Referring to Kepler's
+  celebrated law of planetary motion. He had previously wasted his time on
+  analogies between the planetary orbits and the polyhedrons.&mdash;A. De
+  M.</p>
+
+  <p><a name="Nt_782" href="#NtA_782">[782]</a> See note <a
+  href="#Nt_117">117</a>, page <a href="#page76">76</a>.</p>
+
+  <p><a name="Nt_783" href="#NtA_783">[783]</a> "It does move though."</p>
+
+  <p><a name="Nt_784" href="#NtA_784">[784]</a> As great a lie as ever was
+  told: but in 1800 a compliment to Newton without a fling at Descartes
+  would have been held a lopsided structure.&mdash;A. De M.</p>
+
+  <p><a name="Nt_785" href="#NtA_785">[785]</a> Jean-le-Rond D'Alembert
+  (1717-1783), the foundling who was left on the steps of Jean-le-Rond in
+  Paris, and who became one of the greatest mathematical physicists and
+  astronomers of his century.</p>
+
+  <p><a name="Nt_786" href="#NtA_786">[786]</a> Leonhard Euler (1707-1783),
+  friend of the Bernoullis, the greatest of Swiss mathematicians, prominent
+  in the theory of numbers, and known for discoveries in all lines of
+  mathematics as then studied.</p>
+
+  <p><a name="Nt_787" href="#NtA_787">[787]</a> See notes <a
+  href="#Nt_478">478</a>, <a href="#Nt_479">479</a>, page <a
+  href="#page219">219</a>.</p>
+
+  <p><a name="Nt_788" href="#NtA_788">[788]</a> See note <a
+  href="#Nt_621">621</a>, page <a href="#page288">288</a>.</p>
+
+  <p><a name="Nt_789" href="#NtA_789">[789]</a> See note <a
+  href="#Nt_584">584</a>, page <a href="#page255">255</a>.</p>
+
+  <p><a name="Nt_790" href="#NtA_790">[790]</a> The <i>siderial</i> day is
+  about four minutes short of the solar; there are 366 sidereal days in the
+  year.&mdash;A. De M.</p>
+
+  <p><a name="Nt_791" href="#NtA_791">[791]</a> The founding of the London
+  Mathematical Society is discussed by Mrs. De Morgan in her <i>Memoir</i>
+  (p. 281). The idea came from a conversation between her brilliant son,
+  George Campbell De Morgan, and his friend Arthur Cowper Ranyard in 1864.
+  The meeting of organization was held on Nov. 7, 1864, with Professor De
+  Morgan in the chair, and the first regular meeting on January 16,
+  1865.</p>
+
+  <p><a name="Nt_792" href="#NtA_792">[792]</a> See note <a
+  href="#Nt_33">33</a>, page <a href="#page43">43</a>.</p>
+
+  <p><a name="Nt_793" href="#NtA_793">[793]</a> See note <a
+  href="#Nt_119">119</a>, page <a href="#page80">80</a>.</p>
+
+  <p><a name="Nt_794" href="#NtA_794">[794]</a> John Russell Hind (b.
+  1823), the astronomer. Between 1847 and 1854 he discovered ten
+  planetoids.</p>
+
+  <p><a name="Nt_795" href="#NtA_795">[795]</a> Sir Roderick Impey
+  Murchison (1792-1871), the great geologist. He was knighted in 1846 and
+  devoted the latter part of his life to the work of the Royal Geographical
+  Society and to the geology of Scotland.</p>
+
+  <p><a name="Nt_796" href="#NtA_796">[796]</a> Friedrich Wilhelm Bessel
+  (1784-1846), the astronomer and physicist. He was professor of astronomy
+  at Königsberg.</p>
+
+  <p><a name="Nt_797" href="#NtA_797">[797]</a> This was the <i>Reduction
+  of the Observations of Planets made ... from 1750 to 1830: computed ...
+  under the superintendence of George Biddell Airy</i> (1848). See note <a
+  href="#Nt_129">129</a>, page <a href="#page85">85</a>.</p>
+
+  <p><a name="Nt_798" href="#NtA_798">[798]</a> The expense of this
+  magnificent work was defrayed by Government grants, obtained, at the
+  instance of the British Association, in 1833&mdash;A. De M.</p>
+
+  <p><a name="Nt_799" href="#NtA_799">[799]</a> See note <a
+  href="#Nt_32">32</a>, page <a href="#page43">43</a>.</p>
+
+  <p><a name="Nt_800" href="#NtA_800">[800]</a> Franz Friedrich Ernst
+  Brünnow (1821-1891) was at that time or shortly before director of the
+  observatory at Dusseldorf. He then went to Berlin and thence (1854) to
+  Ann Arbor, Michigan. He then went to Dublin and finally became Royal
+  Astronomer of Ireland.</p>
+
+  <p><a name="Nt_801" href="#NtA_801">[801]</a> Johann Gottfried Galle
+  (1812-1910), at that time connected with the Berlin observatory, and
+  later professor of astronomy at Breslau.</p>
+
+  <p><a name="Nt_802" href="#NtA_802">[802]</a> George Bishop (1785-1861),
+  in whose observatory in Regent's Park important observations were made by
+  Dawes, Hind, and Marth.</p>
+
+  <p><a name="Nt_803" href="#NtA_803">[803]</a> James Challis (1803-1882),
+  director of the Cambridge observatory, and successor of Airy as Plumian
+  professor of astronomy.</p>
+
+  <p><a name="Nt_804" href="#NtA_804">[804]</a> On Leverrier and Arago see
+  note <a href="#Nt_33">33</a>, page <a href="#page43">43</a>, and note <a
+  href="#Nt_561">561</a>, page <a href="#page243">243</a>.</p>
+
+  <p><a name="Nt_805" href="#NtA_805">[805]</a> Robert Grant's (1814-1892)
+  <i>History of Physical Astronomy from the Earliest Ages to the Middle of
+  the Nineteenth Century</i> appeared in 1852. He was professor of
+  astronomy and director of the observatory at Glasgow.</p>
+
+  <p><a name="Nt_806" href="#NtA_806">[806]</a> John Debenham was more
+  interested in religion than in astronomy. He wrote <i>The Strait Gate;
+  or, the true scripture doctrine of salvation clearly explained</i>,
+  London, 1843, and <i>Tractatus de magis et Bethlehemæ stella et Christi
+  in deserto tentatione</i>, privately printed at London in 1845.</p>
+
+  <p><a name="Nt_807" href="#NtA_807">[807]</a> More properly the Sydney
+  Smirke reading room, since it was built from his designs.</p>
+
+  <p><a name="Nt_808" href="#NtA_808">[808]</a> The Antinomians were
+  followers of Johannes Agricola (1494-1566). They believed that Christians
+  as such were released from all obligations to the Old Testament. Some
+  went so far as to assert that, since all Christians were sanctified, they
+  could not lose this sanctity even though they disobeyed God. The sect was
+  prominent in England in the seventeenth century, and was transferred to
+  New England. Here it suffered a check in the condemnation of Mrs. Ann
+  Hutchinson (1636) by the Newton Synod.</p>
+
+  <p><a name="Nt_809" href="#NtA_809">[809]</a> Aside from this work and
+  his publications on Reeve and Muggleton he wrote nothing. With Joseph
+  Frost he published <i>A list</i> <i>of Books and general index to J.
+  Reeve and L. Muggleton's works</i> (1846), <i>Divine Songs of the
+  Muggletonians</i> (1829), and the work mentioned on page <a
+  href="#page396">396</a>. <i>The works of J. Reeve and L. Muggleton</i>
+  (1832).</p>
+
+  <p><a name="Nt_810" href="#NtA_810">[810]</a> About 1650 he and his
+  cousin John Reeve (1608-1658) began to have visions. As part of their
+  creed they taught that astronomy was opposed by the Bible. They asserted
+  that the sun moves about the earth, and Reeve figured out that heaven was
+  exactly six miles away. Both Muggleton and Reeve were imprisoned for
+  their unitarian views. Muggleton wrote a <i>Transcendant Spirituall
+  Treatise</i> (1652). I have before me <i>A true Interpretation of All the
+  Chief Texts ... of the whole Book of the Revelation of St. John.... By
+  Lodowick Muggleton, one of the two last Commissioned Witnesses &amp;
+  Prophets of the onely high, immortal, glorious God, Christ Jesus</i>
+  (1665), in which the interpretation of the "number of the beast" occupies
+  four pages without arriving anywhere.</p>
+
+  <p><a name="Nt_811" href="#NtA_811">[811]</a> In 1652 he was, in a
+  vision, named as the Lord's "last messenger," with Muggleton as his
+  "mouth," and died six years later, probably of nervous tension resulting
+  from his divine "illumination." He was the more spiritual of the two.</p>
+
+  <p><a name="Nt_812" href="#NtA_812">[812]</a> William Guthrie (1708-1770)
+  was a historian and political writer. His <i>History of England</i>
+  (1744-1751) was the first attempt to base history on parliamentary
+  records. He also wrote a <i>General History of Scotland</i> in 10 volumes
+  (1767). The work to which Frost refers is the <i>Geographical,
+  Historical, and Commercial Grammar</i> (1770) which contained an
+  astronomical part by J. Ferguson. By 1827 it had passed through 24
+  editions.</p>
+
+  <p><a name="Nt_813" href="#NtA_813">[813]</a> George Fox (1624-1691),
+  founder of the Society of Friends; a mystic and a disciple of Boehme. He
+  was eight times imprisoned for heresy.</p>
+
+  <p><a name="Nt_814" href="#NtA_814">[814]</a> If they were friends they
+  were literary antagonists, for Muggleton wrote against Fox <i>The Neck of
+  the Quakers Broken</i> (1663), and Fox replied in 1667. Muggleton also
+  wrote <i>A Looking Glass for George Fox</i>.</p>
+
+  <p><a name="Nt_815" href="#NtA_815">[815]</a> John Conduitt (1688-1737),
+  who married (1717) Newton's half niece, Mrs. Katherine Barton. See note
+  <a href="#Nt_284">284</a>, page <a href="#page136">136</a>.</p>
+
+  <p><a name="Nt_816" href="#NtA_816">[816]</a> Probably Peter Mark Roget's
+  (1779-1869) <i>Thesaurus of English Words</i> (1852) is not much used at
+  present, but it went through 28 editions in his lifetime. Few who use the
+  valuable work are aware that Roget was a professor of physiology at the
+  Royal Institution (London), that he achieved his title of F. R. S.
+  because of his work in perfecting the slide rule, and that he followed
+  Sir John Herschel as secretary of the Royal Society.</p>
+
+  <p><a name="Nt_817" href="#NtA_817">[817]</a> See note <a
+  href="#Nt_703">703</a>, page <a href="#page327">327</a>. This work went
+  into a second edition in the year of its first publication.</p>
+
+  <p><a name="Nt_818" href="#NtA_818">[818]</a> See note <a
+  href="#Nt_398">398</a>, page <a href="#page177">177</a>.</p>
+
+  <p><a name="Nt_819" href="#NtA_819">[819]</a> See note <a
+  href="#Nt_528">528</a>, page <a href="#page233">233</a>.</p>
+
+  <p><a name="Nt_820" href="#NtA_820">[820]</a> George Jacob Holyoake
+  (1817-1906) entered into a controversial life at an early age. In 1841 he
+  was imprisoned for six months for blasphemy. He founded and edited <i>The
+  Reasoner</i> (Vols. 1-26, 1846-1861). In his later life he did much to
+  promote cooperation among the working class.</p>
+
+  <p><a name="Nt_821" href="#NtA_821">[821]</a> See note <a
+  href="#Nt_176">176</a>, page <a href="#page102">102</a>.</p>
+
+  <p><a name="Nt_822" href="#NtA_822">[822]</a> William Thomas Lowndes
+  (1798-1843), whose <i>Bibliographer's Manual of English Literature</i>, 4
+  vols., London, 1834 (also 1857-1864, and 1869) is a classic in its
+  line.</p>
+
+  <p><a name="Nt_823" href="#NtA_823">[823]</a> Jacques Charles Brunet
+  (1780-1867), the author of the great French bibliography, the <i>Manuel
+  du Libraire</i> (1810).</p>
+
+</div>
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of the Project Gutenberg EBook of A Budget of Paradoxes, Volume I (of II), by 
+Augustus De Morgan
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@@ -0,0 +1,16250 @@
+The Project Gutenberg EBook of A Budget of Paradoxes, Volume I (of II), by
+Augustus De Morgan
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: A Budget of Paradoxes, Volume I (of II)
+
+Author: Augustus De Morgan
+
+Editor: David Eugene Smith
+
+Release Date: October 20, 2007 [EBook #23100]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK A BUDGET OF PARADOXES ***
+
+
+
+
+Produced by David Starner, Keith Edkins and the Online
+Distributed Proofreading Team at http://www.pgdp.net
+
+
+
+
+
+Transcriber's note: A few typographical errors have been corrected: they
+are listed at the end of the text.
+
+       *       *       *       *       *
+
+
+BY AUGUSTUS DE MORGAN
+
+A BUDGET OF
+PARADOXES
+
+REPRINTED WITH THE AUTHOR'S ADDITIONS FROM THE ATHENAEUM
+
+
+
+SECOND EDITION EDITED BY DAVID EUGENE SMITH
+
+WITH A NEW INTRODUCTION BY ERNEST NAGEL
+
+PROFESSOR OF PHILOSOPHY, COLUMBIA UNIVERSITY
+
+UNABRIDGED EDITION--TWO VOLUMES BOUND AS ONE
+
+
+
+Volume I
+
+
+
+DOVER PUBLICATIONS, INC., NEW YORK
+
+       *       *       *       *       *
+
+
+PREFACE TO THE FIRST EDITION.
+
+(1872)
+
+It is not without hesitation that I have taken upon myself the editorship
+of a work left avowedly imperfect by the author, and, from its
+miscellaneous and discursive character, difficult of completion with due
+regard to editorial limitations by a less able hand.
+
+Had the author lived to carry out his purpose he would have looked through
+his Budget again, amplifying and probably rearranging some of its contents.
+He had collected materials for further illustration of Paradox of the kind
+treated of in this book; and he meant to write a second part, in which the
+contradictions and inconsistencies of orthodox learning would have been
+subjected to the same scrutiny and castigation as heterodox ignorance had
+already received.
+
+It will be seen that the present volume contains more than the _Athenaeum_
+Budget. Some of the additions formed a Supplement to the original articles.
+These supplementary paragraphs were, by the author, placed after those to
+which they respectively referred, being distinguished from the rest of the
+text by brackets. I have omitted these brackets as useless, except where
+they were needed to indicate subsequent writing.
+
+Another and a larger portion of the work consists of discussion of matters
+of contemporary interest, for the Budget was in some degree a receptacle
+for the author's thoughts on any literary, scientific, or social question.
+Having grown thus gradually to its present size, the book as it was left
+was not quite in a fit condition for publication, but the alterations which
+have been made are slight and few, being in most cases verbal, and such as
+the sense absolutely required, or transpositions of sentences to secure
+coherence with the rest, in places where the author, in his more recent
+insertion of them, had overlooked the connection in which they stood. In no
+case has the meaning been in any degree modified or interfered with.
+
+One rather large omission must be mentioned here. It is an account of the
+quarrel between Sir James South and Mr. Troughton on the mounting, etc. of
+the equatorial telescope at Campden Hill. At some future time when the
+affair has passed entirely out of the memory of living Astronomers, the
+appreciative sketch, which is omitted in this edition of the Budget, will
+be an interesting piece of history and study of character.[1]
+
+A very small portion of Mr. James Smith's circle-squaring has been left
+out, with a still smaller portion of Mr. De Morgan's answers to that
+Cyclometrical Paradoxer.
+
+In more than one place repetitions, which would have disappeared under the
+author's revision, have been allowed to remain, because they could not have
+been taken away without leaving a hiatus, not easy to fill up without
+damage to the author's meaning.
+
+I give these explanations in obedience to the rules laid down for the
+guidance of editors at page 15.[2] If any apology for the fragmentary
+character of the book be thought necessary, it may be found in the author's
+own words at page 281 of the second volume.[3]
+
+The publication of the Budget could not have been delayed without lessening
+the interest attaching to the writer's thoughts upon questions of our own
+day. I trust that, incomplete as the work is compared with what it might
+have been, I shall not be held mistaken in giving it to the world. Rather
+let me hope that it will be welcomed as an old friend returning under great
+disadvantages, but bringing a pleasant remembrance of the amusement which
+its weekly appearance in the _Athenaeum_ gave to both writer and reader.
+
+The Paradoxes are dealt with in chronological order. This will be a guide
+to the reader, and with the alphabetical Index of Names, etc., will, I
+trust, obviate all difficulty of reference.
+
+SOPHIA DE MORGAN.
+
+    6 MERTON ROAD, PRIMROSE HILL.
+
+       *       *       *       *       *
+
+
+PREFACE TO THE SECOND EDITION.
+
+If Mrs. De Morgan felt called upon to confess her hesitation at taking upon
+herself the labor of editing these Paradoxes, much more should one who was
+born two generations later, who lives in another land and who was reared
+amid different influences, confess to the same feeling when undertaking to
+revise this curious medley. But when we consider the nature of the work,
+the fact that its present rarity deprives so many readers of the enjoyment
+of its delicious satire, and the further fact that allusions that were
+commonplace a half century ago are now forgotten, it is evident that some
+one should take up the work and perform it _con amore_.
+
+Having long been an admirer of De Morgan, having continued his work in the
+bibliography of early arithmetics, and having worked in his library among
+the books of which he was so fond, it is possible that the present editor,
+whatever may be his other shortcomings, may undertake the labor with as
+much of sympathy as any one who is in a position to perform it. With this
+thought in mind, two definite rules were laid down at the beginning of the
+task: (1) That no alteration in the text should be made, save in slightly
+modernizing spelling and punctuation and in the case of manifest
+typographical errors; (2) That whenever a note appeared it should show at
+once its authorship, to the end that the material of the original edition
+might appear intact.
+
+In considering, however, the unbroken sequence of items that form the
+Budget, it seems clear that readers would be greatly aided if the various
+leading topics were separated in some convenient manner. After considerable
+thought it was decided to insert brief captions from time to time that
+might aid the eye in selecting the larger subjects of the text. In some
+parts of the work these could easily be taken from the original folio
+heads, but usually they had to be written anew. While, therefore, the
+present editor accepts the responsibility for the captions of the various
+subdivisions, he has endeavored to insert them in harmony with the original
+text.
+
+As to the footnotes, the first edition had only a few, some due to De
+Morgan himself and others to Mrs. De Morgan. In the present edition those
+due to the former are signed A. De M., and those due to Mrs. De Morgan
+appear with her initials, S. E. De M. For all other footnotes the present
+editor is responsible. In preparing them the effort has been made to
+elucidate the text by supplying such information as the casual reader might
+wish as he passes over the pages. Hundreds of names are referred to in the
+text that were more or less known in England half a century ago, but are
+now forgotten there and were never familiar elsewhere. Many books that were
+then current have now passed out of memory, and much that agitated England
+in De Morgan's prime seems now like ancient history. Even with respect to
+well-known names, a little information as to dates and publications will
+often be welcome, although the editor recognizes that it will quite as
+often be superfluous. In order, therefore, to derive the pleasure that
+should come from reading the Budget, the reader should have easy access to
+the information that the notes are intended to supply. That they furnish
+too much here and too little there is to be expected. They are a human
+product, and if they fail to serve their purpose in all respects it is
+hoped that this failure will not seriously interfere with the reader's
+pleasure.
+
+In general the present editor has refrained from expressing any opinions
+that would strike a discordant note in the reading of the text as De Morgan
+left it. The temptation is great to add to the discussion at various
+points, but it is a temptation to be resisted. To furnish such information
+as shall make the reading more pleasant, rather than to attempt to improve
+upon one of the most delicious bits of satire of the nineteenth century,
+has been the editor's wish. It would have been an agreeable task to review
+the history of circle squaring, of the trisection problem, and of the
+duplication of the cube. This, however, would be to go too far afield. For
+the benefit of those who wish to investigate the subject the editor can
+only refer to such works and articles as the following: F. Rudio,
+_Archimedes, Huygens, Lambert, Legendre,--mit einer Uebersicht ueber die
+Geschichte des Problemes von der Quadratur des Zirkels_, Leipsic, 1892;
+Thomas Muir, "Circle," in the eleventh edition of the _Encyclopaedia
+Britannica_; the various histories of mathematics; and to his own article
+on "The Incommensurability of [pi]" in Prof. J. W. A. Young's _Monographs
+on Topics of Modern Mathematics_, New York, 1911.
+
+The editor wishes to express his appreciation and thanks to Dr. Paul Carus,
+editor of _The Monist_ and _The Open Court_ for the opportunity of
+undertaking this work; to James Earl Russell, LL.D., Dean of Teachers
+College, Columbia University, for his encouragement in its prosecution; to
+Miss Caroline Eustis Seely for her intelligent and painstaking assistance
+in securing material for the notes; and to Miss Lydia G. Robinson and Miss
+Anna A. Kugler for their aid and helpful suggestions in connection with the
+proof-sheets. Without the generous help of all five this work would have
+been impossible.
+
+DAVID EUGENE SMITH.
+
+    TEACHERS COLLEGE, COLUMBIA UNIVERSITY.
+
+       *       *       *       *       *
+
+
+A BUDGET OF PARADOXES
+
+{1}
+
+INTRODUCTORY.
+
+If I had before me a fly and an elephant, having never seen more than one
+such magnitude of either kind; and if the fly were to endeavor to persuade
+me that he was larger than the elephant, I might by possibility be placed
+in a difficulty. The apparently little creature might use such arguments
+about the effect of distance, and might appeal to such laws of sight and
+hearing as I, if unlearned in those things, might be unable wholly to
+reject. But if there were a thousand flies, all buzzing, to appearance,
+about the great creature; and, to a fly, declaring, each one for himself,
+that he was bigger than the quadruped; and all giving different and
+frequently contradictory reasons; and each one despising and opposing the
+reasons of the others--I should feel quite at my ease. I should certainly
+say, My little friends, the case of each one of you is destroyed by the
+rest. I intend to show flies in the swarm, with a few larger animals, for
+reasons to be given.
+
+In every age of the world there has been an established system, which has
+been opposed from time to time by isolated and dissentient reformers. The
+established system has sometimes fallen, slowly and gradually: it has
+either been upset by the rising influence of some one man, or it has been
+sapped by gradual change of opinion in the many.
+
+I have insisted on the isolated character of the dissentients, as an
+element of the _a priori_ probabilities of the case. Show me a schism,
+especially a growing schism, and it is another thing. The homeopathists,
+for instance, shall be, if any one so think, as wrong as St. John Long; but
+an {2} organized opposition, supported by the efforts of many acting in
+concert, appealing to common arguments and experience, with perpetual
+succession and a common seal, as the Queen says in the charter, is, be the
+merit of the schism what it may, a thing wholly different from the case of
+the isolated opponent in the mode of opposition to it which reason points
+out.
+
+During the last two centuries and a half, physical knowledge has been
+gradually made to rest upon a basis which it had not before. It has become
+_mathematical_. The question now is, not whether this or that hypothesis is
+better or worse to the pure thought, but whether it accords with observed
+phenomena in those consequences which can be shown necessarily to follow
+from it, if it be true. Even in those sciences which are not yet under the
+dominion of mathematics, and perhaps never will be, a working copy of the
+mathematical process has been made. This is not known to the followers of
+those sciences who are not themselves mathematicians and who very often
+exalt their horns against the mathematics in consequence. They might as
+well be squaring the circle, for any sense they show in this particular.
+
+A great many individuals, ever since the rise of the mathematical method,
+have, each for himself, attacked its direct and indirect consequences. I
+shall not here stop to point out how the very accuracy of exact science
+gives better aim than the preceding state of things could give. I shall
+call each of these persons a _paradoxer_, and his system a _paradox_. I use
+the word in the old sense: a paradox is something which is apart from
+general opinion, either in subject-matter, method, or conclusion.
+
+Many of the things brought forward would now be called _crotchets_, which
+is the nearest word we have to old _paradox_. But there is this difference,
+that by calling a thing a _crotchet_ we mean to speak lightly of it; which
+was not the necessary sense of _paradox_. Thus in the sixteenth century
+many spoke of the earth's motion as the _paradox of {3} Copernicus_, who
+held the ingenuity of that theory in very high esteem, and some, I think,
+who even inclined towards it. In the seventeenth century, the depravation
+of meaning took place, in England at least. Phillips says _paradox_ is "a
+thing which seemeth strange"--here is the old meaning: after a colon he
+proceeds--"and absurd, and is contrary to common opinion," which is an
+addition due to his own time.
+
+Some of my readers are hardly inclined to think that the word _paradox_
+could once have had no disparagement in its meaning; still less that
+persons could have applied it to themselves. I chance to have met with a
+case in point against them. It is Spinoza's _Philosophia Scripturae
+Interpres, Exercitatio Paradoxa_, printed anonymously at Eleutheropolis, in
+1666. This place was one of several cities in the clouds, to which the
+cuckoos resorted who were driven away by the other birds; that is, a
+feigned place of printing, adopted by those who would have caught it if
+orthodoxy could have caught them. Thus, in 1656, the works of Socinus could
+only be printed at Irenopolis. The author deserves his self-imposed title,
+as in the following:[4]
+
+"Quanto sane satius fuisset illam [Trinitatem] pro mysterio non habuisse,
+et Philosophiae ope, antequam quod esset statuerent, secundum verae logices
+praecepta quid esset cum Cl. Kleckermanno investigasse; tanto fervore ac
+labore in profundissimas speluncas et obscurissimos metaphysicarum
+speculationum atque fictionum recessus se recipere ut ab adversariorum
+telis sententiam suam in tuto collocarent. {4} Profecto magnus ille vir ...
+dogma illud, quamvis apud theologos eo nomine non multum gratiae iniverit,
+ita ex immotis Philosophiae fundamentis explicat ac demonstrat, ut paucis
+tantum immutatis, atque additis, nihil amplius animus veritate sincere
+deditus desiderare possit."
+
+This is properly paradox, though also heterodox. It supposes, contrary to
+all opinion, orthodox and heterodox, that philosophy can, with slight
+changes, explain the Athanasian doctrine so as to be at least compatible
+with orthodoxy. The author would stand almost alone, if not quite; and this
+is what he meant. I have met with the counter-paradox. I have heard it
+maintained that the doctrine as it stands, in all its mystery is _a priori_
+more likely than any other to have been Revelation, if such a thing were to
+be; and that it might almost have been predicted.
+
+After looking into books of paradoxes for more than thirty years, and
+holding conversation with many persons who have written them, and many who
+might have done so, there is one point on which my mind is fully made up.
+The manner in which a paradoxer will show himself, as to sense or nonsense,
+will not depend upon what he maintains, but upon whether he has or has not
+made a sufficient knowledge of what has been done by others, _especially as
+to the mode of doing it_, a preliminary to inventing knowledge for himself.
+That a little knowledge is a dangerous thing is one of the most fallacious
+of proverbs. A person of small knowledge is in danger of trying to make his
+_little_ do the work of _more_; but a person without any is in more danger
+of making his _no_ knowledge do the work of _some_. Take the speculations
+on the tides as an instance. Persons with nothing but a little geometry
+have certainly exposed themselves in their modes of objecting to results
+which require the higher mathematics to be known before an independent
+opinion can be formed on sufficient grounds. But persons with no geometry
+at all have done the same thing much more completely. {5}
+
+There is a line to be drawn which is constantly put aside in the arguments
+held by paradoxers in favor of their right to instruct the world. Most
+persons must, or at least will, like the lady in Cadogan Place,[5] form and
+express an immense variety of opinions on an immense variety of subjects;
+and all persons must be their own guides in many things. So far all is
+well. But there are many who, in carrying the expression of their own
+opinions beyond the usual tone of private conversation, whether they go no
+further than attempts at oral proselytism, or whether they commit
+themselves to the press, do not reflect that they have ceased to stand upon
+the ground on which their process is defensible. Aspiring to lead _others_,
+they have never given themselves the fair chance of being first led by
+_other_ others into something better than they can start for themselves;
+and that they should first do this is what both those classes of others
+have a fair right to expect. New knowledge, when to any purpose, must come
+by contemplation of old knowledge in every matter which concerns thought;
+mechanical contrivance sometimes, not very often, escapes this rule. All
+the men who are now called discoverers, in every matter ruled by thought,
+have been men versed in the minds of their predecessors, and learned in
+what had been before them. There is not one exception. I do not say that
+every man has made direct acquaintance with the whole of his mental
+ancestry; many have, as I may say, only known their grandfathers by the
+report of their fathers. But even on this point it is remarkable how many
+of the greatest names in all departments of knowledge have been real
+antiquaries in their several subjects.
+
+I may cite, among those who have wrought strongly upon opinion or practice
+in science, Aristotle, Plato, Ptolemy, Euclid, Archimedes, Roger Bacon,
+Copernicus, Francis Bacon, Ramus, Tycho Brahe, Galileo, Napier, Descartes,
+Leibnitz, Newton, Locke. I take none but names known out of their {6}
+fields of work; and all were learned as well as sagacious. I have chosen my
+instances: if any one will undertake to show a person of little or no
+knowledge who has established himself in a great matter of pure thought,
+let him bring forward his man, and we shall see.
+
+This is the true way of putting off those who plague others with their
+great discoveries. The first demand made should be--Mr. Moses, before I
+allow you to lead me over the Red Sea, I must have you show that you are
+learned in all the wisdom of the Egyptians upon your own subject. The plea
+that it is unlikely that this or that unknown person should succeed where
+Newton, etc. have failed, or should show Newton, etc. to be wrong, is
+utterly null and void. It was worthily versified by Sylvanus Morgan (the
+great herald who in his _Sphere of Gentry_ gave coat armor to "Gentleman
+Jesus," as he said), who sang of Copernicus as follows (1652):
+
+ "If Tellus winged be,
+  The earth a motion round;
+  Then much deceived are they
+  Who nere before it found.
+  Solomon was the wisest,
+  His wit nere this attained;
+  Cease, then, Copernicus,
+  Thy hypothesis is vain."
+
+Newton, etc. were once unknown; but they made themselves known by what they
+knew, and then brought forward what they could do; which I see is as good
+verse as that of Herald Sylvanus. The demand for previous knowledge
+disposes of twenty-nine cases out of thirty, and the thirtieth is worth
+listening to.
+
+I have not set down Copernicus, Galileo, etc. among the paradoxers, merely
+because everybody knows them; if my list were quite complete, they would
+have been in it. But the reader will find Gilbert, the great precursor of
+sound magnetical theory; and several others on whom no censure can be cast,
+though some of their paradoxes are inadmissible, {7} some unprovoked, and
+some capital jokes, true or false: the author of _Vestiges of Creation_ is
+an instance. I expect that my old correspondent, General Perronet Thompson,
+will admit that his geometry is part and parcel of my plan; and also that,
+if that plan embraced politics, he would claim a place for his _Catechism
+on the Corn Laws_, a work at one time paradoxical, but which had more to do
+with the abolition of the bread-tax than Sir Robert Peel.
+
+My intention in publishing this Budget in the _Athenaeum_ is _to enable
+those who have been puzzled by one or two discoverers to see how they look
+in a lump_. The only question is, has the selection been fairly made? To
+this my answer is, that no selection at all has been made. The books are,
+without exception, those which I have in my own library; and I have taken
+_all_--I mean all of the kind: Heaven forbid that I should be supposed to
+have no other books! But I may have been a collector, influenced in choice
+by bias? I answer that I never have collected books of this sort--that is,
+I have never searched for them, never made up my mind to look out for this
+book or that. I have bought what happened to come in my way at show or
+auction; I have retained what came in as part of the _undescribed_ portion
+of miscellaneous auction lots; I have received a few from friends who found
+them among what they called their rubbish; and I have preserved books sent
+to me for review. In not a few instances the books have been bound up with
+others, unmentioned at the back; and for years I knew no more I had them
+than I knew I had Lord Macclesfield's speech on moving the change of Style,
+which, after I had searched shops, etc. for it in vain, I found had been
+reposing on my own shelves for many years, at the end of a summary of
+Leibnitz's philosophy. Consequently, I may positively affirm that the
+following list is formed by accident and circumstance alone, and that it
+truly represents the casualties of about a third of a century. For
+instance, the large proportion of works {8} on the quadrature of the circle
+is not my doing: it is the natural share of this subject in the actual run
+of events.
+
+[I keep to my plan of inserting only such books as I possessed in 1863,
+except by casual notice in aid of my remarks. I have found several books on
+my shelves which ought to have been inserted. These have their titles set
+out at the commencement of their articles, in leading paragraphs; the
+casuals are without this formality.[6]]
+
+Before proceeding to open the Budget, I say something on my personal
+knowledge of the class of discoverers who square the circle, upset Newton,
+etc. I suspect I know more of the English class than any man in Britain. I
+never kept any reckoning; but I know that one year with another--and less
+of late years than in earlier time--I have talked to more than five in each
+year, giving more than a hundred and fifty specimens. Of this I am sure,
+that it is my own fault if they have not been a thousand. Nobody knows how
+they swarm, except those to whom they naturally resort. They are in all
+ranks and occupations, of all ages and characters. They are very earnest
+people, and their purpose is _bona fide_ the dissemination of their
+paradoxes. A great many--the mass, indeed--are illiterate, and a great many
+waste their means, and are in or approaching penury. But I must say that
+never, in any one instance, has the quadrature of the circle, or the like,
+been made a pretext for begging; even to be asked to purchase a book is of
+the very rarest occurrence--it has happened, and that is all.
+
+These discoverers despise one another: if there were the concert among them
+which there is among foreign mendicants, a man who admitted one to a
+conference would be plagued to death. I once gave something to a very
+genteel French applicant, who overtook me in the street, at my own door,
+saying he had picked up my handkerchief: whether he picked it up in my
+pocket for an introduction, I know not. {9} But that day week came another
+Frenchman to my house, and that day fortnight a French lady; both failed,
+and I had no more trouble. The same thing happened with Poles. It is not so
+with circle-squarers, etc.: they know nothing of each other. Some will read
+this list, and will say I am right enough, generally speaking, but that
+there _is_ an exception, if I could but see it.
+
+I do not mean, by my confession of the manner in which I have sinned
+against the twenty-four hours, to hold myself out as accessible to personal
+explanation of new plans. Quite the contrary: I consider myself as having
+made my report, and being discharged from further attendance on the
+subject. I will not, from henceforward, talk to any squarer of the circle,
+trisector of the angle, duplicator of the cube, constructor of perpetual
+motion, subverter of gravitation, stagnator of the earth, builder of the
+universe, etc. I will receive any writings or books which require no
+answer, and read them when I please: I will certainly preserve them--this
+list may be enlarged at some future time.
+
+There are three subjects which I have hardly anything upon; astrology,
+mechanism, and the infallible way of winning at play. I have never cared to
+preserve astrology. The mechanists make models, and not books. The
+infallible winners--though I have seen a few--think their secret too
+valuable, and prefer _mutare quadrata rotundis_--to turn dice into coin--at
+the gaming-house: verily they have their reward.
+
+I shall now select, to the mystic number seven, instances of my personal
+knowledge of those who think they have discovered, in illustration of as
+many misconceptions.
+
+1. _Attempt by help of the old philosophy, the discoverer not being in
+possession of modern knowledge._ A poor schoolmaster, in rags, introduced
+himself to a scientific friend with whom I was talking, and announced that
+he had found out the composition of the sun. "How was that done?"--"By
+consideration of the four elements."--"What are {10} they?"--"Of course,
+fire, air, earth, and water."--"Did you not know that air, earth, and
+water, have long been known to be no elements at all, but
+compounds?"--"What do you mean, sir? Who ever heard of such a thing?"
+
+2. _The notion that difficulties are enigmas, to be overcome in a moment by
+a lucky thought._ A nobleman of very high rank, now long dead, read an
+article by me on the quadrature, in an early number of the _Penny
+Magazine_. He had, I suppose, school recollections of geometry. He put
+pencil to paper, drew a circle, and constructed what seemed likely to
+answer, and, indeed, was--as he said--certain, if only this bit were equal
+to that; which of course it was not. He forwarded his diagram to the
+Secretary of the Diffusion Society, to be handed to the author of the
+article, in case the difficulty should happen to be therein overcome.
+
+3. _Discovery at all hazards, to get on in the world._ Thirty years ago, an
+officer of rank, just come from foreign service, and trying for a
+decoration from the Crown, found that his claims were of doubtful amount,
+and was told by a friend that so and so, who had got the order, had the
+additional claim of scientific distinction. Now this officer, while abroad,
+had bethought himself one day, that there really could be no difficulty in
+finding the circumference of a circle: if a circle were rolled upon a
+straight line until the undermost point came undermost again, there would
+be the straight line equal to the circle. He came to me, saying that he did
+not feel equal to the statement of his claim in this respect, but that if
+some clever fellow would put the thing in a proper light, he thought his
+affair might be managed. I was clever enough to put the thing in a proper
+light to himself, to this extent at least, that, though perhaps they were
+wrong, the advisers of the Crown would never put the letters K.C.B. to such
+a circle as his.
+
+4. _The notion that mathematicians cannot find the circle for common
+purposes._ A working man measured the altitude of a cylinder accurately,
+and--I think the process of {11} Archimedes was one of his
+proceedings--found its bulk. He then calculated the ratio of the
+circumference to the diameter, and found it answered very well on other
+modes of trial. His result was about 3.14. He came to London, and somebody
+sent him to me. Like many others of his pursuit, he seemed to have turned
+the whole force of his mind upon one of his points, on which alone he would
+be open to refutation. He had read some of Kater's experiments, and had got
+the Act of 1825 on weights and measures. Say what I would, he had for a
+long time but one answer--"Sir! I go upon Captain Kater and the Act of
+Parliament." But I fixed him at last. I happened to have on the table a
+proof-sheet of the _Astronomical Memoirs_, in which were a large number of
+observed places of the planets compared with prediction, and asked him
+whether it could be possible that persons who did not know the circle
+better than he had found it could make the calculations, of which I gave
+him a notion, so accurately? He was perfectly astonished, and took the
+titles of some books which he said he would read.
+
+5. _Application for the reward from abroad._ Many years ago, about
+twenty-eight, I think, a Jesuit came from South America, with a quadrature,
+and a cutting from a newspaper announcing that a reward was ready for the
+discovery in England. On this evidence he came over. After satisfying him
+that nothing had ever been offered here, I discussed his quadrature, which
+was of no use. I succeeded better when I told him of Richard White, also a
+Jesuit, and author of a quadrature published before 1648, under the name of
+_Chrysaespis_, of which I can give no account, having never seen it. This
+White (_Albius_) is the only quadrator who was ever convinced of his error.
+My Jesuit was struck by the instance, and promised to read more
+geometry--he was no Clavius--before he published his book. He relapsed,
+however, for I saw his book advertised in a few days. I may say, as
+sufficient proof of my being no collector, that I had not the curiosity to
+buy his book; and my friend the {12} Jesuit did not send me a copy, which
+he ought to have done, after the hour I had given him.
+
+6. _Application for the reward at home._ An agricultural laborer squared
+the circle, and brought the proceeds to London. He left his papers with me,
+one of which was the copy of a letter to the Lord Chancellor, desiring his
+Lordship to hand over forthwith 100,000 pounds, the amount of the alleged
+offer of reward. He did not go quite so far as M. de Vausenville, who, I
+think in 1778, brought an action against the Academy of Sciences to recover
+a reward to which he held himself entitled. I returned the papers, with a
+note, stating that he had not the knowledge requisite to see in what the
+problem consisted. I got for answer a letter in which I was told that a
+person who could not see that he had done the thing should "change his
+business, and appropriate his time and attention to a Sunday-school, to
+learn what he could, and keep the _litle_ children from _durting_ their
+_close_." I also received a letter from a friend of the quadrator,
+informing me that I knew his friend had succeeded, and had been heard to
+say so. These letters were printed--without the names of the writers--for
+the amusement of the readers of _Notes and Queries_, First Series, xii. 57,
+and they will appear again in the sequel.
+
+[There are many who have such a deep respect for any attempt at thought
+that they are shocked at ridicule even of those who have made themselves
+conspicuous by pretending to lead the world in matters which they have not
+studied. Among my anonyms is a gentleman who is angry at my treatment of
+the "poor but thoughtful" man who is described in my introduction as
+recommending me to go to a Sunday-school because I informed him that he did
+not know in what the difficulty of quadrature consisted. My impugner quite
+forgets that this man's "thoughtfulness" chiefly consisted in his demanding
+a hundred thousand pounds from the Lord Chancellor for his discovery; and I
+may add, that his greatest stretch of invention was finding out that "the
+clergy" {13} were the means of his modest request being unnoticed. I
+mention this letter because it affords occasion to note a very common
+error, namely, that men unread in their subjects have, by natural wisdom,
+been great benefactors of mankind. My critic says, "Shakspeare, whom the
+Pro^r (_sic_) may admit to be a wisish man, though an object of contempt as
+to learning ..." Shakespeare an object of contempt as to learning! Though
+not myself a thoroughgoing Shakespearean--and adopting the first half of
+the opinion given by George III, "What! is there not sad stuff? only one
+must not say so"--I am strongly of opinion that he throws out the masonic
+signs of learning in almost every scene, to all who know what they are. And
+this over and above every kind of direct evidence. First, foremost, and
+enough, the evidence of Ben Jonson that he had "little Latin and less
+Greek"; then Shakespeare had as much Greek as Jonson would call _some_,
+even when he was depreciating. To have any Greek at all was in those days
+exceptional. In Shakespeare's youth St. Paul's and Merchant Taylor's
+schools were to have masters learned in good and clean Latin literature,
+_and also in Greek if such may be gotten_. When Jonson spoke as above, he
+intended to put Shakespeare low among the learned, but not out of their
+pale; and he spoke as a rival dramatist, who was proud of his own learned
+sock; and it may be a subject of inquiry how much Latin _he_ would call
+_little_. If Shakespeare's learning on certain points be very much less
+visible than Jonson's, it is partly because Shakespeare's writings hold it
+in chemical combination, Jonson's in mechanical aggregation.]
+
+7. An elderly man came to me to show me how the universe was created. There
+was one molecule, which by vibration became--Heaven knows how!--the Sun.
+Further vibration produced Mercury, and so on. I suspect the nebular
+hypothesis had got into the poor man's head by reading, in some singular
+mixture with what it found there. Some modifications of vibration gave
+heat, electricity, etc. I {14} listened until my informant ceased to
+vibrate--which is always the shortest way--and then said, "Our knowledge of
+elastic fluids is imperfect." "Sir!" said he, "I see you perceive the truth
+of what I have said, and I will reward your attention by telling you what I
+seldom disclose, never, except to those who can receive my theory--the
+little molecule whose vibrations have given rise to our solar system is the
+Logos of St. John's Gospel!" He went away to Dr. Lardner, who would not go
+into the solar system at all--the first molecule settled the question. So
+hard upon poor discoverers are men of science who are not antiquaries in
+their subject! On leaving, he said, "Sir, Mr. De Morgan received me in a
+very different way! he heard me attentively, and I left him perfectly
+satisfied of the truth of my system." I have had much reason to think that
+many discoverers, of all classes, believe they have convinced every one who
+is not peremptory to the verge of incivility.
+
+My list is given in chronological order. My readers will understand that my
+general expressions, where slighting or contemptuous, refer to the
+ignorant, who teach before they have learned. In every instance, those of
+whom I am able to speak with respect, whether as right or wrong, have
+sought knowledge in the subject they were to handle before they completed
+their speculations. I shall further illustrate this at the conclusion of my
+list.
+
+Before I begin the list, I give prominence to the following letter,
+addressed by me to the _Correspondent_ of October 28, 1865. Some of my
+paradoxers attribute to me articles in this or that journal; and others may
+think--I know some do think--they know me as the writer of reviews of some
+of the very books noticed here. The following remarks will explain the way
+in which they may be right, and in which they may be wrong. {15}
+
+       *       *       *       *       *
+
+THE EDITORIAL SYSTEM.
+
+"Sir,--I have reason to think that many persons have a very inaccurate
+notion of the _Editorial System_. What I call by this name has grown up in
+the last _centenary_--a word I may use to signify the hundred years now
+ending, and to avoid the ambiguity of _century_. It cannot conveniently be
+explained by editors themselves, and _edited_ journals generally do not
+like to say much about it. In _your_ paper perhaps, in which editorial
+duties differ somewhat from those of ordinary journals, the common system
+may be freely spoken of.
+
+"When a reviewed author, as very often happens, writes to the editor of the
+reviewing journal to complain of what has been said of him, he
+frequently--even more often than not--complains of 'your reviewer.' He
+sometimes presumes that 'you' have, 'through inadvertence' in this
+instance, 'allowed some incompetent person to lower the character of your
+usually accurate pages.' Sometimes he talks of 'your scribe,' and, in
+extreme cases, even of 'your hack.' All this shows perfect ignorance of the
+journal system, except where it is done under the notion of letting the
+editor down easy. But the editor never accepts the mercy.
+
+"All that is in a journal, except what is marked as from a correspondent,
+either by the editor himself or by the correspondent's real or fictitious
+signature, is published entirely on editorial responsibility, as much as if
+the editor had written it himself. The editor, therefore, may claim, and
+does claim and exercise, unlimited right of omission, addition, and
+alteration. This is so well understood that the editor performs his last
+function on the last revise without the 'contributor' knowing what is done.
+The word _contributor_ is the proper one; it implies that he furnishes
+materials without stating what he furnishes or how much of it is accepted,
+or whether he be the only contributor. All this applies both to political
+and literary journals. No editor acknowledges {16} the right of a
+contributor to withdraw an article, if he should find alterations in the
+proof sent to him for correction which would make him wish that the article
+should not appear. If the _demand_ for suppression were made--I say nothing
+about what might be granted to _request_--the answer would be, 'It is not
+your article, but mine; I have all the responsibility; if it should contain
+a libel, I could not give you up, even at your own desire. You have
+furnished me with materials, on the known and common understanding that I
+was to use them at my discretion, and you have no right to impede my
+operations by making the appearance of the article depend on your
+approbation of my use of your materials.'
+
+"There is something to be said for this system, and something against it--I
+mean simply on its own merits. But the all-conquering argument in its favor
+is, that the only practicable alternative is the modern French plan of no
+articles without the signature of the writers. I need not discuss this
+plan; there is no collective party in favor of it. Some may think it is not
+the only alternative; they have not produced any intermediate proposal in
+which any dozen of persons have concurred. Many will say, Is not all this,
+though perfectly correct, well known to be matter of form? Is it not
+practically the course of events that an engaged contributor writes the
+article, and sends it to the editor, who admits it as
+written--substantially, at least? And is it not often very well known, by
+style and in other ways, who it was wrote the article? This system is
+matter of form just as much as loaded pistols are matter of form so long as
+the wearer is not assailed; but matter of form takes the form of matter in
+the pulling of a trigger, so soon as the need arises. Editors and
+contributors who can work together find each other out by elective
+affinity, so that the common run of events settles down into most articles
+appearing much as they are written. And there are two safety-valves; that
+is, when judicious persons come together. In the first place, the editor
+himself, when he has selected his contributor, feels that {17} the
+contributor is likely to know his business better than an editor can teach
+him; in fact, it is on that principle that the selection is made. But he
+feels that he is more competent than the writer to judge questions of
+strength and of tone, especially when the general purpose of the journal is
+considered, of which the editor is the judge without appeal. An editor who
+meddles with substantive matter is likely to be wrong, even when he knows
+the subject; but one who prunes what he deems excess, is likely to be
+right, even when he does not know the subject. In the second place, a
+contributor knows that he is supplying an editor, and learns, without
+suppressing truth or suggesting falsehood, to make the tone of his
+communications suit the periodical in which they are to appear. Hence it
+very often arises that a reviewed author, who thinks he knows the name of
+his reviewer, and proclaims it with expressions of dissatisfaction, is only
+wrong in supposing that his critic has given all his mind. It has happened
+to myself more than once, to be announced as the author of articles which I
+could not have signed, because they did not go far enough to warrant my
+affixing my name to them as to a sufficient expression of my own opinion.
+
+"There are two other ways in which a reviewed author may be wrong about his
+critic. An editor frequently makes slight insertions or omissions--I mean
+slight in quantity of type--as he goes over the last proof; this he does in
+a comparative hurry, and it may chance that he does not know the full sting
+of his little alteration. The very bit which the writer of the book most
+complains of may not have been seen by the person who is called the writer
+of the article until after the appearance of the journal; nay, if he be one
+of those--few, I daresay--who do not read their own articles, may never
+have been seen by him at all. Possibly, the insertion or omission would not
+have been made if the editor could have had one minute's conversation with
+his contributor. Sometimes it actually contradicts something which is {18}
+allowed to remain in another part of the article; and sometimes, especially
+in the case of omission, it renders other parts of the article
+unintelligible. These are disadvantages of the system, and a judicious
+editor is not very free with his _unus et alter pannus_. Next, readers in
+general, when they see the pages of a journal with the articles so nicely
+fitting, and so many ending with the page or column, have very little
+notion of the cutting and carving which goes to the process. At the very
+last moment arises the necessity of some trimming of this kind; and the
+editor, who would gladly call the writer to counsel if he could, is obliged
+to strike out ten or twelve lines. He must do his best, but it may chance
+that the omission selected would take from the writer the power of owning
+the article. A few years ago, an able opponent of mine wrote to a journal
+some criticisms upon an article which he expressly attributed to me. I
+replied as if I were the writer, which, in a sense, I was. But if any one
+had required of me an unmodified 'Yes' or 'No' to the question whether I
+wrote the article, I must, of two falsehoods, have chosen 'No': for certain
+omissions, dictated by the necessities of space and time, would have
+amounted, had my signature been affixed, to a silent surrender of points
+which, in my own character, I must have strongly insisted on, unless I had
+chosen to admit certain inferences against what I had previously published
+in my own name. I may here add that the forms of journalism obliged me in
+this case to remind my opponent that it could not be permitted to me, _in
+that journal_, either to acknowledge or deny the authorship of the
+articles. The cautions derived from the above remarks are particularly
+wanted with reference to the editorial comments upon letters of complaint.
+There is often no time to send these letters to the contributor, and even
+when this can be done, an editor is--and very properly--never of so
+editorial a mind as when he is revising the comments of a contributor upon
+an assailant of the article. He is then in a better position as to
+information, and a more {19} critical position as to responsibility. Of
+course, an editor never meddles, except under notice, with the letter of a
+correspondent, whether of a complainant, of a casual informant, or of a
+contributor who sees reason to become a correspondent. Omissions must
+sometimes be made when a grievance is too highly spiced. It did once happen
+to me that a waggish editor made an insertion without notice in a letter
+signed by me with some fiction, which insertion contained the name of a
+friend of mine, with a satire which I did not believe, and should not have
+written if I had. To my strong rebuke, he replied--'I know it was very
+wrong; but human nature could not resist.' But this was the only occasion
+on which such a thing ever happened to me.
+
+"I daresay what I have written may give some of your readers to understand
+some of the _pericula et commoda_ of modern journalism. I have known men of
+deep learning and science as ignorant of the prevailing system as any
+uneducated reader of a newspaper in a country town. I may perhaps induce
+some writers not to be too sure about this, that, or the other person. They
+may detect their reviewer, and they may be safe in attributing to him the
+general matter and tone of the article. But about one and another point,
+especially if it be a short and stinging point, they may very easily chance
+to be wrong. It has happened to myself, and within a few weeks to
+publication, to be wrong in two ways in reading a past article--to
+attribute to editorial insertion what was really my own, and to attribute
+to myself what was really editorial insertion."
+
+
+
+What is a man to do who is asked whether he wrote an article? He may, of
+course, refuse to answer; which is regarded as an admission. He may say, as
+Swift did to Serjeant Bettesworth, "Sir, when I was a young man, a friend
+of mine advised me, whenever I was asked whether I had written a certain
+paper, to deny it; and I accordingly tell that I did _not_ write it." He
+may say, as I often do, {20} when charged with having invented a joke,
+story, or epigram, "I want all the credit I can get, and therefore I always
+acknowledge all that is attributed to me, truly or not; the story, etc.
+_is_ mine." But for serious earnest, in the matter of imputed criticism,
+the answer may be, "The article was of my material, but the editor has not
+let it stand as I gave it; I cannot own it as a whole." He may then refuse
+to be particular as to the amount of the editor's interference. Of this
+there are two extreme cases. The editor may have expunged nothing but a
+qualifying adverb. Or he may have done as follows. We all remember the
+account of Adam which satirizes woman, but eulogizes her if every second
+and third line be transposed. As in:
+
+ "Adam could find no solid peace
+    When Eve was given him for a mate,
+  Till he beheld a woman's face,
+    Adam was in a happy state."
+
+If this had been the article, and a gallant editor had made the
+transpositions, the author could not with truth acknowledge. If the
+alteration were only an omitted adverb, or a few things of the sort, the
+author could not with truth deny. In all that comes between, every man must
+be his own casuist. I stared, when I was a boy, to hear grave persons
+approve of Sir Walter Scott's downright denial that he was the author of
+Waverley, in answer to the Prince Regent's downright question. If I
+remember rightly, Samuel Johnson would have approved of the same course.
+
+It is known that, whatever the law gives, it also gives all that is
+necessary to full possession; thus a man whose land is environed by land of
+others has a right of way over the land of these others. By analogy, it is
+argued that when a man has a right to his secret, he has a right to all
+that is necessary to keep it, and that is not unlawful. If, then, he can
+only keep his secret by denial, he has a right to denial. This I admit to
+be an answer against all men except the denier himself; if conscience and
+self-respect will allow {21} it, no one can impeach it. But the question
+cannot be solved on a case. That question is, A lie, is it _malum in se_,
+without reference to meaning and circumstances? This is a question with two
+sides to it. Cases may be invented in which a lie is the only way of
+preventing a murder, or in which a lie may otherwise save a life. In these
+cases it is difficult to acquit, and almost impossible to blame; discretion
+introduced, the line becomes very hard to draw.
+
+I know but one work which has precisely--as at first appears--the character
+and object of my Budget. It is the _Review of the Works of the Royal
+Society of London_, by Sir John Hill, M.D. (1751 and 1780, 4to.). This man
+offended many: the Royal Society, by his work, the medical profession, by
+inventing and selling extra-pharmacopoeian doses; Garrick, by resenting the
+rejection of a play. So Garrick wrote:
+
+ "For physic and farces his equal there scarce is;
+  His farces are physic; his physic a farce is."
+
+I have fired at the Royal Society and at the medical profession, but I have
+given a wide berth to the drama and its wits; so there is no epigram out
+against me, as yet. He was very able and very eccentric. Dr. Thomson
+(_Hist. Roy. Soc._) says he has no humor, but Dr. Thomson was a man who
+never would have discovered humor.
+
+Mr. Weld (_Hist. Roy. Soc._) backs Dr. Thomson, but with a remarkable
+addition. Having followed his predecessor in observing that the
+_Transactions_ in Martin Folkes's time have an unusual proportion of
+trifling and puerile papers, he says that Hill's book is a poor attempt at
+humor, and glaringly exhibits the feelings of a disappointed man. It is
+probable, he adds, that the points told with some effect on the Society;
+for shortly after its publication the _Transactions_ possess a much higher
+scientific value.
+
+I copy an account which I gave elsewhere.
+
+When the Royal Society was founded, the Fellows set {22} to work to prove
+all things, that they might hold fast that which was good. They bent
+themselves to the question whether sprats were young herrings. They made a
+circle of the powder of a unicorn's horn, and set a spider in the middle of
+it; "but it immediately ran out." They tried several times, and the spider
+"once made some stay in the powder." They inquired into Kenelm Digby's
+sympathetic powder. "Magnetic cures being discoursed of, Sir Gilbert Talbot
+promised to communicate what he knew of sympathetical cures; and those
+members who had any of the powder of sympathy, were desired to bring some
+of it at the next meeting."
+
+June 21, 1661, certain gentlemen were appointed "curators of the proposal
+of tormenting a man with the sympathetic powder"; I cannot find any record
+of the result. And so they went on until the time of Sir John Hill's
+satire, in 1751. This once well-known work is, in my judgment, the greatest
+compliment the Royal Society ever received. It brought forward a number of
+what are now feeble and childish researches in the Philosophical
+Transactions. It showed that the inquirers had actually been inquiring; and
+that they did not pronounce decision about "natural _knowledge_" by help of
+"_natural_ knowledge." But for this, Hill would neither have known what to
+assail, nor how. Matters are now entirely changed. The scientific bodies
+are far too well established to risk themselves. _Ibit qui zonam perdidit:_
+
+    "Let him take castles who has ne'er a groat."
+
+These great institutions are now without any collective purpose, except
+that of promoting individual energy; they print for their contributors, and
+guard themselves by a general declaration that they will not be answerable
+for the things they print. Of course they will not put forward anything for
+everybody; but a writer of a certain reputation, or matter of a certain
+look of plausibility and safety, {23} will find admission. This is as it
+should be; the pasturer of flocks and herds and the hunters of wild beasts
+are two very different bodies, with very different policies. The scientific
+academies are what a spiritualist might call "publishing mediums," and
+_their_ spirits fall occasionally into writing which looks as if minds in
+the higher state were not always impervious to nonsense.
+
+The following joke is attributed to Sir John Hill. I cannot honestly say I
+believe it; but it shows that his contemporaries did not believe he had no
+humor. Good stories are always in some sort of keeping with the characters
+on which they are fastened. Sir John Hill contrived a communication to the
+Royal Society from Portsmouth, to the effect that a sailor had broken his
+leg in a fall from the mast-head; that bandages and a plentiful application
+of tarwater had made him, in three days, able to use his leg as well as
+ever. While this communication was under grave discussion--it must be
+remembered that many then thought tarwater had extraordinary remedial
+properties--the joker contrived that a second letter should be delivered,
+which stated that the writer had forgotten, in his previous communication,
+to mention that the leg was a wooden leg! Horace Walpole told this story, I
+suppose for the first time; he is good authority for the fact of
+circulation, but for nothing more.
+
+Sir John Hill's book is droll and cutting satire. Dr. Maty, (Sec. Royal
+Society) wrote thus of it in the _Journal Britannique_ (Feb. 1751), of
+which he was editor:
+
+"Il est facheux que cet ingenieux Naturaliste, qui nous a deja donne et qui
+nous prepare encore des ouvrages plus utiles, emploie a cette odieuse tache
+une plume qu'il trempe dans le fiel et dans l'absinthe. Il est vrai que
+plusieurs de ses remarques sont fondees, et qu'a l'erreur qu'il indique, il
+joint en meme tems la correction. Mais il n'est pas toujours equitable, et
+ne manque jamais d'insulter. Que peut {24} apres tout prouver son livre, si
+ce n'est que la quarante-cinquieme partie d'un tres-ample et tres-utile
+Recueil n'est pas exempte d'erreurs? Devoit-il confondre avec des Ecrivains
+superficiels, dont la Liberte du Corps ne permet pas de restreindre la
+fertilite, cette foule de savans du Premier ordre, dont les Ecrits ont orne
+et ornent encore les Transactions? A-t-il oublie qu'on y a vu frequemment
+les noms des Boyle, des Newton, des Halley, des De Moivres, des Hans
+Sloane, etc.? Et qu'on y trouve encore ceux des Ward, des Bradley, des
+Graham, des Ellicot, des Watson, et d'un Auteur que Mr. Hill prefere a tous
+les autres, je veux dire de Mr. Hill lui-meme?"[7]
+
+This was the only answer; but it was no answer at all. Hill's object was to
+expose the absurdities; he therefore collected the absurdities. I feel sure
+that Hill was a benefactor of the Royal Society; and much more than he
+would have been if he had softened their errors and enhanced their praises.
+No reviewer will object to me that I have omitted Young, Laplace, etc. But
+then my book has a true title. Hill should not have called his a review of
+the "Works."
+
+It was charged against Sir John Hill that he had tried to become a Fellow
+of the Royal Society and had failed. This he denied, and challenged the
+production of the certificate which a candidate always sends in, and which
+is preserved. {25} But perhaps he could not get so far as a
+certificate--that is, could not find any one to recommend him; he was a
+likely man to be in such a predicament. As I have myself run foul of the
+Society on some little points, I conceive it possible that I may fall under
+a like suspicion. Whether I could have been a Fellow, I cannot know; as the
+gentleman said who was asked if he could play the violin, I never tried. I
+have always had a high opinion of the Society upon its whole history. A
+person used to historical inquiry learns to look at wholes; the
+Universities of Oxford and Cambridge, the College of Physicians, etc. are
+taken in all their duration. But those who are not historians--I mean not
+possessed of the habit of history--hold a mass of opinions about current
+things which lead them into all kinds of confusion when they try to look
+back. Not to give an instance which will offend any set of existing
+men--this merely because I can do without it--let us take the country at
+large. Magna Charta for ever! glorious safeguard of our liberties! _Nullus
+liber homo capiatur aut imprisonetur ... aut aliquo modo destruatur, nisi
+per judicium parium_ ....[8] _Liber homo: frank home_; a capital thing for
+him--but how about the _villeins_? Oh, there are none _now_! But there
+were. Who cares for villains, or barbarians, or helots? And so England, and
+Athens, and Sparta, were free States; all the freemen in them were free.
+Long after Magna Charta, villains were sold with their "chattels and
+offspring," named in that order. Long after Magna Charta, it was law that
+"Le Seigniour poit rob, naufrer, et chastiser son villein a son volunt,
+salve que il ne poit luy maim."[9]
+
+The Royal Society was founded as a co-operative body, and co-operation was
+its purpose. The early charters, etc. do not contain a trace of the
+intention to create a _scientific distinction_, a kind of Legion of Honor.
+It is clear that the {26} qualification was ability and willingness to do
+good work for the promotion of natural knowledge, no matter in how many
+persons, nor of what position in society. Charles II gave a smart rebuke
+for exclusiveness, as elsewhere mentioned. In time arose, almost of course,
+the idea of distinction attaching to the title; and when I first began to
+know the Society, it was in this state. Gentlemen of good social position
+were freely elected if they were really educated men; but the moment a
+claimant was announced as resting on his science, there was a disposition
+to inquire whether he was scientific enough. The maxim of the poet was
+adopted; and the Fellows were practically divided into _Drink-deeps_ and
+_Taste-nots_.
+
+I was, in early life, much repelled by the tone taken by the Fellows of the
+Society with respect to their very mixed body. A man high in science--some
+thirty-seven years ago (about 1830)--gave me some encouragement, as he
+thought. "We shall have you a Fellow of the Royal Society in time," said
+he. Umph! thought I: for I had that day heard of some recent elections, the
+united science of which would not have demonstrated I. 1, nor explained the
+action of a pump. Truly an elevation to look up at! It came, further, to my
+knowledge that the Royal Society--if I might judge by the claims made by
+very influential Fellows--considered itself as entitled to the best of
+everything: second-best being left for the newer bodies. A secretary, in
+returning thanks for the Royal at an anniversary of the Astronomical, gave
+rather a lecture to the company on the positive duty of all present to send
+the very best to the old body, and the absolute right of the old body to
+expect it. An old friend of mine, on a similar occasion, stated as a fact
+that the thing was always done, as well as that it ought to be done.
+
+Of late years this pretension has been made by a President of the Society.
+In 1855, Lord Rosse presented a confidential memorandum to the Council on
+the expediency of enlarging their number. He says, "In a Council so small
+it {27} is impossible to secure a satisfactory representation of the
+leading scientific Societies, and it is scarcely to be expected that, under
+such circumstances, they will continue to publish inferior papers while
+they send the best to our _Transactions_."
+
+And, again, with all the Societies represented on the Council, "even if
+every Science had its Society, and if they published everything,
+withholding their best papers [i.e., from the Royal Society], which they
+would not be likely to do, still there would remain to the Royal Society
+...." Lord Rosse seems to imagine that the minor Societies themselves
+transfer their best papers to the Royal Society; that if, for instance, the
+Astronomical Society were to receive from A.B. a paper of unusual merit,
+the Society would transfer it to the Royal Society. This is quite wrong:
+any preference of the Royal to another Society is the work of the
+contributor himself. But it shows how well hafted is the Royal Society's
+claim, that a President should acquire the notion that it is acknowledged
+and acted upon by the other Societies, in their joint and corporate
+capacities. To the pretension thus made I never could give any sympathy.
+When I first heard Mr. Christie, Sec. R. S., set it forth at the
+anniversary dinner of the Astronomical Society, I remembered the Baron in
+Walter Scott:
+
+ "Of Gilbert the Galliard a heriot he sought,
+  Saying, Give thy best steed as a vassal ought."
+
+And I remembered the answer:
+
+ "Lord and Earl though thou be, I trow
+  I can rein Buck's-foot better than thou."
+
+Fully conceding that the Royal Society is entitled to preeminent rank and
+all the respect due to age and services, I could not, nor can I now, see
+any more obligation in a contributor to send his best to that Society than
+he can make out to be due to himself. This pretension, in my mind, was
+hooked on, by my historical mode of viewing things already mentioned, to my
+knowledge of the fact that the Royal {28} Society--the chief fault,
+perhaps, lying with its President, Sir Joseph Banks--had sternly set itself
+against the formation of other societies; the Geological and Astronomical,
+for instance, though it must be added that the chief rebels came out of the
+Society itself. And so a certain not very defined dislike was generated in
+my mind--an anti-aristocratic affair--to the body which seemed to me a
+little too uplifted. This would, I daresay, have worn off; but a more
+formidable objection arose. My views of physical science gradually arranged
+themselves into a form which would have rendered F.R.S., as attached to my
+name, a false representation symbol. The Royal Society is the great
+fortress of general physics: and in the philosophy of our day, as to
+general physics, there is something which makes the banner of the R.S. one
+under which I cannot march. Everybody who saw the three letters after my
+name would infer certain things as to my mode of thought which would not be
+true inference. It would take much space to explain this in full. I may
+hereafter, perhaps, write a budget of collected results of the _a priori
+philosophy_, the nibbling at the small end of omniscience, and the effect
+it has had on common life, from the family parlor to the jury-box, from the
+girls'-school to the vestry-meeting. There are in the Society those who
+would, were there no others, prevent my criticism, be its conclusions true
+or false, from having any basis; but they are in the minority.
+
+There is no objection to be made to the principles of philosophy in vogue
+at the Society, when they are stated as principles; but there is an
+omniscience in daily practice which the principles repudiate. In like
+manner, the most retaliatory Christians have a perfect form of round words
+about behavior to those who injure them; none of them are as candid as a
+little boy I knew, who, to his mother's admonition, You should love your
+enemies, answered--Catch me at it!
+
+Years ago, a change took place which would alone have {29} put a sufficient
+difficulty in the way. The co-operative body got tired of getting funds
+from and lending name to persons who had little or no science, and wanted
+F.R.S. to be in every case a Fellow Really Scientific. Accordingly, the
+number of yearly elections was limited to fifteen recommended by the
+Council, unless the general body should choose to elect more; which it does
+not do. The election is now a competitive examination: it is no longer--Are
+you able and willing to promote natural knowledge; it is--Are you one of
+the upper fifteen of those who make such claim. In the list of
+candidates--a list rapidly growing in number--each year shows from thirty
+to forty of those whom Newton and Boyle would have gladly welcomed as
+fellow-laborers. And though the rejected of one year may be the accepted of
+the next--or of the next but one, or but two, if self-respect will permit
+the candidate to hang on--yet the time is clearly coming when many of those
+who ought to be welcomed will be excluded for life, or else shelved at
+last, when past work, with a scientific peerage. Coupled with this attempt
+to create a kind of order of knighthood is an absurdity so glaring that it
+should always be kept before the general eye. This distinction, this mark
+set by science upon successful investigation, is of necessity a
+class-distinction. Rowan Hamilton, one of the greatest names of our day in
+mathematical science, never could attach F.R.S. to his name--_he could not
+afford it_. There is a condition precedent--Four Red Sovereigns. It is four
+pounds a year, or--to those who have contributed to the Transactions--forty
+pounds down. This is as it should be: the Society must be supported. But it
+is not as it should be that a kind of title of honor should be forged, that
+a body should take upon itself to confer distinctions _for science_, when
+it is in the background--and kept there when the distinction is
+trumpeted--that the wearer is a man who can spare four pounds a year. I am
+well aware that in England a person who is not gifted either by nature or
+art, with this amount of money power, {30} is, with the mass, a very
+second-rate sort of Newton, whatever he may be in the field of
+investigation. Even men of science, so called, have this feeling. I know
+that the _scientific advisers_ of the Admiralty, who, years ago, received
+100 pounds a year each for his trouble, were sneered at by a wealthy
+pretender as "fellows to whom a hundred a year is an object." Dr. Thomas
+Young was one of them. To a bookish man--I mean a man who can manage to
+collect books--there is no tax. To myself, for example, 40 pounds worth of
+books deducted from my shelves, and the life-use of the Society's splendid
+library instead, would have been a capital exchange. But there may be, and
+are, men who want books, and cannot pay the Society's price. The Council
+would be very liberal in allowing books to be consulted. I have no doubt
+that if a known investigator were to call and ask to look at certain books,
+the Assistant-Secretary would forthwith seat him with the books before him,
+absence of F.R.S. not in any wise withstanding. But this is not like having
+the right to consult any book on any day, and to take it away, if farther
+wanted.
+
+So much for the Royal Society as concerns myself. I must add that there is
+not a spark of party feeling against those who wilfully remain outside. The
+better minds of course know better; and the smaller _savants_ look
+complacently on the idea of an outer world which makes _elite_ of them. I
+have done such a thing as serve on a committee of the Society, and report
+on a paper: they had the sense to ask, and I had the sense to see that none
+of my opinions were compromised by compliance. And I will be of any use
+which does not involve the status of _homo trium literarum_; as I have
+elsewhere explained, I would gladly be _Fautor Realis Scientiae_, but I
+would not be taken for _Falsae Rationis Sacerdos_.
+
+Nothing worse will ever happen to me than the smile which individuals
+bestow on a man who does not _groove_. Wisdom, like religion, belongs to
+majorities; who can {31} wonder that it should be so thought, when it is so
+clearly pictured in the New Testament from one end to the other?
+
+The counterpart of _paradox_, the isolated opinion of one or of few, is the
+general opinion held by all the rest; and the counterpart of false and
+absurd paradox is what is called the "vulgar error," the _pseudodox_. There
+is one great work on this last subject, the _Pseudodoxia Epidemica_ of Sir
+Thomas Browne, the famous author of the _Religio Medici_; it usually goes
+by the name of Browne "On Vulgar Errors" (1st ed. 1646; 6th, 1672). A
+careful analysis of this work would show that vulgar errors are frequently
+opposed by scientific errors; but good sense is always good sense, and
+Browne's book has a vast quantity of it.
+
+As an example of bad philosophy brought against bad observation. The
+Amphisbaena serpent was supposed to have two heads, one at each end; partly
+from its shape, partly because it runs backwards as well as forwards. On
+this Sir Thomas Browne makes the following remarks:
+
+"And were there any such species or natural kind of animal, it would be
+hard to make good those six positions of body which, according to the three
+dimensions, are ascribed unto every Animal; that is, _infra_, _supra_,
+_ante_, _retro_, _dextrosum_, _sinistrosum_: for if (as it is determined)
+that be the anterior and upper part wherein the senses are placed, and that
+the posterior and lower part which is opposite thereunto, there is no
+inferior or former part in this Animal; for the senses, being placed at
+both extreams, doth make both ends anterior, which is impossible; the terms
+being Relative, which mutually subsist, and are not without each other. And
+therefore this duplicity was ill contrived to place one head at both
+extreams, and had been more tolerable to have settled three or four at one.
+And therefore also Poets have been more reasonable than Philosophers, and
+_Geryon_ or _Cerberus_ less monstrous than _Amphisbaena_." {32}
+
+There may be paradox upon paradox: and there is a good instance in the
+eighth century in the case of Virgil, an Irishman, Bishop of Salzburg and
+afterwards Saint, and his quarrels with Boniface, an Englishman, Archbishop
+of Mentz, also afterwards Saint. All we know about the matter is, that
+there exists a letter of 748 from Pope Zachary, citing Virgil--then, it
+seems, at most a simple priest, though the Pope was not sure even of
+that--to Rome to answer the charge of maintaining that there is another
+world (_mundus_) under our earth (_terra_), with another sun and another
+moon. Nothing more is known: the letter contains threats in the event of
+the charge being true; and there history drops the matter. Since Virgil was
+afterwards a Bishop and a Saint, we may fairly conclude that he died in the
+full flower of his orthodox reputation. It has been supposed--and it seems
+probable--that Virgil maintained that the earth is peopled all the way
+round, so that under some spots there are antipodes; that his
+contemporaries, with very dim ideas about the roundness of the earth, and
+most of them with none at all, interpreted him as putting another earth
+under ours--turned the other way, probably, like the second piece of
+bread-and-butter in a sandwich, with a sun and moon of its own. In the
+eighth century this would infallibly have led to an underground Gospel, an
+underground Pope, and an underground Avignon for him to live in. When, in
+later times, the idea of inhabitants for the planets was started, it was
+immediately asked whether they had sinned, whether Jesus Christ died for
+_them_, whether their wine and their water could be lawfully used in the
+sacraments, etc.
+
+On so small a basis as the above has been constructed a companion case to
+the persecution of Galileo. On one side the positive assertion, with
+indignant comment, that Virgil was deposed for antipodal heresy, on the
+other, serious attempts at justification, palliation, or mystification.
+Some writers say that Virgil was found guilty; others that he gave
+satisfactory explanation, and became very good friends with {33} Boniface:
+for all which see Bayle. Some have maintained that the antipodist was a
+different person from the canonized bishop: there is a second Virgil, made
+to order. When your shoes pinch, and will not stretch, always throw them
+away and get another pair: the same with your facts. Baronius was not up to
+the plan of a substitute: his commentator Pagi (probably writing about
+1690) argues for it in a manner which I think Baronius would not have
+approved. This Virgil was perhaps a slippery fellow. The Pope says he hears
+that Virgil pretended licence from him to claim one of some new bishoprics:
+this he declares is totally false. It is part of the argument that such a
+man as this could not have been created a Bishop and a Saint: on this point
+there will be opinions and opinions.[10]
+
+Lactantius, four centuries before, had laughed at the antipodes in a manner
+which seems to be ridicule thrown on the idea of the earth's roundness.
+Ptolemy, without reference to the antipodes, describes the extent of the
+inhabited part of the globe in a way which shows that he could have had no
+objection to men turned opposite ways. Probably, in the eighth century, the
+roundness of the earth was matter of thought only to astronomers. It should
+always be remembered, especially by those who affirm persecution of a true
+opinion, that but for our knowing from Lactantius that the antipodal notion
+had been matter of assertion and denial among theologians, we could never
+have had any great confidence in Virgil really having maintained the simple
+theory of the existence of antipodes. And even now we are not entitled to
+affirm it as having historical proof: the evidence {34} goes to Virgil
+having been charged with very absurd notions, which it seems more likely
+than not were the absurd constructions which ignorant contemporaries put
+upon sensible opinions of his.
+
+One curious part of this discussion is that neither side has allowed Pope
+Zachary to produce evidence to character. He shall have been an Urban, say
+the astronomers; an Urban he ought to have been, say the theologians. What
+sort of man was Zachary? He was eminently sensible and conciliatory; he
+contrived to make northern barbarians hear reason in a way which puts him
+high among that section of the early popes who had the knack of managing
+uneducated swordsmen. He kept the peace in Italy to an extent which
+historians mention with admiration. Even Bale, that Maharajah of
+pope-haters, allows himself to quote in favor of Zachary, that "multa
+Papalem dignitatem decentia, eademque praeclara (scilicet) opera
+confecit."[11] And this, though so willing to find fault that, speaking of
+Zachary putting a little geographical description of the earth on the
+portico of the Lateran Church, he insinuates that it was intended to affirm
+that the Pope was lord of the whole. Nor can he say how long Zachary held
+the see, except by announcing his death in 752, "cum decem annis
+pestilentiae sedi praefuisset."[12]
+
+There was another quarrel between Virgil and Boniface which is an
+illustration. An ignorant priest had baptized "in nomine Patri_a_, et
+Fili_a_ et Spiritu_a_ Sancta." Boniface declared the rite null and void:
+Virgil maintained the contrary; and Zachary decided in favor of Virgil, on
+the ground that the absurd form was only ignorance of Latin, and not
+heresy. It is hard to believe that this man deposed a priest for asserting
+the whole globe to be inhabited. To me the little information that we have
+seems {35} to indicate--but not with certainty--that Virgil maintained the
+antipodes: that his ignorant contemporaries travestied his theory into that
+of an underground cosmos; that the Pope cited him to Rome to explain his
+system, which, as reported, looked like what all would then have affirmed
+to be heresy; that he gave satisfactory explanations, and was dismissed
+with honor. It may be that the educated Greek monk, Zachary, knew his
+Ptolemy well enough to guess what the asserted heretic would say; we have
+seen that he seems to have patronized geography. The _description_ of the
+earth, according to historians, was a _map_; this Pope may have been more
+ready than another to prick up his ears at any rumor of geographical
+heresy, from hope of information. And Virgil, who may have entered the
+sacred presence as frightened as Jacquard, when Napoleon I sent for him and
+said, with a stern voice and threatening gesture, "You are the man who can
+tie a knot in a stretched string," may have departed as well pleased as
+Jacquard with the riband and pension which the interview was worth to him.
+
+A word more about Baronius. If he had been pope, as he would have been but
+for the opposition of the Spaniards, and if he had lived ten years longer
+than he did, and if Clavius, who would have been his astronomical adviser,
+had lived five years longer than he did, it is probable, nay almost
+certain, that the great exhibition, the proceeding against Galileo, would
+not have furnished a joke against theology in all time to come. For
+Baronius was sensible and witty enough to say that in the Scriptures the
+Holy Spirit intended to teach how to go to Heaven, not how Heaven goes; and
+Clavius, in his last years, confessed that the whole system of the heavens
+had broken down, and must be mended.
+
+The manner in which the Galileo case, a reality, and the Virgil case, a
+fiction, have been hawked against the Roman see are enough to show that the
+Pope and his adherents have not cared much about physical philosophy. In
+truth, orthodoxy has always had other fish to fry. Physics, which {36} in
+modern times has almost usurped the name _philosophy_, in England at least,
+has felt a little disposed to clothe herself with all the honors of
+persecution which belong to the real owner of the name. But the bishops,
+etc. of the Middle Ages knew that the contest between nominalism and
+realism, for instance, had a hundred times more bearing upon orthodoxy than
+anything in astronomy, etc. A wrong notion about _substance_ might play the
+mischief with _transubstantiation_.
+
+The question of the earth's motion was the single point in which orthodoxy
+came into real contact with science. Many students of physics were
+suspected of magic, many of atheism: but, stupid as the mistake may have
+been, it was _bona fide_ the magic or the atheism, not the physics, which
+was assailed. In the astronomical case it was the very doctrine, as a
+doctrine, independently of consequences, which was the _corpus delicti_:
+and this because it contradicted the Bible. And so it did; for the
+stability of the earth is as clearly assumed from one end of the Old
+Testament to the other as the solidity of iron. Those who take the Bible to
+be _totidem verbis_ dictated by the God of Truth can refuse to believe it;
+and they make strange reasons. They undertake, _a priori_, to settle Divine
+intentions. The Holy Spirit did not _mean_ to teach natural philosophy:
+this they know beforehand; or else they infer it from finding that the
+earth does move, and the Bible says it does not. Of course, ignorance
+apart, every word is truth, or the writer did not mean truth. But this puts
+the whole book on its trial: for we never can find out what the writer
+meant, until we otherwise find out what is true. Those who like may, of
+course, declare for an inspiration over which they are to be viceroys; but
+common sense will either accept verbal meaning or deny verbal inspiration.
+
+       *       *       *       *       *
+
+
+{37}
+
+A BUDGET OF PARADOXES.
+
+VOLUME I.
+
+THE STORY OF BURIDAN'S ASS.
+
+    Questiones Morales, folio, 1489 [Paris]. By T. Buridan.
+
+This is the title from the Hartwell Catalogue of Law Books. I suppose it is
+what is elsewhere called the "Commentary on the Ethics of Aristotle,"
+printed in 1489.[13] Buridan[14] (died about 1358) is the creator of the
+famous ass which, as _Burdin's_[15] ass, was current in Burgundy, perhaps
+is, as a vulgar proverb. Spinoza[16] says it was a jenny ass, and that a
+man would not have been so foolish; but whether the compliment is paid to
+human or to masculine character does not appear--perhaps to both in one.
+The story _told_ about the famous paradox is very curious. The Queen of
+France, Joanna or Jeanne, was in the habit of sewing her lovers up in
+sacks, and throwing them into the Seine; not for blabbing, but that they
+might not blab--certainly the safer plan. Buridan was exempted, and, in
+gratitude, invented the sophism. What it has to do with the matter {38} has
+never been explained. Assuredly _qui facit per alium facit per se_ will
+convict Buridan of prating. The argument is as follows, and is seldom told
+in full. Buridan was for free-will--that is, will which determines conduct,
+let motives be ever so evenly balanced. An ass is _equally_ pressed by
+hunger and by thirst; a bundle of hay is on one side, a pail of water on
+the other. Surely, you will say, he will not be ass enough to die for want
+of food or drink; he will then make a choice--that is, will choose between
+alternatives of equal force. The problem became famous in the schools; some
+allowed the poor donkey to die of indecision; some denied the possibility
+of the balance, which was no answer at all.
+
+
+
+MICHAEL SCOTT'S DEVILS.
+
+The following question is more difficult, and involves free-will to all who
+answer--"Which you please." If the northern hemisphere were land, and all
+the southern hemisphere water, ought we to call the northern hemisphere an
+island, or the southern hemisphere a lake? Both the questions would be good
+exercises for paradoxers who must be kept employed, like Michael
+Scott's[17] devils. The wizard {39} knew nothing about squaring the circle,
+etc., so he set them to make ropes out of sea sand, which puzzled them.
+Stupid devils; much of our glass is sea sand, and it makes beautiful
+thread. Had Michael set them to square the circle or to find a perpetual
+motion, he would have done his work much better. But all this is
+conjecture: who knows that I have not hit on the very plan he adopted?
+Perhaps the whole race of paradoxers on hopeless subjects are Michael's
+subordinates, condemned to transmigration after transmigration, until their
+task is done.
+
+The above was not a bad guess. A little after the time when the famous
+Pascal papers[18] were produced, I came into possession of a correspondence
+which, but for these papers, I should have held too incredible to be put
+before the world. But when one sheep leaps the ditch, another will follow:
+so I gave the following account in the _Athenaeum_ of October 5, 1867:
+
+"The recorded story is that Michael Scott, being bound by contract to
+produce perpetual employment for a number of young demons, was worried out
+of his life in inventing jobs for them, until at last he set them to make
+ropes out of sea sand, which they never could do. We have obtained a very
+curious correspondence between the wizard Michael and his demon-slaves; but
+we do not feel at liberty to say how it came into our hands. We much regret
+that we did not receive it in time for the British Association. It appears
+that the story, true as far as it goes, was never finished. The demons
+easily conquered the rope difficulty, by the simple process of making the
+sand into glass, and spinning the glass into thread, which they twisted.
+Michael, thoroughly disconcerted, hit upon the plan of setting some to {40}
+square the circle, others to find the perpetual motion, etc. He commanded
+each of them to transmigrate from one human body into another, until their
+tasks were done. This explains the whole succession of cyclometers, and all
+the heroes of the Budget. Some of this correspondence is very recent; it is
+much blotted, and we are not quite sure of its meaning: it is full of
+figurative allusions to driving something illegible down a steep into the
+sea. It looks like a humble petition to be allowed some diversion in the
+intervals of transmigration; and the answer is--
+
+  Rumpat et serpens iter institutum,[19]
+
+--a line of Horace, which the demons interpret as a direction to come
+athwart the proceedings of the Institute by a sly trick. Until we saw this,
+we were suspicious of M. Libri,[20] the unvarying blunders of the
+correspondence look like knowledge. To be always out of the road requires a
+map: genuine ignorance occasionally lapses into truth. We thought it
+possible M. Libri might have played the trick to show how easily the French
+are deceived; but with our present information, our minds are at rest on
+the subject. We see M. Chasles does not like to avow the real source of
+information: he will not confess himself a spiritualist."
+
+
+
+PHILO OF GADARA.
+
+Philo of Gadara[21] is asserted by Montucla,[22] on the {41} authority of
+Eutocius,[23] the commentator on Archimedes, to have squared the circle
+within the _ten-thousandth_ part of a unit, that is, to _four_ places of
+decimals. A modern classical dictionary represents it as done by Philo to
+_ten thousand_ places of decimals. Lacroix comments on Montucla to the
+effect that _myriad_ (in Greek _ten thousand_) is here used as we use it,
+vaguely, for an immense number. On looking into Eutocius, I find that not
+one definite word is said about the extent to which Philo carried the
+matter. I give a translation of the passage:
+
+"We ought to know that Apollonius Pergaeus, in his Ocytocium [this work is
+lost], demonstrated the same by other numbers, and came nearer, which seems
+more accurate, but has nothing to do with Archimedes; for, as before said,
+he aimed only at going near enough for the wants of life. Neither is Porus
+of Nicaea fair when he takes Archimedes to task for not giving a line
+accurately equal to the circumference. He says in his Cerii that his
+teacher, Philo of Gadara, had given a more accurate approximation ([Greek:
+eis akribesterous arithmous agagein]) than that of Archimedes, or than 7 to
+22. But all these [the rest as well as Philo] miss the intention. They
+multiply and divide by _tens of thousands_, which no one can easily do,
+unless he be versed in the logistics [fractional computation] of Magnus
+[now unknown]."
+
+Montucla, or his source, ought not to have made this mistake. He had been
+at the Greek to correct Philo _Gadetanus_, as he had often been called, and
+he had brought away {42} and quoted [Greek: apo Gadaron]. Had he read two
+sentences further, he would have found the mistake.
+
+We here detect a person quite unnoticed hitherto by the moderns, Magnus the
+arithmetician. The phrase is ironical; it is as if we should say, "To do
+this a man must be deep in Cocker."[24] Accordingly, Magnus, Baveme,[25]
+and Cocker, are three personifications of arithmetic; and there may be
+more.
+
+
+
+ON SQUARING THE CIRCLE.
+
+Aristotle, treating of the category of relation, denies that the quadrature
+has been found, but appears to assume that it can be done. Boethius,[26] in
+his comment on the passage, says that it has been done since Aristotle, but
+that the demonstration is too long for him to give. Those who have no
+notion of the quadrature question may look at the _English Cyclopaedia_,
+art. "Quadrature of the Circle."
+
+    Tetragonismus. Id est circuli quadratura per Campanum, Archimedem
+    Syracusanum, atque Boetium mathematicae perspicacissimos adinventa.--At
+    the end, Impressum Venetiis per Ioan. Bapti. Sessa. Anno ab
+    incarnatione Domini, 1503. Die 28 Augusti.
+
+{43}
+
+This book has never been noticed in the history of the subject, and I
+cannot find any mention of it. The quadrature of Campanus[27] takes the
+ratio of Archimedes,[28] 7 to 22 to be absolutely correct; the account
+given of Archimedes is not a translation of his book; and that of Boetius
+has more than is in Boet_h_ius. This book must stand, with the next, as the
+earliest in print on the subject, until further showing: Murhard[29] and
+Kastner[30] have nothing so early. It is edited by Lucas Gauricus,[31] who
+has given a short preface. Luca Gaurico, Bishop of Civita Ducale, an
+astrologer of astrologers, published this work at about thirty years of
+age, and lived to eighty-two. His works are collected in folios, but I do
+not know whether they contain this production. The poor fellow could never
+tell his own fortune, because his father neglected to note the hour and
+minute of his birth. But if there had been anything in astrology, he could
+have worked back, as Adams[32] and Leverrier[33] did when they caught {44}
+Neptune: at sixty he could have examined every minute of his day of birth,
+by the events of his life, and so would have found the right minute. He
+could then have gone on, by rules of prophecy. Gauricus was the
+mathematical teacher of Joseph Scaliger,[34] who did him no credit, as we
+shall see.
+
+
+
+BOVILLUS ON THE QUADRATURE PROBLEM.
+
+    In hoc opere contenta Epitome.... Liber de quadratura Circuli....
+    Paris, 1503, folio.
+
+The quadrator is Charles Bovillus,[35] who adopted the views of Cardinal
+Cusa,[36] presently mentioned. Montucla is hard on his compatriot, who, he
+says, was only saved from the laughter of geometers by his obscurity.
+Persons must guard against most historians of mathematics in one point:
+they frequently attribute to _his own_ age the obscurity which a writer has
+in _their own_ time. This tract was printed by Henry Stephens,[37] at the
+instigation of Faber Stapulensis,[38] {45} and is recorded by Dechales,[39]
+etc. It was also introduced into the _Margarita Philosophica_ of 1815,[40]
+in the same appendix with the new perspective from Viator. This is not
+extreme obscurity, by any means. The quadrature deserved it; but that is
+another point.
+
+It is stated by Montucla that Bovillus makes [pi] = [root]10. But Montucla
+cites a work of 1507, _Introductorium Geometricum_, which I have never
+seen.[41] He finds in it an account which Bovillus gives of the quadrature
+of the peasant laborer, and describes it as agreeing with his own. But the
+description makes [pi] = 3-1/8, which it thus appears Bovillus could not
+distinguish from [root]10. It seems also that this 3-1/8, about which we
+shall see so much in the sequel, takes its rise in the thoughtful head of a
+poor laborer. It does him great honor, being so near the truth, and he
+having no means of instruction. In our day, when an ignorant person chooses
+to bring his fancy forward in opposition to demonstration which he will not
+study, he is deservedly laughed at.
+
+{46}
+
+
+
+THE STORY OF LACOMME'S ATTEMPT AT QUADRATURE.
+
+Mr. James Smith,[42] of Liverpool--hereinafter notorified--attributes the
+first announcement of 3-1/8 to M. Joseph Lacomme, a French well-sinker, of
+whom he gives the following account:
+
+"In the year 1836, at which time Lacomme could neither read nor write, he
+had constructed a circular reservoir and wished to know the quantity of
+stone that would be required to pave the bottom, and for this purpose
+called on a professor of mathematics. On putting his question and giving
+the diameter, he was surprised at getting the following answer from the
+Professor: _'Qu'il lui etait impossible de le lui dire au juste, attendu
+que personne n'avait encore pu trouver d'une maniere exacte le rapport de
+la circonference au diametre.'_[43] From this he was led to attempt the
+solution of the problem. His first process was purely mechanical, and he
+was so far convinced he had made the discovery that he took to educating
+himself, and became an expert arithmetician, and then found that
+arithmetical results agreed with his mechanical experiments. He appears to
+have eked out a bare existence for many years by teaching arithmetic, all
+the time struggling to get a hearing from some of the learned societies,
+but without success. In the year 1855 he found his way to Paris, where, as
+if by accident, he made the acquaintance of a young gentleman, son of M.
+Winter, a commissioner of police, and taught him his peculiar methods of
+calculation. The young man was so enchanted that he strongly recommended
+Lacomme to his father, and {47} subsequently through M. Winter he obtained
+an introduction to the President of the Society of Arts and Sciences of
+Paris. A committee of the society was appointed to examine and report upon
+his discovery, and the society at its _seance_ of March 17, 1856, awarded a
+silver medal of the first class to M. Joseph Lacomme for his discovery of
+the true ratio of diameter to circumference in a circle. He subsequently
+received three other medals from other societies. While writing this I have
+his likeness before me, with his medals on his breast, which stands as a
+frontispiece to a short biography of this extraordinary man, for which I am
+indebted to the gentleman who did me the honor to publish a French
+translation of the pamphlet I distributed at the meeting of the British
+Association for the Advancement of Science, at Oxford, in
+1860."--_Correspondent_, May 3, 1866.
+
+My inquiries show that the story of the medals is not incredible. There are
+at Paris little private societies which have not so much claim to be
+exponents of scientific opinion as our own Mechanics' Institutes. Some of
+them were intended to give a false lustre: as the "Institut Historique,"
+the members of which are "Membre de l'Institut Historique." That M. Lacomme
+should have got four medals from societies of this class is very possible:
+that he should have received one from any society at Paris which has the
+least claim to give one is as yet simply incredible.
+
+
+
+NICOLAUS OF CUSA'S ATTEMPT.
+
+    Nicolai de Cusa Opera Omnia. Venice, 1514. 3 vols. folio.
+
+The real title is "Haec accurata recognitio trium voluminum operum clariss.
+P. Nicolai Cusae ... proxime sequens pagina monstrat."[44] Cardinal Cusa,
+who died in 1464, is one of the earliest modern attempters. His quadrature
+is found in the second volume, and is now quite unreadable.
+
+{48} In these early days every quadrator found a geometrical opponent, who
+finished him. Regimontanus[45] did this office for the Cardinal.
+
+
+
+HENRY CORNELIUS AGRIPPA.
+
+    De Occulta Philosophia libri III. By Henry Cornelius Agrippa. Lyons,
+    1550, 8vo.
+
+    De incertitudine et vanitate scientiarum. By the same. Cologne, 1531,
+    8vo.
+
+The first editions of these works were of 1530, as well as I can make out;
+but the first was in progress in 1510.[46] In the second work Agrippa
+repents of having wasted time on the magic of the first; but all those who
+actually deal with demons are destined to eternal fire with Jamnes and
+Mambres and Simon Magus. This means, as is the fact, that his occult
+philosophy did not actually enter upon _black_ magic, but confined itself
+to the power of the stars, of numbers, etc. The fourth book, which appeared
+after the death of Agrippa, and really concerns dealing with evil spirits,
+is undoubtedly spurious. It is very difficult to make out what Agrippa
+really believed on the subject. I have introduced his books as the most
+marked specimens of treatises on magic, a paradox of our day, though not
+far from orthodoxy in his; and here I should have ended my notice, if I had
+not casually found something more interesting to the reader of our day.
+
+{49}
+
+
+
+WHICH LEADS TO WALTER SCOTT.
+
+Walter Scott, it is well known, was curious on all matters connected with
+magic, and has used them very widely. But it is hardly known how much pains
+he has taken to be correct, and to give the real thing. The most decided
+detail of a magical process which is found in his writings is that of
+Dousterswivel in _The Antiquary_; and it is obvious, by his accuracy of
+process, that he does not intend the adept for a mere impostor, but for one
+who had a lurking belief in the efficacy of his own processes, coupled with
+intent to make a fraudulent use of them. The materials for the process are
+taken from Agrippa. I first quote Mr. Dousterswivel:
+
+"... I take a silver plate when she [the moon] is in her fifteenth mansion,
+which mansion is in de head of _Libra_, and I engrave upon one side de
+worts _Schedbarschemoth Scharta_ch_an_ [_ch_ should be _t_]--dat is, de
+Intelligence of de Intelligence of de moon--and I make his picture like a
+flying serpent with a turkey-cock's head--vary well--Then upon this side I
+make de table of de moon, which is a square of nine, multiplied into
+itself, with eighty-one numbers [nine] on every side and diameter nine...."
+
+In the _De Occulta Philosophia_, p. 290, we find that the fifteenth mansion
+of the moon _incipit capite Librae_, and is good _pro extrahendis
+thesauris_, the object being to discover hidden treasure. In p. 246, we
+learn that a _silver_ plate must be used with the moon. In p. 248, we have
+the words which denote the Intelligence, etc. But, owing to the falling of
+a number into a wrong line, or the misplacement of a line, one or
+other--which takes place in all the editions I have examined--Scott has,
+sad to say, got hold of the wrong words; he has written down the _demon of
+the demons_ of the moon. Instead of the gibberish above, it should have
+been _Malcha betarsisim hed beruah schenhakim_. In p. 253, we have the
+magic square of the moon, with eighty-one numbers, and the symbol for the
+Intelligence, which Scott likens to a flying {50} serpent with a
+turkey-cock's head. He was obliged to say something; but I will stake my
+character--and so save a woodcut--on the scratches being more like a pair
+of legs, one shorter than the other, without a body, jumping over a
+six-barred gate placed side uppermost. Those who thought that Scott forged
+his own nonsense, will henceforth stand corrected. As to the spirit
+Peolphan, etc., no doubt Scott got it from the authors he elsewhere
+mentions, Nicolaus Remigius[47] and Petrus Thyracus; but this last word
+should be Thyraeus.
+
+The tendency of Scott's mind towards prophecy is very marked, and it is
+always fulfilled. Hyder, in his disguise, calls out to Tippoo: "Cursed is
+the prince who barters justice for lust; he shall die in the gate by the
+sword of the stranger." Tippoo was killed in a gateway at Seringapatam.[48]
+
+
+
+FINAEUS ON CIRCLE SQUARING.
+
+    Orontii Finaei ... Quadratura Circuli. Paris, 1544, 4to.
+
+Orontius[49] squared the circle out of all comprehension; but he was killed
+by a feather from his own wing. His {51} former pupil, John Buteo,[50] the
+same who--I believe for the first time--calculated the question of Noah's
+ark, as to its power to hold all the animals and stores, unsquared him
+completely. Orontius was the author of very many works, and died in 1555.
+Among the laudatory verses which, as was usual, precede this work, there is
+one of a rare character: a congratulatory ode to the wife of the author.
+The French now call this writer Oronce Finee; but there is much difficulty
+about delatinization. Is this more correct than Oronce Fine, which the
+translator of De Thou uses? Or than Horonce Phine, which older writers
+give? I cannot understand why M. de Viette[51] should be called Viete,
+because his Latin name is Vieta. It is difficult to restore Buteo; for not
+only now is _butor_ a blockhead as well as a bird, but we really cannot
+know what kind of bird Buteo stood for. We may be sure that Madame Fine was
+Denise Blanche; for Dionysia Candida can mean nothing else. Let her shade
+rejoice in the fame which Hubertus Sussannaeus has given her.
+
+I ought to add that the quadrature of Orontius, and solutions of all the
+other difficulties, were first published in _De Rebus Mathematicis Hactenus
+Desideratis_,[52] of which I have not the date.
+
+
+
+{52}
+
+DUCHESNE, AND A DISQUISITION ON ETYMOLOGY.
+
+    Nicolai Raymari Ursi Dithmarsi Fundamentum Astronomicum, id est, nova
+    doctrina sinuum et triangulorum.... Strasburg, 1588, 4to.[53]
+
+People choose the name of this astronomer for themselves: I take _Ursus_,
+because he _was_ a bear. This book gave the quadrature of Simon
+Duchesne,[54] or a Quercu, which excited Peter Metius,[55] as presently
+noticed. It also gave that unintelligible reference to Justus Byrgius which
+has been used in the discussion about the invention of logarithms.[56]
+
+The real name of Duchesne is Van der Eycke. I have met with a tract in
+Dutch, _Letterkundige Aanteekeningen_, upon Van Eycke, Van Ceulen,[57]
+etc., by J. J. Dodt van Flensburg,[58] which I make out to be since 1841 in
+date. I should {53} much like a translation of this tract to be printed,
+say in the _Phil. Mag._ Dutch would be clear English if it were properly
+spelt. For example, _learn-master_ would be seen at once to be _teacher_;
+but they will spell it _leermeester_. _Of these_ they write as _van deze_;
+_widow_ they make _weduwe_. All this is plain to me, who never saw a Dutch
+dictionary in my life; but many of their misspellings are quite
+unconquerable.
+
+
+
+FALCO'S RARE TRACT.
+
+    Jacobus Falco Valentinus, miles Ordinis Montesiani, hanc circuli
+    quadraturam invenit. Antwerp, 1589, 4to.[59]
+
+The attempt is more than commonly worthless; but as Montucla and others
+have referred to the verses at the end, and as the tract is of the rarest,
+I will quote them:
+
+      _Circulus loquitur._
+  Vocabar ante circulus
+  Eramque curvus undique
+  Ut alta solis orbita
+  Et arcus ille nubium.
+  Eram figura nobilis
+  Carensque sola origine
+  Carensque sola termino.
+  Modo indecora prodeo
+  Novisque foedor angulis.
+  Nec hoc peregit Archytas[60]
+  Neque Icari pater neque
+  Tuus, Iapete, filius.
+  Quis ergo casus aut Deus
+  Meam quadravit aream?
+
+      _Respondet auctor._
+  Ad alta Turiae ostia
+  Lacumque limpidissimum
+  Sita est beata civitas
+  {54}
+  Parum Saguntus abfuit
+  Abestque Sucro plusculum.
+  Hic est poeta quispiam
+  Libenter astra consulens
+  Sibique semper arrogans
+  Negata doctioribus,
+  Senex ubique cogitans
+  Sui frequenter immemor
+  Nec explicare circinum
+  Nec exarare lineas
+  Sciens ut ipse praedicat.
+  Hic ergo bellus artifex
+  Tuam quadravit aream.[61]
+
+Falco's verses are pretty, if the U-mysteries be correct; but of these
+things I have forgotten--what I knew. [One mistake has been pointed out to
+me: it is Arch[=y]tas].
+
+As a specimen of the way in which history is written, I copy the account
+which Montucla--who is accurate when he writes about what he has
+seen--gives of these verses. He gives the date 1587; he places the verses
+at the beginning instead of the end; he says the circle thanks its
+quadrator affectionately; and he says the good and modest chevalier gives
+all the glory to the patron saint of his order. All of little consequence,
+as it happens; but writing at second-hand makes as complete mistakes about
+more important matters.
+
+{55}
+
+
+
+BUNGUS ON THE MYSTERY OF NUMBER.
+
+    Petri Bungi Bergomatis Numerorum mysteria. Bergomi [Bergamo], 1591,
+    4to. Second Edition.
+
+The first edition is said to be of 1585;[62] the third, Paris, 1618. Bungus
+is not for my purpose on his own score, but those who gave the numbers
+their mysterious characters: he is but a collector. He quotes or uses 402
+authors, as we are informed by his list; this just beats Warburton,[63]
+whom some eulogist or satirist, I forget which, holds up as having used 400
+authors in some one work. Bungus goes through 1, 2, 3, etc., and gives the
+account of everything remarkable in which each number occurs; his accounts
+not being always mysterious. The numbers which have nothing to say for
+themselves are omitted: thus there is a gap between 50 and 60. In treating
+666, Bungus, a good Catholic, could not compliment the Pope with it, but he
+fixes it on Martin Luther with a little forcing. If from A to I represent
+1-10, from K to S 10-90, and from T to Z 100-500, we see:
+
+   M   A   R   T   I   N     L   U   T   E   R   A
+  30   1  80  100  9  40    20  200 100  5  80   1
+
+which gives 666. Again, in Hebrew, _Lulter_ does the same:
+
+  [Hebrew:   R    T    L    W   L]
+            200  400  30    6  30
+
+And thus two can play at any game. The second is better than the first: to
+Latinize the surname and not the Christian {56} name is very unscholarlike.
+The last number mentioned is a thousand millions; all greater numbers are
+dismissed in half a page. Then follows an accurate distinction between
+_number_ and _multitude_--a thing much wanted both in arithmetic and logic.
+
+
+
+WHICH LEADS TO A STORY ABOUT THE ROYAL SOCIETY.
+
+What may be the use of such a book as this? The last occasion on which it
+was used was the following. Fifteen or sixteen years ago the Royal Society
+determined to restrict the number of yearly admissions to fifteen men of
+science, and noblemen _ad libitum_; the men of science being selected and
+recommended by the Council, with a power, since practically surrendered, to
+the Society to elect more. This plan appears to me to be directly against
+the spirit of their charter, the true intent of which is, that all who are
+fit should be allowed to promote natural knowledge in association, from and
+after the time at which they are both fit and willing. It is also working
+more absurdly from year to year; the tariff of fifteen per annum will soon
+amount to the practical exclusion of many who would be very useful. This
+begins to be felt already, I suspect. But, as appears above, the body of
+the Society has the remedy in its own hands. When the alteration was
+discussed by the Council, my friend the late Mr. Galloway,[64] then one of
+the body, opposed it strongly, and inquired particularly into the reason
+why _fifteen_, of all numbers, was the one to be selected. Was it because
+fifteen is seven and eight, typifying the Old Testament Sabbath, and the
+New Testament day of the resurrection following? Was it because Paul strove
+fifteen days against Peter, proving that he was a doctor both of the Old
+and New Testament? Was it because the prophet Hosea bought a lady {57} for
+fifteen pieces of silver? Was it because, according to Micah, seven
+shepherds and eight chiefs should waste the Assyrians? Was it because
+Ecclesiastes commands equal reverence to be given to both Testaments--such
+was the interpretation--in the words "Give a portion to seven, and also to
+eight"? Was it because the waters of the Deluge rose fifteen cubits above
+the mountains?--or because they lasted fifteen decades of days? Was it
+because Ezekiel's temple had fifteen steps? Was it because Jacob's ladder
+has been supposed to have had fifteen steps? Was it because fifteen years
+were added to the life of Hezekiah? Was it because the feast of unleavened
+bread was on the fifteenth day of the month? Was it because the scene of
+the Ascension was fifteen stadia from Jerusalem? Was it because the
+stone-masons and porters employed in Solomon's temple amounted to fifteen
+myriads? etc. The Council were amused and astounded by the volley of
+fifteens which was fired at them; they knowing nothing about Bungus, of
+which Mr. Galloway--who did not, as the French say, indicate his
+sources--possessed the copy now before me. In giving this anecdote I give a
+specimen of the book, which is exceedingly rare. Should another edition
+ever appear, which is not very probable, he would be but a bungling Bungus
+who should forget the _fifteen_ of the Royal Society.
+
+
+
+AND ALSO TO A QUESTION OF EVIDENCE.
+
+[I make a remark on the different colors which the same person gives to one
+story, according to the bias under which he tells it. My friend Galloway
+told me how he had quizzed the Council of the Royal Society, to my great
+amusement. Whenever I am struck by the words of any one, I carry away a
+vivid recollection of position, gestures, tones, etc. I do not know whether
+this be common or uncommon. I never recall this joke without seeing before
+me my friend, leaning against his bookcase, with Bungus open in his hand,
+and a certain half-depreciatory tone which he often used {58} when speaking
+of himself. Long after his death, an F.R.S. who was present at the
+discussion, told me the story. I did not say I had heard it, but I watched
+him, with Galloway at the bookcase before me. I wanted to see whether the
+two would agree as to the fact of an enormous budget of fifteens having
+been fired at the Council, and they did agree perfectly. But when the
+paragraph of the Budget appeared in the _Athenaeum_, my friend, who seemed
+rather to object to the _showing-up_, assured me that the thing was grossly
+exaggerated; there was indeed a fifteen or two, but nothing like the number
+I had given. I had, however, taken sharp note of the previous narration.
+
+
+
+AND TO ANOTHER QUESTION OF EVIDENCE.
+
+I will give another instance. An Indian officer gave me an account of an
+elephant, as follows. A detachment was on the march, and one of the
+gun-carriages got a wheel off the track, so that it was also off the
+ground, and hanging over a precipice. If the bullocks had moved a step,
+carriages, bullocks, and all must have been precipitated. No one knew what
+could be done until some one proposed to bring up an elephant, and let him
+manage it his own way. The elephant took a moment's survey of the fix, put
+his trunk under the axle of the free wheel, and waited. The surrounders,
+who saw what he meant, moved the bullocks gently forward, the elephant
+followed, supporting the axle, until there was ground under the wheel, when
+he let it quietly down. From all I had heard of the elephant, this was not
+too much to believe. But when, years afterwards, I reminded my friend of
+his story, he assured me that I had misunderstood him, that the elephant
+was _directed_ to put his trunk under the wheel, and saw in a moment why.
+This is reasonable sagacity, and very likely the correct account; but I am
+quite sure that, in the fit of elephant-worship under which the story was
+first told, it was told as I have first stated it.] {59}
+
+
+
+GIORDANO BRUNO AND HIS PARADOXES.
+
+    [Jordani Bruni Nolani de Monade, Numero et Figura ... item de
+    Innumerabilibus, Immenso, et Infigurabili ... Frankfort, 1591, 8vo.[65]
+
+I cannot imagine how I came to omit a writer whom I have known so many
+years, unless the following story will explain it. The officer reproved the
+boatswain for perpetual swearing; the boatswain answered that he heard the
+officers swear. "Only in an emergency," said the officer. "That's just it,"
+replied the other; "a boatswain's life is a life of 'mergency." Giordano
+Bruno was all paradox; and my mind was not alive to his paradoxes, just as
+my ears might have become dead to the boatswain's oaths. He was, as has
+been said, a vorticist before Descartes,[66] an optimist before Leibnitz, a
+Copernican before Galileo. It would be easy to collect a hundred strange
+opinions of his. He was born about 1550, and was roasted alive at Rome,
+February 17, 1600, for the maintenance and defence of the holy Church, and
+the rights and liberties of the same. These last words are from the writ of
+our own good James I, under which Leggatt[67] was roasted at Smithfield, in
+March 1612; and if I had a copy of the instrument under which Wightman[68]
+was roasted at Lichfield, a month afterwards, I daresay I should {60} find
+something quite as edifying. I extract an account which I gave of Bruno in
+the _Comp. Alm._ for 1855:
+
+"He was first a Dominican priest, then a Calvinist; and was roasted alive
+at Rome, in 1600, for as many heresies of opinion, religious and
+philosophical, as ever lit one fire. Some defenders of the papal cause have
+at least worded their accusations so to be understood as imputing to him
+villainous actions. But it is positively certain that his death was due to
+opinions alone, and that retractation, even after sentence, would have
+saved him. There exists a remarkable letter, written from Rome on the very
+day of the murder, by Scioppius[69] (the celebrated scholar, a waspish
+convert from Lutheranism, known by his hatred to Protestants and Jesuits)
+to Rittershusius,[70] a well-known Lutheran writer on civil and canon law,
+whose works are in the index of prohibited books. This letter has been
+reprinted by Libri (vol. iv. p. 407). The writer informs his friend (whom
+he wished to convince that even a Lutheran would have burnt Bruno) that all
+Rome would tell him that Bruno died for Lutheranism; but this is because
+the Italians do not know the difference between one heresy and another, in
+which simplicity (says the writer) may God preserve them. That is to say,
+they knew the difference between a live heretic and a roasted one by actual
+inspection, but had no idea of the difference between a Lutheran and a
+Calvinist. The countrymen of Boccaccio would have smiled at the idea which
+the German scholar entertained of them. They said Bruno was burnt for
+Lutheranism, a name under which they classed all Protestants: and they are
+better witnesses than Schopp, or Scioppius. He then proceeds to describe to
+his Protestant friend (to whom he would certainly not have omitted any act
+which both their churches would have condemned) the mass of opinions with
+which Bruno was charged; as that there {61} are innumerable worlds, that
+souls migrate, that Moses was a magician, that the Scriptures are a dream,
+that only the Hebrews descended from Adam and Eve, that the devils would be
+saved, that Christ was a magician and deservedly put to death, etc. In
+fact, says he, Bruno has advanced all that was ever brought forward by all
+heathen philosophers, and by all heretics, ancient and modern. A time for
+retractation was given, both before sentence and after, which should be
+noted, as well for the wretched palliation which it may afford, as for the
+additional proof it gives that opinions, and opinions only, brought him to
+the stake. In this medley of charges the Scriptures are a dream, while
+Adam, Eve, devils, and salvation are truths, and the Saviour a deceiver. We
+have examined no work of Bruno except the _De Monade_, etc., mentioned in
+the text. A strong though strange _theism_ runs through the whole, and
+Moses, Christ, the Fathers, etc., are cited in a manner which excites no
+remark either way. Among the versions of the cause of Bruno's death is
+_atheism_: but this word was very often used to denote rejection of
+revelation, not merely in the common course of dispute, but by such
+writers, for instance, as Brucker[71] and Morhof.[72] Thus Morhof says of
+the _De Monade, etc._, that it exhibits no manifest signs of atheism. What
+he means by the word is clear enough, when he thus speaks of a work which
+acknowledges God in hundreds of places, and rejects opinions as blasphemous
+in several. The work of Bruno in which his astronomical opinions are
+contained is _De Monade, etc._ (Frankfort, 1591, 8vo). He is the most
+thorough-going Copernican possible, and throws out almost every opinion,
+true or false, which has ever been discussed by astronomers, from the
+theory of innumerable inhabited worlds and systems to that {62} of the
+planetary nature of comets. Libri (vol. iv)[73] has reprinted the most
+striking part of his expressions of Copernican opinion."
+
+
+
+THIS LEADS TO THE CHURCH QUESTION.
+
+The Satanic doctrine that a church may employ force in aid of its dogma is
+supposed to be obsolete in England, except as an individual paradox; but
+this is difficult to settle. Opinions are much divided as to what the Roman
+Church would do in England, if she could: any one who doubts that she
+claims the right does not deserve an answer. When the hopes of the
+Tractarian section of the High Church were in bloom, before the most
+conspicuous intellects among them had _transgressed_ their ministry, that
+they might go to their own place, I had the curiosity to see how far it
+could be ascertained whether they held the only doctrine which makes me the
+personal enemy of a sect. I found in one of their tracts the assumption of
+a right to persecute, modified by an asserted conviction that force was not
+efficient. I cannot now say that this tract was one of the celebrated
+ninety; and on looking at the collection I find it so poorly furnished with
+contents, etc., that nothing but searching through three thick volumes
+would decide. In these volumes I find, augmenting as we go on, declarations
+about the character and power of "the Church" which have a suspicious
+appearance. The suspicion is increased by that curious piece of sophistry,
+No. 87, on religious reserve. The queer paradoxes of that tract leave us in
+doubt as to everything but this, that the church(man) is not bound to give
+his whole counsel in all things, and not bound to say what the things are
+in which he does not give it. It is likely enough that some of the "rights
+and liberties" are but scantily described. There is now no fear; but the
+time was when, if not fear, there might be a looking for of fear to come;
+nobody could then be so {63} sure as we now are that the lion was only
+asleep. There was every appearance of a harder fight at hand than was
+really found needful.
+
+Among other exquisite quirks of interpretation in the No. 87 above
+mentioned is the following. God himself employs reserve; he is said to be
+decked with light as with a garment (the old or prayer-book version of
+Psalm civ. 2). To an ordinary apprehension this would be a strong image of
+display, manifestation, revelation; but there is something more. "Does not
+a garment veil in some measure that which it clothes? Is not that very
+light concealment?"
+
+This No. 87, admitted into a series, fixes upon the managers of the series,
+who permitted its introduction, a strong presumption of that underhand
+intent with which they were charged. At the same time it is honorable to
+our liberty that this series could be published: though its promoters were
+greatly shocked when the Essayists and Bishop Colenso[74] took a swing on
+the other side. When No. 90 was under discussion, Dr. Maitland,[75] the
+librarian at Lambeth, asked Archbishop Howley[76] a question about No. 89.
+"I did not so much as know there _was_ a No. 89," was the answer. I am
+almost sure I have seen this in print, and quite sure that Dr. Maitland
+told it to me. It is creditable that there was so much freedom; but No. 90
+was _too bad_, and was stopped.
+
+The Tractarian mania has now (October 1866) settled down into a chronic
+vestment disease, complicated with fits of transubstantiation, which has
+taken the name of {64} _Ritualism_. The common sense of our national
+character will not put up with a continuance of this grotesque folly;
+millinery in all its branches will at last be advertised only over the
+proper shops. I am told that the Ritualists give short and practical
+sermons; if so, they may do good in the end. The English Establishment has
+always contained those who want an excitement; the New Testament, in its
+plain meaning, can do little for them. Since the Revolution, Jacobitism,
+Wesleyanism, Evangelicism, Puseyism,[77] and Ritualism, have come on in
+turn, and have furnished hot water for those who could not wash without it.
+If the Ritualists should succeed in substituting short and practical
+teaching for the high-spiced lectures of the doctrinalists, they will be
+remembered with praise. John the Baptist would perhaps not have brought all
+Jerusalem out into the wilderness by his plain and good sermons: it was the
+camel's hair and the locusts which got him a congregation, and which,
+perhaps, added force to his precepts. When at school I heard a dialogue,
+between an usher and the man who cleaned the shoes, about Mr. ----, a
+minister, a very corporate body with due area of waistcoat. "He is a man of
+great erudition," said the first. "Ah, yes sir," said Joe; "any one can see
+that who looks at that silk waistcoat."]
+
+
+
+OF THOMAS GEPHYRANDER SALICETUS.
+
+[When I said at the outset that I had only taken books from my own store, I
+should have added that I did not make any search for information given as
+_part_ of a work. Had I looked _through_ all my books, I might have made
+some curious additions. For instance, in Schott's _Magia Naturalis_[78]
+{65} (vol. iii. pp. 756-778) is an account of the quadrature of
+Gephyra_u_der, as he is misprinted in Montucla. He was Thomas Gephyrander
+Salicetus; and he published two editions, in 1608 and 1609.[79] I never
+even heard of a copy of either. His work is of the extreme of absurdity: he
+makes a distinction between geometrical and arithmetical fractions, and
+evolves theorems from it. More curious than his quadrature is his name;
+what are we to make of it? If a German, he is probably a German form of
+_Bridgeman_. and Salicetus refers him to _Weiden_. But _Thomas_ was hardly
+a German Christian name of his time; of 526 German philosophers,
+physicians, lawyers, and theologians who were biographed by Melchior
+Adam,[80] only two are of this name. Of these one is Thomas Erastus,[81]
+the physician whose theological writings against the Church as a separate
+power have given the name of Erastians to those who follow his doctrine,
+whether they have heard of him or not. Erastus is little known;
+accordingly, some have supposed that he must be Erastus, the friend of St.
+Paul and Timothy (Acts xix. 22; 2 Tim. iv. 20; Rom. xvi. 23), but what this
+gentleman did to earn the character is not hinted at. Few words would have
+done: Gaius (Rom. xvi. 23) has an immortality which many more noted men
+have missed, given by John Bunyan, out of seven words of St. Paul. I was
+once told that the Erastians got their name from _Blastus_, and I could not
+solve _bl = er_: at last I remembered that Blastus was a _chamberlain_[82]
+as well as Erastus; hence the association which {66} caused the mistake.
+The real heresiarch was a physician who died in 1583; his heresy was
+promulgated in a work, published immediately after his death by his widow,
+_De Excommunicatione Ecclesiastica_. He denied the power of excommunication
+on the principle above stated; and was answered by Besa.[83] The work was
+translated by Dr. R. Lee[84] (Edinb. 1844, 8vo). The other is Thomas
+Grynaeus,[85] a theologian, nephew of Simon, who first printed Euclid in
+Greek; of him Adam says that of works he published none, of learned sons
+four. If Gephyrander were a Frenchman, his name is not so easily guessed
+at; but he must have been of La Saussaye. The account given by Schott is
+taken from a certain Father Philip Colbinus, who wrote against him.
+
+In some manuscripts lately given to the Royal Society, David Gregory,[86]
+who seems to have seen Gephyrander's work, calls him Salicetus
+_Westphalus_, which is probably on the title-page. But the only Weiden I
+can find is in Bavaria. Murhard has both editions in his Catalogue, but had
+plainly never seen the books: he gives the author as Thomas Gep. Hyandrus,
+Salicettus Westphalus. Murhard is a very old referee of mine; but who the
+_non nominandus_ was to see Montucla's _Gephyrander_ in Murhard's _Gep.
+Hyandrus_, both writers being usually accurate?]
+
+
+
+NAPIER ON REVELATIONS.
+
+    A plain discoverie of the whole Revelation of St. John ... whereunto
+    are annexed certain oracles of Sibylla.... Set Foorth by John Napeir L.
+    of Marchiston. London, 1611, 4to.[87]
+
+{67}
+
+The first edition was Edinburgh, 1593,[88] 4to. Napier[89] always believed
+that his great mission was to upset the Pope, and that logarithms, and such
+things, were merely episodes and relaxations. It is a pity that so many
+books have been written about this matter, while Napier, as good as any, is
+forgotten and unread. He is one of the first who gave us the six thousand
+years. "There is a sentence of the house of Elias reserved in all ages,
+bearing these words: The world shall stand six thousand years, and then it
+shall be consumed by fire: two thousand yeares voide or without lawe, two
+thousand yeares under the law, and two thousand yeares shall be the daies
+of the Messias...."
+
+I give Napier's parting salute: it is a killing dilemma:
+
+"In summar conclusion, if thou o _Rome_ aledges thyselfe reformed, and to
+beleeue true Christianisme, then beleeue Saint _John_ the Disciple, whome
+Christ loued, publikely here in this Reuelation proclaiming thy wracke, but
+if thou remain Ethnick in thy priuate thoghts, beleeuing[90] the old
+Oracles of the _Sibyls_ reuerently keeped somtime in thy _Capitol_: then
+doth here this _Sibyll_ proclame also thy wracke. Repent therefore alwayes,
+in this thy latter breath, as thou louest thine Eternall salvation.
+_Amen_."
+
+--Strange that Napier should not have seen that this appeal could not
+succeed, unless the prophecies of the Apocalypse were no true prophecies at
+all.
+
+{68}
+
+
+
+OF GILBERT'S DE MAGNETE.
+
+    De Magnete magneticisque corporibus, et de magno magnete tellure. By
+    William Gilbert. London, 1600, folio.--There is a second edition; and a
+    third, according to Watt.[91]
+
+Of the great work on the magnet there is no need to speak, though it was a
+paradox in its day. The posthumous work of Gilbert, "De Mundo nostro
+sublunari philosophia nova" (Amsterdam, 1651, 4to)[92] is, as the title
+indicates, confined to the physics of the globe and its atmosphere. It has
+never excited attention: I should hope it would be examined with our
+present lights.
+
+
+
+OF GIOVANNI BATISTA PORTA.
+
+    Elementorum Curvilineorium Libri tres. By John Baptista Porta. Rome,
+    1610, 4to.[93]
+
+This is a ridiculous attempt, which defies description, except that it is
+all about lunules. Porta was a voluminous writer. His printer announces
+fourteen works printed, and four to come, besides thirteen plays printed,
+and eleven waiting. His name is, and will be, current in treatises on
+physics for more reasons than one.
+
+{69}
+
+
+
+CATALDI ON THE QUADRATURE.
+
+    Trattato della quadratura del cerchio. Di Pietro Antonio Cataldi.
+    Bologna, 1612, folio.[94]
+
+Rheticus,[95] Vieta, and Cataldi are the three untiring computers of
+Germany, France, and Italy; Napier in Scotland, and Briggs[96] in England,
+come just after them. This work claims a place as beginning with the
+quadrature of Pellegrino Borello[97] of Reggio, who will have the circle to
+be exactly 3 diameters and 69/484 of a diameter. Cataldi, taking Van
+Ceulen's approximation, works hard at the finding of integers which nearly
+represent the ratio. He had not then the _continued fraction_, a mode of
+representation which he gave the next year in his work on the square root.
+He has but twenty of Van Ceulen's thirty places, which he takes from
+Clavius[98]: and any one might be puzzled to know whence the Italians got
+the result; Van Ceulen, in 1612, not having been translated from Dutch. But
+Clavius names his comrade Gruenberger, and attributes the approximation to
+them {70} jointly; "Lud. a Collen et Chr. Gruenbergerus[99] invenerunt,"
+which he had no right to do, unless, to his private knowledge, Gruenberger
+had verified Van Ceulen. And Gruenberger only handed over twenty of the
+places. But here is one instance, out of many, of the polyglot character of
+the Jesuit body, and its advantages in literature.
+
+
+
+OF LANSBERGIUS.
+
+    Philippi Lausbergii Cyclometriae Novae Libri Duo. Middleburg, 1616,
+    4to.[100]
+
+This is one of the legitimate quadratures, on which I shall here only
+remark that by candlelight it is quadrature under difficulties, for all the
+diagrams are in red ink.
+
+
+
+A TEXT LEADING TO REMARKS ON PRESTER JOHN.
+
+    Recherches Curieuses des Mesures du Monde. By S. C. de V. Paris, 1626,
+    8vo (pp. 48).[101]
+
+It is written by some Count for his son; and if all the French nobility
+would have given their sons the same kind of instruction about rank, the
+old French aristocracy would have been as prosperous at this moment as the
+English peerage and squireage. I sent the tract to Capt. Speke,[102]
+shortly after his arrival in England, thinking he might like {71} to see
+the old names of the Ethiopian provinces. But I first made a copy of all
+that relates to Prester John,[103] himself a paradox. The tract contains,
+_inter alia_, an account of the four empires; of the great Turk, the great
+Tartar, the great Sophy, and the great Prester John. This word _great_
+(_grand_), which was long used in the phrase "the great Turk," is a generic
+adjunct to an emperor. Of the Tartars it is said that "c'est vne nation
+prophane et barbaresque, sale et vilaine, qui mangent la chair demie crue,
+qui boiuent du laict de jument, et qui n'vsent de nappes et seruiettes que
+pour essuyer leurs bouches et leurs mains."[104] Many persons have heard of
+Prester John, and have a very indistinct idea of him. I give all that is
+said about him, since the recent discussions about the Nile may give an
+interest to the old notions of geography.
+
+"Le grand Prestre Jean qui est le quatriesme en rang, est Empereur
+d'Ethiopie, et des Abyssins, et se vante d'estre issu de la race de Dauid,
+comme estant descendu de la Royne de Saba, Royne d'Ethiopie, laquelle
+estant venue en Hierusalem pour voir la sagesse de Salomon, enuiron l'an du
+monde 2952, s'en retourna grosse d'vn fils qu'ils nomment Moylech, duquel
+ils disent estre descendus en ligne directe. Et ainsi il se glorifie
+d'estre le plus ancien Monarque de la terre, disant que son Empire a dure
+plus de trois mil ans, ce que nul autre Empire ne peut dire. Aussi met-il
+en ses tiltres ce qui s'ensuit: Nous, N. Souuerain en mes Royaumes,
+vniquement ayme de Dieu, colomne de la foy, sorty de la race de Inda, etc.
+Les limites de cet Empire touchent a la mer Rouge, et aux montagnes d'Azuma
+vers {72} l'Orient, et du coste de l'Occident, il est borne du fleuue du
+Nil, qui le separe de la Nubie, vers le Septentrion il a l'AEgypte, et au
+Midy les Royaumes de Congo, et de Mozambique, sa longueur contenant
+quarante degre, qui font mille vingt cinq lieues, et ce depuis Congo ou
+Mozambique qui sont au Midy, iusqu'en AEgypte qui est au Septentrion, et sa
+largeur contenant depuis le Nil qui est a l'Occident, iusqu'aux montagnes
+d'Azuma, qui sont a l'Orient, sept cens vingt cinq lieues, qui font vingt
+neuf degrez. Cet empire a sous soy trente grandes Prouinces, scavoir,
+Medra, Gaga, Alchy, Cedalon, Mantro, Finazam, Barnaquez, Ambiam, Fungy,
+Angote, Cigremaon, Gorga, Cafatez, Zastanla, Zeth, Barly, Belangana, Tygra,
+Gorgany, Barganaza, d'Ancut, Dargaly, Ambiacatina, Caracogly, Amara, Maon
+(_sic_), Guegiera, Bally, Dobora et Macheda. Toutes ces Prouinces cy dessus
+sont situees iustement sous la ligne equinoxiale, entres les Tropiques de
+Capricorne, et de Cancer. Mais elles s'approchent de nostre Tropique, de
+deux cens cinquante lieues plus qu'elles ne font de l'autre Tropique. Ce
+mot de Prestre Jean signifie grand Seigneur, et n'est pas Prestre comme
+plusieurs pense, il a este tousiours Chrestien, mais souuent Schismatique:
+maintenant il est Catholique, et reconnaist le Pape pour Souuerain Pontife.
+I'ay veu quelqu'vn des ses Euesques, estant en Hierusalem, auec lequel i'ay
+confere souuent par le moyen de nostre trucheman: il estoit d'vn port graue
+et serieux, succiur (_sic_) en son parler, mais subtil a merueilles en tout
+ce qu'il disoit. Il prenoit grand plaisir au recit que je luy faisais de
+nos belles ceremonies, et de la grauite de nos Prelats en leurs habits
+Pontificaux, et autres choses que je laisse pour dire, que l'Ethiopien est
+ioyoux et gaillard, ne ressemblant en rien a la salete du Tartare, ny a
+l'affreux regard du miserable Arabe, mais ils sont fins et cauteleux, et ne
+se fient en personne, soupconneux a merueilles, et fort devotieux, ils ne
+sont du tout noirs comme l'on croit, i'entens parler de ceux qui ne sont
+pas sous la ligne Equinoxiale, ny trop proches {73} d'icelle, car ceux qui
+sont dessous sont les Mores que nous voyons."[105]
+
+It will be observed that the author speaks of his conversation with an
+Ethiopian bishop, about that bishop's sovereign. Something must have passed
+between the two which satisfied the writer that the bishop acknowledged his
+own sovereign under some title answering to Prester John.
+
+{74}
+
+
+
+CONCERNING A TRACT BY FIENUS.
+
+    De Cometa anni 1618 dissertationes Thomae Fieni[106] et Liberti
+    Fromondi[107] ... Equidem Thomae Fieni epistolica quaestio, An verum sit
+    Coelum moveri et Terram quiescere? London, 1670, 8vo.
+
+This tract of Fienus against the motion of the earth is a reprint of one
+published in 1619.[108] I have given an account of it as a good summary of
+arguments of the time, in the _Companion to the Almanac_ for 1836.
+
+{75}
+
+
+
+ON SNELL'S WORK.
+
+    Willebrordi Snellii. R. F. Cyclometricus. Leyden, 1621, 4to.
+
+This is a celebrated work on the approximative quadrature, which, having
+the suspicious word _cyclometricus_, must be noticed here for
+distinction.[109]
+
+
+
+ON BACON'S NOVUM ORGANUM.
+
+1620. In this year, Francis Bacon[110] published his _Novum Organum_,[111]
+which was long held in England--but not until the last century--to be the
+work which taught Newton and all his successors how to philosophize. That
+Newton never mentions Bacon, nor alludes in any way to his works, passed
+for nothing. Here and there a paradoxer ventured not to find all this
+teaching in Bacon, but he was pronounced blind. In our day it begins to be
+seen that, great as Bacon was, and great as his book really is, he is not
+the philosophical father of modern discovery.
+
+But old prepossession will find reason for anything. A learned friend of
+mine wrote to me that he had discovered proof that Newton owned Bacon for
+his master: the proof was that Newton, in some of his earlier writings,
+used the {76} phrase _experimentum crucis_, which is Bacon's. Newton may
+have read some of Bacon, though no proof of it appears. I have a dim idea
+that I once saw the two words attributed to the alchemists: if so, there is
+another explanation; for Newton was deeply read in the alchemists.
+
+I subjoin a review which I wrote of the splendid edition of Bacon by
+Spedding,[112] Ellis,[113] and Heath.[114] All the opinions therein
+expressed had been formed by me long before: most of the materials were
+collected for another purpose.
+
+
+
+    The Works of Francis Bacon. Edited by James Spedding, R. Leslie Ellis,
+    and Douglas D. Heath. 5 vols.[115]
+
+No knowledge of nature without experiment and observation: so said
+Aristotle, so said Bacon, so acted Copernicus, Tycho Brahe,[116] Gilbert,
+Kepler, Galileo, Harvey, etc., before Bacon wrote.[117] No derived
+knowledge _until_ experiment and observation are concluded: so said Bacon,
+and no one else. We do not mean to say that he laid down his principle in
+these words, or that he carried it to the utmost extreme: we mean that
+Bacon's ruling idea was the {77} collection of enormous masses of facts,
+and then digested processes of arrangement and elimination, so artistically
+contrived, that a man of common intelligence, without any unusual sagacity,
+should be able to announce the truth sought for. Let Bacon speak for
+himself, in his editor's English:
+
+"But the course I propose for the discovery of sciences is such as leaves
+but little to the acuteness and strength of wits, but places all wits and
+understandings nearly on a level. For, as in the drawing of a straight line
+or a perfect circle, much depends on the steadiness and practice of the
+hand, if it be done by aim of hand only, but if with the aid of rule or
+compass little or nothing, so it is exactly with my plan.... For my way of
+discovering sciences goes far to level men's wits, and leaves but little to
+individual excellence; because it performs everything by the surest rules
+and demonstrations."
+
+To show that we do not strain Bacon's meaning, we add what is said by
+Hooke,[118] whom we have already mentioned as his professed disciple, and,
+we believe, his only disciple of the day of Newton. We must, however,
+remind the reader that Hooke was very little of a mathematician, and spoke
+of algebra from his own idea of what others had told him:
+
+"The intellect is not to be suffered to act without its helps, but is
+continually to be assisted by some method or engine, which shall be as a
+guide to regulate its actions, so as that it shall not be able to act
+amiss. Of this engine, no man except the incomparable Verulam hath had any
+thoughts and he indeed hath promoted it to a very good pitch; but there is
+yet somewhat more to be added, which he seemed to want time to complete. By
+this, as by that {78} art of algebra in geometry, 'twill be very easy to
+proceed in any natural inquiry, regularly and certainly.... For as 'tis
+very hard for the most acute wit to find out any difficult problem in
+geometry without the help of algebra ... and altogether as easy for the
+meanest capacity acting by that method to complete and perfect it, so will
+it be in the inquiry after natural knowledge."
+
+Bacon did not live to mature the whole of this plan. Are we really to
+believe that if he had completed the _Instauratio_ we who write this--and
+who feel ourselves growing bigger as we write it--should have been on a
+level with Newton in physical discovery? Bacon asks this belief of us, and
+does not get it. But it may be said, Your business is with what he _did_
+leave, and with its consequences. Be it so. Mr. Ellis says: "That his
+method is impracticable cannot, I think, be denied, if we reflect not only
+that it never has produced any result, but also that the process by which
+scientific truths have been established cannot be so presented as even to
+appear to be in accordance with it." That this is very true is well known
+to all who have studied the history of discovery: those who deny it are
+bound to establish either that some great discovery has been made by
+Bacon's method--we mean by the part peculiar to Bacon--or, better still, to
+show that some new discovery can be made, by actually making it. No general
+talk about _induction_: no reliance upon the mere fact that certain
+experiments or observations have been made; let us see where _Bacon's
+induction_ has been actually used or can be used. Mere induction,
+_enumeratio simplex_, is spoken of by himself with contempt, as utterly
+incompetent. For Bacon knew well that a thousand instances may be
+contradicted by the thousand and first: so that no enumeration of
+instances, however large, is "sure demonstration," so long any are left.
+
+The immortal Harvey, who was _inventing_--we use the word in its old
+sense--the circulation of the blood, while {79} Bacon was in the full flow
+of thought upon his system, may be trusted to say whether, when the system
+appeared, he found any likeness in it to his own processes, or what would
+have been any help to him, if he had waited for the _Novum Organum_. He
+said of Bacon, "He writes philosophy like a Lord Chancellor." This has been
+generally supposed to be only a sneer at the _sutor ultra crepidam_; but we
+cannot help suspecting that there was more intended by it. To us, Bacon is
+eminently the philosopher of _error prevented_, not of _progress
+facilitated_. When we throw off the idea of being _led right_, and betake
+ourselves to that of being _kept from going wrong_, we read his writings
+with a sense of their usefulness, his genius, and their probable effect
+upon purely experimental science, which we can be conscious of upon no
+other supposition. It amuses us to have to add that the part of Aristotle's
+logic of which he saw the value was the book on _refutation of fallacies_.
+Now is this not the notion of things to which the bias of a practised
+lawyer might lead him? In the case which is before the Court, generally
+speaking, truth lurks somewhere about the facts, and the elimination of all
+error will show it in the residuum. The two senses of the word _law_ come
+in so as to look almost like a play upon words. The judge can apply the law
+so soon as the facts are settled: the physical philosopher has to deduce
+the law from the facts. Wait, says the judge, until the facts are
+determined: did the prisoner take the goods with felonious intent? did the
+defendant give what amounts to a warranty? or the like. Wait, says Bacon,
+until all the facts, or all the obtainable facts, are brought in: apply my
+rules of separation to the facts, and the result shall come out as easily
+as by ruler and compasses. We think it possible that Harvey might allude to
+the legal character of Bacon's notions: we can hardly conceive so acute a
+man, after seeing what manner of writer Bacon was, meaning only that he was
+a lawyer and had better stick to his business. We do ourselves believe that
+Bacon's philosophy {80} more resembles the action of mind of a common-law
+judge--not a Chancellor--than that of the physical inquirers who have been
+supposed to follow in his steps. It seems to us that Bacon's argument is,
+there can be nothing of law but what must be either perceptible, or
+mechanically deducible, when all the results of law, as exhibited in
+phenomena, are before us. Now the truth is, that the physical philosopher
+has frequently to conceive law which never was in his previous thought--to
+educe the unknown, not to choose among the known. Physical discovery would
+be very easy work if the inquirer could lay down his this, his that, and
+his t'other, and say, "Now, one of these it must be; let us proceed to try
+which." Often has he done this, and failed; often has the truth turned out
+to be neither this, that, nor t'other. Bacon seems to us to think that the
+philosopher is a judge who has to choose, upon ascertained facts, which of
+known statutes is to rule the decision: he appears to us more like a person
+who is to write the statute-book, with no guide except the cases and
+decisions presented in all their confusion and all their conflict.
+
+Let us take the well-known first aphorism of the _Novum Organum_:
+
+"Man being the servant and interpreter of nature, can do and understand so
+much, and so much only, as he has observed in fact or in thought of the
+course of nature: beyond this he neither knows anything nor can do
+anything."
+
+This aphorism is placed by Sir John Herschel[119] at the head of his
+_Discourse on the Study of Natural Philosophy_: a book containing notions
+of discovery far beyond any of which Bacon ever dreamed; and this because
+it was written {81} after discovery, instead of before. Sir John Herschel,
+in his version, has avoided the translation of _re vel mente observaverit_,
+and gives us only "by his observation of the order of nature." In making
+this the opening of an excellent sermon, he has imitated the theologians,
+who often employ the whole time of the discourse in stuffing matter into
+the text, instead of drawing matter out of it. By _observation_ he
+(Herschel) means the whole course of discovery, observation, hypothesis,
+deduction, comparison, etc. The type of the Baconian philosopher as it
+stood in his mind, had been derived from a noble example, his own father,
+William Herschel,[120] an inquirer whose processes would have been held by
+Bacon to have been vague, insufficient, compounded of chance work and
+sagacity, and too meagre of facts to deserve the name of induction. In
+another work, his treatise on Astronomy,[121] Sir John Herschel, after
+noting that a popular account can only place the reader on the threshold,
+proceeds to speak as follows of all the higher departments of science. The
+italics are his own:
+
+"Admission to its sanctuary, and to the privileges and feelings of a
+votary, is only to be gained by one means--_sound and sufficient knowledge
+of mathematics, the great instrument of all exact inquiry, without which no
+man can ever make such advances in this or any other of the higher
+departments of science as can entitle him to form an independent opinion on
+any subject of discussion within their range_."
+
+How is this? Man can know no more than he gets from observation, and yet
+mathematics is the great instrument of all exact inquiry. Are the results
+of mathematical deduction results of observation? We think it likely that
+{82} Sir John Herschel would reply that Bacon, in coupling together
+_observare re_ and _observare mente_, has done what some wags said Newton
+afterwards did in his study-door--cut a large hole of exit for the large
+cat, and a little hole for the little cat.[122] But Bacon did no such
+thing: he never included any deduction under observation. To mathematics he
+had a dislike. He averred that logic and mathematics should be the
+handmaids, not the mistresses, of philosophy. He meant that they should
+play a subordinate and subsequent part in the dressing of the vast mass of
+facts by which discovery was to be rendered equally accessible to Newton
+and to us. Bacon himself was very ignorant of all that had been done by
+mathematics; and, strange to say, he especially objected to astronomy being
+handed over to the mathematicians. Leverrier and Adams, calculating an
+unknown planet into visible existence by enormous heaps of algebra, furnish
+the last comment of note on this specimen of the goodness of Bacon's views.
+The following account of his knowledge of what had been done in his own day
+or before it, is Mr. Spedding's collection of casual remarks in Mr. Ellis's
+several prefaces:
+
+"Though he paid great attention to astronomy, discussed carefully the
+methods in which it ought to be studied, constructed for the satisfaction
+of his own mind an elaborate theory of the heavens, and listened eagerly
+for the news from the stars brought by Galileo's telescope, he appears to
+have been utterly ignorant of the discoveries which had just been made by
+Kepler's calculations. Though he complained in 1623 of the want of
+compendious methods for facilitating arithmetical computations, especially
+with regard to the doctrine of Series, and fully recognized the importance
+of them as an aid to physical inquiries--he does not say a word about
+Napier's Logarithms, which had been published only nine years before and
+reprinted more than once in the {83} interval. He complained that no
+considerable advance had made in geometry beyond Euclid, without taking any
+notice of what had been done by Archimedes and Apollonius. He saw the
+importance of determining accurately the specific gravity of different
+substances, and himself attempted to form a table of them by a rude process
+of his own, without knowing of the more scientific though still imperfect
+methods previously employed by Archimedes, Ghetaldus,[123] and Porta. He
+speaks of the [Greek: heureka] of Archimedes in a manner which implies that
+he did not clearly apprehend either the nature of the problem to be solved
+or the principles upon which the solution depended. In reviewing the
+progress of mechanics, he makes no mention of Archimedes himself, or of
+Stevinus,[124] Galileo, Guldinus,[125] or Ghetaldus. He makes no allusion
+to the theory of equilibrium. He observes that a ball of one pound weight
+will fall nearly as fast through the air as a ball of two, without alluding
+to the theory of the acceleration of falling bodies, which had been made
+known by Galileo more than thirty years before. He proposes an inquiry with
+regard to the lever--namely, whether in a balance with arms of different
+length but equal weight the distance from the fulcrum has any effect upon
+the inclination,--though the theory of the lever was as well understood in
+his own time as it is now. In making an experiment {84} of his own to
+ascertain the cause of the motion of a windmill, he overlooks an obvious
+circumstance which makes the experiment inconclusive, and an equally
+obvious variation of the same experiment which would have shown him that
+his theory was false. He speaks of the poles of the earth as fixed, in a
+manner which seems to imply that he was not acquainted with the precession
+of the equinoxes; and in another place, of the north pole being above and
+the south pole below, as a reason why in our hemisphere the north winds
+predominate over the south."
+
+Much of this was known before, but such a summary of Bacon's want of
+knowledge of the science of his own time was never yet collected in one
+place. We may add, that Bacon seems to have been as ignorant of
+Wright's[126] memorable addition to the resources of navigation as of
+Napier's addition to the means of calculation. Mathematics was beginning to
+be the great instrument of exact inquiry: Bacon threw the science aside,
+from ignorance, just at the time when his enormous sagacity, applied to
+knowledge, would have made him see the part it was to play. If Newton had
+taken Bacon for his master, not he, but somebody else, would have been
+Newton.[127]
+
+
+
+ON METEOROLOGICAL OBSERVATORIES.
+
+There is an attempt at induction going on, which has yielded little or no
+fruit, the observations made in the meteorological observatories. This
+attempt is carried on in a manner which would have caused Bacon to dance
+for joy; for he lived in times when Chancellors did dance. {85} Russia,
+says M. Biot,[128] is covered by an army of meteorographs, with generals,
+high officers, subalterns, and privates with fixed and defined duties of
+observation. Other countries have also their systematic observations. And
+what has come of it? Nothing, says M. Biot, and nothing will ever come of
+it; the veteran mathematician and experimental philosopher declares, as
+does Mr. Ellis, that no single branch of science has ever been fruitfully
+explored in this way. There is no _special object_, he says. Any one would
+suppose that M. Biot's opinion, given to the French Government upon the
+proposal to construct meteorological observatories in Algeria (_Comptes
+Rendus_, vol. xli, Dec. 31, 1855), was written to support the mythical
+Bacon, modern physics, against the real Bacon of the _Novum Organum_. There
+is no _special object_. In these words lies the difference between the two
+methods.
+
+
+
+[In the report to the Greenwich Board of Visitors for 1867 Mr. Airy,[129]
+speaking of the increase of meteorological observatories, remarks, "Whether
+the effect of this movement will be that millions of useless observations
+will be added to the millions that already exist, or whether something may
+be expected to result which will lead to a meteorological theory, I cannot
+hazard a conjecture." This _is_ a conjecture, and a very obvious one: if
+Mr. Airy would have given 2-3/4d. for the chance of a meteorological theory
+formed by masses of observations, he would never have said what I have
+quoted.]
+
+
+
+BASIS OF MODERN DISCOVERY.
+
+Modern discoveries have not been made by large collections of facts, with
+subsequent discussion, separation, and {86} resulting deduction of a truth
+thus rendered perceptible. A few facts have suggested an _hypothesis_,
+which means a _supposition_, proper to explain them. The necessary results
+of this supposition are worked out, and then, and not till then, other
+facts are examined to see if these ulterior results are found in nature.
+The trial of the hypothesis is the _special object_: prior to which,
+hypothesis must have been started, not by rule, but by that sagacity of
+which no description can be given, precisely because the very owners of it
+do not act under laws perceptible to themselves.[130] The inventor of
+hypothesis, if pressed to explain his method, must answer as did Zerah
+Colburn,[131] when asked for his mode of instantaneous calculation. When
+the poor boy had been bothered for some time in this manner, he cried out
+in a huff, "God put it into my head, and I can't put it into yours."[132]
+{87} Wrong hypotheses, rightly worked from, have produced more useful
+results than unguided observation. But this is not the Baconian plan.
+Charles the Second, when informed of the state of navigation, founded a
+Baconian observatory at Greenwich, to observe, observe, observe away at the
+moon, until her motions were known sufficiently well to render her useful
+in guiding the seaman. And no doubt Flamsteed's[133] observations, twenty
+or thirty of them at least, were of signal use. But how? A somewhat
+fanciful thinker, one Kepler, had hit upon the approximate orbits of the
+planets by trying one hypothesis after another: he found the _ellipse_,
+which the Platonists, well despised of Bacon, and who would have despised
+him as heartily if they had known him, had investigated and put ready to
+hand nearly 2000 years before.[134] The sun in the focus, the motions of
+the planet more and more rapid as they approach the sun, led Kepler--and
+Bacon would have reproved him for his rashness--to imagine that a force
+residing in the sun might move the planets, a force inversely as the
+distance. Bouillaud,[135] upon a fanciful analogy, rejected the inverse
+distance, {88} and, rejecting the force altogether, declared that if such a
+thing there were, it would be as the inverse _square_ of the distance.
+Newton, ready prepared with the mathematics of the subject, tried the fall
+of the moon towards the earth, away from her tangent, and found that, as
+compared with the fall of a stone, the law of the inverse square did hold
+for the moon. He deduced the ellipse, he proceeded to deduce the effect of
+the disturbance of the sun upon the moon, upon the assumed theory of
+_universal_ gravitation. He found result after result of his theory in
+conformity with observed fact: and, by aid of Flamsteed's observations,
+which amended what mathematicians call his _constants_, he constructed his
+lunar theory. Had it not been for Newton, the whole dynasty of Greenwich
+astronomers, from Flamsteed of happy memory, to Airy whom Heaven
+preserve,[136] might have worked away at nightly observation and daily
+reduction, without any remarkable result: looking forward, as to a
+millennium, to the time when any man of moderate intelligence was to see
+the whole explanation. What are large collections of facts for? To make
+theories _from_, says Bacon: to try ready-made theories _by_, says the
+history of discovery: it's all the same, says the idolater: nonsense, say
+we!
+
+Time and space run short: how odd it is that of the three leading ideas of
+mechanics, time, space, and matter, the first two should always fail a
+reviewer before the third. We might dwell upon many points, especially if
+we attempted a more descriptive account of the valuable edition before us.
+No one need imagine that the editors, by their uncompromising attack upon
+the notion of Bacon's influence common even among mathematicians and
+experimental philosophers, have lowered the glory of the great man whom it
+was, many will think, their business to defend through thick and thin. They
+have given a clearer notion of his {89} excellencies, and a better idea of
+the power of his mind, than ever we saw given before. Such a correction as
+theirs must have come, and soon, for as Hallam says--after noting that the
+_Novum Organum_ was _never published separately in England_, Bacon has
+probably been more read in the last thirty years--now forty--than in the
+two hundred years which preceded. He will now be more read than ever he
+was. The history of the intellectual world is the history of the worship of
+one idol after another. No sooner is it clear that a Hercules has appeared
+among men, than all that imagination can conceive of strength is attributed
+to him, and his labors are recorded in the heavens. The time arrives when,
+as in the case of Aristotle, a new deity is found, and the old one is
+consigned to shame and reproach. A reaction may afterwards take place, and
+this is now happening in the case of the Greek philosopher. The end of the
+process is, that the opposing deities take their places, side by side, in a
+Pantheon dedicated not to gods, but to heroes.
+
+
+
+THE REAL VALUE OF BACON'S WORKS.
+
+Passing over the success of Bacon's own endeavors to improve the details of
+physical science, which was next to nothing, and of his method as a whole,
+which has never been practised, we might say much of the good influence of
+his writings. Sound wisdom, set in sparkling wit, must instruct and amuse
+to the end of time: and, as against error, we repeat that Bacon is soundly
+wise, so far as he goes. There is hardly a form of human error within his
+scope which he did not detect, expose, and attach to a satirical metaphor
+which never ceases to sting. He is largely indebted to a very extensive
+reading; but the thoughts of others fall into his text with such a
+close-fitting compactness that he can make even the words of the Sacred
+Writers pass for his own. A saying of the prophet Daniel, rather a
+hackneyed quotation in our day, _Multi pertransibunt, et augebitur
+scientia_, stands in the title-page of the first edition {90} of Montucla's
+_History of Mathematics_ as a quotation from Bacon--and it is not the only
+place in which this mistake occurs. When the truth of the matter, as to
+Bacon's system, is fully recognized, we have little fear that there will be
+a reaction against the man. First, because Bacon will always live to speak
+for himself, for he will not cease to be read: secondly, because those who
+seek the truth will find it in the best edition of his works, and will be
+most ably led to know what Bacon was, in the very books which first showed
+at large what he _was not_.
+
+
+
+THE CONGREGATION OF THE INDEX, ON COPERNICUS.
+
+In this year (1620) appeared the corrections under which the Congregation
+of the Index--i.e., the Committee of Cardinals which superintended the
+_Index_ of forbidden books--proposed to allow the work of Copernicus to be
+read. I insert these conditions in full, because they are often alluded to,
+and I know of no source of reference accessible to a twentieth part of
+those who take interest in the question.
+
+By a decree of the Congregation of the Index, dated March 5, 1616, the work
+of Copernicus, and another of Didacus Astunica,[137] are suspended _donec
+corrigantur_, as teaching:
+
+"Falsam illam doctrinam Pythagoricam, divinae que Scripturae omnino
+adversantem, de mobilitate Terrae et immobilitate Solis."[138]
+
+But a work of the Carmelite Foscarini[139] is:
+
+{91}
+
+"Omnino prohibendum atque damnandum," because "ostendere conatur praefatam
+doctrinam ... consonam esse veritati et non adversari Sacrae
+Scripturae."[140]
+
+Works which teach the false doctrine of the earth's motion are to be
+corrected; those which declare the doctrine conformable to Scripture are to
+be utterly prohibited.
+
+In a "Monitum ad Nicolai Copernici lectorem, ejusque emendatio, permissio,
+et correctio," dated 1620 without the month or day, permission is given to
+reprint the work of Copernicus with certain alterations; and, by
+implication, to read existing copies after correction in writing. In the
+preamble the author is called _nobilis astrologus_; not a compliment to his
+birth, which was humble, but to his fame. The suspension was because:
+
+"Sacrae Scripturae, ejusque verae et Catholicae interpretationi repugnantia
+(quod in homine Christiano minime tolerandum) non _per hypothesin_
+tractare, sed _ut verissima_ adstruere non dubitat!"[141]
+
+And the corrections relate:
+
+"Locis in quibus non _ex hypothesi_, sed _asserendo_ de situ et motu Terrae
+disputat."[142]
+
+That is, the earth's motion may be an hypothesis for elucidation of the
+heavenly motions, but must not be asserted as a fact.
+
+
+
+(In Pref. circa finem.) "_Copernicus._ Si fortasse erunt [Greek:
+mataiologoi], qui cum omnium Mathematum ignari sint, tamen de illis
+judicium sibi summunt, propter aliquem locum scripturae, male ad suum
+propositum detortum, ausi fuerint meum {92} hoc institutum reprehendere ac
+insectari: illos nihil moror adeo ut etiam illorum judicium tanquam
+temerarium contemnam. Non enim obscurum est Lactantium, celebrem alioqui
+scriptorem, sed Mathematicum parum, admodum pueriliter de forma terrae
+loqui, cum deridet eos, qui terram globi formam habere prodiderunt. Itaque
+non debet mirum videri studiosis, si qui tales nos etiam videbunt.
+Mathemata Mathematicis scribuntur, quibus et hi nostri labores, si me non
+fallit opinio, videbuntur etiam Reipub. ecclesiasticae conducere aliquid....
+_Emend._ Ibi _si fortasse_ dele omnia, usque ad verbum _hi nostri labores_
+et sic accommoda--_Coeterum hi nostri labores_."[143]
+
+All the allusion to Lactantius, who laughed at the notion of the earth
+being round, which was afterwards found true, is to be struck out.
+
+
+
+(Cap. 5. lib. i. p. 3) "_Copernicus._ Si tamen attentius rem consideremus,
+videbitur haec quaestio nondum absoluta, et ideireo minime contemnenda.
+_Emend._ Si tamen attentius rem consideremus, nihil refert an Terram in
+medio Mundi, an extra Medium existere, quoad solvendas coelestium motuum
+apparentias existimemus."[144]
+
+{93}
+
+We must not say the question is not yet settled, but only that it may be
+settled either way, so far as mere explanation of the celestial motions is
+concerned.
+
+
+
+(Cap. 8. lib. i.) "Totum hoc caput potest expungi, quia ex professo tractat
+de veritate motus Terrae, dum solvit veterum rationes probantes ejus
+quietem. Cum tamen problematice videatur loqui; ut studiosis satisfiat,
+seriesque et ordo libri integer maneat; emendetur ut infra."[145]
+
+A chapter which seems to assert the motion should perhaps be expunged; but
+it may perhaps be problematical; and, not to break up the book, must be
+amended as below.
+
+
+
+(p. 6.) "_Copernicus._ Cur ergo hesitamus adhuc, mobilitatem illi formae suae
+a natura congruentem concedere, magisquam quod totus labatur mundus, cujus
+finis ignoratur, scirique nequit, neque fateamur ipsius cotidianae
+revolutionis in coelo apparentiam esse, et in terra veritatem? Et haec
+perinde se habere, ac si diceret Virgilianus AEneas: Provehimur portu ...
+_Emend._ Cur ergo non possum mobilitatem illi formae suae concedere, magisque
+quod totus labatur mundus, cujus finis ignoratur scirique nequit, et quae
+apparent in coelo, perinde se habere ac si ..."[146]
+
+{94}
+
+"Why should we hesitate to allow the earth's motion," must be altered into
+"I cannot concede the earth's motion."
+
+
+
+(p. 7.) "_Copernicus._ Addo etiam, quod satis absurdum videretur,
+continenti sive locanti motum adscribi, et non potius contento et locato,
+quod est terra. _Emend._ Addo etiam difficilius non esse contento et
+locato, quod est Terra, motum adscribere, quam continenti."[147]
+
+We must not say it is absurd to refuse motion to the _contained_ and
+_located_, and to give it to the containing and locating; say that neither
+is more difficult than the other.
+
+
+
+(p. 7.) "_Copernicus._ Vides ergo quod ex his omnibus probabilior sit
+mobilitas Terrae, quam ejus quies, praesertim in cotidiana revolutione,
+tanquam terrae maxime propria. _Emend._ _Vides_ ... delendus est usque ad
+finem capitis."[148]
+
+Strike out the whole of the chapter from this to the end; it says that the
+motion of the earth is the most probable hypothesis.
+
+
+
+(Cap. 9. lib. i. p. 7.) "_Copernicus._ Cum igitur nihil prohibeat
+mobilitatem Terrae, videndum nunc arbitror, an etiam plures illi motus
+conveniant, ut possit una errantium syderum existimari. _Emend._ Cum igitur
+Terram moveri assumpserim, videndum nunc arbitror, an etiam illi plures
+possint convenire motus."[149]
+
+{95}
+
+We must not say that nothing prohibits the motion of the earth, only that
+having _assumed_ it, we may inquire whether our explanations require
+several motions.
+
+
+
+(Cap. 10. lib. i. p. 9.) "_Copernicus._ Non pudet nos fateri ... hoc potius
+in mobilitate terrae verificari. _Emend._ Non pudet nos assumere ... hoc
+consequenter in mobilitate verificari."[150]
+
+(Cap. 10. lib. i. p. 10.) "_Copernicus._ Tanta nimirum est divina haec. Opt.
+Max. fabrica. _Emend._ Dele illa verba postrema."[151]
+
+(Cap. ii. lib. i.[152]) "_Copernicus._ De triplici motu telluris
+demonstratio. _Emend._ De hypothesi triplicis motus Terrae, ejusque
+demonstratione."[153]
+
+(Cap. 10. lib. iv. p. 122.[154]) "_Copernicus._ De magnitudine horum trium
+siderum, Solis, Lunae, et Terrae. _Emend._ Dele verba _horum trium siderum_,
+quia terra non est sidus, ut facit eam Copernicus."[155]
+
+We must not say we are not ashamed to _acknowledge_; _assume_ is the word.
+We must not call this assumption a _Divine work_. A chapter must not be
+headed _demonstration_, but _hypothesis_. The earth must not be called a
+_star_; the word implies motion.
+
+It will be seen that it does not take much to reduce Copernicus to pure
+hypothesis. No personal injury being done to the author--who indeed had
+been 17 years out of {96} reach--the treatment of his book is now an
+excellent joke. It is obvious that the Cardinals of the Index were a little
+ashamed of their position, and made a mere excuse of a few corrections.
+Their mode of dealing with chap. 8, this _problematice videtur loqui, ut
+studiosis satisfiat_,[156] is an excuse to avoid corrections. But they
+struck out the stinging allusion to Lactantius[157] in the preface, little
+thinking, honest men, for they really believed what they said--that the
+light of Lactantius would grow dark before the brightness of their own.
+
+
+
+THE CONVOCATION AT OXFORD EQUALLY AT FAULT.
+
+1622. I make no reference to the case of Galileo, except this. I have
+pointed out (_Penny Cycl. Suppl._ "Galileo"; _Engl. Cycl._ "Motion of the
+Earth") that it is clear the absurdity was the act of the _Italian_
+Inquisition--for the private and personal pleasure of the Pope, who _knew_
+that the course he took would not commit him as _Pope_--and not of the body
+which calls itself the _Church_. Let the dirty proceeding have its right
+name. The Jesuit Riccioli,[158] the stoutest and most learned
+Anti-Copernican in Europe, and the Puritan Wilkins, a strong Copernican and
+Pope-hater, are equally positive that the Roman _Church_ never pronounced
+any decision: and this in the time immediately following the ridiculous
+proceeding of the Inquisition. In like manner a decision of the Convocation
+of Oxford is not a law of the _English_ Church; which is fortunate, for
+that Convocation, in 1622, came to a decision quite as absurd, and a great
+deal {97} more wicked than the declaration against the motion of the earth.
+The second was a foolish mistake; the first was a disgusting surrender of
+right feeling. The story is told without disapprobation by Anthony Wood,
+who never exaggerated anything against the university of which he is
+writing eulogistic history.
+
+In 1622, one William Knight[159] put forward in a sermon preached before
+the University certain theses which, looking at the state of the times, may
+have been improper and possibly of seditious intent. One of them was that
+the bishop might excommunicate the civil magistrate: this proposition the
+clerical body could not approve, and designated it by the term
+_erronea_,[160] the mildest going. But Knight also declared as follows:
+
+"Subditis mere privatis, si Tyrannus tanquam latro aut stuprator in ipsos
+faciat impetum, et ipsi nec potestatem ordinariam implorare, nec alia
+ratione effugere periculum possint, in presenti periculo se et suos contra
+tyrannum, sicut contra privatum grassatorem, defendere licet."[161]
+
+That is, a man may defend his purse or a woman her honor, against the
+personal attack of a king, as against that of a private person, if no other
+means of safety can be found. The Convocation sent Knight to prison,
+declared the proposition _"falsa_, periculosa, et _impia_," and enacted
+that all applicants for degrees should subscribe this censure, and make
+oath that they would neither hold, teach, nor defend Knight's opinions.
+
+The thesis, in the form given, was unnecessary and improper. Though strong
+opinions of the king's rights were advanced at the time, yet no one
+ventured to say that, {98} ministers and advisers apart, the king might
+_personally_ break the law; and we know that the first and only attempt
+which his successor made brought on the crisis which cost him his throne
+and his head. But the declaration that the proposition was _false_ far
+exceeds in all that is disreputable the decision of the Inquisition against
+the earth's motion. We do not mention this little matter in England. Knight
+was a Puritan, and Neal[162] gives a short account of his sermon. From
+comparison with Wood,[163] I judge that the theses, as given, were not
+Knight's words, but the digest which it was customary to make in criminal
+proceedings against opinion. This heightens the joke, for it appears that
+the qualifiers of the Convocation took pains to present their condemnation
+of Knight in the terms which would most unequivocally make their censure
+condemn themselves. This proceeding took place in the interval between the
+two proceedings against Galileo: it is left undetermined whether we must
+say pot-kettle-pot or kettle-pot-kettle.
+
+
+
+    Liberti Fromondi.... Ant-Aristarchus, sive orbis terrae immobilis.
+    Antwerp, 1631, 8vo.[164]
+
+This book contains the evidence of an ardent opponent of Galileo to the
+fact, that Roman Catholics of the day did not consider the decree of the
+_Index_ or of the _Inquisition_ as a declaration of their _Church_. Fromond
+would have been glad to say as much, and tries to come near it, but
+confesses he must abstain. See _Penny Cyclop. Suppl._ "Galileo," and _Eng.
+Cycl._ "Motion of the Earth." The author of a celebrated article in the
+_Dublin Review_, in defence of the {99} Church of Rome, seeing that
+Drinkwater Bethune[165] makes use of the authority of Fromondus, but for
+another purpose, sneers at him for bringing up a "musty old Professor." If
+he had known Fromondus, and used him he would have helped his own case,
+which is very meagre for want of knowledge.[166]
+
+
+
+    Advis a Monseigneur l'eminentissime Cardinal Duc de Richelieu, sur la
+    Proposition faicte par le Sieur Morin pour l'invention des longitudes.
+    Paris, 1634, 8vo.[167]
+
+This is the Official Report of the Commissioners appointed by the Cardinal,
+of whom Pascal is the one now best known, to consider Morin's plan. See the
+full account in Delambre, _Hist. Astr. Mod._ ii. 236, etc.
+
+
+
+THE METIUS APPROXIMATION.
+
+    Arithmetica et Geometria practica. By Adrian Metius. Leyden, 1640,
+    4to.[168]
+
+This book contains the celebrated approximation _guessed at_ by his father,
+Peter Metius,[169] namely that the diameter is {100} to the circumference
+as 113 to 355. The error is at the rate of about a foot in 2,000 miles.
+Peter Metius, having his attention called to the subject by the false
+quadrature of Duchesne, found that the ratio lay between 333/106 and
+377/120. He then took the liberty of taking the mean of both numerators and
+denominators, giving 355/113. He had no right to presume that this mean was
+better than either of the extremes; nor does it appear positively that he
+did so. He published nothing; but his son Adrian,[170] when Van Ceulen's
+work showed how near his father's result came to the truth, first made it
+known in the work above. (See _Eng. Cyclop._, art. "Quadrature.")
+
+
+
+ON INHABITABLE PLANETS.
+
+    A discourse concerning a new world and another planet, in two books.
+    London, 1640, 8vo.[171]
+
+    Cosmotheoros: or conjectures concerning the planetary worlds and their
+    inhabitants. Written in Latin, by Christianus Huyghens. This
+    translation was first published in 1698. Glasgow, 1757, 8vo. [The
+    original is also of 1698.][172]
+
+The first work is by Bishop Wilkins, being the third edition, [first in
+1638] of the first book, "That the Moon may be a Planet"; and the first
+edition of the second work, {101} "That the Earth may be a Planet." [See
+more under the reprint of 1802.] Whether other planets be inhabited or not,
+that is, crowded with organisations some of them having consciousness, is
+not for me to decide; but I should be much surprised if, on going to one of
+them, I should find it otherwise. The whole dispute tacitly assumes that,
+if the stars and planets be inhabited, it must be by things of which we can
+form some idea. But for aught we know, what number of such bodies there
+are, so many organisms may there be, of which we have no way of thinking
+nor of speaking. This is seldom remembered. In like manner it is usually
+forgotten that the _matter_ of other planets may be of different chemistry
+from ours. There may be no oxygen and hydrogen in Jupiter, which may have
+_gens_ of its own.[173] But this must not be said: it would limit the
+omniscience of the _a priori_ school of physical inquirers, the larger half
+of the whole, and would be very _unphilosophical_. Nine-tenths of my best
+paradoxers come out from among this larger half, because they are just a
+little more than of it at their entrance.
+
+There was a discussion on the subject some years ago, which began with
+
+    The plurality of worlds: an Essay. London, 1853, 8vo. [By Dr. Wm.
+    Whewell, Master of Trinity College, Cambridge]. A dialogue on the
+    plurality of worlds, being a supplement to the Essay on that subject.
+    [First found in the second edition, 1854; removed to the end in
+    subsequent editions, and separate copies issued.][174]
+
+A work of skeptical character, insisting on analogies which prohibit the
+positive conclusion that the planets, stars, etc., are what we should call
+_inhabited_ worlds. It produced {102} several works and a large amount of
+controversy in reviews. The last predecessor of whom I know was
+
+    Plurality of Worlds.... By Alexander Maxwell. Second Edition. London,
+    1820, 8vo.
+
+This work is directed against the plurality by an author who does not admit
+modern astronomy. It was occasioned by Dr. Chalmers's[175] celebrated
+discourses on religion in connection with astronomy. The notes contain many
+citations on the gravity controversy, from authors now very little read:
+and this is its present value. I find no mention of Maxwell, not even in
+Watt.[176] He communicated with mankind without the medium of a publisher;
+and, from Vieta till now, this method has always been favorable to loss of
+books.
+
+A correspondent informs me that Alex. Maxwell, who wrote on the plurality
+of worlds, in 1820, was a law-bookseller and publisher (probably his own
+publisher) in Bell Yard. He had peculiar notions, which he was fond of
+discussing with his customers. He was a bit of a Swedenborgian.
+
+
+
+INHABITED PLANETS IN FICTION.
+
+There is a class of hypothetical creations which do not belong to my
+subject, because they are _acknowledged_ to be fictions, as those of
+Lucian,[177] Rabelais,[178] Swift, Francis {103} Godwin,[179] Voltaire,
+etc. All who have more positive notions as to either the composition or
+organization of other worlds, than the reasonable conclusion that our
+Architect must be quite able to construct millions of other buildings on
+millions of other plans, ought to rank with the writers just mentioned, in
+all but self-knowledge. Of every one of their systems I say, as the Irish
+Bishop said of Gulliver's book,--I don't believe half of it. Huyghens had
+been preceded by Fontenelle,[180] who attracted more attention. Huyghens is
+very fanciful and very positive; but he gives a true account of his method.
+"But since there's no hopes of a Mercury to carry us such a journey, we
+shall e'en be contented with what's in our power: we shall suppose
+ourselves there...." And yet he says, "We have proved that they live in
+societies, have hands and feet...." Kircher[181] had gone to the stars
+before him, but would not find any life in them, either animal or
+vegetable.
+
+The question of the inhabitants of a particular planet is one which has
+truth on one side or the other: either there are some inhabitants, or there
+are none. Fortunately, it is of no consequence which is true. But there are
+many cases where the balance is equally one of truth and falsehood, in
+which the choice is a matter of importance. My work selects, for the most
+part, sins against demonstration: but the world is full of questions of
+fact or opinion, in which a struggling minority will become a majority, or
+else will {104} be gradually annihilated: and each of the cases subdivides
+into results of good, and results of evil. What is to be done?
+
+ "Periculosum est credere et non credere;
+  Hippolitus obiit quia novercae creditum est;
+  Cassandrae quia non creditum ruit Ilium:
+  Ergo exploranda est veritas multum prius
+  Quam stulta prove judicet sententia."[182]
+
+
+
+    Nova Demonstratio immobilitatis terrae petita ex virtute magnetica. By
+    Jacobus Grandamicus. Flexiae (La Fleche), 1645, 4to.[183]
+
+No magnetic body can move about its poles: the earth is a magnetic body,
+therefore, etc. The iron and its magnetism are typical of two natures in
+one person; so it is said, "Si exaltatus fuero a terra, omnia traham ad me
+ipsum."[184]
+
+
+
+A VENETIAN BUDGET OF PARADOXES.
+
+    Le glorie degli incogniti, o vero gli huomini illustri dell' accademia
+    de' signori incogniti di Venetia. Venice, 1647, 4to.
+
+This work is somewhat like a part of my own: it is a budget of Venetian
+nobodies who wished to be somebodies; but paradox is not the only means
+employed. It is of a serio-comic character, gives genuine portraits in
+copperplate, and grave lists of works; but satirical accounts. The
+astrologer Andrew Argoli[185] is there, and his son; both of whom, with
+some of the others, have place in modern works {105} on biography. Argoli's
+discovery that logarithms facilitate easy processes, but increase the labor
+of difficult ones, is worth recording.
+
+
+
+    Controversiae de vera circuli mensura ... inter ... C. S. Longomontanum
+    et Jo. Pellium.[186] Amsterdam, 1647, 4to.
+
+Longomontanus,[187] a Danish astronomer of merit, squared the circle in
+1644: he found out that the diameter 43 gives the square root of 18252 for
+the circumference; which gives 3.14185... for the ratio. Pell answered him,
+and being a kind of circulating medium, managed to engage in the
+controversy names known and unknown, as Roberval, Hobbes, Carcavi, Lord
+Charles Cavendish, Pallieur, Mersenne, Tassius, Baron Wolzogen, Descartes,
+Cavalieri and Golius.[188] Among them, of course, Longomontanus was made
+{106} mincemeat: but he is said to have insisted on the discovery of his
+epitaph.[189]
+
+{107}
+
+
+
+THE CIRCULATING MEDIA OF MATHEMATICS.
+
+The great circulating mediums, who wrote to everybody, heard from
+everybody, and sent extracts to everybody else, have been Father Mersenne,
+John Collins, and the late Professor Schumacher: all "late" no doubt, but
+only the last recent enough to be so styled. If M.C.S. should ever again
+stand for "Member of the Corresponding Society," it should raise an
+acrostic thought of the three. There is an allusion to Mersenne's
+occupation in Hobbes's reply to him. He wanted to give Hobbes, who was very
+ill at Paris, the Roman Eucharist: but Hobbes said, "I have settled all
+that long ago; when did you hear from Gassendi?" We are reminded of
+William's answer to Burnet. John Collins disseminated Newton, among others.
+Schumacher ought to have been called the postmaster-general of astronomy,
+as Collins was called the attorney-general of mathematics.[190]
+
+{108}
+
+
+
+THE SYMPATHETIC POWDER.
+
+    A late discourse ... by Sir Kenelme Digby.... Rendered into English by
+    R. White. London, 1658, 12mo.
+
+On this work see _Notes and Queries_, 2d series, vii. 231, 299, 445, viii.
+190. It contains the celebrated sympathetic powder. I am still in much
+doubt as to the connection of Digby with this tract.[191] Without entering
+on the subject here, I observe that in Birch's _History of the Royal
+Society_,[192] to which both Digby and White belonged, Digby, though he
+brought many things before the Society, never mentioned the powder, which
+is connected only with the names of Evelyn[193] and Sir Gilbert
+Talbot.[194] The sympathetic powder was that which cured by anointing the
+weapon with its salve instead of the wound. I have long been convinced that
+it was efficacious. The directions were to keep the {109} wound clean and
+cool, and to take care of diet, rubbing the salve on the knife or
+sword.[195] If we remember the dreadful notions upon drugs which prevailed,
+both as to quantity and quality, we shall readily see that any way of _not_
+dressing the wound would have been useful. If the physicians had taken the
+hint, had been careful of diet etc., and had poured the little barrels of
+medicine down the throat of a practicable doll, _they_ would have had their
+magical cures as well as the surgeons.[196] Matters are much improved now;
+the quantity of medicine given, even by orthodox physicians, would have
+been called infinitesimal by their professional ancestors. Accordingly, the
+College of Physicians has a right to abandon its motto, which is _Ars
+longa, vita brevis_, meaning _Practice is long, so life is short_.
+
+
+
+HOBBES AS A MATHEMATICIAN.
+
+    Examinatio et emendatio Mathematicae Hodiernae. By Thomas Hobbes. London,
+    1666, 4to.
+
+In six dialogues: the sixth contains a quadrature of the circle.[197] But
+there is another edition of this work, without place or date on the
+title-page, in which the quadrature is omitted. This seems to be connected
+with the publication {110} of another quadrature, without date, but about
+1670, as may be judged from its professing to answer a tract of Wallis,
+printed in 1669.[198] The title is "Quadratura circuli, cubatio sphaerae,
+duplicatio cubi," 4to.[199] Hobbes, who began in 1655, was very wrong in
+his quadrature; but, though not a Gregory St. Vincent,[200] he was not the
+ignoramus in geometry that he is sometimes supposed. His writings,
+erroneous as they are in many things, contain acute remarks on points of
+principle. He is wronged by being coupled with Joseph Scaliger, as the two
+great instances of men of letters who have come into geometry to help the
+mathematicians out of their difficulty. I have never seen Scaliger's
+quadrature,[201] except in the answers of Adrianus Romanus,[202] Vieta and
+Clavius, and in the extracts of Kastner.[203] Scaliger had no right to such
+strong opponents: Erasmus or Bentley might just as well have tried the
+problem, and either would have done much better in any twenty minutes of
+his life.[204]
+
+
+
+AN ESTIMATE OF SCALIGER.
+
+Scaliger inspired some mathematicians with great respect for his
+geometrical knowledge. Vieta, the first man of his time, who answered him,
+had such regard for his opponent {111} as made him conceal Scaliger's name.
+Not that he is very respectful in his manner of proceeding: the following
+dry quiz on his opponent's logic must have been very cutting, being true.
+"In grammaticis, dare navibus Austros, et dare naves Austris, sunt aeque
+significantia. Sed in Geometricis, aliud est adsumpsisse circulum BCD non
+esse majorem triginta sex segmentis BCDF, aliud circulo BCD non esse majora
+triginta sex segmenta BCDF. Illa adsumptiuncula vera est, haec falsa."[205]
+Isaac Casaubon,[206] in one of his letters to De Thou,[207] relates that,
+he and another paying a visit to Vieta, the conversation fell upon
+Scaliger, of whom the host said that he believed Scaliger was the only man
+who perfectly understood mathematical writers, especially the Greek ones:
+and that he thought more of Scaliger when wrong than of many others when
+right; "pluris se Scaligerum vel errantem facere quam multos [Greek:
+katorthountas]."[208] This must have been before Scaliger's quadrature
+(1594). There is an old story of some one saying, "Mallem cum Scaligero
+errare, quam cum Clavio recte sapere."[209] This I cannot help suspecting
+to have been a version of Vieta's speech with Clavius satirically inserted,
+on account of the great hostility which Vieta showed towards Clavius in the
+latter years of his life.
+
+Montucla could not have read with care either Scaliger's quadrature or
+Clavius's refutation. He gives the first a wrong date: he assures the world
+that there is no question about Scaliger's quadrature being wrong, in the
+eyes of geometers at least: and he states that Clavius mortified him {112}
+extremely by showing that it made the circle less than its inscribed
+dodecagon, which is, of course, equivalent to asserting that a straight
+line is not always the shortest distance between two points. Did _Clavius_
+show this? No, it was Scaliger himself who showed it, boasted of it, and
+declared it to be a "noble paradox" that a theorem false in geometry is
+true in arithmetic; a thing, he says with great triumph, not noticed by
+Archimedes himself! He says in so many words that the periphery of the
+dodecagon is greater than that of the circle; and that the more sides there
+are to the inscribed figure, the more does it exceed the circle in which it
+is. And here _are_ the words, on the independent testimonies of Clavius and
+Kastner:
+
+"Ambitus dodecagoni circulo inscribendi plus potest quam circuli ambitus.
+Et quanto deinceps plurium laterum fuerit polygonum circulo inscribendum,
+tanto plus poterit ambitus polygoni quam ambitus circuli."[210]
+
+There is much resemblance between Joseph Scaliger and William
+Hamilton,[211] in a certain impetuousity of character, and inaptitude to
+think of quantity. Scaliger maintained that the arc of a circle is less
+than its chord in arithmetic, though greater in geometry; Hamilton arrived
+at two quantities which are identical, but the greater the one the less the
+other. But, on the whole, I liken Hamilton rather to Julius than to Joseph.
+On this last hero of literature I repeat Thomas Edwards,[212] who says that
+a man is unlearned who, be his other knowledge what it may, does not {113}
+understand the subject he writes about. And now one of many instances in
+which literature gives to literature character in science. Anthony
+Teissier,[213] the learned annotator of De Thou's biographies, says of
+Finaeus, "Il se vanta sans raison avoir trouve la quadrature du cercle; la
+gloire de cette admirable decouverte etait reservee a Joseph Scalinger,
+comme l'a ecrit Scevole de St. Marthe."[214]
+
+
+
+JOHN GRAUNT AS A PARADOXER.
+
+    Natural and Political Observations ... upon the Bills of Mortality. By
+    John Graunt, citizen of London. London, 1662, 4to.[215]
+
+This is a celebrated book, the first great work upon mortality. But the
+author, going _ultra crepidam_, has attributed to the motion of the moon in
+her orbit all the tremors which she gets from a shaky telescope.[216] But
+there is another paradox about this book: the above absurd opinion is
+attributed to that excellent mechanist, Sir William Petty, who passed his
+days among the astronomers. Graunt did not write his own book! Anthony
+Wood[217] hints that Petty "assisted, or put into a way" his old
+benefactor: no doubt the two friends talked the matter over many a time.
+Burnet and Pepys[218] state that Petty wrote the book. It is enough for me
+that {114} Graunt, whose honesty was never impeached, uses the plainest
+incidental professions of authorship throughout; that he was elected into
+the Royal Society because he was the author; that Petty refers to him as
+author in scores of places, and published an edition, as editor, after
+Graunt's death, with Graunt's name of course. The note on Graunt in the
+_Biographia Britannica_ may be consulted; it seems to me decisive. Mr.
+C. B. Hodge, an able actuary, has done the best that can be done on the
+other side in the _Assurance Magazine_, viii. 234. If I may say what is in
+my mind, without imputation of disrespect, I suspect some actuaries have a
+bias: they would rather have Petty the greater for their Coryphaeus than
+Graunt the less.[219]
+
+Pepys is an ordinary gossip: but Burnet's account has an animus which is of
+a worse kind. He talks of "one Graunt, a Papist, under whose name Sir
+William Petty[220] published his observations on the bills of mortality."
+He then gives the cock without a bull story of Graunt being a trustee of
+the New River Company, and shutting up the cocks and carrying off their
+keys, just before the fire of London, by which a supply of water was
+delayed.[221] It was one of the first objections made to Burnet's work,
+that Graunt was _not_ a trustee at the time; and Maitland, the historian of
+London, ascertained from the books of the Company that he was not admitted
+until twenty-three days after the breaking out of the fire. Graunt's first
+admission {115} to the Company took place on the very day on which a
+committee was appointed to inquire into the cause of the fire. So much for
+Burnet. I incline to the view that Graunt's setting London on fire strongly
+corroborates his having written on the bills of mortality: every practical
+man takes stock before he commences a grand operation in business.
+
+
+
+MANKIND A GULLIBLE LOT.
+
+    De Cometis: or a discourse of the natures and effects of Comets, as
+    they are philosophically, historically, and astrologically considered.
+    With a brief (yet full) account of the III late Comets, or blazing
+    stars, visible to all Europe. And what (in a natural way of judicature)
+    they portend. Together with some observations on the nativity of the
+    Grand Seignior. By John Gadbury, [Greek: Philomathematikos]. London,
+    1665, 4to.
+
+Gadbury, though his name descends only in astrology, was a well-informed
+astronomer.[222] D'Israeli[223] sets down Gadbury, Lilly, Wharton, Booker,
+etc., as rank rogues: I think him quite wrong. The easy belief in roguery
+and intentional imposture which prevails in educated society is, to my
+mind, a greater presumption against the honesty of mankind than all the
+roguery and imposture itself. Putting aside mere swindling for the sake of
+gain, and looking at speculation and paradox, I find very little reason to
+suspect wilful deceit.[224] My opinion of mankind is founded upon the {116}
+mournful fact that, so far as I can see, they find within themselves the
+means of believing in a thousand times as much as there is to believe in,
+judging by experience. I do not say anything against Isaac D'Israeli for
+talking his time. We are all in the team, and we all go the road, but we do
+not all draw.
+
+
+
+A FORERUNNER OF A WRITTEN ESPERANTO.
+
+    An essay towards a real character and a philosophical language. By John
+    Wilkins [Dean of Ripon, afterwards Bishop of Chester].[225] London,
+    1668, folio.
+
+This work is celebrated, but little known. Its object gives it a right to a
+place among paradoxes. It proposes a language--if that be the proper
+name--in which _things_ and their relations shall be denoted by signs, not
+_words_: so that any person, whatever may be his mother tongue, may read it
+in his own words. This is an obvious possibility, and, I am afraid, an
+obvious impracticability. One man may construct such a system--Bishop
+Wilkins has done it--but where is the man who will learn it? The second
+tongue makes a language, as the second blow makes a fray. There has been
+very little curiosity about his performance, the work is scarce; and I do
+not know where to refer the reader for any account of its details, except,
+to the partial reprint of Wilkins presently mentioned under 1802, in which
+there is an unsatisfactory abstract. There is nothing in the _Biographia
+Britannica_, except discussion of Anthony Wood's statement that the hint
+was derived from Dalgarno's book, {117} _De Signis_, 1661.[226] Hamilton
+(_Discussions_, Art. 5, "Dalgarno") does not say a word on this point,
+beyond quoting Wood; and Hamilton, though he did now and then write about
+his countrymen with a rough-nibbed pen, knew perfectly well how to protect
+their priorities.
+
+
+
+GREGOIRE DE ST. VINCENT.
+
+    Problema Austriacum. Plus ultra Quadratura Circuli. Auctore P. Gregorio
+    a Sancto Vincentio Soc. Jesu., Antwerp, 1647, folio.--Opus Geometricum
+    posthumum ad Mesolabium. By the same. Gandavi [Ghent], 1668,
+    folio.[227]
+
+The first book has more than 1200 pages, on all kinds of geometry. Gregory
+St. Vincent is the greatest of circle-squarers, and his investigations led
+him into many truths: he found the property of the area of the
+hyperbola[228] which led to Napier's logarithms being called _hyperbolic_.
+Montucla says of him, with sly truth, that no one has ever squared the
+circle with so much genius, or, excepting his principal object, with so
+much success.[229] His reputation, and the many merits of his work, led to
+a sharp controversy on his quadrature, which ended in its complete exposure
+by Huyghens and others. He had a small school of followers, who defended
+him in print.
+
+{118}
+
+
+
+RENE DE SLUSE.
+
+    Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liege], 1668,
+    4to.[230]
+
+The Mesolabum is the solution of the problem of finding two mean
+proportionals, which Euclid's geometry does not attain. Slusius is a true
+geometer, and uses the ellipse, etc.: but he is sometimes ranked with the
+trisecters, for which reason I place him here, with this explanation.
+
+The finding of two mean proportionals is the preliminary to the famous old
+problem of the duplication of the cube, proposed by Apollo (not Apollonius)
+himself. D'Israeli speaks of the "six follies of science,"--the quadrature,
+the duplication, the perpetual motion, the philosopher's stone, magic, and
+astrology. He might as well have added the trisection, to make the mystic
+number seven: but had he done so, he would still have been very lenient;
+only seven follies in all science, from mathematics to chemistry! Science
+might have said to such a judge--as convicts used to say who got seven
+years, expecting it for life, "Thank you, my Lord, and may you sit there
+till they are over,"--may the Curiosities of Literature outlive the Follies
+of Science!
+
+
+
+JAMES GREGORY.
+
+1668. In this year James Gregory, in his _Vera Circuli et Hyperbolae
+Quadratura_,[231] held himself to have proved that {119} the _geometrical_
+quadrature of the circle is impossible. Few mathematicians read this very
+abstruse speculation, and opinion is somewhat divided. The regular
+circle-squarers attempt the _arithmetical_ quadrature, which has long been
+proved to be impossible. Very few attempt the geometrical quadrature. One
+of the last is Malacarne, an Italian, who published his _Solution
+Geometrique_, at Paris, in 1825. His method would make the circumference
+less than three times the diameter.
+
+
+
+BEAULIEU'S QUADRATURE.
+
+    La Geometrie Francoise, ou la Pratique aisee.... La quadracture du
+    cercle. Par le Sieur de Beaulieu, Ingenieur, Geographe du Roi ...
+    Paris, 1676, 8vo. [not Pontault de Beaulieu, the celebrated
+    topographer; he died in 1674].[232]
+
+If this book had been a fair specimen, I might have pointed to it in
+connection with contemporary English works, and made a scornful comparison.
+But it is not a fair specimen. Beaulieu was attached to the Royal
+Household, and throughout the century it may be suspected that the
+household forced a royal road to geometry. Fifty years before, Beaugrand,
+the king's secretary, made a fool of himself, and [so?] contrived to pass
+for a geometer. He had interest enough to get Desargues, the most powerful
+geometer of his time,[233] the teacher and friend of Pascal, prohibited
+from {120} lecturing. See some letters on the History of Perspective, which
+I wrote in the _Athenaeum_, in October and November, 1861. Montucla, who
+does not seem to know the true secret of Beaugrand's greatness, describes
+him as "un certain M. de Beaugrand, mathematicien, fort mal traite par
+Descartes, et a ce qu'il paroit avec justice."[234]
+
+Beaulieu's quadrature amounts to a geometrical construction[235] which
+gives [pi] = [root]10. His depth may be ascertained from the following
+extracts. First on Copernicus:
+
+"Copernic, Allemand, ne s'est pas moins rendu illustre par ses doctes
+ecrits; et nous pourrions dire de luy, qu'il seroit le seul et unique en la
+force de ses Problemes, si sa trop grande presomption ne l'avoit porte a
+avancer en cette Science une proposition aussi absurde, qu'elle est contre
+la Foy et raison, en faisant la circonference d'un Cercle fixe, immobile,
+et le centre mobile, sur lequel principe Geometrique, il a avance en son
+Traitte Astrologique le Soleil fixe, et la Terre mobile."[236]
+
+I digress here to point out that though our quadrators, etc., very often,
+and our historians sometimes, assert that men of the character of
+Copernicus, etc., were treated with contempt and abuse until their day of
+ascendancy came, nothing can be more incorrect. From Tycho Brahe[237] to
+Beaulieu, there is but one expression of admiration for the genius of
+Copernicus. There is an exception, which, I {121} believe, has been quite
+misunderstood. Maurolycus,[238] in his _De Sphaera_, written many years
+before its posthumous publication in 1575, and which it is not certain he
+would have published, speaking of the safety with which various authors may
+be read after his cautions, says, "Toleratur et Nicolaus Copernicus qui
+Solem fixum et Terram _in girum circumverti_ posuit: et scutica potius, aut
+flagello, quam reprehensione dignus est."[239] Maurolycus was a mild and
+somewhat contemptuous satirist, when expressing disapproval: as we should
+now say, he pooh-poohed his opponents; but, unless the above be an
+instance, he was never savage nor impetuous. I am fully satisfied that the
+meaning of the sentence is, that Copernicus, who turned the earth like a
+boy's top, ought rather to have a whip given him wherewith to keep up his
+plaything than a serious refutation. To speak of _tolerating_ a person _as
+being_ more worthy of a flogging than an argument, is almost a
+contradiction.
+
+I will now extract Beaulieu's treatise on algebra, entire.
+
+"L'Algebre est la science curieuse des Scavans et specialement d'un General
+d'Armee ou Capitaine, pour promptement ranger une Armee en bataille, et
+nombre de Mousquetaires et Piquiers qui composent les bataillons d'icelle,
+outre les figures de l'Arithmetique. Cette science a 5 figures
+particulieres en cette sorte. P signifie _plus_ au commerce, et a l'Armee
+_Piquiers_. M signifie _moins_, et _Mousquetaire_ en l'Art des bataillons.
+[It is quite true that P and M were used for _plus_ and _minus_ in a great
+many old works.] R signifie _racine_ en la mesure du Cube, et en l'Armee
+_rang_. Q signifie _quare_ en l'un et l'autre usage. C signifie _cube_ en
+la mesure, et _Cavallerie_ en la composition des bataillons et escadrons.
+Quant a l'operation de cette science, c'est {122} d'additionner un _plus_
+d'avec _plus_, la somme sera _plus_, et _moins_ d'avec _plus_, on soustrait
+le moindre du _plus_, et la reste est la somme requise ou nombre trouve. Je
+dis seulement cecy en passant pour ceux qui n'en scavent rien du
+tout."[240]
+
+This is the algebra of the Royal Household, seventy-three years after the
+death of Vieta. Quaere, is it possible that the fame of Vieta, who himself
+held very high stations in the household all his life, could have given
+people the notion that when such an officer chose to declare himself an
+algebraist, he must be one indeed? This would explain Beaugrand, Beaulieu,
+and all the _beaux_. Beaugrand--not only secretary to the king, but
+"mathematician" to the Duke of Orleans--I wonder what his "fool" could have
+been like, if indeed he kept the offices separate,--would have been in my
+list if I had possessed his _Geostatique_, published about 1638.[241] He
+makes bodies diminish in weight as they approach the earth, because the
+effect of a weight on a lever is less as it approaches the fulcrum.
+
+{123}
+
+
+
+SIR MATTHEW HALE.
+
+    Remarks upon two late ingenious discourses.... By Dr. Henry More.[242]
+    London, 1676, 8vo.
+
+In 1673 and 1675, Matthew Hale,[243] then Chief Justice, published two
+tracts, an "Essay touching Gravitation," and "Difficiles Nugae" on the
+Torricellian experiment. Here are the answers by the learned and voluminous
+Henry More. The whole would be useful to any one engaged in research about
+ante-Newtonian notions of gravitation.
+
+
+
+    Observations touching the principles of natural motions; and especially
+    touching rarefaction and condensation.... By the author of _Difficiles
+    Nugae_. London, 1677, 8vo.
+
+This is another tract of Chief Justice Hale, published the year after his
+death. The reader will remember that _motion_, in old philosophy, meant any
+change from state to state: what we now describe as _motion_ was _local
+motion_. This is a very philosophical book, about _flux_ and _materia
+prima_, _virtus activa_ and _essentialis_, and other fundamentals. I think
+Stephen Hales, the author of the "Vegetable Statics," has the writings of
+the Chief Justice sometimes attributed to him, which is very puny justice
+indeed.[244] Matthew Hale died in 1676, and from his devotion to science it
+probably arose that his famous _Pleas of the Crown_[245] and other law
+works did not appear until after his death. One of his {124} contemporaries
+was the astronomer Thomas Street, whose _Caroline Tables_[246] were several
+times printed: another contemporary was his brother judge, Sir Thomas
+Street.[247] But of the astronomer absolutely nothing is known: it is very
+unlikely that he and the judge were the same person, but there is not a bit
+of positive evidence either for or against, so far as can be ascertained.
+Halley[248]--no less a person--published two editions of the _Caroline
+Tables_, no doubt after the death of the author: strange indeed that
+neither Halley nor any one else should leave evidence that Street was born
+or died.
+
+Matthew Hale gave rise to an instance of the lengths a lawyer will go when
+before a jury who cannot detect him. Sir Samuel Shepherd,[249] the Attorney
+General, in opening Hone's[250] first trial, calls him "one who was the
+most learned man that ever adorned the Bench, the most even man that ever
+blessed domestic life, the _most eminent man that ever advanced the
+progress of science_, and one of the [very moderate] best and most purely
+religious men that ever lived."
+
+{125}
+
+
+
+ON THE DISCOVERY OF ANTIMONY.
+
+    Basil Valentine his triumphant Chariot of Antimony, with annotations of
+    Theodore Kirkringius, M.D. With the true book of the learned Synesius,
+    a Greek abbot, taken out of the Emperour's library, concerning the
+    Philosopher's Stone. London, 1678, 8vo.[251]
+
+There are said to be three Hamburg editions of the collected works of
+Valentine, who discovered the common antimony, and is said to have given
+the name _antimoine_, in a curious way. Finding that the pigs of his
+convent throve upon it, he gave it to his brethren, who died of it.[252]
+The impulse given to chemistry by R. Boyle[253] seems to have brought out a
+vast number of translations, as in the following tract:
+
+
+
+ON ALCHEMY.
+
+    _Collectanea Chymica_: A collection of ten several treatises in
+    chymistry, concerning the liquor Alkehest, the Mercury of Philosophers,
+    and other curiosities worthy the perusal. Written by Eir.
+    Philaletha,[254] Anonymus, J. B. Van-Helmont,[255] Dr. Fr. {126}
+    Antonie,[256] Bernhard Earl of Trevisan,[257] Sir Geo. Ripley,[258]
+    Rog. Bacon,[259] Geo. Starkie,[260] Sir Hugh Platt,[261] and the Tomb
+    of Semiramis. See more in the contents. London, 1684, 8vo.
+
+In the advertisements at the ends of these tracts there are upwards of a
+hundred English tracts, nearly all of the period, and most of them
+translations. Alchemy looks up since the chemists have found perfectly
+different substances composed of the same elements and proportions. It is
+true the chemists cannot yet _transmute_; but they may in time: they poke
+about most assiduously. It seems, then, that the conviction that alchemy
+_must_ be impossible was a delusion: but we do not mention it.
+
+{127}
+
+The astrologers and the alchemists caught it in company in the following,
+of which I have an unreferenced note.
+
+"Mendacem et futilem hominem nominare qui volunt, calendariographum dicunt;
+at qui sceleratum simul ac impostorem, chimicum.[262]
+
+ "Crede ratem ventis corpus ne crede chimistis;
+      Est quaevis chimica tutior aura fide."[263]
+
+Among the smaller paradoxes of the day is that of the _Times_ newspaper,
+which always spells it _chymistry_: but so, I believe, do Johnson, Walker,
+and others. The Arabic work is very likely formed from the Greek: but it
+may be connected either with [Greek: chemeia] or with [Greek: chumeia].
+
+
+
+    Lettre d'un gentil-homme de province a une dame de qualite, sur le
+    sujet de la Comete. Paris, 1681, 4to.
+
+An opponent of astrology, whom I strongly suspect to have been one of the
+members of the Academy of Sciences under the name of a country
+gentleman,[264] writes very good sense on the tremors excited by comets.
+
+
+
+    The Petitioning-Comet: or a brief Chronology of all the famous Comets
+    and their events, that have happened from the birth of Christ to this
+    very day. Together with a modest enquiry into this present comet,
+    London, 1681, 4to.
+
+A satirical tract against the cometic prophecy:
+
+"This present comet (it's true) is of a menacing aspect, but if the _new
+parliament_ (for whose convention so many good men pray) continue long to
+sit, I fear not but the star will lose its virulence and malignancy, or at
+least its portent be averted from this our nation; which being the humble
+request to God of all good men, makes me thus entitle it, a
+Petitioning-Comet."
+
+{128}
+
+The following anecdote is new to me:
+
+"Queen Elizabeth (1558) being then at Richmond, and being disswaded from
+looking on a comet which did then appear, made answer, _jacta est alea_,
+the dice are thrown; thereby intimating that the pre-order'd providence of
+God was above the influence of any star or comet."
+
+The argument was worth nothing: for the comet might have been _on the dice_
+with the event; the astrologers said no more, at least the more rational
+ones, who were about half of the whole.
+
+
+
+    An astrological and theological discourse upon this present great
+    conjunction (the like whereof hath not (likely) been in some ages)
+    ushered in by a great comet. London, 1682, 4to. By C. N.[265]
+
+The author foretells the approaching "sabbatical jubilee," but will not fix
+the date: he recounts the failures of his predecessors.
+
+
+
+    A judgment of the comet which became first generally visible to us in
+    Dublin, December 13, about 15 minutes before 5 in the evening, A.D.
+    1680. By a person of quality. Dublin, 1682, 4to.
+
+The author argues against cometic astrology with great ability.
+
+
+
+    A prophecy on the conjunction of Saturn and Jupiter in this present
+    year 1682. With some prophetical predictions of what is likely to ensue
+    therefrom in the year 1684. By John Case, Student in physic and
+    astrology.[266] London, 1682, 4to.
+
+{129}
+
+According to this writer, great conjunctions of Jupiter and Saturn occur
+"in the fiery trigon," about once in 800 years. Of these there are to be
+seven: six happened in the several times of Enoch, Noah, Moses, Solomon,
+Christ, Charlemagne. The seventh, which is to happen at "the lamb's
+marriage with the bride," seems to be that of 1682; but this is only
+vaguely hinted.
+
+
+
+    De Quadrature van de Circkel. By Jacob Marcelis. Amsterdam, 1698, 4to.
+
+    Ampliatie en demonstratie wegens de Quadrature ... By Jacob Marcelis.
+    Amsterdam, 1699, 4to.
+
+    Eenvoudig vertoog briev-wys geschrevem am J. Marcelis ... Amsterdam,
+    1702, 4to.
+
+    De sleutel en openinge van de quadrature ... Amsterdam, 1704, 4to.
+
+Who shall contradict Jacob Marcelis?[267] He says the circumference
+contains the diameter exactly times
+
+    1008449087377541679894282184894
+  3 --------------------------------
+    6997183637540819440035239271702
+
+But he does not come very near, as the young arithmetician will find.
+
+
+
+MATHEMATICAL THEOLOGY.
+
+    Theologiae Christianae Principia Mathematica. Auctore Johanne Craig.[268]
+    London, 1699, 4to.
+
+This is a celebrated speculation, and has been reprinted abroad, and
+seriously answered. Craig is known in the early history of fluxions, and
+was a good mathematician. {130} He professed to calculate, on the
+hypothesis that the suspicions against historical evidence increase with
+the square of the time, how long it will take the evidence of Christianity
+to die out. He finds, by formulae, that had it been oral only, it would have
+gone out A.D. 800; but, by aid of the written evidence, it will last till
+A.D. 3150. At this period he places the second coming, which is deferred
+until the extinction of evidence, on the authority of the question "When
+the Son of Man cometh, shall he find faith on the earth?" It is a pity that
+Craig's theory was not adopted: it would have spared a hundred treatises on
+the end of the world, founded on no better knowledge than his, and many of
+them falsified by the event. The most recent (October, 1863) is a tract in
+proof of Louis Napoleon being Antichrist, the Beast, the eighth Head, etc.;
+and the present dispensation is to close soon after 1864.
+
+In order rightly to judge Craig, who added speculations on the variations
+of pleasure and pain treated as functions of time, it is necessary to
+remember that in Newton's day the idea of force, as a quantity to be
+measured, and as following a law of variation, was very new: so likewise
+was that of probability, or belief, as an object of measurement.[269] The
+success of the _Principia_ of Newton put it into many heads to speculate
+about applying notions of quantity to other things not then brought under
+measurement. Craig imitated Newton's title, and evidently thought he was
+making a step in advance: but it is not every one who can plough with
+Samson's heifer.
+
+It is likely enough that Craig took a hint, directly or indirectly, from
+Mohammedan writers, who make a reply to the argument that the Koran has not
+the evidence derived {131} from miracles. They say that, as evidence of
+Christian miracles is daily becoming weaker, a time must at last arrive
+when it will fail of affording assurance that they were miracles at all:
+whence would arise the necessity of another prophet and other miracles.
+Lee,[270] the Cambridge Orientalist, from whom the above words are taken,
+almost certainly never heard of Craig or his theory.
+
+
+
+THE ARISTOCRAT AS A SCIENTIST.
+
+    Copernicans of all sorts convicted ... to which is added a Treatise of
+    the Magnet. By the Hon. Edw. Howard, of Berks. London, 1705, 8vo.
+
+Not all the blood of all the Howards will gain respect for a writer who
+maintains that eclipses admit no possible explanation under the Copernican
+hypothesis, and who asks how a man can "go 200 yards to any place if the
+moving superficies of the earth does carry it from him?" Horace Walpole, at
+the beginning of his _Royal and Noble Authors_, has mottoed his book with
+the Cardinal's address to Ariosto, "Dove diavolo, Messer Ludovico, avete
+pigliato tante coglionerie?"[271] Walter Scott says you could hardly pick
+out, on any principle of selection--except badness itself, he means of
+course--the same number of plebeian authors whose works are so bad. But his
+implied satire on aristocratic writing forgets two points. First, during a
+large period of our history, when persons of rank condescended to write,
+they veiled themselves under "a person of honor," "a person of quality,"
+and the like, when not wholly undescribed. Not one of these has Walpole
+got; he omits, {132} for instance, Lord Brounker's[272] translation of
+Descartes on Music. Secondly, Walpole only takes the heads of houses: this
+cuts both ways; he equally eliminates the Hon. Robert Boyle and the
+precious Edward Howard. The last writer is hardly out of the time in which
+aristocracy suppressed its names; the avowal was then usually meant to make
+the author's greatness useful to the book. In our day, literary peers and
+honorables are very favorably known, and contain an eminent class.[273]
+They rough it like others, and if such a specimen as Edw. Howard were now
+to appear, he would be greeted with
+
+ "Hereditary noodle! knowest thou not
+  Who would be wise, himself must make him so?"
+
+
+
+THE LONGITUDE PROBLEM.
+
+    A new and easy method to find the longitude at land or sea. London,
+    1710, 4to.
+
+This tract is a little earlier than the great epoch of such publications
+(1714), and professes to find the longitude by the observed altitudes of
+the moon and two stars.[274] {133}
+
+
+
+    A new method for discovering the longitude both at sea and land, humbly
+    proposed to the consideration of the public.[275] By Wm. Whiston[276]
+    and Humphry Ditton.[277] London, 1714, 8vo.
+
+This is the celebrated tract, written by the two Arian heretics. Swift,
+whose orthodoxy was as undoubted as his meekness, wrote upon it the
+epigram--if, indeed, that be epigram of which the point is pious
+wish--which has been so often recited for the purity of its style, a purity
+which transcends modern printing. Perhaps some readers may think that Swift
+cared little for Whiston and Ditton, except as a chance hearing of their
+plan pointed them out as good marks. But it was not so: the clique had
+their eye on the guilty pair before the publication of the tract. The
+preface is dated July 7; and ten days afterwards Arbuthnot[278] writes as
+follows to Swift:
+
+"Whiston has at last published his project of the longitude; the most
+ridiculous thing that ever was thought on. But a pox on him! he has spoiled
+one of my papers of Scriblerus, which was a proposition for the longitude
+not very unlike his, to this purpose; that since there was no pole for east
+and west, that all the princes of Europe should join and build two
+prodigious poles, upon high mountains, {134} with a vast lighthouse to
+serve for a polestar. I was thinking of a calculation of the time, charges,
+and dimensions. Now you must understand his project is by lighthouses, and
+explosion of bombs at a certain hour."
+
+The plan was certainly impracticable; but Whiston and Ditton might have
+retorted that they were nearer to the longitude than their satirist to the
+kingdom of heaven, or even to a bishopric. Arbuthnot, I think, here and
+elsewhere, reveals himself as the calculator who kept Swift right in his
+proportions in the matter of the Lilliputians, Brobdingnagians, etc. Swift
+was very ignorant about things connected with number. He writes to Stella
+that he has discovered that leap-year comes every four years, and that all
+his life he had thought it came every three years. Did he begin with the
+mistake of Caesar's priests? Whether or no, when I find the person who did
+not understand leap-year inventing satellites of Mars in correct accordance
+with Kepler's third law, I feel sure he must have had help.
+
+
+
+THE AURORA BOREALIS.
+
+    An essay concerning the late apparition in the heavens on the 6th of
+    March. Proving by mathematical, logical, and moral arguments, that it
+    cou'd not have been produced meerly by the ordinary course of nature,
+    but must of necessity be a prodigy. Humbly offered to the consideration
+    of the Royal Society. London, 1716, 8vo.
+
+The prodigy, as described, was what we should call a very decided and
+unusual aurora borealis. The inference was, that men's sins were bringing
+on the end of the world. The author thinks that if one of the old
+"threatening prophets" were then alive, he would give "something like the
+following." I quote a few sentences of the notion which the author had of
+the way in which Ezekiel, for instance, would have addressed his Maker in
+the reign of George the First:
+
+"Begin! Begin! O Sovereign, for once, with an {135} effectual clap of
+thunder.... O Deity! either thunder to us no more, or when you thunder, do
+it home, and strike with vengeance to the mark.... 'Tis not enough to raise
+a storm, unless you follow it with a blow, and the thunder without the
+bolt, signifies just nothing at all.... Are then your lightnings of so
+short a sight, that they don't know how to hit, unless a mountain stands
+like a barrier in their way? Or perhaps so many eyes open in the firmament
+make you lose your aim when you shoot the arrow? Is it this? No! but, my
+dear Lord, it is your custom never to take hold of your arms till you have
+first bound round your majestic countenance with gathered mists and
+clouds."
+
+
+
+    The principles of the Philosophy of the Expansive and Contractive
+    Forces ... By Robert Greene,[279] M.A., Fellow of Clare Hall.
+    Cambridge, 1727, folio.
+
+Sanderson[280] writes to Jones,[281] "The gentleman has been reputed mad
+for these two years last past, but never gave the world such ample
+testimony of it before." This was said of a former work of Greene's, on
+solid geometry, published in 1712, in which he gives a quadrature.[282] He
+gives the same or another, I do not know which, in the present work, in
+which the circle is 3-1/5 diameters. This volume is of 981 good folio
+pages, and treats of all things, mental and material. The author is not at
+all mad, only wrong on {136} many points. It is the weakness of the
+orthodox follower of any received system to impute insanity to the solitary
+dissentient: which is voted (in due time) a very wrong opinion about
+Copernicus, Columbus, or Galileo, but quite right about Robert Greene. If
+misconceptions, acted on by too much self-opinion, be sufficient evidence
+of madness, it would be a curious inquiry what is the least per-centage of
+the reigning school which has been insane at any one time. Greene is one of
+the sources for Newton being led to think of gravitation by the fall of an
+apple: his authority is the gossip of Martin Folkes.[283] Probably Folkes
+had it from Newton's niece, Mrs. Conduitt, whom Voltaire acknowledges as
+_his authority_.[284] It is in the draft found among Conduitt's papers of
+memoranda to be sent to Fontenelle. But Fontenelle, though a great retailer
+of anecdote, does not mention it in his _eloge_ of Newton; whence it may be
+suspected that it was left out in the copy forwarded to France. D'Israeli
+has got an improvement on the story: the apple "struck him a smart blow on
+the head": no doubt taking him just on the organ of causality. He was
+"surprised at the force of the stroke" from so small an apple: but then the
+apple had a mission; Homer would have said {137} it was Minerva in the form
+of an apple. "This led him to consider the accelerating motion of falling
+bodies," which Galileo had settled long before: "from whence he deduced the
+principle of gravity," which many had considered before him, but no one had
+_deduced anything from it_. I cannot imagine whence D'Israeli got the rap
+on the head, I mean got it for Newton: this is very unlike his usual
+accounts of things. The story is pleasant and possible: its only defect is
+that various writings, well known to Newton, a very _learned_
+mathematician, had given more suggestion than a whole sack of apples could
+have done, if they had tumbled on that mighty head all at once. And
+Pemberton, speaking from Newton himself, says nothing more than that the
+idea of the moon being retained by the same force which causes the fall of
+bodies struck him for the first time while meditating in a garden. One
+particular tree at Woolsthorpe has been selected as the gallows of the
+appleshaped goddess: it died in 1820, and Mr. Turnor[285] kept the wood;
+but Sir D. Brewster[286] brought away a bit of root in 1814, and must have
+had it on his conscience for 43 years that he may have killed the tree.
+Kepler's suggestion of gravitation with the inverse distance, and
+Bouillaud's proposed substitution of the inverse square of the distance,
+are things which Newton knew better than his modern readers. I discovered
+two anagrams on his name, which are quite conclusive; the notion of
+gravitation was _not new_; but Newton _went on_. Some wandering spirit,
+probably whose business it was to resent any liberty taken with Newton's
+name, put into the head of a friend of mine _eighty-one_ anagrams on my own
+pair, some of which hit harder than any apple.
+
+{138}
+
+
+
+DE MORGAN ANAGRAMS.
+
+This friend, whom I must not name, has since made it up to about 800
+anagrams on my name, of which I have seen about 650. Two of them I have
+joined in the title-page: the reader may find the sense. A few of the
+others are personal remarks.
+
+ "Great gun! do us a sum!"
+
+is a sneer at my pursuits: but,
+
+ "Go! great sum! [Integral]a u^{n} du"
+
+is more dignified.
+
+ "Sunt agro! gaudemus,"[287]
+
+is happy as applied to one of whom it may be said:
+
+ "Ne'er out of town; 'tis such a horrid life;
+   But duly sends his family and wife."
+
+ "Adsum, nugator, suge!"[288]
+
+is addressed to a student who continues talking after the lecture has
+commenced: oh! the rascal!
+
+ "Graduatus sum! nego"[289]
+
+applies to one who declined to subscribe for an M.A. degree.
+
+ "Usage mounts guard"
+
+symbolizes a person of very fixed habits.
+
+ "Gus! Gus! a mature don!
+    August man! sure, god!
+  And Gus must argue, O!
+    Snug as mud to argue,
+  Must argue on gauds.
+    A mad rogue stung us.
+  Gag a numerous stud
+    Go! turn us! damage us!
+  Tug us! O drag us! Amen.
+    Grudge us! moan at us!
+  {139}
+  Daunt us! gag us more!
+    Dog-ear us, man! gut us!
+  D---- us! a rogue tugs!"
+
+are addressed to me by the circle-squarers; and,
+
+ "O! Gus! tug a mean surd!"
+
+is smart upon my preference of an incommensurable value of [pi] to 3-1/5,
+or some such simple substitute. While,
+
+ "Gus! Gus! at 'em a' round!"
+
+ought to be the backing of the scientific world to the author of the
+_Budget of Paradoxes_.
+
+The whole collection commenced existence in the head of a powerful
+mathematician during some sleepless nights. Seeing how large a number was
+practicable, he amused himself by inventing a digested plan of finding
+more.
+
+Is there any one whose name cannot be twisted into either praise or satire?
+I have had given to me,
+
+ "Thomas Babington Macaulay
+   Mouths big: a Cantab anomaly."
+
+
+
+NEWTON'S DE MUNDI SYSTEMATE LIBER.
+
+    A treatise of the system of the world. By Sir Isaac Newton. Translated
+    into English. London, 1728, 8vo.
+
+I think I have a right to one little paradox of my own: I greatly doubt
+that Newton wrote this book. Castiglione,[290] in his _Newtoni
+Opuscula_,[291] gives it in the Latin which appeared in 1731,[292] not for
+the first time; he says _Angli omnes Newtono tribuunt_.[293] It appeared
+just after Newton's death, without the name of any editor, or any allusion
+to Newton's {140} recent departure, purporting to be that popular treatise
+which Newton, at the beginning of the third book of the _Principia_, says
+he wrote, intending it to be the third book. It is very possible that some
+observant turnpenny might construct such a treatise as this from the third
+book, that it might be ready for publication the moment Newton could not
+disown it. It has been treated with singular silence: the name of the
+editor has never been given. Rigaud[294] mentions it without a word: I
+cannot find it in Brewster's _Newton_, nor in the _Biographia Britannica_.
+There is no copy in the Catalogue of the Royal Society's Library, either in
+English or Latin, except in Castiglione. I am open to correction; but I
+think nothing from Newton's acknowledged works will prove--as laid down in
+the suspected work--that he took Numa's temple of Vesta, with a central
+fire, to be intended to symbolize the sun as the center of our system, in
+the Copernican sense.[295]
+
+Mr. Edleston[296] gives an account of the _lectures_ "de motu corporum,"
+and gives the corresponding pages of the _Latin_ "De Systemate Mundi" of
+1731. But no one mentions the _English_ of 1728. This English seems to
+agree with the Latin; but there is a mystery about it. The preface says,
+"That this work as here published is genuine will so clearly appear by the
+intrinsic marks it bears, that it will be but losing words and the reader's
+time to take pains in giving him any other satisfaction." Surely fewer
+words would have been lost if the prefator had said at once that the work
+was from the manuscript preserved at Cambridge. Perhaps it was a mangled
+copy clandestinely taken and interpreted. {141}
+
+
+
+A BACONIAN CONTROVERSY.
+
+    Lord Bacon not the author of "The Christian Paradoxes," being a reprint
+    of "Memorials of Godliness and Christianity," by Herbert Palmer,
+    B.D.[297] With Introduction, Memoir, and Notes, by the Rev. Alexander
+    B. Grosart,[298] Kenross. (Private circulation, 1864).
+
+I insert the above in this place on account of a slight connection with the
+last. Bacon's Paradoxes,--so attributed--were first published as his in
+some asserted "Remains," 1648.[299] They were admitted into his works in
+1730, and remain there to this day. The title is "The Character of a
+believing Christian, set forth in paradoxes and seeming contradictions."
+The following is a specimen:
+
+"He believes three to be one and one to be three; a father not to be older
+than his son; a son to be equal with his father; and one proceeding from
+both to be equal with both: he believes three persons in one nature, and
+two natures in one person.... He believes the God of all grace to have been
+angry with one that never offended Him; and that God that hates sin to be
+reconciled to himself though sinning continually, and never making or being
+able to make Him any satisfaction. He believes a most just God to have
+punished a most just person, and to have justified himself, though a most
+ungodly sinner. He believes himself freely pardoned, and yet a sufficient
+satisfaction was made for him."
+
+Who can doubt that if Bacon had written this it must have been wrong? Many
+writers, especially on the {142} Continent, have taken him as sneering at
+(Athanasian) Christianity right and left. Many Englishmen have taken him to
+be quite in earnest, and to have produced a body of edifying doctrine. More
+than a century ago the Paradoxes were published as a penny tract; and,
+again, at the same price, in the _Penny Sunday Reader_, vol. vi, No. 148, a
+few passages were omitted, as _too strong_. But all did not agree: in my
+copy of Peter Shaw's [300] edition (vol. ii, p. 283) the Paradoxes have
+been cut out by the binder, who has left the backs of the leaves. I never
+had the curiosity to see whether other copies of the edition have been
+served in the same way. The Religious Tract Society republished them
+recently in _Selections from the Writings of Lord Bacon_, (no date; bad
+plan; about 1863, I suppose). No omissions were made, so far as I find.
+
+I never believed that Bacon wrote this paper; it has neither his _sparkle_
+nor his idiom. I stated my doubts even before I heard that Mr. Spedding,
+one of Bacon's editors, was of the same mind. (_Athenaeum_, July 16, 1864).
+I was little moved by the wide consent of orthodox men: for I knew how
+Bacon, Milton, Newton, Locke, etc., were always claimed as orthodox until
+almost the present day. Of this there is a remarkable instance.
+
+
+
+LOCKE AND SOCINIANISM.
+
+Among the books which in my younger day were in some orthodox publication
+lists--I think in the list of the Christian Knowledge Society, but I am not
+sure--was Locke's [301] "Reasonableness of Christianity." It seems to have
+come down from the eighteenth century, when the battle was belief in Christ
+against unbelief, _simpliciter_, as the {143} logicians say. Now, if ever
+there was a Socinian[302] book in the world, it is this work of Locke.
+"These two," says Locke, "faith and repentance, i.e., believing Jesus to be
+the Messiah, and a good life, are the indispensable conditions of the new
+covenant, to be performed by all those who would obtain eternal life." All
+the book is amplification of this doctrine. Locke, in this and many other
+things, followed Hobbes, whose doctrine, in the Leviathan, is _fidem,
+quanta ad salutem necessaria est, contineri in hoc articulo, Jesus est
+Christus_.[303] For this Hobbes was called an atheist, which {144} many
+still believe him to have been: some of his contemporaries called him,
+rightly, a Socinian. Locke was known for a Socinian as soon as his work
+appeared: Dr. John Edwards,[304] his assailant, says he is "Socinianized
+all over." Locke, in his reply, says "there is not one word of Socinianism
+in it:" and he was right: the positive Socinian doctrine has _not one word
+of Socinianism in it_; Socinianism consists in omissions. Locke and Hobbes
+did not dare _deny_ the Trinity: for such a thing Hobbes might have been
+roasted, and Locke might have been strangled. Accordingly, the well-known
+way of teaching Unitarian doctrine was the collection of the asserted
+essentials of Christianity, without naming the Trinity, etc. This is the
+plan Newton followed, in the papers which have at last been published.[305]
+
+So I, for one, thought little about the general tendency of orthodox
+writers to claim Bacon by means of the Paradoxes. I knew that, in his
+"Confession of Faith"[306] he is a Trinitarian of a heterodox stamp. His
+second Person takes human nature before he took flesh, not for redemption,
+but as a condition precedent of creation. "God is so holy, pure, and
+jealous, that it is impossible for him to be pleased in any creature,
+though the work of his own hands.... [Gen. i. 10, 12, 18, 21, 25, 31,
+freely rendered]. But--purposing to become a Creator, and to communicate to
+his creatures, he ordained in his eternal counsel that one person of the
+Godhead should be united to one nature, and to one particular of his
+creatures; that so, in the person of the Mediator, the true ladder might be
+fixed, whereby God might {145} descend to his creatures and his creatures
+might ascend to God...."
+
+This is republished by the Religious Tract Society, and seems to suit their
+theology, for they confess to having omitted some things of which they
+disapprove.
+
+In 1864, Mr. Grosart published his discovery that the Paradoxes are by
+Herbert Palmer; that they were first published surreptitiously, and
+immediately afterwards by himself, both in 1645; that the "Remains" of
+Bacon did not appear until 1648; that from 1645 to 1708, thirteen editions
+of the "Memorials" were published, all containing the Paradoxes. In spite
+of this, the Paradoxes were introduced into Bacon's works in 1730, where
+they have remained.
+
+Herbert Palmer was of good descent, and educated as a Puritan. He was an
+accomplished man, one of the few of his day who could speak French as well
+as English. He went into the Church, and was beneficed by Laud,[307] in
+spite of his puritanism; he sat in the Assembly of Divines, and was finally
+President of Queens' College, Cambridge, in which post he died, August 13,
+1647, in the 46th year of his age.
+
+Mr. Grosart says, speaking of Bacon's "Remains," "All who have had occasion
+to examine our early literature are aware that it was a common trick to
+issue imperfect, false, and unauthorized writings under any recently
+deceased name that might be expected to take. The Puritans, down to John
+Bunyan, were perpetually expostulating and protesting against such
+procedure." I have met with instances of all this; but I did not know that
+there was so much of it: a good collection would be very useful. The work
+of 1728, attributed to Newton, is likely enough to be one of the class.
+
+{146}
+
+
+
+    Demonstration de l'immobilitez de la Terre.... Par M. de la
+    Jonchere,[308] Ingenieur Francais. Londres, 1728, 8vo.
+
+A synopsis which is of a line of argument belonging to the beginning of the
+preceding century.
+
+
+
+TWO FORGOTTEN CIRCLE SQUARERS.
+
+    The Circle squared; together with the Ellipsis and several reflections
+    on it. The finding two geometrical mean proportionals, or doubling the
+    cube geometrically. By Richard Locke[309].... London, no date, probably
+    about 1730, 8vo.
+
+According to Mr. Locke, the circumference is three diameters, three-fourths
+the difference of the diameter and the side of the inscribed equilateral
+triangle, and three-fourths the difference between seven-eighths of the
+diameter and the side of the same triangle. This gives, he says, 3.18897.
+There is an addition to this tract, being an appendix to a book on the
+longitude.
+
+
+
+    The Circle squar'd. By Thos. Baxter, Crathorn, Cleaveland, Yorkshire.
+    London, 1732, 8vo.
+
+Here [pi] = 3.0625. No proof is offered.[310]
+
+
+
+    The longitude discovered by the Eclipses, Occultations, and
+    Conjunctions of Jupiter's planets. By William Whiston. London, 1738.
+
+This tract has, in some copies, the celebrated preface containing the
+account of Newton's appearance before the Parliamentary Committee on the
+longitude question, in 1714 {147} (Brewster, ii. 257-266). This "historical
+preface," is an insertion and is dated April 28, 1741, with four additional
+pages dated August 10, 1741. The short "preface" is by the publisher, John
+Whiston,[311] the author's son.
+
+
+
+THE STEAMSHIP SUGGESTED.
+
+    A description and draught of a new-invented machine for carrying
+    vessels or ships out of, or into any harbour, port, or river, against
+    wind and tide, or in a calm. For which, His Majesty has granted letters
+    patent, for the sole benefit of the author, for the space of fourteen
+    years. By Jonathan Hulls.[312] London: printed for the author, 1737.
+    Price sixpence (folding plate and pp. 48, beginning from title).
+
+(I ought to have entered this tract in its place. It is so rare that its
+existence was once doubted. It is the earliest description of steam-power
+applied to navigation. The plate shows a barge, with smoking funnel, and
+paddles at the stem, towing a ship of war. The engine, as described, is
+Newcomen's.[313]
+
+In 1855, John Sheepshanks,[314] so well known as a friend of Art and a
+public donor, reprinted this tract, in fac-simile, from his own copy;
+twenty-seven copies of the original 12mo size, and twelve on old paper,
+small 4to. I have an original copy, wanting the plate, and with "Price
+sixpence" carefully erased, to the honor of the book.[315]
+
+{148}
+
+It is not known whether Hulls actually constructed a boat.[316] In all
+probability his tract suggested to Symington, as Symington[317] did to
+Fulton.)
+
+
+
+THE NEWTONIANS ATTACKED.
+
+    Le vrai systeme de physique generale de M. Isaac Newton expose et
+    analyse en parallele avec celui de Descartes. By Louis Castel[318]
+    [Jesuit and F.R.S.] Paris, 1743, 4to.
+
+This is an elaborate correction of Newton's followers, and of Newton
+himself, who it seems did not give his own views with perfect fidelity.
+Father Castel, for instance, assures us that Newton placed the sun _at
+rest_ in the center of the system. Newton left the sun to arrange that
+matter with the planets and the rest of the universe. In this volume of 500
+pages there is right and wrong, both clever.
+
+
+
+    A dissertation on the AEther of Sir Isaac Newton. By Bryan
+    Robinson,[319] M.D. Dublin, 1743, 8vo.[320]
+
+{149}
+
+A mathematical work professing to prove that the assumed ether causes
+gravitation.
+
+
+
+MATHEMATICAL THEOLOGY.
+
+    Mathematical principles of theology, or the existence of God
+    geometrically demonstrated. By Richard Jack, teacher of Mathematics.
+    London, 1747, 8vo.[321]
+
+Propositions arranged after the manner of Euclid, with beings represented
+by circles and squares. But these circles and squares are logical symbols,
+not geometrical ones. I brought this book forward to the Royal Commission
+on the British Museum as an instance of the absurdity of attempting a
+_classed_ catalogue from the _titles_ of books. The title of this book
+sends it either to theology or geometry: when, in fact, it is a logical
+vagary. Some of the houses which Jack built were destroyed by the fortune
+of war in 1745, at Edinburgh: who will say the rebels did no good whatever?
+I suspect that Jack copied the ideas of J.B. Morinus, "Quod Deus sit,"
+Paris, 1636,[322] 4to, containing an attempt of the same kind, but not
+stultified with diagrams.
+
+
+
+TWO MODEL INDORSEMENTS.
+
+    Dissertation, decouverte, et demonstrations de la quadrature
+    mathematique du cercle. Par M. de Faure, geometre. [_s. l._, probably
+    Geneva] 1747, 8vo.
+
+    Analyse de la Quadrature du Cercle. Par M. de Faure, Gentilhomme
+    Suisse. Hague, 1749,[323] 4to.
+
+According to this octavo geometer and quarto gentleman, a diameter of 81
+gives a circumference of 256. There is an amusing circumstance about the
+quarto which has been overlooked, if indeed the book has ever been {150}
+examined. John Bernoulli (the one of the day)[324] and Koenig[325] have
+both given an attestation: my mathematical readers may stare as they
+please, such is the fact. But, on examination, there will be reason to
+think the two sly Swiss played their countryman the same trick as the
+medical man played Miss Pickle, in the novel of that name. The lady only
+wanted to get his authority against sousing her little nephew, and said,
+"Pray, doctor, is it not both dangerous and cruel to be the means of
+letting a poor tender infant perish by sousing it in water as cold as
+ice?"--"Downright murder, I affirm," said the doctor; and certified
+accordingly. De Faure had built a tremendous scaffolding of equations,
+quite out of place, and feeling cock-sure that his solutions, if correct,
+would square the circle, applied to Bernoulli and Koenig--who after his
+tract of two years before, must have known what he was at--for their
+approbation of the solutions. And he got it, as follows, well guarded:
+
+    "Suivant les suppositions posees dans ce Memoire, il est si evident que
+    t doit etre = 34, y = 1, et z = 1, que cela n'a besoin ni de preuve ni
+    d'autorite pour etre reconnu par tout le monde.[326]
+
+    "a Basle le 7e Mai 1749. JEAN BERNOULLI."
+
+    "Je souscris au jugement de Mr. Bernoulli, en consequence de ces
+    suppositions.[327]
+
+    "a la Haye le 21 Juin 1749. S. KOENIG."
+
+On which de Faure remarks with triumph--as I have no doubt it was intended
+he should do--"il conste clairement par ma presente Analyse et
+Demonstration, qu'ils y ont deja {151} reconnu et approuve parfaitement que
+la quadrature du cercle est mathematiquement demontree."[328] It should
+seem that it is easier to square the circle than to get round a
+mathematician.
+
+
+
+    An attempt to demonstrate that all the Phenomena in Nature may be
+    explained by two simple active principles, Attraction and Repulsion,
+    wherein the attraction of Cohesion, Gravity and Magnetism are shown to
+    be one the same. By Gowin Knight. London, 1748, 4to.
+
+Dr. Knight[329] was Mr. Panizzi's[330] archetype, the first Principal
+Librarian of the British Museum. He was celebrated for his magnetical
+experiments. This work was long neglected; but is now recognized as of
+remarkable resemblance to modern speculations.
+
+
+
+THOMAS WRIGHT OF DURHAM.
+
+    An original theory or Hypothesis of the Universe. By Thomas Wright[331]
+    of Durham. London, 4to, 1750.
+
+Wright is a speculator whose thoughts are now part of our current
+astronomy. He took that view--or most of it--of the milky way which
+afterwards suggested itself to William Herschel. I have given an account of
+him and his work in the _Philosophical Magazine_ for April, 1848.
+
+Wright was mathematical instrument maker to the King, {152} and kept a shop
+in Fleet Street. Is the celebrated business of Troughton & Simms, also in
+Fleet Street, a lineal descendant of that of Wright? It is likely enough,
+more likely that that--as I find him reported to have affirmed--Prester
+John was the descendant of Solomon and the Queen of Sheba. Having settled
+it thus, it struck me that I might apply to Mr. Simms, and he informs me
+that it is as I thought, the line of descent being Wright, Cole, John
+Troughton, Edward Troughton,[332] Troughton & Simms.[333]
+
+
+
+BISHOP HORNE ON NEWTON.
+
+    The theology and philosophy in Cicero's _Somnium Scipionis_ explained.
+    Or, a brief attempt to demonstrate, that the Newtonian system is
+    perfectly agreeable to the notions of the wisest ancients: and that
+    mathematical principles are the only sure ones. [By Bishop Horne,[334]
+    at the age of nineteen.] London, 1751, 8vo.
+
+This tract, which was not printed in the collected works, and is now
+excessively rare, is mentioned in _Notes and Queries_, 1st S., v, 490, 573;
+2d S., ix, 15. The boyish satire on Newton is amusing. Speaking of old
+Benjamin Martin,[335] he goes on as follows:
+
+{153}
+
+"But the most elegant account of the matter [attraction] is by that
+hominiform animal, Mr. Benjamin Martin, who having attended Dr.
+Desaguliers'[336] fine, raree, gallanty shew for some years [Desaguliers
+was one of the first who gave public experimental lectures, before the
+saucy boy was born] in the capacity of a turnspit, has, it seems, taken it
+into his head to set up for a philosopher."
+
+Thus is preserved the fact, unknown to his biographers, that Benj. Martin
+was an assistant to Desaguliers in his lectures. Hutton[337] says of him,
+that "he was well skilled in the whole circle of the mathematical and
+philosophical sciences, and wrote useful books on every one of them": this
+is quite true; and even at this day he is read by twenty where Horne is
+read by one; see the stalls, _passim_. All that I say of him, indeed my
+knowledge of the tract, is due to this contemptuous mention of a more
+durable man than himself. My assistant secretary at the Astronomical
+Society, the late Mr. Epps,[338] bought the copy at a stall because his eye
+was caught by the notice of "Old Ben Martin," of whom he was a great
+reader. Old Ben could not be a Fellow of the Royal Society, because he kept
+a shop: even though the shop sold nothing but philosophical instruments.
+Thomas Wright, similarly situated as to shop and goods, never was a Fellow.
+The Society of our day has greatly degenerated: those of the old time would
+be pleased, no doubt, that the glories of their day {154} should be
+commemorated. In the early days of the Society, there was a similar
+difficulty about Graunt, the author of the celebrated work on mortality.
+But their royal patron, "who never said a foolish thing," sent them a sharp
+message, and charged them if they found any more such tradesmen, they
+should "elect them without more ado."
+
+Horne's first pamphlet was published when he was but twenty-one years old.
+Two years afterwards, being then a Fellow of his college, and having seen
+more of the world, he seems to have felt that his manner was a little too
+pert. He endeavored, it is said, to suppress his first tract: and copies
+are certainly of extreme rarity. He published the following as his maturer
+view:
+
+    A fair, candid, and impartial state of the case between Sir Isaac
+    Newton and Mr. Hutchinson.[339] In which is shown how far a system of
+    physics is capable of mathematical demonstration; how far Sir Isaac's,
+    as such a system, has that demonstration; and consequently, what regard
+    Mr. Hutchinson's claim may deserve to have paid to it. By George Horne,
+    M.A. Oxford, 1753, 8vo.
+
+It must be remembered that the successors of Newton were very apt to
+declare that Newton had demonstrated attraction as a _physical_ cause: he
+had taken reasonable pains to show that he did not pretend to this. If any
+one had said to Newton, I hold that every particle of matter is a
+responsible being of vast intellect, ordered by the Creator to move as it
+would do if every other particle attracted it, and gifted with power to
+make its way in true accordance with that law, as easily as a lady picks
+her way across the street; what have you to say against it?--Newton must
+have replied, Sir! if you really undertake to maintain this as
+_demonstrable_, your soul had better borrow a little power {155} from the
+particles of which your body is made: if you merely ask me to refute it, I
+tell you that I neither can nor need do it; for whether attraction comes in
+this way or in any other, _it comes_, and that is all I have to do with it.
+
+The reader should remember that the word attraction, as used by Newton and
+the best of his followers, only meant a _drawing towards_, without any
+implication as to the cause. Thus whether they said that matter attracts
+matter, or that young lady attracts young gentleman, they were using one
+word in one sense. Newton found that the law of the first is the inverse
+square of the distance: I am not aware that the law of the second has been
+discovered; if there be any chance, we shall see it at the year 1856 in
+this list.
+
+In this point young Horne made a hit. He justly censures those who fixed
+upon Newton a more positive knowledge of what attraction is than he
+pretended to have. "He has owned over and over he did not know what he
+meant by it--it might be this, or it might be that, or it might be
+anything, or it might be nothing." With the exception of the _nothing_
+clause, this is true, though Newton might have answered Horne by "Thou hast
+said it."
+
+(I thought everybody knew the meaning of "Thou hast said it": but I was
+mistaken. In three of the evangelists [Greek: Su legeis] is the answer to
+"Art thou a king?" The force of this answer, as always understood, is "That
+is your way of putting it." The Puritans, who lived in Bible phrases, so
+understood it: and Walter Scott, who caught all peculiarities of language
+with great effect, makes a marked instance, "Were you armed?--I was not--I
+went in my calling, as a preacher of God's word, to encourage them that
+drew the sword in His cause. In other words, to aid and abet the rebels,
+said the Duke. _Thou hast spoken it_, replied the prisoner.")
+
+Again, Horne quotes Rowning[340] as follows:
+
+{156}
+
+"Mr. Rowning, pt. 2, p. 5 in a note, has a very pretty conceit upon this
+same subject of attraction, about every particle of a fluid being
+intrenched in three spheres of attraction and repulsion, one within
+another, 'the innermost of which (he says) is a sphere of repulsion, which
+keeps them from approaching into contact; the next, a sphere of attraction,
+diffused around this of repulsion, by which the particles are disposed to
+run together into drops; and the outermost of all, a sphere of repulsion,
+whereby they repel each other, when removed out of the attraction.' So that
+between the _urgings_, and _solicitations_, of one and t'other, a poor
+unhappy particle must ever be at his wit's end, not knowing which way to
+turn, or whom to obey first."
+
+Rowning has here started the notion which Boscovich[341] afterwards
+developed.
+
+I may add to what precedes that it cannot be settled that, as Granger[342]
+says, Desaguliers was the first who gave experimental lectures in London.
+William Whiston gave some, and Francis Hauksbee[343] made the experiments.
+The prospectus, as we should now call it, is extant, a quarto tract of
+plates and descriptions, without date. Whiston, in his life, {157} gives
+1714 as the first date of publication, and therefore, no doubt, of the
+lectures. Desaguliers removed to London soon after 1712, and commenced his
+lectures soon after that. It will be rather a nice point to settle which
+lectured first; probabilities seem to go in favor of Whiston.
+
+
+
+FALLACIES IN A THEORY OF ANNUITIES.
+
+    An Essay to ascertain the value of leases, and annuities for years and
+    lives. By W[eyman] L[ee]. London, 1737, 8vo.
+
+    A valuation of Annuities and Leases certain, for a single life. By
+    Weyman Lee, Esq. of the Inner Temple. London, 1751, 8vo. Third edition,
+    1773.
+
+Every branch of exact science has its paradoxer. The world at large cannot
+tell with certainty who is right in such questions as squaring the circle,
+etc. Mr. Weyman Lee[344] was the assailant of what all who had studied
+called demonstration in the question of annuities. He can be exposed to the
+world: for his error arose out of his not being able to see that the whole
+is the sum of all its parts.
+
+By an annuity, say of L100, now bought, is meant that the buyer is to have
+for his money L100 in a year, if he be then alive, L100 at the end of two
+years, if then alive, and so on. It is clear that he would buy a life
+annuity if he should buy the first L100 in one office, the second in
+another, and so on. All the difference between buying the whole from one
+office and buying all the separate contingent payments at different
+offices, is immaterial to calculation. Mr. Lee would have agreed with the
+rest of the world about the payments to be made to the several different
+offices, in consideration of their several contracts: but he differed from
+every one else about the sum to be paid to _one_ office. He contended that
+the way to value an annuity is to find out the term of years which the
+individual has an even chance of surviving, and to charge for the life
+annuity the value of an annuity certain for that term.
+
+{158}
+
+It is very common to say that Lee took the average life, or expectation, as
+it is wrongly called, for his term: and this I have done myself, taking the
+common story. Having exposed the absurdity of this second supposition,
+taking it for Lee's, in my _Formal Logic_,[345] I will now do the same with
+the first.
+
+A mathematical truth is true in its extreme cases. Lee's principle is that
+an annuity on a life is the annuity made certain for the term within which
+it is an even chance the life drops. If, then, of a thousand persons, 500
+be sure to die within a year, and the other 500 be immortal, Lee's price of
+an annuity to any one of these persons is the present value of one payment:
+for one year is the term which each one has an even chance of surviving and
+not surviving. But the true value is obviously half that of a perpetual
+annuity: so that at 5 percent Lee's rule would give less than the tenth of
+the true value. It must be said for the poor circle-squarers, that they
+never err so much as this.
+
+Lee would have said, if alive, that I have put an _extreme case_: but any
+_universal_ truth is true in its extreme cases. It is not fair to bring
+forward an extreme case against a person who is speaking as of usual
+occurrences: but it is quite fair when, as frequently happens, the proposer
+insists upon a perfectly general acceptance of his assertion. And yet many
+who go the whole hog protest against being tickled with the tail. Counsel
+in court are good instances: they are paradoxers by trade. June 13, 1849,
+at Hertford, there was an action about a ship, insured against a _total_
+loss: some planks were saved, and the underwriters refused to pay. Mr. Z.
+(for deft.) "There can be no degrees of totality; and some timbers were
+saved."--L. C. B. "Then if the vessel were burned to the water's edge, and
+some rope saved in the boat, there would be no total loss."--Mr. Z. "This
+is putting a very extreme case."--L. C. B. "The argument {159} would go
+that length." What would _Judge_ Z.--as he now is--say to the extreme case
+beginning somewhere between six planks and a bit of rope?
+
+
+
+MONTUCLA'S WORK ON THE QUADRATURE.
+
+    Histoire des recherches sur la quadrature du cercle ... avec une
+    addition concernant les problemes de la duplication du cube et de la
+    trisection de l'angle. Paris, 1754, 12mo. [By Montucla.]
+
+This is _the_ history of the subject.[346] It was a little episode to the
+great history of mathematics by Montucla, of which the first edition
+appeared in 1758. There was much addition at the end of the fourth volume
+of the second edition; this is clearly by Montucla, though the bulk of the
+volume is put together, with help from Montucla's papers, by Lalande.[347]
+There is also a second edition of the history of the quadrature, Paris,
+1831, 8vo, edited, I think, by Lacroix; of which it is the great fault that
+it makes hardly any use of the additional matter just mentioned.
+
+Montucla is an admirable historian when he is writing from his own direct
+knowledge: it is a sad pity that he did not tell us when he was depending
+on others. We are not to trust a quarter of his book, and we must read many
+other books to know which quarter. The fault is common enough, but
+Montucla's good three-quarters is so good that the fault is greater in him
+than in most others: I mean the fault of not acknowledging; for an
+historian cannot read everything. But it must be said that mankind give
+little encouragement to candor on this point. Hallam, in his {160} _History
+of Literature_, states with his own usual instinct of honesty every case in
+which he depends upon others: Montucla does not. And what is the
+consequence?--Montucla is trusted, and believed in, and cried up in the
+bulk; while the smallest talker can lament that Hallam should be so unequal
+and apt to depend on others, without remembering to mention that Hallam
+himself gives the information. As to a universal history of any great
+subject being written entirely upon primary knowledge, it is a thing of
+which the possibility is not yet proved by an example. Delambre attempted
+it with astronomy, and was removed by death before it was finished,[348] to
+say nothing of the gaps he left.
+
+Montucla was nothing of a bibliographer, and his descriptions of books in
+the first edition were insufficient. The Abbe Rive[349] fell foul of him,
+and as the phrase is, gave it him. Montucla took it with great good humor,
+tried to mend, and, in his second edition, wished his critic had lived to
+see the _vernis de bibliographe_ which he had given himself.
+
+I have seen Montucla set down as an _esprit fort_, more than once: wrongly,
+I think. When he mentions Barrow's[350] address to the Almighty, he adds,
+"On voit, au reste, par la, que Barrow etoit un pauvre philosophe; car il
+croyait en l'immortalite de l'ame, et en une Divinite autre que la nature
+{161} universelle."[351] This is irony, not an expression of opinion. In
+the book of mathematical recreations which Montucla constructed upon that
+of Ozanam,[352] and Ozanam upon that of Van Etten,[353] now best known in
+England by Hutton's similar treatment of Montucla, there is an amusing
+chapter on the quadrators. Montucla refers to his own anonymous book of
+1754 as a curious book published by Jombert.[354] He seems to have been a
+little ashamed of writing about circle-squarers: what a slap on the face
+for an unborn Budgeteer!
+
+Montucla says, speaking of France, that he finds three notions prevalent
+among the cyclometers: (1) that there is a large reward offered for
+success; (2) that the longitude problem depends on that success; (3) that
+the solution is the great end and object of geometry. The same three {162}
+notions are equally prevalent among the same class in England. No reward
+has ever been offered by the government of either country. The longitude
+problem in no way depends upon perfect solution; existing approximations
+are sufficient to a point of accuracy far beyond what can be wanted.[355]
+And geometry, content with what exists, has long passed on to other
+matters. Sometimes a cyclometer persuades a skipper who has made land in
+the wrong place that the astronomers are in fault, for using a wrong
+measure of the circle; and the skipper thinks it a very comfortable
+solution! And this is the utmost that the problem ever has to do with
+longitude.
+
+
+
+ANTINEWTONIANISMUS.
+
+    Antinewtonianismus.[356] By Caelestino Cominale,[357] M.D. Naples, 1754
+    and 1756, 2 vols. 4to.
+
+The first volume upsets the theory of light; the second vacuum, vis
+inertiae, gravitation, and attraction. I confess I never attempted these big
+Latin volumes, numbering 450 closely-printed quarto pages. The man who
+slays Newton in a pamphlet is the man for me. But I will lend them to
+anybody who will give security, himself in L500, and two sureties in L250
+each, that he will read them through, and give a full abstract; and I will
+not exact security for their return. I have never seen any mention of this
+book: it has a printer, but not a publisher, as happens with so many
+unrecorded books.
+
+{163}
+
+
+
+OFFICIAL BLOW TO CIRCLE SQUARERS.
+
+1755. The French Academy of Sciences came to the determination not to
+examine any more quadratures or kindred problems. This was the consequence,
+no doubt, of the publication of Montucla's book: the time was well chosen;
+for that book was a full justification of the resolution. The Royal Society
+followed the same course, I believe, a few years afterwards. When our Board
+of Longitude was in existence, most of its time was consumed in listening
+to schemes, many of which included the quadrature of the circle. It is
+certain that many quadrators have imagined the longitude problem to be
+connected with theirs: and no doubt the notion of a reward offered by
+Government for a true quadrature is a result of the reward offered for the
+longitude. Let it also be noted that this longitude reward was not a
+premium upon excogitation of a mysterious difficulty. The legislature was
+made to know that the rational hopes of the problem were centered in the
+improvement of the lunar tables and the improvement of chronometers. To
+these objects alone, and by name, the offer was directed: several persons
+gained rewards for both; and the offer was finally repealed.
+
+
+
+AN INTERESTING HOAX.
+
+    Fundamentalis Figura Geometrica, primas tantum lineas circuli
+    quadraturae possibilitatis ostendens. By Niels Erichsen (Nicolaus
+    Ericius), shipbuilder, of Copenhagen. Copenhagen, 1755, 12mo.
+
+This was a gift from my oldest friend who was not a relative, Dr. Samuel
+Maitland of the "Dark Ages."[358] He found it among his books, and could
+not imagine how he came by it: I could have told him. He once collected
+interpretations of the Apocalypse: and auction lots of such {164} books
+often contain quadratures. The wonder is he never found more than one.
+
+The quadrature is not worth notice. Erichsen is the only squarer I have met
+with who has distinctly asserted the particulars of that reward which has
+been so frequently thought to have been offered in England. He says that in
+1747 the Royal Society on the 2d of June, offered to give a large reward
+for the quadrature of the circle and a true explanation of magnetism, in
+addition to L30,000 previously promised for the same. I need hardly say
+that the Royal Society had not L30,000 at that time, and would not, if it
+had had such a sum, have spent it on the circle, nor on magnetic theory;
+nor would it have coupled the two things. On this book, see _Notes and
+Queries_, 1st S., xii, 306. Perhaps Erichsen meant that the L30,000 had
+been promised by the Government, and the addition by the Royal Society.
+
+October 8, 1866. I receive a letter from a cyclometer who understands that
+a reward is offered to any one who will square the circle, and that all
+competitors are to send their plans to me. The hoaxers have not yet failed
+out of the land.
+
+
+
+TWO JESUIT CONTRIBUTIONS.
+
+    Theoria Philosophiae Naturalis redacta ad unicam legem virium in natura
+    existentium. Editio _Veneta_ prima. By Roger Joseph Boscovich. Venice,
+    1763, 4to.
+
+The first edition is said to be of Vienna, 1758.[359] This is a celebrated
+work on the molecular theory of matter, grounded on the hypothesis of
+spheres of alternate attraction and repulsion. Boscovich was a Jesuit of
+varied pursuit. During his measurement of a degree of the meridian, while
+on horseback or waiting for his observations, he composed a Latin poem of
+about five thousand verses on eclipses, {165} with notes, which he
+dedicated to the Royal Society: _De Solis et Lunae defectibus_,[360] London,
+Millar and Dodsley, 1760, 4to.
+
+
+
+    Traite de paix entre Des Cartes et Newton, _precede_ des vies
+    litteraires de ces deux chefs de la physique moderne.... By Aime Henri
+    Paulian.[361] Avignon, 1763, 12mo.
+
+I have had these books for many years without feeling the least desire to
+see how a lettered Jesuit would atone Descartes and Newton. On looking at
+my two volumes, I find that one contains nothing but the literary life of
+Descartes; the other nothing but the literary life of Newton. The preface
+indicates more: and Watt mentions _three_ volumes.[362] I dare say the
+first two contain all that is valuable. On looking more attentively at the
+two volumes, I find them both readable and instructive; the account of
+Newton is far above that of Voltaire, but not so popular. But he should not
+have said that Newton's family came from Newton in Ireland. Sir Rowland
+Hill gives fourteen _Newtons_ in Ireland;[363] twice the number of the
+cities that contended for the birth of Homer may now contend for the origin
+of Newton, on the word of Father Paulian.
+
+
+
+    Philosophical Essays, in three parts. By R. Lovett, Lay Clerk of the
+    Cathedral Church of Worcester. Worcester, 1766, 8vo.
+
+    The Electrical Philosopher: containing a new system of physics {166}
+    founded upon the principle of an universal Plenum of elementary
+    fire.... By R. Lovett, Worcester, 1774, 8vo.
+
+Mr. Lovett[364] was one of those ether philosophers who bring in elastic
+fluid as an explanation by imposition of words, without deducing any one
+phenomenon from what we know of it. And yet he says that attraction has
+received no support from geometry; though geometry, applied to a particular
+law of attraction, had shown how to predict the motions of the bodies of
+the solar system. He, and many of his stamp, have not the least idea of the
+confirmation of a theory by accordance of deduced results with observation
+posterior to the theory.
+
+
+
+BAILLY'S EXAGGERATED VIEW OF ASTRONOMY.
+
+    Lettres sur l'Atlantide de Platon, et sur l'ancien Histoire de l'Asie,
+    pour servir de suite aux lettres sur l'origine des Sciences, adressees
+    a M. de Voltaire, par M. Bailly.[365] London and Paris, 1779, 8vo.
+
+I might enter here all Bailly's histories of astronomy.[366] The paradox
+which runs through them all more or less, is the doctrine that astronomy is
+of immense antiquity, coming from some forgotten source, probably the
+drowned island of Plato, peopled by a race whom Bailly makes, as has {167}
+been said, to teach us everything except their existence and their name.
+These books, the first scientific histories which belong to readable
+literature, made a great impression by power of style: Delambre created a
+strong reaction, of injurious amount, in favor of history founded on
+contemporary documents, which early astronomy cannot furnish. These letters
+are addressed to Voltaire, and continue the discussion. There is one letter
+of Voltaire, being the fourth, dated Feb. 27, 1777, and signed "le vieux
+malade de Ferney, V. puer centum annorum."[367] Then begin Bailly's
+letters, from January 16 to May 12, 1778. From some ambiguous expressions
+in the Preface, it would seem that these are fictitious letters, supposed
+to be addressed to Voltaire at their dates. Voltaire went to Paris February
+10, 1778, and died there May 30. Nearly all this interval was his closing
+scene, and it is very unlikely that Bailly would have troubled him with
+these letters.[368]
+
+
+
+    An inquiry into the cause of motion, or a general theory of physics. By
+    S. Miller. London, 1781, 4to
+
+Newton all wrong: matter consists of two kinds of particles, one inert, the
+other elastic and capable of expanding themselves _ad infinitum_.
+
+
+
+SAINT-MARTIN ON ERRORS AND TRUTH.
+
+    Des Erreurs et de la Verite, ou les hommes rappeles au principe
+    universel de la science; ouvrage dans lequel, en faisant remarquer aux
+    observateurs l'incertitude de leurs recherches, et leurs meprises
+    continuelles, on leur indique la route qu'ils auroient du suivre, pour
+    acquerir l'evidence physique sur l'origine du bien et du mal, sur
+    l'homme, sur la nature materielle, et la nature sacree; sur la base des
+    gouvernements {168} politiques, sur l'autorite des souverains, sur la
+    justice civile et criminelle, sur les sciences, les langues, et les
+    arts. Par un Ph.... Inc.... A Edimbourg. 1782.[369] Two vols. 8vo.
+
+This is the famous work of Louis Claude de Saint-Martin[370] (1743-1803),
+for whose other works, vagaries included, the reader must look elsewhere:
+among other things, he was a translator of Jacob Behmen.[371] The title
+promises much, and the writer has smart thoughts now and then; but the
+whole is the wearisome omniscience of the author's day and country, which
+no reader of our time can tolerate. Not that we dislike omniscience; but we
+have it of our own country, both home-made and imported; and fashions vary.
+But surely there can be but one omniscience? Must a man have but one wife?
+Nay, may not a man have a new wife while the old one is living? There was a
+famous instrumental professor forty years ago, who presented a friend to
+Madame ----. The friend started, and looked surprised; for, not many weeks
+before, he had been presented to another lady, with the same title, at
+Paris. The musician observed his surprise, and quietly said, "Celle-ci est
+Madame ---- de Londres." In like manner we have a London omniscience now
+current, which would make any one start who only knew the old French
+article.
+
+The book was printed at Lyons, but it was a trick of French authors to
+pretend to be afraid of prosecution: it {169} made a book look wicked-like
+to have a feigned place of printing, and stimulated readers. A Government
+which had undergone Voltaire would never have drawn its sword upon quiet
+Saint-Martin. To make himself look still worse, he was only ph[ilosophe]
+Inc...., which is generally read _Inconnu_[372] but sometimes _Incredule_;
+[373] most likely the ambiguity was intended. There is an awful paradox
+about the book, which explains, in part, its leaden sameness. It is all
+about _l'homme_, _l'homme_, _l'homme_,[374] except as much as treats of
+_les hommes_, _les hommes_, _les hommes_;[375] but not one single man is
+mentioned by name in its 500 pages. It reminds one of
+
+ "Water, water everywhere,
+  And not a drop to drink."
+
+Not one opinion of any other man is referred to, in the way of agreement or
+of opposition. Not even a town is mentioned: there is nothing which brings
+a capital letter into the middle of a sentence, except, by the rarest
+accident, such a personification as _Justice_. A likely book to want an
+_Edimbourg_ godfather!
+
+Saint-Martin is great in mathematics. The number _four_ essentially belongs
+to straight lines, and _nine_ to curves. The object of a straight line is
+to perpetuate _ad infinitum_ the production of a point from which it
+emanates. A circle [circle] bounds the production of all its radii, tends
+to destroy them, and is in some sort their enemy. How is it possible that
+things so distinct should not be distinguished in their _number_ as well as
+in their action? If this important observation had been made earlier,
+immense trouble would have been saved to the mathematicians, who would have
+been prevented from searching for a common measure to lines which have
+nothing in common. But, though all straight lines have the number _four_,
+it must not be supposed that they are all equal, for a line is the result
+of its law and {170} its number; but though both are the same for all lines
+of a sort, they act differently, as to force, energy, and duration, in
+different individuals; which explains all differences of length, etc. I
+congratulate the reader who understands this; and I do not pity the one who
+does not.
+
+Saint-Martin and his works are now as completely forgotten as if they had
+never been born, except so far as this, that some one may take up one of
+the works as of heretical character, and lay it down in disappointment,
+with the reflection that it is as dull as orthodoxy. For a person who was
+once in some vogue, it would be difficult to pick out a more fossil writer,
+from Aa to Zypoeus, except,--though it is unusual for (,--) to represent an
+interval of more than a year--his unknown opponent. This opponent, in the
+very year of the _Des Erreurs_ ... published a book in two parts with the
+same fictitious place of printing;
+
+    Tableau Naturel des Rapports qui existent entre Dieu, l'Homme, et
+    l'Univers. A Edimbourg, 1782, 8vo.[376]
+
+There is a motto from the _Des Erreurs_ itself, "Expliquer les choses par
+l'homme, et non l'homme par les choses. _Des Erreurs et de la Verite_, par
+un PH.... INC...., p. 9."[377] This work is set down in various catalogues
+and biographies as written by the PH.... INC.... himself. But it is not
+usual for a writer to publish two works in the same year, one of which
+takes a motto from the other. And the second work is profuse in capitals
+and italics, and uses Hebrew learning: its style differs much from the
+first work. The first work sets out from man, and has nothing to do with
+God: the second is religious and raps the knuckles of the first as follows:
+"Si nous voulons nous preserver de toutes {171} les illusions, et surtout
+des amorces de l'orgueil par lesquelles l'homme est si souvent seduit, ne
+prenons jamais les hommes, mais toujours _Dieu_ pour notre terme de
+comparaison."[378] The first uses _four_ and _nine_ in various ways, of
+which I have quoted one: the second says, "Et ici se trouve deja une
+explication des nombres _quatre_ et _neuf_, qui ont peu embarrasse dans
+l'ouvrage deja cite. L'homme s'est egare en allant de _quatre_ a
+_neuf_...."[379] The work cited is the _Erreurs_, etc., and the citation is
+in the motto, which is the text of the opposition sermon.
+
+
+
+A FORERUNNER OF THE METRIC SYSTEM.
+
+    Method to discover the difference of the earth's diameters; proving its
+    true ratio to be not less variable than as 45 is to 46, and shortest in
+    its pole's axis 174 miles.... likewise a method for fixing an universal
+    standard for weights and measures. By Thomas Williams.[380] London,
+    1788, 8vo.
+
+Mr. Williams was a paradoxer in his day, and proposed what was, no doubt,
+laughed at by some. He proposed the sort of plan which the
+French--independently of course--carried into effect a few years after. He
+would have the 52d degree of latitude divided into 100,000 parts and each
+part a geographical yard. The geographical ton was to be the cube of a
+geographical yard filled with sea-water taken some leagues from land. All
+multiples and sub-divisions were to be decimal.
+
+I was beginning to look up those who had made similar proposals, when a
+learned article on the proposal of a {172} metrical system came under my
+eye in the _Times_ of Sept. 15, 1863. The author cites Mouton,[381] who
+would have the minute of a degree divided into 10,000 _virgulae_; James
+Cassini,[382] whose foot was to be six thousandths of a minute; and
+Paucton,[383] whose foot was the 400,000th of a degree. I have verified the
+first and third statements; surely the second ought to be the
+_six-thousandth_.
+
+
+
+    An inquiry into the Copernican system ... wherein it is proved, in the
+    clearest manner, that the earth has only her diurnal motion ... with an
+    attempt to point out the only true way whereby mankind can receive any
+    real benefit from the study of the heavenly bodies. By John
+    Cunningham.[384] London, 1789, 8vo.
+
+The "true way" appears to be the treatment of heaven and earth as
+emblematical of the Trinity.
+
+
+
+    Cosmology. An inquiry into the cause of what is called gravitation or
+    attraction, in which the motions of the heavenly bodies, and the
+    preservation and operations of all nature, are deduced from an
+    universal principle of efflux and reflux. By T. Vivian,[385] vicar of
+    Cornwood, Devon. Bath, 1792, 12mo.
+
+{173}
+
+Attraction, an influx of matter to the sun; centrifugal force, the solar
+rays; cohesion, the pressure of the atmosphere. The confusion about
+centrifugal _force_, so called, as demanding an external agent, is very
+common.
+
+
+
+THOMAS PAINE'S RIGHTS OF MAN.
+
+    The rights of MAN, being an answer to Mr. Burke's attack on the French
+    Revolution.[386] By Thomas Paine.[387] In two parts. 1791-1792. 8vo.
+    (Various editions.)[388]
+
+    A vindication of the rights of WOMAN, with strictures on political and
+    moral subjects. By Mary Wollstonecraft.[389] 1792. 8vo.
+
+    A sketch of the rights of BOYS and GIRLS. By Launcelot Light, of
+    Westminster School; and Laetitia Lookabout, of Queen's Square,
+    Bloomsbury. [By the Rev. Samuel Parr,[390] LL.D.] 1792. 8vo. (pp.64).
+
+When did we three meet before? The first work has sunk into oblivion: had
+it merited its title, it might have {174} lived. It is what the French call
+a _piece de circonstance_; it belongs in time to the French Revolution, and
+in matter to Burke's opinion of that movement. Those who only know its name
+think it was really an attempt to write a philosophical treatise on what we
+now call socialism. Silly government prosecutions gave it what it never
+could have got for itself.
+
+Mary Wollstonecraft seldom has her name spelled right. I suppose the O! O!
+character she got made her W_oo_lstonecraft. Watt gives double insinuation,
+for his cross-reference sends us to G_oo_dwin.[391] No doubt the title of
+the book was an act of discipleship to Paine's _Rights of Man_; but this
+title is very badly chosen. The book was marred by it, especially when the
+authoress and her husband assumed the right of dispensing with legal
+sanction until the approach of offspring brought them to a sense of their
+child's interest.[392] Not a hint of such a claim is found in the book,
+which is mostly about female education. The right claimed for woman is to
+have the education of a rational human being, and not to be considered as
+nothing but woman throughout youthful training. The maxims of Mary
+Wollstonecraft are now, though not derived from her, largely followed in
+the education of girls, especially in home education: just as many of the
+political principles of Tom Paine, again not derived from him, are the
+guides of our actual legislation. I remember, forty years ago, an old lady
+used to declare that she disliked girls from the age of sixteen to
+five-and-twenty. "They are full," said she, "of _femalities_." She spoke of
+their behavior to women as well as to men. She {175} would have been
+shocked to know that she was a follower of Mary Wollstonecraft, and had
+packed half her book into one sentence.
+
+The third work is a satirical attack on Mary Wollstonecraft and Tom Paine.
+The details of the attack would convince any one that neither has anything
+which would now excite reprobation. It is utterly unworthy of Dr. Parr, and
+has quite disappeared from lists of his works, if it were ever there. That
+it was written by him I take to be evident, as follows. Nichols,[393] who
+could not fail to know, says (_Anecd._, vol. ix, p. 120): "This is a
+playful essay by a first-rate scholar, who is elsewhere noticed in this
+volume, but whose name I shall not bring forward on so trifling an
+occasion." Who the scholar was is made obvious by Master Launcelot being
+made to talk of Bellendenus.[394] Further, the same boy is made to say,
+"Let Dr. Parr lay his hand upon his heart, if his conscience will let him,
+and ask himself how many thousands of wagon-loads of this article [birch]
+he has cruelly misapplied." How could this apply to Parr, with his handful
+of private pupils,[395] and no reputation for severity? Any one except
+himself would have called on the head-master of Westminster or Eton. I
+doubt whether the name of Parr could be connected with the rod by anything
+in print, except the above and an anecdote of his pupil, Tom Sheridan.[396]
+The Doctor had dressed for a dinner visit, and {176} was ready a quarter of
+an hour too soon to set off. "Tom," said he, "I think I had better whip you
+now; you are sure to do something while I am out."--"I wish you would,
+sir!" said the boy; "it would be a letter of licence for the whole
+evening." The Doctor saw the force of the retort: my two tutelaries will
+see it by this time. They paid in advance; and I have given liberal
+interpretation to the order.
+
+The following story of Dr. Parr was told me and others, about 1829, by the
+late Leonard Horner,[397] who knew him intimately. Parr was staying in a
+house full of company, I think in the north of England. Some gentlemen from
+America were among the guests, and after dinner they disputed some of
+Parr's assertions or arguments. So the Doctor broke out with "Do you know
+what country you come from? You come from the place to which we used to
+send our thieves!" This made the host angry, and he gave Parr such a severe
+rebuke as sent him from the room in ill-humor. The rest walked on the lawn,
+amusing the Americans with sketches of the Doctor. There was a dark cloud
+overhead, and from that cloud presently came a voice which called _Tham_
+(Parr-lisp for _Sam_). The company were astonished for a moment, but
+thought the Doctor was calling his servant in the house, and that the
+apparent direction was an illusion arising out of inattention. But
+presently the sound was repeated, certainly from the cloud,
+
+    "And nearer, clearer, deadlier than before."
+
+There was now a little alarm: where could the Doctor have got to? They ran
+to his bedroom, and there they discovered a sufficient rather than
+satisfactory explanation. The Doctor had taken his pipe into his bedroom,
+and had seated himself, in sulky mood, upon the higher bar of a large and
+deep old-fashioned grate with a high mantelshelf. Here he had {177} tumbled
+backwards, and doubled himself up between the bars and the back of the
+grate. He was fixed tight, and when he called for help, he could only throw
+his voice up the chimney. The echo from the cloud was the warning which
+brought his friends to the rescue.
+
+
+
+ATTACKS ON RELIGIOUS CUSTOMS.
+
+Days of political paradox were coming, at which we now stare. Cobbett[398]
+said, about 1830, in earnest, that in the country every man who did not
+take off his hat to the clergyman was suspected, and ran a fair chance of
+having something brought against him. I heard this assertion canvassed,
+when it was made, in a party of elderly persons. The Radicals backed it,
+the old Tories rather denied it, but in a way which satisfied me they ought
+to have denied it less if they could not deny it more. But it must be said
+that the Governments stopped far short of what their partisans would have
+had them do. All who know Robert Robinson's[399] very quiet assault on
+church-made festivals in his _History and Mystery of Good Friday_
+(1777)[400] will hear or remember with surprise that the _British Critic_
+pronounced it a direct, unprovoked, and malicious libel on the most {178}
+sacred institutions of the national Church. It was reprinted again and
+again: in 1811 it was in a cheap form at 6s. 6d. a hundred. When the
+Jacobin day came, the State was really in a fright: people thought twice
+before they published what would now be quite disregarded. I examined a
+quantity of letters addressed to George Dyer[401] (Charles Lamb's G.D.) and
+what between the autographs of Thelwall, Hardy, Horne Tooke, and all the
+rebels,[402] put together a packet which produced five guineas, or
+thereabouts, for the widow. Among them were the following verses, sent by
+the author--who would not put his name, even in a private letter, for fear
+of accidents--for consultation whether they could safely be sent to an
+editor: and they were _not_ sent. The occasion was the public thanksgiving
+at St. Paul's for the naval victories, December 19, 1797.
+
+ "God bless me! what a thing!
+  Have you heard that the King
+    Goes to St. Paul's?
+  {179}
+  Good Lord! and when he's there,
+  He'll roll his eyes in prayer,
+  To make poor Johnny stare
+    At this fine thing.
+
+ "No doubt the plan is wise
+  To blind poor Johnny's eyes
+    By this grand show;
+  For should he once suppose
+  That he's led by the nose,
+  Down the whole fabric goes,
+    Church, lords, and king.
+
+ "As he shouts Duncan's[403] praise,
+  Mind how supplies they'll raise
+    In wondrous haste.
+  For while upon the sea
+  We gain one victory,
+  John still a dupe will be
+    And taxes pay.
+
+ "Till from his little store
+  Three-fourths or even more
+    Goes to the Crown.
+  Ah, John! you little think
+  How fast we downward sink
+  And touch the fatal brink
+    At which we're slaves."
+
+I would have indicted the author for not making his thirds and sevenths
+rhyme. As to the rhythm, it is not much better than what the French sang in
+the Calais theater when the Duke of Clarence[404] took over Louis XVIII in
+1814.
+
+ "God save noble Clarence,
+  Who brings our king to France;
+    God save Clarence!
+  He maintains the glory
+  Of the British navy,
+    etc., etc."
+
+{180} Perhaps had this been published, the Government would have assailed
+it as a libel on the church service. They got into the way of defending
+themselves by making libels on the Church, of what were libels, if on
+anything, on the rulers of the State; until the celebrated trials of Hone
+settled the point for ever, and established that juries will not convict
+for one offence, even though it have been committed, when they know the
+prosecution is directed at another offence and another intent.
+
+
+
+HONE'S FAMOUS TRIALS.
+
+The results of Hone's trials (William Hone, 1779-1842) are among the
+important constitutional victories of our century. He published parodies on
+the Creeds, the Lord's Prayer, the Catechism, etc., with intent to bring
+the Ministry into contempt: everybody knew that was his _purpose_. The
+Government indicted him for impious, profane, blasphemous intent, but not
+for seditious intent. They hoped to wear him out by proceeding day by day.
+December 18, 1817, they hid themselves under the Lord's Prayer, the Creed,
+and the Commandments; December 19, under the Litany; December 20, under the
+Athanasian Creed, an odd place for shelter when they could not find it in
+the previous places. Hone defended himself for six, seven, and eight hours
+on the several days: and the jury acquitted him in 15, 105, and 20 minutes.
+In the second trial the offense was laid both as profanity and as sedition,
+which seems to have made the jury hesitate. And they probably came to think
+that the second count was false pretence: but the length of their
+deliberation is a satisfactory addition to the value of the whole. In the
+first trial the Attorney-General (Shepherd) had the impudence to say that
+the libel had nothing of a political tendency about it, but was _avowedly_
+set off against the religion and worship of the Church of England. The
+whole {181} is political in every sentence; neither more nor less political
+than the following, which is part of the parody on the Catechism: "What is
+thy duty towards the Minister? My duty towards the Minister is, to trust
+him as much as I can; to honor him with all my words, with all my bows,
+with all my scrapes, and with all my cringes; to flatter him; to give him
+thanks; to give up my whole soul to him; to idolize his name, and obey his
+word, and serve him blindly all the days of his political life." And the
+parody on the Creed begins, "I believe in George, the Regent almighty,
+maker of new streets and Knights of the Bath." This is what the
+Attorney-General said had nothing of a political tendency about it. But
+this was _on the first trial_: Hone was not known. The first day's trial
+was under Justice Abbott (afterwards C. J. Tenterden).[405] It was
+perfectly understood, when Chief Justice Ellenborough[406] appeared in
+Court on the second day, that he was very angry at the first result, and
+put his junior aside to try his own rougher dealing. But Hone tamed the
+lion. An eye-witness told me that when he implored of Hone not to detail
+his own father Bishop Law's[407] views on the Athanasian Creed, which
+humble petition Hone kindly granted, he held by the desk for support. And
+the same when--which is not reported--the Attorney-General appealed to the
+Court for protection against a {182} stinging attack which Hone made on the
+Bar: he _held on_, and said, "Mr. Attorney, what _can_ I do!" I was a boy
+of twelve years old, but so strong was the feeling of exultation at the
+verdicts that boys at school were not prohibited from seeing the parodies,
+which would have been held at any other time quite unfit to meet their
+eyes. I was not able to comprehend all about the Lord Chief Justice until I
+read and heard again in after years. In the meantime, Joe Miller had given
+me the story of the leopard which was sent home on board a ship of war, and
+was in two days made as docile as a cat by the sailors.[408] "You have got
+that fellow well under," said an officer. "Lord bless your Honor!" said
+Jack, "if the Emperor of Marocky would send us a cock rhinoceros, we'd
+bring him to his bearings in no time!" When I came to the subject again, it
+pleased me to entertain the question whether, if the Emperor had sent a
+cock rhinoceros to preside on the third day in the King's Bench, Hone would
+have mastered _him_: I forget how I settled it. There grew up a story that
+Hone caused Lord Ellenborough's death, but this could not have been true.
+Lord Ellenborough resigned his seat in a few months, and died just a year
+after the trials; but sixty-eight years may have had more to do with it
+than his defeat.
+
+A large subscription was raised for Hone, headed by the Duke of
+Bedford[409] for L105. Many of the leading anti-ministerialists joined: but
+there were many of the other side who avowed their disapprobation of the
+false pretense. Many could not venture their names. In the list I find:
+{183} A member of the House of Lords, an enemy to persecution, and
+especially to religious persecution employed for political purposes--No
+parodist, but an enemy to persecution--A juryman on the third day's
+trial--Ellen Borough--My name would ruin me--Oh! minions of Pitt--Oil for
+the Hone--The Ghosts of Jeffries[410] and Sir William Roy [Ghosts of
+Jeffries in abundance]--A conscientious Jury and a conscientious Attorney,
+L1 6s. 8d.--To Mr. Hone, for defending in his own person the freedom of the
+press, attacked for a political object, under the old pretense of
+supporting Religion--A cut at corruption--An Earldom for myself and a
+translation for my brother--One who disapproves of parodies, but abhors
+persecution--From a schoolboy who wishes Mr. Hone to have a very grand
+subscription--"For delicacy's sake forbear," and "Felix trembled"--"I will
+go myself to-morrow"--Judge Jeffries' works rebound in calf by Law--Keep us
+from Law, and from the Shepherd's paw--I must not give you my name, but God
+bless you!--As much like Judge Jeffries as the present times will
+permit--May Jeffries' fame and Jeffries' fate on every modern Jeffries
+wait--No parodist, but an admirer of the man who has proved the fallacy of
+the Lawyer's Law, that when a man is his own advocate he has a fool for his
+client--A Mussulman who thinks it would not be an impious libel to parody
+the Koran--May the suspenders of the Habeas Corpus Act be speedily
+suspended--Three times twelve for thrice-tried Hone, who cleared the cases
+himself alone, and won three heats by twelve to one, L1 16s.--A
+conscientious attorney, L1 6s. 8d.--Rev. T. B. Morris, rector of
+Shelfanger, who disapproves of the parodies, but abhors the making an
+affected zeal for religion the pretext for political persecution--A Lawyer
+opposed in principle to {184} Law--For the Hone that set the razor that
+shaved the rats--Rev. Dr. Samuel Parr, who most seriously disapproves of
+all parodies upon the hallowed language of Scripture and the contents of
+the Prayer-book, but acquits Mr. Hone of intentional impiety, admires his
+talents and fortitude, and applauds the good sense and integrity of his
+juries--Religion without hypocrisy, and Law without impartiality--O Law! O
+Law! O Law!
+
+These are specimens of a great many allusive mottoes. The subscription was
+very large, and would have bought a handsome annuity, but Hone employed it
+in the bookselling trade, and did not thrive. His _Everyday Book_[411] and
+his _Apocryphal New Testament_,[412] are useful books. On an annuity he
+would have thriven as an antiquarian writer and collector. It is well that
+the attack upon the right to ridicule Ministers roused a dormant power
+which was equal to the occasion. Hone declared, on his honor, that he had
+never addressed a meeting in his life, nor spoken a word before more than
+twelve persons. Had he--which however could not then be done--employed
+counsel and had a _guilty defense_ made for him, he would very likely have
+been convicted, and the work would have been left to be done by another. No
+question that the parodies disgusted all who reverenced Christianity, and
+who could not separate the serious and the ludicrous, and prevent their
+existence in combination.
+
+My extracts, etc., are from the nineteenth, seventeenth, and sixteenth
+editions of the three trials, which seem to have been contemporaneous (all
+in 1818) as they are made up into one book, with additional title over all,
+and the motto "Thrice the brindled cat hath mew'd." They are published by
+Hone himself, who I should have said was a publisher {185} as well as was
+to be. And though the trials only ended Dec. 20, 1817, the preface attached
+to this common title is dated Jan. 23, 1818.[413]
+
+The spirit which was roused against the false dealing of the Government,
+i.e., the pretense of prosecuting for impiety when all the world knew the
+real offense was, if anything, sedition--was not got up at the moment:
+there had been previous exhibitions of it. For example, in the spring of
+1818 Mr. Russell, a little printer in Birmingham, was indicted for
+publishing the Political Litany[414] on which Hone was afterwards tried. He
+took his witnesses to the summer Warwick assizes, and was told that the
+indictment had been removed by certiorari into the King's Bench. He had
+notice of trial for the spring assizes at Warwick: he took his witnesses
+there, and the trial was postponed by the Crown. He then had notice for the
+summer assizes at Warwick; and so on. The policy seems to have been to wear
+out the obnoxious parties, either by delays or by heaping on trials. The
+Government was odious, and knew it could _not_ get verdicts against
+ridicule, and _could_ get verdicts against impiety. No difficulty was found
+in convicting the sellers of Paine's works, and the like. When Hone was
+held to bail it was seen that a crisis was at hand. All parties in politics
+furnished him with parodies in proof of religious persons having made
+instruments of them. The parodies by Addison and Luther were contributed by
+a Tory lawyer, who was afterwards a judge.
+
+Hone had published, in 1817, tracts of purely political ridicule: _Official
+Account of the Noble Lord's Bite,_[415] _Trial of the Dog for Biting the
+Noble Lord_, etc. These were not touched. After the trials, it is manifest
+that Hone was {186} to be unassailed, do what he might. _The Political
+House that Jack built_, in 1819; _The Man in the Moon_, 1820; _The Queen's
+Matrimonial Ladder_, _Non mi ricordo_, _The R--l Fowls_, 1820; _The
+Political Showman at Home_, with plates by G. Cruickshank,[416] 1821 [he
+did all the plates]; _The Spirit of Despotism_, 1821--would have been
+legitimate marks for prosecution in previous years. The biting caricature
+of several of these works are remembered to this day. _The Spirit of
+Despotism_ was a tract of 1795, of which a few copies had been privately
+circulated with great secrecy. Hone reprinted it, and prefixed the
+following address to "Robert Stewart, _alias_ Lord Castlereagh"[417]: "It
+appears to me that if, unhappily, your counsels are allowed much longer to
+prevail in the Brunswick Cabinet, they will bring on a crisis, in which the
+king may be dethroned or the people enslaved. Experience has shown that the
+people will not be enslaved--the alternative is the affair of your
+employers." Hone might say this without notice.
+
+In 1819 Mr. Murray[418] published Lord Byron's _Don Juan_,[419] and Hone
+followed it with _Don John, or Don Juan Unmasked_, a little account of what
+the publisher to the Admiralty was allowed to issue without prosecution.
+The parody on the Commandments was a case very much in point: and Hone
+makes a stinging allusion to the use of the "_unutterable Name_, with a
+profane levity unsurpassed by {187} any other two lines in the English
+language." The lines are
+
+ "'Tis strange--the Hebrew noun which means 'I am,'
+  The English always use to govern d----n."
+
+Hone ends with: "Lord Byron's dedication of 'Don Juan' to Lord Castlereagh
+was suppressed by Mr. Murray from delicacy to Ministers. Q. Why did not Mr.
+Murray suppress Lord Byron's _parody_ on the Ten Commandments? _A._ Because
+it contains nothing in ridicule of Ministers, and therefore nothing that
+_they_ could suppose would lead to the displeasure of Almighty God."
+
+The little matters on which I have dwelt will never appear in history from
+their political importance, except in a few words of result. As a mode of
+thought, silly evasions of all kinds belong to such a work as the present.
+Ignorance, which seats itself in the chair of knowledge, is a mother of
+revolutions in politics, and of unread pamphlets in circle-squaring. From
+1815 to 1830 the question of revolution or no revolution lurked in all our
+English discussions. The high classes must govern; the high classes shall
+not govern; and thereupon issue was to be joined. In 1828-33 the question
+came to issue; and it was, Revolution with or without civil war; choose.
+The choice was wisely made; and the Reform Bill started a new system so
+well dovetailed into the old that the joinings are hardly visible. And now,
+in 1867, the thing is repeated with a marked subsidence of symptoms; and
+the party which has taken the place of the extinct Tories is carrying
+through Parliament a wider extension of the franchise than their opponents
+would have ventured. Napoleon used to say that a decided nose was a sign of
+power: on which it has been remarked that he had good reason to say so
+before the play was done. And so had our country; it was saved from a
+religious war, and from a civil war, by the power of that nose over its
+colleagues. {188}
+
+
+
+THOMAS TAYLOR, THE PLATONIST.
+
+    The Commentaries of Proclus.[420] Translated by Thomas Taylor.[421]
+    London, 1792, 2 vols. 4to.[422]
+
+The reputation of "the Platonist" begins to grow, and will continue to
+grow. The most authentic account is in the _Penny Cyclopaedia_, written by
+one of the few persons who knew him well, and one of the fewer who possess
+all his works. At page lvi of the Introduction is Taylor's notion of the
+way to find the circumference. It is not geometrical, for it proceeds on
+the motion of a point: the words "on account of the simplicity of the
+impulsive motion, such a line must be either straight or circular" will
+suffice to show how Platonic it is. Taylor certainly professed a kind of
+heathenism. D'lsraeli said, "Mr. T. Taylor, the Platonic philosopher and
+the modern Plethon,[423] consonant to that philosophy, professes
+polytheism." Taylor printed this in large type, in a page by itself after
+the dedication, without any disavowal. I have seen the following, Greek and
+translation both, in his handwriting: "[Greek: Pas agathos hei agathos
+ethnikos; kai pas christianos hei christianos kakos.] Every good man, so
+far as he is a good man, is a heathen; and every Christian, so far as he is
+a Christian, is a bad man." Whether Taylor had in his head the Christian of
+the New Testament, or whether he drew from those members of the "religious
+world" who make manifest the religious flesh and the religious devil, {189}
+cannot be decided by us, and perhaps was not known to himself. If a
+heathen, he was a virtuous one.
+
+
+
+A NEW ERA IN FICTION.
+
+(1795.) This is the date of a very remarkable paradox. The religious
+world--to use a name claimed by a doctrinal sect--had long set its face
+against amusing literature, and all works of imagination. Bunyan, Milton,
+and a few others were irresistible; but a long face was pulled at every
+attempt to produce something readable for poor people and _poor children_.
+In 1795, a benevolent association began to circulate the works of a lady
+who had been herself a dramatist, and had nourished a pleasant vein of
+satire in the society of Garrick and his friends; all which is carefully
+suppressed in some biographies. Hannah More's[424] _Cheap Repository
+Tracts_,[425] which were bought by millions of copies, destroyed the
+vicious publications with which the hawkers deluged the country, by the
+simple process of furnishing the hawkers with something more saleable.
+
+_Dramatic fiction_, in which the _characters_ are drawn by themselves, was,
+at the middle of the last century, the monopoly of writers who required
+indecorum, such as Fielding and Smollett. All, or nearly all, which could
+be permitted to the young, was dry narrative, written by people who could
+not make their personages _talk character_; they all spoke {190} alike. The
+author of the _Rambler_[426] is ridiculed, because his young ladies talk
+Johnsonese; but the satirists forget that all the presentable novel-writers
+were equally incompetent; even the author of _Zeluco_ (1789)[427] is the
+strongest possible case in point.
+
+Dr. Moore,[428] the father of the hero of Corunna,[429] with good narrative
+power, some sly humor, and much observation of character, would have been,
+in our day, a writer of the _Peacock_[430] family. Nevertheless, to one who
+is accustomed to our style of things, it is comic to read the dialogue of a
+jealous husband, a suspected wife, a faithless maid-servant, a tool of a
+nurse, a wrong-headed pomposity of a priest, and a sensible physician, all
+talking Dr. Moore through their masks. Certainly an Irish soldier does say
+"by Jasus," and a cockney footman "this here" and "that there"; and this
+and the like is all the painting of characters which is effected out of the
+mouths of the bearers by a narrator of great power. I suspect that some
+novelists repressed their power under a rule that a narrative should
+narrate, and that the dramatic should be confined to the drama.
+
+I make no exception in favor of Miss Burney;[431] though she was the
+forerunner of a new era. Suppose a country {191} in which dress is always
+of one color; suppose an importer who brings in cargoes of blue stuff, red
+stuff, green stuff, etc., and exhibits dresses of these several colors,
+that person is the similitude of Miss Burney. It would be a delightful
+change from a universal dull brown, to see one person all red, another all
+blue, etc.; but the real inventor of pleasant dress would be the one who
+could mix his colors and keep down the bright and gaudy. Miss Burney's
+introduction was so charming, by contrast, that she nailed such men as
+Johnson, Burke, Garrick, etc., to her books. But when a person who has read
+them with keen pleasure in boyhood, as I did, comes back to them after a
+long period, during which he has made acquaintance with the great novelists
+of our century, three-quarters of the pleasure is replaced by wonder that
+he had not seen he was at a puppet-show, not at a drama. Take some
+_labeled_ characters out of our humorists, let them be put together into
+one piece, to speak only as labeled: let there be a Dominie with nothing
+but "Prodigious!" a Dick Swiveller with nothing but adapted quotations; a
+Dr. Folliott with nothing but sneers at Lord Brougham;[432] and the whole
+will pack up into one of Miss Burney's novels.
+
+Maria Edgeworth,[433] Sydney Owenson (Lady Morgan),[434] Jane Austen,[435]
+Walter Scott,[436] etc., are all of our century; as {192} are, I believe,
+all the Minerva Press novels, as they were called, which show some of the
+power in question. Perhaps dramatic talent found its best encouragement in
+the drama itself. But I cannot ascertain that any such power was directed
+at the multitude, whether educated or uneducated, with natural mixture of
+character, under the restraints of decorum, until the use of it by two
+religious writers of the school called "evangelical," Hannah More and
+Rowland Hill.[437] The _Village Dialogues_, though not equal to the
+_Repository Tracts_, are in many parts an approach, and perhaps a copy;
+there is frequently humorous satire, in that most effective form,
+self-display. They were published in 1800, and, partly at least, by the
+Religious Tract Society, the lineal successor of the _Repository_
+association, though knowing nothing about its predecessor. I think it right
+to add that Rowland Hill here mentioned is not the regenerator of the Post
+Office.[438] Some do not distinguish accurately; I have heard of more than
+one who took me to have had a logical controversy with a diplomatist who
+died some years before I was born.
+
+
+
+THE RELIGIOUS TRACT SOCIETY.
+
+A few years ago, an attempt was made by myself and others to collect some
+information about the _Cheap Repository_ (see _Notes and Queries_, 3d
+Series, vi. 241, 290, 353; _Christian Observer_, Dec. 1864, pp. 944-49). It
+appeared that after the Religious Tract Society had existed more than fifty
+years, a friend presented it with a copy of the original prospectus of the
+_Repository_, a thing the existence of which was not known. In this
+prospectus it is announced that from the plan "will be carefully excluded
+whatever is enthusiastic, absurd, or superstitious." The "evangelical"
+{193} party had, from the foundation of the Religious Tract Society,
+regretted that the _Repository Tracts_ "did not contain a fuller statement
+of the great evangelical principles"; while in the prospectus it is also
+stated that "no cause of any particular party is intended to be served by
+it, but general Christianity will be promoted upon practical principles."
+This explains what has often been noticed, that the tracts contain a mild
+form of "evangelical" doctrine, free from that more fervid dogmatism which
+appears in the _Village Dialogues_; and such as H. More's friend, Bishop
+Porteus[439]--a great promoter of the scheme--might approve. The Religious
+Tract Society (in 1863) republished some of H. More's tracts, with
+alterations, additions, and omissions _ad libitum_. This is an improper way
+of dealing with the works of the dead; especially when the reprints are of
+popular works. A small type addition to the preface contains: "Some
+alterations and abridgements have been made to adapt them to the present
+times and the aim of the Religious Tract Society." I think every publicity
+ought to be given to the existence of such a practice; and I reprint what I
+said on the subject in _Notes and Queries_.
+
+Alterations in works which the Society republishes are a necessary part of
+their plan, though such notes as they should judge to be corrective would
+be the best way of proceeding. But the fact of alteration should be very
+distinctly announced on the title of the work itself, not left to a little
+bit of small type at the end of the preface, in the place where trade
+advertisements, or directions to the binder, are often found. And the
+places in which alteration has been made should be pointed out, either by
+marks of omission, when omission is the alteration, or by putting the
+altered sentences in brackets, when change has been made. May any one alter
+the works of the dead at his own discretion? {194} We all know that readers
+in general will take each sentence to be that of the author whose name is
+on the title; so that a correcting republisher _makes use of his author's
+name to teach his own variation_. The tortuous logic of "the trade," which
+is content when "the world" is satisfied, is not easily answered, any more
+than an eel is easily caught; but the Religious Tract Society may be
+_convinced_ [in the old sense] in a sentence. On which course would they
+feel most safe in giving their account to the God of truth? "In your own
+conscience, now?"
+
+I have tracked out a good many of the variations made by the Religious
+Tract Society in the recently published volume of _Repository Tracts_. Most
+of them are doctrinal insertions or amplifications, to the matter of which
+Hannah More would not have objected--all that can be brought against them
+is the want of notice. But I have found two which the respect I have for
+the Religious Tract Society, in spite of much difference on various points,
+must not prevent my designating as paltry. In the story of Mary Wood, a
+kind-hearted clergyman converses with the poor girl who has ruined herself
+by lying. In the original, he "assisted her in the great work of
+repentance;" in the reprint it is to be shown in some detail how he did
+this. He is to begin by pointing out that "the heart is deceitful above all
+things and desperately wicked." Now the clergyman's name is _Heartwell_: so
+to prevent his name from contradicting his doctrine, he is actually cut
+down to _Harwell_. Hannah Moore meant this good man for one of those
+described in Acts xv. 8, 9, and his name was appropriate.
+
+Again, Mr. Flatterwell, in persuasion of Parley the porter to let him into
+the castle, declares that the worst he will do is to "play an innocent game
+of cards just to keep you awake, or sing a cheerful song with the maids."
+Oh fie! Miss Hannah More! and you a single lady too, and a contemporary of
+the virtuous Bowdler![440] Though Flatterwell be an {195} allegory of the
+devil, this is really too indecorous, even for him. Out with the three last
+words! and out it is.
+
+The Society cuts a poor figure before a literary tribunal. Nothing was
+wanted except an admission that the remarks made by me were unanswerable,
+and this was immediately furnished by the Secretary (_N. and Q._, 3d S.,
+vi. 290). In a reply of which six parts out of seven are a very amplified
+statement that the Society did not intend to reprint _all_ Hannah More's
+tracts, the remaining seventh is as follows:
+
+"I am not careful [perhaps this should be _careful not_] to notice
+Professor De Morgan's objections to the changes in 'Mary Wood' or 'Parley
+the Porter,' but would merely reiterate that the tracts were neither
+designed nor announced to be 'reprints' of the originals [design is only
+known to the designers; as to announcement, the title is ''Tis all for the
+best, The Shepherd of Salisbury Plain, and other narratives by Hannah
+More']; and much less [this must be _careful not_; further removed from
+answer than _not careful_] can I occupy your space by a treatise on the
+Professor's question: 'May any one alter the works of the dead at his own
+discretion?'"
+
+To which I say: Thanks for help!
+
+I predict that Hannah More's _Cheap Repository Tracts_ will somewhat
+resemble the _Pilgrim's Progress_ in their fate. Written for the cottage,
+and long remaining in their original position, they will become classical
+works of their kind. Most assuredly this will happen if my assertion cannot
+be upset, namely, that they contain the first specimens of fiction
+addressed to the world at large, and widely circulated, in which
+dramatic--as distinguished from puppet--power is shown, and without
+indecorum.
+
+{196}
+
+According to some statements I have seen, but which I have not verified,
+other publishing bodies, such as the Christian Knowledge Society, have
+taken the same liberty with the names of the dead as the Religious Tract
+Society. If it be so, the impropriety is the work of the smaller spirits
+who have not been sufficiently overlooked. There must be an overwhelming
+majority in the higher councils to feel that, whenever _altered_ works are
+published, _the fact of alteration should be made as prominent as the name
+of the author_. Everything short of this is suppression of truth, and will
+ultimately destroy the credit of the Society. Equally necessary is it that
+the alterations should be noted. When it comes to be known that the author
+before him is altered, he knows not where nor how nor by whom, the lowest
+reader will lose his interest.
+
+
+
+A TRIBUTE TO WILLIAM FREND.
+
+    The principles of Algebra. By William Frend.[441] London, 1796, 8vo.
+    Second Part, 1799.
+
+This Algebra, says Dr. Peacock,[442] shows "great distrust {197} of the
+results of algebraical science which were in existence at the time when it
+was written." Truly it does; for, as Dr. Peacock had shown by full
+citation, it makes war of extermination upon all that distinguishes algebra
+from arithmetic. Robert Simson[443] and Baron Maseres[444] were Mr. Frend's
+predecessors in this opinion.
+
+The genuine respect which I entertained for my father-in-law did not
+prevent my canvassing with perfect freedom his anti-algebraical and
+anti-Newtonian opinions, in a long obituary memoir read at the Astronomical
+Society in February 1842, which was written by me. It was copied into the
+_Athenaeum_ of March 19. It must be said that if the manner in which algebra
+_was_ presented to the learner had been true algebra, he would have been
+right: and if he had confined himself to protesting against the imposition
+of attraction as a fundamental part of the existence of matter, he would
+have been in unity with a great many, including Newton himself. I wish he
+had preferred amendment to rejection when he was a college tutor: he wrote
+and spoke English with a clearness which is seldom equaled.
+
+His anti-Newtonian discussions are confined to the preliminary chapters of
+his _Evening Amusements_,[445] a series of astronomical lessons in nineteen
+volumes, following the moon through a period of the golden numbers.
+
+There is a mistake about him which can never be destroyed. It is constantly
+said that, at his celebrated trial in 1792, for sedition and opposition to
+the Liturgy, etc., he was _expelled_ from the University. He was
+_banished_. People cannot see the difference; but it made all the
+difference to {198} Mr. Frend. He held his fellowship and its profits till
+his marriage in 1808, and was a member of the University and of its Senate
+till his death in 1841, as any Cambridge Calendar up to 1841 will show.
+That they would have expelled him if they could, is perfectly true; and
+there is a funny story--also perfectly true--about their first proceedings
+being under a statute which would have given the power, had it not been
+discovered during the proceedings that the statute did not exist. It had
+come so near to existence as to be entered into the Vice-Chancellor's book
+for his signature, which it wanted, as was not seen till Mr. Frend exposed
+it: in fact, the statute had never actually passed.
+
+There is an absurd mistake in Gunning's[446] _Reminiscences of Cambridge_.
+In quoting a passage of Mr. Frend's pamphlet, which was very obnoxious to
+the existing Government, it is printed that the poor market-women
+complained that they were to be _scotched_ a quarter of their wages by
+taxation; and attention is called to the word by its being three times
+printed in italics. In the pamphlet it is "sconced"; that very common old
+word for fined or mulcted.
+
+Lord Lyndhurst,[447] who has [1863] just passed away under a load of years
+and honors, was Mr. Frend's private pupil at Cambridge. At the time of the
+celebrated trial, he and two others amused themselves, and vented the
+feeling which was very strong among the undergraduates, by chalking the
+walls of Cambridge with "Frend for ever!" While thus engaged in what, using
+the term legally, we are probably to call his first publication, he and his
+friends were surprised by the proctors. Flight and chase followed of
+course: Copley and one of the others, Serjeant Rough,[448] escaped: the
+{199} third, whose name I forget, but who afterwards, I have been told was
+a bishop,[449] being lame, was captured and impositioned. Looking at the
+Cambridge Calendar to verify the fact that Copley was an undergraduate at
+the time, I find that there are but two other men in the list of honors of
+his year whose names are now widely remembered. And they were both
+celebrated schoolmasters; Butler[450] of Harrow, and Tate[451] of Richmond.
+
+But Mr. Frend had another noted pupil. I once had a conversation with a
+very remarkable man, who was generally called "Place,[452] the tailor," but
+who was politician, political economist, etc., etc. He sat in the room
+above his shop--he was then a thriving master tailor at Charing
+Cross--surrounded by books enough for nine, to shame a proverb. The blue
+books alone, cut up into strips, would have measured Great Britain for
+oh-no-we-never-mention-'ems, the Highlands included. I cannot find a
+biography of this worthy and able man. I happened to mention William Frend,
+and he said, "Ah! my old master, as I always call him. Many and many a
+time, and year after year, did he come in every {200} now and then to give
+me instruction, while I was sitting on the board, working for my living,
+you know."
+
+Place, who really was a sound economist, is joined with Cobbett, because
+they were together at one time, and because he was, in 1800, etc., a great
+Radical. But for Cobbett he had a great contempt. He told me the following
+story. He and others were advising with Cobbett about the defense he was to
+make on a trial for seditious libel which was coming on. Said Place, "You
+must put in the letters you have received from Ministers, members of the
+Commons from the Speaker downwards, etc., about your Register, and their
+wish to have subjects noted. You must then ask the jury whether a person so
+addressed must be considered as a common sower of sedition, etc. You will
+be acquitted; nay, if your intention should get about, very likely they
+will manage to stop proceedings." Cobbett was too much disturbed to listen;
+he walked about the room ejaculating "D---- the prison!" and the like. He
+had not the sense to follow the advice, and was convicted.
+
+Cobbett, to go on with the chain, was a political acrobat, ready for any
+kind of posture. A friend of mine gave me several times an account of a
+mission to him. A Tory member--those who know the old Tory world may look
+for his initials in initials of two consecutive words of "Pay his money
+with interest"--who was, of course, a political opponent, thought Cobbett
+had been hardly used, and determined to subscribe handsomely towards the
+expenses he was incurring as a candidate. My friend was commissioned to
+hand over the money--a bag of sovereigns, that notes might not be traced.
+He went into Cobbett's committee-room, told the patriot his errand, and put
+the money on the table. "And to whom, sir, am I indebted?" said Cobbett.
+"The donor," was the answer, "is Mr. Andrew Theophilus Smith," or some such
+unlikely pair of baptismals. "Ah!" said Cobbett, "I have known Mr. A. T. S.
+a long time! he was always a true friend of his country!" {201}
+
+To return to Place. He is a noted instance of the advantage of our jury
+system, which never asks a man's politics, etc. The late King of Hanover,
+when Duke of Cumberland, being unpopular, was brought under unjust
+suspicions by the suicide of his valet: he must have seduced the wife and
+murdered the husband. The charges were as absurd as those brought against
+the Englishman in the Frenchman's attempt at satirical verses upon him:
+
+ "The Englishman is a very bad man;
+  He drink the beer and he steal the can:
+  He kiss the wife and he beat the man;
+  And the Englishman is a very G---- d----."
+
+The charges were revived in a much later day, and the defense might have
+given some trouble. But Place, who had been the foreman at the inquest,
+came forward, and settled the question in a few lines. Every one knew that
+the old Radical was quite free of all disposition to suppress truth from
+wish to curry favor with royalty.
+
+John Speed,[453] the author of the _English History_,[454] (1632) which
+Bishop Nicolson[455] calls the best chronicle extant, was a man, like
+Place, of no education, but what he gave himself. The bishop says he would
+have done better if he had a better training: but what, he adds, could have
+been expected from a tailor! This Speed was, as well as Place. But he was
+{202} released from manual labor by Sir Fulk Grevil,[456] who enabled him
+to study.
+
+
+
+A STORY ON SIMSON.
+
+I have elsewhere noticed that those who oppose the mysteries of algebra do
+not ridicule them; this I want the cyclometers to do. Of the three who
+wrote against the great point, the negative quantity, and the uses of 0
+which are connected with it, only one could fire a squib. That Robert
+Simson[457] should do such a thing will be judged impossible by all who
+admit tradition. I do not vouch for the following; I give it as a proof of
+the impression which prevailed about him:
+
+He used to sit at his open window on the ground floor, as deep in geometry
+as a Robert Simson ought to be. Here he would be accosted by beggars, to
+whom he generally gave a trifle, he roused himself to hear a few words of
+the story, made his donation, and instantly dropped down into his depths.
+Some wags one day stopped a mendicant who was on his way to the window with
+"Now, my man, do as we tell you, and you will get something from that
+gentleman, and a shilling from us besides. You will go and say you are in
+distress, he will ask you who you are, and you will say you are Robert
+Simson, son of John Simson of Kirktonhill." The man did as he was told;
+Simson quietly gave him a coin, and dropped off. The wags watched a little,
+and saw him rouse himself again, and exclaim "Robert Simson, son of John
+Simson of Kirktonhill! why, that is myself. That man must be an impostor."
+Lord Brougham tells the same story, with some difference of details.
+
+{203}
+
+
+
+BARON MASERES.
+
+Baron Maseres[458] was, as a writer, dry; those who knew his writings will
+feel that he seldom could have taken in a joke or issued a pun. Maseres was
+the fourth wrangler of 1752, and first Chancellor's medallist (or highest
+in classics); his second was Porteus[459] (afterward Bishop of London).
+Waring[460] came five years after him: he could not get Maseres through the
+second page of his first book on algebra; a negative quantity stood like a
+lion in the way. In 1758 he published his _Dissertation on the Use of the
+Negative Sign_,[461] 4to. There are some who care little about + and -, who
+would give it house-room for the sake of the four words "Printed by Samuel
+Richardson."
+
+Maseres speaks as follows: "A single quantity can never be marked with
+either of those signs, or considered as either affirmative or negative; for
+if any single quantity, as b, is marked either with the sign + or with the
+sign - without assigning some other quantity, as a, to which it is to be
+added, or from which it is to be subtracted, the mark will have no meaning
+or signification: thus if it be said that the square of -5, or the product
+of -5 into -5, is equal to +25, such an assertion must either signify no
+more than that 5 times 5 is equal to 25 without any regard to the signs, or
+it must be mere nonsense and unintelligible jargon. I speak according to
+the foregoing definition, by which the affirmativeness or negativeness of
+any quantity implies a relation to another quantity of the same kind to
+which it {204} is added, or from which it is subtracted; for it may perhaps
+be very clear and intelligible to those who have formed to themselves some
+other idea of affirmative and negative quantities different from that above
+defined."
+
+Nothing can be more correct, or more identically logical: +5 and -5,
+standing alone, are jargon if +5 and -5 are to be understood as without
+reference to another quantity. But those who have "formed to themselves
+some other idea" see meaning enough. The great difficulty of the opponents
+of algebra lay in want of power or will to see extension of terms. Maseres
+is right when he implies that extension, accompanied by its refusal, makes
+jargon. One of my paradoxers was present at a meeting of the Royal Society
+(in 1864, I think) and asked permission to make some remarks upon a paper.
+He rambled into other things, and, naming me, said that I had written a
+book in which two sides of a triangle are pronounced _equal_ to the
+third.[462] So they are, in the sense in which the word is used in complete
+algebra; in which A + B = C makes A, B, C, three sides of a triangle, and
+declares that going over A and B, one after the other, is equivalent, in
+change of place, to going over C at once. My critic, who might, if he
+pleased, have objected to extension, insisted upon reading me in unextended
+meaning.
+
+On the other hand, it must be said that those who wrote on the other idea
+wrote very obscurely about it and justified Des Cartes (_De Methodo_)[463]
+when he said: "Algebram vero, ut solet doceri, animadverti certis regulis
+et numerandi formulis ita esse contentam, ut videatur potius ars quaedam
+confusa, cujus usu ingenium quodam modo turbatur et obscuratur, quam
+scientia qua excolatur et perspicacius {205} reddatur."[464] Maseres wrote
+this sentence on the title of his own work, now before me; he would have
+made it his motto if he had found it earlier.
+
+There is, I believe, in Cobbett's _Annual Register_,[465] an account of an
+interview between Maseres and Cobbett when in prison.
+
+The conversation of Maseres was lively, and full of serious anecdote: but
+only one attempt at humorous satire is recorded of him; it is an
+instructive one. He was born in 1731 (Dec. 15), and his father was a
+refugee. French was the language of the house, with the pronunciation of
+the time of Louis XIV. He lived until 1824 (May 19), and saw the race of
+refugees who were driven out by the first Revolution. Their pronunciation
+differed greatly from his own; and he used to amuse himself by mimicking
+them. Those who heard him and them had the two schools of pronunciation
+before them at once; a thing which seldom happens. It might even yet be
+worth while to examine the Canadian pronunciation.
+
+Maseres went as Attorney-General to Quebec; and was appointed Cursitor
+Baron of our Exchequer in 1773. There is a curious story about his mission
+to Canada, which I have heard as good tradition, but have never seen in
+print. The reader shall have it as cheap as I; and I confess I rather
+believe it. Maseres was inveterately honest; he could not, at the bar, bear
+to see his own client victorious, when he knew his cause was a bad one. On
+a certain occasion he was in a cause which he knew would go against him if
+a certain case were quoted. Neither the judge nor the opposite counsel
+seemed to remember this case, and Maseres could not help dropping an
+allusion which brought it out. {206} His business as a barrister fell off,
+of course. Some time after, Mr. Pitt (Chatham) wanted a lawyer to send to
+Canada on a private mission, and wanted a _very honest man_. Some one
+mentioned Maseres, and told the above story: Pitt saw that he had got the
+man he wanted. The mission was satisfactorily performed, and Maseres
+remained as Attorney-General.
+
+The _Doctrine of Life Annuities_[466] (4to, 726 pages, 1783) is a strange
+paradox. Its size, the heavy dissertations on the national debt, and the
+depth of algebra supposed known, put it out of the question as an
+elementary work, and it is unfitted for the higher student by its elaborate
+attempt at elementary character, shown in its rejection of forms derived
+from chances in favor of _the average_, and its exhibition of the separate
+values of the years of an annuity, as arithmetical illustrations. It is a
+climax of unsaleability, unreadability, and inutility. For intrinsic
+nullity of interest, and dilution of little matter with much ink, I can
+compare this book to nothing but that of Claude de St. Martin, elsewhere
+mentioned, or the lectures _On the Nature and Properties of Logarithms_, by
+James Little,[467] Dublin, 1830, 8vo. (254 heavy pages of many words and
+few symbols), a wonderful weight of weariness.
+
+The stock of this work on annuities, very little diminished, was given by
+the author to William Frend, who paid warehouse room for it until about
+1835, when he consulted me as to its disposal. As no publisher could be
+found who would take it as a gift, for any purpose of sale, it was
+consigned, all but a few copies, to a buyer of waste paper.
+
+Baron Maseres's republications are well known: the _Scriptores
+Logarithmici_[468] is a set of valuable reprints, mixed {207} with much
+which might better have entered into another collection. It is not so well
+known that there is a volume of optical reprints, _Scriptores Optici_,
+London, 1823, 4to, edited for the veteran of ninety-two by Mr. Babbage[469]
+at twenty-nine. This excellent volume contains James Gregory, Des Cartes,
+Halley, Barrow, and the optical writings of Huyghens, the _Principia_ of
+the undulatory theory. It also contains, by the sort of whim in which such
+men as Maseres, myself, and some others are apt to indulge, a reprint of
+"The great new Art of weighing Vanity,"[470] by M. Patrick Mathers,
+Arch-Bedel to the University of St. Andrews, Glasgow, 1672. Professor
+Sinclair,[471] of Glasgow, a good man at clearing mines of the water which
+they did not want, and furnishing cities with water which they did want,
+seems to have written absurdly about hydrostatics, and to have attacked a
+certain Sanders,[472] M.A. So Sanders, assisted by James Gregory, published
+a heavy bit of jocosity about him. This story of the authorship rested on a
+note made in his {208} copy by Robert Gray, M.D.; but it has since been
+fully confirmed by a letter of James Gregory to Collins, in the
+Macclesfield Correspondence. "There is one Master Sinclair, who did write
+the _Ars Magna et Nova_,[473] a pitiful ignorant fellow, who hath lately
+written horrid nonsense in the hydrostatics, and hath abused a master in
+the University, one Mr. Sanders, in print. This Mr. Sanders ... is resolved
+to cause the Bedel of the University to write against him.... We resolve to
+make excellent sport with him."
+
+On this I make two remarks: First, I have learned from experience that old
+notes, made in books by their possessors, are statements of high authority:
+they are almost always confirmed. I do not receive them without hesitation;
+but I believe that of all the statements about books which rest on one
+authority, there is a larger percentage of truth in the written word than
+in the printed word. Secondly, I mourn to think that when the New Zealander
+picks up his old copy of this book, and reads it by the associations of his
+own day, he may, in spite of the many assurances I have received that my
+_Athenaeum Budget_ was amusing, feel me to be as heavy as I feel James
+Gregory and Sanders. But he will see that I knew what was coming, which
+Gregory did not.
+
+
+
+MR. FREND'S BURLESQUE.
+
+It was left for Mr. Frend to prove that an impugner of algebra could
+attempt ridicule. He was, in 1803, editor of a periodical _The Gentleman's
+Monthly Miscellany_, which lasted a few months.[474] To this, among other
+things, he contributed the following, in burlesque of the use made of 0, to
+which he objected.[475] The imitation of Rabelais, a writer {209} in whom
+he delighted, is good: to those who have never dipped, it may give such a
+notion as they would not easily get elsewhere. The point of the satire is
+not so good. But in truth it is not easy to make pungent scoffs upon what
+is common sense to all mankind. Who can laugh with effect at six times
+nothing is nothing, as false or unintelligible? In an article intended for
+that undistinguishing know-0 the "general reader," there would have been no
+force of satire, if _division_ by 0 had been separated from multiplication
+by the same.
+
+I have followed the above by another squib, by the same author, on the
+English language. The satire is covertly aimed at theological phraseology;
+and any one who watches this subject will see that it is a very just
+observation that the Greek words are not boiled enough.
+
+PANTAGRUEL'S DECISION _of the_ QUESTION _about_ NOTHING.
+
+"Pantagruel determined to have a snug afternoon with Epistemon and Panurge.
+Dinner was ordered to be set in a small parlor, and a particular batch of
+Hermitage with some choice Burgundy to be drawn from a remote corner of the
+cellar upon the occasion. By way of lunch, about an hour before dinner,
+Pantagruel was composing his stomach with German sausages, reindeer's
+tongues, oysters, brawn, and half a dozen different sorts of English beer
+just come into fashion, when a most thundering knocking was heard at the
+great gate, and from the noise they expected it to announce the arrival at
+least of the First Consul, or king Gargantua. Panurge was sent to
+reconnoiter, and after a quarter of an hour's absence, returned with the
+news that the University of Pontemaca was waiting his highness's leisure in
+the great hall, to propound a question which {210} had turned the brains of
+thirty-nine students, and had flung twenty-seven more into a high fever.
+With all my heart, says Pantagruel, and swallowed down three quarts of
+Burton ale; but remember, it wants but an hour of dinner time, and the
+question must be asked in as few words as possible; for I cannot deprive
+myself of the pleasure I expected to enjoy in the company of my good
+friends for a set of mad-headed masters. I wish brother John was here to
+settle these matters with the black gentry.
+
+"Having said or rather growled this, he proceeded to the hall of ceremony,
+and mounted his throne; Epistemon and Panurge standing on each side, but
+two steps below him. Then advanced to the throne the three beadles of the
+University of Pontemaca with their silver staves on their shoulders, and
+velvet caps on their heads, and they were followed by three times three
+doctors, and thrice three times three masters of art; for everything was
+done in Pontemaca by the number three, and on this account the address was
+written on parchment, one foot in breadth, and thrice three times thrice
+three feet in length. The beadles struck the ground with their heads and
+their staves three times in approaching the throne; the doctors struck the
+ground with their heads thrice three times, and the masters did the same
+thrice each time, beating the ground with their heads thrice three times.
+This was the accustomed form of approaching the throne, time out of mind,
+and it was said to be emblematic of the usual prostration of science to the
+throne of greatness.
+
+"The mathematical professor, after having spit, and hawked, and cleared his
+throat, and blown his nose on a handkerchief lent to him, for he had
+forgotten to bring his own, began to read the address. In this he was
+assisted by three masters of arts, one of whom, with a silver pen, pointed
+out the stops; the second with a small stick rapped his knuckles when he
+was to raise or lower his voice; and a third pulled his hair behind when he
+was to look Pantagruel in the face. Pantagruel began to chafe like a lion:
+{211} he turned first on one side, then on the other: he listened and
+groaned, and groaned and listened, and was in the utmost cogitabundity of
+cogitation. His countenance began to brighten, when, at the end of an hour,
+the reader stammered out these words:
+
+"'It has therefore been most clearly proved that as all matter may be
+divided into parts infinitely smaller than the infinitely smallest part of
+the infinitesimal of nothing, so nothing has all the properties of
+something, and may become, by just and lawful right, susceptible of
+addition, subtraction, multiplication, division, squaring, and cubing: that
+it is to all intents and purposes as good as anything that has been, is, or
+can be taught in the nine universities of the land, and to deprive it of
+its rights is a most cruel innovation and usurpation, tending to destroy
+all just subordination in the world, making all universities superfluous,
+leveling vice-chancellors, doctors, and proctors, masters, bachelors, and
+scholars, to the mean and contemptible state of butchers and
+tallow-chandlers, bricklayers and chimney-sweepers, who, if it were not for
+these learned mysteries, might think that they knew as much as their
+betters. Every one then, who has the good of science at heart, must pray
+for the interference of his highness to put a stop to all the disputes
+about nothing, and by his decision to convince all gainsayers that the
+science of nothing is taught in the best manner in the universities, to the
+great edification and improvement of all the youth in the land.'
+
+"Here Pantagruel whispered in the ear of Panurge, who nodded to Epistemon,
+and they two left the assembly, and did not return for an hour, till the
+orator had finished his task. The three beadles had thrice struck the
+ground with their heads and staves, the doctors had finished their
+compliments, and the masters were making their twenty-seven prostrations.
+Epistemon and Panurge went up to Pantagruel, whom they found fast asleep
+and snoring; nor could he be roused but by as many tugs as there had been
+{212} bowings from the corps of learning. At last he opened his eyes, gave
+a good stretch, made half a dozen yawns, and called for a stoup of wine. I
+thank you, my masters, says he; so sound a nap I have not had since I came
+from the island of Priestfolly. Have you dined, my masters? They answered
+the question by as many bows as at entrance; but his highness left them to
+the care of Panurge, and retired to the little parlor with Epistemon, where
+they burst into a fit of laughter, declaring that this learned Baragouin
+about nothing was just as intelligible as the lawyer's Galimathias. Panurge
+conducted the learned body into a large saloon, and each in his way hearing
+a clattering of plates and glasses, congratulated himself on his
+approaching good cheer. There they were left by Panurge, who took his chair
+by Pantagruel just as the soup was removed, but he made up for the want of
+that part of his dinner by a pint of champagne. The learning of the
+university had whetted their appetites; what they each ate it is needless
+to recite; good wine, good stories, and hearty laughs went round, and three
+hours elapsed before one soul of them recollected the hungry students of
+Pontemaca.
+
+"Epistemon reminded them of the business in hand, and orders were given for
+a fresh dozen of hermitage to be put upon table, and the royal attendants
+to get ready. As soon as the dozen bottles were emptied, Pantagruel rose
+from table, the royal trumpets sounded, and he was accompanied by the great
+officers of his court into the large dining hall, where was a table with
+forty-two covers. Pantagruel sat at the head, Epistemon at the bottom, and
+Panurge in the middle, opposite an immense silver tureen, which would hold
+fifty gallons of soup. The wise men of Pontemaca then took their seats
+according to seniority. Every countenance glistened with delight; the music
+struck up; the dishes were uncovered. Panurge had enough to do to handle
+the immense silver ladle: Pantagruel and Epistemon had no time for eating,
+they were fully employed in carving. The bill {213} of fare announced the
+names of a hundred different dishes. From Panurge's ladle came into the
+soup plate as much as he took every time out of the tureen; and as it was
+the rule of the court that every one should appear to eat, as long as he
+sat at table, there was the clattering of nine and thirty spoons against
+the silver soup-plates for a quarter of an hour. They were then removed,
+and knives and forks were in motion for half an hour. Glasses were
+continually handed round in the mean time, and then everything was removed,
+except the great tureen of soup. The second course was now served up, in
+dispatching which half an hour was consumed; and at the conclusion the wise
+men of Pontemaca had just as much in their stomachs as Pantagruel in his
+head from their address: for nothing was cooked up for them in every
+possible shape that Panurge could devise.
+
+"Wine-glasses, large decanters, fruit dishes, and plates were now set on.
+Pantagruel and Epistemon alternately gave bumper toasts: the University of
+Pontemaca, the eye of the world, the mother of taste and good sense and
+universal learning, the patroness of utility, and the second only to
+Pantagruel in wisdom and virtue (for these were her titles), was drank
+standing with thrice three times three, and huzzas and clattering of
+glasses; but to such wine the wise men of Pontemaca had not been
+accustomed; and though Pantagruel did not suffer one to rise from table
+till the eighty-first glass had been emptied, not even the weakest headed
+master of arts felt his head in the least indisposed. The decanters indeed
+were often removed, but they were brought back replenished, filled always
+with nothing.
+
+"Silence was now proclaimed, and in a trice Panurge leaped into the large
+silver tureen. Thence he made his bows to Pantagruel and the whole company,
+and commenced an oration of signs, which lasted an hour and a half, and in
+which he went over all the matter contained in the Pontemaca address; and
+though the wise men looked very serious during the whole time, Pantagruel
+himself and his whole {214} court could not help indulging in repeated
+bursts of laughter. It was universally acknowledged that he excelled
+himself, and that the arguments by which he beat the English masters of
+arts at Paris were nothing to the exquisite selection of attitudes which he
+this day assumed. The greatest shouts of applause were excited when he was
+running thrice round the tureen on its rim, with his left hand holding his
+nose, and the other exercising itself nine and thirty times on his back. In
+this attitude he concluded with his back to the professor of mathematics;
+and at the instant he gave his last flap, by a sudden jump, and turning
+heels over head in the air, he presented himself face to face to the
+professor, and standing on his left leg, with his left hand holding his
+nose, he presented to him, in a white satin bag, Pantagruel's royal decree.
+Then advancing his right leg, he fixed it on the professor's head, and
+after three turns, in which he clapped his sides with both hands thrice
+three times, down he leaped, and Pantagruel, Epistemon, and himself took
+their leaves of the wise men of Pontemaca.
+
+"The wise men now retired, and by royal orders were accompanied by a guard,
+and according to the etiquette of the court, no one having a royal order
+could stop at any public house till it was delivered. The procession
+arrived at Pontemaca at nine o'clock the next morning, and the sound of
+bells from every church and college announced their arrival. The
+congregation was assembled; the royal decree was saluted in the same manner
+as if his highness had been there in person; and after the proper
+ceremonies had been performed, the satin bag was opened exactly at twelve
+o'clock. A finely emblazoned roll was drawn forth, and the public orator
+read to the gaping assembly the following words:
+
+"'They who can make something out of nothing shall have nothing to eat at
+the court of--PANTAGRUEL.'" {215}
+
+ORIGIN _of the_ ENGLISH LANGUAGE, _related by a_ SWEDE.
+
+"Some months ago in a party in Holland, consisting of natives of various
+countries, the merit of their respective languages became a topic of
+conversation. A Swede, who had been a great traveler, and could converse in
+most of the modern languages of Europe, laughed very heartily at an
+Englishman, who had ventured to speak in praise of the tongue of his dear
+country. I never had any trouble, says he, in learning English. To my very
+great surprise, the moment I sat foot on shore at Gravesend, I found out,
+that I could understand, with very little trouble, every word that was
+said. It was a mere jargon, made up of German, French, and Italian, with
+now and then a word from the Spanish, Latin or Greek. I had only to bring
+my mouth to their mode of speaking, which was done with ease in less than a
+week, and I was everywhere taken for a true-born Englishman; a privilege by
+the way of no small importance in a country, where each man, God knows why,
+thinks his foggy island superior to any other part of the world: and though
+his door is never free from some dun or other coming for a tax, and if he
+steps out of it he is sure to be knocked down or to have his pocket picked,
+yet he has the insolence to think every foreigner a miserable slave, and
+his country the seat of everything wretched. They may talk of liberty as
+they please, but Spain or Turkey for my money: barring the bowstring and
+the inquisition, they are the most comfortable countries under heaven, and
+you need not be afraid of either, if you do not talk of religion and
+politics. I do not see much difference too in this respect in England, for
+when I was there, one of their most eminent men for learning was put in
+prison for a couple of years, and got his death for translating one of
+AEsop's fables into English, which every child in Spain and Turkey is
+taught, as soon as he comes out of his leading strings. Here all the
+company unanimously cried out against the Swede, that it was {216}
+impossible: for in England, the land of liberty, the only thing its worst
+enemies could say against it, was, that they paid for their liberty a much
+greater price than it was worth.--Every man there had a fair trial
+according to laws, which everybody could understand; and the judges were
+cool, patient, discerning men, who never took the part of the crown against
+the prisoner, but gave him every assistance possible for his defense.
+
+"The Swede was borne down, but not convinced; and he seemed determined to
+spit out all his venom. Well, says he, at any rate you will not deny that
+the English have not got a language of their own, and that they came by it
+in a very odd way. Of this at least I am certain, for the whole history was
+related to me by a witch in Lapland, whilst I was bargaining for a wind.
+Here the company were all in unison again for the story.
+
+"In ancient times, said the old hag, the English occupied a spot in
+Tartary, where they lived sulkily by themselves, unknowing and unknown. By
+a great convulsion that took place in China, the inhabitants of that and
+the adjoining parts of Tartary were driven from their seats, and after
+various wanderings took up their abode in Germany. During this time nobody
+could understand the English, for they did not talk, but hissed like so
+many snakes. The poor people felt uneasy under this circumstance, and in
+one of their parliaments, or rather hissing meetings, it was determined to
+seek a remedy: and an embassy was sent to some of our sisterhood then
+living on Mount Hecla. They were put to a nonplus, and summoned the Devil
+to their relief. To him the English presented their petitions, and
+explained their sad case; and he, upon certain conditions, promised to
+befriend them, and to give them a language. The poor Devil was little aware
+of what he had promised; but he is, as all the world knows, a man of too
+much honor to break his word. Up and down the world then he went in quest
+of this new language: visited all the universities, and all {217} the
+schools, and all the courts of law, and all the play-houses, and all the
+prisons; never was poor devil so fagged. It would have made your heart
+bleed to see him. Thrice did he go round the earth in every parallel of
+latitude; and at last, wearied and jaded out, back came he to Hecla in
+despair, and would have thrown himself into the volcano, if he had been
+made of combustible materials. Luckily at that time our sisters were
+engaged in settling the balance of Europe; and whilst they were looking
+over projects, and counter-projects, and ultimatums, and post ultimatums,
+the poor Devil, unable to assist them was groaning in a corner and
+ruminating over his sad condition.
+
+"On a sudden, a hellish joy overspread his countenance; up he jumped, and,
+like Archimedes of old, ran like a madman amongst the throng, turning over
+tables, and papers, and witches, roaring out for a full hour together
+nothing else but 'tis found, 'tis found! Away were sent the sisterhood in
+every direction, some to traverse all the corners of the earth, and others
+to prepare a larger caldron than had ever yet been set upon Hecla. The
+affairs of Europe were at a stand: its balance was thrown aside; prime
+ministers and ambassadors were everywhere in the utmost confusion; and, by
+the way, they have never been able to find the balance since that time, and
+all the fine speeches upon the subject, with which your newspapers are
+every now and then filled, are all mere hocus-pocus and rhodomontade.
+However, the caldron was soon set on, and the air was darkened by witches
+riding on broomsticks, bringing a couple of folios under each arm, and
+across each shoulder. I remember the time exactly: it was just as the
+council of Nice had broken up, so that they got books and papers there dog
+cheap; but it was a bad thing for the poor English, as these were the worst
+materials that entered into the caldron. Besides, as the Devil wanted some
+amusement, and had not seen an account of the transactions of this famous
+council, he had all the books brought from it laid before him, and split
+his sides almost {218} with laughing, whilst he was reading the speeches
+and decrees of so many of his old friends and acquaintances. All this while
+the witches were depositing their loads in the great caldron. There were
+books from the Dalai Lama, and from China: there were books from the
+Hindoos, and tallies from the Caffres: there were paintings from Mexico,
+and rocks of hieroglyphics from Egypt: the last country supplied besides
+the swathings of two thousand mummies, and four-fifths of the famed library
+of Alexandria. Bubble! bubble! toil and trouble! never was a day of more
+labor and anxiety; and if our good master had but flung in the Greek books
+at the proper time, they would have made a complete job of it. He was a
+little too impatient: as the caldron frothed up, he skimmed it off with a
+great ladle, and filled some thousands of our wind-bags with the froth,
+which the English with great joy carried back to their own country. These
+bags were sent to every district: the chiefs first took their fill, and
+then the common people; hence they now speak a language which no foreigner
+can understand, unless he has learned half a dozen other languages; and the
+poor people, not one in ten, understand a third part of what is said to
+them. The hissing, however, they have not entirely got rid of, and every
+seven years, when the Devil, according to agreement, pays them a visit,
+they entertain him at their common halls and county meetings with their
+original language.
+
+"The good-natured old hag told me several other circumstances, relative to
+this curious transaction, which, as there is an Englishman in company, it
+will be prudent to pass over in silence: but I cannot help mentioning one
+thing which she told me as a very great secret. You know, says she to me,
+that the English have more religions among them than any other nation in
+Europe, and that there is more teaching and sermonizing with them than in
+any other country. The fact is this; it matters not who gets up to teach
+them, the hard words of the Greek were not sufficiently {219} boiled, and
+whenever they get into a sentence, the poor people's brains are turned, and
+they know no more what the preacher is talking about, than if he harangued
+them in Arabic. Take my word for it if you please; but if not, when you get
+to England, desire the bettermost sort of people that you are acquainted
+with to read to you an act of parliament, which of course is written in the
+clearest and plainest style in which anything can be written, and you will
+find that not one in ten will be able to make tolerable sense of it. The
+language would have been an excellent language, if it had not been for the
+council of Nice, and the words had been well boiled.
+
+"Here the company burst out into a fit of laughter. The Englishman got up
+and shook hands with the Swede: _si non e vero_, said he, _e ben
+trovato_.[476] But, however I may laugh at it here, I would not advise you
+to tell this story on the other side of the water. So here's a bumper to
+Old England for ever, and God save the king."
+
+
+
+ON YOUTHFUL PRODIGIES.
+
+The accounts given of extraordinary children and adolescents frequently
+defy credence.[477] I will give two well-attested instances.
+
+The celebrated mathematician Alexis Claude Clairault (now Clairaut)[478]
+was certainly born in May, 1713. His treatise on curves of double curvature
+(printed in 1731)[479] received {220} the approbation of the Academy of
+Sciences, August 23, 1729. Fontenelle, in his certificate of this, calls
+the author sixteen years of age, and does not strive to exaggerate the
+wonder, as he might have done, by reminding his readers that this work, of
+original and sustained mathematical investigation, must have been coming
+from the pen at the ages of fourteen and fifteen. The truth was, as
+attested by De Molieres,[480] Clairaut had given public proofs of his power
+at twelve years old. His age being thus publicly certified, all doubt is
+removed: say he had been--though great wonder would still have been
+left--twenty-one instead of sixteen, his appearance, and the remembrances
+of his friends, schoolfellows, etc., would have made it utterly hopeless to
+knock off five years of that age while he was on view in Paris as a young
+lion. De Molieres, who examined the work officially for the _Garde des
+Sceaux_, is transported beyond the bounds of official gravity, and says
+that it "ne merite pas seulement d'etre imprime, mais d'etre admire comme
+un prodige d'imagination, de conception, et de capacite."[481]
+
+That Blaise Pascal was born in June, 1623, is perfectly well established
+and uncontested.[482] That he wrote his conic sections at the age of
+sixteen might be difficult to establish, though tolerably well attested, if
+it were not for {221} one circumstance, for the book was not published. The
+celebrated theorem, "Pascal's hexagram,"[483] makes all the rest come very
+easy. Now Curabelle,[484] in a work published in 1644, sneers at
+Desargues,[485] whom he quotes, for having, in 1642, deferred a discussion
+until "cette grande proposition nommee le Pascale verra le jour."[486] That
+is, by the time Pascal was nineteen, the _hexagram_ was circulating under a
+name derived from the author. The common story about Pascal, given by his
+sister,[487] is an absurdity which no doubt has prejudiced many against
+tales of early proficiency. He is made, when quite a boy, to invent
+geometry _in the order of Euclid's propositions_: as if that order were
+natural sequence of investigation. The hexagram at ten years old would be a
+hundred times less unlikely.
+
+The instances named are painfully astonishing: I give one which has fallen
+out of sight, because it will preserve an imperfect biography. John
+Wilson[488] is Wilson of that {222} Ilk, that is, of "Wilson's Theorem." It
+is this: if _p_ be a prime number, the product of all the numbers up to
+_p_-1, increased by 1, is divisible without remainder by _p_. All
+mathematicians know this as Wilson's theorem, but few know who Wilson was.
+He was born August 6, 1741, at the Howe in Applethwaite, and he was heir to
+a small estate at Troutbeck in Westmoreland. He was sent to Peterhouse, at
+Cambridge, and while an undergraduate was considered stronger in algebra
+than any one in the University, except Professor Waring, one of the most
+powerful algebraists of the century.[489] He was the senior wrangler of
+1761, and was then for some time a private tutor. When Paley,[490] then in
+his third year, determined to make a push for the senior wranglership,
+which he got, Wilson was recommended to him as a tutor. Both were ardent in
+their work, except that sometimes Paley, when he came for his lesson, would
+find "Gone a fishing" written on his tutor's outer door: which was insult
+added to injury, for Paley was very fond of fishing. Wilson soon left
+Cambridge, and went to the bar. He practised on the northern circuit with
+great success; and, one day, while passing his vacation on his little
+property at Troutbeck, he received information, to his great surprise, that
+Lord Thurlow,[491] with whom he had {223} no acquaintance, had recommended
+him to be a Judge of the Court of Common Pleas. He died, Oct. 18, 1793,
+with a very high reputation as a lawyer and a Judge. These facts are partly
+from Meadley's _Life of Paley_,[492] no doubt from Paley himself, partly
+from the _Gentleman's Magazine_, and from an epitaph written by Bishop
+Watson.[493] Wilson did not publish anything: the theorem by which he has
+cut his name in the theory of numbers was communicated to Waring, by whom
+it was published. He married, in 1788, a daughter of Serjeant Adair,[494]
+and left issue. _Had a family_, many will say: but a man and his wife are a
+family, even without children. An actuary may be allowed to be accurate in
+this matter, of which I was reminded by what an actuary wrote of another
+actuary. William Morgan,[495] in the life of his uncle Dr. Richard
+Price,[496] says that the Doctor and his {224} wife were "never blessed
+with an addition to their family." I never met with such accuracy
+elsewhere. Of William Morgan I add that my surname and pursuits have
+sometimes, to my credit be it said, made a confusion between him and me.
+Dates are nothing to the mistaken; the last three years of Morgan's life
+were the first three years of my actuary-life (1830-33). The mistake was to
+my advantage as well as to my credit. I owe to it the acquaintance of one
+of the noblest of the human race, I mean Elizabeth Fry,[497] who came to me
+for advice about a philanthropic design, which involved life questions,
+under a general impression that some Morgan had attended to such
+things.[498]
+
+{225}
+
+
+
+NEWTON AGAIN OVERTHROWN.
+
+    A treatise on the sublime science of heliography, satisfactorily
+    demonstrating our great orb of light, the sun, to be absolutely no
+    other than a body of ice! Overturning all the received systems of the
+    universe hitherto extant; proving the celebrated and indefatigable Sir
+    Isaac Newton, in his theory of the solar system, to be as far distant
+    from the truth, as many of the heathen authors of Greece and Rome. By
+    Charles Palmer,[499] Gent. London, 1798, 8vo.
+
+Mr. Palmer burned some tobacco with a burning glass, saw that a lens of ice
+would do as well, and then says:
+
+"If we admit that the sun could be removed, and a terrestrial body of ice
+placed in its stead, it would produce the same effect. The sun is a
+crystaline body receiving the radiance of God, and operates on this earth
+in a similar manner as the light of the sun does when applied to a convex
+mirror or glass."
+
+Nov. 10, 1801. The Rev. Thomas Cormouls,[500] minister of Tettenhall,
+addressed a letter to Sir Wm. Herschel, from which I extract the following:
+
+"Here it may be asked, then, how came the doctrines of Newton to solve all
+astronomic Phenomina, and all problems concerning the same, both _a parte
+ante_ and _a parte post_.[501] It is answered that he certainly wrought the
+principles he made use of into strickt analogy with the real Phenomina of
+the heavens, and that the rules and results arizing from them {226} agree
+with them and resolve accurately all questions concerning them. Though they
+are not fact and true, or nature, but analogous to it, in the manner of the
+artificial numbers of logarithms, sines, &c. A very important question
+arises here, Did Newton mean to impose upon the world? By no means: he
+received and used the doctrines reddy formed; he did a little extend and
+contract his principles when wanted, and commit a few oversights of
+consequences. But when he was very much advanced in life, he suspected the
+fundamental nullity of them: but I have from a certain anecdote strong
+ground to believe that he knew it before his decease and intended to have
+retracted his error. But, however, somebody did deceive, if not wilfully,
+negligently at least. That was a man to whom the world has great
+obligations too. It was no less a philosopher than Galileo."
+
+That Newton wanted to retract before his death, is a notion not uncommon
+among paradoxers. Nevertheless, there is no retraction in the third edition
+of the _Principia_, published when Newton was eighty-four years old! The
+moral of the above is, that a gentleman who prefers instructing William
+Herschel to learning how to spell, may find a proper niche in a proper
+place, for warning to others. It seems that gravitation is not truth, but
+only the logarithm of it.
+
+
+
+BISHOPS AS PARADOXERS.
+
+    The mathematical and philosophical works of the Right Rev. John
+    Wilkins[502].... In two volumes. London, 1802, 8vo.
+
+This work, or at least part of the edition--all for aught I know--is
+printed on wood; that is, on paper made from wood-pulp. It has a rough
+surface; and when held before a candle is of very unequal transparency.
+There is in it a reprint of the works on the earth and moon. The discourse
+on the possibility of going to the moon, in this and the edition of 1640,
+is incorporated: but from the account in the {227} life prefixed, and a
+mention by D'Israeli, I should suppose that it had originally a separate
+title-page, and some circulation as a separate tract. Wilkins treats this
+subject half seriously, half jocosely; he has evidently not quite made up
+his mind. He is clear that "arts are not yet come to their solstice," and
+that posterity will bring hidden things to light. As to the difficulty of
+carrying food, he thinks, scoffing Puritan that he is, the Papists may be
+trained to fast the voyage, or may find the bread of their Eucharist "serve
+well enough for their _viaticum_."[503] He also puts the case that the
+story of Domingo Gonsales may be realized, namely, that wild geese find
+their way to the moon. It will be remembered--to use the usual substitute
+for, It has been forgotten--that the posthumous work of Bishop Francis
+Godwin[504] of Llandaff was published in 1638, the very year of Wilkins's
+first edition, in time for him to mention it at the end. Godwin makes
+Domingo Gonsales get to the moon in a chariot drawn by wild geese, and, as
+old books would say, discourses fully on that head. It is not a little
+amusing that Wilkins should have been seriously accused of plagiarizing
+Godwin, Wilkins writing in earnest, or nearly so, and Godwin writing
+fiction. It may serve to show philosophers how very near pure speculation
+comes to fable. From the sublime to the ridiculous is but a step: which is
+the sublime, and which the ridiculous, every one must settle for himself.
+With me, good fiction is the sublime, and bad speculation the ridiculous.
+The number of bishops in my list is small. I might, had I possessed the
+book, have opened the list of quadrators with an Archbishop of Canterbury,
+or at least with a divine who was not wholly not archbishop. Thomas
+Bradwardine[505] (Bragvardinus, Bragadinus) was elected in {228} 1348; the
+Pope put in another, who died unconsecrated; and Bradwardine was again
+elected in 1349, and lived five weeks longer, dying, I suppose, unconfirmed
+and unconsecrated.[506] Leland says he held the see a year, _unus tantum
+annulus_,[507] which seems to be a confusion: the whole business, from the
+first election, took about a year. He squared the circle, and his
+performance was printed at Paris in 1494. I have never seen it, nor any
+work of the author, except a tract on proportion.
+
+As Bradwardine's works are very scarce indeed, I give two titles from one
+of the Libri catalogues.
+
+    "ARITHMETIC. BRAUARDINI (Thomae) Arithmetica speculativa revisa et
+    correcta a Petro Sanchez Ciruelo Aragonesi, black letter, _elegant
+    woodcut title-page_, VERY RARE, _folio. Parisiis, per Thomam Anguelast
+    (pro Olivier Senant), s. a. circa 1510_.[508]
+
+"This book, by Thomas Bradwardine, Archbishop of Canterbury must be
+exceedingly scarce as it has escaped the notice of Professor De Morgan,
+who, in his _Arithmetical Books_, speaks of a treatise of the same author
+on proportions,[509] printed at Vienna in 1515, but does not mention the
+present work.
+
+{229}
+
+    "Bradwardine (Archbp. T.). Brauardini (Thomae) Geometria speculativa,
+    com Tractato de Quadratura Circuli bene revisa a Petro Sanchez Ciruelo,
+    SCARCE, _folio. Parisiis, J. Petit_, 1511.[510]
+
+"In this work we find the _polygones etoiles_,[511] see Chasles (_Apercu_,
+pp. 480, 487, 521, 523, &c.) on the merit of the discoveries of this
+English mathematician, who was Archbishop of Canterbury in the XIVth
+Century (_tempore_ Edward III. A.D. 1349); and who applied geometry to
+theology. M. Chasles says that the present work of Bradwardine contains
+'Une theorie nouvelle qui doit faire honneur au XIVe Siecle.'"[512]
+
+The titles do not make it quite sure that Bradwardine is the quadrator; it
+may be Peter Sanchez after all.[513]
+
+
+
+THE QUESTION OF PARALLELS.
+
+    Nouvelle theorie des paralleles. Par Adolphe Kircher[514] [so signed at
+    the end of the appendix]. Paris, 1803, 8vo.
+
+An alleged emendation of Legendre.[515] The author refers {230} to attempts
+by Hoffman,[516] 1801, by Hauff,[517] 1799, and to a work of Karsten,[518]
+or at least a theory of Karsten, contained in "Tentamen novae parallelarum
+theoriae notione situs fundatae; auctore G. C. Schwal,[519] Stuttgardae, 1801,
+en 8 volumes." Surely this is a misprint; _eight_ volumes on the theory of
+parallels? If there be such a work, I trust I and it may never meet, though
+ever so far produced.
+
+{231}
+
+
+
+    Soluzione ... della quadratura del Circolo. By Gaetano Rossi.[520]
+    London, 1804, 8vo.
+
+The three remarkable points of this book are, that the household of the
+Prince of Wales took ten copies, Signora Grassini[521] sixteen, and that
+the circumference is 3-1/5 diameters. That is, the appetite of Grassini for
+quadrature exceeded that of the whole household (_loggia_) of the Prince of
+Wales in the ratio in which the semi-circumference exceeds the diameter.
+And these are the first two in the list of subscribers. Did the author see
+this theorem?
+
+
+
+A PATRIOTIC PARADOX.
+
+    Britain independent of commerce; or proofs, deduced from an
+    investigation into the true cause of the wealth of nations, that our
+    riches, prosperity, and power are derived from sources inherent in
+    ourselves, and would not be affected, even though our commerce were
+    annihilated. By Wm. Spence.[522] 4th edition, 1808, 8vo.
+
+A patriotic paradox, being in alleviation of the Commerce panic which the
+measures of Napoleon I.--who _felt_ our Commerce, while Mr. Spence only
+_saw_ it--had awakened. In this very month (August, 1866), the Pres. Brit.
+Assoc. has applied a similar salve to the coal panic; it is fit that
+science, which rubbed the sore, should find a plaster. We ought to have an
+iron panic and a timber panic; and {232} a solemn embassy to the Americans,
+to beg them not to whittle, would be desirable. There was a gold panic
+beginning, before the new fields were discovered. For myself, I am the
+unknown and unpitied victim of a chronic gutta-percha panic: I never could
+get on without it; to me, gutta percha and Rowland Hill are the great
+discoveries of our day; and not unconnected either, gutta percha being to
+the submarine post what Rowland Hill is to the superterrene. I should be
+sorry to lose cow-choke--I gave up trying to spell it many years ago--but
+if gutta percha go, I go too. I think, that perhaps when, five hundred
+years hence, the people say to the Brit. Assoc. (if it then exist) "Pray
+gentlemen, is it not time for the coal to be exhausted?" they will be
+answered out of Moliere (who will certainly then exist): "_Cela etait
+autrefois ainsi, mais nous avons change tout cela._"[523] A great many
+people think that if the coal be used up, it will be announced some
+unexpected morning by all the yards being shut up and written notice
+outside, "Coal all gone!" just like the "Please, ma'am, there ain't no more
+sugar," with which the maid servant damps her mistress just at
+breakfast-time. But these persons should be informed that there is every
+reason to think that there will be time, as the city gentleman said, to
+_venienti_ the _occurrite morbo_.[524]
+
+
+
+SOME SCIENTIFIC PARADOXES.
+
+    An appeal to the republic of letters in behalf of injured science, from
+    the opinions and proceedings of some modern authors of elements of
+    geometry. By George Douglas.[525] Edinburgh, 1810, 8vo.
+
+Mr. Douglas was the author of a very good set of {233} mathematical tables,
+and of other works. He criticizes Simson,[526] Playfair,[527] and
+others,--sometimes, I think, very justly. There is a curious phrase which
+occurs more than once. When he wants to say that something or other was
+done before Simson or another was born, he says "before he existed, at
+least as an author." He seems to reserve the possibility of Simson's
+_pre-existence_, but at the same time to assume that he never wrote
+anything in his previous state. Tell me that Simson pre-existed in any
+other way than as editor of some pre-existent Euclid? Tell Apella![528]
+
+1810. In this year Jean Wood, Professor of Mathematics in the University of
+Virginia (Richmond),[529] addressed a printed circular to "Dr. Herschel,
+Astronomer, Greenwich Observatory." No mistake was more common than the
+natural one of imagining that the _Private Astronomer_ of the king was the
+_Astronomer Royal_. The letter was on the {234} difference of velocities of
+the two sides of the earth, arising from the composition of the rotation
+and the orbital motion. The _paradox_ is a fair one, and deserving of
+investigation; but, perhaps it would not be easy to deduce from it tides,
+trade-winds, aerolithes, &c., as Mr. Wood thought he had done in a work
+from which he gives an extract, and which he describes as published. The
+composition of rotations, &c., is not for the world at large: the paradox
+of the non-rotation of the moon about her axis is an instance. How many
+persons know that when a wheel rolls on the ground, the lowest point is
+moving upwards, the highest point forwards, and the intermediate points in
+all degrees of betwixt and between? This is too short an explanation, with
+some good difficulties.
+
+
+
+    The Elements of Geometry. In 2 vols. [By the Rev. J. Dobson,[530] B.D.]
+    Cambridge, 1815. 4to.
+
+Of this unpunctuating paradoxer I shall give an account in his own way: he
+would not stop for any one; why should I stop for him? It is worth while to
+try how unpunctuated sentences will read.
+
+The reverend J Dobson BD late fellow of saint Johns college Cambridge was
+rector of Brandesburton in Yorkshire he was seventh wrangler in 1798 and
+died in 1847 he was of that sort of eccentricity which permits account of
+his private life if we may not rather say that in such cases private life
+becomes public there is a tradition that he was called Death Dobson on
+account of his head and aspect of countenance being not very unlike the
+ordinary pictures of a human skull his mode of life is reported to have
+been very singular whenever he visited Cambridge he was never known to go
+twice to the same inn he never would sleep at the rectory with another
+person in the house some ancient charwoman used to attend to the house but
+never slept in it he has been known in the time of coach travelling to have
+{235} deferred his return to Yorkshire on account of his disinclination to
+travel with a lady in the coach he continued his mathematical studies until
+his death and till his executors sold the type all his tracts to the number
+of five were kept in type at the university press none of these tracts had
+any stops except full stops at the end of paragraphs only neither had they
+capitals except one at the beginning of a paragraph so that a full stop was
+generally followed by some white as there is not a single proper name in
+the whole of the book I have I am not able to say whether he would have
+used capitals before proper names I have inserted them as usual for which I
+hope his spirit will forgive me if I be wrong he also published the
+elements of geometry in two volumes quarto Cambridge 1815 this book had
+also no stops except when a comma was wanted between letters as in the
+straight lines AB, BC I should also say that though the title is
+unpunctuated in the author's part it seems the publishers would not stand
+it in their imprint this imprint is punctuated as usual and Deighton and
+Sons to prove the completeness of their allegiance have managed that comma
+semicolon and period shall all appear in it why could they not have
+contrived interrogation and exclamation this is a good precedent to
+establish the separate right of the publisher over the imprint it is said
+that only twenty of the tracts were printed and very few indeed of the book
+on geometry it is doubtful whether any were sold there is a copy of the
+geometry in the university library at Cambridge and I have one myself the
+matter of the geometry differs entirely from Euclid and is so fearfully
+prolix that I am sure no mortal except the author ever read it the man went
+on without stops and without stop save for a period at the end of a
+paragraph this is the unpunctuated account of the unpunctuating geometer
+_suum cuique tribuito_[531] Mrs Thrale[532] would have been amused {236} at
+a Dobson who managed to come to a full stop without either of the three
+warnings.
+
+I do not find any difficulty in reading Dobson's geometry; and I have read
+more of it to try reading without stops than I should have done had it been
+printed in the usual way. Those who dip into the middle of my paragraph may
+be surprised for a moment to see "on account of his disinclination to
+travel with a lady in the coach he continued his mathematical studies until
+his death and [further, of course] until his executors sold the type." But
+a person reading straight through would hardly take it so. I should add
+that, in order to give a fair trial, I did not compose as I wrote, but
+copied the words of the correspondent who gave me the facts, so far as they
+went.
+
+
+
+A RELIGIOUS PARADOX.
+
+    _Philosophia Sacra, or the principles of natural Philosophy. Extracted
+    from Divine Revelation._ By the Rev. Samuel Pike.[533] Edited by the
+    Rev. Samuel Kittle.[534] Edinburgh, 1815, 8vo.
+
+This is a work of modified Hutchinsonianism, which I have seen cited by
+several. Though rather dark on the subject, it seems not to contradict the
+motion of the earth, or the doctrine of gravitation. Mr. Kittle gives a
+list of some Hutchinsonians,--as Bishop Horne;[535] Dr. Stukeley;[536] the
+Rev. {237} W. Jones,[537] author of _Physiological Disquisitions_; Mr.
+Spearman,[538] author of _Letters on the Septuagint_ and editor of
+Hutchinson; Mr. Barker,[539] author of _Reflexions on Learning_; Dr.
+Catcott,[540] author of a work on the creation, &c.; Dr. Robertson,[541]
+author of a _Treatise on the Hebrew Language_; _Dr. Holloway_,[542] author
+of _Originals, Physical and Theological_; Dr. Walter Hodges,[543] author of
+a work on _Elohim_; Lord President Forbes (_ob._ 1747).[544]
+
+The Rev. William Jones, above mentioned (1726-1800), the friend and
+biographer of Bishop Horne and his stout {238} defender, is best known as
+William Jones of Nayland, who (1757)[545] published the _Catholic Doctrine
+of the Trinity_; he was also strong for the Hutchinsonian physical trinity
+of fire, light, and spirit. This well-known work was generally recommended,
+as the defence of the orthodox system, to those who could not go into the
+learning of the subject. There is now a work more suited to our time: _The
+Rock of Ages_, by the Rev. E. H. Bickersteth,[546] now published by the
+Religious Tract Society, without date, answered by the Rev. Dr.
+Sadler,[547] in a work (1859) entitled _Gloria Patri_, in which, says Mr.
+Bickersteth, "the author has not even attempted to grapple with my main
+propositions." I have read largely on the controversy, and I think I know
+what this means. Moreover, when I see the note "There are two other
+passages to which Unitarians sometimes refer, but the deduction they draw
+from them is, in each case, refuted by the context"--I think I see why the
+two texts are not named. Nevertheless, the author is a little more disposed
+to yield to criticism than his foregoers; he does not insist on texts and
+readings which the greatest editors have rejected. And he writes with
+courtesy, both direct and oblique, towards his antagonists; which, on his
+side of this subject, is like letting in fresh air. So that I suspect the
+two books will together make a tolerably good introduction to the subject
+for those who cannot go deep. Mr. Bickersteth's book is well arranged and
+indexed, which is a point of superiority to Jones of Nayland. There is a
+point which I should gravely recommend to writers on the orthodox side. The
+Unitarians in {239} England have frequently contended that the method of
+proving the divinity of Jesus Christ from the New Testament would equally
+prove the divinity of Moses. I have not fallen in the way of any orthodox
+answers specially directed at the repeated tracts written by Unitarians in
+proof of their assertion. If there be any, they should be more known; if
+there be none, some should be written. Which ever side may be right, the
+treatment of this point would be indeed coming to close quarters. The
+heterodox assertion was first supported, it is said, by John Bidle or
+Biddle (1615-1662) of Magdalen College, Oxford, the earliest of the English
+Unitarian writers, previously known by a translation of part of Virgil and
+part of Juvenal.[548] But I cannot find that he wrote on it.[549] It is the
+subject of "[Greek: haireseon anastasis], or a new way of deciding old
+controversies. By Basanistes. Third edition, enlarged," London, 1815,
+8vo.[550] It is the appendix to the amusing, "Six more letters to Granville
+Sharp, Esq., ... By Gregory Blunt, Esq." London, 8vo., 1803.[551] This much
+I can confidently say, that the study of these tracts would prevent
+orthodox writers from some curious slips, which are slips obvious to all
+sides of opinion. The lower defenders of orthodoxy frequently vex the
+spirits of the higher ones.
+
+Since writing the above I have procured Dr. Sadler's answer. I thought I
+knew what the challenger meant when he said the respondent had not grappled
+with his main {240} propositions. I should say that he is clung on to from
+beginning to end. But perhaps Mr. B. has his own meaning of logical terms,
+such as "proposition": he certainly has his own meaning of "cumulative." He
+says his evidence is cumulative; not a catena, the strength of which is in
+its weakest part, but distinct and independent lines, each of which
+corroborates the other. This is the very opposite of _cumulative_: it is
+_distributive_. When different arguments are each necessary to a
+conclusion, the evidence is _cumulative_; when any one will do, even though
+they strengthen each other, it is _distributive_. The word "cumulative" is
+a synonym of the law word "constructive"; a whole which will do made out of
+parts which separately will not. Lord Strafford [552] opens his defence
+with the use of both words: "They have invented a kind of _accumulated_ or
+_constructive_ evidence; by which many actions, either totally innocent in
+themselves, or criminal in a much inferior degree, shall, when united,
+_amount_ to treason." The conclusion is, that Mr. B. is a Cambridge man;
+the Oxford men do not confuse the elementary terms of logic. O dear old
+Cambridge! when the New Zealander comes let him find among the relics of
+your later sons some proof of attention to the elementary laws of thought.
+A little-go of logic, please!
+
+Mr. B., though apparently not a Hutchinsonian, has a nibble at a physical
+Trinity. "If, as we gaze on the sun shining in the firmament, we see any
+faint adumbration of the doctrine of the Trinity in the fontal orb, the
+light ever generated, and the heat proceeding from the sun and its
+beams--threefold and yet one, the sun, its light, and its {241} heat,--that
+luminous globe, and the radiance ever flowing from it, are both evident to
+the eye; but the vital warmth is felt, not seen, and is only manifested in
+the life it transfuses through creation. The proof of its real existence is
+self-demonstrating."
+
+We shall see how Revilo[553] illustrates orthodoxy by mathematics. It was
+my duty to have found one of the many illustrations from physics; but
+perhaps I should have forgotten it if this instance had not come in my way.
+It is very bad physics. The sun, apart from its light, evident to the eye!
+Heat more self-demonstrating than light, because _felt_! Heat only
+manifested by the life it diffuses! Light implied not necessary to life!
+But the theology is worse than Sabellianism[554]. To adumbrate--i.e., make
+a picture of--the orthodox doctrine, the sun must be heavenly body, the
+light heavenly body, the heat heavenly body; and yet, not three heavenly
+bodies, but one heavenly body. The truth is, that this illustration and
+many others most strikingly illustrate the Trinity of fundamental doctrine
+held by the Unitarians, in all its differences from the Trinity of persons
+held by the Orthodox. Be right which may, the right or wrong of the
+Unitarians shines out in the comparison. Dr. Sadler confirms me--by which I
+mean that I wrote the above before I saw what he says--in the following
+words: "The sun is one object with two _properties_, and these properties
+have a parallel not in the second and third persons of the Trinity, but in
+the attributes of Deity."
+
+The letting light alone, as self-evident, and making heat
+self-demonstrating, because felt--i.e., perceptible now and then--has the
+character of the Irishman's astronomy:
+
+{242}
+
+ "Long life to the moon, for a dear noble cratur,
+  Which serves us for lamplight all night in the dark,
+  While the sun only shines in the day, which by natur,
+  Wants no light at all, as ye all may remark."
+
+
+
+SIR RICHARD PHILLIPS.
+
+_Sir Richard Phillips_[555] (born 1768) was conspicuous in 1793, when he
+was sentenced to a year's imprisonment[556] for selling Paine's _Rights of
+Man_; and again when, in 1807[557], he was knighted as Sheriff of London.
+As a bookseller, he was able to enforce his opinions in more ways than
+others. For instance, in James Mitchell's[558] _Dictionary of the
+Mathematical and Physical Sciences_, 1823, 12mo, which, though he was not
+technically a publisher, was printed for him--a book I should recommend to
+the collector of works of reference--there is a temperate description of
+his doctrines, which one may almost swear was one of his conditions
+previous to undertaking the work. Phillips himself was not only an
+anti-Newtonian, but carried to a fearful excess the notion that statesmen
+and Newtonians were in league to deceive the world. He saw this plot in
+Mrs. Airy's[559] pension, and in Mrs. Somerville's[560]. In 1836, he {243}
+did me the honor to attempt my conversion. In his first letter he says:
+
+"Sir Richard Phillips has an inveterate abhorrence of all the pretended
+wisdom of philosophy derived from the monks and doctors of the middle ages,
+and not less of those of higher name who merely sought to make the monkish
+philosophy more plausible, or so to disguise it as to mystify the mob of
+small thinkers."
+
+So little did his writings show any knowledge of antiquity, that I strongly
+suspect, if required to name one of the monkish doctors, he would have
+answered--Aristotle. These schoolmen, and the "philosophical trinity of
+gravitating force, projectile force, and void space," were the bogies of
+his life.
+
+I think he began to publish speculations in the _Monthly Magazine_ (of
+which he was editor) in July 1817: these he republished separately in 1818.
+In the Preface, perhaps judging the feelings of others by his own, he says
+that he "fully expects to be vilified, reviled, and anathematized, for many
+years to come." Poor man! he was let alone. He appeals with confidence to
+the "impartial decision of posterity"; but posterity does not appoint a
+hearing for one per cent. of the appeals which are made; and it is much to
+be feared that an article in such a work of reference as this will furnish
+nearly all her materials fifty years hence. The following, addressed to M.
+Arago,[561] in 1835, will give posterity as good a notion as she will
+probably need:
+
+"Even the present year has afforded EVER-MEMORABLE examples, paralleled
+only by that of the Romish Conclave which persecuted Galileo. Policy has
+adopted that maxim of Machiavel which teaches that it is _more prudent_ to
+_reward_ {244} partisans than to _persecute_ opponents. Hence, a bigotted
+party had influence enough with the late short-lived administration [I
+think he is wrong as to the administration] of Wellington, Peel, &c., to
+confer munificent royal pensions on three writers whose sole distinction
+was their advocacy of the Newtonian philosophy. A Cambridge professor last
+year published an elaborate volume in illustration of _Gravitation_, and on
+him has been conferred a pension of 300l. per annum. A lady has written a
+light popular view of the Newtonian Dogmas, and she has been complimented
+by a pension of 200l. per annum. And another writer, who has recently
+published a volume to prove that the only true philosophy is that of Moses,
+has been endowed with a pension of 200l. per annum. Neither of them were
+needy persons, and the political and ecclesiastical bearing of the whole
+was indicated by another pension of 300l. bestowed on a political writer,
+the advocate of all abuses and prejudices. Whether the conduct of the
+Romish Conclave was more base for visiting with legal penalties the
+promulgation of the doctrines that the Earth turns on its axis and revolves
+around the Sun; or that of the British Court, for its craft in conferring
+pensions on the opponents of the plain corollary, that all the motions of
+the Earth are 'part and parcel' of these great motions, and those again and
+all like them consecutive displays of still greater motions in equality of
+action and reaction, is A QUESTION which must be reserved for the casuists
+of other generations.... I cannot expect that on a sudden you and your
+friends will come to my conclusion, that the present philosophy of the
+Schools and Universities of Europe, based on faith in witchcraft, magic,
+&c., is a system of execrable nonsense, _by which quacks live on the faith
+of fools_; but I desire a free and fair examination of my Aphorisms, and if
+a few are admitted to be true, merely as courteous concessions to
+arithmetic, my purpose will be effected, for men will thus be led to think;
+and if they think, then the fabric {245} of false assumptions, and
+degrading superstitions will soon tumble in ruins."
+
+This for posterity. For the present time I ground the fame of Sir R.
+Phillips on his having squared the circle without knowing it, or intending
+to do it. In the _Protest_ presently noted he discovered that "the force
+taken as 1 is equal to the sum of all its fractions ... thus 1 = 1/4 + 1/9
++ 1/16 + 1/25, &c., carried to infinity." This the mathematician instantly
+sees is equivalent to the theorem that the circumference of any circle is
+double of the diagonal of the cube on its diameter.[562]
+
+I have examined the following works of Sir R. Phillips, and heard of many
+others:
+
+    Essays on the proximate mechanical causes of the general phenomena of
+    the Universe, 1818, 12mo.[563]
+
+    Protest against the prevailing principles of natural philosophy, with
+    the development of a common sense system (no date, 8vo, pp. 16).[564]
+
+    Four dialogues between an Oxford Tutor and a disciple of the
+    common-sense philosophy, relative to the proximate causes of material
+    phenomena. 8vo, 1824.
+
+    A century of original aphorisms on the proximate causes of the
+    phenomena of nature, 1835, 12mo.
+
+Sir Richard Phillips had four valuable qualities; honesty, zeal, ability,
+and courage. He applied them all to teaching {246} matters about which he
+knew nothing; and gained himself an uncomfortable life and a ridiculous
+memory.
+
+
+
+    Astronomy made plain; or only way the true perpendicular distance of
+    the Sun, Moon, or Stars, from this earth, can be obtained. By Wm.
+    Wood.[565] Chatham, 1819, 12mo.
+
+If this theory be true, it will follow, of course, that this earth is the
+only one God made, and that it does not whirl round the sun, but _vice
+versa_, the sun round it.
+
+
+
+WHATELY'S FAMOUS PARADOX.
+
+    Historic doubts relative to Napoleon Buonaparte. London, 1819, 8vo.
+
+This tract has since been acknowledged by Archbishop Whately[566] and
+reprinted. It is certainly a paradox: but differs from most of those in my
+list as being a joke, and a satire upon the reasoning of those who cannot
+receive narrative, no matter what the evidence, which is to them utterly
+improbable _a priori_. But had it been serious earnest, it would not have
+been so absurd as many of those which I have brought forward. The next on
+the list is not a joke.
+
+The idea of the satire is not new. Dr. King,[567] in the dispute on the
+genuineness of Phalaris, proved with humor that Bentley did not write his
+own dissertation. An attempt has lately been made, for the honor of Moses,
+to prove, {247} without humor, that Bishop Colenso did not write his own
+book. This is intolerable: anybody who tries to use such a weapon without
+banter, plenty and good, and of form suited to the subject, should get the
+drubbing which the poor man got in the Oriental tale for striking the
+dervishes with the wrong hand.
+
+The excellent and distinguished author of this tract has ceased to live. I
+call him the Paley of our day: with more learning and more purpose than his
+predecessor; but perhaps they might have changed places if they had changed
+centuries. The clever satire above named is not the only work which he
+published without his name. The following was attributed to him, I believe
+rightly: "Considerations on the Law of Libel, as relating to Publications
+on the subject of Religion, by John Search." London, 1833, 8vo. This tract
+excited little attention: for those who should have answered, could not.
+Moreover, it wanted a prosecution to call attention to it: the fear of
+calling such attention may have prevented prosecutions. Those who have read
+it will have seen why.
+
+The theological review elsewhere mentioned attributes the pamphlet of John
+Search on blasphemous libel to Lord Brougham. This is quite absurd: the
+writer states points of law on credence where the judge must have spoken
+with authority. Besides which, a hundred points of style are decisive
+between the two. I think any one who knows Whately's writing will soon
+arrive at my conclusion. Lord Brougham himself informs me that he has no
+knowledge whatever of the pamphlet.
+
+It is stated in _Notes and Queries_ (3 S. xi. 511) that Search was answered
+by the Bishop of Ferns[568] as S. N., with {248} a rejoinder by Blanco
+White.[569] These circumstances increase the probability that Whately was
+written against and for.
+
+
+
+    VOLTAIRE A CHRISTIAN.
+
+    Voltaire Chretien; preuves tirees de ses ouvrages. Paris, 1820, 12mo.
+
+If Voltaire have not succeeded in proving himself a strong theist and a
+strong anti-revelationist, who is to succeed in proving himself one thing
+or the other in any matter whatsoever? By occasional confusion between
+theism and Christianity; by taking advantage of the formal phrases of
+adhesion to the Roman Church, which very often occur, and are often the
+happiest bits of irony in an ironical production; by citations of his
+morality, which is decidedly Christian, though often attributed to
+Brahmins; and so on--the author makes a fair case for his paradox, in the
+eyes of those who know no more than he tells them. If he had said that
+Voltaire was a better Christian than himself knew of, towards all mankind
+except men of letters, I for one should have agreed with him.
+
+_Christian!_ the word has degenerated into a synonym of _man_, in what are
+called Christian countries. So we have the parrot who "swore for all the
+world like a Christian," and the two dogs who "hated each other just like
+Christians." When the Irish duellist of the last century, whose name may be
+spared in consideration of its historic fame {249} and the worthy people
+who bear it, was (June 12, 1786) about to take the consequence of his last
+brutal murder, the rope broke, and the criminal got up, and exclaimed, "By
+---- Mr. Sheriff, you ought to be ashamed of yourself! this rope is not
+strong enough to hang a dog, far less a Christian!" But such things as this
+are far from the worst depravations. As to a word so defiled by usage, it
+is well to know that there is a way of escape from it, without renouncing
+the New Testament. I suppose any one may assume for himself what I have
+sometimes heard contended for, that no New Testament word is to be used in
+religion in any sense except that of the New Testament. This granted, the
+question is settled. The word _Christian_, which occurs three times, is
+never recognized as anything but a term of contempt from those without the
+pale to those within. Thus, Herod Agrippa, who was deep in Jewish
+literature, and a correspondent of Josephus, says to Paul (Acts xxvi. 28),
+"Almost thou persuadest me to be (what I and other followers of the state
+religion despise under the name) a Christian." Again (Acts xi. 26), "The
+disciples (as they called _themselves_) were called (by the surrounding
+heathens) Christians first in Antioch." Thirdly (1 Peter iv. 16), "Let none
+of you suffer as a _murderer_.... But if as a _Christian_ (as the heathen
+call it by whom the suffering comes), let him not be ashamed." That is to
+say, no _disciple_ ever called _himself_ a Christian, or applied the name,
+as from himself, to another disciple, from one end of the New Testament to
+the other; and no disciple need apply that name to himself in our day, if
+he dislike the associations with which the conduct of Christians has
+clothed it.
+
+
+
+WRONSKI ON THE LONGITUDE PROBLEM.
+
+    Address of M. Hoene Wronski to the British Board of Longitude, upon the
+    actual state of the mathematics, their reform, {250} and upon the new
+    celestial mechanics, giving the definitive solution of the problem of
+    longitude.[570] London, 1820, 8vo.
+
+M. Wronski[571] was the author of seven quartos on mathematics, showing
+very great power of generalization. He was also deep in the transcendental
+philosophy,[572] and had the Absolute at his fingers' ends. All this
+knowledge was rendered useless by a persuasion that he had greatly advanced
+beyond the whole world, with many hints that the Absolute would not be
+forthcoming, unless prepaid. He was a man of the widest extremes. At one
+time he desired people to see all possible mathematics in
+
+  F_x_ = A_{0}[Omega]_{0} + A_{1}[Omega]_{1} + A_{2}[Omega]_{2} +
+      A_{3}[Omega]_{3} + &c.
+
+which he did not explain, though there is meaning to it in the quartos. At
+another time he was proposing the general solution of the[573] fifth degree
+by help of 625 independent equations of one form and 125 of another. The
+first separate memoir from any Transactions that I ever possessed was given
+to me when at Cambridge; the refutation (1819) of this asserted solution,
+presented to the Academy of Lisbon by Evangelista Torriano. I cannot say I
+read it. The tract above is an attack on modern mathematicians in general,
+and on the Board of Longitude, and Dr. Young.[574]
+
+{251}
+
+
+
+DR. MILNER'S PARADOXES.
+
+1820. In this year died Dr. Isaac Milner,[575] President of Queens'
+College, Cambridge, one of the class of rational paradoxers. Under this
+name I include all who, in private life, and in matters which concern
+themselves, take their own course, and suit their own notions, no matter
+what other people may think of them. These men will put things to uses they
+were never intended for, to the great distress and disgust of their
+gregarious friends. I am one of the class, and I could write a little book
+of cases in which I have incurred absolute reproach for not "doing as other
+people do." I will name two of my atrocities: I took one of those
+butter-dishes which have for a top a dome with holes in it, which is turned
+inward, out of reach of accident, when not in use. Turning the dome
+inwards, I filled the dish with water, and put a sponge in the dome: the
+holes let it fill with water, and I had a penwiper, always moist, and worth
+its price five times over. "Why! what do you mean? It was made to hold
+butter. You are always at some queer thing or other!" I bought a leaden
+comb, intended to dye the hair, it being supposed that the application of
+lead will have this effect. I did not try: but I divided the comb into two,
+separated the part of closed prongs from the other; and thus I had two
+ruling machines. The lead marks paper, and by drawing the end of one of the
+machines along a ruler, I could rule twenty lines at a time, quite fit to
+write on. I thought I should have killed a friend to whom I explained it:
+he could not for the life of him understand how leaden _lines_ on paper
+would dye the hair.
+
+But Dr. Milner went beyond me. He wanted a seat suited to his shape, and he
+defied opinion to a fearful point. {252} He spread a thick block of putty
+over a wooden chair and sat in it until it had taken a ceroplast copy of
+the proper seat. This he gave to a carpenter to be imitated in wood. One of
+the few now living who knew him--my friend, General Perronet
+Thompson[576]--answers for the wood, which was shown him by Milner himself;
+but he does not vouch for the material being putty, which was in the story
+told me at Cambridge; William Frend[577] also remembered it. Perhaps the
+Doctor took off his great seal in green wax, like the Crown; but some soft
+material he certainly adopted; and very comfortable he found the wooden
+copy.
+
+[Illustration]
+
+The same gentleman vouches for Milner's lamp: but this had visible
+_science_ in it; the vulgar see no science in the construction of the
+chair. A hollow semi-cylinder, but not with a circular curve, revolved on
+pivots. The curve was calculated on the law that, whatever quantity of oil
+might be in the lamp, the position of equilibrium just brought the oil up
+to the edge of the cylinder, at which a bit of wick was placed. As the wick
+exhausted the oil, the cylinder slowly revolved about the pivots so as to
+keep the oil always touching the wick.
+
+Great discoveries are always laughed at; but it is very often not the laugh
+of incredulity; it is a mode of distorting the sense of inferiority into a
+sense of superiority, or a mimicry of superiority interposed between the
+laugher and his feeling of inferiority. Two persons in conversation {253}
+agreed that it was often a nuisance not to be able to lay hands on a bit of
+paper to mark the place in a book, every bit of paper on the table was sure
+to contain something not to be spared. I very quietly said that I always
+had a stock of bookmarkers ready cut, with a proper place for them: my
+readers owe many of my anecdotes to this absurd practice. My two
+colloquials burst into a fit of laughter; about what? Incredulity was out
+of the question; and there could be nothing foolish in my taking measures
+to avoid what they knew was an inconvenience. I was in this matter
+obviously their superior, and so they laughed at me. Much more candid was
+the Royal Duke of the last century, who was noted for slow ideas. "The rain
+comes into my mouth," said he, while riding. "Had not your Royal Highness
+better shut your mouth?" said the equerry. The Prince did so, and ought, by
+rule, to have laughed heartily at his adviser; instead of this, he said
+quietly, "It doesn't come in now."
+
+
+
+HERBART'S MATHEMATICAL PSYCHOLOGY.
+
+    De Attentionis mensura causisque primariis. By J. F. Herbart.[578]
+    Koenigsberg, 1822, 4to.
+
+{254}
+
+This celebrated philosopher maintained that mathematics ought to be applied
+to psychology, in a separate tract, published also in 1822: the one above
+seems, therefore, to be his challenge on the subject. It is on _attention_,
+and I think it will hardly support Herbart's thesis. As a specimen of his
+formula, let _t_ be the time elapsed since the consideration began, [beta]
+the whole perceptive intensity of the individual, [phi] the whole of his
+mental force, and _z_ the force given to a notion by attention during the
+time _t_. Then,
+
+z = [phi] (1 - [epsilon]^{-[beta]t})
+
+Now for a test. There is a _jactura_, _v_, the meaning of which I do not
+comprehend. If there be anything in it, my mathematical readers ought to
+interpret it from the formula
+
+_v_ = [pi][phi][beta]/(1 - [beta])[epsilon]^{-[beta]t} + C[epsilon]^{-t}
+
+and to this task I leave them, wishing them better luck than mine. The time
+may come when other manifestations of mind, besides _belief_, shall be
+submitted to calculation: at that time, should it arrive, a final decision
+may be passed upon Herbart.
+
+
+
+ON THE WHIZGIG.
+
+    The theory of the Whizgig considered; in as much as it mechanically
+    exemplifies the three working properties of nature; which are now set
+    forth under the guise of this toy, for children of all ages. London,
+    1822, 12mo (pp. 24, B. McMillan, Bow Street, Covent Garden).
+
+The toy called the _whizgig_ will be remembered by many. The writer is a
+follower of Jacob Behmen,[579] William Law,[580] {255} Richard Clarke,[581]
+and Eugenius Philalethes.[582] Jacob Behmen first announced the three
+working properties of nature, which Newton stole, as described in the
+_Gentleman's Magazine_, July, 1782, p. 329. These laws are illustrated in
+the whizgig. There is the harsh astringent, attractive compression; the
+bitter compunction, repulsive expansion; and the stinging anguish, duplex
+motion. The author hints that he has written other works, to which he gives
+no clue. I have heard that Behmen was pillaged by Newton, and
+Swedenborg[583] by Laplace,[584] and Pythagoras by Copernicus,[585] and
+Epicurus by Dalton,[586] &c. I do not think this mention will revive
+Behmen; but it may the whizgig, a very pretty toy, and philosophical
+withal, for few of those who used it could explain it.
+
+{256}
+
+
+
+SOME MYTHOLOGICAL PARADOXES.
+
+    A Grammar of infinite forms; or the mathematical elements of ancient
+    philosophy and mythology. By Wm. Howison.[587] Edinburgh, 1823, 8vo.
+
+A curius combination of geometry and mythology. Perseus, for instance, is
+treated under the head, "the evolution of diminishing hyperbolic branches."
+
+
+
+    The Mythological Astronomy of the Ancients; part the second: or the key
+    of Urania, the words of which will unlock all the mysteries of
+    antiquity. Norwich, 1823, 12mo.
+
+    A Companion to the Mythological Astronomy, &c., containing remarks on
+    recent publications.... Norwich, 1824, 12mo.
+
+    A new Theory of the Earth and of planetary motion; in which it is
+    demonstrated that the Sun is vicegerent of his own system. Norwich,
+    1825, 12mo.
+
+    The analyzation of the writings of the Jews, so far as they are found
+    to have any connection with the sublime science of astronomy. [This is
+    pp. 97-180 of some other work, being all I have seen.]
+
+These works are all by Sampson Arnold Mackey,[588] for whom see _Notes and
+Queries_, 1st S. viii. 468, 565, ix. 89, 179. Had it not been for actual
+quotations given by one correspondent only (1st S. viii. 565), that journal
+would have handed him down as a man of some real learning. An extraordinary
+man he certainly was: it is not one illiterate shoemaker in a thousand who
+could work upon such a singular mass of Sanskrit and Greek words, without
+showing {257} evidence of being able to read a line in any language but his
+own, or to spell that correctly. He was an uneducated Godfrey Higgins.[589]
+A few extracts will put this in a strong light: one for history of science,
+one for astronomy, and one for philology:
+
+"Sir Isaac Newton was of opinion that 'the atmosphere of the earth was the
+sensory of God; by which he was enabled to see quite round the earth:'
+which proves that Sir Isaac had no idea that God could see through the
+earth.
+
+"Sir Richard [Phillips] has given the most rational explanation of the
+cause of the earth's elliptical orbit that I have ever seen in print. It is
+because the earth presents its watery hemisphere to the sun at one time and
+that of solid land the other; but why has he made his Oxonian astonished at
+the coincidence? It is what I taught in my attic twelve years before.
+
+"Again, admitting that the Eloim were powerful and intelligent beings that
+managed these things, we would accuse _them_ of being the authors of all
+the sufferings of Chrisna. And as they and the constellation of Leo were
+below the horizon, and consequently cut off from the end of the zodiac,
+there were but eleven constellations of the zodiac to be seen; the three at
+the end were wanted, but those three would be accused of bringing Chrisna
+into the troubles which at last ended in his death. All this would be
+expressed in the Eastern language by saying that Chrisna was persecuted by
+those Judoth Ishcarioth!!!!! [the five notes of exclamation are the
+author's]. But the astronomy of those distant ages, when the sun was at the
+south pole in winter, would leave five of those Decans cut off from our
+view, in the latitude of twenty-eight degrees; hence Chrisna died of {258}
+wounds from five Decans, but the whole five may be included in Judoth
+Ishcarioth! for the phrase means 'the men that are wanted at the extreme
+parts.' Ishcarioth is a compound of _ish_, a man, and _carat_ wanted or
+taken away, and oth the plural termination, more ancient than _im_...."
+
+I might show at length how Michael is the sun, and the D'-ev-'l in French
+Di-ob-al, also 'L-evi-ath-an--the evi being the radical part both of
+d_evi_l and l_evi_athan--is the Nile, which the sun dried up for Moses to
+pass: a battle celebrated by Jude. Also how _Moses_, the same name as
+_Muses_, is from _mesha_, drawn out of the water, "and hence we called our
+land which is saved from the water by the name of _marsh_." But it will be
+of more use to collect the character of S. A. M. from such correspondents
+of _Notes and Queries_ as have written after superficial examination. Great
+astronomical and philological attainments, much ability and learning; had
+evidently read and studied deeply; remarkable for the originality of his
+views upon the very abstruse subject of mythological astronomy, in which he
+exhibited great sagacity. Certainly his views were _original_; but their
+sagacity, if it be allowable to copy his own mode of etymologizing, is of
+an _ori-gin-ale_ cast, resembling that of a person who puts to his mouth
+liquors both distilled and fermented.
+
+
+
+A KANTESIAN JEWELER.
+
+    Principles of the Kantesian, or transcendental philosophy. By Thomas
+    Wirgman.[590] London, 1824, 8vo.
+
+Mr. Wirgman's mind was somewhat attuned to psychology; but he was cracky
+and vagarious. He had been a fashionable jeweler in St. James's Street, no
+doubt the son or grandson of Wirgman at "the well-known toy-shop in {259}
+St. James's Street," where Sam Johnson smartened himself with silver
+buckles. (Boswell, _aet._ 69). He would not have the ridiculous large ones
+in fashion; and he would give no more than a guinea a pair; such, says
+Boswell, in Italics, were the _principles_ of the business: and I think
+this may be the first place in which the philosophical word was brought
+down from heaven to mix with men. However this may be, _my_ Wirgman sold
+snuff-boxes, among other things, and fifty years ago a fashionable
+snuff-boxer would be under inducement, if not positively obliged, to have a
+stock with very objectionable pictures. So it happened that Wirgman--by
+reason of a trifle too much candor--came under the notice of the
+_Suppression_ Society, and ran considerable risk. Mr. Brougham was his
+counsel; and managed to get him acquitted. Years and years after this, when
+Mr. Brougham was deep in the formation of the London University (now
+University College), Mr. Wirgman called on him. "What now?" said Mr. B.
+with his most sarcastic look--a very perfect thing of its kind--"you're in
+a scrape again, I suppose!" "No! indeed!" said W., "my present object is to
+ask your interest for the chair of Moral Philosophy in the new University!"
+He had taken up Kant!
+
+Mr. Wirgman, an itinerant paradoxer, called on me in 1831: he came to
+convert me. "I assure you," said he, "I am nothing but an old brute of a
+jeweler;" and his eye and manner were of the extreme of jocosity, as good
+in their way, as the satire of his former counsel. I mention him as one of
+that class who go away quite satisfied that they have wrought conviction.
+"Now," said he, "I'll make it clear to you! Suppose a number of gold-fishes
+in a glass bowl,--you understand? Well! I come with my cigar and go puff,
+puff, puff, over the bowl, until there is a little cloud of smoke: now,
+tell me, what will the gold-fishes say to that?" "I should imagine," said
+I, "That they would not know what to make of it." "By Jove! you're a
+Kantian;" said he, and with this and the like, he left me, vowing that
+{260} it was delightful to talk to so intelligent a person. The greatest
+compliment Wirgman ever received was from James Mill, who used to say he
+did not _understand_ Kant. That such a man as Mill should think this worth
+saying is a feather in the cap of the jocose jeweler.
+
+Some of my readers will stare at my supposing that Boswell may have been
+the first down-bringer of the word _principles_ into common life; the best
+answer will be a prior instance of the word as true vernacular; it has
+never happened to me to notice one. Many words have very common uses which
+are not old. Take the following from Nichols (_Anecd._ ix. 263): "Lord
+Thurlow presents his best respects to Mr. and Mrs. Thicknesse, and assures
+them that he knows of no cause to complain of any part of Mr. Thicknesse's
+carriage; least of all the circumstance of sending the head to Ormond
+Street." Surely Mr. T. had lent Lord T. a satisfactory carriage with a
+movable head, and the above is a polite answer to inquiries. Not a bit of
+it! _carriage_ is here _conduct_, and the _head_ is a _bust_. The vehicles
+of the rich, at the time, were coaches, chariots, chaises, etc., never
+carriages, which were rather _carts_. Gibbon has the word for
+baggage-wagons. In Jane Austen's novels the word carriage is established.
+
+
+
+WALSH'S DELUSIONS.
+
+_John Walsh_,[591] of Cork (1786-1847). This discoverer has had the honor
+of a biography from Professor Boole, who, at my request, collected
+information about him on the scene of his labors. It is in the
+_Philosophical Magazine_ for November, 1851, and will, I hope, be
+transferred to some biographical collection where it may find a larger
+class of readers. It is the best biography of a single hero of the kind
+that I know. Mr. Walsh introduced himself to me, {261} as he did to many
+others, in the anterowlandian days of the Post-office; his unpaid letters
+were double, treble, &c. They contained his pamphlets, and cost their
+weight in silver: all have the name of the author, and all are in octavo or
+in quarto letter-form: most are in four pages, and all dated from Cork. I
+have the following by me:
+
+    The Geometric Base, 1825.--The theory of plane angles. 1827.--Three
+    Letters to Dr. Francis Sadleir. 1838.--The invention of polar geometry.
+    By Irelandus. 1839.--The theory of partial functions. Letter to Lord
+    Brougham. 1839.--On the invention of polar geometry. 1839.--Letter to
+    the Editor of the Edinburgh Review. 1840.--Irish Manufacture. A new
+    method of tangents. 1841.--The normal diameter in curves. 1843.--Letter
+    to Sir R. Peel. 1845.--[Hints that Government should compel the
+    introduction of Walsh's Geometry into Universities.]--Solution of
+    Equations of the higher orders. 1845.
+
+Besides these, there is a _Metalogia_, and I know not how many others.
+
+Mr. Boole,[592] who has taken the moral and social features of Walsh's
+delusions from the commiserating point of view, which makes ridicule out of
+place, has been obliged to treat Walsh as Scott's Alan Fairford treated his
+client Peter Peebles; namely, keep the scarecrow out of court while the
+case was argued. My plan requires me to bring him in: and when he comes in
+at the door, pity and sympathy fly out at the window. Let the reader
+remember that he was not an ignoramus in mathematics: he might have won his
+spurs if he could have first served as an esquire. Though so illiterate
+that even in Ireland he never picked up anything more Latin than
+_Irelandus_, he was a very pretty mathematician spoiled in the making by
+intense self-opinion.
+
+This is part of a private letter to me at the back of a page of print: I
+had never addressed a word to him:
+
+{262}
+
+"There are no limits in mathematics, and those that assert there are, are
+infinite ruffians, ignorant, lying blackguards. There is no differential
+calculus, no Taylor's theorem, no calculus of variations, &c. in
+mathematics. There is no quackery whatever in mathematics; no % equal to
+anything. What sheer ignorant blackguardism that!
+
+"In mechanics the parallelogram of forces is quackery, and is dangerous;
+for nothing is at rest, or in uniform, or in rectilinear motion, in the
+universe. Variable motion is an essential property of matter. Laplace's
+demonstration of the parallelogram of forces is a begging of the question;
+and the attempts of them all to show that the difference of twenty minutes
+between the sidereal and actual revolution of the earth round the sun
+arises from the tugging of the Sun and Moon at the pot-belly of the earth,
+without being sure even that the earth has a pot-belly at all, is perfect
+quackery. The said difference arising from and demonstrating the revolution
+of the Sun itself round some distant center."
+
+In the letter to Lord Brougham we read as follows:
+
+"I ask the Royal Society of London, I ask the Saxon crew of that crazy
+hulk, where is the dogma of their philosophic god now?... When the Royal
+Society of London, and the Academy of Sciences of Paris, shall have read
+this memorandum, how will they appear? Like two cur dogs in the paws of the
+noblest beast of the forest.... Just as this note was going to press, a
+volume lately published by you was put into my hands, wherein you attempt
+to defend the fluxions and _Principia_ of Newton. Man! what are you about?
+You come forward now with your special pleading, and fraught with national
+prejudice, to defend, like the philosopher Grassi,[593] the persecutor of
+Galileo, principles {263} and reasoning which, unless you are actually
+insane, or an ignorant quack in mathematics, you know are mathematically
+false. What a moral lesson this for the students of the University of
+London from its head! Man! demonstrate corollary 3, in this note, by the
+lying dogma of Newton, or turn your thoughts to something you understand.
+
+"WALSH IRELANDUS."
+
+Mr. Walsh--honor to his memory--once had the consideration to save me
+postage by addressing a pamphlet under cover to a Member of Parliament,
+with an explanatory letter. In that letter he gives a candid opinion of
+himself:
+
+(1838.) "Mr. Walsh takes leave to send the enclosed corrected copy to Mr.
+Hutton as one of the Council of the University of London, and to save
+postage for the Professor of Mathematics there. He will find in it geometry
+more deep and subtle, and at the same time more simple and elegant, than it
+was ever contemplated human genius could invent."
+
+He then proceeds to set forth that a certain "tomfoolery lemma," with its
+"tomfoolery" superstructure, "never had existence outside the shallow
+brains of its inventor," Euclid. He then proceeds thus:
+
+"The same spirit that animated those philosophers who sent Galileo to the
+Inquisition animates all the philosophers of the present day without
+exception. If anything can free them from the yoke of error, it is the
+[Walsh] problem of double tangence. But free them it will, how deeply
+soever they may be sunk into mental slavery--and God knows that is deeply
+enough; and they bear it with an admirable grace; for none bear slavery
+with a better grace than tyrants. The lads must adopt my theory.... It will
+be a sad reverse for all our great professors to be compelled to become
+schoolboys in their gray years. But the sore scratch is to be compelled, as
+they had before been compelled one thousand years ago, to have recourse to
+Ireland for instruction." {264}
+
+The following "Impromptu" is no doubt by Walsh himself: he was more of a
+poet than of an astronomer:
+
+   "Through ages unfriended,
+    With sophistry blended,
+  Deep science in Chaos had slept;
+    Its limits were fettered,
+    Its voters unlettered,
+  Its students in movements but crept.
+    Till, despite of great foes,
+    Great WALSH first arose,
+  And with logical might did unravel
+    Those mazes of knowledge,
+    Ne'er known in a college,
+  Though sought for with unceasing travail.
+    With cheers we now hail him,
+    May success never fail him,
+  In Polar Geometrical mining;
+    Till his foes be as tamed
+    As his works are far-famed
+  For true philosophic refining."
+
+Walsh's system is, that all mathematics and physics are wrong: there is
+hardly one proposition in Euclid which is demonstrated. His example ought
+to warn all who rely on their own evidence to their own success. He was
+not, properly speaking, insane; he only spoke his mind more freely than
+many others of his class. The poor fellow died in the Cork union, during
+the famine. He had lived a happy life, contemplating his own perfections,
+like Brahma on the lotus-leaf.[594]
+
+{265}
+
+
+
+GROWTH OF FREEDOM OF OPINION.
+
+The year 1825 brings me to about the middle of my _Athenaeum_ list: that is,
+so far as mere number of names mentioned is concerned. Freedom of opinion,
+beyond a doubt, is gaining ground, for good or for evil, according to what
+the speaker happens to think: admission of authority is no longer made in
+the old way. If we take soul-cure and body-cure, divinity and medicine, it
+is manifest that a change has come over us. Time was when it was enough
+that dose or dogma should be certified by "Il a ete ordonne, Monsieur, il a
+ete ordonne,"[595] as the apothecary said when he wanted to operate upon
+poor de Porceaugnac. Very much changed: but whether for good or for evil
+does not now matter; the question is, whether contempt of _demonstration_
+such as our paradoxers show has augmented with the rejection of _dogmatic
+authority_. It ought to be just the other way: for the worship of reason is
+the system on which, if we trust them, the deniers of guidance ground their
+plan of life. The following attempt at an experiment on this point is the
+best which I can make; and, so far as I know, the first that ever was made.
+
+Say that my list of paradoxers divides in 1825: this of itself proves
+nothing, because so many of the earlier books are lost, or not likely to be
+come at. It would be a fearful rate of increase which would make the number
+of paradoxes since 1825 equal to the whole number before that date. Let us
+turn now to another collection of mine, arithmetical books, of which I have
+published a list. The two collections are similarly circumstanced as to new
+and old books; the paradoxes had no care given to the collection of either;
+the arithmetical books equal care to both. The list of arithmetical books,
+published in 1847, divides at 1735; the paradoxes, up to 1863, divide at
+1825. If we take the process which is most against the distinction, and
+allow every year {266} from 1847 to 1863 to add a year to 1735, we should
+say that the arithmetical writers divide at 1751. This rough process may
+serve, with sufficient certainty, to show that the proportion of paradoxes
+to books of sober demonstration is on the increase; and probably, quite as
+much as the proportion of heterodoxes to books of orthodox adherence. So
+that divinity and medicine may say to geometry, Don't _you_ sneer: if
+rationalism, homoeopathy, and their congeners are on the rise among us,
+your enemies are increasing quite as fast. But geometry replies--Dear
+friends, content yourselves with the rational inference that the rise of
+heterodoxy within your pales is not conclusive against you, taken alone;
+for it rises at the same time within mine. Store within your garners the
+precious argument that you are not proved wrong by increase of dissent;
+because there is increase of dissent against exact science. But do not
+therefore _even_ yourselves to me: remember that you, Dame Divinity, have
+inflicted every kind of penalty, from the stake to the stocks, in aid of
+your reasoning; remember that you, Mother Medicine, have not many years ago
+applied to Parliament for increase of forcible hindrance of
+antipharmacopoeal drenches, pills, and powders. Who ever heard of my asking
+the legislature to fine blundering circle-squarers? Remember that the D in
+dogma is the D in decay; but the D in demonstration is the D in durability.
+
+
+
+THE STATUS OF MEDICINE.
+
+I have known a medical man--a young one--who was seriously of the opinion
+that the country ought to be divided into medical parishes, with a
+practitioner appointed to each, and a penalty for calling in any but the
+incumbent curer. How should people know how to choose? The hair-dressers
+once petitioned Parliament for an act to compel people to wear wigs. My own
+opinion is of the opposite extreme, as in the following letter (_Examiner_,
+April 5, 1856); which, to my surprise, I saw reprinted in a medical
+journal, as a {267} plan not absolutely to be rejected. I am perfectly
+satisfied that it would greatly promote true medical orthodoxy, the
+predominance of well educated thinkers, and the development of their
+desirable differences.
+
+
+
+"SIR. The Medical Bill and the medical question generally is one on which
+experience would teach, if people would be taught.
+
+"The great soul question took three hundred years to settle: the little
+body question might be settled in thirty years, if the decisions in the
+former question were studied.
+
+"Time was when the State believed, as honestly as ever it believed
+anything, that it _might_, _could_, and _should_ find out the true doctrine
+for the poor ignorant community; to which, like a worthy honest state, it
+added _would_. Accordingly, by the assistance of the Church, which
+undertook the physic, the surgery, and the pharmacy of sound doctrine all
+by itself, it sent forth its legally qualified teachers into every parish,
+and woe to the man who called in any other. They burnt that man, they
+whipped him, they imprisoned him, they did everything but what was
+Christian to him, all for his soul's health and the amendment of his
+excesses.
+
+"But men would not submit. To the argument that the State was a father to
+the ignorant, they replied that it was at best the ignorant father of an
+ignorant son, and that a blind man could find his way into a ditch without
+another blind man to help him. And when the State said--But here we have
+the Church, which knows all about it, the ignorant community declared that
+it had a right to judge that question, and that it would judge it. It also
+said that the Church was never one thing long, and that it progressed, on
+the whole, rather more slowly than the ignorant community.
+
+"The end of it was, in this country, that every one who chose taught all
+who chose to let him teach, on condition only of an open and true
+registration. The State was {268} allowed to patronize one particular
+Church, so that no one need trouble himself to choose a pastor from the
+mere necessity of choosing. But every church is allowed its colleges, its
+studies, its diplomas; and every man is allowed his choice. There is no
+proof that our souls are worse off than in the sixteenth century; and,
+judging by fruits, there is much reason to hope they are better off.
+
+"Now the little body question is a perfect parallel to the great soul
+question in all its circumstances. The only things in which the parallel
+fails are the following: Every one who believes in a future state sees that
+the soul question is incomparably more important than the body question,
+and every one can try the body question by experiment to a larger extent
+than the soul question. The proverb, which always has a spark of truth at
+the bottom, says that every man of forty is either a fool or a physician;
+but did even the proverb maker ever dare to say that every man is at any
+age either a fool or a fit teacher of religion?
+
+"Common sense points out the following settlement of the medical question:
+and to this it will come sooner or later.
+
+"Let every man who chooses--subject to one common law of manslaughter for
+all the _crass_ cases--doctor the bodies of all who choose to trust him,
+and recover payment according to agreement in the courts of law. Provided
+always that every person practising should be registered at a moderate fee
+in a register to be republished every six months.
+
+"Let the register give the name, address, and asserted qualification of
+each candidate--as licentiate, or doctor, or what not, of this or that
+college, hall, university, &c., home or foreign. Let it be competent to any
+man to describe himself as qualified by study in public schools without a
+diploma, or by private study, or even by intuition or divine inspiration,
+if he please. But whatever he holds his qualification to be, that let him
+declare. Let all qualification {269} which of its own nature admits of
+proof be proved, as by the diploma or certificate, &c., leaving things
+which cannot be proved, as asserted private study, intuition, inspiration,
+&c., to work their own way.
+
+"Let it be highly penal to assert to the patient any qualification which is
+not in the register, and let the register be sold very cheap. Let the
+registrar give each registered practitioner a copy of the register in his
+own case; let any patient have the power to demand a sight of this copy;
+and let no money for attendance be recoverable in any case in which there
+has been false representation.
+
+"Let any party in any suit have a right to produce what medical testimony
+he pleases. Let the medical witness produce his register, and let his
+evidence be for the jury, as is that of an engineer or a practitioner of
+any art which is not attested by diplomas.
+
+"Let any man who practises without venturing to put his name on the
+register be liable to fine and imprisonment.
+
+"The consequence would be that, as now, anybody who pleases might practise;
+for the medical world is well aware that there is no power of preventing
+what they call quacks from practising. But very different from what is now,
+every man who practises would be obliged to tell the whole world what his
+claim is, and would run a great risk if he dared to tell his patient in
+private anything different from what he had told the whole world.
+
+"The consequence would be that a real education in anatomy, physiology,
+chemistry, surgery, and what is known of the thing called medicine, would
+acquire more importance than it now has.
+
+"It is curious to see how completely the medical man of the nineteenth
+century squares with the priest of the sixteenth century. The clergy of all
+sects are now better divines and better men than they ever were. They have
+lost Bacon's reproach that they took a smaller measure of things than any
+other educated men; and the physicians are now {270} in this particular the
+rearguard of the learned world; though it may be true that the rear in our
+day is further on in the march than the van of Bacon's day. Nor will they
+ever recover the lost position until medicine is as free as religion.
+
+"To this it must come. To this the public, which will decide for itself,
+has determined it shall come. To this the public has, in fact, brought it,
+but on a plan which it is not desirable to make permanent. We will be as
+free to take care of our bodies as of our souls and of our goods. This is
+the profession of all who sign as I do, and the practice of most of those
+who would not like the name
+
+"HETEROPATH."
+
+
+
+    The motion of the Sun in the Ecliptic, proved to be uniform in a
+    circular orbit ... with preliminary observations on the fallacy of the
+    Solar System. By Bartholomew Prescott,[596] 1825, 8vo.
+
+The author had published, in 1803, a _Defence of the Divine System_, which
+I never saw; also, _On the inverted scheme of Copernicus_. The above work
+is clever in its satire.
+
+
+
+THE CHRISTIAN EVIDENCE SOCIETY.
+
+    Manifesto of the Christian Evidence Society, established Nov. 12, 1824.
+    Twenty-four plain questions to honest men.
+
+These are two broadsides of August and November, 1826, signed by Robert
+Taylor,[597] A.B., Orator of the Christian Evidence Society. This gentleman
+was a clergyman, {271} and was convicted of blasphemy in 1827, for which he
+suffered imprisonment, and got the name of the _Devil's Chaplain_. The
+following are quotations:
+
+"For the book of Revelation, there was no original Greek at all, but
+_Erasmus_ wrote it himself in Switzerland, in the year 1516. Bishop
+Marsh,[598] vol. i. p. 320."--"Is not God the author of your reason? Can he
+then be the author of anything which is contrary to your reason? If reason
+be a sufficient guide, why should God give you any other? if it be not a
+sufficient guide, why has he given you _that_?"
+
+I remember a votary of the Society being asked to substitute for _reason_
+"the right leg," and for _guide_ "support," and to answer the two last
+questions: he said there must be a quibble, but he did not see what. It is
+pleasant to reflect that the _argumentum a carcere_[599] is obsolete. One
+great defect of it was that it did not go far enough: there should have
+been laws against subscriptions for blasphemers, against dealing at their
+shops, and against rich widows marrying them.
+
+Had I taken in theology, I must have entered books against Christianity. I
+mention the above, and Paine's _Age of Reason_, simply because they are the
+only English modern works that ever came in my way without my asking for
+them. The three parts of the _Age of Reason_ were published in Paris 1793,
+Paris 1795, and New York 1807. Carlile's[600] edition is of London, 1818,
+8vo. It must be republished when the time comes, to show what stuff
+governments and clergy were afraid of at the beginning of this century. I
+should never have seen the book, if it {272} had not been prohibited: a
+bookseller put it under my nose with a fearful look round him; and I could
+do no less, in common curiosity, than buy a work which had been so
+complimented by church and state. And when I had read it, I said in my mind
+to church and state,--Confound you! you have taken me in worse than any
+reviewer I ever met with. I forget what I gave for the book, but I ought to
+have been able to claim compensation somewhere.
+
+
+
+THE CABBALA.
+
+    Cabbala Algebraica. Auctore Gul. Lud. Christmann.[601] Stuttgard, 1827,
+    4to.
+
+Eighty closely printed pages of an attempt to solve equations of every
+degree, which has a process called by the author _cabbala_. An anonymous
+correspondent spells _cabbala_ as follows, [Greek: chabball], and makes 666
+out of its letters. This gentleman has sent me since my Budget commenced, a
+little heap of satirical communications, each having a 666 or two; for
+instance, alluding to my remarks on the spelling of _chemistry_, he finds
+the fated number in [Greek: chimeia]. With these are challenges to explain
+them, and hints about the end of the world. All these letters have
+different fantastic seals; one of them with the legend "keep your
+temper,"--another bearing "bank token five pence." The only signature is a
+triangle with a little circle in it, which I interpret to mean that the
+writer confesses himself to be the round man stuck in the three-cornered
+hole, to be explained as in Sydney Smith's joke.
+
+{273}
+
+There is a kind of Cabbala Alphabetica which the investigators of the
+numerals in words would do well to take up: it is the formation of
+sentences which contain all the letters of the alphabet, and each only
+once. No one has done it with _v_ and _j_ treated as consonants; but you
+and I can do it. Dr. Whewell[602] and I amused ourselves, some years ago,
+with attempts. He could not make sense, though he joined words: he gave me
+
+  Phiz, styx, wrong, buck, flame, quid.
+
+I gave him the following, which he agreed was "admirable sense": I
+certainly think the words would never have come together except in this
+way:
+
+  I, quartz pyx, who fling muck beds.
+
+I long thought that no human being could say this under any circumstances.
+At last I happened to be reading a religious writer--as he thought
+himself--who threw aspersions on his opponents thick and threefold. Heyday!
+came into my head, this fellow flings muck beds; he must be a quartz pyx.
+And then I remembered that a pyx is a sacred vessel, and quartz is a hard
+stone, as hard as the heart of a religious foe-curser. So that the line is
+the motto of the ferocious sectarian, who turns his religious vessels into
+mudholders, for the benefit of those who will not see what he sees.
+
+I can find no circumstances for the following, which I received from
+another:
+
+  Fritz! quick! land! hew gypsum box.
+
+From other quarters I have the following:
+
+  Dumpy quiz! whirl back fogs next.
+
+This might be said in time of haze to the queer little figure in the Dutch
+weather-toy, which comes out or goes in with the change in the atmosphere.
+Again,
+
+{274}
+
+  Export my fund!  Quiz black whigs.
+
+This Squire Western might have said, who was always afraid of the whigs
+sending the sinking-fund over to Hanover. But the following is the best: it
+is good advice to a young man, very well expressed under the circumstances:
+
+  Get nymph; quiz sad brow; fix luck.
+
+Which in more sober English would be, Marry; be cheerful; watch your
+business. There is more edification, more religion in this than in all the
+666-interpretations put together.
+
+Such things would make excellent writing copies, for they secure attention
+to every letter; _v_ and _j_ might be placed at the end.
+
+
+
+ON GODFREY HIGGINS.
+
+    The Celtic Druids. By Godfrey Higgins,[603] Esq. of Skellow Grange,
+    near Doncaster. London, 1827, 4to.
+
+    Anacalypsis, or an attempt to draw aside the veil of the Saitic Isis:
+    or an inquiry into the origin of languages, nations, and religions. By
+    Godfrey Higgins, &c..., London, 1836, 2 vols. 4to.
+
+The first work had an additional preface and a new index in 1829. Possibly,
+in future time, will be found bound up with copies of the second work two
+sheets which Mr. Higgins circulated among his friends in 1831: the first a
+"Recapitulation," the second "Book vi. ch. 1."
+
+The system of these works is that--
+
+"The Buddhists of Upper India (of whom the Phenician Canaanite,
+Melchizedek, was a priest), who built the Pyramids, Stonehenge, Carnac, &c.
+will be shown to have founded all the ancient mythologies of the world,
+which, however varied and corrupted in recent times, were originally one,
+and that one founded on principles sublime, beautiful, and true."
+
+{275}
+
+These works contain an immense quantity of learning, very honestly put
+together. I presume the enormous number of facts, and the goodness of the
+index, to be the reasons why the _Anacalypsis_ found a permanent place in
+the _old_ reading-room of the British Museum, even before the change which
+greatly increased the number of books left free to the reader in that room.
+
+Mr. Higgins, whom I knew well in the last six years of his life, and
+respected as a good, learned, and (in his own way) _pious_ man, was
+thoroughly and completely the man of a system. He had that sort of mental
+connection with his theory that made his statements of his authorities
+trustworthy: for, besides perfect integrity, he had no bias towards
+alteration of facts: he saw his system in the way the fact was presented to
+him by his authority, be that what it might.
+
+He was very sure of a fact which he got from any of his authorities:
+nothing could shake him. Imagine a conversation between him and an Indian
+officer who had paid long attention to Hindoo antiquities and their
+remains: a third person was present, _ego qui scribo_. _G. H._ "You know
+that in the temples of I-forget-who the Ceres is always sculptured
+precisely as in Greece." _Col._ ----, "I really do not remember it, and I
+have seen most of these temples." _G. H._ "It is so, I assure you,
+especially at I-forget-where." _Col._ ----, "Well, I am sure! I was
+encamped for six weeks at the gate of that very temple, and, except a
+little shooting, had nothing to do but to examine its details, which I did,
+day after day, and I found nothing of the kind." It was of no use at all.
+
+Godfrey Higgins began life by exposing and conquering, at the expense of
+two years of his studies, some shocking abuses which existed in the York
+Lunatic Asylum. This was a proceeding which called much attention to the
+treatment of the insane, and produced much good effect. He was very
+resolute and energetic. The magistracy of his {276} time had such scruples
+about using the severity of law to people of such station as well-to-do
+farmers, &c.: they would allow a great deal of resistance, and endeavor to
+mollify the rebels into obedience. A young farmer flatly refused to pay
+under an order of affiliation made upon him by Godfrey Higgins. He was duly
+warned; and persisted: he shortly found himself in gaol. He went there sure
+to conquer the Justice, and the first thing he did was to demand to see his
+lawyer. He was told, to his horror, that as soon as he had been cropped and
+prison-dressed, he might see as many lawyers as he pleased, to be looked
+at, laughed at, and advised that there was but one way out of the scrape.
+Higgins was, in his speculations, a regular counterpart of Bailly; but the
+celebrated Mayor of Paris had not his nerve. It was impossible to say, if
+their characters had been changed, whether the unfortunate crisis in which
+Bailly was not equal to the occasion would have led to very different
+results if Higgins had been in his place: but assuredly constitutional
+liberty would have had one chance more. There are two works of his by which
+he was known, apart from his paradoxes. First, _An apology for the life and
+character of the celebrated prophet of Arabia, called Mohamed, or the
+Illustrious_. London, 8vo. 1829. The reader will look at this writing of
+our English Buddhist with suspicious eye, but he will not be able to avoid
+confessing that the Arabian prophet has some reparation to demand at the
+hands of Christians. Next, _Horae Sabaticae; or an attempt to correct certain
+superstitions and vulgar errors respecting the Sabbath_. Second edition,
+with a large appendix. London, 12mo. 1833. This book was very heterodox at
+the time, but it has furnished material for some of the clergy of our day.
+
+I never could quite make out whether Godfrey Higgins took that system which
+he traced to the Buddhists to have a Divine origin, or to be the result of
+good men's meditations. Himself a strong theist, and believer in a future
+{277} state, one would suppose that he would refer a _universal_ religion,
+spread in different forms over the whole earth from one source, directly to
+the universal Parent. And this I suspect he did, whether he knew it or not.
+The external evidence is balanced. In his preface he says:
+
+"I cannot help smiling when I consider that the priests have objected to
+admit my former book, _The Celtic Druids_, into libraries, because it was
+antichristian; and it has been attacked by Deists, because it was
+superfluously religious. The learned Deist, the Rev. R. Taylor [already
+mentioned], has designated me as the _religious_ Mr. Higgins."
+
+The time will come when some profound historian of literature will make
+himself much clearer on the point than I am.
+
+
+
+ON POPE'S DIPPING NEEDLE.
+
+    The triumphal Chariot of Friction: or a familiar elucidation of the
+    origin of magnetic attraction, &c. &c. By William Pope.[604] London,
+    1829, 4to.
+
+Part of this work is on a dipping-needle of the author's construction. It
+must have been under the impression that a book of naval magnetism was
+proposed, that a great many officers, the Royal Naval Club, etc. lent their
+names to the subscription list. How must they have been surprised to find,
+right opposite to the list of subscribers, the plate presenting "the three
+emphatic letters, J. A. O." And how much more when they saw it set forth
+that if a square be inscribed in a circle, a circle within that, then a
+square again, &c., it is impossible to have more than fourteen circles, let
+the first circle be as large as you please. From this the seven attributes
+of God are unfolded; and further, that all matter was _moral_, until
+Lucifer _churned_ it into _physical_ "as far as the third circle in Deity":
+this Lucifer, called Leviathan in Job, being thus the moving cause of {278}
+chaos. I shall say no more, except that the friction of the air is the
+cause of magnetism.
+
+
+
+    Remarks on the Architecture, Sculpture, and Zodiac of Palmyra; with a
+    Key to the Inscriptions. By B. Prescot.[605] London, 1830, 8vo.
+
+Mr. Prescot gives the signs of the zodiac a Hebrew origin.
+
+
+
+THE JACOTOT METHOD.
+
+    Epitome de mathematiques. Par F. Jacotot,[606] Avocat. 3ieme edition,
+    Paris, 1830, 8vo. (pp. 18).
+
+    Methode Jacotot. Choix de propositions mathematiques. Par P. Y.
+    Sepres.[607] 2nde edition. Paris, 1830, 8vo. (pp. 82).
+
+Of Jacotot's method, which had some vogue in Paris, the principle was _Tout
+est dans tout_,[608] and the process _Apprendre quelque chose, et a y
+rapporter tout le reste_.[609] The first tract has a proposition in conic
+sections and its preliminaries: the second has twenty exercises, of which
+the first is finding the greatest common measure of two numbers, and the
+last is the motion of a point on a surface, acted on by given forces. This
+is topped up with the problem of sound in a tube, and a slice of Laplace's
+theory of the tides. All to be studied until known by heart, and all the
+rest will come, or at least join on easily when it comes. There is much
+truth in the assertion that new knowledge {279} hooks on easily to a little
+of the old, thoroughly mastered. The day is coming when it will be found
+out that crammed erudition, got up for examinations, does not cast out any
+hooks for more.
+
+
+
+    Lettre a MM. les Membres de l'Academie Royale des Sciences, contenant
+    un developpement de la refutation du systeme de la gravitation
+    universelle, qui leur a ete presentee le 30 aout, 1830. Par Felix
+    Passot.[610] Paris, 1830, 8vo.
+
+Works of this sort are less common in France than in England. In France
+there is only the Academy of Sciences to go to: in England there is a
+reading public out of the Royal Society, &c.
+
+
+
+A DISCOURSE ON PROBABILITY.
+
+About 1830 was published, in the _Library of Useful Knowledge_, the tract
+on _Probability_, the joint work of the late Sir John Lubbock[611] and Mr.
+Drinkwater (Bethune).[612] It is one of the best elementary openings of the
+subject. A binder put my name on the outside (the work was anonymous) and
+the consequence was that nothing could drive out of people's heads that it
+was written by me. I do not know how many denials I have made, from a
+passage in one of my own works to a letter in the _Times_: and I am not
+sure that I have succeeded in establishing the truth, even now. I
+accordingly note the fact once more. But as a book has no right here unless
+it contain a paradox--or thing counter to general opinion or practice--I
+will produce two small ones. Sir John Lubbock, with whom lay the executive
+arrangement, had a strong objection to the last word in "Theory of
+Probabilities," he maintained that the singular _probability_, should be
+used; and I hold him quite right.
+
+{280}
+
+The second case was this: My friend Sir J. L., with a large cluster of
+intellectual qualities, and another of social qualities, had one point of
+character which I will not call bad and cannot call good; he never used a
+slang expression. To such a length did he carry his dislike, that he could
+not bear _head_ and _tail_, even in a work on games of chance: so he used
+_obverse_ and _reverse_. I stared when I first saw this: but, to my
+delight, I found that the force of circumstances beat him at last. He was
+obliged to take an example from the race-course, and the name of one of the
+horses was _Bessy Bedlam_! And he did not put her down as _Elizabeth
+Bethlehem_, but forced himself to follow the jockeys.
+
+
+
+    [Almanach Romain sur la Loterie Royale de France, ou les Etrennes
+    necessaires aux Actionnaires et Receveurs de la dite Loterie. Par M.
+    Menut de St.-Mesmin. Paris, 1830. 12mo.
+
+This book contains all the drawings of the French lottery (two or three,
+each month) from 1758 to 1830. It is intended for those who thought they
+could predict the future drawings from the past: and various sets of
+_sympathetic_ numbers are given to help them. The principle is, that
+anything which has not happened for a long time must be soon to come. At
+_rouge et noir_, for example, when the red has won five times running,
+sagacious gamblers stake on the black, for they think the turn which must
+come at last is nearer than it was. So it is: but observation would have
+shown that if a large number of those cases had been registered which show
+a run of five for the red, the next game would just as often have made the
+run into six as have turned in favor of the black. But the gambling
+reasoner is incorrigible: if he would but take to squaring the circle, what
+a load of misery would be saved. A writer of 1823, who appeared to be
+thoroughly acquainted with the gambling of Paris and London, says that the
+gamesters by {281} profession are haunted by a secret foreboding of their
+future destruction, and seem as if they said to the banker at the table, as
+the gladiators said to the emperor, _Morituri te salutant_.[613]
+
+In the French lottery, five numbers out of ninety were drawn at a time. Any
+person, in any part of the country, might stake any sum upon any event he
+pleased, as that 27 should be drawn; that 42 and 81 should be drawn; that
+42 and 81 should be drawn, and 42 first; and so on up to a _quine
+determine_, if he chose, which is betting on five given numbers in a given
+order. Thus, in July, 1821, one of the drawings was
+
+  8   46   16   64   13.
+
+A gambler had actually predicted the five numbers (but not their order),
+and won 131,350 francs on a trifling stake. M. Menut seems to insinuate
+that the hint what numbers to choose was given at his own office. Another
+won 20,852 francs on the quaterne, 8, 16, 46, 64, in this very drawing.
+These gains, of course, were widely advertised: of the multitudes who lost
+nothing was said. The enormous number of those who played is proved to all
+who have studied chances arithmetically by the numbers of simple quaternes
+which were gained: in 1822, fourteen; in 1823, six; in 1824, sixteen; in
+1825, nine, &c.
+
+The paradoxes of what is called chance, or hazard, might themselves make a
+small volume. All the world understands that there is a long run, a general
+average; but great part of the world is surprised that this general average
+should be computed and predicted. There are many remarkable cases of
+verification; and one of them relates to the quadrature of the circle. I
+give some account of this and another. Throw a penny time after time until
+_head_ arrives, which it will do before long: let this be called a _set_.
+Accordingly, H is the smallest set, TH the next smallest, then TTH, &c. For
+abbreviation, let a set in which seven _tails_ {282} occur before _head_
+turns up be T^{7}H. In an immense number of trials of sets, about half will
+be H; about a quarter TH; about an eighth, T^{2}H. Buffon[614] tried 2,048
+sets; and several have followed him. It will tend to illustrate the
+principle if I give all the results; namely, that many trials will with
+moral certainty show an approach--and the greater the greater the number of
+trials--to that average which sober reasoning predicts. In the first column
+is the most likely number of the theory: the next column gives Buffon's
+result; the three next are results obtained from trial by correspondents of
+mine. In each case the number of trials is 2,048.
+
+  H         1,024    1,061    1,048    1,017    1,039
+  TH          512      494      507      547      480
+  T^{2}H      256      232      248      235      267
+  T^{3}H      128      137       99      118      126
+  T^{4}H       64       56       71       72       67
+  T^{5}H       32       29       38       32       33
+  T^{6}H       16       25       17       10       19
+  T^{7}H        8        8        9        9       10
+  T^{8}H        4        6        5        3        3
+  T^{9}H        2                 3        2        4
+  T^{10}H       1                 1        1
+  T^{11}H                         0        1
+  T^{12}H                         0        0
+  T^{13}H       1                 1        0
+  T^{14}H                         0        0
+  T^{15}H                         1        1
+  &c.                             0        0
+            -----    -----    -----    -----    -----
+            2,048    2,048    2,048    2,048    2,048
+
+{283}
+
+In very many trials, then, we may depend upon something like the predicted
+average. Conversely, from many trials we may form a guess at what the
+average will be. Thus, in Buffon's experiment the 2,048 first throws of the
+sets gave _head_ in 1,061 cases: we have a right to infer that in the long
+run something like 1,061 out of 2,048 is the proportion of heads, even
+before we know the reasons for the equality of chance, which tell us that
+1,024 out of 2,048 is the real truth. I now come to the way in which such
+considerations have led to a mode in which mere pitch-and-toss has given a
+more accurate approach to the quadrature of the circle than has been
+reached by some of my paradoxers. What would my friend[615] in No. 14 have
+said to this? The method is as follows: Suppose a planked floor of the
+usual kind, with thin visible seams between the planks. Let there be a thin
+straight rod, or wire, not so long as the breadth of the plank. This rod,
+being tossed up at hazard, will either fall quite clear of the seams, or
+will lay across one seam. Now Buffon, and after him Laplace, proved the
+following: That in the long run the fraction of the whole number of trials
+in which a seam is intersected will be the fraction which twice the length
+of the rod is of the circumference of the circle having the breadth of a
+plank for its diameter. In 1855 Mr. _Ambrose_ Smith, of Aberdeen, made
+3,204 trials with a rod three-fifths of the distance between the planks:
+there were 1,213 clear intersections, and 11 contacts on which it was
+difficult to decide. Divide these contacts equally, and we have 1,2181/2 to
+3,204 for the ratio of 6 to 5[pi], presuming that the greatness of the
+number of trials gives something near to the final average, or result in
+the long run: this gives [pi] = 3.1553. If all the 11 contacts had been
+treated as intersections, the result would have been {284} [pi] = 3.1412,
+exceedingly near. A pupil of mine made 600 trials with a rod of the length
+between the seams, and got [pi] = 3.137.
+
+This method will hardly be believed until it has been repeated so often
+that "there never could have been any doubt about it."
+
+The first experiment strongly illustrates a truth of the theory, well
+confirmed by practice: whatever can happen will happen if we make trials
+enough. Who would undertake to throw tail eight times running?
+Nevertheless, in the 8,192 sets tail 8 times running occurred 17 times; 9
+times running, 9 times; 10 times running, twice; 11 times and 13 times,
+each once; and 15 times twice.]
+
+
+
+ON CURIOSITIES OF [pi].
+
+1830. The celebrated interminable fraction 3.14159..., which the
+mathematician calls [pi], is the ratio of the circumference to the
+diameter. But it is thousands of things besides. It is constantly turning
+up in mathematics: and if arithmetic and algebra had been studied without
+geometry, [pi] must have come in somehow, though at what stage or under
+what name must have depended upon the casualties of algebraical invention.
+This will readily be seen when it is stated that [pi] is nothing but four
+times the series
+
+  1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...
+
+_ad infinitum_.[616] It would be wonderful if so simple a series {285} had
+but one kind of occurrence. As it is, our trigonometry being founded on the
+circle, [pi] first appears as the ratio stated. If, for instance, a deep
+study of probable fluctuation from average had preceded, [pi] might have
+emerged as a number perfectly indispensable in such problems as: What is
+the chance of the number of aces lying between a million + x and a million
+- x, when six million of throws are made with a die? I have not gone into
+any detail of all those cases in which the paradoxer finds out, by his
+unassisted acumen, that results of mathematical investigation _cannot be_:
+in fact, this discovery is only an accompaniment, though a necessary one,
+of his paradoxical statement of that which _must be_. Logicians are
+beginning to see that the notion of _horse_ is inseparably connected with
+that of _non-horse_: that the first without the second would be no notion
+at all. And it is clear that the positive affirmation of that which
+contradicts mathematical demonstration cannot but be accompanied by a
+declaration, mostly overtly made, that demonstration is false. If the
+mathematician were interested in punishing this indiscretion, he could make
+his denier ridiculous by inventing asserted results which would completely
+take him in.
+
+More than thirty years ago I had a friend, now long gone, who was a
+mathematician, but not of the higher branches: he was, _inter alia_,
+thoroughly up in all that relates to mortality, life assurance, &c. One
+day, explaining to him how it should be ascertained what the chance is of
+the survivors of a large number of persons now alive lying between given
+limits of number at the end of a certain time, I came, of course upon the
+introduction of [pi], which I could only describe as the ratio of the
+circumference of a circle to its diameter. "Oh, my dear friend! that must
+be a delusion; what can the circle have to do with the numbers alive at the
+end of a given time?"--"I cannot demonstrate it to you; but it is
+demonstrated."--"Oh! stuff! I think you can prove anything with your
+differential calculus: figment, {286} depend upon it." I said no more; but,
+a few days afterwards, I went to him and very gravely told him that I had
+discovered the law of human mortality in the Carlisle Table, of which he
+thought very highly. I told him that the law was involved in this
+circumstance. Take the table of expectation of life, choose any age, take
+its expectation and make the nearest integer a new age, do the same with
+that, and so on; begin at what age you like, you are sure to end at the
+place where the age past is equal, or most nearly equal, to the expectation
+to come. "You don't mean that this always happens?"--"Try it." He did try,
+again and again; and found it as I said. "This is, indeed, a curious thing;
+this _is_ a discovery." I might have sent him about trumpeting the law of
+life: but I contented myself with informing him that the same thing would
+happen with any table whatsoever in which the first column goes up and the
+second goes down; and that if a proficient in the higher mathematics chose
+to palm a figment upon him, he could do without the circle: _a corsaire,
+corsaire et demi_,[617] the French proverb says. "Oh!" it was remarked, "I
+see, this was Milne!"[618] It was _not_ Milne: I remember well showing the
+formula to him some time afterwards. He raised no difficulty about [pi]; he
+knew the forms of Laplace's results, and he was much interested. Besides,
+Milne never said stuff! and figment! And he would not have been taken in:
+he would have quietly tried it with the Northampton and all the other
+tables, and would have got at the truth.
+
+{287}
+
+
+
+EUCLID WITHOUT AXIOMS.
+
+    The first book of Euclid's Elements. With alterations and familiar
+    notes. Being an attempt to get rid of axioms altogether; and to
+    establish the theory of parallel lines, without the introduction of any
+    principle not common to other parts of the elements. By a member of the
+    University of Cambridge. Third edition. In usum serenissimae filiolae.
+    London, 1830.
+
+The author was Lieut. Col. (now General) Perronet Thompson,[619] the author
+of the "Catechism on the Corn Laws." I reviewed the fourth edition--which
+had the name of "Geometry without Axioms," 1833--in the quarterly _Journal
+of Education_ for January, 1834. Col. Thompson, who then was a contributor
+to--if not editor of--the _Westminster Review_, replied in an article the
+authorship of which could not be mistaken.
+
+Some more attempts upon the problem, by the same author, will be found in
+the sequel. They are all of acute and legitimate speculation; but they do
+not conquer the difficulty in the manner demanded by the conditions of the
+problem. The paradox of parallels does not contribute much to my pages: its
+cases are to be found for the most part in geometrical systems, or in notes
+to them. Most of them consist in the proposal of additional postulates;
+some are attempts to do without any new postulate. Gen. Perronet Thompson,
+whose paradoxes are always constructed on much study of previous writers,
+has collected in the work above named, a budget of attempts, the heads of
+which are in the _Penny_ and _English Cyclopaedias_, at "Parallels." He has
+given thirty instances, selected from what he had found.[620]
+
+{288}
+
+Lagrange,[621] in one of the later years of his life, imagined that he had
+overcome the difficulty. He went so far as to write a paper, which he took
+with him to the Institute, and began to read it. But in the first paragraph
+something struck him which he had not observed: he muttered _Il faut que
+j'y songe encore_,[622] and put the paper in his pocket.
+
+
+
+THE LUNAR CAUSTIC JOKE.
+
+The following paragraph appeared in the _Morning Post_, May 4, 1831:
+
+"We understand that although, owing to circumstances with which the public
+are not concerned, Mr. Goulburn[623] declined becoming a candidate for
+University honors, that his scientific attainments are far from
+inconsiderable. He is well known to be the author of an essay in the
+Philosophical Transactions on the accurate rectification of a circular arc,
+and of an investigation of the equation of a lunar caustic--a problem
+likely to become of great use in nautical astronomy."
+
+{289}
+
+This hoax--which would probably have succeeded with any journal--was palmed
+upon the _Morning Post_, which supported Mr. Goulburn, by some Cambridge
+wags who supported Mr. Lubbock, the other candidate for the University of
+Cambridge. Putting on the usual concealment, I may say that I always
+suspected Dr-nkw-t-r B-th-n-[624] of having a share in the matter. The
+skill of the hoax lies in avoiding the words "quadrature of the circle,"
+which all know, and speaking of "the accurate rectification of a circular
+arc," which all do not know for its synonyme. The _Morning Post_ next day
+gave a reproof to hoaxers in general, without referring to any particular
+case. It must be added, that although there are _caustics_ in mathematics,
+there is no _lunar_ caustic.
+
+So far as Mr. Goulburn was concerned, the above was poetic justice. He was
+the minister who, in old time, told a deputation from the Astronomical
+Society that the Government "did not care twopence for all the science in
+the country." There may be some still alive who remember this: I heard it
+from more than one of those who were present, and are now gone. Matters are
+much changed. I was thirty years in office at the Astronomical Society;
+and, to my certain knowledge, every Government of that period, Whig and
+Tory, showed itself ready to help with influence when wanted, and with
+money whenever there was an answer for the House of Commons. The following
+correction subsequently appeared. Referring to the hoax about Mr. Goulburn,
+Messrs. C. H. and Thompson Cooper[625] have corrected an error, by stating
+that the election which gave rise to the hoax was that in which Messrs.
+Goulburn {290} and Yates Peel[626] defeated Lord Palmerston[627] and Mr.
+Cavendish.[628] They add that Mr. Gunning, the well-known Esquire Bedell of
+the University, attributed the hoax to the late Rev. R. Sheepshanks, to
+whom, they state, are also attributed certain clever fictitious
+biographies--of public men, as I understand it--which were palmed upon the
+editor of the _Cambridge Chronicle_, who never suspected their genuineness
+to the day of his death. Being in most confidential intercourse with Mr.
+Sheepshanks,[629] both at the time and all the rest of his life
+(twenty-five years), and never heard him allude to any such things--which
+were not in his line, though he had satirical power of quite another {291}
+kind--I feel satisfied he had nothing to do with them. I may add that
+others, his nearest friends, and also members of his family, never heard
+him allude to these hoaxes as their author, and disbelieve his authorship
+as much as I do myself. I say this not as imputing any blame to the true
+author, such hoaxes being fair election jokes in all time, but merely to
+put the saddle off the wrong horse, and to give one more instance of the
+insecurity of imputed authorship. Had Mr. Sheepshanks ever told me that he
+had perpetrated the hoax, I should have had no hesitation in giving it to
+him. I consider all clever election squibs, free from bitterness and
+personal imputation, as giving the multitude good channels for the vent of
+feelings which but for them would certainly find bad ones.
+
+[But I now suspect that Mr. Babbage[630] had some hand in the hoax. He
+gives it in his "Passages, &c." and is evidently writing from memory, for
+he gives the wrong year. But he has given the paragraph, though not
+accurately, yet with such a recollection of the points as brings suspicion
+of the authorship upon him, perhaps in conjunction with D. B.[631] Both
+were on Cavendish's committee. Mr. Babbage adds, that "late one evening a
+cab drove up in hot haste to the office of the _Morning Post_, delivered
+the copy as coming from Mr. Goulburn's committee, and at the same time
+ordered fifty extra copies of the _Post_ to be sent next morning to their
+committee-room." I think the man--the only one I ever heard of--who knew
+all about the cab and the extra copies must have known more.]
+
+
+
+ON M. DEMONVILLE.
+
+_Demonville._--A Frenchman's Christian name is his own secret, unless there
+be two of the surname. M. Demonville is a very good instance of the
+difference between a {292} French and English discoverer. In England there
+is a public to listen to discoveries in mathematical subjects made without
+mathematics: a public which will hear, and wonder, and think it possible
+that the pretensions of the discoverer have some foundation. The unnoticed
+man may possibly be right: and the old country-town reputation which I once
+heard of, attaching to a man who "had written a book about the signs of the
+zodiac which all the philosophers in London could not answer," is fame as
+far as it goes. Accordingly, we have plenty of discoverers who, even in
+astronomy, pronounce the learned in error because of mathematics. In
+France, beyond the sphere of influence of the Academy of Sciences, there is
+no one to cast a thought upon the matter: all who take the least interest
+repose entire faith in the Institute. Hence the French discoverer turns all
+his thoughts to the Institute, and looks for his only hearing in that
+quarter. He therefore throws no slur upon the means of knowledge, but would
+say, with M. Demonville: "A l'egard de M. Poisson,[632] j'envie loyalement
+la millieme partie de ses connaissances mathematiques, pour prouver mon
+systeme d'astronomie aux plus incredules."[633] This system is that the
+only bodies of our system are the earth, the sun, and the moon; all the
+others being illusions, caused by reflection of the sun and moon from the
+ice of the polar regions. In mathematics, addition and subtraction are for
+men; multiplication and division, which are in truth creation and
+destruction, are prerogatives of deity. But _nothing_ multiplied by
+_nothing_ is _one_. M. Demonville obtained an introduction to William the
+Fourth, who desired the opinion of the Royal Society upon his system: the
+{293} answer was very brief. The King was quite right; so was the Society:
+the fault lay with those who advised His Majesty on a matter they knew
+nothing about. The writings of M. Demonville in my possession are as
+follows.[634] The dates--which were only on covers torn off in
+binding--were about 1831-34:
+
+_Petit cours d'astronomie_[635] followed by _Sur l'unite
+mathematique._--_Principes de la physique de la creation implicitement
+admis dans la notice sur le tonnerre par M. Arago._--_Question de longitude
+sur mer._[636]--_Vrai systeme du monde_[637] (pp. 92). Same title, four
+pages, small type. Same title, four pages, addressed to the British
+Association. Same title, four pages, addressed to M. Mathieu. Same title,
+four pages, on M. Bouvard's report.--_Resume de la physique de la creation;
+troisieme partie du vrai systeme du monde._[638]
+
+
+
+PARSEY'S PARADOX.
+
+    The quadrature of the circle discovered, by Arthur Parsey,[639] author
+    of the 'art of miniature painting.' Submitted to the consideration of
+    the Royal Society, on whose protection the author humbly throws
+    himself. London, 1832, 8vo.
+
+Mr. Parsey was an artist, who also made himself conspicuous by a new view
+of perspective. Seeing that the sides of a tower, for instance, would
+appear to meet in a point if the tower were high enough, he thought that
+these sides ought to slope to one another in the picture. On this {294}
+theory he published a small work, of which I have not the title, with a
+Grecian temple in the frontispiece, stated, if I remember rightly, to be
+the first picture which had ever been drawn in true perspective. Of course
+the building looked very Egyptian, with its sloping sides. The answer to
+his notion is easy enough. What is called the picture is not the picture
+from which the mind takes its perception; that picture is on the retina.
+The _intermediate_ picture, as it may be called--the human artist's
+work--is itself seen perspectively. If the tower were so high that the
+sides, though parallel, appeared to meet in a point, the picture must also
+be so high that the _picture-sides_, though parallel, would appear to meet
+in a point. I never saw this answer given, though I have seen and heard the
+remarks of artists on Mr. Parsey's work. I am inclined to think it is
+commonly supposed that the artist's picture is the representation which
+comes before the mind: this is not true; we might as well say the same of
+the object itself. In July 1831, reading an article on squaring the circle,
+and finding that there was a difficulty, he set to work, got a light denied
+to all mathematicians in--some would say through--a crack, and advertised
+in the _Times_ that he had done the trick. He then prepared this work, in
+which, those who read it will see how, he showed that 3.14159... should be
+3.0625. He might have found out his error by _stepping_ a draughtsman's
+circle with the compasses.
+
+Perspective has not had many paradoxes. The only other one I remember is
+that of a writer on perspective, whose name I forget, and whose four pages
+I do not possess. He circulated remarks on my notes on the subject,
+published in the _Athenaeum_, in which he denies that the stereographic
+projection is a case of perspective, the reason being that the whole
+hemisphere makes too large a picture for the eye conveniently to grasp at
+once. That is to say, it is no perspective because there is too much
+perspective. {295}
+
+
+
+ON A COUPLE OF GEOMETRIES.
+
+    Principles of Geometry familiarly illustrated. By the Rev. W.
+    Ritchie,[640] LL.D. London, 1833, 12mo.
+
+    A new Exposition of the system of Euclid's Elements, being an attempt
+    to establish his work on a different basis. By Alfred Day,[641] LL.D.
+    London, 1839, 12mo.
+
+These works belong to a small class which have the peculiarity of insisting
+that in the general propositions of geometry a proposition gives its
+converse: that "Every B is A" follows from "Every A is B." Dr. Ritchie
+says, "If it be proved that the equality of two of the angles of a triangle
+depends _essentially_ upon the equality of the opposite sides, it follows
+that the equality of opposite sides depends _essentially_ on the equality
+of the angles." Dr. Day puts it as follows:
+
+"That the converses of Euclid, so called, where no particular limitation is
+specified or implied in the leading proposition, more than in the converse,
+must be necessarily true; for as by the nature of the reasoning the leading
+proposition must be universally true, should the converse be not so, it
+cannot be so universally, but has at least all the exceptions conveyed in
+the leading proposition, and the case is therefore unadapted to geometric
+reasoning; or, what is the same thing, by the very nature of geometric
+reasoning, the particular exceptions to the extended converse must be
+identical with some one or other of the cases under the universal
+affirmative proposition with which we set forth, which is absurd."
+
+{296}
+
+On this I cannot help transferring to my reader the words of the Pacha when
+he orders the bastinado,--May it do you good! A rational study of logic is
+much wanted to show many mathematicians, of all degrees of proficiency,
+that there is nothing in the _reasoning_ of mathematics which differs from
+other reasoning. Dr. Day repeated his argument in _A Treatise on
+Proportion_, London, 1840, 8vo. Dr. Ritchie was a very clear-headed man. He
+published, in 1818, a work on arithmetic, with rational explanations. This
+was too early for such an improvement, and nearly the whole of his
+excellent work was sold as waste paper. His elementary introduction to the
+Differential Calculus was drawn up while he was learning the subject late
+in life. Books of this sort are often very effective on points of
+difficulty.
+
+
+
+NEWTON AGAIN OBLITERATED.
+
+    Letter to the Royal Astronomical Society in refutation of Mistaken
+    Notions held in common, by the Society, and by all the Newtonian
+    philosophers. By Capt. Forman,[642] R.N. Shepton-Mallet, 1833, 8vo.
+
+Capt. Forman wrote against the whole system of gravitation, and got no
+notice. He then wrote to Lord Brougham, Sir J. Herschel, and others I
+suppose, desiring them to procure notice of his books in the reviews: this
+not being acceded to, he wrote (in print) to Lord John Russell[643] to
+complain of their "dishonest" conduct. He then sent a manuscript letter to
+the Astronomical Society, inviting controversy: he was answered by a
+recommendation to study {297} dynamics. The above pamphlet was the
+consequence, in which, calling the Council of the Society "craven dunghill
+cocks," he set them right about their doctrines. From all I can learn, the
+life of a worthy man and a creditable officer was completely embittered by
+his want of power to see that no person is bound in reason to enter into
+controversy with every one who chooses to invite him to the field. This
+mistake is not peculiar to philosophers, whether of orthodoxy or paradoxy;
+a majority of educated persons imply, by their modes of proceeding, that no
+one has a right to any opinion which he is not prepared to defend against
+all comers.
+
+
+
+    David and Goliath, or an attempt to prove that the Newtonian system of
+    Astronomy is directly opposed to the Scriptures. By Wm. Lauder,[644]
+    Sen., Mere, Wilts. Mere, 1833, 12mo.
+
+Newton is Goliath; Mr. Lauder is David. David took five pebbles; Mr. Lauder
+takes five arguments. He expects opposition; for Paul and Jesus both met
+with it.
+
+Mr. Lauder, in his comparison, seems to put himself in the divinely
+inspired class. This would not be a fair inference in every case; but we
+know not what to think when we remember that a tolerable number of
+cyclometers have attributed their knowledge to direct revelation. The works
+of this class are very scarce; I can only mention one or two from
+Montucla.[645] Alphonso Cano de Molina,[646] in the last century, upset all
+Euclid, and squared the circle upon the ruins; he found a follower, Janson,
+who translated him from Spanish into Latin. He declared that he believed in
+Euclid, until God, who humbles the proud, taught him better. One Paul Yvon,
+called from his estate de la Leu, a merchant at Rochelle, supported by his
+book-keeper, M. Pujos, and a {298} Scotchman, John Dunbar, solved the
+problem by divine grace, in a manner which was to convert all Jews,
+Infidels, etc. There seem to have been editions of his work in 1619 and
+1628, and a controversial "Examen" in 1630, by Robert Sara. There was a
+noted discussion, in which Mydorge,[647] Hardy,[648] and others took part
+against de la Leu. I cannot find this name either in Lipenius[649] or
+Murhard,[650] and I should not have known the dates if it had not been for
+one of the keenest bibliographers of any time, my friend Prince Balthasar
+Boncompagni,[651] who is trying to find copies of the works, and has
+managed to find copies of the titles. In 1750, Henry Sullamar, an
+Englishman, squared the circle by the number of the Beast: he published a
+pamphlet every two or three years; but I cannot find any mention of him in
+English works.[652] In France, in 1753, M. de Causans,[653] of the Guards,
+cut a circular piece of turf, squared it, and {299} deduced original sin
+and the Trinity. He found out that the circle was equal to the square in
+which it is inscribed; and he offered a reward for detection of any error,
+and actually deposited 10,000 francs as earnest of 300,000. But the courts
+would not allow any one to recover.
+
+
+
+SIR JOHN HERSCHEL.
+
+1834. In this year Sir John Herschel[654] set up his telescope at
+Feldhausen, Cape of Good Hope. He did much for astronomy, but not much for
+the _Budget of Paradoxes_. He gives me, however, the following story. He
+showed a resident a remarkable blood-red star, and some little time after
+he heard of a sermon preached in those parts in which it was asserted that
+the statements of the Bible must be true, for that Sir J. H. had seen in
+his telescope "the very place where wicked people go."
+
+But red is not always the color. Sir J. Herschel has in his possession a
+letter written to his father, Sir W. H.,[655] dated April 3, 1787, and
+signed "Eliza Cumyns," begging to know if any of the stars be _indigo_ in
+color, "because, if there be, I think it may be deemed a strong conjectural
+illustration of the expression, so often used by our Saviour in the Holy
+Gospels, that 'the disobedient shall be cast into outer darkness'; for as
+the Almighty Being can doubtless confine any of his creatures, whether
+corporeal or spiritual, to what part of his creation He pleases, if
+therefore any of the stars (which are beyond all doubt so many suns to
+other systems) be of so dark a color as that above mentioned, they may be
+calculated to give the most insufferable heat to those dolorous systems
+dependent upon them (and to reprobate spirits placed there), without one
+ray of cheerful light; and may therefore be the scenes of future
+punishments." This letter is addressed to Dr. Heirschel at Slow. Some have
+placed the infernal regions inside the earth, but {300} others have filled
+this internal cavity--for cavity they will have--with refulgent light, and
+made it the abode of the blessed. It is difficult to build without knowing
+the number to be provided for. A friend of mine heard the following (part)
+dialogue between two strong Scotch Calvinists: "Noo! hoo manny d'ye thank
+there are of the alact on the arth at this moment?--Eh! mabbee a
+doozen--Hoot! mon! nae so mony as thot!"
+
+
+
+THE NAUTICAL ALMANAC.
+
+1834. From 1769 to 1834 the _Nautical Almanac_ was published on a plan
+which gradually fell behind what was wanted. In 1834 the new series began,
+under a new superintendent (Lieut. W. S. Stratford).[656] There had been a
+long scientific controversy, which would not be generally intelligible. To
+set some of the points before the reader, I reprint a cutting which I have
+by me. It is from the Nautical _Magazine_, but I did hear that some had an
+idea that it was in the Nautical _Almanac_ itself. It certainly was not,
+and I feel satisfied the Lords of the Admiralty would not have permitted
+the insertion; they are never in advance of their age. The Almanac for 1834
+was published in July 1833.
+
+    THE NEW NAUTICAL ALMANAC--Extract from the 'Primum Mobile,' and 'Milky
+    Way Gazette.' Communicated by AEROLITH.
+
+A meeting of the different bodies composing the Solar System was this day
+held at the Dragon's Tail, for the purpose of taking into consideration the
+alterations and amendments introduced into the New Nautical Almanac. The
+honorable luminaries had been individually summoned {301} by fast-sailing
+comets, and there was a remarkably full attendance. Among the visitors we
+_observed_ several nebulae, and almost all the stars whose proper motions
+would admit of their being present.
+
+The SUN was unanimously called to the focus. The small planets took the
+oaths, and their places, after a short discussion, in which it was decided
+that the places should be those of the Almanac itself, with leave reserved
+to move for corrections.
+
+Petitions were presented from [alpha] and [delta] Ursae Minoris, complaining
+of being put on daily duty, and praying for an increase of salary.--Laid on
+the plane of the ecliptic.
+
+The trustees of the eccentricity[657] and inclination funds reported a
+balance of .00001 in the former, and a deficit of 0".009 in the latter.
+This announcement caused considerable surprise, and a committee was moved
+for, to ascertain which of the bodies had more or less than his share.
+After some discussion, in which the small planets offered to consent to a
+reduction, if necessary, the motion was carried.
+
+The FOCAL BODY then rose to address the meeting. He remarked that the
+subject on which they were assembled was one of great importance to the
+routes and revolutions of the heavenly bodies. For himself, though a
+private arrangement between two of his honourable neighbours (here he
+looked hard at the Earth and Venus) had prevented his hitherto paying that
+close attention to the predictions of the Nautical Almanac which he
+declared he always had wished to do; yet he felt consoled by knowing that
+the conductors of that work had every disposition to take his peculiar
+circumstances into consideration. He declared that he had never passed the
+wires of a transit without deeply feeling his inability to adapt himself to
+the present state of his theory; a feeling which he was afraid had
+sometimes caused a slight tremor in his limb. Before {302} he sat down, he
+expressed a hope that honourable luminaries would refrain as much as
+possible from eclipsing each other, or causing mutual perturbations.
+Indeed, he should be very sorry to see any interruption of the harmony of
+the spheres. (Applause.)
+
+The several articles of the New Nautical Almanac were then read over
+without any comment; only we observed that Saturn shook his ring at every
+novelty, and Jupiter gave his belt a hitch, and winked at the satellites at
+page 21 of each month.
+
+The MOON rose to propose a resolution. No one, he said, would be surprised
+at his bringing this matter forward in the way he did, when it was
+considered in how complete and satisfactory a manner his motions were now
+represented. He must own he had trembled when the Lords of the Admiralty
+dissolved the Board of Longitude, but his tranquillity was more than
+reestablished by the adoption of the new system. He did not know but that
+any little assistance he could give in Nautical Astronomy was becoming of
+less and less value every day, owing to the improvement of chronometers.
+But there was one thing, of which nothing could deprive him--he meant the
+regulation of the tides. And, perhaps, when his attention was not occupied
+by more than the latter, he should be able to introduce a little more
+regularity into the phenomena. (Here the honourable luminary gave a sort of
+modest libration, which convulsed the meeting with laughter.) They might
+laugh at his natural infirmity if they pleased, but he could assure them it
+arose only from the necessity he was under, when young, of watching the
+motions of his worthy primary. He then moved a resolution highly laudatory
+of the alterations which appeared in the New Nautical Almanac.
+
+The EARTH rose, to second the motion. His honourable satellite had fully
+expressed his opinions on the subject. He joined his honourable friend in
+the focus in wishing to pay every attention to the Nautical Almanac, but,
+{303} really, when so important an alteration had taken place in his
+magnetic pole[658] (hear) and there might, for aught he knew, be a
+successful attempt to reach his pole of rotation, he thought he could not
+answer for the preservation of the precession in its present state. (Here
+the hon. luminary, scratching his side, exclaimed, as he sat down, "More
+steamboats--confound 'em!")
+
+An honourable satellite (whose name we could not learn) proposed that the
+resolution should be immediately despatched, corrected for refraction, when
+he was called to order by the Focal Body, who reminded him that it was
+contrary to the moving orders of the system to take cognizance of what
+passed inside the atmosphere of any planet.
+
+SATURN and PALLAS rose together. (Cries of "New member!" and the former
+gave way.) The latter, in a long and eloquent speech, praised the
+liberality with which he and his colleagues had at length been relieved
+from astronomical disqualifications. He thought that it was contrary to the
+spirit of the laws of gravitation to exclude any planet from office on
+account of the eccentricity or inclination of his orbit. Honourable
+luminaries need not talk of the want of convergency of his series. What had
+they to do with any private arrangements between him and the general
+equations of the system? (Murmurs from the opposition.) So long as he
+obeyed the laws of motion, to which he had that day taken a solemn oath, he
+would ask, were old planets, which were now so well known that nobody
+trusted them, to....
+
+The FOCAL BODY said he was sorry to break the continuity of the
+proceedings, but he thought that remarks upon character, with a negative
+sign, would introduce {304} differences of too high an order. The
+honourable luminary must eliminate the expression which he had brought out,
+in finite terms, and use smaller inequalities in future. (Hear, hear.)
+
+PALLAS explained, that he was far from meaning to reflect upon the orbital
+character of any planet present. He only meant to protest against being
+judged by any laws but those of gravitation, and the differential calculus:
+he thought it most unjust that astronomers should prevent the small planets
+from being observed, and then reproach them with the imperfections of the
+tables, which were the result of their own narrow-minded policy. (Cheers.)
+
+SATURN thought that, as an old planet, he had not been treated with due
+respect. (Hear, from his satellites.) He had long foretold the wreck of the
+system from the friends of innovation. Why, he might ask, were his
+satellites to be excluded, when small planets, trumpery comets, which could
+not keep their mean distances (cries of oh! oh!), double stars, with
+graphical approximations, and such obscure riff-raff of the heavens (great
+uproar) found room enough. So help him Arithmetic, nothing could come of
+it, but a stoppage of all revolution. His hon. friend in the focus might
+smile, for he would be a gainer by such an event; but as for him (Saturn),
+he had something to lose, and hon. luminaries well knew that, whatever they
+might think _under_ an atmosphere, _above_ it continual revolution was the
+only way of preventing perpetual anarchy. As to the hon. luminary who had
+risen before him, he was not surprised at his remarks, for he had
+invariably observed that he and his colleagues allowed themselves _too much
+latitude_. The stability of the system required that they should be brought
+down, and he, for one, would exert all his powers of attraction to
+accomplish that end. If other bodies would cordially unite with him,
+particularly his noble friend next him, than whom no luminary possessed
+greater weight--
+
+JUPITER rose to order. He conceived his noble friend {305} had no right to
+allude to him in that manner, and was much surprised at his proposal,
+considering the matters which remained in dispute between them. In the
+present state of affairs, he would take care never to be in conjunction
+with his hon. neighbour one moment longer than he could help. (Cries of
+"Order, order, no long inequalities," during which he sat down.)
+
+SATURN proceeded to say, that he did not know till then that a planet with
+a ring could affront one who had only a belt, by proposing mutual
+co-operation. He would now come to the subject under discussion. He should
+think meanly of his hon. colleagues if they consented to bestow their
+approbation upon a mere astronomical production. Had they forgotten that
+they once were considered the arbiters of fate, and the prognosticators of
+man's destiny? What had lost them that proud position? Was it not the
+infernal march of intellect, which, after having turned the earth
+topsy-turvy, was now disturbing the very universe? For himself (others
+might do as they pleased), but he stuck to the venerable Partridge,[659]
+and the Stationers' Company, and trusted that they would outlive infidels
+and anarchists, whether of Astronomical or Diffusion of Knowledge
+Societies. (Cries of oh! oh!)
+
+MARS said he had been told, for he must confess he had not seen the work,
+that the places of the planets were given for Sundays. This, he must be
+allowed to say, was an indecorum he had not expected; and he was convinced
+the Lords of the Admiralty had given no orders to that effect. He hoped
+this point would be considered in the measure which had been introduced in
+another place, and that some {306} one would move that the prohibition
+against travelling on Sundays extend to the heavenly as well as earthly
+bodies.
+
+Several of the stars here declared, that they had been much annoyed by
+being observed on Sunday evenings, during the hours of divine service.
+
+The room was then cleared for a division, but we are unable to state what
+took place. Several comets-at-arms were sent for, and we heard rumors of a
+personal collision having taken place between two luminaries in opposition.
+We were afterwards told that the resolution was carried by a majority, and
+the luminaries elongated at 2 h. 15 m. 33,41 s. sidereal time.
+
+* * * It is reported, but we hope without foundation, that Saturn, and
+several other discontented planets, have accepted an invitation from Sirius
+to join his system, on the most liberal appointments. We believe the report
+to have originated in nothing more than the discovery of the annual
+parallax of Sirius from the orbit of Saturn; but we may safely assure our
+readers that no steps have as yet been taken to open any communication.
+
+We are also happy to state, that there is no truth in the rumor of the laws
+of gravitation being about to be repealed. We have traced this report, and
+find it originated with a gentleman living near Bath (Captain Forman,
+R.N),[660] whose name we forbear to mention.
+
+A great excitement has been observed among the nebulae, visible to the
+earth's southern hemisphere, particularly among those which have not yet
+been discovered from thence. We are at a loss to conjecture the cause, but
+we shall not fail to report to our readers the news of any movement which
+may take place. (Sir J. Herschel's visit. He could just see this before he
+went out.)
+
+{307}
+
+
+
+WOODLEY'S DIVINE SYSTEM.
+
+    A Treatise on the Divine System of the Universe, by Captain Woodley,
+    R.N.,[661] and as demonstrated by his Universal Time-piece, and
+    universal method of determining a ship's longitude by the apparent true
+    place of the moon; with an introduction refuting the solar system of
+    Copernicus, the Newtonian philosophy, and mathematics. 1834.[662] 8vo.
+
+    Description of the Universal Time-piece. (4pp. 12mo.)
+
+I think this divine system was published several years before, and was
+republished with an introduction in 1834.[663] Capt. Woodley was very sure
+that the earth does not move: he pointed out to me, in a conversation I had
+with him, something--I forget what--in the motion of the Great Bear,
+visible to any eye, which could not possibly be if the earth moved. He was
+exceedingly ignorant, as the following quotation from his account of the
+usual opinion will show:
+
+"The north pole of the Earth's axis deserts, they say, the north star or
+pole of the Heavens, at the rate of 1 deg. in 713/4 years.... The fact is,
+nothing can be more certain than that the Stars have not changed their
+latitudes or declinations _one degree_ in the last 713/4 years."
+
+This is a strong specimen of a class of men by whom all accessible persons
+who have made any name in science are hunted. It is a pity that they cannot
+be admitted into scientific societies, and allowed fairly to state their
+cases, and stand quiet cross-examination, being kept in their answers very
+close to the questions, and the answers written down. I am perfectly
+satisfied that if one meeting in the year were devoted to the hearing of
+those who chose to come forward on such conditions, much good would be
+done. But I strongly suspect few would come forward {308} at first, and
+none in a little while: and I have had some experience of the method I
+recommend, privately tried. Capt. Woodley was proposed, a little after
+1834, as a Fellow of the Astronomical Society; and, not caring whether he
+moved the sun or the earth, or both--I could not have stood _neither_--I
+signed the proposal. I always had a sneaking kindness for paradoxers, such
+a one, perhaps, as Petit Andre had for his _lambs_, as he called them.
+There was so little feeling against his opinions, that he only failed by a
+fraction of a ball. Had I myself voted, he would have been elected; but
+being engaged in conversation, and not having heard the slightest objection
+to him, I did not think it worth while to cross the room for the purpose. I
+regretted this at the time, but had I known how ignorant he was I should
+not have supported him. Probably those who voted against him knew more of
+his book than I did.
+
+I remember no other instance of exclusion from a scientific society on the
+ground of opinion, even if this be one; of which it may be that ignorance
+had more to do with it than paradoxy. Mr. Frend,[664] a strong
+anti-Newtonian, was a Fellow of the Astronomical Society, and for some
+years in the Council. Lieut. Kerigan[665] was elected to the Royal Society
+at a time when his proposers must have known that his immediate object was
+to put F.R.S. on the title-page of a work against the tides. To give all I
+know, I may add that the editor of some very ignorant bombast about the
+"forehead of the solar sky," who did not know the difference between
+_Bailly_[666] and _Baily_,[667] received hints which induced him to
+withdraw his proposal for election into the Astronomical Society. But this
+was an act of kindness; {309} for if he had seen Mr. Baily in the chair,
+with his head on, he might have been political historian enough to faint
+away.
+
+
+
+    De la formation des Corps. Par Paul Laurent.[668] Nancy, 1834, 8vo.
+
+Atoms, and ether, and ovules or eggs, which are planets, and their eggs,
+which are satellites. These speculators can create worlds, in which they
+cannot be refuted; but none of them dare attack the problem of a grain of
+wheat, and its passage from a seed to a plant, bearing scores of seeds like
+what it was itself.
+
+
+
+ON JOHN FLAMSTEED.
+
+    An account of the Rev. John Flamsteed,[669] the First
+    Astronomer-Royal.... By Francis Baily,[670] Esq. London, 1835, 4to.
+    Supplement, London, 1837, 4to.
+
+My friend Francis Baily was a paradoxer: he brought forward things counter
+to universal opinion. That Newton was impeccable in every point was the
+national creed; and failings of temper and conduct would have been utterly
+disbelieved, if the paradox had not come supported by very unusual
+evidence. Anybody who impeached Newton on existing evidence might as well
+have been squaring the circle, for any attention he would have got. About
+this book I will tell a story. It was published by the Admiralty for
+distribution; and the distribution was entrusted to Mr. Baily. On the eve
+of its appearance, rumors of its extraordinary revelations got about, and
+persons of influence applied to the Admiralty for copies. The Lords were in
+a difficulty: but on looking at the list they saw names, as they {310}
+thought, which were so obscure that they had a right to assume Mr. Baily
+had included persons who had no claim to such a compliment as presentation
+from the Admiralty. The Secretary requested Mr. Baily to call upon him.
+"Mr. Baily, my Lords are inclined to think that some of the persons in this
+list are perhaps not of that note which would justify their Lordships in
+presenting this work."--"To whom does your observation apply, Mr.
+Secretary?"--"Well, now, let us examine the list; let me see;
+now,--now,--now,--come!--here's Gauss[671]--_who's Gauss_?"--"Gauss, Mr.
+Secretary, is the oldest mathematician now living, and is generally thought
+to be the greatest."--"O-o-oh! Well, Mr. Baily, we will see about it, and I
+will write you a letter." The letter expressed their Lordships' perfect
+satisfaction with the list.
+
+There was a controversy about the revelations made in this work; but as the
+eccentric anomalies took no part in it, there is nothing for my purpose.
+The following valentine from Mrs. Flamsteed,[672] which I found among
+Baily's papers, illustrates some of the points:
+
+"3 Astronomers' Row, Paradise: February 14, 1836.
+
+"Dear Sir,--I suppose you hardly expected to receive a letter from me,
+dated from this place; but the truth is, a gentleman from our street was
+appointed guardian angel to the American Treaty, in which there is some
+astronomical question about boundaries. He has got leave to go back to
+fetch some instruments which he left behind, and I take this opportunity of
+making your acquaintance. That America has become a wonderful place since I
+was down among you; you have no idea how grand the fire at New York {311}
+looked up here. Poor dear Mr. Flamsteed does not know I am writing a letter
+to a gentleman on Valentine's day; he is walked out with Sir Isaac Newton
+(they are pretty good friends now, though they do squabble a little
+sometimes) and Sir William Herschel, to see a new nebula. Sir Isaac says he
+can't make out at all how it is managed; and I am sure I cannot help him. I
+never bothered my head about those things down below, and I don't intend to
+begin here.
+
+"I have just received the news of your having written a book about my poor
+dear man. It's a chance that I heard it at all; for the truth is, the
+scientific gentlemen are somehow or other become so wicked, and go so
+little to church, that very few of them are considered fit company for this
+place. If it had not been for Dr. Brinkley,[673] who came here of course, I
+should not have heard about it. He seems a nice man, but is not yet used to
+our ways. As to Mr. Halley,[674] he is of course not here; which is lucky
+for him, for Mr. Flamsteed swore the moment he caught him in a place where
+there are no magistrates, he would make a sacrifice of him to heavenly
+truth. It was very generous in Mr. F. not appearing against Sir Isaac when
+he came up, for I am told that if he had, Sir Isaac would not have been
+allowed to come in at all. I should have been sorry for that, for he is a
+companionable man enough, only holds his head rather higher than he should
+do. I met him the other day walking with Mr. Whiston,[675] and disputing
+about the deluge. 'Well, Mrs. Flamsteed,' says he, 'does old Poke-the-Stars
+understand gravitation yet?' Now you must know that is rather a sore point
+with poor dear Mr. Flamsteed. He says that Sir Isaac is as crochetty about
+the moon as ever; and as to {312} what some people say about what has been
+done since his time, he says he should like to see somebody who knows
+something about it of himself. For it is very singular that none of the
+people who have carried on Sir Isaac's notions have been allowed to come
+here.
+
+"I hope you have not forgotten to tell how badly Sir Isaac used Mr.
+Flamsteed about that book. I have never quite forgiven him; as for Mr.
+Flamsteed, he says that as long as he does not come for observations, he
+does not care about it, and that he will never trust him with any papers
+again as long as he lives. I shall never forget what a rage he came home in
+when Sir Isaac had called him a puppy. He struck the stairs all the way up
+with his crutch, and said puppy at every step, and all the evening, as soon
+as ever a star appeared in the telescope, he called it puppy. I could not
+think what was the matter, and when I asked, he only called me puppy.
+
+"I shall be very glad to see you if you come our way. Pray keep up some
+appearances, and go to church a little. St. Peter is always uncommonly
+civil to astronomers, and indeed to all scientific persons, and never
+bothers them with many questions. If they can make anything out of the
+case, he is sure to let them in. Indeed, he says, it is perfectly out of
+the question expecting a mathematician to be as religious as an apostle,
+but that it is as much as his place is worth to let in the greater number
+of those who come. So try if you cannot manage it, for I am very curious to
+know whether you found all the letters. I remain, dear sir, your faithful
+servant,
+
+"MARGARET FLAMSTEED.
+
+  Francis Baily, Esq.
+
+"P.S. Mr. Flamsteed has come in, and says he left Sir Isaac riding
+cockhorse upon the nebula, and poring over it as if it were a book. He has
+brought in his old acquaintance Ozanam,[676] who says that it was always
+his maxim on {313} earth, that 'il appartient aux docteurs de Sorbonne de
+disputer, au Pape de prononcer, et au mathematicien d'aller en Paradis en
+ligne perpendiculaire.'"[677]
+
+
+
+ON STEVIN.
+
+The Secretary of the Admiralty was completely extinguished. I can recall
+but two instances of demolition as complete, though no doubt there are many
+others. The first is in
+
+  Simon Stevin[678] and M. Dumortier. Nieuport, 1845, 12mo.
+
+M. Dumortier was a member of the Academy of Brussels: there was a
+discussion, I believe, about a national Pantheon for Belgium. The name of
+Stevinus suggested itself as naturally as that of Newton to an Englishman;
+probably no Belgian is better known to foreigners as illustrious in
+science. Stevinus is great in the _Mecanique Analytique_ of Lagrange;[679]
+Stevinus is great in the _Tristram Shandy_ of Sterne. M. Dumortier, who
+believed that not one Belgian in a thousand knew Stevinus, and who
+confesses with ironical shame that he was not the odd man, protested
+against placing the statue of an obscure man in the Pantheon, to give
+foreigners the notion that Belgium could show nothing greater. The work
+above named is a slashing retort: any one who knows the history of science
+ever so little may imagine what a dressing was given, by mere extract from
+foreign writers. The tract is a letter signed J. du Fan, but this is a
+pseudonym of Mr. Van de Weyer.[680] The Academician says Stevinus was a man
+who was not {314} without merit for the time at which he lived: Sir! is the
+answer, he was as much before his own time as you are behind yours. How
+came a man who had never heard of Stevinus to be a member of the Brussels
+Academy?
+
+The second story was told me by Mr. Crabb Robinson,[681] who was long
+connected with the _Times_, and intimately acquainted with Mr. W***.[682]
+When W*** was an undergraduate at Cambridge, taking a walk, he came to a
+stile, on which sat a bumpkin who did not make way for him: the gown in
+that day looked down on the town. "Why do you not make way for a
+gentleman?"--"Eh?"--"Yes, why do you not move? You deserve a good hiding,
+and you shall get it if you don't take care!" The bumpkin raised his
+muscular figure on its feet, patted his menacer on the head, and said, very
+quietly,--"Young man! I'm Cribb."[683] W*** seized the great pugilist's
+hand, and shook it warmly, got him to his own rooms in college, collected
+some friends, and had a symposium which lasted until the large end of the
+small hours.
+
+
+
+FINLEYSON AS A PARADOXER.
+
+    God's Creation of the Universe as it is, in support of the Scriptures.
+    By Mr. Finleyson.[684] Sixth Edition, 1835, 8vo.
+
+{315}
+
+This writer, by his own account, succeeded in delivering the famous Lieut.
+Richard Brothers[685] from the lunatic asylum, and tending him, not as a
+keeper but as a disciple, till he died. Brothers was, by his own account,
+the nephew of the Almighty, and Finleyson ought to have been the nephew of
+Brothers. For Napoleon came to him in a vision, with a broken sword and an
+arrow in his side, beseeching help: Finleyson pulled out the arrow, but
+refused to give a new sword; whereby poor Napoleon, though he got off with
+life, lost the battle of Waterloo. This story was written to the Duke of
+Wellington, ending with "I pulled out the arrow, but left the broken sword.
+Your Grace can supply the rest, and what followed is amply recorded in
+history." The book contains a long account of applications to Government to
+do three things: to pay 2,000l. for care taken of Brothers, to pay 10,000l.
+for discovery of the longitude, and to prohibit the teaching of the
+Newtonian system, which makes God a liar. The successive administrations
+were threatened that they would have to turn out if they refused, which, it
+is remarked, came to pass in every case. I have heard of a joke of Lord
+Macaulay, that the House of Commons must be the Beast of the Revelations,
+since 658 members, with the officers necessary for the action of the House,
+make 666. Macaulay read most things, and the greater part of the rest: so
+that he might be suspected of having appropriated as a joke one of
+Finleyson's serious points--"I wrote Earl Grey[686] upon the 13th of July,
+1831, informing him that his Reform {316} Bill could not be carried, as it
+reduced the members below the present amount of 658, which, with the eight
+principal clerks or officers of the House, make the number 666." But a
+witness has informed me that Macaulay's joke was made in his hearing a
+great many years before the Reform Bill was proposed; in fact, when both
+were students at Cambridge. Earl Grey was, according to Finleyson, a
+descendant of Uriah the Hittite. For a specimen of Lieut. Brothers, this
+book would be worth picking up. Perhaps a specimen of the Lieutenant's
+poetry may be acceptable: Brothers _loquitur_, remember:
+
+ "Jerusalem ! Jerusalem! shall be built again!
+    More rich, more grand then ever;
+  And through it shall Jordan flow!(!)
+    My people's favourite river.
+  There I'll erect a splendid throne,
+    And build on the wasted place;
+  To fulfil my ancient covenant
+    To King David and his race.
+      *    *    *    *    *    *
+ "Euphrates' stream shall flow with ships,
+    And also my wedded Nile;
+  And on my coast shall cities rise,
+    Each one distant but a mile.
+      *    *    *    *    *    *
+ "My friends the Russians on the north
+    With Persees and Arabs round,
+  Do show the limits of my land,
+    Here! Here! then I mark the ground."
+
+
+
+ON THEOLOGICAL PARADOXERS.
+
+Among the paradoxers are some of the theologians who in their own organs of
+the press venture to criticise science. These may hold their ground when
+they confine themselves to the geology of long past periods and to general
+cosmogony: for it is the tug of Greek against Greek; and both sides deal
+much in what is grand when called _hypothesis_, petty when called
+_supposition_. And very often they are not conspicuous when they venture
+upon things within knowledge; {317} wrong, but not quite wrong enough for a
+Budget of Paradoxes. One case, however, is destined to live, as an instance
+of a school which finds writers, editors, and readers. The double stars
+have been seen from the seventeenth century, and diligently observed by
+many from the time of Wm. Herschel, who first devoted continuous attention
+to them. The year 1836 was that of a remarkable triumph of astronomical
+prediction. The theory of gravitation had been applied to the motion of
+binary stars about each other, in elliptic orbits, and in that year the two
+stars of [gamma] Virginis, as had been predicted should happen within a few
+years of that time--for years are small quantities in such long
+revolutions--the two stars came to their nearest: in fact, they appeared to
+be one as much with the telescope as without it. This remarkable
+turning-point of the history of a long and widely-known branch of astronomy
+was followed by an article in the _Church of England Quarterly Review_ for
+April 1837, written against the Useful Knowledge Society. The notion that
+there are any such things as double stars is (p. 460) implied to be
+imposture or delusion, as in the following extract. I suspect that I myself
+am the _Sidrophel_, and that my companion to the maps of the stars, written
+for the Society and published in 1836, is the work to which the writer
+refers:
+
+"We have forgotten the name of that Sidrophel who lately discovered that
+the fixed stars were not single stars, but appear in the heavens like soles
+at Billingsgate, in pairs; while a second astronomer, under the influence
+of that competition in trade which the political economists tell us is so
+advantageous to the public, professes to show us, through his superior
+telescope, that the apparently single stars are really three. Before such
+wondrous mandarins of science, how continually must _homunculi_ like
+ourselves keep in the background, lest we come between the wind and their
+nobility."
+
+If the _homunculus_ who wrote this be still above ground, {318} how
+devoutly must he hope he may be able to keep in the background! But the
+chief blame falls on the editor. The title of the article is:
+
+"The new school of superficial pantology; a speech intended to be delivered
+before a defunct Mechanics' Institute. By Swallow Swift, late M.P. for the
+Borough of Cockney-Cloud, Witsbury: reprinted Balloon Island, Bubble year,
+month _Ventose_. Long live Charlatan!"
+
+As a rule, orthodox theologians should avoid humor, a weapon which all
+history shows to be very difficult to employ in favor of establishment, and
+which, nine times out of ten, leaves its wielder fighting on the side of
+heterodoxy. Theological argument, when not enlivened by bigotry, is seldom
+worse than narcotic: but theological fun, when not covert heresy, is almost
+always sialagogue. The article in question is a craze, which no editor
+should have admitted, except after severe inspection by qualified persons.
+The author of this wit committed a mistake which occurs now and then in old
+satire, the confusion between himself and the party aimed at. He ought to
+be reviewing this fictitious book, but every now and then the article
+becomes the book itself; not by quotation, but by the writer forgetting
+that _he_ is not Mr. Swallow Swift, but his reviewer. In fact he and Mr. S.
+Swift had each had a dose of the _Devil's Elixir_. A novel so called,
+published about forty years ago, proceeds upon a legend of this kind. If
+two parties both drink of the elixir, their identities get curiously
+intermingled; each turns up in the character of the other throughout the
+three volumes, without having his ideas clear as to whether he be himself
+or the other. There is a similar confusion in the answer made to the famous
+_Epistolae Obscurorum Virorum_:[687] it is headed _Lamentationes Obscurorum
+Virorum_.[688] {319} This is not a retort of the writer, throwing back the
+imputation: the obscure men who had been satirized are themselves made, by
+name, to wince under the disapprobation which the Pope had expressed at the
+satire upon themselves.
+
+Of course the book here reviewed is a transparent forgery. But I do not
+know how often it may have happened that the book, in the journals which
+always put a title at the head, may have been written after the review.
+About the year 1830 a friend showed me the proof of an article of his on
+the malt tax, for the next number of the _Edinburgh Review_. Nothing was
+wanting except the title of the book reviewed; I asked what it was. He sat
+down, and wrote as follows at the head, "The Maltster's Guide (pp. 124),"
+and said that would do as well as anything.
+
+But I myself, it will be remarked, have employed such humor as I can
+command "in favor of establishment." What it is worth I am not to judge; as
+usual in such cases, those who are of my cabal pronounce it good, but
+cyclometers and other paradoxers either call it very poor, or commend it as
+sheer buffoonery. Be it one or the other, I observe that all the effective
+ridicule is, in this subject, on the side of establishment. This is partly
+due to the difficulty of quizzing plain and sober demonstration; but so
+much, if not more, to the ignorance of the paradoxers. For that which
+cannot be _ridiculed_, can be _turned into ridicule_ by those who know how.
+But by the time a person is deep enough in _negative_ quantities, and
+_impossible_ quantities, to be able to satirize them, he is caught, and
+being inclined to become a _user_, shrinks from being an _abuser_. Imagine
+a person with a gift of ridicule, and knowledge enough, trying his hand on
+the junction of the assertions which he will find in various books of
+algebra. First, that a negative quantity has no logarithm; secondly, that a
+{320} negative quantity has no square root; thirdly, that the first
+non-existent is to the second as the circumference of a circle to its
+diameter. One great reason of the allowance of such unsound modes of
+expression is the confidence felt by the writers that [root]-1 and log(-1)
+will make their way, however inaccurately described. I heartily wish that
+the cyclometers had knowledge enough to attack the weak points of
+algebraical diction: they would soon work a beneficial change.[689]
+
+
+
+AN EARLY METEOROLOGIST.
+
+    Recueil de ma vie, mes ouvrages et mes pensees. Par Thomas Ignace Marie
+    Forster.[690] Brussels, 1836, 12mo.
+
+Mr. Forster, an Englishman settled at Bruges, was an observer in many
+subjects, but especially in meteorology. He communicated to the
+Astronomical Society, in 1848, the information that, in the registers kept
+by his grandfather, his father, and himself, beginning in 1767, new moon on
+Saturday was followed, nineteen times out of twenty, by twenty days of rain
+and wind. This statement being published in the _Athenaeum_, a cluster of
+correspondents averred that the belief is common among seamen, in all parts
+of the world, and among landsmen too. Some one quoted a distich:
+
+ "Saturday's moon and Sunday's full
+  Never were fine and never _wull_."
+
+{321} Another brought forward:
+
+ "If a Saturday's moon
+  Comes once in seven years it comes too soon."
+
+Mr. Forster did not say he was aware of the proverbial character of the
+phenomenon. He was a very eccentric man. He treated his dogs as friends,
+and buried them with ceremony. He quarrelled with the _cure_ of his parish,
+who remarked that he could not take his dogs to heaven with him. I will go
+nowhere, said he, where I cannot take my dog. He was a sincere Catholic:
+but there is a point beyond which even churches have no influence.
+
+The following is some account of the announcement of 1849. The _Athenaeum_
+(Feb. 17), giving an account of the meeting of the Astronomical Society in
+December, 1858, says:
+
+"Dr. Forster of Bruges, who is well known as a meteorologist, made a
+communication at which our readers will stare: he declares that by journals
+of the weather kept by his grandfather, father, and himself, ever since
+1767, to the present time, _whenever the new moon has fallen on a Saturday,
+the following twenty days have been wet and windy_, in nineteen cases out
+of twenty. In spite of our friend Zadkiel[691] and the others who declare
+that we would smother every truth that does not happen to agree with us, we
+are glad to see that the Society had the sense to publish this
+communication, coming, as it does, from a veteran observer, and one whose
+love of truth is undoubted. It must be that the fact is so set down in the
+journals, because Dr. Forster says it: and whether it be only a fact of the
+journals, or one of the heavens, can soon be tried. The new moon of March
+next, falls on _Saturday_ the 24th, at 2 in the afternoon. We shall
+certainly look out."
+
+{322}
+
+The following appeared in the number of March 31:
+
+"The first _Saturday Moon_ since Dr. Forster's announcement came off a week
+ago. We had previously received a number of letters from different
+correspondents--all to the effect that the notion of new moon on Saturday
+bringing wet weather is one of widely extended currency. One correspondent
+(who gives his name) states that he has constantly heard it at sea, and
+among the farmers and peasantry in Scotland, Ireland, and the North of
+England. He proceeds thus: 'Since 1826, nineteen years of the time I have
+spent in a seafaring life. I have constantly observed, though unable to
+account for, the phenomenon. I have also heard the stormy qualities of a
+Saturday's moon remarked by American, French, and Spanish seamen; and,
+still more distant, a Chinese pilot, who was once doing duty on board my
+vessel seemed to be perfectly cognizant of the fact.' So that it seems we
+have, in giving currency to what we only knew as a very curious
+communication from an earnest meteorologist, been repeating what is common
+enough among sailors and farmers. Another correspondent affirms that the
+thing is most devoutly believed in by seamen; who would as soon sail on a
+Friday as be in the Channel after a Saturday moon.--After a tolerable
+course of dry weather, there was some snow, accompanied by wind on Saturday
+last, here in London; there were also heavy louring clouds. Sunday was
+cloudy and cold, with a little rain; Monday was louring, Tuesday unsettled;
+Wednesday quite overclouded, with rain in the morning. The present occasion
+shows only a general change of weather with a tendency towards rain. If Dr.
+Forster's theory be true, it is decidedly one of the minor instances, as
+far as London weather is concerned.--It will take a good deal of evidence
+to make us believe in the omen of a Saturday Moon. But, as we have said of
+the Poughkeepsie Seer, the thing is very curious whether true or false.
+Whence comes this universal proverb--and a hundred others--while the
+meteorological observer {323} cannot, when he puts down a long series of
+results, detect any weather cycles at all? One of our correspondents wrote
+us something of a lecture for encouraging, he said, the notion that _names_
+could influence the weather. He mistakes the question. If there be any
+weather cycles depending on the moon, it is possible that one of them may
+be so related to the week cycle of seven days, as to show recurrences which
+are of the kind stated, or any other. For example, we know that if the new
+moon of March fall on a Saturday in this year, it will most probably fall
+on a Saturday nineteen years hence. This is not connected with the spelling
+of Saturday--but with the connection between the motions of the sun and
+moon. Nothing but the Moon can settle the question--and we are willing to
+wait on her for further information. If the adage be true, then the
+philosopher has missed what lies before his eyes; if false, then the world
+can be led by the nose in spite of the eyes. Both these things happen
+sometimes; and we are willing to take whichever of the two solutions is
+borne out by future facts. In the mean time, we announce the next Saturday
+Moon for the 18th of August."
+
+How many coincidences are required to establish a law of connection? It
+depends on the way in which the mind views the matter in question. Many of
+the paradoxers are quite set up by a very few instances. I will now tell a
+story about myself, and then ask them a question.
+
+So far as instances can prove a law, the following is proved: no failure
+has occurred. Let a clergyman be known to me, whether by personal
+acquaintance or correspondence, or by being frequently brought before me by
+those with whom I am connected in private life: that clergyman does not,
+except in few cases, become a bishop; but _if_ he become a bishop, he is
+sure, first or last, to become an arch-bishop. This has happened in every
+case. As follows:
+
+1. My last schoolmaster, a former Fellow of Oriel, was {324} a very
+intimate college friend of Richard Whately[692], a younger man. Struck by
+his friend's talents, he used to talk of him perpetually, and predict his
+future eminence. Before I was sixteen, and before Whately had even given
+his Bampton Lectures, I was very familiar with his name, and some of his
+sayings. I need not say that he became Archbishop of Dublin.
+
+2. When I was a child, a first cousin of John Bird Sumner[693] married a
+sister of my mother. I cannot remember the time when I first heard his
+name, but it was made very familiar to me. In time he became Bishop of
+Chester, and then, Archbishop of Canterbury. My reader may say that Dr.
+C. R. Sumner,[694] Bishop of Winchester, has just as good a claim: but it
+is not so: those connected with me had more knowledge of Dr. J. B.
+Sumner;[695] and said nothing, or next to nothing, of the other. Rumor says
+that the Bishop of Winchester has _declined_ an Archbishopric: if so, my
+rule is a rule of gradations.
+
+3. Thomas Musgrave,[696] Fellow of Trinity College, Cambridge, was _Dean_
+of the college when I was an undergraduate: this brought me into connection
+with him, he giving impositions for not going to chapel, I writing them out
+according. We had also friendly intercourse in after life; I forgiving, he
+probably forgetting. Honest Tom {325} Musgrave, as he used to be called,
+became Bishop of Hereford, and Archbishop of York.
+
+4. About the time when I went to Cambridge, I heard a great deal about Mr.
+C. T. Longley,[697] of Christchurch, from a cousin of my own of the same
+college, long since deceased, who spoke of him much, and most
+affectionately. Dr. Longley passed from Durham to York, and thence to
+Canterbury. I cannot quite make out the two Archbishoprics; I do not
+remember any other private channel through which the name came to me:
+perhaps Dr. Longley, having two strings to his bow, would have been one
+archbishop if I had never heard of him.
+
+5. When Dr. Wm. Thomson[698] was appointed to the see of Gloucester in
+1861, he and I had been correspondents on the subject of logic--on which we
+had both written--for about fourteen years. On his elevation I wrote to
+him, giving the preceding instances, and informing him that he would
+certainly be an Archbishop. The case was a strong one, and the law acted
+rapidly; for Dr. Thomson's elevation to the see of York took place in 1862.
+
+Here are five cases; and there is no opposing instance. I have searched the
+almanacs since 1828, and can find no instance of a Bishop not finally
+Archbishop of whom I had known through private sources, direct or indirect.
+Now what do my paradoxers say? Is this a pre-established harmony, or a
+chain of coincidences? And how many instances will it require to establish
+a law?[699]
+
+{326}
+
+
+
+THE HERSCHEL HOAX.
+
+    Some account of the great astronomical discoveries lately made by Sir
+    John Herschel at the Cape of Good Hope. Second Edition. London, 12mo.
+    1836.
+
+This is a curious hoax, evidently written by a person versed in astronomy
+and clever at introducing probable circumstances and undesigned
+coincidences.[700] It first appeared in a newspaper. It makes Sir J.
+Herschel discover men, animals, etc. in the moon, of which much detail is
+given. There seems to have been a French edition, the original, and English
+editions in America, whence the work came into Britain: but whether the
+French was published in America or at Paris I do not know. There is no
+doubt that it was produced in the United States, by M. Nicollet,[701] an
+astronomer, once of Paris, and a fugitive of some kind. About him I have
+heard two stories. First that he fled to America with funds not his own,
+and that this book was a mere device to raise the wind. Secondly, that he
+was a protege of Laplace, and of the Polignac party, and also an outspoken
+man. That after the revolution he was so obnoxious to the republican party
+that he judged it prudent to quit France; which he did in debt, leaving
+money for his creditors, but not enough, with M. Bouvard. In America he
+connected himself with an assurance office. {327} The moon-story was
+written, and sent to France, chiefly with the intention of entrapping M.
+Arago, Nicollet's especial foe, into the belief of it. And those who
+narrate this version of the story wind up by saying that M. Arago _was_
+entrapped, and circulated the wonders through Paris, until a letter from
+Nicollet to M. Bouvard[702] explained the hoax. I have no personal
+knowledge of either story: but as the poor man had to endure the first, it
+is but right that the second should be told with it.
+
+
+
+SOME MORE METEOROLOGY.
+
+    The Weather Almanac for the Year 1838. By P. Murphy,[703] Esq., M.N.S.
+
+By M. N. S. is meant _member of no society._. This almanac bears on the
+title-page two recommendations. The _Morning Post_ calls it one of the most
+important-if-true publications of our generation. The _Times_ says: "If the
+basis of his theory prove sound, and its principles be sanctioned by a more
+extended experience, it is not too much to say that the importance of the
+discovery is equal to that of the longitude." Cautious journalist! Three
+times that of the longitude would have been too little to say. That the
+landsman might predict the weather of all the year, at its beginning, Jack
+would cheerfully give up astronomical longitude--_the_ problem--altogether,
+and fall back on chronometers with the older Ls, lead, latitude, and
+look-out, applied to dead-reckoning. Mr. Murphy attempted to give the
+weather day by day: thus the first seven days of March {328} bore
+Changeable; Rain; Rain; Rain-_wind_; Changeable; Fair; Changeable. To aim
+at such precision as to put a fair day between two changeable ones by
+weather theory was going very near the wind and weather too. Murphy opened
+the year with cold and frost; and the weather did the same. But Murphy,
+opposite to Saturday, January 20, put down "Fair, Probable lowest degree of
+winter temperature." When this Saturday came, it was not merely the
+probably coldest of 1838, but certainly the coldest of many consecutive
+years. Without knowing anything of Murphy, I felt it prudent to cover my
+nose with my glove as I walked the street at eight in the morning. The
+fortune of the Almanac was made. Nobody waited to see whether the future
+would dement the prophecy: the shop was beset in a manner which brought the
+police to keep order; and it was said that the Almanac for 1838 was a gain
+of 5,000l. to the owners. It very soon appeared that this was only a lucky
+hit: the weather-prophet had a modified reputation for a few years; and is
+now no more heard of. A work of his will presently appear in the list.
+
+
+
+THE GREAT PYRAMIDS.
+
+    Letter from Alexandria on the evidence of the practical application of
+    the quadrature of the circle in the great pyramids of Gizeh. By H. C.
+    Agnew,[704] Esq. London, 1838, 4to.
+
+{329}
+
+Mr. Agnew detects proportions which he thinks were suggested by those of
+the circumference and diameter of a circle.
+
+
+
+THE MATHEMATICS OF A CREED.
+
+    The creed of St. Athanasius proved by a mathematical parallel. Before
+    you censure, condemn, or approve; read, examine, and understand. E. B.
+    REVILO.[705] London, 1839, 8vo.
+
+This author really believed himself, and was in earnest. He is not the only
+person who has written nonsense by confounding the mathematical infinite
+(of quantity) with what speculators now more correctly express by the
+unlimited, the unconditioned, or the absolute. This tract is worth
+preserving, as the extreme case of a particular kind. The following is a
+specimen. Infinity being represented by [infinity], as usual, and f, s, g,
+being finite integers, the three Persons are denoted by [infinity]^{f}, (m
+[infinity])^{s}, [infinity]^{g}, the finite fraction m representing human
+nature, as opposed to [infinity]. The clauses of the Creed are then given
+with their mathematical parallels. I extract a couple:
+
+ "But the Godhead of the
+  Father, of the Son, and of
+  the Holy Ghost, is all one:
+  the glory equal, the Majesty
+  co-eternal.
+
+ "It has been shown that
+  [infinity]^f, [infinity]^g, and (m [infinity])^s, together,
+  are but [infinity], and that
+  each is [infinity], and any magnitude
+  in existence represented
+  by [infinity] always was and always
+  will be: for it cannot
+  be made, or destroyed, and
+  yet exists.
+
+{330}
+
+ "Equal to the Father, as
+  touching his Godhead: and
+  inferior  to the  Father,
+  touching his Manhood."
+
+ "(m [infinity])^s is equal to [infinity]^f as
+  touching [infinity], but inferior to
+  [infinity]^f as touching m: because
+  m is not infinite."
+
+I might have passed this over, as beneath even my present subject, but for
+the way in which I became acquainted with it. A bookseller, _not the
+publisher_, handed it to me over his counter: one who had published
+mathematical works. He said, with an air of important communication, Have
+you seen _this_, Sir! In reply, I recommended him to show it to my friend
+Mr.----, for whom he had published mathematics. Educated men, used to books
+and to the converse of learned men, look with mysterious wonder on such
+productions as this: for which reason I have made a quotation which many
+will judge had better have been omitted. But it would have been an
+imposition on the public if I were, omitting this and some other uses of
+the Bible and Common Prayer, to pretend that I had given a true picture of
+my school.
+
+[Since the publication of the above, it has been stated that the author is
+Mr. Oliver Byrne, the author of the _Dual Arithmetic_ mentioned further on:
+E. B. Revilo seems to be obviously a reversal.]
+
+
+
+LOGIC HAS NO PARADOXERS.
+
+    Old and new logic contrasted: being an attempt to elucidate, for
+    ordinary comprehension, how Lord Bacon delivered the human mind from
+    its 2,000 years' enslavement under Aristotle. By Justin Brenan.[706]
+    London, 1839, 12mo.
+
+Logic, though the other exact science, has not had the sort of assailants
+who have clustered about mathematics. There is a sect which disputes the
+utility of logic, but there are no special points, like the quadrature of
+the circle, which {331} excite dispute among those who admit other things.
+The old story about Aristotle having one logic to trammel us, and Bacon
+another to set us free,--always laughed at by those who really knew either
+Aristotle or Bacon,--now begins to be understood by a large section of the
+educated world. The author of this tract connects the old logic with the
+indecencies of the classical writers, and the new with moral purity: he
+appeals to women, who, "when they see plainly the demoralizing tendency of
+syllogistic logic, they will no doubt exert their powerful influence
+against it, and support the Baconian method." This is the only work against
+logic which I can introduce, but it is a rare one, I mean in contents. I
+quote the author's idea of a syllogism:
+
+"The basis of this system is the syllogism. This is a form of couching the
+substance of your argument or investigation into one short line or
+sentence--then corroborating or supporting it in another, and drawing your
+conclusion or proof in a third."
+
+On this definition he gives an example, as follows: "Every sin deserves
+death," the substance of the "argument or investigation." Then comes,
+"Every unlawful wish is a sin," which "corroborates or supports" the
+preceding: and, lastly, "therefore every unlawful wish deserves death,"
+which is the "conclusion or proof." We learn, also, that "sometimes the
+first is called the premises (_sic_), and sometimes the first premiss"; as
+also that "the first is sometimes called the proposition, or subject, or
+affirmative, and the next the predicate, and sometimes the middle term." To
+which is added, with a mark of exclamation at the end, "but in analyzing
+the syllogism, there is a middle term, and a predicate too, in each of the
+lines!" It is clear that Aristotle never enslaved this mind.
+
+I have said that logic has no paradoxers, but I was speaking of old time.
+This science has slept until our own day: Hamilton[707] says there has been
+"no progress made in {332} the _general_ development of the syllogism since
+the time of Aristotle; and in regard to the few _partial_ improvements, the
+professed historians seem altogether ignorant." But in our time, the
+paradoxer, the opponent of common opinion, has appeared in this field. I do
+not refer to Prof. Boole,[708] who is not a _paradoxer_, but a
+_discoverer_: his system could neither oppose nor support common opinion,
+for its grounds were not in the conception of any one. I speak especially
+of two others, who fought like cat and dog: one was dogmatical, the other
+categorical. The first was Hamilton himself--Sir William Hamilton of
+Edinburgh, the metaphysician, not Sir William _Rowan_ Hamilton[709] of
+Dublin, the mathematician, a combination of peculiar genius with
+unprecedented learning, erudite in all he could want except mathematics,
+for which he had no turn, and in which he had not even a schoolboy's
+knowledge, thanks to the Oxford of his younger day. The other was the
+author of this work, so fully described in Hamilton's writings that there
+is no occasion to describe him here. I shall try to say a few words in
+common language about the paradoxers.
+
+Hamilton's great paradox was the _quantification of the predicate_; a
+fearful phrase, easily explained. We all know that when we say "Men are
+animals," a form wholly unquantified in phrase, we speak of _all_ men, but
+not of all animals: it is _some or all_, some may be all for aught the
+proposition says. This some-may-be-all-for-aught-we-say, or _not-none,_ is
+the logician's _some_. One would suppose {333} that "all men are some
+animals," would have been the logical phrase in all time: but the predicate
+never was quantified. The few who alluded to the possibility of such a
+thing found reasons for not adopting it over and above the great reason,
+that Aristotle did not adopt it. For Aristotle never ruled in physics or
+metaphysics _in the old time_ with near so much of absolute sway as he has
+ruled in logic _down to our own time_. The logicians knew that in the
+proposition "all men are animals" the "animal" is not _universal_, but
+_particular_ yet no one dared to say that _all_ men are _some_ animals, and
+to invent the phrase, "_some_ animals are _all_ men" until Hamilton leaped
+the ditch, and not only completed a system of enunciation, but applied it
+to syllogism.
+
+My own case is as peculiar as his: I have proposed to introduce
+mathematical _thought_ into logic to an extent which makes the old stagers
+cry:
+
+ "St. Aristotle! what wild notions!
+  Serve a _ne exeat regno_[710] on him!"
+
+Hard upon twenty years ago, a friend and opponent who stands high in these
+matters, and who is not nearly such a sectary of Aristotle and
+establishment as most, wrote to me as follows: "It is said that next to the
+man who forms the taste of the nation, the greatest genius is the man who
+corrupts it. I mean therefore no disrespect, but very much the reverse,
+when I say that I have hitherto always considered you as a great logical
+heresiarch." Coleridge says he thinks that it was Sir Joshua Reynolds who
+made the remark: which, to copy a bull I once heard, I cannot deny, because
+I was not there when he said it. My friend did not call me to repentance
+and reconciliation with the church: I think he had a guess that I was a
+reprobate sinner. My offences at that time were but small: I went on
+spinning syllogism systems, all alien from the common logic, until I had
+six, the initial letters of which, put together, from the {334} names I
+gave before I saw what they would make, bar all repentance by the words
+
+  RUE NOT!
+
+leaving to the followers of the old school the comfortable option of
+placing the letters thus:
+
+  TRUE? NO!
+
+It should however be stated that the question is not about absolute truth
+or falsehood. No one denies that anything I call an inference is an
+inference: they say that my alterations are _extra-logical_; that they are
+_material_, not _formal_; and that logic is a _formal_ science.
+
+The distinction between material and formal is easily made, where the usual
+perversions are not required. A _form_ is an empty machine, such as "Every
+X is Y"; it may be supplied with _matter_, as in "Every _man_ is _animal_."
+The logicians will not see that their _formal_ proposition, "Every X is Y,"
+is material in three points, the degree of assertion, the quantity of the
+proposition, and the copula. The purely formal proposition is "There is the
+probability [alpha] that X stands in the relation L to Y." The time will
+come when it will be regretted that logic went without paradoxers for two
+thousand years: and when much that has been said on the distinction of form
+and matter will breed jokes.
+
+I give one instance of one mood of each of the systems, in the order of the
+letters first written above.
+
+_Relative._--In this system the formal relation is taken, that is, the
+copula may be any whatever. As a material instance, in which the
+_relations_ are those of consanguinity (of men understood), take the
+following: X is the brother of Y; X is not the uncle of Z; therefore, Z is
+not the child of Y. The discussion of relation, and of the objections to
+the extension, is in the _Cambridge Transactions_, Vol. X, Part 2; a
+crabbed conglomerate.
+
+_Undecided._--In this system one premise, and want of power over another,
+infer want of power over a conclusion. {335} As "Some men are not capable
+of tracing consequences; we cannot be sure that there are beings
+responsible for consequences who are incapable of tracing consequences;
+therefore, we cannot be sure that all men are responsible for the
+consequences of their actions."
+
+_Exemplar._--This, long after it suggested itself to me as a means of
+correcting a defect in Hamilton's system, I saw to be the very system of
+Aristotle himself, though his followers have drifted into another. It makes
+its subject and predicate examples, thus: Any one man is an animal; any one
+animal is a mortal; therefore, any one man is a mortal.
+
+_Numerical._--Suppose 100 Ys to exist: then if 70 Xs be Ys, and 40 Zs be
+Ys, it follows that 10 Xs (at least) are Zs. Hamilton, whose mind could not
+generalize on symbols, saw that the word _most_ would come under this
+system, and admitted, as valid, such a syllogism as "most Ys are Xs; most
+Ys are Zs; therefore, some Xs are Zs."
+
+_Onymatic._--This is the ordinary system much enlarged in propositional
+forms. It is fully discussed in my _Syllabus of Logic_.
+
+_Transposed._--In this syllogism the quantity in one premise is transposed
+into the other. As, some Xs are not Ys; for every X there is a Y which is
+Z; therefore, some Zs are not Xs.
+
+Sir William Hamilton of Edinburgh was one of the best friends and allies I
+ever had. When I first began to publish speculation on this subject, he
+introduced me to the logical world as having plagiarized from him. This
+drew their attention: a mathematician might have written about logic under
+forms which had something of mathematical look long enough before the
+Aristotelians would have troubled themselves with him: as was done by John
+Bernoulli,[711] {336} James Bernoulli,[712] Lambert,[713] and
+Gergonne;[714] who, when our discussion began, were not known even to
+omnilegent Hamilton. He retracted his accusation of _wilful_ theft in a
+manly way when he found it untenable; but on this point he wavered a
+little, and was convinced to the last that I had taken his principle
+unconsciously. He thought I had done the same with Ploucquet[715] and
+Lambert. It was his pet notion that I did not understand the commonest
+principles of logic, that I did not always know the difference between the
+middle term of a syllogism and its conclusion. It went against his grain to
+imagine that a mathematician could be a logician. So long as he took me to
+be riding my own hobby, he laughed consumedly: but when he thought he could
+make out that I was mounted behind Ploucquet or Lambert, the current ran
+thus: "It would indeed have been little short of a miracle had he, ignorant
+even of the common principles of logic, been able of himself to rise to
+generalization so lofty and so accurate as are supposed in the peculiar
+doctrines of both the rival logicians, Lambert and Ploucquet--how useless
+soever these may in practice prove to be." All this has been sufficiently
+discussed elsewhere: "but, masters, remember that I am an ass."
+
+I know that I never saw Lambert's work until after all Hamilton supposed me
+to have taken was written: he himself, who read almost everything, knew
+nothing about it until after I did. I cannot prove what I say about my
+knowledge of Lambert: but the means of doing it may turn up. For, by the
+casual turning up of an old letter, I _have_ {337} found the means of
+clearing myself as to Ploucquet. Hamilton assumed that (unconsciously) I
+took from Ploucquet the notion of a logical notation in which the symbol of
+the conclusion is seen in the joint symbols of the premises. For example,
+in my own fashion I write down ( . ) ( . ), two symbols of premises. By
+these symbols I see that there is a valid conclusion, and that it may be
+written in symbol by striking out the two middle parentheses, which gives (
+. . ) and reading the two negative dots as an affirmative. And so I see in
+( . ) ( . ) that ( ) is the conclusion. This, in full, is the perception
+that "all are either Xs or Ys" and "all are either Ys or Zs" necessitates
+"some Xs are Zs." Now in Ploucquet's book of 1763, is found, "Deleatur in
+praemissis medius; id quod restat indicat conclusionem."[716] In the paper
+in which I explain my symbols--which are altogether different from
+Ploucquet's--there is found "Erase the symbols of the middle term; the
+remaining symbols show the inference." There is very great likeness: and I
+would have excused Hamilton for his notion if he had fairly given reference
+to the part of the book in which his quotation was found. For I had shown
+in my _Formal Logic_ what part of Ploucquet's book I had used: and a fair
+disputant would either have strengthened his point by showing that I had
+been at his part of the book, or allowed me the advantage of it being
+apparent that I had not given evidence of having seen that part of the
+book. My good friend, though an honest man, was sometimes unwilling to
+allow due advantage to controversial opponents.
+
+But to my point. The only work of Ploucquet I ever saw was lent me by my
+friend Dr. Logan,[717] with whom I have often corresponded on logic, etc. I
+chanced (in 1865) {338} to turn up the letter which he sent me (Sept. 12,
+1847) _with the book_. Part of it runs thus: "I congratulate you on your
+success in your logical researches [that is, in asking for the book, I had
+described some results]. Since the reading of your first paper I have been
+satisfied as to the possibility of inventing a logical notation in which
+the rationale of the inference is contained in the symbol, though I never
+attempted to verify it [what I communicated, then, satisfied the writer
+that I had done and communicated what he, from my previous paper, suspected
+to be practicable]. I send you Ploucquet's dissertation....'
+
+It now being manifest that I cannot be souring grapes which have been taken
+from me, I will say what I never said in print before. There is not the
+slightest merit in making the symbols of the premises yield that of the
+conclusion by erasure: _the thing must do itself in every system which
+symbolises quantities_. For in every syllogism (except the inverted
+_Bramantip_ of the Aristotelians) the conclusion is manifest in this way
+without symbols. This _Bramantip_ destroys system in the Aristotelian lot:
+and circumstances which I have pointed out destroy it in Hamilton's own
+collection. But in that enlargement of the reputed Aristotelian system
+which I have called _onymatic_, and in that correction of Hamilton's system
+which I have called _exemplar_, the rule of erasure is universal, and may
+be seen without symbols.
+
+Our first controversy was in 1846. In 1847, in my _Formal Logic_, I gave
+him back a little satire for satire, just to show, as I stated, that I
+could employ ridicule if I pleased. He was so offended with the appendix in
+which this was contained, that he would not accept the copy of the book I
+sent him, but returned it. Copies of controversial works, sent from
+opponent to opponent, are not _presents_, in the usual sense: it was a
+marked success to make him angry enough to forget this. It had some effect
+however: during the rest of his life I wished to avoid provocation; for I
+{339} could not feel sure that excitement might not produce consequences. I
+allowed his slashing account of me in the _Discussions_ to pass unanswered:
+and before that, when he proposed to open a controversy in the _Athenaeum_
+upon my second Cambridge paper, I merely deferred the dispute until the
+next edition of my _Formal Logic_. I cannot expect the account in the
+_Discussions_ to amuse an unconcerned reader as much as it amused myself:
+but for a cut-and-thrust, might-and-main, tooth-and-nail, hammer-and-tongs
+assault, I can particularly recommend it. I never knew, until I read it,
+how much I should enjoy a thundering onslought on myself, done with racy
+insolence by a master hand, to whom my good genius had whispered _Ita feri
+ut se sentiat emori_.[718] Since that time I have, as the Irishman said,
+become "dry moulded for want of a bating." Some of my paradoxers have done
+their best: but theirs is mere twopenny--"small swipes," as Peter Peebles
+said. Brandy for heroes! I hope a reviewer or two will have mercy on me,
+and will give me as good discipline as Strafford would have given Hampden
+and his set: "much beholden," said he, "should they be to any one that
+should thoroughly take pains with them in that kind"--meaning _objective_
+flagellation. And I shall be the same to any one who will serve me so--but
+in a literary and periodical sense: my corporeal cuticle is as thin as my
+neighbors'.
+
+Sir W. H. was suffering under local paralysis before our controversy
+commenced: and though his mind was quite unaffected, a retort of as
+downright a character as the attack might have produced serious effect upon
+a person who had shown himself sensible of ridicule. Had a second attack of
+his disorder followed an answer from me, I should have been held to have
+caused it: though, looking at Hamilton's genial love of combat, I strongly
+suspected that a retort in kind
+
+{340}
+
+ "Would cheer his heart, and warm his blood,
+  And make him fight, and do him good."
+
+But I could not venture to risk it. So all I did, in reply to the article
+in the _Discussions_, was to write to him the following note: which, as
+illustrating an etiquette of controversy, I insert.
+
+"I beg to acknowledge and thank you for.... It is necessary that I should
+say a word on my retention of this work, with reference to your return of
+the copy of my _Formal Logic_, which I presented to you on its publication:
+a return made on the ground of your disapproval of the account of our
+controversy which that work contained. According to my view of the subject,
+any one whose dealing with the author of a book is specially attacked in
+it, has a right to expect from the author that part of the book in which
+the attack is made, together with so much of the remaining part as is
+fairly context. And I hold that the acceptance by the party assailed of
+such work or part of a work does not imply any amount of approval of the
+contents, or of want of disapproval. On this principle (though I am not
+prepared to add the word _alone_) I forwarded to you the whole of my work
+on _Formal Logic_ and my second Cambridge Memoir. And on this principle I
+should have held you wanting in due regard to my literary rights if you had
+not forwarded to me your asterisked pages, with all else that was necessary
+to a full understanding of their scope and meaning, so far as the contents
+of the book would furnish it. For the remaining portion, which it would be
+a hundred pities to separate from the pages in which I am directly
+concerned, I am your debtor on another principle; and shall be glad to
+remain so if you will allow me to make a feint of balancing the account by
+the offer of two small works on subjects as little connected with our
+discussion as the _Epistolae Obscurorum Virorum_, or the Lutheran dispute. I
+trust that by accepting my _Opuscula_ you will enable me to avoid the {341}
+use of the knife, and leave me to cut you up with the pen as occasion shall
+serve, I remain, etc. (April 21, 1852)."
+
+I received polite thanks, but not a word about the body of the letter: my
+argument, I suppose, was admitted.
+
+
+
+SOME DOGGEREL AND COUNTER DOGGEREL.
+
+I find among my miscellaneous papers the following _jeu d'esprit_, or _jeu
+de betise_,[719] whichever the reader pleases--I care not--intended, before
+I saw ground for abstaining, to have, as the phrase is, come in somehow. I
+think I could manage to bring anything into anything: certainly into a
+Budget of Paradoxes. Sir W. H. rather piqued himself upon some caniculars,
+or doggerel verses, which he had put together _in memoriam_ [_technicam_]
+of the way in which A E I O are used in logic: he added U, Y, for the
+addition of _meet_, etc., to the system. I took the liberty of concocting
+some counter-doggerel, just to show that a mathematician may have
+architectonic power as well as a metaphysician.
+
+
+
+          DOGGEREL.
+      BY SIR W.  HAMILTON.
+  A it affirms of _this_, _these_, _all_,
+    Whilst E denies of _any_;
+  I it affirms (whilst O denies)
+    Of some (or few, or many).
+
+  Thus A affirms, as E denies,
+    And definitely either;
+  Thus I affirms, as O denies,
+    And definitely neither.
+
+  A half, left semidefinite,
+    Is worthy of its score;
+  U, then, affirms, as Y denies,
+    This, neither less nor more.
+
+  Indefinito-definites,
+    I, UI, YO, last we come;
+  {342}
+  And this affirms, as that denies
+    Of _more_, _most_ (_half_, _plus_, _some_).
+
+    COUNTER DOGGEREL.
+      BY PROF. DE MORGAN.
+          (1847.)
+  Great A affirms of all;
+    Sir William does so too:
+  When the subject is "my suspicion,"
+    And the predicate "must be true."
+
+  Great E denies of all;
+    Sir William of all but one:
+  When he speaks about this present time,
+    And of those who in logic have done.
+
+  Great I takes up but _some_;
+    Sir William! my dear soul!
+  Why then in all your writings,
+    Does "Great I" fill[720] the whole!
+
+  Great O says some are not;
+    Sir William's readers catch,
+  That some (modern) Athens is not without
+    An Aristotle to match.
+
+ "A half, left semi-definite,
+    Is worthy of its score:"
+  This looked very much like balderdash,
+    And neither less nor more.
+
+  It puzzled me like anything;
+    In fact, it puzzled me worse:
+  Isn't schoolman's logic hard enough,
+    Without being in Sibyl's verse?
+
+  {343}
+  At last, thinks I, 'tis German;
+    And I'll try it with some beer!
+  The landlord asked what bothered me so,
+    And at once he made it clear.
+
+  It's _half-and-half_, the gentleman means;
+    Don't you see he talks of _score_?
+  That's the bit of memorandum
+    That we chalk behind the door.
+
+  _Semi-definite_'s outlandish;
+    But I see, in half a squint,
+  That he speaks of the lubbers who call for a quart,
+    When they can't manage more than a pint.
+
+  Now I'll read it into English,
+    And then you'll answer me this:
+  If it isn't good logic all the world round,
+    I should like to know what is?
+
+  When you call for a pot of half-and-half,
+    If you're lost to sense of shame,
+  You may leave it _semi-definite_,
+    But you pay for it all just the same.
+      *    *    *    *    *    *
+
+I am unspeakably comforted when I look over the above in remembering that
+the question is not whether it be Pindaric or Horatian, but whether the
+copy be as good as the original. And I say it is: and will take no denial.
+
+Long live--long will live--the glad memory of William Hamilton, Good,
+Learned, Acute, and Disputatious! He fought upon principle: the motto of
+his book is:
+
+ "Truth, like a torch, the more it's shook it shines."
+
+There is something in this; but metaphors, like puddings, quarrels, rivers,
+and arguments, always have two sides to them. For instance,
+
+ "Truth, like a torch, the more it's shook it shines;
+    But those who want to use it, hold it steady.
+  They shake the flame who like a glare to gaze at,
+    They keep it still who want a light to see by."
+
+{344}
+
+
+
+ANOTHER THEORY OF PARALLELS.
+
+    Theory of Parallels. The proof of Euclid's axiom looked for in the
+    properties of the Equiangular Spiral. By Lieut-Col. G. Perronet
+    Thompson.[721] The same, second edition, revised and corrected. The
+    same, third edition, shortened, and freed from dependence on the theory
+    of limits. The same, fourth edition, ditto, ditto. All London, 1840,
+    8vo.
+
+To explain these editions it should be noted that General Thompson rapidly
+modified his notions, and republished his tracts accordingly.
+
+
+
+SOME PRIMITIVE DARWINISM.
+
+    Vestiges of the Natural History of Creation.[722] London, 1840, 12mo.
+
+This is the first edition of this celebrated work. Its form is a case of
+the theory: the book is an undeniable duodecimo, but the size of its paper
+gives it the look of not the smallest of octavos. Does not this illustrate
+the law of development, the gradation of families, the transference of
+species, and so on? If so, I claim the discovery of this esoteric testimony
+of the book to its own contents; I defy any one to point out the reviewer
+who has mentioned it. The work itself is described by its author as "the
+first attempt to connect the natural sciences into a history of creation."
+The attempt was commenced, and has been carried on, both with marked
+talent, and will be continued. Great advantage will result: at the worst we
+are but in the alchemy of some new chemistry, or the astrology of some new
+astronomy. Perhaps it would be as well not to be too sure on the matter,
+until we have an antidote to possible consequences as exhibited under
+another theory, on which {345} it is as reasonable to speculate as on that
+of the _Vestiges_. I met long ago with a splendid player on the guitar, who
+assured me, and was confirmed by his friends, that he _never practised_,
+except in thought, and did not possess an instrument: he kept his fingers
+acting in his mind, until they got their habits; and thus he learnt the
+most difficult novelties of execution. Now what if this should be a minor
+segment of a higher law? What if, by constantly thinking of ourselves as
+descended from primeval monkeys, we should--if it be true--actually _get
+our tails again_? What if the first man who was detected with such an
+appendage should be obliged to confess himself the author of the
+_Vestiges_--a person yet unknown--who would naturally get the start of his
+species by having had the earliest habit of thinking on the matter? I
+confess I never hear a man of note talk fluently about it without a curious
+glance at his proportions, to see whether there may be ground to conjecture
+that he may have more of "mortal coil" than others, in anaxyridical
+concealment. I do not feel sure that even a paternal love for his theory
+would induce him, in the case I am supposing, to exhibit himself at the
+British Association,
+
+  With a hole behind which his tail peeped through.
+
+The first sentence of this book (1840) is a cast of the log, which shows
+our rate of progress. "It is familiar knowledge that the earth which we
+inhabit is a globe of somewhat less than 8,000 miles in diameter, being one
+of a series of eleven which revolve at different distances around the sun."
+The _eleven_! Not to mention the Iscariot which Le Verrier and Adams
+calculated into existence, there is more than a septuagint of _new_
+planetoids.
+
+
+
+ON RELIGIOUS INSURANCE.
+
+    The Constitution and Rules of the Ancient and Universal 'Benefit
+    Society' established by Jesus Christ, exhibited, and its advantages and
+    claims maintained, against all Modern and {346} merely Human
+    Institutions of the kind: A Letter very respectfully addressed to the
+    Rev. James Everett,[723] and occasioned by certain remarks made by him,
+    in a speech to the Members of the 'Wesleyan Centenary Institute'
+    Benefit Society. Dated York, Dec. 7, 1840. By Thomas Smith.[724] 12mo,
+    (pp. 8.)
+
+The Wesleyan minister addressed had advocated provision against old age,
+etc.: the writer declares all _private_ provision un-Christian. After
+decent maintenance and relief of family claims of indigence, he holds that
+all the rest is to go to the "Benefit Society," of which he draws up the
+rules, in technical form, with chapters of "Officers," "Contributors" etc.,
+from the Acts of the Apostles, etc., and some of the early Fathers. He
+holds that a Christian may not "make a _private_ provision against the
+contingencies of the future": and that the great "Benefit Society" is the
+divinely-ordained recipient of all the surplus of his income; capital,
+beyond what is necessary for business, he is to have none. A real good
+speculator shuts his eyes by instinct, when opening them would not serve
+the purpose: he has the vizor of the Irish fairy tale, which fell of itself
+over the eyes of the wearer the moment he turned them upon the enchanted
+light which would have destroyed him if he had caught sight of it. "Whiles
+it remained, was it not thine own? and after it was sold, was it (the
+purchase-money) not in thine own power?" would have been awkward to quote,
+and accordingly nothing is stated except the well-known result, which is
+rule 3, cap. 5, "Prevention of Abuses." By putting his principles together,
+the author can be made, logically, to mean that the successors of the
+apostles should put to death all contributors who are detected in not
+paying their full premiums.
+
+{347}
+
+I have known one or two cases in which policy-holders have surrendered
+their policies through having arrived at a conviction that direct provision
+is unlawful. So far as I could make it out, these parties did not think it
+unlawful to lay by out of income, except when this was done in a manner
+which involved calculation of death-chances. It is singular they did not
+see that the entrance of chance of death was the entrance of the very
+principle of the benefit society described in the Acts of the Apostles. The
+family of the one who died young received more in proportion to _premiums_
+paid than the family of one who died old. Every one who understands life
+assurance sees that--_bonus_ apart--the difference between an assurance
+office and a savings bank consists in the adoption, _pro tanto_, of the
+principle of community of goods. In the original constitution of the oldest
+assurance office, the _Amicable Society_, the plan with which they started
+was nothing but this: persons of all ages under forty-five paid one common
+premium, and the proceeds were divided among the representatives of those
+who died within the year.
+
+
+
+THE TWO OLD PARADOXES AGAIN.
+
+[I omitted from its proper place a manuscript quadrature (3.1416 exactly)
+addressed to an eminent mathematician, dated in 1842 from the debtor's ward
+of a country gaol. The unfortunate speculator says, "I have labored many
+years to find the precise ratio." I have heard of several cases in which
+squaring the circle has produced an inability to square accounts. I remind
+those who feel a kind of inspiration to employ native genius upon
+difficulties, without gradual progression from elements, that the call is
+one which becomes stronger and stronger, and may lead, as it has led, to
+abandonment of the duties of life, and all the consequences.] {348}
+
+
+
+    1842. Provisional Prospectus of the Double Acting Rotary Engine
+    Company. Also Mechanic's Magazine, March 26, 1842.
+
+Perpetual motion by a drum with one vertical half in mercury, the other in
+a vacuum: the drum, I suppose, working round forever to find an easy
+position. Steam to be superseded: steam and electricity convulsions of
+nature never intended by Providence for the use of man. The price of the
+present engines, as old iron, will buy new engines that will work without
+fuel and at no expense. Guaranteed by the Count de Predaval,[725] the
+discoverer. I was to have been a Director, but my name got no further than
+ink, and not so far as official notification of the honor, partly owing to
+my having communicated to the _Mechanic's Magazine_ information privately
+given to me, which gave premature publicity, and knocked up the plan.
+
+
+
+    An Exposition of the Nature, Force, Action, and other properties of
+    Gravitation on the Planets. London, 1842, 12mo.
+
+    An Investigation of the principles of the Rules for determining the
+    Measures of the Areas and Circumferences of Circular Plane Surfaces ...
+    London, 1844, 8vo.
+
+These are anonymous; but the author (whom I believe to be Mr. Denison,[726]
+presently noted) is described as author of a new system of mathematics, and
+also of mechanics. He had need have both, for he shows that the line which
+has a square equal to a given circle, has a cube equal to the sphere on the
+same diameter: that is, in old mathematics, the diameter is to the
+circumference as 9 to 16! Again, admitting that the velocities of planets
+in circular orbits are inversely as the square roots of their distances,
+that is, admitting Kepler's law, he manages to prove that gravitation is
+inversely as the square _root_ of the distance: and suspects magnetism of
+doing the difference between this and Newton's law. {349} Magnetism and
+electricity are, in physics, the member of parliament and the cabman--at
+every man's bidding, as Henry Warburton[727] said.
+
+The above is an outrageous quadrature. In the preceding year, 1841, was
+published what I suppose at first to be a Maori quadrature, by Maccook. But
+I get it from a cutting out of some French periodical, and I incline to
+think that it must be by a Mr. M^cCook. He makes [pi] to be 2 +
+2[root](8[root]2 - 11).
+
+
+
+THE DUPLICATION PROBLEM.
+
+    Refutation of a Pamphlet written by the Rev. John Mackey, R.C.P.,[728]
+    entitled "A method of making a cube double of a cube, founded on the
+    principles of elementary geometry," wherein his principles are proved
+    erroneous, and the required solution not yet obtained. By Robert
+    Murphy.[729] Mallow, 1824, 12mo.
+
+This refutation was the production of an Irish boy of eighteen years old,
+self-educated in mathematics, the son of a shoemaker at Mallow. He died in
+1843, leaving a name which is well known among mathematicians. His works on
+the theory of equations and on electricity, and his papers in the
+_Cambridge Transactions_, are all of high genius. The only account of him
+which I know of is that which I wrote for the _Supplement_ of the _Penny
+Cyclopaedia_. He was thrown by his talents into a good income at Cambridge,
+with no social training except penury, and very little intellectual
+training except mathematics. He fell into dissipation, and his scientific
+career was almost arrested: but he had great good in him, to my knowledge.
+A sentence in {350} a letter from the late Dean Peacock[730] to me--giving
+some advice about the means of serving Murphy--sets out the old case:
+"Murphy is a man whose _special_ education is in advance of his _general_;
+and such men are almost always difficult subjects to manage." This article
+having been omitted in its proper place, I put it at 1843, the date of
+Murphy's death.
+
+
+
+A NEW VALUE OF [pi].
+
+    The Invisible Universe disclosed; or, the real Plan and Government of
+    the Universe. By Henry Coleman Johnson, Esq. London, 1843, 8vo.
+
+The book opens abruptly with:
+
+"First demonstration. Concerning the centre: showing that, because the
+centre is an innermost point at an equal distance between two extreme
+points of a right line, and from every two relative and opposite
+intermediate points, it is composed of the two extreme internal points of
+each half of the line; each extreme internal point attracting towards
+itself all parts of that half to which it belongs...."
+
+Of course the circle is squared: and the circumference is 3-1/21 diameters.
+
+
+
+SOME MODERN ASTROLOGY.
+
+    Combination of the Zodiacal and Cometical Systems. Printed for the
+    London Society, Exeter Hall. Price Sixpence. (n. d. 1843.)
+
+What this London Society was, or the "combination," did not appear. There
+was a remarkable comet in 1843, the tail of which was at first confounded
+with what is called the _zodiacal light_. This nicely-printed little tract,
+evidently got up with less care for expense than is usual in such works,
+brings together all the announcements of the astronomers, and adds a short
+head and tail piece, which I shall quote entire. As the announcements are
+very ordinary {351} astronomy, the reader will be able to detect, if
+detection be possible, what is the meaning and force of the "Combination of
+the Zodiacal and Cometical Systems":
+
+"_Premonition._ It has pleased the AUTHOR _of_ CREATION to cause (to His
+_human and reasoning_ Creatures of this generation, by a '_combined_'
+appearance in His _Zodiacal_ and _Cometical_ system) a '_warning Crisis_'
+of universal concernment to this our GLOBE. It is this '_Crisis_' that has
+so generally 'ROUSED' at this moment the '_nations throughout the Earth_'
+that no equal interest has ever before been excited by MAN; unless it be in
+that caused by the 'PAGAN-TEMPLE IN ROME,' which is recorded by the elder
+Pliny, '_Nat. Hist._' i. 23. iii. 3. HARDOUIN."
+
+After the accounts given by the unperceiving astronomers, comes what
+follows:
+
+"Such has been (_hitherto_) the only object discerned by the '_Wise of this
+World_,' in this _twofold union_ of the '_Zodiacal_' and '_Cometical_'
+systems: yet it is nevertheless a most '_Thrilling Warning_,' to _all_ the
+inhabitants of this precarious and transitory EARTH. We have no authorized
+intimation or reasonable prospective contemplation, of '_current time_'
+beyond a year 1860, of the present century; or rather, except '_the
+interval which may now remain from the present year 1843, to a year 1860_'
+([Greek: hemeras HEXEKONTA]--'_threescore or sixty days_'--'_I have
+appointed each_ "DAY" _for a_ "YEAR,"' _Ezek._ iv. 6): and we know, from
+our '_common experience_,' how speedily such a measure of time will pass
+away.
+
+"No words can be '_more explicit_' than these of OUR BLESSED LORD: viz.
+'THIS GOSPEL _of the Kingdom shall be preached in_ ALL the EARTH, _for a
+Witness to_ ALL NATIONS; AND THEN, _shall the_ END COME.' The '_next 18
+years_' must therefore supply the interval of the '_special Episcopal
+forerunners_.'
+
+(Matt. xxiv. 14.)
+
+"See the 'JEWISH INTELLIGENCER' of the present month (_April_), p. 153, for
+the '_Debates in Parliament_,' respecting {352} the BISHOP OF JERUSALEM,
+_viz._ Dr. Bowring,[731] Mr. Hume,[732] Sir R. Inglis,[733] Sir R.
+Peel,[734] Viscount Palmerston.[735]"
+
+I have quoted this at length, to show the awful threats which were
+published at a time of some little excitement about the phenomenon, under
+the name of the _London Society_. The assumption of a corporate appearance
+is a very unfair trick: and there are junctures at which harm might be done
+by it.
+
+
+
+THE NUMBER OF THE BEAST.
+
+    _Wealth_ the name and number of the Beast, 666, in the Book of
+    Revelation. [by John Taylor.[736]] London, 1844, 8vo.
+
+Whether Junius or the Beast be the more difficult to identify, must be
+referred to Mr. Taylor, the only person who has attempted both. His cogent
+argument on the political secret is not unworthily matched in his treatment
+of the theological riddle. He sees the solution in [Greek: euporia], which
+occurs in the Acts of the Apostles as the word for wealth in one of its
+most disgusting forms, and makes 666 in the most straightforward way. This
+explanation has as good a chance as any other. The work contains a general
+{353} attempt at explanation of the Apocalypse, and some history of opinion
+on the subject. It has not the prolixity which is so common a fault of
+apocalyptic commentators.
+
+
+
+    A practical Treatise on Eclipses ... with remarks on the anomalies of
+    the present Theory of the Tides. By T. Kerigan,[737] F.R.S. 1844, 8vo.
+
+Containing also a refutation of the theory of the tides, and afterwards
+increased by a supplement, "Additional facts and arguments against the
+theory of the tides," in answer to a short notice in the _Athenaeum_
+journal. Mr. Kerigan was a lieutenant in the Navy: he obtained admission to
+the Royal Society just before the publication of his book.
+
+
+
+    A new theory of Gravitation. By Joseph Denison,[738] Esq. London, 1844,
+    12mo.
+
+    Commentaries on the Principia. By the author of 'A new theory of
+    Gravitation.' London, 1846, 8vo.
+
+Honor to the speculator who can be put in his proper place by one sentence,
+be that place where it may.
+
+"But we have shown that the velocities are inversely as the square roots of
+the mean distances from the sun; wherefore, by equality of ratios, the
+forces of the sun's gravitation upon them are also inversely as the square
+roots of their distances from the sun."
+
+
+
+EASTER DAY PARADOXERS.
+
+In the years 1818 and 1845 the full moon fell on Easter Day, having been
+particularly directed to fall before it in the act for the change of style
+and in the English missals and prayer-books of all time: perhaps it would
+be more correct to say that Easter Day was directed to fall after the full
+moon; "but the principle is the same." No explanation was given in 1818,
+but Easter was kept by the tables, {354} in defiance of the rule, and of
+several protests. A chronological panic was beginning in December 1844,
+which was stopped by the _Times_ newspaper printing extracts from an
+article of mine in the _Companion to the Almanac_ for 1845, which had then
+just appeared. No one had guessed the true reason, which is that the thing
+called the moon in the Gregorian Calendar is not the moon of the heavens,
+but a fictitious imitation put wrong on purpose, as will presently appear,
+partly to keep Easter out of the way of the Jews' Passover, partly for
+convenience of calculation. The apparent error happens but rarely; and all
+the work will perhaps have to be gone over next time. I now give two bits
+of paradox.
+
+Some theologians were angry at this explanation. A review called the
+_Christian Observer_ (of which Christianity I do not know) got up a
+crushing article against me. I did not look at it, feeling sure that an
+article on such a subject which appeared on January 1, 1845, against a
+publication made in December 1844, must be a second-hand job. But some
+years afterwards (Sept. 10, 1850), the reviews, etc. having been just
+placed at the disposal of readers in the _old_ reading-room of the Museum,
+I made a tour of inspection, came upon my critic on his perch, and took a
+look at him. I was very glad to remember this, for, though expecting only
+second-hand, yet even of this there is good and bad; and I expected to find
+some hints in the good second-hand of a respectable clerical publication. I
+read on, therefore, attentively, but not long: I soon came to the
+information that some additions to Delambre's[739] statement of the rule
+for finding Easter, belonging to distant years, had been made by Sir Harris
+Nicolas![740] Now as I myself furnished my friend Sir H. N. with Delambre's
+digest of {355} Clavius's[741] rule, which I translated out of algebra into
+common language for the purpose, I was pretty sure this was the ignorant
+reading of a person to whom Sir H. N. was the highest _arithmetical_
+authority on the subject. A person pretending to chronology, without being
+able to distinguish the historical points--so clearly as they stand out--in
+which Sir H. N. speaks with authority, from the arithmetical points of pure
+reckoning on which he does not pretend to do more than directly repeat
+others, must be as fit to talk about the construction of Easter Tables as
+the Spanish are to talk French. I need hardly say that the additions for
+distant years are as much from Clavius as the rest: my reviewer was not
+deep enough in his subject to know that Clavius made and published, from
+his rules, the full table up to A.D. 5000, for all the movable feasts of
+every year! I gave only a glance at the rest: I found I was either knave or
+fool, with a leaning to the second opinion; and I came away satisfied that
+my critic was either ignoramus or novice, with a leaning to the first. I
+afterwards found an ambiguity of expression in Sir H. N.'s account--whether
+his or mine I could not tell--which might mislead a novice or content an
+ignoramus, but would have been properly read or further inquired into by a
+competent person.
+
+The second case is this. Shortly after the publication of my article, a
+gentleman called at my house, and, finding I was not at home, sent up his
+card--with a stylish west-end club on it--to my wife, begging for a few
+words on pressing business. With many well-expressed apologies, he stated
+that he had been alarmed by hearing that Prof. De M. had an intention of
+altering Easter next year. Mrs. De M. kept her countenance, and assured him
+that I had no such intention, and further, that she greatly doubted my
+having the power to do it. Was she quite sure? his authority was very good:
+fresh assurances given. He was greatly relieved, for he had some horses
+training for after Easter, which {356} would not be ready to run if it were
+altered the wrong way. A doubt comes over him: would Mrs. De M., in the
+event of her being mistaken, give him the very earliest information?
+Promise given; profusion of thanks; more apologies; and departure.
+
+Now, candid reader!--or uncandid either!--which most deserves to be laughed
+at? A public instructor, who undertakes to settle for the world whether a
+reader of Clavius, the constructor of the Gregorian Calendar, is fool or
+knave, upon information derived from a compiler--in this matter--of his own
+day; or a gentleman of horse and dog associations, who, misapprehending
+something which he heard about a current topic, infers that the reader of
+Clavius had the ear of the Government on a proposed alteration. I suppose
+the querist had heard some one say, perhaps, that the day ought to be set
+right, and some one else remark that I might be consulted, as the only
+person who had discussed the matter from the original source of the
+Calendar.
+
+To give a better chance of the explanation being at once produced, next
+time the real full moon and Easter Day shall fall together, I insert here a
+summary which was printed in the Irish Prayer-book of the Ecclesiastical
+Society. If the amusement given by paradoxers should prevent a useless
+discussion some years hence, I and the paradoxers shall have done a little
+good between us--at any rate, I have done my best to keep the heavy weight
+afloat by tying bladders to it. I think the next occurrence will be in
+1875.
+
+EASTER DAY.
+
+In the years 1818 and 1845, Easter Day, as given by the _rules in_ 24 Geo.
+II cap. 23. (known as the act for the _change of style_) contradicted the
+_precept_ given in the preliminary explanations. The precept is as follows:
+
+"_Easter Day_, on which the rest" of the moveable feasts "depend, is always
+the First Sunday after the Full Moon, which happens upon or next after the
+Twenty-first Day of {357} _March_; and if the Full Moon happens upon a
+Sunday, _Easter Day_ is the Sunday after."
+
+But in 1818 and 1845, the full moon fell on a Sunday, and yet the rules
+gave _that same Sunday_ for Easter Day. Much discussion was produced by
+this circumstance in 1818: but a repetition of it in 1845 was nearly
+altogether prevented by a timely[742] reference to the intention of those
+who conducted the Gregorian reformation of the Calendar. Nevertheless,
+seeing that the apparent error of the Calendar is due to the precept in the
+Act of Parliament, which is both erroneous and insufficient, and that the
+difficulty will recur so often as Easter Day falls on the day of full moon,
+it may be advisable to select from the two articles cited in the note such
+of their conclusions and rules, without proof or controversy, as will
+enable the reader to understand the main points of the Easter question,
+and, should he desire it, to calculate for himself the Easter of the old or
+new style, for any given year.
+
+1. In the very earliest age of Christianity, a controversy arose as to the
+mode of keeping Easter, some desiring to perpetuate the _Passover_, others
+to keep the _festival of the Resurrection_. The first afterwards obtained
+the name of _Quartadecimans_, from their Easter being always kept on the
+_fourteenth day_ of the moon (Exod. xii. 18, Levit. xxiii. 5.). But though
+it is unquestionable that a Judaizing party existed, it is also likely that
+many dissented on chronological grounds. It is clear that no _perfect_
+anniversary can take place, except when the fourteenth of the moon, and
+with it the passover, falls on a Friday. Suppose, for instance, it falls on
+a Tuesday: one of three things must be {358} done. Either (which seems
+never to have been proposed) the crucifixion and resurrection must be
+celebrated on Tuesday and Sunday, with a wrong interval; or the former on
+Tuesday, the latter on Thursday, abandoning the first day of the week; or
+the former on Friday, and the latter on Sunday, abandoning the paschal
+commemoration of the crucifixion.
+
+The last mode has been, as every one knows, finally adopted. The disputes
+of the first three centuries did not turn on any _calendar_ questions. The
+Easter question was merely the symbol of the struggle between what we may
+call the Jewish and Gentile sects of Christians: and it nearly divided the
+Christian world, the Easterns, for the most part, being _Quartadecimans_.
+It is very important to note that there is no recorded dispute about a
+method of predicting the new moon, that is, no general dispute leading to
+formation of sects: there may have been difficulties, and discussions about
+them. The Metonic cycle, presently mentioned, must have been used by many,
+perhaps most, churches.
+
+2. The question came before the Nicene Council (A.D. 325) not as an
+astronomical, but as a doctrinal, question: it was, in fact, this, Shall
+the _passover_[743] be treated as a part of Christianity? The Council
+resolved this question in the negative, and the only information on its
+premises and conclusion, or either, which comes from itself, is contained
+in the following sentence of the synodical epistle, which epistle is
+preserved by Socrates[744] and Theodoret.[745] "We also send {359} you the
+good news concerning the unanimous consent of all in reference to the
+celebration of the most solemn feast of Easter, for this difference also
+has been made up by the assistance of your prayers: so that all the
+brethren in the East, who formerly celebrated this festival _at the same
+time as the Jews_, will in future conform _to the Romans and to us_, and to
+all who have of old observed _our manner_ of celebrating Easter." This is
+all that can be found on the subject: none of the stories about the Council
+ordaining the astronomical mode of finding Easter, and introducing the
+Metonic cycle into ecclesiastical reckoning, have any contemporary
+evidence: the canons which purport to be those of the Nicene Council do not
+contain a word about Easter; and this is evidence, whether we suppose those
+canons to be genuine or spurious.
+
+3. The astronomical dispute about a lunar cycle for the prediction of
+Easter either commenced, or became prominent, by the extinction of greater
+ones, soon after the time of the Nicene Council. Pope Innocent I[746] met
+with difficulty in 414. S. Leo,[747] in 454, ordained that Easter of 455
+should be April 24; which is right. It is useless to record details of
+these disputes in a summary: the result was, that in the year 463, Pope
+Hilarius[748] employed Victorinus[749] of Aquitaine to correct the
+Calendar, and Victorinus formed a rule which lasted until the sixteenth
+century. He combined the Metonic cycle and the solar cycle presently
+described. But {360} this cycle bears the name of Dionysius Exiguus,[750] a
+Scythian settled at Rome, about A.D. 530, who adapted it to his new yearly
+reckoning, when he abandoned the era of Diocletian as a commencement, and
+constructed that which is now in common use.
+
+4. With Dionysius, if not before, terminated all difference as to the mode
+of keeping Easter which is of historical note: the increasing defects of
+the Easter Cycle produced in time the remonstrance of persons versed in
+astronomy, among whom may be mentioned Roger Bacon,[751] Sacrobosco,[752]
+Cardinal Cusa,[753] Regiomontanus,[754] etc. From the middle of the sixth
+to that of the sixteenth century, one rule was observed.
+
+5. The mode of applying astronomy to chronology has always involved these
+two principles. First, the actual position of the heavenly body is not the
+object of consideration, but what astronomers call its _mean place_, which
+may be described thus. Let a fictitious sun or moon move in the heavens, in
+such manner as to revolve among the fixed stars at an average rate,
+avoiding the alternate accelerations and retardations which take place in
+every planetary motion. Thus the fictitious (say _mean_) sun and moon are
+always very near to the real sun and moon. The ordinary clocks show time by
+the mean, not the real, sun: and it was always laid down that Easter
+depends on the opposition (or full moon) of the mean sun and moon, not of
+the real ones. Thus we see that, were the Calendar ever so correct {361} as
+to the _mean_ moon, it would be occasionally false as to the _true_ one:
+if, for instance, the opposition of the mean sun and moon took place at one
+second before midnight, and that of the real bodies only two seconds
+afterwards, the calendar day of full moon would be one day before that of
+the common almanacs. Here is a way in which the discussions of 1818 and
+1845 might have arisen: the British legislature has defined _the moon_ as
+the regulator of the paschal calendar. But this was only a part of the
+mistake.
+
+6. Secondly, in the absence of perfectly accurate knowledge of the solar
+and lunar motion (and for convenience, even if such knowledge existed),
+cycles are, and always have been taken, which serve to represent those
+motions nearly. The famous Metonic cycle, which is introduced into
+ecclesiastical chronology under the name of the cycle of the golden
+numbers, is a period of 19 Julian[755] years. This period, in the old
+Calendar, was taken to contain exactly 235 _lunations_, or intervals
+between new moons, of the mean moon. Now the state of the case is:
+
+19 average Julian years make 6939 days 18 hours.
+
+235 average lunations make 6939 days 16 hours 31 minutes.
+
+So that successive cycles of golden numbers, supposing the first to start
+right, amount to making the new moons fall too late, gradually, so that the
+mean moon _of this cycle_ gains 1 hour 29 minutes in 19 years upon the mean
+moon of the heavens, or about a day in 300 years. When the Calendar was
+reformed, the calendar new moons were four days in advance of the mean moon
+of the heavens: so that, for instance, calendar full moon on the 18th
+usually meant real full moon on the 14th.
+
+7. If the difference above had not existed, the moon of the heavens (the
+mean moon at least), would have returned {362} permanently to the same days
+of the month in 19 years; with an occasional slip arising from the unequal
+distribution of the leap years, of which a period contains sometimes five
+and sometimes four. As a general rule, the days of new and full moon in any
+one year would have been also the days of new and full moon of a year
+having 19 more units in its date. Again, if there had been no leap years,
+the days of the month would have returned to the same days of the week
+every seven years. The introduction of occasional 29ths of February
+disturbs this, and makes the permanent return of month days to week days
+occur only after 28 years. If all had been true, the lapse of 28 times 19,
+or 532 years, would have restored the year in every point: that is, A.D. 1,
+for instance, and A.D. 533, would have had the same almanac in every matter
+relating to week days, month days, sun, and moon (mean sun and moon at
+least). And on the supposition of its truth, the old system of Dionysius
+was framed. Its errors, are, first, that the moments of mean new moon
+advance too much by 1 h. 29 m. in 19 average Julian years; secondly, that
+the average Julian year of 3651/4 days is too long by 11 m. 10 s.
+
+8. The Council of Trent, moved by the representations made on the state of
+the Calendar, referred the consideration of it to the Pope. In 1577,
+Gregory XIII[756] submitted to the Roman Catholic Princes and Universities
+a plan presented to him by the representatives of Aloysius Lilius,[757]
+then deceased. This plan being approved of, the Pope nominated a commission
+to consider its details, the working member of which was the Jesuit
+Clavius. A short work was prepared by Clavius, descriptive of the new
+Calendar: this {363} was published[758] in 1582, with the Pope's bull
+(dated February 24, 1581) prefixed. A larger work was prepared by Clavius,
+containing fuller explanation, and entitled _Romani Calendarii a Gregorio
+XIII. Pontifice Maximo restituti Explicatio_. This was published at Rome in
+1603, and again in the collection of the works of Clavius in 1612.
+
+9. The following extracts from Clavius settle the question of the meaning
+of the term _moon_, as used in the Calendar:
+
+"Who, except a few who think they are very sharp-sighted in this matter, is
+so blind as not to see that the 14th of the moon and the full moon are not
+the same things in the Church of God?... Although the Church, in finding
+the new moon, and from it the 14th day, _uses neither the true nor the mean
+motion of the moon_, but measures only according to the order of a cycle,
+it is nevertheless undeniable that the mean full moons found from
+astronomical tables are of the greatest use in determining the cycle which
+is to be preferred ... the new moons of which cycle, in order to the due
+celebration of Easter, should be so arranged that the 14th days of those
+moons, reckoning from the day of new moon _inclusive_, should not fall two
+or more days before the mean full moon, but only one day, or else on the
+very day itself, or not long after. And even thus far the Church need not
+take very great pains ... for it is sufficient that all should reckon by
+the 14th day of the moon in the cycle, even though sometimes it _should be
+more than one day before or after_ the mean full moon.... We have taken
+pains that in our cycle the new moons should _follow_ the real new moons,
+so that the 14th of the moon should fall either the day before the mean
+full moon, or on that day, or not long after; and this was done on purpose,
+for if the new moon of the cycle fell on the same day as the mean new moon
+of the {364} astronomers, it might chance that we should celebrate Easter
+on the same day as the Jews or the Quartadeciman heretics, which would be
+absurd, or else before them, which would be still more absurd."
+
+From this it appears that Clavius continued the Calendar of his
+predecessors in the choice of the _fourteenth_ day of the moon. Our
+legislature lays down the day of the _full moon_: and this mistake appears
+to be rather English than Protestant; for it occurs in missals published in
+the reign of Queen Mary. The calendar lunation being 291/2 days, the middle
+day is the _fifteenth_ day, and this is and was reckoned as the day of the
+full moon. There is every right to presume that the original passover was a
+feast of the _real full moon_: but it is most probable that the moons were
+then reckoned, not from the astronomical conjunction with the sun, which
+nobody sees except at an eclipse, but from the day of _first visibility_ of
+the new moon. In fine climates this would be the day or two days after
+conjunction; and the fourteenth day from that of first visibility
+inclusive, would very often be the day of full moon. The following is then
+the proper correction of the precept in the Act of Parliament:
+
+Easter Day, on which the rest depend, is always the First Sunday after the
+_fourteenth day_ of the _calendar_ moon which happens upon or next after
+the Twenty-first day of March, _according to the rules laid down for the
+construction of the Calendar_; and if the _fourteenth day_ happens upon a
+Sunday, Easter Day is the Sunday after.
+
+10. Further, it appears that Clavius valued the celebration of the festival
+after the Jews, etc., more than astronomical correctness. He gives
+comparison tables which would startle a believer in the astronomical
+intention of his Calendar: they are to show that a calendar in which the
+moon is always made a day older than by him, _represents the heavens better
+than he has done, or meant to do_. But it must be observed that this
+diminution of the real moon's age has {365} a tendency to make the English
+explanation often practically accordant with the Calendar. For the
+fourteenth day of Clavius _is_ generally the fifteenth day of the mean moon
+of the heavens, and therefore most often that of the real moon. But for
+this, 1818 and 1845 would not have been the only instances of our day in
+which the English precept would have contradicted the Calendar.
+
+11. In the construction of the Calendar, Clavius adopted the ancient cycle
+of 532 years, but, we may say, without ever allowing it to run out. At
+certain periods, a shift is made from one part of the cycle into another.
+This is done whenever what should be Julian leap year is made a common
+year, as in 1700, 1800, 1900, 2100, etc. It is also done at certain times
+to correct the error of 1 h. 19 m., before referred to, in each cycle of
+golden numbers: Clavius, to meet his view of the amount of that error, put
+forward the moon's age a day 8 times in 2,500 years. As we cannot enter at
+full length into the explanation, we must content ourselves with giving a
+set of rules, independent of tables, by which the reader may find Easter
+for himself in any year, either by the old Calendar or the new. Any one who
+has much occasion to find Easters and movable feasts should procure
+Francoeur's[759] tables.
+
+12. _Rule for determining Easter Day of the Gregorian Calendar in any year
+of the new style._ To the several parts {366} of the rule are annexed, by
+way of example, the results for the year 1849.
+
+I. Add 1 to the given year. (1850).
+
+II. Take the quotient of the given year divided by 4, neglecting the
+remainder. (462).
+
+III. Take 16 from the centurial figures of the given year, if it can be
+done, and take the remainder. (2).
+
+IV. Take the quotient of III. divided by 4, neglecting the remainder. (0).
+
+V. From the sum of I, II, and IV., subtract III. (2310).
+
+VI. Find the remainder of V. divided by 7. (0).
+
+VII. Subtract VI. from 7; this is the number of the dominical letter
+
+  1  2  3  4  5  6  7  (7; dominical letter G).
+  A  B  C  D  E  F  G
+
+VIII. Divide I. by 19, the remainder (or 19, if no remainder) is the
+_golden number_. (7).
+
+IX. From the centurial figures of the year subtract 17, divide by 25, and
+keep the quotient. (0).
+
+X. Subtract IX. and 15 from the centurial figures, divide by 3, and keep
+the quotient. (1).
+
+XI. To VIII. add ten times the next less number, divide by 30, and keep the
+remainder. (7).
+
+XII. To XI. add X. and IV., and take away III., throwing out thirties, if
+any. If this give 24, change it into 25. If 25, change it into 26, whenever
+the golden number is greater than 11. If 0, change it into 30. Thus we have
+the epact, or age of the _Calendar_ moon at the beginning of the year. (6).
+
+_When the Epact is 23, or less._
+
+XIII. Subtract XII., the epact, from 45. (39).
+
+XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7,
+if there be no remainder. (7)
+
+_When the Epact is greater than 23._
+
+XIII. Subtract XII., the epact, from 75.
+
+XIV. Subtract the epact from 57, divide by 7, and keep the remainder, or 7,
+if there be no remainder.
+
+XV. To XIII. add VII., the dominical number, (and 7 besides, if XIV. be
+greater than VII.,) and subtract XIV., the result is the day of March, or
+if more than 31, subtract 31, and {367} the result is the day of April, on
+which Easter Sunday falls. (39; Easter Day is April 8).
+
+In the following examples, the several results leading to the final
+conclusion are tabulated.
+
+  ========================================================
+  GIVEN YEAR | 1592 | 1637 | 1723 | 1853 | 2018 | 4686
+  --------------------------------------------------------
+        I.   | 1593 | 1638 | 1724 | 1854 | 2019 |   4687
+       II.   |  398 |  409 |  430 |  463 |  504 |   1171
+      III.   |  --- |    0 |    1 |    2 |    4 |     30
+       IV.   |  --- |    0 |    0 |    0 |    1 |      7
+        V.   | 1991 | 2047 | 2153 | 2315 | 2520 |   5835
+       VI.   |    3 |    3 |    4 |    5 |    0 |      4
+      VII.   |    4 |    4 |    3 |    2 |    7 |      3
+     VIII.   |   16 |    4 |   14 |   11 |    5 |     13
+       IX.   |  --- |  --- |    0 |    0 |    0 |      1
+        X.   |    0 |    0 |    0 |    1 |    1 |     10
+       XI.   |   16 |    4 |   24 |   21 |   15 |     13
+      XII.   |   16 |    4 |   23 |   20 |   13 |0 say 30
+     XIII.   |   29 |   41 |   22 |   25 |   32 |     45
+      XIV.   |    4 |    2 |    4 |    7 |    7 |      6
+       XV.   |   29 |   43 |   28 |   27 |   32 |     49
+  Easter Day |Mar.29|Apr.12|Mar.28|Mar.27|Apr.1 | Apr.18
+  --------------------------------------------------------
+
+13. _Rule for determining Easter Day of the Antegregorian Calendar in any
+year of the old style._ To the several parts of the rule are annexed, by
+way of example, the results for the year 1287. The steps are numbered to
+correspond with the steps of the Gregorian rule, so that it can be seen
+what augmentations the latter requires.
+
+I. Set down the given year. (1287).
+
+II. Take the quotient of the given year divided by 4, neglecting the
+remainder (321).
+
+V. Take 4 more than the sum of I. and II. (1612).
+
+VI. Find the remainder of V. divided by 7. (2).
+
+VII. Subtract VI. from 7; this is the number of the dominical letter
+
+  1  2  3  4  5  6  7  (5; dominical letter E).
+  A  B  C  D  E  F  G
+
+VIII. Divide one more than the given year by 19, the remainder (or 19 if no
+remainder) is the golden number. (15).
+
+XII. Divide 3 less than 11 times VIII. by 30; the remainder (or 30 if there
+be no remainder) is the epact. (12).
+
+{368}
+
+_When the Epact is 23, or less._
+
+XIII. Subtract XII., the epact, from 45. (33).
+
+XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7,
+if there be no remainder, (1).
+
+_When the Epact is greater than 23._
+
+XIII. Subtract XII., the epact, from 75.
+
+XIV. Subtract the epact from 57, divide by 7, and keep the remainder, or 7,
+if there be no remainder.
+
+XV. To XIII. add VII., the dominical number, (and 7 besides if XIV. be
+greater than VII.,) and subtract XIV., the result is the day of March, or
+if more than 31, subtract 31, and the result is the day of April, on which
+Easter Sunday (old style) falls. (37; Easter Day is April 6).
+
+These rules completely represent the old and new Calendars, so far as
+Easter is concerned. For further explanation we must refer to the articles
+cited at the commencement.
+
+The annexed is the table of new and full moons of the Gregorian Calendar,
+cleared of the errors made for the purpose of preventing Easter from
+coinciding with the Jewish Passover.
+
+The second table (page 370) contains _epacts_, or ages of the moon at the
+beginning of the year: thus in 1913, the epact is 22, in 1868 it is 6. This
+table goes from 1850 to 1999: should the New Zealander not have arrived by
+that time, and should the churches of England and Rome then survive, the
+epact table may be continued from their liturgy-books. The way of using the
+table is as follows: Take the epact of the required year, and find it in
+the first or last column of the first table, in line with it are seen the
+calendar days of new and full moon. Thus, when the epact is 17, the new and
+full moons of March fall on the 13th and 28th. The result is, for the most
+part, correct: but in a minority of cases there is an error of a day. When
+this happens, the error is almost always a fraction of a day much less than
+twelve hours. Thus, when the table gives full moon on the 27th, and the
+real truth is the 28th, we may be sure it is early on the 28th.
+
+{369}
+
+  -------------------------------------------------------------------------
+        |Jan.|Feb.|Mar.|Apr.|May |June|July|Aug.|Sep.|Oct.|Nov.|Dec.|
+  -------------------------------------------------------------------------
+    1   | 29 | 27 | 29 | 27 | 27 | 25 | 25 | 23 | 22 | 21 | 20 | 19 |  1
+        | 14 | 13 | 14 | 13 | 12 | 11 | 10 |  9 |  7 |  7 |  5 |  5 |
+  -------------------------------------------------------------------------
+    2   | 28 | 26 | 28 | 26 | 26 | 24 | 24 | 22 | 21 | 20 | 19 | 18 |  2
+        | 13 | 12 | 13 | 12 | 11 | 10 |  9 |  8 |  6 |  6 |  4 |  4 |
+  -------------------------------------------------------------------------
+    3   | 27 | 25 | 27 | 25 | 25 | 23 | 23 | 21 | 20 | 19 | 18 | 17 |  3
+        | 12 | 11 | 12 | 11 | 10 |  9 |  8 |  7 |  5 |  5 |  3 |  3 |
+  -------------------------------------------------------------------------
+    4   | 26 | 24 | 26 | 24 | 24 | 22 | 22 | 20 | 19 | 18 | 17 | 16 |  4
+        | 11 | 10 | 11 | 10 |  9 |  8 |  7 |  6 |  4 |  4 |  2 |2,31|
+  -------------------------------------------------------------------------
+    5   | 25 | 23 | 25 | 23 | 23 | 21 | 21 | 19 | 18 | 17 | 16 | 15 |  5
+        | 10 |  9 | 10 |  9 |  8 |  7 |  6 |  5 |  3 |  3 |  1 |1,30|
+  -------------------------------------------------------------------------
+    6   | 24 | 22 | 24 | 22 | 22 | 20 | 20 | 18 | 17 | 16 | 15 | 14 |  6
+        |  9 |  8 |  9 |  8 |  7 |  6 |  5 |  4 |  2 |2,31| 30 | 29 |
+  -------------------------------------------------------------------------
+    7   | 23 | 21 | 23 | 21 | 21 | 19 | 19 | 17 | 16 | 15 | 14 | 13 |  7
+        |  8 |  7 |  8 |  7 |  6 |  5 |  4 |  3 |  1 |1,30| 29 | 28 |
+  -------------------------------------------------------------------------
+    8   | 22 | 20 | 22 | 20 | 20 | 18 | 18 | 16 | 15 | 14 | 13 | 12 |  8
+        |  7 |  6 |  7 |  6 |  5 |  4 |  3 |2,31| 30 | 29 | 28 | 27 |
+  -------------------------------------------------------------------------
+    9   | 21 | 19 | 21 | 19 | 19 | 17 | 17 | 15 | 14 | 13 | 12 | 11 |  9
+        |  6 |  5 |  6 |  5 |  4 |  3 |  2 |1,30| 29 | 28 | 27 | 26 |
+  -------------------------------------------------------------------------
+    10  | 20 | 18 | 20 | 18 | 18 | 16 | 16 | 14 | 13 | 12 | 11 | 10 |  10
+        |  5 |  4 |  5 |  4 |  3 |  2 |1,31| 29 | 28 | 27 | 26 | 25 |
+  -------------------------------------------------------------------------
+    11  | 19 | 17 | 19 | 17 | 17 | 15 | 15 | 13 | 12 | 11 | 10 |  9 |  11
+        |  4 |  3 |  4 |  3 |  2 |1,30| 30 | 28 | 27 | 26 | 25 | 24 |
+  -------------------------------------------------------------------------
+    12  | 18 | 16 | 18 | 16 | 16 | 14 | 14 | 12 | 11 | 10 |  9 |  8 |  12
+        |  3 |  2 |  3 |  2 |1,31| 29 | 29 | 27 | 26 | 25 | 24 | 23 |
+  -------------------------------------------------------------------------
+    13  | 17 | 15 | 17 | 15 | 15 | 13 | 13 | 11 | 10 |  9 |  8 |  7 |  13
+        |  2 |  1 |  2 |1,30| 30 | 28 | 28 | 26 | 25 | 24 | 23 | 22 |
+  -------------------------------------------------------------------------
+    14  | 16 | 14 | 16 | 14 | 14 | 12 | 12 | 10 |  9 |  8 |  7 |  6 |  14
+        |1,31| -- |1,31| 29 | 29 | 27 | 27 | 25 | 24 | 23 | 22 | 21 |
+  -------------------------------------------------------------------------
+    15  | 15 | 13 | 15 | 13 | 13 | 11 | 11 |  9 |  8 |  7 |  6 |  5 |  15
+        | 30 | 28 | 30 | 28 | 28 | 26 | 26 | 24 | 23 | 22 | 21 | 20 |
+  -------------------------------------------------------------------------
+    16  | 14 | 12 | 14 | 12 | 12 | 10 | 10 |  8 |  7 |  6 |  5 |  4 |  16
+        | 29 | 27 | 29 | 27 | 27 | 25 | 25 | 23 | 22 | 21 | 20 | 19 |
+  -------------------------------------------------------------------------
+    17  | 13 | 11 | 13 | 11 | 11 |  9 |  9 |  7 |  6 |  5 |  4 |  3 |  17
+        | 28 | 26 | 28 | 26 | 26 | 24 | 24 | 22 | 21 | 20 | 19 | 18 |
+  -------------------------------------------------------------------------
+    18  | 12 | 10 | 12 | 10 | 10 |  8 |  8 |  6 |  5 |  4 |  3 |  2 |  18
+        | 27 | 25 | 27 | 25 | 25 | 23 | 23 | 21 | 20 | 19 | 18 | 17 |
+  -------------------------------------------------------------------------
+    19  | 11 |  9 | 11 |  9 |  9 |  7 |  7 |  5 |  4 |  3 |  2 |1,31|  19
+        | 26 | 24 | 26 | 24 | 24 | 22 | 22 | 20 | 19 | 18 | 17 | 16 |
+  -------------------------------------------------------------------------
+    20  | 10 |  8 | 10 |  8 |  8 |  6 |  6 |  4 |  3 |  2 |1,31| 30 |  20
+        | 25 | 23 | 25 | 23 | 23 | 21 | 21 | 19 | 18 | 17 | 16 | 15 |
+  -------------------------------------------------------------------------
+    21  |  9 |  7 |  9 |  7 |  7 |  5 |  5 |  3 |  2 |1,31| 29 | 29 |  21
+        | 24 | 22 | 24 | 22 | 22 | 20 | 20 | 18 | 17 | 16 | 15 | 14 |
+  -------------------------------------------------------------------------
+    22  |  8 |  6 |  8 |  6 |  6 |  4 |  4 |  2 |1,30| 30 | 28 | 28 |  22
+        | 23 | 21 | 23 | 21 | 21 | 19 | 19 | 17 | 16 | 15 | 14 | 13 |
+  -------------------------------------------------------------------------
+    23  |  7 |  5 |  7 |  5 |  5 |  3 |  3 |1,31| 29 | 29 | 27 | 27 |  23
+        | 22 | 20 | 22 | 20 | 20 | 18 | 18 | 16 | 15 | 14 | 13 | 12 |
+  -------------------------------------------------------------------------
+    24  |  6 |  5 |  6 |  5 |  4 |  3 |  2 |1,30| 29 | 28 | 27 | 26 |  24
+        | 21 | 19 | 21 | 19 | 19 | 17 | 17 | 15 | 14 | 13 | 12 | 11 |
+  -------------------------------------------------------------------------
+    25  |  5 |  4 |  5 |  4 |  3 |  2 |1,31| 29 | 28 | 27 | 26 | 25 |  25
+        | 20 | 19 | 20 | 19 | 18 | 17 | 16 | 15 | 13 | 13 | 11 | 11 |
+  -------------------------------------------------------------------------
+    26  |  4 |  3 |  4 |  3 |  2 |1,30| 30 | 28 | 27 | 26 | 25 | 24 |  26
+        | 19 | 18 | 19 | 18 | 17 | 16 | 15 | 14 | 12 | 12 | 10 | 10 |
+  -------------------------------------------------------------------------
+    27  |  3 |  2 |  3 |  2 |1,31| 29 | 29 | 27 | 26 | 25 | 24 | 23 |  27
+        | 18 | 17 | 18 | 17 | 16 | 15 | 14 | 13 | 11 | 11 |  9 |  9 |
+  -------------------------------------------------------------------------
+    28  |  2 |  1 |  2 |1,30| 30 | 28 | 28 | 26 | 25 | 24 | 23 | 22 |  28
+        | 17 | 16 | 17 | 16 | 15 | 14 | 13 | 12 | 10 | 10 |  8 |  8 |
+  -------------------------------------------------------------------------
+    29  |1,31| -- |1,31| 29 | 29 | 27 | 27 | 25 | 24 | 23 | 22 | 21 |  29
+        | 16 | 15 | 16 | 15 | 14 | 13 | 12 | 11 |  9 |  9 |  7 |  7 |
+  -------------------------------------------------------------------------
+    30  | 30 | 28 | 30 | 28 | 28 | 26 | 26 | 24 | 23 | 22 | 21 | 20 |  30
+        | 15 | 14 | 15 | 14 | 13 | 12 | 11 | 10 |  8 |  8 |  6 |  6 |
+  -------------------------------------------------------------------------
+        |Jan.|Feb.|Mar.|Apr.|May |June|July|Aug.|Sep.|Oct.|Nov.|Dec.|
+  -------------------------------------------------------------------------
+
+{370}
+
+  =======================================================
+       |  0 |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9
+  -------------------------------------------------------
+   185 | 17 | 28 |  9 | 20 |  2 | 12 | 23 |  4 | 15 | 26
+  -------------------------------------------------------
+   186 |  7 | 18 | 30 | 11 | 22 |  3 | 14 | 25 |  6 | 17
+  -------------------------------------------------------
+   187 | 28 |  9 | 20 |  1 | 12 | 23 |  4 | 15 | 26 |  7
+  -------------------------------------------------------
+   188 | 18 | 30 | 11 | 22 |  3 | 14 | 25 |  6 | 17 | 28
+  -------------------------------------------------------
+   189 |  9 | 21 |  1 | 12 | 23 |  4 | 15 | 26 |  7 | 18
+  -------------------------------------------------------
+   190 | 29 | 10 | 21 |  2 | 13 | 24 |  5 | 16 | 27 |  8
+  -------------------------------------------------------
+   191 | 19 | 30 | 11 | 22 |  3 | 14 | 26 |  6 | 17 | 29
+  -------------------------------------------------------
+   192 | 10 | 21 |  2 | 13 | 24 |  5 | 16 | 27 |  8 | 19
+  -------------------------------------------------------
+   193 | 30 | 11 | 22 |  3 | 14 | 26 |  6 | 17 | 29 | 10
+  -------------------------------------------------------
+   194 | 21 |  2 | 13 | 24 |  5 | 16 | 27 |  8 | 19 | 30
+  -------------------------------------------------------
+   195 | 11 | 22 |  3 | 14 | 26 |  6 | 17 | 29 | 10 | 21
+  -------------------------------------------------------
+   196 |  2 | 13 | 24 |  5 | 16 | 27 |  8 | 19 | 30 | 11
+  -------------------------------------------------------
+   197 | 22 |  3 | 14 | 26 |  6 | 17 | 29 | 10 | 21 |  2
+  -------------------------------------------------------
+   198 | 13 | 24 |  5 | 16 | 27 |  8 | 19 | 30 | 11 | 22
+  -------------------------------------------------------
+   199 |  3 | 14 | 26 |  6 | 17 | 29 | 10 | 21 |  2 | 13
+  =======================================================
+
+For example, the year 1867. The epact is 25, and we find in the table:
+
+         J.   F.   M.   AP.  M.   JU.  JL.  AU.  S.   O.   N.   D.
+  New     5+   4    5+   4    3+   2  1,31  29   28-  27   26   25
+  Full   20   19-  20   19-  18   17   16   15   13-  13   11+  11
+
+When the truth is the day after + is written after the date; when the day
+before, -. Thus, the new moon of March is on the 6th; the full moon of
+April is on the 18th. {371}
+
+I now introduce a small paradox of my own; and as I am not able to prove
+it, I am compelled to declare that any one who shall dissent must be either
+very foolish or very dishonest, and will make me quite uncomfortable about
+the state of his soul. This being settled once for all, I proceed to say
+that the necessity of arriving at the truth about the assertions that the
+Nicene Council laid down astronomical tests led me to look at Fathers,
+Church histories, etc. to an extent which I never dreamed of before. One
+conclusion which I arrived at was, that the Nicene Fathers had a knack of
+sticking to the question which many later councils could not acquire. In
+our own day, it is not permitted to Convocation seriously to discuss any
+one of the points which are bearing so hard upon their resources of
+defence--the cursing clauses of the Athanasian Creed, for example. And it
+may be collected that the prohibition arises partly from fear that there is
+no saying where a beginning, if allowed, would end. There seems to be a
+suspicion that debate, once let loose, would play up old Trent with the
+liturgy, and bring the whole book to book. But if any one will examine the
+real Nicene Creed, without the augmentation, he will admire the way in
+which the framers stuck to the point, and settled what they had to decide,
+according to their view of it. With such a presumption of good sense in
+their favor, it becomes easier to believe in any claim which may be made on
+their behalf to tact or sagacity in settling any other matter. And I
+strongly suspect such a claim may be made for them on the Easter question.
+
+I collect from many little indications, both before and after the Council,
+that the division of the Christian world into Judaical and Gentile, though
+not giving rise to a sectarian distinction expressed by names, was of far
+greater force and meaning than historians prominently admit. I took _note_
+of many indications of this, but not _notes_, as it was not to my purpose.
+If it were so, we must admire the discretion of the Council. The Easter
+question was the {372} fighting ground of the struggle: the Eastern or
+Judaical Christians, with some varieties of usage and meaning, would have
+the Passover itself to be the great feast, but taken in a Christian sense;
+the Western or Gentile Christians, would have the commemoration of the
+Resurrection, connected with the Passover only by chronology. To shift the
+Passover in time, under its name, _Pascha_, without allusion to any of the
+force of the change, was gently cutting away the ground from under the feet
+of the Conservatives. And it was done in a very quiet way: no allusion to
+the precise character of the change; no hint that the question was about
+two different festivals: "all the brethren in the East, who formerly
+celebrated this festival at the same time as the Jews, will in future
+conform to the Romans and to us." The Judaizers meant to be keeping the
+Passover _as_ a Christian feast: they are gently assumed to be keeping,
+_not_ the Passover, _but_ a Christian feast; and a doctrinal decision is
+quietly, but efficiently, announced under the form of a chronological
+ordinance. Had the Council issued theses of doctrine, and excommunicated
+all dissentients, the rupture of the East and West would have taken place
+earlier by centuries than it did. The only place in which I ever saw any
+part of my paradox advanced, was in an article in the _Examiner_ newspaper,
+towards the end of 1866, after the above was written.
+
+A story about Christopher Clavius, the workman of the new Calendar. I
+chanced to pick up "Albertus Pighius Campensis de aequinoctiorum
+solsticiorumque inventione... Ejusdem de ratione Paschalis celebrationis,
+De que Restitutione ecclesiastici Kalendarii," Paris, 1520, folio.[760] On
+the title-page were decayed words followed by ".._hristophor.. C..ii_, 1556
+(or 8)," the last blank not entirely erased by time, but showing the lower
+halves of an _l_ and of an _a_, and {373} rather too much room for a _v_.
+It looked very like _E Libris Christophori Clavii_ 1556. By the courtesy of
+some members of the Jesuit body in London, I procured a tracing of the
+signature of Clavius from Rome, and the shapes of the letters, and the
+modes of junction and disjunction, put the matter beyond question. Even the
+extra space was explained; he wrote himself Cla_u_ius. Now in 1556, Clavius
+was nineteen years old: it thus appears probable that the framer of the
+Gregorian Calendar was selected, not merely as a learned astronomer, but as
+one who had attended to the calendar, and to works on its reformation, from
+early youth. When on the subject I found reason to think that Clavius had
+really read this work, and taken from it a phrase or two and a notion or
+two. Observe the advantage of writing the baptismal name at full length.
+
+
+
+A COUPLE OF MINOR PARADOXES.
+
+    The discovery of a general resolution of all superior finite equations,
+    of every numerical both algebraick and transcendent form. By A. P.
+    Vogel,[761] mathematician at Leipzick. Leipzick and London, 1845, 8vo.
+
+This work is written in the English of a German who has not mastered the
+idiom: but it is always intelligible. It professes to solve equations of
+every degree "in a more extent sense, and till to every degree of
+exactness." The general solution of equations of _all_ degrees is a vexed
+question, which cannot have the mysterious interest of the circle problem,
+and is of a comparatively modern date.[762] Mr. Vogel {374} announces a
+forthcoming treatise in which are resolved the "last impossibilities of
+pure mathematics."
+
+
+
+    Elective Polarity the Universal Agent. By Frances Barbara Burton,
+    authoress of 'Astronomy familiarized,' 'Physical Astronomy,' &c.
+    London, 1845, 8vo.[763]
+
+The title gives a notion of the theory. The first sentence states, that
+12,500 years ago [alpha] Lyrae was the pole-star, and attributes the immense
+magnitude of the now fossil animals to a star of such "polaric intensity as
+Vega pouring its magnetic streams through our planet." Miss Burton was a
+lady of property, and of very respectable acquirements, especially in
+Hebrew; she was eccentric in all things.
+
+1867.--Miss Burton is revived by the writer of a book on meteorology which
+makes use of the planets: she is one of his leading minds.[764]
+
+
+
+SPECULATIVE THOUGHT IN ENGLAND.
+
+In the year 1845 the old _Mathematical Society_ was merged in the
+Astronomical Society. The circle-squarers, etc., thrive more in England
+than in any other country: there are most weeds where there is the largest
+crop. Speculation, though not encouraged by our Government so much as by
+those of the Continent, has had, not indeed such forcing, but much wider
+diffusion: few tanks, but many rivulets. On this point I quote from the
+preface to the reprint of the work of Ramchundra,[765] which I
+superintended for the late Court of Directors of the East India Company.
+
+{375}
+
+"That sound judgment which gives men well to know what is best for them, as
+well as that faculty of invention which leads to development of resources
+and to the increase of wealth and comfort, are both materially advanced,
+perhaps cannot rapidly be advanced without, a great taste for pure
+speculation among the general mass of the people, down to the lowest of
+those who can read and write. England is a marked example. Many persons
+will be surprised at this assertion. They imagine that our country is the
+great instance of the refusal of all _unpractical_ knowledge in favor of
+what is _useful_. I affirm, on the contrary, that there is no country in
+Europe in which there has been so wide a diffusion of speculation, theory,
+or what other unpractical word the reader pleases. In our country, the
+scientific _society_ is always formed and maintained by the people; in
+every other, the scientific _academy_--most aptly named--has been the
+creation of the government, of which it has never ceased to be the
+nursling. In all the parts of England in which manufacturing pursuits have
+given the artisan some command of time, the cultivation of mathematics and
+other speculative studies has been, as is well known, a very frequent
+occupation. In no other country has the weaver at his loom bent over the
+_Principia_ of Newton; in no other country has the man of weekly wages
+maintained his own scientific periodical. With us, since the beginning of
+the last century, scores upon scores--perhaps hundreds, for I am far from
+knowing all--of annuals have run, some their ten years, some their
+half-century, some their century and a half, containing questions to be
+answered, from which many of our examiners in the universities have culled
+materials for the academical contests. And these questions have always been
+answered, and in cases without number by the lower order of purchasers, the
+mechanics, the weavers, and the printers' workmen. I cannot here digress to
+point out the manner in which the concentration of manufactures, and the
+general diffusion of education, have affected the {376} state of things; I
+speak of the time during which the present system took its rise, and of the
+circumstances under which many of its most effective promoters were
+trained. In all this there is nothing which stands out, like the
+state-nourished academy, with its few great names and brilliant single
+achievements. This country has differed from all others in the wide
+diffusion of the disposition to speculate, which disposition has found its
+place among the ordinary habits of life, moderate in its action, healthy in
+its amount."
+
+
+
+THE OLD MATHEMATICAL SOCIETY.
+
+Among the most remarkable proofs of the diffusion of speculation was the
+Mathematical Society, which flourished from 1717 to 1845. Its habitat was
+Spitalfields, and I think most of its existence was passed in Crispin
+Street. It was originally a plain society, belonging to the studious
+artisan. The members met for discussion once a week; and I believe I am
+correct in saying that each man had his pipe, his pot, and his problem. One
+of their old rules was that, "If any member shall so far forget himself and
+the respect due to the Society as in the warmth of debate to threaten or
+offer personal violence to any other member, he shall be liable to
+immediate expulsion, or to pay such fine as the majority of the members
+present shall decide." But their great rule, printed large on the back of
+the title page of their last book of regulations, was "By the constitution
+of the Society, it is the duty of every member, if he be asked any
+mathematical or philosophical question by another member, to instruct him
+in the plainest and easiest manner he is able." We shall presently see
+that, in old time, the rule had a more homely form.
+
+I have been told that De Moivre[766] was a member of this {377} Society.
+This I cannot verify: circumstances render it unlikely; even though the
+French refugees clustered in Spitalfields; many of them were of the
+Society, which there is some reason to think was founded by them. But
+Dolland,[767] Thomas Simpson,[768] Saunderson,[769] Crossley,[770] and
+others of known name, were certainly members. The Society gradually
+declined, and in 1845 was reduced to nineteen members. An arrangement was
+made by which sixteen of these members, who where not already in the
+Astronomical Society became Fellows without contribution, all the books and
+other property of the old Society being transferred to the new one. I was
+one of the committee which made the preliminary inquiries, and the reason
+of the decline was soon manifest. The only question which could arise was
+whether the members of the society of working men--for this repute still
+continued--were of that class of educated men who could associate with the
+Fellows of the Astronomical Society on terms agreeable to all parties. We
+found that the artisan element had been extinct for many years; there was
+not a man but might, as to education, manners, and position, have become a
+Fellow in the usual way. The fact was that life in Spitalfields had become
+harder: and the weaver could {378} only live from hand to mouth, and not up
+to the brain. The material of the old Society no longer existed.
+
+In 1798, experimental lectures were given, a small charge for admission
+being taken at the door: by this hangs a tale--and a song. Many years ago,
+I found among papers of a deceased friend, who certainly never had anything
+to do with the Society, and who passed all his life far from London, a
+song, headed "Song sung by the Mathematical Society in London, at a dinner
+given Mr. Fletcher,[771] a solicitor, who had defended the Society gratis."
+Mr. Williams,[772] the Assistant Secretary of the Astronomical Society,
+formerly Secretary of the Mathematical Society, remembered that the Society
+had had a solicitor named Fletcher among the members. Some years elapsed
+before it struck me that my old friend Benjamin Gompertz,[773] who had long
+been a member, might have some recollection of the matter. The following is
+an extract of a letter from him (July 9, 1861):
+
+"As to the Mathematical Society, of which I was a member when only 18 years
+of age, [Mr. G. was born in 1779], having been, contrary to the rules,
+elected under the age of 21. How I came to be a member of that Society--and
+continued so until it joined the Astronomical Society, and was then the
+President--was: I happened to pass a bookseller's small shop, of
+second-hand books, kept by a poor taylor, but a good mathematician, John
+Griffiths. I was very pleased to meet a mathematician, and I asked him if
+he would give me some lessons; and his reply was that I was more capable to
+teach him, but he belonged to a society of mathematicians, and he would
+introduce me. I accepted the offer, and I was elected, and had many
+scholars then to teach, as {379} one of the rules was, if a member asked
+for information, and applied to any one who could give it, he was obliged
+to give it, or fine one penny. Though I might say much with respect to the
+Society which would be interesting, I will for the present reply only to
+your question. I well knew Mr. Fletcher, who was a very clever and very
+scientific person. He did, as solicitor, defend an action brought by an
+informer against the Society--I think for 5,000l.--for giving lectures to
+the public in philosophical subjects [i.e., for unlicensed public
+exhibition with money taken at the doors]. I think the price for admission
+was one shilling, and we used to have, if I rightly recollect, from two to
+three hundred visitors. Mr. Fletcher was successful in his defence, and we
+got out of our trouble. There was a collection made to reward his services,
+but he did not accept of any reward: and I think we gave him a dinner, as
+you state, and enjoyed ourselves; no doubt with astronomical songs and
+other songs; but my recollection does not enable me to say if the
+astronomical song was a drinking song. I think the anxiety caused by that
+action was the cause of some of the members' death. [They had, no doubt,
+broken the law in ignorance; and by the sum named, the informer must have
+been present, and sued for a penalty on every shilling he could prove to
+have been taken]."
+
+I by no means guarantee that the whole song I proceed to give is what was
+sung at the dinner: I suspect, by the completeness of the chain, that
+augmentations have been made. My deceased friend was just the man to add
+some verses, or the addition may have been made before it came into his
+hands, or since his decease, for the scraps containing the verses passed
+through several hands before they came into mine. We may, however, be
+pretty sure that the original is substantially contained in what is given,
+and that the character is therefore preserved. I have had myself to repair
+damages every now and then, in the way of conjectural restoration of
+defects caused by ill-usage. {380}
+
+
+
+THE ASTRONOMER'S DRINKING SONG.
+
+ "Whoe'er would search the starry sky,
+    Its secrets to divine, sir,
+  Should take his glass--I mean, should try
+    A glass or two of wine, sir!
+  True virtue lies in golden mean,
+    And man must wet his clay, sir;
+  Join these two maxims, and 'tis seen
+    He should drink his bottle a day, sir!
+
+ "Old Archimedes, reverend sage!
+    By trump of fame renowned, sir,
+  Deep problems solved in every page,
+    And the sphere's curved surface found,[774] sir:
+  Himself he would have far outshone,
+    And borne a wider sway, sir,
+  Had he our modern secret known,
+    And drank a bottle a day, sir!
+
+ "When Ptolemy,[775] now long ago,
+    Believed the earth stood still, sir,
+  He never would have blundered so,
+    Had he but drunk his fill, sir:
+  He'd then have felt[776] it circulate,
+    And would have learnt to say, sir,
+  The true way to investigate
+    Is to drink your bottle a day, sir!
+
+ "Copernicus,[777] that learned wight,
+    The glory of his nation,
+  With draughts of wine refreshed his sight,
+    And saw the earth's rotation;
+  {381}
+  Each planet then its orb described,
+    The moon got under way, sir;
+  These truths from nature he imbibed
+    For he drank his bottle a day, sir!
+
+ "The noble[778] Tycho placed the stars,
+    Each in its due location;
+  He lost his nose[779] by spite of Mars,
+    But that was no privation:
+  Had he but lost his mouth, I grant
+    He would have felt dismay, sir,
+  Bless you! _he_ knew what he should want
+    To drink his bottle a day, sir!
+
+ "Cold water makes no lucky hits;
+    On mysteries the head runs:
+  Small drink let Kepler[780] time his wits
+    On the regular polyhedrons:
+  He took to wine, and it changed the chime,
+    His genius swept away, sir,
+  Through area varying[781] as the time
+    At the rate of a bottle a day, sir!
+
+ "Poor Galileo,[782] forced to rat
+    Before the Inquisition,
+  _E pur si muove_[783] was the pat
+    He gave them in addition:
+  {382}
+  He meant, whate'er you think you prove,
+    The earth must go its way, sirs;
+  Spite of your teeth I'll make it move,
+    For I'll drink my bottle a day, sirs!
+
+ "Great Newton, who was never beat
+    Whatever fools may think, sir;
+  Though sometimes he forgot to eat,
+    He never forgot to drink, sir:
+  Descartes[784] took nought but lemonade,
+    To conquer him was play, sir;
+  The first advance that Newton made
+    Was to drink his bottle a day, sir!
+
+ "D'Alembert,[785] Euler,[786] and Clairaut,[787]
+    Though they increased our store, sir,
+  Much further had been seen to go
+    Had they tippled a little more, sir!
+  Lagrange[788] gets mellow with Laplace,[789]
+    And both are wont to say, sir,
+  The _philosophe_ who's not an ass
+    Will drink his bottle a day, sir!
+
+ "Astronomers! what can avail
+    Those who calumniate us;
+  Experiment can never fail
+    With such an apparatus:
+  Let him who'd have his merits known
+    Remember what I say, sir;
+  Fair science shines on him alone
+    Who drinks his bottle a day, sir!
+
+  {383}
+ "How light we reck of those who mock
+    By this we'll make to appear, sir,
+  We'll dine by the sidereal[790] clock
+    For one more bottle a year, sir:
+  But choose which pendulum you will,
+    You'll never make your way, sir,
+  Unless you drink--and drink your fill,--
+    At least a bottle a day, sir!"
+
+Old times are changed, old manners gone!
+
+There is a new Mathematical Society,[791] and I am, at this present writing
+(1866), its first President. We are very high in the newest developments,
+and bid fair to take a place among the scientific establishments. Benjamin
+Gompertz, who was President of the old Society when it expired, was the
+link between the old and new body: he was a member of _ours_ at his death.
+But not a drop of liquor is seen at our meetings, except a decanter of
+water: all our heavy is a fermentation of symbols; and we do not draw it
+mild. There is no penny fine for reticence or occult science; and as to a
+song! not the ghost of a chance.
+
+
+
+1826. The time may have come when the original documents connected with the
+discovery of Neptune may be worth revising. The following are extracts from
+the _Athenaeum_ of October 3 and October 17:
+
+
+
+LE VERRIER'S[792] PLANET.
+
+We have received, at the last moment before making up for press, the
+following letter from Sir John Herschel,[793] {384} in reference to the
+matter referred to in the communication from Mr. Hind[794] given below:
+
+"Collingwood, Oct. 1.
+
+"In my address to the British Association assembled at Southampton, on the
+occasion of my resigning the chair to Sir R. Murchison,[795] I stated,
+among the remarkable astronomical events of the last twelvemonth, that it
+had added a new planet to our list,--adding, 'it has done more,--it has
+given us the probable prospect of the discovery of another. We see it as
+Columbus saw America from the shores of Spain. Its movements have been
+felt, trembling along the far-reaching line of our analysis, with a
+certainty hardly inferior to that of ocular demonstration.'--These
+expressions are not reported in any of the papers which profess to give an
+account of the proceedings, but I appeal to all present whether they were
+not used.
+
+"Give me leave to state my reasons for this confidence; and, in so doing,
+to call attention to some facts which deserve to be put on record in the
+history of this noble discovery. On July 12, 1842, the late illustrious
+astronomer, Bessel,[796] honored me with a visit at my present residence.
+On the evening of that day, conversing on the great work of the planetary
+reductions undertaken by the Astronomer Royal[797]--then in progress, and
+since published,[798]--M. Bessel remarked that the motions of Uranus, as he
+had satisfied {385} himself by careful examination of the recorded
+observations, could not be accounted for by the perturbations of the known
+planets; and that the deviations far exceeded any possible limits of error
+of observation. In reply to the question, Whether the deviations in
+question might not be due to the action of an unknown planet?--he stated
+that he considered it highly probable that such was the case,--being
+systematic, and such as might be produced by an exterior planet. I then
+inquired whether he had attempted, from the indications afforded by these
+perturbations, to discover the position of the unknown body,--in order that
+'a hue and cry' might be raised for it. From his reply, the words of which
+I do not call to mind, I collected that he had not then gone into that
+inquiry; but proposed to do so, having now completed certain works which
+had occupied too much of his time. And, accordingly, in a letter which I
+received from him after his return to Koenigsberg, dated November 14, 1842,
+he says,--'In reference to our conversation at Collingwood, I _announce_ to
+you (_melde_ ich Ihnen) that Uranus is not forgotten.' Doubtless,
+therefore, among his papers will be found some researches on the subject.
+
+"The remarkable calculations of M. Le Verrier--which have pointed out, as
+now appears, nearly the true situation of the new planet, by resolving the
+inverse problem of the perturbations--if uncorroborated by repetition of
+the numerical calculations by another hand, or by independent investigation
+from another quarter, would hardly justify so strong an assurance as that
+conveyed by my expressions above alluded to. But it was known to me, at
+that time, (I will take the liberty to cite the Astronomer Royal as my
+authority) that a similar investigation had been independently entered
+into, and a conclusion as to the situation of the new planet very nearly
+coincident with M. Le Verrier's arrived at (in entire ignorance of his
+conclusions), by a young Cambridge mathematician, Mr. Adams;[799]--who
+will, I hope, {386} pardon this mention of his name (the matter being one
+of great historical moment),--and who will, doubtless, in his own good time
+and manner, place his calculations before the public.
+
+"J. F. W. HERSCHEL."
+
+_Discovery of Le Verrier's Planet._
+
+Mr. Hind announces to the _Times_ that he has received a letter from Dr.
+Bruennow, of the Royal Observatory at Berlin, giving the very important
+information that Le Verrier's planet was found by M. Galle, on the night of
+September 23. "In announcing this grand discovery," he says, "I think it
+better to copy Dr. Bruennow's[800] letter."
+
+
+
+"Berlin, Sept. 25.
+
+"My dear Sir--M. Le Verrier's planet was discovered here the 23d of
+September, by M. Galle.[801] It is a star of the 8th magnitude, but with a
+diameter of two or three seconds. Here are its places:
+
+             h. m. s.             R. A.           Declination.
+  Sept. 23,  12  0 14.6 M.T.      328 deg. 19' 16.0"  -13 deg. 24'  8.2"
+  Sept. 24,   8 54 40.9 M.T.      328 deg. 18' 14.3"  -13 deg. 24' 29.7"
+
+The planet is now retrograde, its motion amounting daily to four seconds of
+time.
+
+"Yours most respectfully, BRUeNNOW."
+
+"This discovery," Mr. Hind says, "may be justly considered one of the
+greatest triumphs of theoretical astronomy;" and he adds, in a postscript,
+that the planet was observed at Mr. Bishop's[802] Observatory, in the
+Regent's Park, {387} on Wednesday night, notwithstanding the moonlight and
+hazy sky. "It appears bright," he says, "and with a power of 320 I can see
+the disc. The following position is the result of instrumental comparisons
+with 33 Aquarii:
+
+  Sept. 30, at 8h. 16m. 21s. Greenwich mean time--
+      Right ascension of planet     21h. 52m. 47.15s.
+      South declination             13 deg.  27'  20"."
+
+
+
+THE NEW PLANET.
+
+"Cambridge Observatory, Oct. 15.
+
+"The allusion made by Sir John Herschel, in his letter contained in the
+_Athenaeum_ of October 3, to the theoretical researches of Mr. Adams,
+respecting the newly-discovered planet, has induced me to request that you
+would make the following communication public. It is right that I should
+first say that I have Mr. Adams's permission to make the statements that
+follow, so far as they relate to his labors. I do not propose to enter into
+a detail of the steps by which Mr. Adams was led, by his spontaneous and
+independent researches, to a conclusion that a planet must exist more
+distant than Uranus. The matter is of too great historical moment not to
+receive a more formal record than it would be proper to give here. My
+immediate object is to show, while the attention of the scientific public
+is more particularly directed to the subject, that, with respect to this
+remarkable discovery, English astronomers may lay claim to some merit.
+
+"Mr. Adams formed the resolution of trying, by calculation, to account for
+the anomalies in the motion of Uranus on the hypothesis of a more distant
+planet, when he was an undergraduate in this university, and when his
+exertions for the academical distinction, which he obtained in January
+1843, left him no time for pursuing the research. In the course of that
+year, he arrived at an approximation to the position of the supposed
+planet; which, however, he did not consider to be worthy of confidence, on
+account of his not {388} having employed a sufficient number of
+observations of Uranus. Accordingly, he requested my intervention to obtain
+for him the early Greenwich observations, then in course of
+reduction;--which the Astronomer Royal immediately supplied, in the kindest
+possible manner. This was in February, 1844. In September, 1845, Mr. Adams
+communicated to me values which he had obtained for the heliocentric
+longitude, excentricity of orbit, longitude of perihelion, and mass, of an
+assumed exterior planet,--deduced entirely from unaccounted-for
+perturbations of Uranus. The same results, somewhat corrected, he
+communicated, in October, to the Astronomer Royal. M. Le Verrier, in an
+investigation which was published in June of 1846, assigned very nearly the
+same heliocentric longitude for the probable position of the planet as Mr.
+Adams had arrived at, but gave no results respecting its mass and the form
+of its orbit. The coincidence as to position from two entirely independent
+investigations naturally inspired confidence; and the Astronomer Royal
+shortly after suggested the employing of the Northumberland telescope of
+this observatory in a systematic search after the hypothetical planet;
+recommending, at the same time, a definite plan of operations. I undertook
+to make the search,--and commenced observing on July 29. The observations
+were directed, in the first instance, to the part of the heavens which
+theory had pointed out as the most probable place of the planet; in
+selecting which I was guided by a paper drawn up for me by Mr. Adams. Not
+having hour xxi. of the Berlin star-maps--of the publication of which I was
+not aware--I had to proceed on the principle of comparison of observations
+made at intervals. On July 30, I went over a zone 9' broad, in such a
+manner as to include all stars to the eleventh magnitude. On August 4, I
+took a broader zone and recorded a place of the planet. My next
+observations were on August 12; when I met with a star of the eighth
+magnitude in the zone which I had gone over on July 30,--and which did not
+then {389} contain this star. Of course, this was the planet;--the place of
+which was, thus, recorded a second time in four days of observing. A
+comparison of the observations of July 30 and August 12 would, according to
+the principle of search which I employed, have shown me the planet. I did
+not make the comparison till after the detection of it at Berlin--partly
+because I had an impression that a much more extensive search was required
+to give any probability of discovery--and partly from the press of other
+occupation. The planet, however, was _secured_, and two positions of it
+recorded six weeks earlier here than in any other observatory,--and in a
+systematic search expressly undertaken for that purpose. I give now the
+positions of the planet on August 4 and August 12.
+
+  Greenwich mean time.
+
+  Aug. 4, 13h. 36m. 25s.     {R.A.   21h. 58m. 14.70s.
+                             {N.P.D. 102 deg. 57'  32.2"
+
+  Aug. 12, 13h. 3m. 26s.     {R.A.   21h. 57m. 26.13s.
+                             {N.P.D. 103 deg.  2'   0.2"
+
+"From these places compared with recent observations Mr. Adams has obtained
+the following results:
+
+  Distance of the planet from the sun       30.05
+  Inclination of the orbit                  1 deg. 45'
+  Longitude of the descending node        309 deg. 43'
+  Heliocentric longitude, Aug. 4          326 deg. 39'
+
+"The present distance from the sun is, therefore, thirty times the earth's
+mean distance;--which is somewhat less than the theory had indicated. The
+other elements of the orbit cannot be approximated to till the observations
+shall have been continued for a longer period.
+
+"The part taken by Mr. Adams in the theoretical search after this planet
+will, perhaps, be considered to justify the suggesting of a name. With his
+consent, I mention _Oceanus_ as one which may possibly receive the votes of
+astronomers.--I {390} have authority to state that Mr. Adams's
+investigations will in a short time, be published in detail.
+
+"J. CHALLIS."[803]
+
+
+
+ASTRONOMICAL POLICE REPORT.
+
+"An ill-looking kind of a body, who declined to give any name, was brought
+before the Academy of Sciences, charged with having assaulted a gentleman
+of the name of Uranus in the public highway. The prosecutor was a youngish
+looking person, wrapped up in two or three great coats; and looked chillier
+than anything imaginable, except the prisoner,--whose teeth absolutely
+shook, all the time.
+
+Policeman Le Verrier[804] stated that he saw the prosecutor walking along
+the pavement,--and sometimes turning sideways, and sometimes running up to
+the railings and jerking about in a strange way. Calculated that somebody
+must be pulling his coat, or otherwise assaulting him. It was so dark that
+he could not see; but thought, if he watched the direction in which the
+next odd move was made, he might find out something. When the time came, he
+set Bruennow, a constable in another division of the same force, to watch
+where he told him; and Bruennow caught the prisoner lurking about in the
+very spot,--trying to look as if he was minding his own business. Had
+suspected for a long time that somebody was lurking about in the
+neighborhood. Bruennow was then called, and deposed to his catching the
+prisoner as described.
+
+_M. Arago._--Was the prosecutor sober?
+
+_Le Verrier._--Lord, yes, your worship; no man who had a drop in him ever
+looks so cold as he did.
+
+_M. Arago._--Did you see the assault?
+
+_Le Verrier._--I can't say I did; but I told Bruennow exactly how he'd be
+crouched down;--just as he was.
+
+{391}
+
+_M. Arago (to Bruennow)._--Did _you_ see the assault?
+
+_Bruennow._--No, your worship; but I caught the prisoner.
+
+_M. Arago._--How did you know there was any assault at all?
+
+_Le Verrier._--I reckoned it couldn't be otherwise, when I saw the
+prosecutor making those odd turns on the pavement.
+
+_M. Arago._--You reckon and you calculate! Why, you'll tell me, next, that
+you policemen may sit at home and find out all that's going on in the
+streets by arithmetic. Did you ever bring a case of this kind before me
+till now?
+
+_Le Verrier._--Why, you see, your worship, the police are growing cleverer
+and cleverer every day. We can't help it:--it grows upon us.
+
+_M. Arago._--You're getting too clever for me. What does the prosecutor
+know about the matter?
+
+The prosecutor said, all he knew was that he was pulled behind by somebody
+several times. On being further examined, he said that he had seen the
+prisoner often, but did not know his name, nor how he got his living; but
+had understood he was called Neptune. He himself had paid rates and taxes a
+good many years now. Had a family of six,--two of whom got their own
+living.
+
+The prisoner being called on for his defence, said that it was a quarrel.
+He had pushed the prosecutor--and the prosecutor had pushed him. They had
+known each other a long time, and were always quarreling;--he did not know
+why. It was their nature, he supposed. He further said, that the prosecutor
+had given a false account of himself;--that he went about under different
+names. Sometimes he was called Uranus, sometimes Herschel, and sometimes
+Georgium Sidus; and he had no character for regularity in the neighborhood.
+Indeed, he was sometimes not to be seen for a long time at once.
+
+The prosecutor, on being asked, admitted, after a little hesitation, that
+he had pushed and pulled the prisoner too. {392} In the altercation which
+followed, it was found very difficult to make out which began:--and the
+worthy magistrate seemed to think they must have begun together.
+
+_M. Arago._--Prisoner, have you any family?
+
+The prisoner declined answering that question at present. He said he
+thought the police might as well reckon it out whether he had or not.
+
+_M. Arago_ said he didn't much differ from that opinion.--He then addressed
+both prosecutor and prisoner; and told them that if they couldn't settle
+their differences without quarreling in the streets, he should certainly
+commit them both next time. In the meantime, he called upon both to enter
+into their own recognizances; and directed the police to have an eye upon
+both,--observing that the prisoner would be likely to want it a long time,
+and the prosecutor would be not a hair the worse for it."
+
+
+
+This quib was written by a person who was among the astronomers: and it
+illustrates the fact that Le Verrier had sole possession of the field until
+Mr. Challis's letter appeared. Sir John Herschel's previous communication
+should have paved the way: but the wonder of the discovery drove it out of
+many heads. There is an excellent account of the whole matter in Professor
+Grant's[805] _History of Physical Astronomy_. The squib scandalized some
+grave people, who wrote severe admonitions to the editor. There are
+formalists who spend much time in writing propriety to journals, to which
+they serve as foolometers. In a letter to the _Athenaeum_, speaking of the
+way in which people hawk fine terms for common things, I said that these
+people ought to have a new translation of the Bible, which should contain
+the verse "gentleman and lady, created He them." The editor was handsomely
+fired and brimstoned!
+
+{393}
+
+
+
+A NEW THEORY OF TIDES.
+
+    A new theory of the tides: in which the errors of the usual theory are
+    demonstrated; and proof shewn that the full moon is not the cause of a
+    concomitant spring tide, but actually the cause of the neaps.... By
+    Comm^r. Debenham,[806] R.N. London, 1846, 8vo.
+
+The author replied to a criticism in the _Athenaeum_, and I remember how, in
+a very few words, he showed that he had read nothing on the subject. The
+reviewer spoke of the forces of the planets (i.e., the Sun and Moon) on the
+ocean, on which the author remarks, "But N.B. the Sun is no planet, Mr.
+Critic." Had he read any of the actual investigations on the usual theory,
+he would have known that to this day the sun and moon continue to be called
+_planets_--though the phrase is disappearing--in speaking of the tides; the
+sense, of course, being the old one, wandering bodies.
+
+A large class of the paradoxers, when they meet with something which taken
+in their sense is absurd, do not take the trouble to find out the intended
+meaning, but walk off with the words laden with their own first
+construction. Such men are hardly fit to walk the streets without an
+interpreter. I was startled for a moment, at the time when a recent
+happy--and more recently happier--marriage occupied the public thoughts, by
+seeing in a haberdasher's window, in staring large letters, an unpunctuated
+sentence which read itself to me as "Princess Alexandra! collar and cuff!"
+It immediately occurred to me that had I been any one of some scores of my
+paradoxers, I should, no doubt, have proceeded to raise the mob against the
+unscrupulous person who dared to hint to a young bride such maleficent--or
+at least immellificent--conduct towards her new lord. But, as it was,
+certain material contexts in the shop window suggested a less {394} savage
+explanation. A paradoxer should not stop at reading the advertisements of
+Newton or Laplace; he should learn to look at the stock of goods.
+
+I think I must have an eye for double readings, when presented: though I
+never guess riddles. On the day on which I first walked into the _Panizzi_
+reading room[807]--as it ought to be called--at the Museum, I began my
+circuit of the wall-shelves at the ladies' end: and perfectly coincided in
+the propriety of the Bibles and theological works being placed there. But
+the very first book I looked on the back of had, in flaming gold letters,
+the following inscription--"Blast the Antinomians!"[808] If a line had been
+drawn below the first word, Dr. Blast's history of the Antinomians would
+not have been so fearfully misinterpreted. It seems that neither the binder
+nor the arranger of the room had caught my reading. The book was removed
+before the catalogue of books of reference was printed.
+
+
+
+AN ASTRONOMICAL PARADOXER.
+
+    Two systems of astronomy: first, the Newtonian system, showing the rise
+    and progress thereof, with a short historical account; the general
+    theory with a variety of remarks thereon: second, the system in
+    accordance with the Holy Scriptures, showing the rise and progress from
+    Enoch, the seventh from Adam, the prophets, Moses, and others, in the
+    first Testament; our Lord Jesus Christ, and his apostles, in the new or
+    second Testament; Reeve and Muggleton, in the third and last Testament;
+    with a variety of remarks thereon. By Isaac Frost.[809] London, 1846,
+    4to.
+
+{395}
+
+A very handsomely printed volume, with beautiful plates. Many readers who
+have heard of Muggletonians have never had any distinct idea of Lodowick
+Muggleton,[810] the inspired tailor, (1608-1698) who about 1650 received
+his commission from heaven, wrote a Testament, founded a sect, and
+descended to posterity. Of Reeve[811] less is usually said; according to
+Mr. Frost, he and Muggleton are the two "witnesses." I shall content myself
+with one specimen of Mr. Frost's science:
+
+"I was once invited to hear read over 'Guthrie[812] on Astronomy,' and when
+the reading was concluded I was asked my opinion thereon; when I said,
+'Doctor, it appears to me that Sir I. Newton has only given two proofs in
+support of his theory of the earth revolving round the sun: all the rest is
+assertion without any proofs.'--'What are they?' inquired the
+Doctor.--'Well,' I said, 'they are, first, the power of {396} attraction to
+keep the earth to the sun; the second is the power of repulsion, by virtue
+of the centrifugal motion of the earth: all the rest appears to me
+assertion without proof.' The Doctor considered a short time and then said,
+'It certainly did appear so.' I said, 'Sir Isaac has certainly obtained the
+credit of completing the system, but really he has only half done his
+work.'--'How is that,' inquired my friend the Doctor. My reply was this:
+'You will observe his system shows the earth traverses round the sun on an
+inclined plane; the consequence is, there are four powers required to make
+his system complete:
+
+  1st. The power of _attraction_.
+  2ndly. The power of _repulsion_.
+  3rdly. The power of _ascending_ the inclined plane.
+  4thly. The power of _descending_ the inclined plane.
+
+You will thus easily see the _four_ powers required, and Newton has only
+accounted for _two_; the work is therefore only half done.' Upon due
+reflection the Doctor said, 'It certainly was necessary to have these
+_four_ points cleared up before the system could be said to be complete.'"
+
+
+
+I have no doubt that Mr. Frost, and many others on my list, have really
+encountered doctors who could be puzzled by such stuff as this, or nearly
+as bad, among the votaries of existing systems, and have been encouraged
+thereby to print their objections. But justice requires me to say that from
+the words "power of repulsion by virtue of the centrifugal motion of the
+earth," Mr. Frost may be suspected of having something more like a notion
+of the much-mistaken term "centrifugal force" than many paradoxers of
+greater fame. The Muggletonian sect is not altogether friendless: over and
+above this handsome volume, the works of Reeve and Muggleton were printed,
+in 1832, in three quarto volumes. See _Notes and Queries, 1st Series_, v,
+80; 3d Series, iii, 303. {397}
+
+[The system laid down by Mr. Frost, though intended to be substantially
+that of Lodowick Muggleton, is not so vagarious. It is worthy of note how
+very different have been the fates of two contemporary paradoxers,
+Muggleton and George Fox.[813] They were friends and associates,[814] and
+commenced their careers about the same time, 1647-1650. The followers of
+Fox have made their sect an institution, and deserve to be called the
+pioneers of philanthropy. But though there must still be Muggletonians,
+since expensive books are published by men who take the name, no sect of
+that name is known to the world. Nevertheless, Fox and Muggleton are men of
+one type, developed by the same circumstances: it is for those who
+investigate such men to point out why their teachings have had fates so
+different. Macaulay says it was because Fox found followers of more sense
+than himself. True enough: but why did Fox find such followers and not
+Muggleton? The two were equally crazy, to all appearance: and the
+difference required must be sought in the doctrines themselves.
+
+Fox was not a _rational_ man: but the success of his sect and doctrines
+entitles him to a letter of alteration of the phrase which I am surprised
+has not become current. When Conduitt,[815] the husband of Newton's
+half-niece, wrote a circular to Newton's friends, just after his death,
+inviting them to bear their parts in a proper biography, he said, "As Sir
+I. Newton was a _national_ man, I think every one ought to contribute to a
+work intended to do him justice." Here is the very phrase which is often
+wanted to signify that {398} celebrity which puts its mark, good or bad, on
+the national history, in a manner which cannot be asserted of many
+notorious or famous historical characters. Thus George Fox and Newton are
+both _national_ men. Dr. Roget's[816] _Thesaurus_ gives more than fifty
+synonyms--_colleagues_ would be the better word--of "_celebrated_," any one
+of which might be applied, either in prose or poetry, to Newton or to his
+works, no one of which comes near to the meaning which Conduitt's adjective
+immediately suggests.
+
+The truth is, that we are too _monarchical_ to be _national_. We have the
+Queen's army, the Queen's navy, the Queen's highway, the Queen's English,
+etc.; nothing is national except the _debt_. That this remark is not new is
+an addition to its force; it has hardly been repeated since it was first
+made. It is some excuse that _nation_ is not vernacular English: the
+_country_ is our word, and _country man_ is appropriated.]
+
+
+
+    Astronomical Aphorisms, or Theory of Nature; founded on the immutable
+    basis of Meteoric Action. By P. Murphy,[817] Esq. London, 1847, 12mo.
+
+This is by the framer of the Weather Almanac, who appeals to that work as
+corroborative of his theory of planetary temperature, years after all the
+world knew by experience that this meteorological theory was just as good
+as the others.
+
+{399}
+
+
+
+    The conspiracy of the Bullionists as it affects the present system of
+    the money laws. By Caleb Quotem. Birmingham, 1847, 8vo. (pp. 16).
+
+This pamphlet is one of a class of which I know very little, in which the
+effects of the laws relating to this or that political bone of contention
+are imputed to deliberate conspiracy of one class to rob another of what
+the one knew ought to belong to the other. The success of such writers in
+believing what they have a bias to believe, would, if they knew themselves,
+make them think it equally likely that the inculpated classes might really
+believe what it is _their_ interest to believe. The idea of a _guilty_
+understanding existing among fundholders, or landholders, or any holders,
+all the country over, and never detected except by bouncing pamphleteers,
+is a theory which should have been left for Cobbett[818] to propose, and
+for Apella to believe.[819]
+
+[_August_, 1866. A pamphlet shows how to pay the National Debt. Advance
+paper to railways, etc., receivable in payment of taxes. The railways pay
+interest and principal in money, with which you pay your national debt, and
+redeem your notes. Twenty-five years of interest redeems the notes, and
+then the principal pays the debt. Notes to be kept up to value by
+penalties.]
+
+
+
+THEISM INDEPENDENT OF REVELATION.
+
+    The Reasoner. No. 45. Edited by G.J. Holyoake.[820] Price _2d._ Is
+    there sufficient proof of the existence of God? 8vo. 1847.
+
+This acorn of the holy oak was forwarded to me with a manuscript note,
+signed by the editor, on the part of the {400} "London Society of
+Theological Utilitarians," who say, "they trust you may be induced to give
+this momentous subject your consideration." The supposition that a
+middle-aged person, known as a student of thought on more subjects than
+one, had that particular subject yet to begin, is a specimen of what I will
+call the _assumption-trick_ of controversy, a habit which pervades all
+sides of all subjects. The tract is a proof of the good policy of letting
+opinions find their level, without any assistance from the Court of Queen's
+Bench. Twenty years earlier the thesis would have been positive, "There is
+sufficient proof of the non-existence of God," and bitter in its tone. As
+it stands, we have a moderate and respectful treatment--wrong only in
+making the opponent argue absurdly, as usually happens when one side
+invents the other--of a question in which a great many Christians have
+agreed with the atheist: that question being--Can the existence of God be
+proved independently of revelation? Many very religious persons answer this
+question in the negative, as well as Mr. Holyoake. And, this point being
+settled, all who agree in the negative separate into those who can endure
+scepticism, and those who cannot: the second class find their way to
+Christianity. This very number of _The Reasoner_ announces the secession of
+one of its correspondents, and his adoption of the Christian faith. This
+would not have happened twenty years before: nor, had it happened, would it
+have been respectfully announced.
+
+There are people who are very unfortunate in the expression of their
+meaning. Mr. Holyoake, in the name of the "London Society" etc., forwarded
+a pamphlet on the existence of God, and said that the Society trusted I
+"may be induced to give" the subject my "consideration." How could I know
+the Society was one person, who supposed I had arrived at a conclusion and
+wanted a "_guiding word_"? But so it seems it was: Mr. Holyoake, in the
+_English {401} Leader_ of October 15, 1864, and in a private letter to me,
+writes as follows:
+
+"The gentleman who was the author of the argument, and who asked me to send
+it to Mr. De Morgan, never assumed that that gentleman had 'that particular
+subject to begin'--on the contrary, he supposed that one whom we all knew
+to be eminent as a thinker _had_ come to a conclusion upon it, and would
+perhaps vouchsafe a guiding word to one who was, as yet, seeking the
+solution of the Great Problem of Theology. I told my friend that 'Mr. De
+Morgan was doubtless preoccupied, and that he must be content to wait. On
+some day of courtesy and leisure he might have the kindness to write.' Nor
+was I wrong--the answer appears in your pages at the lapse of seventeen
+years."
+
+I suppose Mr. Holyoake's way of putting his request was the _stylus curiae_
+of the Society. A worthy Quaker who was sued for debt in the King's Bench
+was horrified to find himself charged in the declaration with detaining his
+creditor's money by force and arms, contrary to the peace of our Lord the
+King, etc. It's only the _stylus curiae_, said a friend: I don't know
+_curiae_, said the Quaker, but he shouldn't style us peace-breakers.
+
+The notion that the _non_-existence of God can be _proved_, has died out
+under the light of discussion: had the only lights shone from the pulpit
+and the prison, so great a step would never have been made. The question
+now is as above. The dictum that Christianity is "part and parcel of the
+law of the land" is also abrogated: at the same time, and the coincidence
+is not an accident, it is becoming somewhat nearer the truth that the law
+of the land is part and parcel of Christianity. It must also be noticed
+that _Christianity_ was part and parcel of the articles of _war_; and so
+was _duelling_. Any officer speaking against religion was to be cashiered;
+and any officer receiving an affront without, in the last resort,
+attempting to kill his opponent, was also to be cashiered. Though somewhat
+of a book-hunter, I {402} have never been able to ascertain the date of the
+collected remonstrances of the prelates in the House of Lords against this
+overt inculcation of murder, under the soft name of _satisfaction_: it is
+neither in Watt,[821] nor in Lowndes,[822] nor in any edition of
+Brunet;[823] and there is no copy in the British Museum. Was the collected
+edition really published?
+
+[The publication of the above in the _Athenaeum_ has not produced reference
+to a single copy. The collected edition seems to be doubted. I have even
+met one or two persons who doubt the fact of the Bishops having
+remonstrated at all: but their doubt was founded on an absurd supposition,
+namely, that it was _no business of theirs_; that it was not the business
+of the prelates of the church in union with the state to remonstrate
+against the Crown commanding murder! Some say that the edition was
+published, but under an irrelevant title, which prevented people from
+knowing what it was about. Such things have happened: for example, arranged
+extracts from Wellington's general orders, which would have attracted
+attention, fell dead under the title of "Principles of War." It is surmised
+that the book I am looking for also contains the protests of the Reverend
+bench against other things besides the Thou-shalt-do-murder of the Articles
+(of war), and is called "First Elements of Religion" or some similar title.
+Time clears up all things.]
+
+       *       *       *       *       *
+
+
+Notes
+
+[1] See Mrs. De Morgan's _Memoir of Augustus De Morgan_, London, 1882, p
+61.
+
+[2] In the first edition this reference was to page 11.
+
+[3] In the first edition this read "at page 438," the work then appearing
+in a single volume.
+
+[4] "Just as it would surely have been better not to have considered it
+(i.e., the trinity) as a mystery, and with Cl. Kleckermann to have
+investigated by the aid of philosophy according to the teaching of true
+logic what it might be, before they determined what it was; just so would
+it have been better to withdraw zealously and industriously into the
+deepest caverns and darkest recesses of metaphysical speculations and
+suppositions in order to establish their opinion beyond danger from the
+weapons of their adversaries.... Indeed that great man so explains and
+demonstrates this dogma (although to theologians the word has not much
+charm) from the immovable foundations of philosophy, that with but few
+changes and additions a mind sincerely devoted to truth can desire nothing
+more."
+
+[5] Mrs. Wititterly, in _Nicholas Nickleby_.--A. De M.
+
+[6] The brackets mean that the paragraph is substantially from some one of
+the _Athenaeum Supplements_.--S. E. De M.
+
+[7] "It is annoying that this ingenious naturalist who has already given us
+more useful works and has still others in preparation, uses for this odious
+task, a pen dipped in gall and wormwood. It is true that many of his
+remarks have some foundation, and that to each error that he points out he
+at the same time adds its correction. But he is not always just and never
+fails to insult. After all, what does his book prove except that a
+forty-fifth part of a very useful review is not free from mistakes? Must we
+confuse him with those superficial writers whose liberty of body does not
+permit them to restrain their fruitfulness, that crowd of savants of the
+highest rank whose writings have adorned and still adorn the
+_Transactions_? Has he forgotten that the names of the Boyles, Newtons,
+Halleys, De Moivres, Hans Sloanes, etc. have been seen frequently? and that
+still are found those of the Wards, Bradleys, Grahams, Ellicots, Watsons,
+and of an author whom Mr. Hill prefers to all others, I mean Mr. Hill
+himself?"
+
+[8] "Let no free man be seized or imprisoned or in any way harmed except by
+trial of his peers."
+
+[9] "The master can rob, wreck and punish his slave according to his
+pleasure save only that he may not maim him."
+
+[10] An Irish antiquary informs me that Virgil is mentioned in annals at
+A.D. 784, as "Verghil, i.e., the geometer, Abbot of Achadhbo [and Bishop of
+Saltzburg] died in Germany in the thirteenth year of his bishoprick." No
+allusion is made to his opinions; but it seems he was, by tradition, a
+mathematician. The Abbot of Aghabo (Queen's County) was canonized by
+Gregory IX, in 1233. The story of the second, or scapegoat, Virgil would be
+much damaged by the character given to the real bishop, if there were
+anything in it to dilapidate.--A. De M.
+
+[11] "He performed many acts befitting the Papal dignity, and likewise many
+excellent (to be sure!) works."
+
+[12] "After having been on the throne during ten years of pestilence."
+
+[13] The work is the _Questiones Joannis Buridani super X libros
+Aristotelis ad Nicomachum, curante Egidio Delfo_ ... Parisiis, 1489, folio.
+It also appeared at Paris in editions of 1499, 1513, and 1518, and at
+Oxford in 1637.
+
+[14] Jean Buridan was born at Bethune about 1298, and died at Paris about
+1358. He was professor of philosophy at the University of Paris and several
+times held the office of Rector. As a philosopher he was classed among the
+nominalists.
+
+[15] So in the original.
+
+[16] Baruch Spinoza, or Benedict de Spinoza as he later called himself, the
+pantheistic philosopher, excommunicated from the Jewish faith for heresy,
+was born at Amsterdam in 1632 and died there in 1677.
+
+[17] Michael Scott, or Scot, was born about 1190, probably in Fifeshire,
+Scotland, and died about 1291. He was one of the best known savants of the
+court of Emperor Frederick II, and wrote upon astrology, alchemy, and the
+occult sciences. He was looked upon as a great magician and is mentioned
+among the wizards in Dante's _Inferno_.
+
+             "That other, round the loins
+  So slender of his shape, was Michael Scot,
+  Practised in every slight of magic wile." _Inferno_, XX.
+
+Boccaccio also speaks of him: "It is not long since there was in this city
+(Florence) a great master in necromancy, who was called Michele Scotto,
+because he was a Scot." _Decameron_, Dec. Giorno.
+
+Scott's mention of him in Canto Second of his _Lay of the Last Minstrel_,
+is well known:
+
+ "In these fair climes, it was my lot
+  To meet the wondrous Michael Scott;
+    A wizard of such dreaded fame,
+  That when, in Salamanca's cave,
+  Him listed his magic wand to wave,
+    The bells would ring in Notre Dame!"
+
+Sir Walter's notes upon him are of interest.
+
+[18] These were some of the forgeries which Michel Chasles (1793-1880) was
+duped into buying. They purported to be a correspondence between Pascal and
+Newton and to show that the former had anticipated some of the discoveries
+of the great English physicist and mathematician. That they were forgeries
+was shown by Sir David Brewster in 1855.
+
+[19] "Let the serpent also break from its appointed path."
+
+[20] Guglielmo Brutus Icilius Timoleon Libri-Carucci della Sommaja, born at
+Florence in 1803; died at Fiesole in 1869. His _Histoire des Sciences
+Mathematiques_ appeared at Paris in 1838, the entire first edition of
+volume I, save some half dozen that he had carried home, being burned on
+the day that the printing was completed. He was a great collector of early
+printed works on mathematics, and was accused of having stolen large
+numbers of them from other libraries. This accusation took him to London,
+where he bitterly attacked his accusers. There were two auction sales of
+his library, and a number of his books found their way into De Morgan's
+collection.
+
+[21] Philo of Gadara lived in the second century B.C. He was a pupil of
+Sporus, who worked on the problem of the two mean proportionals.
+
+[22] In his _Histoire des Mathematiques_, the first edition of which
+appeared in 1758. Jean Etienne Montucla was born at Lyons in 1725 and died
+at Versailles in 1799. He was therefore only thirty-three years old when
+his great work appeared. The second edition, with additions by D'Alembert,
+appeared in 1799-1802. He also wrote a work on the quadrature of the
+circle, _Histoire des recherches sur la Quadrature du Cercle_, which
+appeared in 1754.
+
+[23] Eutocius of Ascalon was born in 480 A.D. He wrote commentaries on the
+first four books of the conics of Apollonius of Perga (247-222 B.C.). He
+also wrote on the Sphere and Cylinder and the Quadrature of the Circle, and
+on the two books on Equilibrium of Archimedes (287-212 B.C.)
+
+[24] Edward Cocker was born in 1631 and died between 1671 and 1677. His
+famous arithmetic appeared in 1677 and went through many editions. It was
+written in a style that appealed to teachers, and was so popular that the
+expression "According to Cocker" became a household phrase. Early in the
+nineteenth century there was a similar saying in America, "According to
+Daboll," whose arithmetic had some points of analogy to that of Cocker.
+Each had a well-known prototype in the ancient saying, "He reckons like
+Nicomachus of Gerasa."
+
+[25] So in the original, for Barreme. Francois Barreme was to France what
+Cocker was to England. He was born at Lyons in 1640, and died at Paris in
+1703. He published several arithmetics, dedicating them to his patron,
+Colbert. One of the best known of his works is _L'arithmetique, ou le livre
+facile pour apprendre l'arithmetique soi-meme_, 1677. The French word
+_bareme_ or _barreme_, a ready-reckoner, is derived from his name.
+
+[26] Born at Rome, about 480 A.D.; died at Pavia, 524. Gibbon speaks of him
+as "the last of the Romans whom Cato or Tully could have acknowledged for
+their countryman." His works on arithmetic, music, and geometry were
+classics in the medieval schools.
+
+[27] Johannes Campanus, of Novarra, was chaplain to Pope Urban IV
+(1261-1264). He was one of the early medieval translators of Euclid from
+the Arabic into Latin, and the first printed edition of the _Elements_
+(Venice, 1482) was from his translation. In this work he probably depended
+not a little upon at least two or three earlier scholars. He also wrote _De
+computo ecclesiastico Calendarium_, and _De quadratura circuli_.
+
+[28] Archimedes gave 3-1/7, and 3-10/71 as the limits of the ratio of the
+circumference to the diameter of a circle.
+
+[29] Friedrich W. A. Murhard was born at Cassel in 1779 and died there in
+1853. His _Bibliotheca Mathematica_, Leipsic, 1797-1805, is ill arranged
+and inaccurate, but it is still a helpful bibliography. De Morgan speaks
+somewhere of his indebtedness to it.
+
+[30] Abraham Gotthelf Kaestner was born at Leipsic in 1719, and died at
+Goettingen in 1800. He was professor of mathematics and physics at
+Goettingen. His _Geschichte der Mathematik_ (1796-1800) was a work of
+considerable merit. In the text of the _Budget of Paradoxes_ the name
+appears throughout as Kastner instead of Kaestner.
+
+[31] Lucas Gauricus, or Luca Gaurico, born at Giffoni, near Naples, in
+1476; died at Rome in 1558. He was an astrologer and mathematician, and was
+professor of mathematics at Ferrara in 1531. In 1545 he became bishop of
+Civita Ducale.
+
+[32] John Couch Adams was born at Lidcot, Cornwall, in 1819, and died in
+1892. He and Leverrier predicted the discovery of Neptune from the
+perturbations in Uranus.
+
+[33] Urbain-Jean-Joseph Leverrier was born at Saint-Lo, Manche, in 1811,
+and died at Paris in 1877. It was his data respecting the perturbations of
+Uranus that were used by Adams and himself in locating Neptune.
+
+[34] Joseph-Juste Scaliger, the celebrated philologist, was born at Agen in
+1540, and died at Leyden in 1609. His _Cyclometrica elementa_, to which De
+Morgan refers, appeared at Leyden in 1594.
+
+[35] The title is: _In hoc libra contenta.... Introductio i
+geometri[=a].... Liber de quadratura circuli. Liber de cubicatione sphere.
+Perspectiva introductio_. Carolus Bovillus, or Charles Bouvelles (Boueelles,
+Bouilles, Bouvel), was born at Saucourt, Picardy, about 1470, and died at
+Noyon about 1533. He was canon and professor of theology at Noyon. His
+_Introductio_ contains considerable work on star polygons, a favorite study
+in the Middle Ages and early Renaissance. His work _Que hoc volumine
+contin[=e]tur. Liber de intellectu. Liber de sensu_, etc., appeared at
+Paris in 1509-10.
+
+[36] Nicolaus Cusanus, Nicolaus Chrypffs or Krebs, was born at Kues on the
+Mosel in 1401, and died at Todi, Umbria, August 11, 1464. He held positions
+of honor in the church, including the bishopric of Brescia. He was made a
+cardinal in 1448. He wrote several works on mathematics, his _Opuscula
+varia_ appearing about 1490, probably at Strasburg, but published without
+date or place. His _Opera_ appeared at Paris in 1511 and again in 1514, and
+at Basel in 1565.
+
+[37] Henry Stephens (born at Paris about 1528, died at Lyons in 1598) was
+one of the most successful printers of his day. He was known as
+_Typographus Parisiensis_, and to his press we owe some of the best works
+of the period.
+
+[38] Jacobus Faber Stapulensis (Jacques le Fevre d'Estaples) was born at
+Estaples, near Amiens, in 1455, and died at Nerac in 1536. He was a priest,
+vicar of the bishop of Meaux, lecturer on philosophy at the College Lemoine
+in Paris, and tutor to Charles, son of Francois I. He wrote on philosophy,
+theology, and mathematics.
+
+[39] Claude-Francois Milliet de Challes was born at Chambery in 1621, and
+died at Turin in 1678. He edited _Euclidis Elementorum libri octo_ in 1660,
+and published a _Cursus seu mundus mathematicus_, which included a short
+history of mathematics, in 1674. He also wrote on mathematical geography.
+
+[40] This date should be 1503, if he refers to the first edition. It is
+well known that this is the first encyclopedia worthy the name to appear in
+print. It was written by Gregorius Reisch (born at Balingen, and died at
+Freiburg in 1487), prior of the cloister at Freiburg and confessor to
+Maximilian I. The first edition appeared at Freiburg in 1503, and it passed
+through many editions in the sixteenth and seventeenth centuries. The title
+of the 1504 edition reads: _Aepitoma omnis phylosophiae. alias Margarita
+phylosophica tractans de omni genere scibili: Cum additionibus: Quae in
+alijs non habentur_.
+
+[41] This is the _Introductio in arithmeticam Divi S. Boetii.... Epitome
+rerum geometricarum ex geometrica introductio C. Bovilli. De quadratura
+circuli demonstratio ex Campano_, that appeared without date about 1507.
+
+[42] Born at Liverpool in 1805, and died there about 1872. He was a
+merchant, and in 1865 he published, at Liverpool, a work entitled _The
+Quadrature of the Circle, or the True Ratio between the Diameter and
+Circumference geometrically and mathematically demonstrated_. In this he
+gives the ratio as exactly 3-1/8.
+
+[43] "That it would be impossible to tell him exactly, since no one had yet
+been able to find precisely the ratio of the circumference to the
+diameter."
+
+[44] This is the Paris edition: "Parisiis: ex officina Ascensiana anno
+Christi ... MDXIIII," as appears by the colophon of the second volume to
+which De Morgan refers.
+
+[45] Regiomontanus, or Johann Mueller of Koenigsberg (Regiomontanus), was
+born at Koenigsberg in Franconia, June 5, 1436, and died at Rome July 6,
+1476. He studied at Vienna under the great astronomer Peuerbach, and was
+his most famous pupil. He wrote numerous works, chiefly on astronomy. He is
+also known by the names Ioannes de Monte Regio, de Regiomonte, Ioannes
+Germanus de Regiomonte, etc.
+
+[46] Henry Cornelius Agrippa was born at Cologne in 1486 and died either at
+Lyons in 1534 or at Grenoble in 1535. He was professor of theology at
+Cologne and also at Turin. After the publication of his _De Occulta
+Philosophia_ he was imprisoned for sorcery. Both works appeared at Antwerp
+in 1530, and each passed through a large number of editions. A French
+translation appeared in Paris in 1582, and an English one in London in
+1651.
+
+[47] Nicolaus Remegius was born in Lorraine in 1554, and died at Nancy in
+1600. He was a jurist and historian, and held the office of procurator
+general to the Duke of Lorraine.
+
+[48] This was at the storming of the city by the British on May 4, 1799.
+From his having been born in India, all this appealed strongly to the
+interests of De Morgan.
+
+[49] Orontius Finaeus, or Oronce Fine, was born at Briancon in 1494 and
+died at Paris, October 6, 1555. He was imprisoned by Francois I for
+refusing to recognize the concordat (1517). He was made professor of
+mathematics in the College Royal (later called the College de France) in
+1532. He wrote extensively on astronomy and geometry, but was by no means a
+great scholar. He was a pretentious man, and his works went through several
+editions. His _Protomathesis_ appeared at Paris in 1530-32. The work
+referred to by De Morgan is the _Quadratura circuli tandem inventa &
+clarissime demonstrata_ ... Lutetiae Parisiorum, 1544, fol. In the 1556
+edition of his _De rebus mathematicis, hactenus desideratis, Libri IIII_,
+published at Paris, the subtitle is: _Quibus inter caetera, Circuli
+quadratura Centum modis, & supra, per eundem Orontium recenter excogitatis,
+demonstratus_, so that he kept up his efforts until his death.
+
+[50] Johannes Buteo (Boteo, Buteon, Bateon) was born in Dauphine c.
+1485-1489, and died in a cloister in 1560 or 1564. Some writers give
+Charpey as the place and 1492 as the date of his birth, and state that he
+died at Canar in 1572. He belonged to the order of St. Anthony, and wrote
+chiefly on geometry, exposing the pretenses of Finaeus. His _Opera
+geometrica_ appeared at Lyons in 1554, and his _Logistica_ and _De
+quadratura circuli libri duo_ at Lyons in 1559.
+
+[51] This is the great French algebraist, Francois Viete (Vieta), who was
+born at Fontenay-le-Comte in 1540, and died at Paris, December 13, 1603.
+His well-known _Isagoge in artem analyticam_ appeared at Tours in 1591. His
+_Opera mathematica_ was edited by Van Schooten in 1646.
+
+[52] This is the _De Rebus mathematicis hactenus desideratis, Libri IIII_,
+that appeared in Paris in 1556. For the title page see Smith, D. E., _Rara
+Arithmetica_, Boston, 1908, p. 280.
+
+[53] The title is correct except for a colon after _Astronomicum_. Nicolaus
+Raimarus Ursus was born in Henstede or Hattstede, in Dithmarschen, and died
+at Prague in 1599 or 1600. He was a pupil of Tycho Brahe. He also wrote _De
+astronomis hypothesibus_ (1597) and _Arithmetica analytica vulgo Cosa oder
+Algebra_ (1601).
+
+[54] Born at Dole, Franche-Comte, about 1550, died in Holland about 1600.
+The work to which reference is made is the _Quadrature du cercle, ou
+maniere de trouver un quarre egal au cercle donne_, which appeared at Delft
+in 1584. Duchesne had the courage of his convictions, not only on
+circle-squaring but on religion as well, for he was obliged to leave France
+because of his conversion to Calvinism. De Morgan's statement that his real
+name is Van der Eycke is curious, since he was French born. The Dutch may
+have translated his name when he became professor at Delft, but we might
+equally well say, that his real name was Quercetanus or a Quercu.
+
+[55] This was the father of Adriaan Metius (1571-1635). He was a
+mathematician and military engineer, and suggested the ratio 355/113 for
+[pi], a ratio afterwards published by his son. The ratio, then new to
+Europe, had long been known and used in China, having been found by Tsu
+Ch'ung-chih (428-499 A.D.).
+
+[56] This was Jost Buergi, or Justus Byrgius, the Swiss mathematician of
+whom Kepler wrote in 1627: "Apices logistici Justo Byrgio multis annis ante
+editionem Neperianam viam praeiverunt ad hos ipsissimos logarithmos." He
+constructed a table of antilogarithms (_Arithmetische und geometrische
+Progress-Tabulen_), but it was not published until after Napier's work
+appeared.
+
+[57] Ludolphus Van Ceulen, born at Hildesheim, and died at Leyden in 1610.
+It was he who first carried the computation of [pi] to 35 decimal places.
+
+[58] Jens Jenssen Dodt, van Flensburg, a Dutch historian, who died in 1847.
+
+[59] I do not know this edition. There was one "Antverpiae apud Petrum
+Bellerum sub scuto Burgundiae," 4to, in 1591.
+
+[60] Archytas of Tarentum (430-365 B.C.) who wrote on proportions,
+irrationals, and the duplication of the cube.
+
+[61]
+
+      _The Circle Speaks._
+ "At first a circle I was called,
+  And was a curve around about
+  Like lofty orbit of the sun
+  Or rainbow arch among the clouds.
+  A noble figure then was I--
+  And lacking nothing but a start,
+  And lacking nothing but an end.
+  But now unlovely do I seem
+  Polluted by some angles new.
+  This thing Archytas hath not done
+  Nor noble sire of Icarus
+  Nor son of thine, Iapetus.
+  What accident or god can then
+  Have quadrated mine area?"
+
+      _The Author Replies._
+ "By deepest mouth of Turia
+  And lake of limpid clearness, lies
+  A happy state not far removed
+  From old Saguntus; farther yet
+  A little way from Sucro town.
+  In this place doth a poet dwell,
+  Who oft the stars will closely scan,
+  And always for himself doth claim
+  What is denied to wiser men;--
+  An old man musing here and there
+  And oft forgetful of himself,
+  Not knowing how to rightly place
+  The compasses, nor draw a line,
+  As he doth of himself relate.
+  This craftsman fine, in sooth it is
+  Hath quadrated thine area."
+
+[62] Pietro Bongo, or Petrus Bungus, was born at Bergamo, and died there in
+1601. His work on the Mystery of Numbers is one of the most exhaustive and
+erudite ones of the mystic writers. The first edition appeared at Bergamo
+in 1583-84; the second, at Bergamo in 1584-85; the third, at Venice in
+1585; the fourth, at Bergamo in 1590; and the fifth, which De Morgan calls
+the second, in 1591. Other editions, before the Paris edition to which he
+refers, appeared in 1599 and 1614; and the colophon of the Paris edition is
+dated 1617. See the editor's _Rara Arithmetica_, pp. 380-383.
+
+[63] William Warburton (1698-1779), Bishop of Gloucester, whose works got
+him into numerous literary quarrels, being the subject of frequent satire.
+
+[64] Thomas Galloway (1796-1851), who was professor of mathematics at
+Sandhurst for a time, and was later the actuary of the Amicable Life
+Assurance Company of London. In the latter capacity he naturally came to be
+associated with De Morgan.
+
+[65] Giordano Bruno was born near Naples about 1550. He left the Dominican
+order to take up Calvinism, and among his publications was _L'expulsion de
+la bete triomphante_. He taught philosophy at Paris and Wittenberg, and
+some of his works were published in England in 1583-86. Whether or not he
+was roasted alive "for the maintenance and defence of the holy Church," as
+De Morgan states, depends upon one's religious point of view. At any rate,
+he was roasted as a heretic.
+
+[66] Referring to part of his _Discours de la methode_, Leyden, 1637.
+
+[67] Bartholomew Legate, who was born in Essex about 1575. He denied the
+divinity of Christ and was the last heretic burned at Smithfield.
+
+[68] Edward Wightman, born probably in Staffordshire. He was
+anti-Trinitarian, and claimed to be the Messiah. He was the last man burned
+for heresy in England.
+
+[69] Gaspar Schopp, born at Neumarck in 1576, died at Padua in 1649;
+grammarian, philologist, and satirist.
+
+[70] Konrad Ritterhusius, born at Brunswick in 1560; died at Altdorf in
+1613. He was a jurist of some power.
+
+[71] Johann Jakob Brucker, born at Augsburg in 1696, died there in 1770. He
+wrote on the history of philosophy (1731-36, and 1742-44).
+
+[72] Daniel Georg Morhof, born at Wismar in 1639, died at Luebeck in 1691.
+He was rector of the University of Kiel, and professor of eloquence,
+poetry, and history.
+
+[73] In the _Histoire des Sciences Mathematiques_, vol. IV, note X, pp.
+416-435 of the 1841 edition.
+
+[74] Colenso (1814-1883), missionary bishop of Natal, was one of the
+leaders of his day in the field of higher biblical criticism. De Morgan
+must have admired his mathematical works, which were not without merit.
+
+[75] Samuel Roffey Maitland, born at London in 1792; died at Gloucester in
+1866. He was an excellent linguist and a critical student of the Bible. He
+became librarian at Lambeth in 1838.
+
+[76] Archbishop Howley (1766-1848) was a thorough Tory. He was one of the
+opponents of the Roman Catholic Relief bill, the Reform bill, and the
+Jewish Civil Disabilities Relief bill.
+
+[77] We have, in America at least, almost forgotten the great stir made by
+Edward B. Pusey (1800-1882) in the great Oxford movement in the middle of
+the nineteenth century. He was professor of Hebrew at Oxford, and canon of
+Christ Church.
+
+[78] That is, his _Magia universalis naturae et artis sive recondita
+naturalium et artificialium rerum scientia_, Wuerzburg, 1657, 4to, with
+editions at Bamberg in 1671, and at Frankfort in 1677. Gaspard Schott
+(Koenigshofen 1608, Wuerzburg 1666) was a physicist and mathematician,
+devoting most of his attention to the curiosities of his sciences. His type
+of mind must have appealed to De Morgan.
+
+[79] _Salicetti Quadratura circuli nova, perspicua, expedita, veraque tum
+naturalis, tum geometrica_, etc., 1608.--_Consideratio nova in opusculum
+Archimedis de circuli dimensione_, etc., 1609.
+
+[80] Melchior Adam, who died at Heidelberg in 1622, wrote a collection of
+biographies which was published at Heidelberg and Frankfort from 1615 to
+1620.
+
+[81] Born at Baden in 1524; died at Basel in 1583. The Erastians were
+related to the Zwinglians, and opposed all power of excommunication and the
+infliction of penalties by a church.
+
+[82] See Acts xii. 20.
+
+[83] Theodore de Bese, a French theologian; born at Vezelay, in Burgundy,
+in 1519; died at Geneva, in 1605.
+
+[84] Dr. Robert Lee (1804-1868) had some celebrity in De Morgan's time
+through his attempt to introduce music and written prayers into the service
+of the Scotch Presbyterian church.
+
+[85] Born at Veringen, Hohenzollern, in 1512; died at Roeteln in 1564.
+
+[86] Born at Kinnairdie, Bannfshire, in 1661; died at London in 1708. His
+_Astronomiae Physicae et Geometriae Elementa_, Oxford, 1702, was an
+influential work.
+
+[87] The title was carelessly copied by De Morgan, not an unusual thing in
+his case. The original reads: A Plaine Discovery, of the whole Revelation
+of S. Iohn: set downe in two treatises ... set foorth by John Napier L. of
+Marchiston ... whereunto are annexed, certaine Oracles of Sibylla ...
+London ... 1611.
+
+[88] I have not seen the first edition, but it seems to have appeared in
+Edinburgh, in 1593, with a second edition there in 1594. The 1611 edition
+was the third.
+
+[89] It seems rather certain that Napier felt his theological work of
+greater importance than that in logarithms. He was born at Merchiston, near
+(now a part of) Edinburgh, in 1550, and died there in 1617, three years
+after the appearance of his _Mirifici logarithmorum canonis descriptio_.
+
+[90] Followed, in the third edition, from which he quotes, by a comma.
+
+[91] There was an edition published at Stettin in 1633. An English
+translation by P. F. Mottelay appeared at London in 1893. Gilbert
+(1540-1603) was physician to Queen Elizabeth and President of the College
+of Physicians at London. His _De Magnete_ was the first noteworthy treatise
+on physics printed in England. He treated of the earth as a spherical
+magnet and suggested the variation and declination of the needle as a means
+of finding latitude at sea.
+
+[92] The title says "ab authoris fratre collectum," although it was edited
+by J. Gruterus.
+
+[93] Porta was born at Naples in 1550 and died there in 1615. He studied
+the subject of lenses and the theory of sight, did some work in hydraulics
+and agriculture, and was well known as an astrologer. His _Magiae naturalis
+libri XX_ was published at Naples in 1589. The above title should read
+_curvilineorum_.
+
+[94] Cataldi was born in 1548 and died at Bologna in 1626. He was professor
+of mathematics at Perugia, Florence, and Bologna, and is known in
+mathematics chiefly for his work in continued fractions. He was one of the
+scholarly men of his day.
+
+[95] Georg Joachim Rheticus was born at Feldkirch in 1514 and died at
+Caschau, Hungary, in 1576. He was one of the most prominent pupils of
+Copernicus, his _Narratio de libris revolutionum Copernici_ (Dantzig, 1540)
+having done much to make the theory of his master known.
+
+[96] Henry Briggs, who did so much to make logarithms known, and who used
+the base 10, was born at Warley Wood, in Yorkshire, in 1560, and died at
+Oxford in 1630. He was Savilian professor of mathematics at Oxford, and his
+grave may still be seen there.
+
+[97] He lived at "Reggio nella Emilia" in the 16th and 17th centuries. His
+_Regola e modo facilissimo di quadrare il cerchio_ was published at Reggio
+in 1609.
+
+[98] Christoph Klau (Clavius) was born at Bamberg in 1537, and died at Rome
+in 1612. He was a Jesuit priest and taught mathematics in the Jesuit
+College at Rome. He wrote a number of works on mathematics, including
+excellent text-books on arithmetic and algebra.
+
+[99] Christopher Gruenberger, or Grienberger, was born at Halle in Tyrol in
+1561, and died at Rome in 1636. He was, like Clavius, a Jesuit and a
+mathematician, and he wrote a little upon the subject of projections. His
+_Prospectiva nova coelestis_ appeared at Rome in 1612.
+
+[100] The name should, of course, be Lansbergii in the genitive, and is so
+in the original title. Philippus Lansbergius was born at Ghent in 1560, and
+died at Middelburg in 1632. He was a Protestant theologian, and was also a
+physician and astronomer. He was a well-known supporter of Galileo and
+Copernicus. His _Commentationes in motum terrae diurnum et annuum_ appeared
+at Middelburg in 1630 and did much to help the new theory.
+
+[101] I have never seen the work. It is rare.
+
+[102] The African explorer, born in Somersetshire in 1827, died at Bath in
+1864. He was the first European to cross Central Africa from north to
+south. He investigated the sources of the Nile.
+
+[103] Prester (Presbyter, priest) John, the legendary Christian king whose
+realm, in the Middle Ages, was placed both in Asia and in Africa, is first
+mentioned in the chronicles of Otto of Freisingen in the 12th century. In
+the 14th century his kingdom was supposed to be Abyssinia.
+
+[104] "It is a profane and barbarous nation, dirty and slovenly, who eat
+their meat half raw and drink mare's milk, and who use table-cloths and
+napkins only to wipe their hands and mouths."
+
+[105] "The great Prester John, who is the fourth in rank, is emperor of
+Ethiopia and of the Abyssinians, and boasts of his descent from the race of
+David, as having descended from the Queen of Sheba, Queen of Ethiopia. She,
+having gone to Jerusalem to see the wisdom of Solomon, about the year of
+the world 2952, returned pregnant with a son whom they called Moylech, from
+whom they claim descent in a direct line. And so he glories in being the
+most ancient monarch in the world, saying that his empire has endured for
+more than three thousand years, which no other empire is able to assert. He
+also puts into his titles the following: 'We, the sovereign in my realms,
+uniquely beloved of God, pillar of the faith, sprung from the race of
+Judah, etc.' The boundaries of this empire touch the Red Sea and the
+mountains of Azuma on the east, and on the western side it is bordered by
+the River Nile which separates it from Nubia. To the north lies Egypt, and
+to the south the kingdoms of Congo and Mozambique. It extends forty degrees
+in length, or one thousand twenty-five leagues, from Congo or Mozambique on
+the south to Egypt on the north; and in width it reaches from the Nile on
+the west to the mountains of Azuma on the east, seven hundred twenty-five
+leagues, or twenty-nine degrees. This empire contains thirty large
+provinces, namely Medra, Gaga, Alchy, Cedalon, Mantro, Finazam, Barnaquez,
+Ambiam, Fungy, Angote, Cigremaon, Gorga, Cafatez, Zastanla, Zeth, Barly,
+Belangana, Tygra, Gorgany, Barganaza, d'Ancut, Dargaly, Ambiacatina,
+Caracogly, Amara, Maon (_sic_), Guegiera, Bally, Dobora, and Macheda. All
+of these provinces are situated directly under the equinoctial line between
+the tropics of Capricorn and Cancer; but they are two hundred fifty leagues
+nearer our tropic than the other. The name of Prester John signifies Great
+Lord, and is not Priest [Presbyter] as many think. He has always been a
+Christian, but often schismatic. At the present time he is a Catholic and
+recognizes the Pope as sovereign pontiff. I met one of his bishops in
+Jerusalem, and often conversed with him through the medium of our guide. He
+was of grave and serious bearing, pleasant of speech, but wonderfully
+subtle in everything he said. He took great delight in what I had to relate
+concerning our beautiful ceremonies and the dignity of our prelates in
+their pontifical vestments. As to other matters I will only say that the
+Ethiopian is joyous and merry, not at all like the Tartar in the matter of
+filth, nor like the wretched Arab. They are refined and subtle, trusting no
+one, wonderfully suspicious, and very devout. They are not at all black as
+is commonly supposed, by which I refer to those who do not live under the
+equator or too near to it, for these are Moors as we shall see."
+
+With respect to this translation it should be said that the original forms
+of the proper names have been preserved, although they are not those found
+in modern works. It should also be stated that the meaning of Prester is
+not the one that was generally accepted by scholars at the time the work
+was written, nor is it the one accepted to-day. There seems to be no doubt
+that the word is derived from Presbyter as stated in note 103 on page 71,
+since the above-mentioned chronicles of Otto, bishop of Freisingen about
+the middle of the twelfth century, states this fact clearly. Otto received
+his information from the bishop of Gabala (the Syrian Jibal) who told him
+the story of John, _rex et sacerdos_, or Presbyter John as he liked to be
+called. He goes on to say "Should it be asked why, with all this power and
+splendor, he calls himself merely 'presbyter,' this is because of his
+humility, and because it was not fitting for one whose server was a primate
+and king, whose butler an archbishop and king, whose chamberlain a bishop
+and king, whose master of the horse an archimandrite and king, whose chief
+cook an abbot and king, to be called by such titles as these."
+
+[106] Thomas Fienus (Fyens) was born at Antwerp in 1567 and died in 1631.
+He was professor of medicine at Louvain. Besides the editions mentioned
+below, his _De cometis anni 1618_ appeared at Leipsic in 1656. He also
+wrote a _Disputatio an coelum moveatur et terra quiescat_, which appeared
+at Antwerp in 1619, and again at Leipsic in 1656.
+
+[107] Libertus Fromondus (1587-c 1653), a Belgian theologian, dean of the
+College Church at Harcourt, and professor at Louvain. The name also appears
+as Froidmont and Froimont.
+
+[108] _L. Fromondi ... meteorologicorum libri sex.... Cui accessit T. Fieni
+et L. Fromondi dissertationes de cometa anni 1618...._ This is from the
+1670 edition. The 1619 edition was published at Antwerp. The
+_Meteorologicorum libri VI_, appeared at Antwerp in 1627. He also wrote
+_Anti-Aristarchus sive orbis terrae immobilis liber unicus_ (Antwerp,
+1631); _Labyrrinthus sive de compositione continui liber unus, Philosophis,
+Mathematicis, Theologis utilis et jucundus_ (Antwerp, 1631) and _Vesta sive
+Anti-Aristarchi vindex adversus Jac. Lansbergium (Philippi filium) et
+copernicanos_ (Antwerp, 1634).
+
+[109] Snell was born at Leyden in 1591, and died there in 1626. He studied
+under Tycho Brahe and Kepler, and is known for Snell's law of the
+refraction of light. He was the first to determine the size of the earth by
+measuring the arc of a meridian with any fair degree of accuracy. The title
+should read: _Willebrordi Snellii R. F. Cyclometricus, de circuli
+dimensione secundum Logistarum abacos, et ad Mechanicem accuratissima...._
+
+[110] Bacon was born at York House, London, in 1561, and died near
+Highgate, London, in 1626. His _Novum Organum Scientiarum or New Method of
+employing the reasoning faculties in the pursuits of Truth_ appeared at
+London in 1620. He had previously published a work entitled _Of the
+Proficience and Advancement of Learning, divine and humane_ (London, 1605),
+which again appeared in 1621. His _De augmentis scientiarum Libri IX_
+appeared at Paris in 1624, and his _Historia naturalis et experimentalis de
+ventis_ at Leyden in 1638. He was successively solicitor general, attorney
+general, lord chancellor (1619), Baron Verulam and Viscount St. Albans. He
+was deprived of office and was imprisoned in the Tower of London in 1621,
+but was later pardoned.
+
+[111] The Greek form, _Organon_, is sometimes used.
+
+[112] James Spedding (1808-1881), fellow of Cambridge, who devoted his life
+to his edition of Bacon.
+
+[113] R. Leslie Ellis (1817-1859), editor of the _Cambridge Mathematical
+Journal_. He also wrote on Roman aqueducts, on Boole's Laws of Thought, and
+on the formation of a Chinese dictionary.
+
+[114] Douglas Derion Heath (1811-1897), a classical and mathematical
+scholar.
+
+[115] There have been numerous editions of Bacon's complete works,
+including the following: Frankfort, 1665; London, 1730, 1740, 1764, 1765,
+1778, 1803, 1807, 1818, 1819, 1824, 1825-36, 1857-74, 1877. The edition to
+which De Morgan refers is that of 1857-74, 14 vols., of which five were
+apparently out at the time he wrote. There were also French editions in
+1800 and 1835.
+
+[116] So in the original for Tycho Brahe.
+
+[117] In general these men acted before Baron wrote, or at any rate, before
+he wrote the _Novum Organum_, but the statement must not be taken too
+literally. The dates are as follows: Copernicus, 1473-1543; Tycho Brahe,
+1546-1601; Gilbert, 1540-1603; Kepler, 1571-1630; Galileo, 1564-1642;
+Harvey, 1578-1657. For example, Harvey's _Exercitatio Anatomica de Motu
+Cordis et Sanguinis_ did not appear until 1628, and his _Exercitationes de
+Generatione_ until 1651.
+
+[118] Robert Hooke (1635-1703) studied under Robert Boyle at Oxford. He was
+"Curator of Experiments" to the Royal Society and its secretary, and was
+professor of geometry at Gresham College, London. It is true that he was
+"very little of a mathematician" although he wrote on the motion of the
+earth (1674), on helioscopes and other instruments (1675), on the rotation
+of Jupiter (1666), and on barometers and sails.
+
+[119] The son of the Sir William mentioned below. He was born in 1792 and
+died in 1871. He wrote a treatise on light (1831) and one on astronomy
+(1836), and established an observatory at the Cape of Good Hope where he
+made observations during 1834-1838, publishing them in 1847. On his return
+to England he was knighted, and in 1848 was made president of the Royal
+Society. The title of the work to which reference is made is: _A
+preliminary discourse on the Study of Natural Philosophy_. It appeared at
+London in 1831.
+
+[120] Sir William was horn at Hanover in 1738 and died at Slough, near
+Windsor in 1822. He discovered the planet Uranus and six satellites,
+besides two satellites of Saturn. He was knighted by George III.
+
+[121] This was the work of 1836. He also published a work entitled
+_Outlines of Astronomy_ in 1849.
+
+[122] While Newton does not tell the story, he refers in the _Principia_
+(1714 edition, p. 293) to the accident caused by his cat.
+
+[123] Marino Ghetaldi (1566-1627), whose _Promotus Archimedes_ appeared at
+Rome in 1603, _Nonnullae propositiones de parabola_ at Rome in 1603. and
+_Apollonius redivivus_ at Venice in 1607. He was a nobleman and was
+ambassador from Venice to Rome.
+
+[124] Simon Stevin (born at Bruges, 1548; died at the Hague, 1620). He was
+an engineer and a soldier, and his _La Disme_ (1585) was the first separate
+treatise on the decimal fraction. The contribution referred to above is
+probably that on the center of gravity of three bodies (1586).
+
+[125] Habakuk Guldin (1577-1643), who took the name Paul on his conversion
+to Catholicism. He became a Jesuit, and was professor of mathematics at
+Vienna and later at Gratz. In his _Centrobaryca seu de centro gravitatis
+trium specierum quantitatis continuae_ (1635), of the edition of 1641,
+appears the Pappus rule for the volume of a solid formed by the revolution
+of a plane figure about an axis, often spoken of as Guldin's Theorem.
+
+[126] Edward Wright was born at Graveston, Norfolkshire, in 1560, and died
+at London in 1615. He was a fellow of Caius College, Cambridge, and in his
+work entitled _The correction of certain errors in Navigation_ (1599) he
+gives the principle of Mercator's projection. He translated the _Portuum
+investigandorum ratio_ of Stevin in 1599.
+
+[127] De Morgan never wrote a more suggestive sentence. Its message is not
+for his generation alone.
+
+[128] The eminent French physicist, Jean Baptiste Biot (1779-1862),
+professor in the College de France. His work _Sur les observatoires
+meteorologiques_ appeared in 1855.
+
+[129] George Biddell Airy (1801-1892), professor of astronomy and physics
+at Cambridge, and afterwards director of the Observatory at Greenwich.
+
+[130] De Morgan would have rejoiced in the role played by Intuition in the
+mathematics of to-day, notably among the followers of Professor Klein.
+
+[131] Colburn was the best known of the calculating boys produced in
+America. He was born at Cabot, Vermont, in 1804, and died at Norwich,
+Vermont, in 1840. Having shown remarkable skill in numbers as early as
+1810, he was taken to London in 1812, whence he toured through Great
+Britain and to Paris. The Earl of Bristol placed him in Westminster School
+(1816-1819). On his return to America he became a preacher, and later a
+teacher of languages.
+
+[132] The history of calculating boys is interesting. Mathieu le Coc (about
+1664), a boy of Lorraine, could extract cube roots at sight at the age of
+eight. Tom Fuller, a Virginian slave of the eighteenth century, although
+illiterate, gave the number of seconds in 7 years 17 days 12 hours after
+only a minute and a half of thought. Jedediah Buxton, an Englishman of the
+eighteenth century, was studied by the Royal Society because of his
+remarkable powers. Ampere, the physicist, made long calculations with
+pebbles at the age of four. Gauss, one of the few infant prodigies to
+become an adult prodigy, corrected his father's payroll at the age of
+three. One of the most remarkable of the French calculating boys was Henri
+Mondeux. He was investigated by Arago, Sturm, Cauchy, and Liouville, for
+the Academie des Sciences, and a report was written by Cauchy. His
+specialty was the solution of algebraic problems mentally. He seems to have
+calculated squares and cubes by a binomial formula of his own invention. He
+died in obscurity, but was the subject of a _Biographie_ by Jacoby (1846).
+George P. Bidder, the Scotch engineer (1806-1878), was exhibited as an
+arithmetical prodigy at the age of ten, and did not attend school until he
+was twelve. Of the recent cases two deserve special mention, Inaudi and
+Diamandi. Jacques Inaudi (born in 1867) was investigated for the Academie
+in 1892 by a commission including Poincare, Charcot, and Binet. (See the
+_Revue des Deux Mondes_, June 15, 1892, and the laboratory bulletins of the
+Sorbonne). He has frequently exhibited his remarkable powers in America.
+Pericles Diamandi was investigated by the same commission in 1893. See
+Alfred Binet, _Psychologie des Grands Calculateurs et Joueurs d'Echecs_,
+Paris, 1894.
+
+[133] John Flamsteed's (1646-1719) "old white house" was the first
+Greenwich observatory. He was the Astronomer Royal and first head of this
+observatory.
+
+[134] It seems a pity that De Morgan should not have lived to lash those of
+our time who are demanding only the immediately practical in mathematics.
+His satire would have been worth the reading against those who seek to
+stifle the science they pretend to foster.
+
+[135] Ismael Bouillaud, or Boulliau, was born in 1605 and died at Paris in
+1694. He was well known as an astronomer, mathematician, and jurist. He
+lived with De Thou at Paris, and accompanied him to Holland. He traveled
+extensively, and was versed in the astronomical work of the Persians and
+Arabs. It was in his _Astronomia philolaica, opus novum_ (Paris, 1645) that
+he attacked Kepler's laws. His tables were shown to be erroneous by the
+fact that the solar eclipse did not take place as predicted by him in 1645.
+
+[136] As it did, until 1892, when Airy had reached the ripe age of
+ninety-one.
+
+[137] _Didaci a Stunica ... In Job commentaria_ appeared at Toledo in 1584.
+
+[138] "The false Pythagorean doctrine, absolutely opposed to the Holy
+Scriptures, concerning the mobility of the earth and the immobility of the
+sun."
+
+[139] Paolo Antonio Foscarini (1580-1616), who taught theology and
+philosophy at Naples and Messina, was one of the first to champion the
+theories of Copernicus. This was in his _Lettera sopra l'opinione de'
+Pittagorici e del Copernico, della mobilita della Terra e stabilita del
+Sole, e il nuovo pittagorico sistema del mondo_, 4to, Naples, 1615. The
+condemnation of the Congregation was published in the following spring, and
+in the year of Foscarini's death at the early age of thirty-six.
+
+[140] "To be wholly prohibited and condemned," because "it seeks to show
+that the aforesaid doctrine is consonant with truth and is not opposed to
+the Holy Scriptures."
+
+[141] "As repugnant to the Holy Scriptures and to its true and Catholic
+interpretation (which in a Christian man cannot be tolerated in the least),
+he does not hesitate to treat (of his subject) '_by hypothesis_', but he
+even adds '_as most true_'!"
+
+[142] "To the places in which he discusses not by hypothesis but by making
+assertions concerning the position and motion of the earth."
+
+[143] "_Copernicus._ If by chance there shall be vain talkers who, although
+ignorant of all mathematics, yet taking it upon themselves to sit in
+judgment upon the subject on account of a certain passage of Scripture
+badly distorted for their purposes, shall have dared to criticize and
+censure this teaching of mine, I pay no attention to them, even to the
+extent of despising their judgment as rash. For it is not unknown that
+Lactantius, a writer of prominence in other lines although but little
+versed in mathematics, spoke very childishly about the form of the earth
+when he ridiculed those who declared that it was spherical. Hence it should
+not seem strange to the learned if some shall look upon us in the same way.
+Mathematics is written for mathematicians, to whom these labors of ours
+will seem, if I mistake not, to add something even to the republic of the
+Church.... _Emend._ Here strike out everything from 'if by chance' to the
+words 'these labors of ours,' and adapt it thus: 'But these labors of
+ours.'"
+
+[144] "_Copernicus._ However if we consider the matter more carefully it
+will be seen that the investigation is not yet completed, and therefore
+ought by no means to be condemned. _Emend._ However, if we consider the
+matter more carefully it is of no consequence whether we regard the earth
+as existing in the center of the universe or outside of the center, so far
+as the solution of the phenomena of celestial movements is concerned."
+
+[145] "The whole of this chapter may be cut out, since it avowedly treats
+of the earth's motion, while it refutes the reasons of the ancients proving
+its immobility. Nevertheless, since it seems to speak problematically, in
+order that it may satisfy the learned and keep intact the sequence and
+unity of the book let it be emended as below."
+
+[146] "_Copernicus._ Therefore why do we still hesitate to concede to it
+motion which is by nature consistent with its form, the more so because the
+whole universe is moving, whose end is not and cannot be known, and not
+confess that there is in the sky an appearance of daily revolution, while
+on the earth there is the truth of it? And in like manner these things are
+as if Virgil's AEneas should say, 'We are borne from the harbor' ...
+_Emend._ Hence I cannot concede motion to this form, the more so because
+the universe would fall, whose end is not and cannot be known, and what
+appears in the heavens is just as if ..."
+
+[147] "_Copernicus_. I also add that it would seem very absurd that motion
+should be ascribed to that which contains and locates, and not rather to
+that which is contained and located, that is the earth. _Emend._ I also add
+that it is not more difficult to ascribe motion to the contained and
+located, which is the earth, than to that which contains it."
+
+[148] "_Copernicus._ You see, therefore, that from all these things the
+motion of the earth is more probable than its immobility, especially in the
+daily revolution which is as it were a particular property of it. _Emend._
+Omit from 'You see' to the end of the chapter."
+
+[149] "_Copernicus._ Therefore, since there is nothing to hinder the motion
+of the earth, it seems to me that we should consider whether it has several
+motions, to the end that it may be looked upon as one of the moving stars.
+_Emend._ Therefore, since I have assumed that the earth moves, it seems to
+me that we should consider whether it has several motions."
+
+[150] "_Copernicus._ We are not ashamed to acknowledge ... that this is
+preferably verified in the motion of the earth. _Emend._ We are not ashamed
+to assume ... that this is consequently verified in the motion."
+
+[151] "_Copernicus._ So divine is surely this work of the Best and
+Greatest. _Emend._ Strike out these last words."
+
+[152] This should be Cap. 11, lib. i, p. 10.
+
+[153] "_Copernicus._ Demonstration of the threefold motion of the earth.
+_Emend._ On the hypothesis of the threefold motion of the earth and its
+demonstration."
+
+[154] This should be Cap. 20, lib. iv, p. 122.
+
+[155] "_Copernicus._ Concerning the size of these three stars, the sun, the
+moon and the earth. _Emend._ Strike out the words 'these three stars,'
+because the earth is not a star as Copernicus would make it."
+
+[156] He seems to speak problematically in order to satisfy the learned.
+
+[157] One of the Church Fathers, born about 250 A.D., and died about 330,
+probably at Treves. He wrote _Divinarum Institutionum Libri VII._ and other
+controversial and didactic works against the learning and philosophy of the
+Greeks.
+
+[158] Giovanni Battista Riccioli (1598-1671) taught philosophy and theology
+at Parma and Bologna, and was later professor of astronomy. His _Almagestum
+novum_ appeared in 1651, and his _Argomento fisico-matematico contro il
+moto diurno della terra_ in 1668.
+
+[159] He was a native of Arlington, Sussex, and a pensioner of Christ's
+College, Cambridge. In 1603 he became a master of arts at Oxford.
+
+[160] Straying, i.e., from the right way.
+
+[161] "Private subjects may, in the presence of danger, defend themselves
+or their families against a monarch as against any malefactor, if the
+monarch assaults them like a bandit or a ravisher, and provided they are
+unable to summon the usual protection and cannot in any way escape the
+danger."
+
+[162] Daniel Neal (1678-1743), an independent minister, wrote a _History of
+the Puritans_ that appeared in 1732. The account may be found in the New
+York edition of 1843-44, vol. I, p. 271.
+
+[163] Anthony Wood (1632-1695), whose _Historia et Antiquitates
+Universitatis Oxoniensis_ (1674) and _Athenae Oxoniensis_ (1691) are among
+the classics on Oxford.
+
+[164] Part of the title, not here quoted, shows the nature of the work more
+clearly: "liber unicus, in quo decretum S. Congregationis S. R. E.
+Cardinal. an. 1616, adversus Pythagorico-Copernicanos editum defenditur."
+
+[165] This was John Elliot Drinkwater Bethune (1801-1851), the statesman
+who did so much for legislative and educational reform in India. His
+father, John Drinkwater Bethune, wrote a history of the siege of Gibraltar.
+
+[166] The article referred to is about thirty years old; since it appeared
+another has been given (_Dubl. Rev._, Sept. 1865) which is of much greater
+depth. In it will also be found the Roman view of Bishop Virgil (_ante_, p.
+32).--A. De M.
+
+[167] Jean Baptiste Morin (1583-1656), in his younger days physician to the
+Bishop of Boulogne and the Duke of Luxemburg, became in 1630 professor of
+mathematics at the College Royale. His chief contribution to the problem of
+the determination of longitude is his _Longitudinum terrestrium et
+coelestium nova et hactenus optata scientia_ (1634). He also wrote against
+Copernicus in his _Famosi problematis de telluris motu vel quiete hactenus
+optata solutio_ (1631), and against Lansberg in his _Responsio pro telluris
+quiete_ (1634).
+
+[168] The work appeared at Leyden in 1626, at Amsterdam in 1634, at
+Copenhagen in 1640 and again at Leyden in 1650. The title of the 1640
+edition is _Arithmeticae Libri II et Geometriae Libri VI_. The work on
+which it is based is the _Arithmeticae et Geometriae Practica_, which
+appeared in 1611.
+
+[169] The father's name was Adriaan, and Lalande says that it was Montucla
+who first made the mistake of calling him Peter, thinking that the initials
+P. M. stood for Petrus Metius, when in reality they stood for _piae
+memoriae_! The ratio 355/113 was known in China hundreds of years before
+his time. See note 55, page 52.
+
+[170] Adrian Metius (1571-1635) was professor of medicine at the University
+of Franeker. His work was, however, in the domain of astronomy, and in this
+domain he published several treatises.
+
+[171] The first edition was entitled: _The Discovery of a World in the
+Moone. Or, a Discourse Tending to prove that 'tis probable there may be
+another habitable World in that Planet_. 1638, 8vo. The fourth edition
+appeared in 1684. John Wilkins (1614-1672) was Warden of Wadham College,
+Oxford; master of Trinity, Cambridge; and, later, Bishop of Chester. He was
+influential in founding the Royal Society.
+
+[172] The first edition was entitled: _C. Hugenii_ [Greek: Kosmotheoros],
+_sive de Terris coelestibus, earumque ornatu, conjecturae_, The Hague,
+1698, 4to. There were several editions. It was also translated into French
+(1718), and there was another English edition (1722). Huyghens (1629-1695)
+was one of the best mathematical physicists of his time.
+
+[173] It is hardly necessary to say that science has made enormous advance
+in the chemistry of the universe since these words were written.
+
+[174] William Whewell (1794-1866) is best known through his _History of the
+Inductive Sciences_ (1837) and _Philosophy of the Inductive Sciences_
+(1840).
+
+[175] Thomas Chalmers (1780-1847), the celebrated Scotch preacher. These
+discourses were delivered while he was minister in a large parish in the
+poorest part of Glasgow, and in them he attempted to bring science into
+harmony with the Bible. He was afterwards professor of moral philosophy at
+St. Andrew's (1823-28), and professor of theology at Edinburgh (1828). He
+became the leader of a schism from the Scotch Presbyterian Church,--the
+Free Church.
+
+[176] That is, in Robert Watt's (1774-1819) _Bibliotheca Britannica_
+(posthumous, 1824). Nor is it given in the _Dictionary of National
+Biography_.
+
+[177] The late Greek satirist and poet, c. 120-c. 200 A.D.
+
+[178] Francois Rabelais (c. 1490-1553) the humorist who created Pantagruel
+(1533) and Gargantua (1532). His work as a physician and as editor of the
+works of Galen and Hippocrates is less popularly known.
+
+[179] Francis Godwin (1562-1633) bishop of Llandaff and Hereford. Besides
+some valuable historical works he wrote _The Man in the Moone, or a
+Discourse of a voyage thither by Domingo Gonsales, the Speed Messenger of
+London_, 1638.
+
+[180] Bernard Le Bovier de Fontenelle (1657-1757), historian, critic,
+mathematician, Secretary of the Academie des Sciences, and member of the
+Academie Francaise. His _Entretien sur la pluralite des mondes_ appeared at
+Paris in 1686.
+
+[181] Athanasius Kircher (1602-1680), Jesuit, professor of mathematics and
+philosophy, and later of Hebrew and Syriac, at Wurzburg; still later
+professor of mathematics and Hebrew at Rome. He wrote several works on
+physics. His collection of mathematical instruments and other antiquities
+became the basis of the Kircherian Museum at Rome.
+
+[182] "Both belief and non-belief are dangerous. Hippolitus died because
+his stepmother was believed. Troy fell because Cassandra was not believed.
+Therefore the truth should be investigated long before foolish opinion can
+properly judge." (Prove = probe?).
+
+[183] Jacobus Grandamicus (Jacques Grandami) was born at Nantes in 1588 and
+died at Paris in 1672. He was professor of theology and philosophy in the
+Jesuit colleges at Rennes, Tours, Rouen, and other places. He wrote several
+works on astronomy.
+
+[184] "And I, if I be lifted up from the earth, will draw all men unto me."
+John xii. 32.
+
+[185] Andrea Argoli (1568-1657) wrote a number of works on astronomy, and
+computed ephemerides from 1621 to 1700.
+
+[186] So in the original edition of the _Budget_. It is Johannem Pellum in
+the original title. John Pell (1610 or 1611-1685) studied at Cambridge and
+Oxford, and was professor of mathematics at Amsterdam (1643-46) and Breda
+(1646-52). He left many manuscripts but published little. His name attaches
+by accident to an interesting equation recently studied with care by Dr.
+E. E. Whitford (New York, 1912).
+
+[187] Christianus Longomontanus (Christen Longberg or Lumborg) was born in
+1569 at Longberg, Jutland, and died in 1647 at Copenhagen. He was an
+assistant of Tycho Brahe and accepted the diurnal while denying the orbital
+motion of the earth. His _Cyclometria e lunulis reciproce demonstrata_
+appeared in 1612 under the name of Christen Severin, the latter being his
+family name. He wrote several other works on the quadrature problem, and
+some treatises on astronomy.
+
+[188] The names are really pretty well known. Giles Persone de Roberval was
+born at Roberval near Beauvais in 1602, and died at Paris in 1675. He was
+professor of philosophy at the College Gervais at Paris, and later at the
+College Royal. He claimed to have discovered the theory of indivisibles
+before Cavalieri, and his work is set forth in his _Traite des
+indivisibles_ which appeared posthumously in 1693.
+
+Hobbes (1588-1679), the political and social philosopher, lived a good part
+of his time (1610-41) in France where he was tutor to several young
+noblemen, including the Cavendishes. His _Leviathan_ (1651) is said to have
+influenced Spinoza, Leibnitz, and Rousseau. His _Quadratura circuli,
+cubatio sphaerae, duplicatio cubi ..._ (London, 1669), _Rosetum geometricum
+..._ (London, 1671), and _Lux Mathematica, censura doctrinae Wallisianae
+contra Rosetum Hobbesii_ (London, 1674) are entirely forgotten to-day. (See
+a further note, _infra_.)
+
+Pierre de Carcavi, a native of Lyons, died at Paris in 1684. He was a
+member of parliament, royal librarian, and member of the Academie des
+Sciences. His attempt to prove the impossibility of the quadrature appeared
+in 1645. He was a frequent correspondent of Descartes.
+
+Cavendish (1591-1654) was Sir (not Lord) Charles. He was, like De Morgan
+himself, a bibliophile in the domain of mathematics. His life was one of
+struggle, his term as member of parliament under Charles I being followed
+by gallant service in the royal army. After the war he sought refuge on the
+continent where he met most of the mathematicians of his day. He left a
+number of manuscripts on mathematics, which his widow promptly disposed of
+for waste paper. If De Morgan's manuscripts had been so treated we should
+not have had his revision of his _Budget of Paradoxes_.
+
+Marin Mersenne (1588-1648), a minorite, living in the cloisters at Nevers
+and Paris, was one of the greatest Franciscan scholars. He edited Euclid,
+Apollonius, Archimedes, Theodosius, and Menelaus (Paris, 1626), translated
+the Mechanics of Galileo into French (1634), wrote _Harmonicorum Libri XII_
+(1636), and _Cogitata physico-mathematica_ (1644), and taught theology and
+philosophy at Nevers.
+
+Johann Adolph Tasse (Tassius) was born in 1585 and died at Hamburg in 1654.
+He was professor of mathematics in the Gymnasium at Hamburg, and wrote
+numerous works on astronomy, chronology, statics, and elementary
+mathematics.
+
+Johann Ludwig, Baron von Wolzogen, seems to have been one of the early
+unitarians, called _Fratres Polonorum_ because they took refuge in Poland.
+Some of his works appear in the _Bibliotheca Fratrum Polonorum_ (Amsterdam,
+1656). I find no one by the name who was contributing to mathematics at
+this time.
+
+Descartes is too well known to need mention in this connection.
+
+Bonaventura Cavalieri (1598-1647) was a Jesuit, a pupil of Galileo, and
+professor of mathematics at Bologna. His greatest work, _Geometria
+indivisibilibus continuorum nova quadam ratione promota_, in which he makes
+a noteworthy step towards the calculus, appeared in 1635.
+
+Jacob (Jacques) Golius was born at the Hague in 1596 and died at Leyden in
+1667. His travels in Morocco and Asia Minor (1622-1629) gave him such
+knowledge of Arabic that he became professor of that language at Leyden.
+After Snell's death he became professor of mathematics there. He translated
+Arabic works on mathematics and astronomy into Latin.
+
+[189] It would be interesting to follow up these rumors, beginning perhaps
+with the tomb of Archimedes. The Ludolph van Ceulen story is very likely a
+myth. The one about Fagnano may be such. The Bernoulli tomb does have the
+spiral, however (such as it is), as any one may see in the cloisters at
+Basel to-day.
+
+[190] Collins (1625-1683) was secretary of the Royal Society, and was "a
+kind of register of all new improvements in mathematics." His office
+brought him into correspondence with all of the English scientists, and he
+was influential in the publication of various important works, including
+Branker's translation of the algebra by Rhonius, with notes by Pell, which
+was the first work to contain the present English-American symbol of
+division. He also helped in the publication of editions of Archimedes and
+Apollonius, of Kersey's Algebra, and of the works of Wallis. His profession
+was that of accountant and civil engineer, and he wrote three unimportant
+works on mathematics (one published posthumously, and the others in 1652
+and 1658).
+
+Heinrich Christian Schumacher (1780-1850) was professor of astronomy at
+Copenhagen and director of the observatory at Altona. His translation of
+Carnot's _Geometrie de position_ (1807) brought him into personal relations
+with Gauss, and the friendship was helpful to Schumacher. He was a member
+of many learned societies and had a large circle of acquaintances. He
+published numerous monographs and works on astronomy.
+
+Gassendi (1592-1655) might well have been included by De Morgan in the
+group, since he knew and was a friend of most of the important
+mathematicians of his day. Like Mersenne, he was a minorite, but he was a
+friend of Galileo and Kepler, and wrote a work under the title _Institutio
+astronomica, juxta hypotheses Copernici, Tychonis-Brahaei et Ptolemaei_
+(1645). He taught philosophy at Aix, and was later professor of mathematics
+at the College Royal at Paris.
+
+Burnet is the Bishop Gilbert Burnet (1643-1715) who was so strongly
+anti-Romanistic that he left England during the reign of James II and
+joined the ranks of the Prince of Orange. William made him bishop of
+Salisbury.
+
+[191] There is some substantial basis for De Morgan's doubts as to the
+connection of that _mirandula_ of his age, Sir Kenelm Digby (1603-1665),
+with the famous _poudre de sympathie_. It is true that he was just the one
+to prepare such a powder. A dilletante in everything,--learning, war,
+diplomacy, religion, letters, and science--he was the one to exploit a
+fraud of this nature. He was an astrologer, an alchemist, and a fabricator
+of tales, and well did Henry Stubbes characterize him as "the very Pliny of
+our age for lying." He first speaks of the powder in a lecture given at
+Montpellier in 1658, and in the same year he published the address at Paris
+under the title: _Discours fait en une celebre assemblee par le chevalier
+Digby .... touchant la guerison de playes par la poudre de sympathie_. The
+London edition referred to by De Morgan also came out in 1658, and several
+editions followed it in England, France and Germany. But Nathaniel Highmore
+in his _History of Generation_ (1651) referred to the concoction as
+"Talbot's Powder" some years before Digby took it up. The basis seems to
+have been vitriol, and it was claimed that it would heal a wound by simply
+being applied to a bandage taken from it.
+
+[192] This work by Thomas Birch (1705-1766) came out in 1756-57. Birch was
+a voluminous writer on English history. He was a friend of Dr. Johnson and
+of Walpole, and he wrote a life of Robert Boyle.
+
+[193] We know so much about John Evelyn (1620-1706) through the diary which
+he began at the age of eleven, that we forget his works on navigation and
+architecture.
+
+[194] I suppose this was the seventh Earl of Shrewsbury (1553-1616).
+
+[195] This is interesting in view of the modern aseptic practice of surgery
+and the antiseptic treatment of wounds inaugurated by the late Lord Lister.
+
+[196] Perhaps De Morgan had not heard the _bon mot_ of Dr. Holmes: "I
+firmly believe that if the whole _materia medica_ could be sunk to the
+bottom of the sea, it would be all the better for mankind and all the worse
+for the fishes."
+
+[197] The full title is worth giving, because it shows the mathematical
+interests of Hobbes, and the nature of the six dialogues: _Examinatio et
+emendatio mathematicae hodiernae qualis explicatur in libris Johannis
+Wallisii geometriae professoris Saviliani in Academia Oxoniensi: distributa
+in sex dialogos (1. De mathematicae origine ...; 2. De principiis traditis
+ab Euclide; 3. De demonstratione operationum arithmeticarum ...; 4. De
+rationibus; 5. De angula contactus, de sectionibus coni, et arithmetica
+infinitorum; 6. Dimensio circuli tribus methodis demonstrata ... item
+cycloidis verae descriptio et proprietates aliquot.)_ Londini, 1660 (not
+1666). For a full discussion of the controversy over the circle, see George
+Croom Robertson's biography of Hobbes in the eleventh edition of the
+_Encyclopaedia Britannica_.
+
+[198] This is his _Animadversions upon Mr. Hobbes' late book De principiis
+et ratiocinatione geometrarum_, 1666, or his _Hobbianae quadraturae
+circuli, cubationis sphaerae et duplicationis cubi confutatio_, also of
+1669.
+
+[199] This is the work of 1669 referred to above.
+
+[200] Gregoire de St. Vincent (1584-1667) published his _Opus geometricum
+quadraturae circuli et sectionum coni_ at Antwerp in 1647.
+
+[201] This appears in _J. Scaligeri cyclometrica elementa duo_, Lugduni
+Batav., 1594.
+
+[202] Adriaen van Roomen (1561-1615) gave the value of [pi] to sixteen
+decimal places in his _Ideae mathematicae pars prima_ (1593), and wrote his
+_In Archimedis circuli dimensionem expositio & analysis_ in 1597.
+
+[203] Kaestner. See note 30 on page 43.
+
+[204] Bentley (1662-1742) might have done it, for as the head of Trinity
+College, Cambridge, and a follower of Newton, he knew some mathematics.
+Erasmus (1466-1536) lived a little too early to attempt it, although his
+brilliant satire might have been used to good advantage against those who
+did try.
+
+[205] "In grammar, to give the winds to the ships and to give the ships to
+the winds mean the same thing. But in geometry it is one thing to assume
+the circle BCD not greater than thirty-six segments BCDF, and another (to
+assume) the thirty-six segments BCDF not greater than the circle. The one
+assumption is true, the other false."
+
+[206] The Greek scholar (1559-1614) who edited a Greek and Latin edition of
+Aristotle in 1590.
+
+[207] Jacques Auguste de Thou (1553-1617), the historian and statesman.
+
+[208] "To value Scaliger higher even when wrong, than the multitude when
+right."
+
+[209] "I would rather err with Scaliger than be right with Clavius."
+
+[210] "The perimeter of the dodecagon to be inscribed in a circle is
+greater than the perimeter of the circle. And the more sides a polygon to
+be inscribed in a circle successively has, so much the greater will the
+perimeter of the polygon be than the perimeter of the circle."
+
+[211] De Morgan took, perhaps, the more delight in speaking thus of Sir
+William Hamilton (1788-1856) because of a spirited controversy that they
+had in 1847 over the theory of logic. Possibly, too, Sir William's low
+opinion of mathematics had its influence.
+
+[212] Edwards (1699-1757) wrote _The canons of criticism_ (1747) in which
+he gave a scathing burlesque on Warburton's Shakespeare. It went through
+six editions.
+
+[213] Antoine Teissier (born in 1632) published his _Eloges des hommes
+savants, tires de l'histoire de M. de Thou_ in 1683.
+
+[214] "He boasted without reason of having found the quadrature of the
+circle. The glory of this admirable discovery was reserved for Joseph
+Scaliger, as Scevole de St. Marthe has written."
+
+[215] _Natural and political observations mentioned in the following Index,
+and made upon the Bills of Mortality.... With reference to the government,
+religion, trade, growth, ayre, and diseases of the said city._ London,
+1662, 4to. The book went through several editions.
+
+[216] _Ne sutor ultra crepidam_, "Let the cobbler stick to his last," as we
+now say.
+
+[217] The author (1632-1695) of the _Historia et Antiquitates Universitatis
+Oxoniensis_ (1674). See note 163, page 98.
+
+[218] The mathematical guild owes Samuel Pepys (1633-1703) for something
+besides his famous diary (1659-1669). Not only was he president of the
+Royal Society (1684), but he was interested in establishing Sir William
+Boreman's mathematical school at Greenwich.
+
+[219] John Graunt (1620-1674) was a draper by trade, and was a member of
+the Common Council of London until he lost office by turning Romanist.
+Although a shopkeeper, he was elected to the Royal Society on the special
+recommendation of Charles II. Petty edited the fifth edition of his work,
+adding much to its size and value, and this may be the basis of Burnet's
+account of the authorship.
+
+[220] Petty (1623-1687) was a mathematician and economist, and a friend of
+Pell and Sir Charles Cavendish. His survey of Ireland, made for Cromwell,
+was one of the first to be made on a large scale in a scientific manner. He
+was one of the founders of the Royal Society.
+
+[221] The story probably arose from Graunt's recent conversion to the Roman
+Catholic faith.
+
+[222] He was born in 1627 and died in 1704. He published a series of
+ephemerides, beginning in 1659. He was imprisoned in 1679, at the time of
+the "Popish Plot," and again for treason in 1690. His important
+astrological works are the _Animal Cornatum, or the Horn'd Beast_ (1654)
+and _The Nativity of the late King Charls_ (1659).
+
+[223] Isaac D'Israeli (1766-1848), in his _Curiosities of Literature_
+(1791), speaking of Lilly, says: "I shall observe of this egregious
+astronomer, that there is in this work, so much artless narrative, and at
+the same time so much palpable imposture, that it is difficult to know when
+he is speaking what he really believes to be the truth." He goes on to say
+that Lilly relates that "those adepts whose characters he has drawn were
+the lowest miscreants of the town. Most of them had taken the air in the
+pillory, and others had conjured themselves up to the gallows. This seems a
+true statement of facts."
+
+[224] It is difficult to estimate William Lilly (1602-1681) fairly. His
+_Merlini Anglici ephemeris_, issued annually from 1642 to 1681, brought him
+a great deal of money. Sir George Wharton (1617-1681) also published an
+almanac annually from 1641 to 1666. He tried to expose John Booker
+(1603-1677) by a work entitled _Mercurio-Coelicio-Mastix; or, an
+Anti-caveat to all such, as have (heretofore) had the misfortune to be
+Cheated and Deluded by that Grand and Traiterous Impostor of this
+Rebellious Age, John Booker_, 1644. Booker was "licenser of mathematical
+[astrological] publications," and as such he had quarrels with Lilly,
+Wharton, and others.
+
+[225] See note 171 on page 100.
+
+[226] This is the _Ars Signorum, vulgo character universalis et lingua
+philosophica_, that appeared at London in 1661, 8vo. George Dalgarno
+anticipated modern methods in the teaching of the deaf and dumb.
+
+[227] See note 200 on page 110.
+
+[228] If the hyperbola is referred to the asymptotes as axes, the area
+between two ordinates (x = a, x = b) is the difference of the logarithms of
+a and b to the base e. E.g., in the case of the hyperbola xy = 1, the area
+between x = a and x = 1 is log a.
+
+[229] "On ne peut lui refuser la justice de remarquer que personne avant
+lui ne s'est porte dans cette recherche avec autant de genie, & meme, si
+nous en exceptons son objet principal, avec autant de succes." _Quadrature
+du Cercle_, p. 66.
+
+[230] The title proceeds: _Seu duae mediae proportionales inter extremas
+datas per circulum et per infinitas hyperbolas, vel ellipses et per
+quamlibet exhibitae_.... Rene Francois, Baron de Sluse (1622-1685) was
+canon and chancellor of Liege, and a member of the Royal Society. He also
+published a work on tangents (1672). The word _mesolabium_ is from the
+Greek [Greek: mesolabion] or [Greek: mesolabon], an instrument invented by
+Eratosthenes for finding two mean proportionals.
+
+[231] The full title has some interest: _Vera circuli et hyperbolae
+quadratura cui accedit geometriae pars universalis inserviens quantitatum
+curvarum transmutationi et mensurae. Authore Jacobo Gregorio Abredonensi
+Scoto ... Patavii_, 1667. That is, James Gregory (1638-1675) of Aberdeen
+(he was really born near but not in the city), a good Scot, was publishing
+his work down in Padua. The reason was that he had been studying in Italy,
+and that this was a product of his youth. He had already (1663) published
+his _Optica promota_, and it is not remarkable that his brilliancy brought
+him a wide circle of friends on the continent and the offer of a pension
+from Louis XIV. He became professor of mathematics at St Andrews and later
+at Edinburgh, and invented the first successful reflecting telescope. The
+distinctive feature of his _Vera quadratura_ is his use of an infinite
+converging series, a plan that Archimedes used with the parabola.
+
+[232] Jean de Beaulieu wrote several works on mathematics, including _La
+lumiere de l'arithmetique_ (n.d.), _La lumiere des mathematiques_ (1673),
+_Nouvelle invention d'arithmetique_ (1677), and some mathematical tables.
+
+[233] A just estimate. There were several works published by Gerard
+Desargues (1593-1661), of which the greatest was the _Brouillon Proiect_
+(Paris, 1639). There is an excellent edition of the _Oeuvres de Desargues_
+by M. Poudra, Paris, 1864.
+
+[234] "A certain M. de Beaugrand, a mathematician, very badly treated by
+Descartes, and, as it appears, rightly so."
+
+[235] This is a very old approximation for [pi]. One of the latest
+pretended geometric proofs resulting in this value appeared in New York in
+1910, entitled _Quadrimetry_ (privately printed).
+
+[236] "Copernicus, a German, made himself no less illustrious by his
+learned writings; and we might say of him that he stood alone and unique in
+the strength of his problems, if his excessive presumption had not led him
+to set forth in this science a proposition so absurd that it is contrary to
+faith and reason, namely that the circumference of a circle is fixed and
+immovable while the center is movable: on which geometrical principle he
+has declared in his astrological treatise that the sun is fixed and the
+earth is in motion."
+
+[237] So in the original.
+
+[238] Franciscus Maurolycus (1494-1575) was really the best mathematician
+produced by Sicily for a long period. He made Latin translations of
+Theodosius, Menelaus, Euclid, Apollonius, and Archimedes, and wrote on
+cosmography and other mathematical subjects.
+
+[239] "Nicolaus Copernicus is also tolerated who asserted that the sun is
+fixed and that the earth whirls about it; and he rather deserves a whip or
+a lash than a reproof."
+
+[240] "Algebra is the curious science of scholars, and particularly for a
+general of an army, or a captain, in order quickly to draw up an army in
+battle array and to number the musketeers and pikemen who compose it,
+without the figures of arithmetic. This science has five special figures of
+this kind: P means _plus_ in commerce and _pikemen_ in the army; M means
+_minus_, and _musketeer_ in the art of war;... R signifies _root_ in the
+measurement of a cube, and _rank_ in _the army_; Q means _square_ (French
+_quare_, as then spelled) in both cases; C means _cube_ in mensuration, and
+_cavalry_ in arranging batallions and squadrons. As for the operations of
+this science, they are as follows: to add a _plus_ and a _plus_, the sum
+will be _plus_; to add _minus_ with _plus_, take the less from the greater
+and the remainder will be the sum required or the number to be found. I say
+this only in passing, for the benefit of those who are wholly ignorant of
+it."
+
+[241] He refers to the _Joannis de Beaugrand ... Geostatice, seu de vario
+pondere gravium secundum varia a terrae (centro) intervalla dissertatio
+mathematica_, Paris, 1636. Pascal relates that de Beaugrand sent all of
+Roberval's theorems on the cycloid and Fermat's on maxima and minima to
+Galileo in 1638, pretending that they were his own.
+
+[242] More (1614-1687) was a theologian, a fellow of Christ College,
+Cambridge, and a Christian Platonist.
+
+[243] Matthew Hale (1609-1676) the famous jurist, wrote a number of tracts
+on scientific, moral, and religious subjects. These were collected and
+published in 1805.
+
+[244] They might have been attributed to many a worse man than Dr. Hales
+(1677-1761), who was a member of the Royal Society and of the Paris
+Academy, and whose scheme for the ventilation of prisons reduced the
+mortality at the Savoy prison from one hundred to only four a year. The
+book to which reference is made is _Vegetable Staticks or an Account of
+some statical experiments on the sap in Vegetables_, 1727.
+
+[245] _Pleas of the Crown; or a Methodical Summary of the Principal Matters
+relating to the subject_, 1678.
+
+[246] _Thomae Streete Astronomia Carolina, a new theory of the celestial
+motions_, 1661. It also appeared at Nuremberg in 1705, and at London in
+1710 and 1716 (Halley's editions). He wrote other works on astronomy.
+
+[247] This was the Sir Thomas Street (1626-1696) who passed sentence of
+death on a Roman Catholic priest for saying mass. The priest was reprieved
+by the king, but in the light of the present day one would think the
+justice more in need of pardon. He took part in the trial of the Rye House
+Conspirators in 1683.
+
+[248] Edmund Halley (1656-1742), who succeeded Wallis (1703) as Savilian
+professor of mathematics at Oxford, and Flamsteed (1720) as head of the
+Greenwich observatory. It is of interest to note that he was instrumental
+in getting Newton's _Principia_ printed.
+
+[249] Shepherd (born in 1760) was one of the most famous lawyers of his
+day. He was knighted in 1814 and became Attorney General in 1817.
+
+[250] This was William Hone (1780-1842), a book publisher, who wrote
+satires against the government, and who was tried three times because of
+his parodies on the catechism, creed, and litany (illustrated by
+Cruikshank). He was acquitted on all of the charges.
+
+[251] Valentinus was a Benedictine monk and was still living at Erfurt in
+1413. His _Currus triumphalis antimonii_ appeared in 1624. Synesius was
+Bishop of Ptolemaide, who died about 430. His works were printed at Paris
+in 1605. Theodor Kirckring (1640-1693) was a fellow-student of Spinoza's.
+Besides the commentary on Valentine he left several works on anatomy. His
+commentary appeared at Amsterdam in 1671. There were several editions of
+the _Chariot_.
+
+[252] The chief difficulty with this curious "monk-bane" etymology is its
+absurdity. The real origin of the word has given etymologists a good deal
+of trouble.
+
+[253] Robert Boyle (1627-1691), son of "the Great Earl" (of Cork). Perhaps
+his best-known discovery is the law concerning the volume of gases.
+
+[254] The real name of Eirenaeus Philalethes (born in 1622) is unknown. It
+may have been Childe. He claimed to have discovered the philosopher's stone
+in 1645. His tract in this work is _The Secret of the Immortal Liquor
+Alkahest or Ignis-Aqua_. See note 260, _infra_.
+
+[255] Johann Baptist van Helmont, Herr von Merode, Royenborg etc.
+(1577-1644). His chemical discoveries appeared in his _Ortus medicinae_
+(1648), which went through many editions.
+
+[256] De Morgan should have written up Francis Anthony (1550-1623), whose
+_Panacea aurea sive tractatus duo de auro potabili_ (Hamburg, 1619)
+described a panacea that he gave for every ill. He was repeatedly
+imprisoned for practicing medicine without a license from the Royal College
+of Physicians.
+
+[257] Bernardus Trevisanus (1406-1490), who traveled even through Barbary,
+Egypt, Palestine, and Persia in search of the philosopher's stone. He wrote
+several works on alchemy,--_De Chemica_ (1567), _De Chemico Miraculo_
+(1583), _Traite de la nature de l'oeuf des philosophes_ (1659), etc., all
+published long after his death.
+
+[258] George Ripley (1415-1490) was an Augustinian monk, later a
+chamberlain of Innocent VIII, and still later a Carmelite monk. His _Liber
+de mercuris philosophico_ and other tracts first appeared in _Opuscula
+quaedam chymica_ (Frankfort, 1614).
+
+[259] Besides the _Opus majus_, and other of the better known works of this
+celebrated Franciscan (1214-1294), there are numerous tracts on alchemy
+that appeared in the _Thesaurus chymicus_ (Frankfort, 1603).
+
+[260] George Starkey (1606-1665 or 1666) has special interest for American
+readers. He seems to have been born in the Bermudas and to have obtained
+the bachelor's degree in England. He then went to America and in 1646
+obtained the master's degree at Harvard, apparently under the name of
+Stirk. He met Eirenaeus Philalethes (see note 254 above) in America and
+learned alchemy from him. Returning to England, he sold quack medicines
+there, and died in 1666 from the plague after dissecting a patient who had
+died of the disease. Among his works was the _Liquor Alcahest, or a
+Discourse of that Immortal Dissolvent of Paracelsus and Helmont_, which
+appeared (1675) some nine years after his death.
+
+[261] Platt (1552-1611) was the son of a London brewer. Although he left a
+manuscript on alchemy, and wrote a book entitled _Delights for Ladies to
+adorne their Persons_ (1607), he was knighted for some serious work on the
+chemistry of agriculture, fertilizing, brewing, and the preserving of
+foods, published in _The Jewell House of Art and Nature_ (1594).
+
+[262] "Those who wish to call a man a liar and deceiver speak of him a
+writer of almanacs; but those who (would call him) a scoundrel and an
+imposter (speak of him as) a chemist."
+
+[263] "Trust your barque to the winds but not your body to a chemist; any
+breeze is safer than the faith of a chemist."
+
+[264] Probably the Jesuit, Pere Claude Francois Menestrier (1631-1705), a
+well known historian.
+
+[265] The author was Christopher Nesse (1621-1705), a belligerent
+Calvinist, who wrote many controversial works and succeeded in getting
+excommunicated four times. One of his most virulent works was _A Protestant
+Antidote against the Poison of Popery_.
+
+[266] John Case (c. 1660-1700) was a famous astrologer and physician. He
+succeeded to Lilly's practice in London. In a darkened room, wherein he
+kept an array of mystical apparatus, he pretended to show the credulous the
+ghosts of their departed relatives. Besides his astrological works he wrote
+one serious treatise, the _Compendium Anatomicum nova methodo institutum_
+(1695), in which he defends Harvey's theories of embryology.
+
+[267] Marcelis (1636-after 1714) was a soap maker of Amsterdam. It is to be
+hoped that he made better soap than values of [pi].
+
+[268] John Craig (died in 1731) was a Scotchman, but most of his life was
+spent at Cambridge reading and writing on mathematics. He endeavored to
+introduce the Leibnitz differential calculus into England. His mathematical
+works include the _Methodus Figurarum ... Quadraturas determinandi_ (1685),
+_Tractatus ... de Figurarum Curvilinearum Quadraturis et locis Geometricis_
+(1693), and _De Calculo Fluentium libri duo_ (1718).
+
+[269] As is well known, this subject owes much to the Bernoullis. Craig's
+works on the calculus brought him into controversy with them. He also wrote
+on other subjects in which they were interested, as in his memoir _On the
+Curve of the quickest descent_ (1700), _On the Solid of least resistance_
+(1700), and the _Solution of Bernoulli's problem on Curves_ (1704).
+
+[270] This is Samuel Lee (1783-1852), the young prodigy in languages. He
+was apprenticed to a carpenter at twelve and learned Greek while working at
+the trade. Before he was twenty-five he knew Hebrew, Chaldee, Syriac,
+Samaritan, Persian, and Hindustani. He later became Regius professor of
+Hebrew at Cambridge.
+
+[271] "Where the devil, Master Ludovico, did you pick up such a
+collection?"
+
+[272] Lord William Brounker (c. 1620-1684), the first president of the
+Royal Society, is best known in mathematics for his contributions to
+continued fractions.
+
+[273] Horace Walpole (1717-1797) published his _Catalogue of the Royal and
+Noble Authors of England_ in 1758. Since his time a number of worthy names
+in the domain of science in general and of mathematics in particular might
+be added from the peerage of England.
+
+[274] It was written by Charles Hayes (1678-1760), a mathematician and
+scholar of no mean attainments. He travelled extensively, and was deputy
+governor of the Royal African Company. His _Treatise on Fluxions_ (London,
+1704) was the first work in English to explain Newton's calculus. He wrote
+a work entitled _The Moon_ (1723) to prove that our satellite shines by its
+own as well as by reflected light. His _Chronographia Asiatica & Aegyptica_
+(1758) gives the results of his travels.
+
+[275] _Publick_ in the original.
+
+[276] Whiston (1667-1752) succeeded Newton as Lucasian professor of
+mathematics at Cambridge. In 1710 he turned Arian and was expelled from the
+university. His work on _Primitive Christianity_ appeared the following
+year. He wrote many works on astronomy and religion.
+
+[277] Ditton (1675-1715) was, on Newton's recommendation, made Head of the
+mathematical school at Christ's Hospital, London. He wrote a work on
+fluxions (1706). His idea for finding longitude at sea was to place
+stations in the Atlantic to fire off bombs at regular intervals, the time
+between the sound and the flash giving the distance. He also corresponded
+with Huyghens concerning the use of chronometers for the purpose.
+
+[278] This was John Arbuthnot (c. 1658-1735), the mathematician, physician
+and wit. He was intimate with Pope and Swift, and was Royal physician to
+Queen Anne. Besides various satires he published a translation of
+Huyghens's work on probabilities (1692) and a well-known treatise on
+ancient coins, weights, and measures (1727).
+
+[279] Greene (1678-1730) was a very eccentric individual and was generally
+ridiculed by his contemporaries. In his will he directed that his body be
+dissected and his skeleton hung in the library of King's College,
+Cambridge. Unfortunately for his fame, this wish was never carried out.
+
+[280] This was the historian, Robert Sanderson (1660-1741), who spent most
+of his life at Cambridge.
+
+[281] I presume this was William Jones (1675-1749) the friend of Newton and
+Halley, vice-president of the Royal Society, in whose _Synopsis Palmariorum
+Matheseos_ (1706) the symbol [pi] is first used for the circle ratio.
+
+[282] This was the _Geometrica solidorum, sive materiae, seu de varia
+compositione, progressione, rationeque velocitatum_, Cambridge, 1712. The
+work was parodied in _A Taste of Philosophical Fanaticism ... by a
+gentleman of the University of Gratz_.
+
+[283] The antiquary and scientist (1690-1754), president of the Royal
+Society, member of the Academie, friend of Newton, and authority on
+numismatics.
+
+[284] She was Catherine Barton, Newton's step-niece. She married John
+Conduitt, master of the mint, who collected materials for a life of Newton.
+
+_A propos_ of Mrs. Conduitt's life of her illustrious uncle, Sir George
+Greenhill tells a very good story on Poincare, the well-known French
+mathematician. At an address given by the latter at the International
+Congress of Mathematicians held in Rome in 1908 he spoke of the story of
+Newton and the apple as a mere fable. After the address Sir George asked
+him why he had done so, saying that the story was first published by
+Voltaire, who had heard it from Newton's niece, Mrs. Conduitt. Poincare
+looked blank and said, "Newton, et la niece de Newton, et Voltaire,--non!
+je ne vous comprends pas!" He had thought Sir George meant Professor
+Volterra of Rome, whose name in French is Voltaire, and who could not
+possibly have known a niece of Newton without bridging a century or so.
+
+[285] This was the Edmund Turnor (1755-1829) who wrote the _Collections for
+the Town and Soke of Grantham, containing authentic Memoirs of Sir Isaac
+Newton, from Lord Portsmouth's Manuscripts_, London, 1806.
+
+[286] It may be recalled to mind that Sir David (1781-1868) wrote a life of
+Newton (1855).
+
+[287] "They are in the country. We rejoice."
+
+[288] "I am here, chatterbox, suck!"
+
+[289] "I have been graduated! I decline!"
+
+[290] Giovanni Castiglioni (Castillon, Castiglione), was born at
+Castiglione, in Tuscany, in 1708, and died at Berlin in 1791. He was
+professor of mathematics at Utrecht and at Berlin. He wrote on De Moivre's
+equations (1762), Cardan's rule (1783), and Euclid's treatment of parallels
+(1788-89).
+
+[291] This was the _Isaaci Newtoni, equitis aurati, opuscula mathematica,
+philosophica et philologica_, Lausannae & Genevae, 1744.
+
+[292] At London, 4to.
+
+[293] "All the English attribute it to Newton."
+
+[294] Stephen Peter Rigaud (1774-1839), Savilian professor of geometry at
+Oxford (1810-27) and later professor of astronomy and head of the Radcliffe
+Observatory. He wrote _An historical Essay on first publication of Sir
+Isaac Newton's Principia_, Oxford, 1838, and a two-volume work entitled
+_Correspondence of Scientific Men of the 17th Century_, 1841.
+
+[295] It is no longer considered by scholars as the work of Newton.
+
+[296] J. Edleston, the author of the _Correspondence of Sir Isaac Newton
+and Professor Cotes_, London, 1850.
+
+[297] Palmer (1601-1647) was Master of Queen's College, Cambridge, a
+Puritan but not a separatist. His work, _The Characters of a believing
+Christian, in Paradoxes and seeming contradictions_, appeared in 1645.
+
+[298] Grosart (1827-1899) was a Presbyterian clergyman. He was a great
+bibliophile, and issued numerous reprints of rare books.
+
+[299] This was the year after Palmer's death. The title was, _The Remaines
+of ... Francis Lord Verulam....; being Essays and severall Letters to
+severall great personages, and other pieces of various and high concernment
+not heretofore published_, London, 1648, 4to.
+
+[300] Shaw (1694-1763) was physician extraordinary to George II. He wrote
+on chemistry and medicine, and his edition of the _Philosophical Works of
+Francis Bacon_ appeared at London in 1733.
+
+[301] John Locke (1632-1704), the philosopher. This particular work
+appeared in 1695. There was an edition in 1834 (vol. 25 of the _Sacred
+Classics_) and one in 1836 (vol. 2 of the _Christian Library_).
+
+[302] I use the word _Socinian_ because it was so much used in Locke's
+time: it is used in our own day by the small fry, the unlearned clergy and
+their immediate followers, as a term of reproach for _all_ Unitarians. I
+suspect they have a kind of liking for the _word_; it sounds like _so
+sinful_. The learned clergy and the higher laity know better: they know
+that the bulk of the modern Unitarians go farther than Socinus, and are not
+correctly named as his followers. The Unitarians themselves neither desire
+nor deserve a name which puts them one point nearer to orthodoxy than they
+put themselves. That point is the doctrine that direct prayer to Jesus
+Christ is lawful and desirable: this Socinus held, and the modern
+Unitarians do not hold. Socinus, in treating the subject in his own
+_Institutio_, an imperfect catechism which he left, lays much more stress
+on John xiv. 13 than on xv. 16 and xvi. 23. He is not disinclined to think
+that _Patrem_ should be in the first citation, where some put it; but he
+says that to ask the Father in the name of the Son is nothing but praying
+to the Son in prayer to the Father. He labors the point with obvious wish
+to secure a conclusive sanction. In the Racovian Catechism, of which
+Faustus Socinus probably drew the first sketch, a clearer light is arrived
+at. The translation says: "But wherein consists the divine honor due to
+Christ? In adoration likewise and invocation. For we ought at all times to
+adore Christ, and may in our necessities address our prayers to him as
+often as we please; and there are many reasons to induce us to do this
+freely." There are some who like accuracy, even in aspersion--A. De M.
+
+Socinus, or Fausto Paolo Sozzini (1539-1604), was an antitrinitarian who
+believed in prayer and homage to Christ. Leaving Italy after his views
+became known, he repaired to Basel, but his opinions were too extreme even
+for the Calvinists. He then tried Transylvania, attempting to convert to
+his views the antitrinitarian Bishop David. The only result of his efforts
+was the imprisonment of David and his own flight to Poland, in which
+country he spent the rest of his life (1579-1604). His complete works
+appeared first at Amsterdam in 1668, in the _Bibliotheca Fratres
+Polonorum_. The _Racovian Catechism_ (1605) appeared after his death, but
+it seems to have been planned by him.
+
+[303] "As much of faith as is necessary to salvation is contained in this
+article, Jesus is the Christ."
+
+[304] Edwards (1637-1716) was a Cambridge fellow, strongly Calvinistic. He
+published many theological works, attacking the Arminians and Socinians.
+Locke and Whiston were special objects of attack.
+
+[305] _Sir I. Newton's views on points of Trinitarian Doctrine; his
+Articles of Faith, and the General Coincidence of his Opinions with those
+of J. Locke; a Selection of Authorities, with Observations_, London, 1856.
+
+[306] _A Confession of the Faith_, Bristol, 1752, 8vo.
+
+[307] This was really very strange, because Laud (1573-1644), while he was
+Archbishop of Canterbury, forced a good deal of High Church ritual on the
+Puritan clergy, and even wished to compel the use of a prayer book in
+Scotland. It was this intolerance that led to his impeachment and
+execution.
+
+[308] The name is Jonchere. He was a man of some merit, proposing (1718) an
+important canal in Burgundy, and publishing a work on the _Decouverte des
+longitudes estimees generalement impossible a trouver_, 1734 (or 1735).
+
+[309] Locke invented a kind of an instrument for finding longitude, and it
+is described in the appendix, but I can find nothing about the man. There
+was published some years later (London, 1751) another work of his, _A new
+Problem to discover the longitude at sea_.
+
+[310] Baxter, concerning whom I know merely that he was a schoolmaster,
+starts with the assumption of this value, and deduces from it some fourteen
+properties relating to the circle.
+
+[311] John, who died in 1780, was a well-known character in his way. He was
+a bookseller on Fleet Street, and his shop was a general rendezvous for the
+literary men of his time. He wrote the _Memoirs of the Life and Writings of
+Mr. William Whiston_ (1749, with another edition in 1753). He was one of
+the first to issue regular catalogues of books with prices affixed.
+
+[312] The name appears both as Hulls and as Hull. He was born in
+Gloucestershire in 1699. In 1754 he published _The Art of Measuring made
+Easy by the help of a new Sliding Scale_.
+
+[313] Thomas Newcomen (1663-1729) invented the first practical steam engine
+about 1710. It was of about five and a half horse power, and was used for
+pumping water from coal mines. Savery had described such an engine in 1702,
+but Newcomen improved upon it and made it practical.
+
+[314] The well-known benefactor of art (1787-1863).
+
+[315] The tract was again reprinted in 1860.
+
+[316] Hulls made his experiment on the Avon, at Evesham, in 1737, having
+patented his machine in 1736. He had a Newcomen engine connected with six
+paddles. This was placed in the front of a small tow boat. The experiment
+was a failure.
+
+[317] William Symington (1763-1831). In 1786 he constructed a working model
+of a steam road carriage. The machinery was applied to a small boat in
+1788, and with such success as to be tried on a larger boat in 1789. The
+machinery was clumsy, however, and in 1801 he took out a new patent for the
+style of engine still used on paddle wheel steamers. This engine was
+successfully used in 1802, on the Charlotte Dundas. Fulton (1765-1815) was
+on board, and so impressed Robert Livingston with the idea that the latter
+furnished the money to build the Clermont (1807), the beginning of
+successful river navigation.
+
+[318] Louis Bertrand Castel (1688-1757), most of whose life was spent in
+trying to perfect his _Clavecin oculaire_, an instrument on the order of
+the harpsichord, intended to produce melodies and harmonies of color. He
+also wrote _L'Optique des couleurs_ (1740) and _Sur le fond de la Musique_
+(1754).
+
+[319] Dr. Robinson (1680-1754) was professor of physic at Trinity College,
+Dublin, and three times president of King and Queen's College of
+Physicians. In his _Treatise on the Animal Economy_ (1732-3, with a third
+edition in 1738) he anticipated the discoveries of Lavoisier and Priestley
+on the nature of oxygen.
+
+[320] There was another edition, published at London in 1747, 8vo.
+
+[321] The author seems to have shot his only bolt in this work. I can find
+nothing about him.
+
+[322] _Quod Deus sit, mundusque ab ipso creatus fuerit in tempore, ejusque
+providentia gubernetur. Selecta aliquot theoremata adversos atheos_, etc.,
+Paris, 1635, 4to.
+
+[323] The British Museum Catalogue mentions a copy of 1740, but this is
+possibly a misprint.
+
+[324] This was Johann II (1710-1790), son of Johann I, who succeeded his
+father as professor of mathematics at Basel.
+
+[325] Samuel Koenig (1712-1757), who studied under Johann Bernoulli I. He
+became professor of mathematics at Franeker (1747) and professor of
+philosophy at the Hague (1749).
+
+[326] "In accordance with the hypotheses laid down in this memoir it is so
+evident that t must = 34, y = 1, and z = 1, that there is no need of proof
+or authority for it to be recognized by every one."
+
+[327] "I subscribe to the judgment of Mr. Bernoulli as a result of these
+hypotheses."
+
+[328] "It clearly appears from my present analysis and demonstration that
+they have already recognized and perfectly agreed to the fact that the
+quadrature of the circle is mathematically demonstrated."
+
+[329] Dr. Knight (died in 1772) made some worthy contributions to the
+literature of the mariner's compass. As De Morgan states, he was librarian
+of the British Museum.
+
+[330] Sir Anthony Panizzi (1797-1879) fled from Italy under sentence of
+death (1822). He became assistant (1831) and chief (1856) librarian of the
+British Museum, and was knighted in 1869. He began the catalogue of printed
+books of the Museum.
+
+[331] Wright (1711-1786) was a physicist. He was offered the professorship
+of mathematics at the Imperial Academy of St. Petersburg but declined to
+accept it. This work is devoted chiefly to the theory of the Milky Way, the
+_via lactea_ as he calls it after the manner of the older writers.
+
+[332] Troughton (1753-1835) was one of the world's greatest instrument
+makers. He was apprenticed to his brother John, and the two succeeded
+(1770) Wright and Cole in Fleet Street. Airy called his method of
+graduating circles the greatest improvement ever made in instrument making.
+He constructed (1800) the first modern transit circle, and his instruments
+were used in many of the chief observatories of the world.
+
+[333] William Simms (1793-1860) was taken into partnership by Troughton
+(1826) after the death of the latter's brother. The firm manufactured some
+well-known instruments.
+
+[334] This was George Horne (1730-1792), fellow of Magdalen College,
+Oxford, vice-Chancellor of the University (1776), Dean of Canterbury
+(1781), and Bishop of Norwich (1790). He was a great satirist, but most of
+his pamphlets against men like Adam Smith, Swedenborg, and Hume, were
+anonymous, as in the case of this one against Newton. He was so liberal in
+his attitude towards the Methodists that he would not have John Wesley
+forbidden to preach in his diocese. He was twenty-one when this tract
+appeared.
+
+[335] Martin (1704-1782) was by no means "old Benjamin Martin" when Horne
+wrote this pamphlet in 1749. In fact he was then only forty-five. He was a
+physicist and a well-known writer on scientific instruments. He also wrote
+_Philosophia Britannica or a new and comprehensive system of the Newtonian
+Philosophy_ (1759).
+
+[336] Jean Theophile Desaguliers, or Des Aguliers (1683-1744) was the son
+of a Protestant who left France after the revocation of the Edict of
+Nantes. He became professor of physics at Oxford, and afterwards gave
+lectures in London. Later he became chaplain to the Prince of Wales. He
+published several works on physics.
+
+[337] Charles Hutton (1737-1823), professor of mathematics at Woolwich
+(1772-1807). His _Mathematical Tables_ (1785) and _Mathematical and
+Philosophical Dictionary_ (1795-1796) are well known.
+
+[338] James Epps (1773-1839) contributed a number of memoirs on the use and
+corrections of instruments. He was assistant secretary of the Astronomical
+Society.
+
+[339] John Hutchinson (1674-1737) was one of the first to try to reconcile
+the new science of geology with Genesis. He denied the Newtonian hypothesis
+as dangerous to religion, and because it necessitated a vacuum. He was a
+mystic in his interpretation of the Scriptures, and created a sect that
+went under the name of Hutchinsonians.
+
+[340] John Rowning, a Lincolnshire rector, died in 1771. He wrote on
+physics, and published a memoir on _A machine for finding the roots of
+equations universally_ (1770).
+
+[341] It is always difficult to sanction this spelling of the name of this
+Jesuit father who is so often mentioned in the analytic treatment of
+conics. He was born in Ragusa in 1711, and the original spelling was
+Ru[=d]er Josip Bo[vs]kovi['c]. When he went to live in Italy, as professor
+of mathematics at Rome (1740) and at Pavia, the name was spelled Ruggiero
+Giuseppe Boscovich, although Boscovicci would seem to a foreigner more
+natural. His astronomical work was notable, and in his _De maculis
+solaribus_ (1736) there is the first determination of the equator of a
+planet by observing the motion of spots on its surface. Boscovich came near
+having some contact with America, for he was delegated to observe in
+California the transit of Venus in 1755, being prevented by the dissolution
+of his order just at that time. He died in 1787, at Milan.
+
+[342] James Granger (1723-1776) who wrote the _Biographical History of
+England_, London, 1769. His collection of prints was remarkable, numbering
+some fourteen thousand.
+
+[343] He was curator of experiments for the Royal Society. He wrote a large
+number of books and monographs on physics. He died about 1713.
+
+[344] Lee seems to have made no impression on biographers.
+
+[345] This work appeared at London in 1852.
+
+[346] Of course this is no longer true. The most scholarly work to-day is
+that of Rudio, _Archimedes, Huygens, Lambert, Legendre, vier Abhandlungen
+ueber die Kreismessung ... mit einer Uebersicht ueber die Geschichte des
+Problems von der Quadratur des Zirkels, von den aeltesten Zeiten bis auf
+unsere Tage_, Leipsic, 1892.
+
+[347] Joseph Jerome le Francois de Lalande (1732-1807), professor of
+astronomy in the College de France (1753) and director of the Paris
+Observatory (1761). His writings on astronomy and his _Bibliographie
+astronomique, avec l'histoire de l'astronomie depuis 1781 jusqu'en 1802_
+(Paris, 1803) are well known.
+
+[348] De Morgan refers to his _Histoire de l'Astronomie au 18e siecle_,
+which appeared in 1827, five years after Delambre's death. Jean Baptiste
+Joseph Delambre (1749-1822) was a pupil of and a collaborator with Lalande,
+following his master as professor of astronomy in the College de France.
+His work on the measurements for the metric system is well known, and his
+four histories of astronomy, _ancienne_ (1817), _au moyen age_ (1819),
+_moderne_ (1821), and _au 18e siecle_ (posthumous, 1827) are highly
+esteemed.
+
+[349] Jean-Joseph Rive (1730-1792), a priest who left his cure under grave
+charges, and a quarrelsome character. His attack on Montucla was a case of
+the pot calling the kettle black; for while he was a brilliant writer he
+was a careless bibliographer.
+
+[350] Isaac Barrow (1630-1677) was quite as well known as a theologian as
+he was from his Lucasian professorship of mathematics at Cambridge.
+
+[351] "Besides we can see by this that Barrow was a poor philosopher; for
+he believed in the immortality of the soul and in a Divinity other than
+universal nature."
+
+[352] The _Recreations mathematiques et physiques_ (Paris, 1694) of Jacques
+Ozanam (1640-1717) is a work that is still highly esteemed. Among various
+other works he wrote a _Dictionnaire mathematique ou Idee generale des
+mathematiques_ (1690) that was not without merit. The _Recreations_ went
+through numerous editions (Paris, 1694, 1696, 1741, 1750, 1770, 1778, and
+the Montucla edition of 1790; London, 1708, the Montucla-Hutton edition of
+1803 and the Riddle edition of 1840; Dublin, 1790).
+
+[353] Hendryk van Etten, the _nom de plume_ of Jean Leurechon (1591-1670),
+rector of the Jesuit college at Bar, and professor of philosophy and
+mathematics. He wrote on astronomy (1619) and horology (1616), and is known
+for his _Selecta Propositiones in tota sparsim mathematica pulcherrime
+propositae in solemni festo SS. Ignatii et Francesci Xaverii_, 1622. The
+book to which De Morgan refers is his _Recreation mathematicque, composee
+de plusieurs problemes plaisants et facetieux_, Lyons, 1627, with an
+edition at Pont-a-Mousson, 1629. There were English editions published at
+London in 1633, 1653, and 1674, and Dutch editions in 1662 and 1672.
+
+I do not understand how De Morgan happened to miss owning the work by
+Claude Gaspar Bachet de Meziriac (1581-1638), _Problemes plaisans et
+delectables_, which appeared at Lyons in 1612, 8vo, with a second edition
+in 1624. There was a fifth edition published at Paris in 1884.
+
+[354] His title page closes with "Paris, Chez Ch. Ant. Jombert.... M DCC
+LIV."
+
+This was Charles-Antoine Jombert (1712-1784), a printer and bookseller with
+some taste for painting and architecture. He wrote several works and edited
+a number of early treatises.
+
+[355] The late Professor Newcomb made the matter plain even to the
+non-mathematical mind, when he said that "ten decimal places are sufficient
+to give the circumference of the earth to the fraction of an inch, and
+thirty decimal places would give the circumference of the whole visible
+universe to a quantity imperceptible with the most powerful microscope."
+
+[356] _Antinewtonianismi pars prima, in qua Newtoni de coloribus systema ex
+propriis principiis geometrice evertitur, et nova de coloribus theoria
+luculentissimis experimentis demonstrantur_.... Naples, 1754; _pars
+secunda_, Naples, 1756.
+
+[357] Celestino Cominale (1722-1785) was professor of medicine at the
+University of Naples.
+
+[358] The work appeared in the years from 1844 to 1849.
+
+[359] There was a Vienna edition in 1758, 4to, and another in 1759, 4to.
+This edition is described on the title page as _Editio Veneta prima ipso
+auctore praesente, et corrigente_.
+
+[360] The first edition was entitled _De solis ac lunae defectibus libri
+V. P. Rogerii Josephi Boscovich ... cum ejusdem auctoris adnotationibus_,
+London, 1760. It also appeared in Venice in 1761, and in French translation
+by the Abbe de Baruel in 1779, and was a work of considerable influence.
+
+[361] Paulian (1722-1802) was professor of physics at the Jesuit college at
+Avignon. He wrote several works, the most popular of which, the
+_Dictionnaire de physique_ (Avignon, 1761), went through nine editions by
+1789.
+
+[362] This is correct.
+
+[363] Probably referring to the fact that Hill (1795-1879), who had done so
+much for postal reform, was secretary to the postmaster general (1846), and
+his name was a synonym for the post office directory.
+
+[364] Richard Lovett (1692-1780) was a good deal of a charlatan. He claimed
+to have studied electrical phenomena, and in 1758 advertised that he could
+effect marvelous cures, especially of sore throat, by means of electricity.
+Before publishing the works mentioned by De Morgan he had issued others of
+similar character, including _The Subtile Medium proved_ (London, 1756) and
+_The Reviewers Reviewed_ (London, 1760).
+
+[365] Jean Sylvain Bailly (1736-1793), member of the _Academie francaise_
+and of the _Academie des sciences_, first deputy elected to represent Paris
+in the _Etats-generaux_ (1789), president of the first National Assembly,
+and mayor of Paris (1789-1791). For his vigor as mayor in keeping the
+peace, and for his manly defence of the Queen, he was guillotined. He was
+an astronomer of ability, but is best known for his histories of the
+science.
+
+[366] These were the _Histoire de l'Astronomie ancienne_ (1775), _Histoire
+de l'Astronomie moderne_ (1778-1783), _Histoire de l'Astronomie indienne et
+orientale_ (1787), and _Lettres sur l'origine des peuples de l'Asie_
+(1775).
+
+[367] "The sick old man of Ferney, V., a boy of a hundred years." Voltaire
+was born in 1694, and hence was eighty-three at this time.
+
+[368] In Palmezeaux's _Vie de Bailly_, in Bailly's _Ouvrage Posthume_
+(1810), M. de Sales is quoted as saying that the _Lettres sur l'Atlantide_
+were sent to Voltaire and that the latter did not approve of the theory set
+forth.
+
+[369] The British Museum catalogue gives two editions, 1781 and 1782.
+
+[370] A mystic and a spiritualist. His chief work was the one mentioned
+here.
+
+[371] Jacob Behmen, or Boehme (1575-1624), known as "the German
+theosophist," was founder of the sect of Boehmists, a cult allied to the
+Swedenborgians. He was given to the study of alchemy, and brought the
+vocabulary of the science into his mystic writings. His sect was revived in
+England in the eighteenth century through the efforts of William Law.
+Saint-Martin translated into French two of his Latin works under the titles
+_L'Aurore naissante, ou la Racine de la philosophie_ (1800), and _Les trois
+principes de l'essence divine_ (1802). The originals had appeared nearly
+two hundred years earlier,--_Aurora_ in 1612, and _De tribus principiis_ in
+1619.
+
+[372] "Unknown."
+
+[373] "Skeptical."
+
+[374] "Man, man, man."
+
+[375] "Men, men, men."
+
+[376] It is interesting to read De Morgan's argument against Saint-Martin's
+authorship of this work. It is attributed to Saint-Martin both by the
+_Biographie Universelle_ and by the _British Museum Catalogue_, and De
+Morgan says by "various catalogues and biographies."
+
+[377] "To explain things by man and not man by things. _On Errors and
+Truth_, by a Ph.... Inc...."
+
+[378] "If we would preserve ourselves from all illusions, and above all
+from the allurements of pride, by which man is so often seduced, we should
+never take man, but always God, for our term of comparison."
+
+[379] "And here is found already an explanation of the numbers four and
+nine which caused some perplexity in the work cited above. Man is lost in
+passing from four to nine."
+
+[380] Williams also took part in the preparation of some tables for the
+government to assist in the determination of longitude. He had published a
+work two years before the one here cited, on the same subject,--_An entire
+new work and method to discover the variation of the Earth's Diameters_,
+London, 1786.
+
+[381] This is Gabriel Mouton (1618-1694), a vicar at Lyons, who suggested
+as a basis for a natural system of measures the _mille_, a minute of a
+degree of the meridian. This appeared in his _Observationes diametrorum
+solis et lunae apparentium, meridianarumque aliquot altitudinum cum tabula
+declinationum solis_.... Lyons, 1670.
+
+[382] Jacques Cassini (1677-1756), one of the celebrated Cassini family of
+astronomers. After the death of his father he became director of the
+observatory at Paris. The basis for a metric unit was set forth by him in
+his _Traite de la grandeur et de la figure de la terre_, Paris, 1720. He
+was a prolific writer on astronomy.
+
+[383] Alexis Jean Pierre Paucton (1732-1798). He was, for a time, professor
+of mathematics at Strassburg, but later (1796) held office in Paris. His
+leading contribution to metrology was his _Metrologie ou Traite des
+mesures_, Paris, 1780.
+
+[384] He was an obscure writer, born at Deptford.
+
+[385] He was also a writer of no scientific merit, his chief contributions
+being religious tracts. One of his productions, however, went through many
+editions, even being translated into French; _Three dialogues between a
+Minister and one of his Parishioners; on the true principles of Religion
+and salvation for sinners by Jesus Christ_. The twentieth edition appeared
+at Cambridge in 1786.
+
+[386] This was the _Reflections on the Revolution in France, and on the
+proceedings in certain societies in London relative to that event_ (London,
+1790) by Edmund Burke (1729-1797). Eleven editions of the work appeared the
+first year.
+
+[387] Paine (1736-1809) was born in Norfolkshire, of Quaker parents. He
+went to America at the beginning of the Revolution and published, in
+January 1776, a violent pamphlet entitled _Common Sense_. He was a private
+soldier under Washington, and on his return to England after the war he
+published _The Rights of Man_. He was indicted for treason and was outlawed
+to France. He was elected to represent Calais at the French convention, but
+his plea for moderation led him perilously near the guillotine. His _Age of
+Reason_ (1794) was dedicated to Washington. He returned to America in 1802
+and remained there until his death.
+
+[388] Part I appeared in 1791 and was so popular that eight editions
+appeared in that year. It was followed in 1792 by Part II, of which nine
+editions appeared in that year. Both parts were immediately republished in
+Paris, and there have been several subsequent editions.
+
+[389] Mary Wollstonecraft (1759-1797) was only thirty-three when this work
+came out. She had already published _An historical and moral View of the
+Origin and Progress of the French Revolution_ (1790), and _Original Stories
+from Real Life_ (1791). She went to Paris in 1792 and remained during the
+Reign of Terror.
+
+[390] Samuel Parr (1747-1827) was for a time head assistant at Harrow
+(1767-1771), afterwards headmaster in other schools. At the time this book
+was written he was vicar of Hatton, where he took private pupils
+(1785-1798) to the strictly limited number of seven. He was a violent Whig
+and a caustic writer.
+
+[391] On Mary Wollstonecraft's return from France she married (1797)
+William Godwin (1756-1836). He had started as a strong Calvinistic
+Nonconformist minister, but had become what would now be called an
+anarchist, at least by conservatives. He had written an _Inquiry concerning
+Political Justice_ (1793) and a novel entitled _Caleb Williams, or Things
+as they are_ (1794), both of which were of a nature to attract his future
+wife.
+
+[392] This child was a daughter. She became Shelley's wife, and Godwin's
+influence on Shelley was very marked.
+
+[393] This was John Nichols (1745-1826), the publisher and antiquary. He
+edited the _Gentleman's Magazine_ (1792-1826) and his works include the
+_Literary Anecdotes of the Eighteenth Century_ (1812-1815), to which De
+Morgan here refers.
+
+[394] William Bellenden, a Scotch professor at the University of Paris, who
+died about 1633. His textbooks are now forgotten, but Parr edited an
+edition of his works in 1787. The Latin preface, _Praefatio ad Bellendum de
+Statu_, was addressed to Burke, North, and Fox, and was a satire on their
+political opponents.
+
+[395] As we have seen, he had been head-master before he began taking "his
+handful of private pupils."
+
+[396] The story has evidently got mixed up in the telling, for Tom Sheridan
+(1721-1788), the great actor, was old enough to have been Dr. Parr's
+father. It was his son, Richard Brinsley Sheridan (1751-1816), the
+dramatist and politician, who was the pupil of Parr. He wrote _The Rivals_
+(1775) and _The School for Scandal_ (1777) soon after Parr left Harrow.
+
+[397] Horner (1785-1864) was a geologist and social reformer. He was very
+influential in improving the conditions of child labor.
+
+[398] William Cobbett (1762-1835), the journalist, was a character not
+without interest to Americans. Born in Surrey, he went to America at the
+age of thirty and remained there eight years. Most of this time he was
+occupied as a bookseller in Philadelphia, and while thus engaged he was
+fined for libel against the celebrated Dr. Rush. On his return to England
+he edited the _Weekly Political Register_ (1802-1835), a popular journal
+among the working classes. He was fined and imprisoned for two years
+because of his attack (1810) on military flogging, and was also (1831)
+prosecuted for sedition. He further showed his paradox nature by his
+_History of the Protestant Reformation_ (1824-1827), an attack on the
+prevailing Protestant opinion. He also wrote a _Life of Andrew Jackson_
+(1834). After repeated attempts he succeeded in entering parliament, a
+result of the Reform Bill.
+
+[399] Robinson (1735-1790) was a Baptist minister who wrote several
+theological works and a number of hymns. His work at Cambridge so offended
+the students that they at one time broke up the services.
+
+[400] This work had passed through twelve editions by 1823.
+
+[401] Dyer (1755-1841), the poet and reformer, edited Robinson's
+_Ecclesiastical Researches_ (1790). He was a life-long friend of Charles
+Lamb, and in their boyhood they were schoolmates at Christ's Hospital. His
+_Complaints of the Poor People of England_ (1793) made him a worthy
+companion of the paradoxers above mentioned.
+
+[402] These were John Thelwall (1764-1834) whose _Politics for the People
+or Hogswash_ (1794) took its title from the fact that Burke called the
+people the "swinish multitude." The book resulted in sending the author to
+the Tower for sedition. In 1798 he gave up politics and started a school of
+elocution which became very famous. Thomas Hardy (1752-1832), who kept a
+bootmaker's shop in Piccadilly, was a fellow prisoner with Thelwall, being
+arrested for high treason. He was founder (1792) of The London
+Corresponding Society, a kind of clearing house for radical associations
+throughout the country. Horne Tooke was really John Horne (1736-1812), he
+having taken the name of his friend William Tooke in 1782. He was a radical
+of the radicals, and organized a number of reform societies. Among these
+was the Constitutional Society that voted money (1775) to assist the
+American revolutionists, appointing him to give the contribution to
+Franklin. For this he was imprisoned for a year. With his fellow rebels in
+the Tower in 1794, however, he was acquitted. As a philologist he is known
+for his early advocacy of the study of Anglo-Saxon and Gothic, and his
+_Diversions of Purley_ (1786) is still known to readers.
+
+[403] This was the admiral, Adam Viscount Duncan (1731-1804), who defeated
+the Dutch off Camperdown in 1797.
+
+[404] He was created Duke of Clarence and St. Andrews in 1789 and was
+Admiral of the Fleet escorting Louis XVIII on his return to France in 1814.
+He became Lord High Admiral in 1827, and reigned as William IV from 1830 to
+1837.
+
+[405] This was Charles Abbott (1762-1832) first Lord Tenterden. He
+succeeded Lord Ellenborough as Chief Justice (1818) and was raised to the
+peerage in 1827. He was a strong Tory and opposed the Catholic Relief Bill,
+the Reform Bill, and the abolition of the death penalty for forgery.
+
+[406] Edward Law (1750-1818), first Baron Ellenborough. He was chief
+counsel for Warren Hastings, and his famous speech in defense of his client
+is well known. He became Chief Justice and was raised to the peerage in
+1802. He opposed all efforts to modernize the criminal code, insisting upon
+the reactionary principle of new death penalties.
+
+[407] Edmund Law (1703-1787), Bishop of Carlisle (1768), was a good deal
+more liberal than his son. His _Considerations on the Propriety of
+requiring subscription to the Articles of Faith_ (1774) was published
+anonymously. In it he asserts that not even the clergy should be required
+to subscribe to the thirty-nine articles.
+
+[408] Joe Miller (1684-1738), the famous Drury Lane comedian, was so
+illiterate that he could not have written the _Joe Miller's Jests, or the
+Wit's Vade-Mecum_ that appeared the year after his death. It was often
+reprinted and probably contained more or less of Miller's own jokes.
+
+[409] The sixth duke (1766-1839) was much interested in parliamentary
+reform. He was a member of the Society of Friends of the People. He was for
+fourteen years a member of parliament (1788-1802) and was later Lord
+Lieutenant of Ireland (1806-1807). He afterwards gave up politics and
+became interested in agricultural matters.
+
+[410] George Jeffreys (c. 1648-1689), the favorite of James II, who was
+active in prosecuting the Rye House conspirators. He was raised to the
+peerage in 1684 and held the famous "bloody assize" in the following year,
+being made Lord Chancellor as a result. He was imprisoned in the Tower by
+William III and died there.
+
+[411] _The Every Day Book, forming a Complete History of the Year, Months,
+and Seasons, and a perpetual Key to the Almanack_, 1826-1827.
+
+[412] The first and second editions appeared in 1820. Two others followed
+in 1821.
+
+[413] _The three trials of W. H., for publishing three parodies; viz the
+late John Wilkes' Catechism, the Political Litany, and the Sinecurists
+Creed; on three ex-officio informations, at Guildhall, London, ... Dec. 18,
+19, & 20, 1817_,... London, 1818.
+
+[414] The _Political Litany_ appeared in 1817.
+
+[415] That is, Castlereagh's.
+
+[416] The well-known caricaturist (1792-1878), then only twenty-nine years
+old.
+
+[417] Robert Stewart (1769-1822) was second Marquis of Londonderry and
+Viscount Castlereagh. As Chief Secretary for Ireland he was largely
+instrumental in bringing about the union of Ireland and Great Britain. He
+was at the head of the war department during most of the Napoleonic wars,
+and was to a great extent responsible for the European coalition against
+the Emperor. He suicided in 1822.
+
+[418] John Murray (1778-1843), the well-known London publisher. He refused
+to finish the publication of Don Juan, after the first five cantos, because
+of his Tory principles.
+
+[419] Only the first two cantos appeared in 1819.
+
+[420] Proclus (412-485), one of the greatest of the neo-Platonists, studied
+at Alexandria and taught philosophy at Athens. He left commentaries on
+Plato and on part of Euclid's _Elements_.
+
+[421] Thomas Taylor (1758-1835), called "the Platonist," had a liking for
+mathematics, and was probably led by his interest in number mysticism to a
+study of neo-Platonism. He translated a number of works from the Latin and
+Greek, and wrote two works on theoretical arithmetic (1816, 1823).
+
+[422] There was an earlier edition, 1788-89.
+
+[423] Georgius Gemistus, or Georgius Pletho (Plethon), lived in the
+fourteenth and fifteenth centuries. He was a native of Constantinople, but
+spent most of his time in Greece. He devoted much time to the propagation
+of the Platonic philosophy, but also wrote on divinity, geography, and
+history.
+
+[424] Hannah More (1745-1833), was, in her younger days, a friend of Burke,
+Reynolds, Dr. Johnson, and Garrick. At this time she wrote a number of
+poems and aspired to become a dramatist. Her _Percy_ (1777), with a
+prologue and epilogue by Garrick, had a long run at Covent Garden. Somewhat
+later she came to believe that the playhouse was a grave public evil, and
+refused to attend the revival of her own play with Mrs. Siddons in the
+leading part. After 1789 she and her sisters devoted themselves to starting
+schools for poor children, teaching them religion and housework, but
+leaving them illiterate.
+
+[425] These were issued at the rate of three each month,--a story, a
+ballad, and a Sunday tract. They were collected and published in one volume
+in 1795. It is said that two million copies were sold the first year. There
+were also editions in 1798, 1819, 1827, and 1836-37.
+
+[426] That is, Dr. Johnson (1709-1784). The _Rambler_ was published in
+1750-1752, and was an imitation of Addison's _Spectator_.
+
+[427] Dr. Moore, referred to below.
+
+[428] Dr. John Moore (1729-1802), physician and novelist, is now best known
+for his _Journal during a Residence in France from the beginning of August
+to the middle of December, 1792_, a work quoted frequently by Carlyle in
+his _French Revolution_.
+
+[429] Sir John Moore (1761-1809), Lieutenant General in the Napoleonic
+wars. He was killed in the battle of Corunna. The poem by Charles Wolfe
+(1791-1823), _The Burial of Sir John Moore_ (1817), is well known.
+
+[430] Referring to the novels of Thomas Love Peacock (1785-1866), who
+succeeded James Mill as chief examiner of the East India Company, and was
+in turn succeeded by John Stuart Mill.
+
+[431] Frances Burney, Madame d'Arblay (1752-1840), married General
+d'Arblay, a French officer and companion of Lafayette, in 1793. She was
+only twenty-five when she acquired fame by her _Evelina, or a Young Lady's
+Entrance into the World_. Her _Letters and Diaries_ appeared posthumously
+(1842-45).
+
+[432] Henry Peter, Baron Brougham and Vaux (1778-1868), well known in
+politics, science, and letters. He was one of the founders of the
+_Edinburgh Review_, became Lord Chancellor in 1830, and took part with men
+like William Frend, De Morgan's father-in-law, in the establishing of
+London University. He was also one of the founders of the Society for the
+Diffusion of Useful Knowledge. He was always friendly to De Morgan, who
+entered the faculty of London University, whose work on geometry was
+published by the Society mentioned, and who was offered the degree of
+doctor of laws by the University of Edinburgh while Lord Brougham was Lord
+Rector. The Edinburgh honor was refused by De Morgan who said he "did not
+feel like an LL.D."
+
+[433] Maria Edgeworth (1767-1849).
+
+[434] Sydney Owenson (c. 1783-1859) married Sir Thomas Morgan, a well-known
+surgeon, in 1812. Her Irish stories were very popular with the patriots but
+were attacked by the _Quarterly Review_. _The Wild Irish Girl_ (1806) went
+through seven editions in two years.
+
+[435] 1775-1817.
+
+[436] 1771-1832.
+
+[437] The famous preacher (1732-1808). He was the first chairman of the
+Religious Tract Society. He is also known as one of the earliest advocates
+of vaccination, in his _Cow-pock Inoculation vindicated and recommended
+from matters of fact_, 1806.
+
+[438] Sir Rowland Hill (1795-1879), the father of penny postage.
+
+[439] Beilby Porteus (1731-1808), Bishop of Chester (1776) and Bishop of
+London (1787). He encouraged the Sunday-school movement and the
+dissemination of Hannah More's tracts. He was an active opponent of
+slavery, but also of Catholic emancipation.
+
+[440] Henrietta Maria Bowdler (1754-1830), generally known as Mrs. Harriet
+Bowdler. She was the author of many religious tracts and poems. Her _Poems
+and Essays_ (1786) were often reprinted. The story goes that on the
+appearance of her _Sermons on the Doctrines and duties of Christianity_
+(published anonymously), Bishop Porteus offered the author a living under
+the impression that it was written by a man.
+
+[441] William Frend (1757-1841), whose daughter Sophia Elizabeth became De
+Morgan's wife (1837), was at one time a clergyman of the Established
+Church, but was converted to Unitarianism (1787). He came under De Morgan's
+definition of a true paradoxer, carrying on a zealous warfare for what he
+thought right. As a result of his _Address to the Inhabitants of Cambridge_
+(1787), and his efforts to have abrogated the requirement that candidates
+for the M.A. must subscribe to the thirty-nine articles, he was deprived of
+his tutorship in 1788. A little later he was banished (see De Morgan's
+statement in the text) from Cambridge because of his denunciation of the
+abuses of the Church and his condemnation of the liturgy. His eccentricity
+is seen in his declining to use negative quantities in the operations of
+algebra. He finally became an actuary at London and was prominent in
+radical associations. He was a mathematician of ability, having been second
+wrangler and having nearly attained the first place, and he was also an
+excellent scholar in Latin, Greek, and Hebrew.
+
+[442] George Peacock (1791-1858), Fellow of Trinity College, Cambridge,
+Lowndean professor of astronomy, and Dean of Ely Cathedral (1839). His tomb
+may be seen at Ely where he spent the latter part of his life. He was one
+of the group that introduced the modern continental notation of the
+calculus into England, replacing the cumbersome notation of Newton, passing
+from "the _dot_age of fluxions to the _de_ism of the calculus."
+
+[443] Robert Simson (1687-1768); professor of mathematics at Glasgow. His
+restoration of Apollonius (1749) and his translation and restoration of
+Euclid (1756, and 1776--posthumous) are well known.
+
+[444] Francis Maseres (1731-1824), a prominent lawyer. His mathematical
+works had some merit.
+
+[445] These appeared annually from 1804 to 1822.
+
+[446] Henry Gunning (1768-1854) was senior esquire bedell of Cambridge. The
+_Reminiscences_ appeared in two volumes in 1854.
+
+[447] John Singleton Copley, Baron Lyndhurst (1772-1863), the son of John
+Singleton Copley the portrait painter, was born in Boston. He was educated
+at Trinity College, Cambridge, and became a lawyer. He was made Lord
+Chancellor in 1827.
+
+[448] Sir William Rough (c. 1772-1838), a lawyer and poet, became Chief
+Justice of Ceylon in 1836. He was knighted in 1837.
+
+[449] Herbert Marsh, afterwards Bishop of Peterborough, a relation of my
+father.--S. E. De M.
+
+He was born in 1757 and died in 1839. On the trial of Frend he publicly
+protested against testifying against a personal confidant, and was excused.
+He was one of the first of the English clergy to study modern higher
+criticism of the Bible, and amid much opposition he wrote numerous works on
+the subject. He was professor of theology at Cambridge (1707), Bishop of
+Llandaff (1816), and Bishop of Peterborough.
+
+[450] George Butler (1774-1853), Headmaster of Harrow (1805-1829),
+Chancellor of Peterborough (1836), and Dean of Peterborough (1842).
+
+[451] James Tate (1771-1843), Headmaster of Richmond School (1796-1833) and
+Canon of St. Paul's Cathedral (1833). He left several works on the
+classics.
+
+[452] Francis Place (1771-1854), at first a journeyman breeches maker, and
+later a master tailor. He was a hundred years ahead of his time as a strike
+leader, but was not so successful as an agitator as he was as a tailor,
+since his shop in Charing Cross made him wealthy. He was a well-known
+radical, and it was largely due to his efforts that the law against the
+combinations of workmen was repealed in 1824. His chief work was _The
+Principles of Population_ (1822).
+
+[453] Speed (1552-1629) was a tailor until Grevil (Greville) made him
+independent of his trade. He was not only an historian of some merit, but a
+skilful cartographer. His maps of the counties were collected in the
+_Theatre of the Empire of Great Britaine_, 1611. About this same time he
+also published _Genealogies recorded in Sacred Scripture_, a work that had
+passed through thirty-two editions by 1640.
+
+[454] _The history of Great Britaine under the conquests of ye Romans,
+Saxons, Danes, and Normans...._ London, 1611, folio. The second edition
+appeared in 1623; the third, to which De Morgan here refers, posthumously
+in 1632; and the fourth in 1650.
+
+[455] William Nicolson (1655-1727) became Bishop of Carlisle in 1702, and
+Bishop of Derry in 1718. His chief work was the _Historical Library_
+(1696-1724), in the form of a collection of documents and chronicles. It
+was reprinted in 1736 and in 1776.
+
+[456] Sir Fulk Grevil, or Fulke Greville (1554-1628), was a favorite of
+Queen Elizabeth, Chancellor of the Exchequer under James I, a patron of
+literature, and a friend of Sir Philip Sidney.
+
+[457] See note 443 on page 197.
+
+[458] See note 444 on page 197.
+
+[459] See note 439 on page 193.
+
+[460] Edward Waring (1736-1796) was Lucasian professor of mathematics at
+Cambridge. He published several works on analysis and curves. The work
+referred to was the _Miscellanea Analytica de aequationibus algebraicis et
+curvarum proprietatibus_, Cambridge, 1762.
+
+[461] _A Dissertation on the use of the Negative Sign in Algebra...; to
+which is added, Machin's Quadrature of the Circle_, London, 1758.
+
+[462] The paper was probably one on complex numbers, or possibly one on
+quaternions, in which direction as well as absolute value is involved.
+
+[463] De Morgan quotes from one of the Latin editions. Descartes wrote in
+French, the title of his first edition being: _Discours de la methode pour
+bien conduire sa raison et chercher la verite dans les sciences, plus la
+dioptrique, les meteores et la geometrie qui sont des essais de cette
+methode_, Leyden, 1637, 4to.
+
+[464] "I have observed that algebra indeed, as it is usually taught, is so
+restricted by definite rules and formulas of calculation, that it seems
+rather a confused kind of an art, by the practice of which the mind is in a
+certain manner disturbed and obscured, than a science by which it is
+cultivated and made acute."
+
+[465] It appeared in 93 volumes, from 1758 to 1851.
+
+[466] _The principles of the doctrine of life-annuities; explained in a
+familiar manner ... with a variety of new tables_ ..., London, 1783.
+
+[467] I suppose the one who wrote _Conjectures on the physical causes of
+Earthquakes and Volcanoes_, Dublin, 1820.
+
+[468] _Scriptores Logarithmici; or, a Collection of several curious_
+_tracts on the nature and construction of Logarithms ... together with same
+tracts on the Binomial Theorem_ ..., 6 vols., London, 1791-1807.
+
+[469] Charles Babbage (1792-1871), whose work on the calculating machine is
+well known. Maseres was, it is true, ninety-two at this time, but Babbage
+was thirty-one instead of twenty-nine. He had already translated Lacroix's
+_Treatise on the differential and integral calculus_ (1816), in
+collaboration with Herschel and Peacock. He was Lucasian professor of
+mathematics at Cambridge from 1828 to 1839.
+
+[470] _The great and new Art of weighing Vanity, or a discovery of the
+ignorance of the great and new artist in his pseudo-philosophical
+writings._ The "great and new artist" was Sinclair.
+
+[471] George Sinclair, probably a native of East Lothian, who died in 1696.
+He was professor of philosophy and mathematics at Glasgow, and was one of
+the first to use the barometer in measuring altitudes. The work to which De
+Morgan refers is his _Hydrostaticks_ (1672). He was a firm believer in evil
+spirits, his work on the subject going through four editions: _Satan's
+Invisible World Discovered; or, a choice collection of modern relations,
+proving evidently against the Saducees and Athiests of this present age,
+that there are Devils, Spirits, Witches, and Apparitions_, Edinburgh, 1685.
+
+[472] This was probably William Sanders, Regent of St. Leonard's College,
+whose _Theses philosophicae_ appeared in 1674, and whose _Elementa
+geometriae_ came out a dozen years later.
+
+[473] _Ars nova et magna gravitatis et levitatis; sive dialogorum
+philosophicorum libri sex de aeris vera ac reali gravitate_, Rotterdam,
+1669, 4to.
+
+[474] Volume I, Nos. 1 and 2, appeared in 1803.
+
+[475] His daughter, Mrs. De Morgan, says in her _Memoir_ of her husband:
+"My father had been second wrangler in a year in which the two highest were
+close together, and was, as his son-in-law afterwards described him, an
+exceedingly clear thinker. It is possible, as Mr. De Morgan said, that this
+mental clearness and directness may have caused his mathematical heresy,
+the rejection of the use of negative quantities in algebraical operations;
+and it is probable that he thus deprived himself of an instrument of work,
+the use of which might have led him to greater eminence in the higher
+branches." _Memoir of Augustus De Morgan_, London, 1882, p. 19.
+
+[476] "If it is not true it is a good invention." A well-known Italian
+proverb.
+
+[477] See page 86, note 132.
+
+[478] He was born at Paris in 1713, and died there in 1765.
+
+[479] _Recherches sur les courbes a double courbure_, Paris, 1731. Clairaut
+was then only eighteen, and was in the same year made a member of the
+Academie des sciences. His _Elemens de geometrie_ appeared in 1741.
+Meantime he had taken part in the measurement of a degree in Lapland
+(1736-1737). His _Traite de la figure de la terre_ was published in 1741.
+The Academy of St. Petersburg awarded him a prize for his _Theorie de la
+lune_ (1750). His various works on comets are well known, particularly his
+_Theorie du mouvement des cometes_ (1760) in which he applied the "problem
+of three bodies" to Halley's comet as retarded by Jupiter and Saturn.
+
+[480] Joseph Privat, Abbe de Molieres (1677-1742), was a priest of the
+Congregation of the Oratorium. In 1723 he became a professor in the College
+de France. He was well known as an astronomer and a mathematician, and
+wrote in defense of Descartes's theory of vortices (1728, 1729). He also
+contributed to the methods of finding prime numbers (1705).
+
+[481] "Deserves not only to be printed, but to be admired as a marvel of
+imagination, of understanding, and of ability."
+
+[482] Blaise Pascal (1623-1662), the well-known French philosopher and
+mathematician. He lived for some time with the Port Royalists, and defended
+them against the Jesuits in his _Provincial Letters_. Among his works are
+the following: _Essai pour les coniques_ (1640); _Recit de la grande
+experience de l'equilibre des liqueurs_ (1648), describing his experiment
+in finding altitudes by barometric readings; _Histoire de la roulette_
+(1658); _Traite du triangle arithmetique_ (1665); _Aleae geometria_ (1654).
+
+[483] This proposition shows that if a hexagon is inscribed in a conic (in
+particular a circle) and the opposite sides are produced to meet, the three
+points determined by their intersections will be in the same straight line.
+
+[484] Jacques Curabelle, _Examen des Oeuvres du Sr. Desargues_, Paris,
+1644. He also published without date a work entitled: _Foiblesse pitoyable
+du Sr. G. Desargues employee contre l'examen fait de ses oeuvres_.
+
+[485] See page 119, note 233.
+
+[486] Until "this great proposition called Pascal's should see the light."
+
+[487] The story is that his father, Etienne Pascal, did not wish him to
+study geometry until he was thoroughly grounded in Latin and Greek. Having
+heard the nature of the subject, however, he began at the age of twelve to
+construct figures by himself, drawing them on the floor with a piece of
+charcoal. When his father discovered what he was doing he was attempting to
+demonstrate that the sum of the angles of a triangle equals two right
+angles. The story is given by his sister, Mme. Perier.
+
+[488] Sir John Wilson (1741-1793) was knighted in 1786 and became
+Commissioner of the Great Seal in 1792. He was a lawyer and jurist of
+recognized merit. He stated his theorem without proof, the first
+demonstration having been given by Lagrange in the Memoirs of the Berlin
+Academy for 1771,--_Demonstration d'un theoreme nouveau concernant les
+nombres premiers_. Euler also gave a proof in his _Miscellanea Analytica_
+(1773). Fermat's works should be consulted in connection with the early
+history of this theorem.
+
+[489] He wrote, in 1760, a tract in defense of Waring, a point of whose
+algebra had been assailed by a Dr. Powell. Waring wrote another tract of
+the same date.--A. De M.
+
+William Samuel Powell (1717-1775) was at this time a fellow of St. John's
+College, Cambridge. In 1765 he became Vice Chancellor of the University.
+Waring was a Magdalene man, and while candidate for the Lucasian
+professorship he circulated privately his _Miscellanea Analytica_. Powell
+attacked this in his _Observations on the First Chapter of a Book called
+Miscellanea_ (1760). This attack was probably in the interest of another
+candidate, a man of his own college (St. John's), William Ludlam.
+
+[490] William Paley (1743-1805) was afterwards a tutor at Christ's College,
+Cambridge. He never contributed anything to mathematics, but his _Evidences
+of Christianity_ (1794) was long considered somewhat of a classic. He also
+wrote _Principles of Morality and Politics_ (1785), and _Natural Theology_
+(1802).
+
+[491] Edward, first Baron Thurlow (1731-1806) is known to Americans because
+of his strong support of the Royal prerogative during the Revolution. He
+was a favorite of George III, and became Lord Chancellor in 1778.
+
+[492] George Wilson Meadley (1774-1818) published his _Memoirs of ...
+Paley_ in 1809. He also published _Memoirs of Algernon Sidney_ in 1813. He
+was a merchant and banker, and had traveled extensively in Europe and the
+East. He was a convert to unitarianism, to which sect Paley had a strong
+leaning.
+
+[493] Watson (1737-1816) was a strange kind of man for a bishopric. He was
+professor of chemistry at Cambridge (1764) at the age of twenty-seven. It
+was his experiments that led to the invention of the black-bulb
+thermometer. He is said to have saved the government L100,000 a year by his
+advice on the manufacture of gunpowder. Even after he became professor of
+divinity at Cambridge (1771) he published four volumes of _Chemical Essays_
+(vol. I, 1781). He became Bishop of Llandaff in 1782.
+
+[494] James Adair (died in 1798) was counsel for the defense in the trial
+of the publishers of the _Letters of Junius_ (1771). As King's Serjeant he
+assisted in prosecuting Hardy and Horne Tooke.
+
+[495] Morgan (1750-1833) was actuary of the Equitable Assurance Society of
+London (1774-1830), and it was to his great abilities that the success of
+that company was due at a time when other corporations of similar kind were
+meeting with disaster. The Royal Society awarded him a medal (1783) for a
+paper on _Probability of Survivorship_. He wrote several important works on
+insurance and finance.
+
+[496] Dr. Price (1723-1791) was a non-conformist minister and a writer on
+ethics, economics, politics, and insurance. He was a defender of the
+American Revolution and a personal friend of Franklin. In 1778 Congress
+invited him to America to assist in the financial administration of the new
+republic, but he declined. His famous sermon on the French Revolution is
+said to have inspired Burke's _Reflections on the Revolution in France_.
+
+[497] Elizabeth Gurney (1780-1845), a Quaker, who married Joseph Fry
+(1800), a London merchant. She was the prime mover in the Association for
+the Improvement of the Female Prisoners in Newgate, founded in 1817. Her
+influence in prison reform extended throughout Europe, and she visited the
+prisons of many countries in her efforts to improve the conditions of penal
+servitude. The friendship of Mrs. Fry with the De Morgans began in 1837.
+Her scheme for a female benefit society proved worthless from the actuarial
+standpoint, and would have been disastrous to all concerned if it had been
+carried out, and it was therefore fortunate that De Morgan was consulted in
+time. Mrs. De Morgan speaks of the consultation in these words: "My
+husband, who was very sensitive on such points, was charmed with Mrs. Fry's
+voice and manner as much as by the simple self-forgetfulness with which she
+entered into this business; her own very uncomfortable share of it not
+being felt as an element in the question, as long as she could be useful in
+promoting good or preventing mischief. I can see her now as she came into
+our room, took off her little round Quaker cap, and laying it down, went at
+once into the matter. 'I have followed thy advice, and I think nothing
+further can be done in this case; but all harm is prevented.' In the
+following year I had an opportunity of seeing the effect of her most
+musical tones. I visited her at Stratford, taking my little baby and nurse
+with me, to consult her on some articles on prison discipline, which I had
+written for a periodical. The baby--three months old--was restless, and the
+nurse could not quiet her, neither could I entirely, until Mrs. Fry began
+to read something connected with the subject of my visit, when the infant,
+fixing her large eyes on the reader, lay listening till she fell asleep."
+_Memoirs_, p. 91.
+
+[498] Mrs. Fry certainly believed that the writer was the old actuary of
+the Equitable, when she first consulted him upon the benevolent Assurance
+project; but we were introduced to her by our old and dear friend Lady Noel
+Byron, by whom she had been long known and venerated, and who referred her
+to Mr. De Morgan for advice. An unusual degree of confidence in, and
+appreciation of each other, arose on their first meeting between the two,
+who had so much that was externally different, and so much that was
+essentially alike, in their natures.--S. E. De M.
+
+Anne Isabella Milbanke (1792-1860) married Lord Byron in 1815, when both
+took the additional name of Noel, her mother's name. They were separated in
+1816.
+
+[499] An obscure writer not mentioned in the ordinary biographies.
+
+[500] Not mentioned in the ordinary biographies, and for obvious reasons.
+
+[501] "Before" and "after."
+
+[502] On Bishop Wilkins see note 171 on page 100.
+
+[503] Provision for a journey.
+
+[504] See note 179 on page 103.
+
+[505] Thomas Bradwardine (1290-1349), known as _Doctor Profundus_, proctor
+and professor of theology at Oxford, and afterwards Chancellor of St.
+Paul's and confessor to Edward III. The English ascribed their success at
+Crecy to his prayers.
+
+[506] He was consecrated Archbishop of Canterbury by the Pope at Avignon,
+July 13, 1349, and died of the plague at London in the same year.
+
+[507] "One paltry little year."
+
+[508] The title is carelessly copied, as is so frequently the case in
+catalogues, even of the Libri class. It should read: _Arithmetica thome
+brauardini_ || _Olivier Senant_ || _Venum exponuntur ab Oliuiario senant in
+vico diui Jacobi sub signo beate Barbare sedente_. The colophon reads:
+_Explicit arithmetica speculatiua th[=o]e brauardini b[=n] reuisa et
+correcta a Petro sanchez Ciruelo aragonensi mathematicas leg[=e]te
+Parisius, [=i]pressa per Thom[=a] anguelart_. There were Paris editions of
+1495, 1496, 1498, s. a. (c. 1500), 1502, 1504, 1505, s. a. (c. 1510), 1512,
+1530, a Valencia edition of 1503, two Wittenberg editions of 1534 and 1536,
+and doubtless several others. The work is not "very rare," although of
+course no works of that period are common. See the editor's _Rara
+Arithmetica_, page 61.
+
+[509] This is his _Tractatus de proportionibus_, Paris, 1495; Venice, 1505;
+Vienna, 1515, with other editions.
+
+[510] The colophon of the 1495 edition reads: _Et sic explicit Geometria
+Thome brauardini c[=u] tractatulo de quadratura circuli bene reuisa a Petro
+sanchez ciruelo: operaqz Guidonis mercatoris dilig[=e]tissime impresse
+parisi^o in c[=a]po gaillardi. Anno d[=n]i. 1495. die. 20, maij._
+
+This Petro Ciruelo was born in Arragon, and died in 1560 at Salamanca. He
+studied mathematics and philosophy at Paris, and took the doctor's degree
+there. He taught at the University of Alcala and became canon of the
+Cathedral at Salamanca. Besides his editions of Bradwardine he wrote
+several works, among them the _Liber arithmeticae practicae qui dicitur
+algorithmus_ (Paris, 1495) and the _Cursus quatuor mathematicarum artium
+liberalium_ (Alcala, 1516).
+
+[511] Star polygons, a subject of considerable study in the later Middle
+Ages. See note 35 on page 44.
+
+[512] "A new theory that adds lustre to the fourteenth century."
+
+[513] There is nothing in the edition of 1495 that leads to this
+conclusion.
+
+[514] The full title is: _Nouvelle theorie des paralleles, avec un
+appendice contenant la maniere de perfectionner la theorie des paralleles
+de A. M. Legendre_. The author had no standing as a scientist.
+
+[515] Adrien Marie Legendre (1752-1833) was one of the great mathematicians
+of the opening of the nineteenth century. His _Elements de geometrie_
+(1794) had great influence on the geometry of the United States. His _Essai
+sur la theorie des nombres_ (1798) is one of the classics upon the subject.
+The work to which Kircher refers is the _Nouvelle theorie des paralleles_
+(1803), in which the attempt is made to avoid using Euclid's postulate of
+parallels, the result being merely the substitution of another assumption
+that was even more unsatisfactory. The best presentations of the general
+theory are W. B. Frankland's _Theories of Parallelism_, Cambridge, 1910,
+and Engel and Staeckel's _Die Theorie der Parallellinien von Euclid bis auf
+Gauss_, Leipsic, 1895. Legendre published a second work on the theory the
+year of his death, _Reflexions sur ... la theorie des paralleles_ (1833).
+His other works include the _Nouvelles methodes pour la determination des
+orbites des cometes_ (1805), in which he uses the method of least squares;
+the _Traite des fonctions elliptiques et des integrales_ (1827-1832), and
+the _Exercises de calcul integral_ (1811, 1816, 1817).
+
+[516] Johann Joseph Ignatz von Hoffmann (1777-1866), professor of
+mathematics at Aschaffenburg, published his _Theorie der Parallellinien_ in
+1801. He supplemented this by his _Kritik der Parallelen-Theorie_ in 1807,
+and his _Das eilfte Axiom der Elemente des Euclidis neu bewiesen_ in 1859.
+He wrote other works on mathematics, but none of his contributions was of
+any importance.
+
+[517] Johann Karl Friedrich Hauff (1766-1846) was successively professor of
+mathematics at Marburg, director of the polytechnic school at Augsburg,
+professor at the Gymnasium at Cologne, and professor of mathematics and
+physics at Ghent. The work to which Kircher refers is his memoirs on the
+Euclidean _Theorie der Parallelen_ in Hindenburg's _Archiv_, vol. III
+(1799), an article of no merit in the general theory.
+
+[518] Wenceslaus Johann Gustav Karsten (1732-1787) was professor of logic
+at Rostock (1758) and Butzow (1760), and later became professor of
+mathematics and physics at Halle. His work on parallels is the _Versuch
+einer voellig berichtigten Theorie der Parallellinien_ (1779). He also wrote
+a work entitled _Anfangsgruende der mathematischen Wissenschaften_ (1780),
+but neither of these works was more than mediocre.
+
+[519] Johann Christoph Schwab (not Schwal) was born in 1743 and died in
+1821. He was professor at the Karlsschule at Stuttgart. De Morgan's wish
+was met, for the catalogues give "c. fig. 8," so that it evidently had
+eight illustrations instead of eight volumes. He wrote several other works
+on the principles of geometry, none of any importance.
+
+[520] Gaetano Rossi of Catanzaro. This was the libretto writer (1772-1855),
+and hence the imperfections of the work can better be condoned. De Morgan
+should have given a little more of the title: _Solusione esatta e regolare
+... del ... problema della quadratura del circolo_. There was a second
+edition, London, 1805.
+
+[521] This identifies Rossi, for Josephine Grassini (1773-1850) was a
+well-known contralto, _prima donna_ at Napoleon's court opera.
+
+[522] William Spence (1783-1860) was an entomologist and economist of some
+standing, a fellow of the Royal Society, and one of the founders of the
+Entomological Society of London. The work here mentioned was a popular one,
+the first edition appearing in 1807, and four editions being justified in a
+single year. He also wrote _Agriculture the Source of Britain's Wealth_
+(1808) and _Objections against the Corn Bill refuted_ (1815), besides a
+work in four volumes on entomology (1815-1826) in collaboration with
+William Kirby.
+
+[523] "That used to be so, but we have changed all that."
+
+[524] "Meet the coming disease."
+
+[525] George Douglas (or Douglass) was a Scotch writer. He got out an
+edition of the _Elements of Euclid_ in 1776, with an appendix on
+trigonometry and a set of tables. His work on _Mathematical Tables_
+appeared in 1809, and his _Art of Drawing in Perspective, from mathematical
+principles_, in 1810.
+
+[526] See note 443, on page 197.
+
+[527] John Playfair (1748-1848) was professor of mathematics (1785) and
+natural philosophy (1805) at the University of Edinburgh. His _Elements of
+Geometry_ went through many editions.
+
+[528] "Tell Apella" was an expression current in classical Rome to indicate
+incredulity and to show the contempt in which the Jew was held. Horace
+says: _Credat Judaeus Apella_, "Let Apella the Jew believe it." Our "Tell it
+to the marines," is a similar phrase.
+
+[529] As De Morgan says two lines later, "No mistake is more common than
+the natural one of imagining that the"--University of Virginia is at
+Richmond. The fact is that it is not there, and that it did not exist in
+1810. It was not chartered until 1819, and was not opened until 1825, and
+then at Charlottesville. The act establishing the Central College, from
+which the University of Virginia developed, was passed in 1816. The Jean
+Wood to whom De Morgan refers was one John Wood who was born about 1775 in
+Scotland and who emigrated to the United States in 1800. He published a
+_History of the Administration of J. Adams_ (New York, 1802) that was
+suppressed by Aaron Burr. This act called forth two works, a _Narrative of
+the Suppression, by Col. Burr, of the 'History of the Administration of
+John Adams'_ (1802), in which Wood was sustained; and the _Antidote to John
+Wood's Poison_ (1802), in which he was attacked. The work referred to in
+the "printed circular" may have been the _New theory of the diurnal
+rotation of the earth_ (Richmond, Va., 1809). Wood spent the last years of
+his life in Richmond, Va., making county maps. He died there in 1822. A
+careful search through works relating to the University of Virginia fails
+to show that Wood had any connection with it.
+
+[530] There seems to be nothing to add to Dobson's biography beyond what De
+Morgan has so deliciously set forth.
+
+[531] "Give to each man his due."
+
+[532] Hester Lynch Salusbury (1741-1821), the friend of Dr. Johnson,
+married Henry Thrale (1763), a brewer, who died in 1781. She then married
+Gabriel Piozzi (1784), an Italian musician. Her _Anecdotes of the late
+Samuel Johnson_ (1786) and _Letters to and from Samuel Johnson_ (1788) are
+well known. She also wrote numerous essays and poems.
+
+[533] Samuel Pike (c. 1717-1773) was an independent minister, with a chapel
+in London and a theological school in his house. He later became a disciple
+of Robert Sandeman and left the Independents for the Sandemanian church
+(1765). The _Philosophia Sacra_ was first published at London in 1753. De
+Morgan here cites the second edition.
+
+[534] Pike had been dead over forty years when Kittle published this second
+edition. Kittle had already published a couple of works: _King Solomon's
+portraiture of Old Age_ (Edinburgh, 1813), and _Critical and Practical
+Lectures on the Apocalyptical Epistles to the Seven Churches of Asia Minor_
+(London, 1814).
+
+[535] See note 334, on page 152.
+
+[536] William Stukely (1687-1765) was a fellow of the Royal Society and of
+the College of Physicians and Surgeons. He afterwards (1729) entered the
+Church. He was prominent as an antiquary, especially in the study of the
+Roman and Druidic remains of Great Britain. He was the author of numerous
+works, chiefly on paleography.
+
+[537] William Jones (1726-1800), who should not be confused with his
+namesake who is mentioned in note 281 on page 135. He was a lifelong friend
+of Bishop Horne, and his vicarage at Nayland was a meeting place of an
+influential group of High Churchmen. Besides the _Physiological
+Disquisitions_ (1781) he wrote _The Catholic Doctrine of the Trinity_
+(1756) and _The Grand Analogy_ (1793).
+
+[538] Robert Spearman (1703-1761) was a pupil of John Hutchinson, and not
+only edited his works but wrote his life. He wrote a work against the
+Newtonian physics, entitled _An Enquiry after Philosophy and Theology_
+(Edinburgh, 1755), besides the _Letters to a Friend concerning the
+Septuagint Translation_ (Edinburgh, 1759) to which De Morgan refers.
+
+[539] A writer of no importance, at least in the minds of British
+biographers.
+
+[540] Alexander Catcott (1725-1779), a theologian and geologist, wrote not
+only a work on the creation (1756) but a _Treatise on the Deluge_ (1761,
+with a second edition in 1768). Sir Charles Lyell considered the latter
+work a valuable contribution to geology.
+
+[541] James Robertson (1714-1795), professor of Hebrew at the University of
+Edinburgh. Probably De Morgan refers to his _Grammatica Linguae Hebraeae_
+(Edinburgh, 1758; with a second edition in 1783). He also wrote _Clavis
+Pentateuchi_ (1770).
+
+[542] Benjamin Holloway (c. 1691-1759), a geologist and theologian. He
+translated Woodward's _Naturalis Historia Telluris_, and was introduced by
+Woodward to Hutchinson. The work referred to by De Morgan appeared at
+Oxford in two volumes in 1754.
+
+[543] His work was _The Christian plan exhibited in the interpretation of
+Elohim: with observations upon a few other matters relative to the same
+subject_, Oxford, 1752, with a second edition in 1755.
+
+[544] Duncan Forbes (1685-1747) studied Oriental languages and Civil law at
+Leyden. He was Lord President of the Court of Sessions (1737). He wrote a
+number of theological works.
+
+[545] Should be 1756.
+
+[546] Edward Henry Bickersteth (1825-1906), bishop of Exeter (1885-1900);
+published _The Rock of Ages; or scripture testimony to the one Eternal
+Godhead of the Father, and of the Son, and of the Holy Ghost_ at Hampstead
+in 1859. A second edition appeared at London in 1860.
+
+[547] Thomas Sadler (1822-1891) took his Ph.D. at Erlangen in 1844, and
+became a Unitarian minister at Hampstead, where Bickersteth's work was
+published. Besides writing the _Gloria Patri_ (1859), he edited Crabb
+Robinson's Diaries.
+
+[548] This was his _Virgil's Bucolics and the two first Satyrs of Juvenal_,
+1634.
+
+[549] Possibly in his _Twelve Questions or Arguments drawn out of
+Scripture, wherein the commonly received Opinion touching the Deity of the
+Holy Spirit is clearly and fully refuted_, 1647. This was his first
+heretical work, and it was followed by a number of others that were written
+during the intervals in which the Puritan parliament allowed him out of
+prison. It was burned by the hangman as blasphemous. Biddle finally died in
+prison, unrepentant to the last.
+
+[550] The first edition of the anonymous [Greek: Haireseon anastasis] (by
+Vicars?) appeared in 1805.
+
+[551] Possibly by Thomas Pearne (c. 1753-1827), a fellow of St. Peter's
+College, Cambridge, and a Unitarian minister.
+
+[552] Thomas Wentworth, Earl of Strafford, was borne in London in 1593, and
+was executed there in 1641. He was privy councilor to Charles I, and was
+Lord Deputy of Ireland. On account of his repressive measures to uphold the
+absolute power of the king he was impeached by the Long Parliament and was
+executed for treason. The essence of his defence is in the sentence quoted
+by De Morgan, to which Pym replied that taken as a whole, the acts tended
+to show an intention to change the government, and this was in itself
+treason.
+
+[553] The name assumed by a writer who professed to give a mathematical
+explanation of the Trinity, see farther on.--S. E. De M.
+
+[554] Sabellius (fl. 230 A.D.) was an early Christian of Libyan origin. He
+taught that Father, Son, and Holy Spirit were different names for the same
+person.
+
+[555] Sir Richard Phillips was born in London in 1767 (not 1768 as stated
+above), and died there in 1840. He was a bookseller and printer in
+Leicester, where he also edited a radical newspaper. He went to London to
+live in 1795 and started the _Monthly Magazine_ there in 1796. Besides the
+works mentioned by De Morgan he wrote on law and economics.
+
+[556] It was really eighteen months.
+
+[557] While he was made sheriff in 1807 he was not knighted until the
+following year.
+
+[558] James Mitchell (c. 1786-1844) was a London actuary, or rather a
+Scotch actuary living a good part of his life in London. Besides the work
+mentioned he compiled a _Dictionary of Chemistry, Mineralogy, and Geology_
+(1823), and wrote _On the Plurality of Worlds_ (1813) and _The Elements of
+Astronomy_ (1820).
+
+[559] Richarda Smith, wife of Sir George Biddell Airy (see note 129, page
+85) the astronomer. In 1835 Sir Robert Peel offered a pension of L300 a
+year to Airy, who requested that it be settled on his wife.
+
+[560] Mary Fairfax (1780-1872) married as her second husband Dr. William
+Somerville. In 1826 she presented to the Royal Society a paper on _The
+Magnetic Properties of the Violet Rays of the Solar Spectrum_, which
+attracted much attention. It was for her _Mechanism of the Heavens_ (1831),
+a popular translation of Laplace's _Mecanique Celeste_, that she was
+pensioned.
+
+[561] Dominique Francois Jean Arago (1786-1853) the celebrated French
+astronomer and physicist.
+
+[562] For there is a well-known series
+
+  1 + 1/2^2 + 1/3^2 + ... = [pi]^2/6.
+
+If, therefore, the given series equals 1, we have
+
+  2 = 1/6 [pi]^2
+
+  or [pi]^2 = 12,
+
+  whence [pi] = 2 [root]3.
+
+But c = [pi]d, and twice the diagonal of a cube on the diameter is 2d
+[root]3.
+
+[563] There was a second edition in 1821.
+
+[564] London, 1830.
+
+[565] He was a resident of Chatham, and seems to have published no other
+works.
+
+[566] Richard Whately (1787-1863) was, as a child, a calculating prodigy
+(see note 132, page 86), but lost the power as is usually the case with
+well-balanced minds. He was a fellow of Oriel College, Oxford, and in 1825
+became principal of St. Alban Hall. He was a friend of Newman, Keble, and
+others who were interested in the religious questions of the day. He became
+archbishop of Dublin in 1831. He was for a long time known to students
+through his _Logic_ (1826) and _Rhetoric_ (1828).
+
+[567] William King, D.C.L. (1663-1712), student at Christ Church, Oxford,
+and celebrated as a wit and scholar. His _Dialogues of the Dead_ (1699) is
+a satirical attack on Bentley.
+
+[568] Thomas Ebrington (1760-1835) was a fellow of Trinity College, Dublin,
+and taught divinity, mathematics, and natural philosophy there. He became
+provost of the college in 1811, bishop of Limerick in 1820, and bishop of
+Leighlin and Ferns in 1822. His edition of Euclid was reprinted a dozen
+times. The _Reply to John Search's Considerations on the Law of Libel_
+appeared at Dublin in 1834.
+
+[569] Joseph Blanco White (1775-1841) was the son of an Irishman living in
+Spain. He was born at Seville and studied for orders there, being ordained
+priest in 1800. He lost his faith in the Roman Catholic Church, and gave up
+the ministry, escaping to England at the time of the French invasion. At
+London he edited _Espanol_, a patriotic journal extensively circulated in
+Spain, and for this service he was pensioned after the expulsion of the
+French. He then studied at Oriel College, Oxford, and became intimate with
+men like Whately, Newman, and Keble. In 1835 he became a Unitarian. Among
+his theological writings is his _Evidences against Catholicism_ (1825). The
+"rejoinder" to which De Morgan refers consisted of two letters: _The law of
+anti-religious Libel reconsidered_ (Dublin, 1834) and _An Answer to some
+Friendly Remarks on "The Law of Anti-Religious Libel Reconsidered"_
+(Dublin, 1834).
+
+[570] The work was translated from the French.
+
+[571] J. Hoene Wronski (1778-1853) served, while yet a mere boy, as an
+artillery officer in Kosciusko's army (1791-1794). He was imprisoned after
+the battle of Maciejowice. He afterwards lived in Germany, and (after 1810)
+in Paris. For the bibliography of his works see S. Dickstein's article in
+the _Bibliotheca Mathematica_, vol. VI (2), page 48.
+
+[572] Perhaps referring to his _Introduction a la philosophie des
+mathematiques_ (1811).
+
+[573] Read "equation of the."
+
+[574] Thomas Young (1773-1829), physician and physicist, sometimes called
+the founder of physiological optics. He seems to have initiated the theory
+of color blindness that was later developed by Helmholtz. The attack
+referred to was because of his connection with the Board of Longitude, he
+having been made (1818) superintendent of the Nautical Almanac and
+secretary of the Board. He opposed introducing into the Nautical Almanac
+anything not immediately useful to navigation, and this antagonized many
+scientists.
+
+[575] Isaac Milner (1750-1820) was professor of natural philosophy at
+Cambridge (1783) and later became, as De Morgan states, president of
+Queens' College (1788). In 1791 he became dean of Carlisle, and in 1798
+Lucasian professor of mathematics. His chief interest was in chemistry and
+physics, but he contributed nothing of importance to these sciences or to
+mathematics.
+
+[576] Thomas Perronet Thompson (1783-1869), fellow of Queens' College,
+Cambridge, saw service in Spain and India, but after 1822 lived in England.
+He became major general in 1854, and general in 1868. Besides some works on
+economics and politics he wrote a _Geometry without Axioms_ (1830) that De
+Morgan includes later on in his _Budget_. In it Thompson endeavored to
+prove the parallel postulate.
+
+[577] De Morgan's father-in-law. See note 441, page 196.
+
+[578] Johann Friedrich Herbart (1776-1841), successor of Kant as professor
+of philosophy at Koenigsberg (1809-1833), where he established a school of
+pedagogy. From 1833 until his death he was professor of philosophy at
+Goettingen. The title of the pamphlet is: _De Attentionis mensura causisque
+primariis. Psychologiae principia statica et mechanica exemplo
+illustraturus.... Regiomonti,... 1822_. The formulas in question are given
+on pages 15 and 17, and De Morgan has omitted the preliminary steps, which
+are, for the first one:
+
+  [beta] ([phi] - z) [delta]t = [delta]z
+
+  unde [beta]t= Const / ([phi] - z).
+
+  Pro t = 0 etiam z = 0; hinc [beta]t = log [phi]/([phi] - z).
+
+  z = [phi] (1 - [epsilon]^{-[beta]t});
+
+  et   [delta]z/[delta]t = [beta][phi][epsilon]^{-[beta]t}
+
+These are, however, quite elementary as compared with other portions of the
+theory.
+
+[579] See note 371, page 168.
+
+[580] William Law (1686-1761) was a clergyman, a fellow of Emanuel College,
+Cambridge, and in later life a convert to Behmen's philosophy. He was so
+free in his charities that the village in which he lived became so infested
+by beggars that he was urged by the citizens to leave. He wrote _A serious
+call to a devout and holy life_ (1728).
+
+[581] He was a curate at Cheshunt, and wrote the _Spiritual voice to the
+Christian Church and to the Jews_ (London, 1760), _A second warning to the
+world by the Spirit of Prophecy_ (London, 1760), and _Signs of the Times;
+or a Voice to Babylon_ (London, 1773).
+
+[582] His real name was Thomas Vaughan (1622-1666). He was a fellow of
+Jesus College, Oxford, taking orders, but was deprived of his living on
+account of drunkenness. He became a mystic philosopher and gave attention
+to alchemy. His works had a large circulation, particularly on the
+continent. He wrote _Magia Adamica_ (London, 1650), _Euphrates; or the
+Waters of the East_ (London, 1655), and _The Chymist's key to shut, and to
+open; or the True Doctrine of Corruption and Generation_ (London, 1657).
+
+[583] Emanuel Swedenborg, or Svedberg (1688-1772) the mystic. It is not
+commonly known to mathematicians that he was one of their guild, but he
+wrote on both mathematics and chemistry. Among his works are the
+_Regelkonst eller algebra_ (Upsala, 1718) and the _Methodus nova inveniendi
+longitudines locorum, terra marique, ope lunae_ (Amsterdam, 1721, 1727, and
+1766). After 1747 he devoted his attention to mystic philosophy.
+
+[584] Pierre Simon Laplace (1749-1827), whose _Exposition du systeme du
+monde_ (1796) and _Traite de mecanique celeste_ (1799) are well known.
+
+[585] See note 117, page 76.
+
+[586] John Dalton (1766-1844), who taught mathematics and physics at New
+College, Manchester (1793-1799) and was the first to state the law of the
+expansion of gases known by his name and that of Gay-Lussac. His _New
+system of Chemical Philosophy_ (Vol. I, pt. i, 1808; pt. ii, 1810; vol. II,
+1827) sets forth his atomic theory.
+
+[587] Howison was a poet and philosopher. He lived in Edinburgh and was a
+friend of Sir Walter Scott. This work appeared in 1822.
+
+[588] He was a shoemaker, born about 1765 at Haddiscoe, and his
+"astro-historical" lectures at Norwich attracted a good deal of attention
+at one time. He traced all geologic changes to differences in the
+inclination of the earth's axis to the plane of its orbit. Of the works
+mentioned by De Morgan the first appeared at Norwich in 1822-1823, and
+there was a second edition in 1824. The second appeared in 1824-1825. The
+fourth was _Urania's Key to the Revelation; or the analyzation of the
+writings of the Jews..._, and was first published at Norwich in 1823, there
+being a second edition at London in 1833. His books were evidently not a
+financial success, for Mackey died in an almshouse at Norwich.
+
+[589] Godfrey Higgins (1773-1833), the archeologist, was interested in the
+history of religious beliefs and in practical sociology. He wrote _Horae
+Sabbaticae_ (1826), _The Celtic Druids_ (1827 and 1829), and _Anacalypsis,
+an attempt to draw aside the veil of the Saitic Isis; or an Inquiry into
+the Origin of Languages, Nations, and Religions_ (posthumously published,
+1836), and other works. See also page 274, _infra_.
+
+[590] The work also appeared in French. Wirgman wrote, or at least began,
+two other works: _Divarication of the New Testament into Doctrine and
+History; part I, The Four Gospels_ (London, 1830), and _Mental Philosophy;
+part I, Grammar of the five senses; being the first step to infant
+education_ (London, 1838).
+
+[591] He was born at Shandrum, County Limerick, and supported himself by
+teaching writing and arithmetic. He died in an almshouse at Cork.
+
+[592] George Boole (1815-1864), professor of mathematics at Queens'
+College, Cork. His _Laws of Thought_ (1854) was the first work on the
+algebra of logic.
+
+[593] Oratio Grassi (1582-1654), the Jesuit who became famous for his
+controversy with Galileo over the theory of comets. Galileo ridiculed him
+in _Il Saggiatore_, although according to the modern view Grassi was the
+more nearly right. It is said that the latter's resentment led to the
+persecution of Galileo.
+
+[594] De Morgan might have found much else for his satire in the letters of
+Walsh. He sought, in his _Theory of Partial Functions_, to substitute
+"partial equations" for the differential calculus. In his diary there is an
+entry: "Discovered the general solution of numerical equations of the fifth
+degree at 114 Evergreen Street, at the Cross of Evergreen, Cork, at nine
+o'clock in the forenoon of July 7th, 1844; exactly twenty-two years after
+the invention of the Geometry of Partial Equations, and the expulsion of
+the differential calculus from Mathematical Science."
+
+[595] "It has been ordered, sir, it has been ordered."
+
+[596] Bartholomew Prescot was a Liverpool accountant. De Morgan gives this
+correct spelling on page 278. He died after 1849. His _Inverted Scheme of
+Copernicus_ appeared in Liverpool in 1822.
+
+[597] Robert Taylor (1784-1844) had many more ups and downs than De Morgan
+mentions. He was a priest of the Church of England, but resigned his parish
+in 1818 after preaching against Christianity. He soon recanted and took
+another parish, but was dismissed by the Bishop almost immediately on the
+ground of heresy. As stated in the text, he was convicted of blasphemy in
+1827 and was sentenced to a year's imprisonment, and again for two years on
+the same charge in 1831. He then married a woman who was rich in money and
+in years, and was thereupon sued for breach of promise by another woman. To
+escape paying the judgment that was rendered against him he fled to Tours
+where he took up surgery.
+
+[598] Herbert Marsh, Bishop of Peterborough. See note 449 on page 199.
+
+[599] "Argument from the prison."
+
+[600] Richard Carlile (1790-1843), one of the leading radicals of his time.
+He published Hone's parodies (see note 250, page 124) after they had been
+suppressed, and an edition of Thomas Paine (1818). He was repeatedly
+imprisoned, serving nine years in all. His continued conflict with the
+authorities proved a good advertisement for his bookshop.
+
+[601] Wilhelm Ludwig Christmann (1780-1835) was a protestant clergyman and
+teacher of mathematics. For a while he taught under Pestalozzi.
+Disappointed in his ambition to be professor of mathematics at Tubingen, he
+became a confirmed misanthrope and is said never to have left his house
+during the last ten years of his life. He wrote several works: _Ein Wort
+ueber Pestalozzi und Pestalozzismus_ (1812); _Ars cossae promota_ (1814);
+_Philosophia cossica_ (1815); _Aetas argentea cossae_ (1819); _Ueber
+Tradition und Schrift, Logos und Kabbala_ (1829), besides the one mentioned
+above. The word _coss_ in the above titles was a German name for algebra,
+from the Italian _cosa_ (thing), the name for the unknown quantity. It
+appears in English in the early name for algebra, "the cossic art."
+
+[602] See note 174, page 101.
+
+[603] See note 589, page 257.
+
+[604] He seems to have written nothing else.
+
+[605] See note 596 on page 270. The name is here spelled correctly.
+
+[606] Joseph Jacotot (1770-1840), the father of this Fortune Jacotot, was
+an infant prodigy. At nineteen he was made professor of the humanities at
+Dijon. He served in the army, and then became professor of mathematics at
+Dijon. He continued in his chair until the restoration of the Bourbons, and
+then fled to Louvain. It was here that he developed the method with which
+his name is usually connected. He wrote a _Mathematiques_ in 1827, which
+went through four editions. The _Epitome_ is by his son, Fortune.
+
+[607] He wrote on educational topics and a _Sacred History_ that went
+through several editions.
+
+[608] "All is in all."
+
+[609] "Know one thing and refer everything else to it," as it is often
+translated.
+
+[610] A writer of no reputation.
+
+[611] Sir John Lubbock (1803-1865), banker, scientist, publicist,
+astronomer, one of the versatile men of his time.
+
+[612] See note 165, page 99.
+
+[613] "Those about to die salute you."
+
+[614] Georges Louis Leclerc Buffon (1707-1788), the well-known biologist.
+He also experimented with burning mirrors, his results appearing in his
+_Invention des miroirs ardens pour bruler a une grande distance_ (1747).
+The reference here may be to his _Resolution des problemes qui regardent le
+jeu du franc carreau_ (1733). The prominence of his _Histoire naturelle_
+(36 volumes, 1749-1788) has overshadowed the credit due to him for his
+translation of Newton's work on Fluxions.
+
+[615] See page 285. This article was a supplement to No. 14 in the
+_Athenaeum_ Budget.--A. De M.
+
+[616] There are many similar series and products. Among the more
+interesting are the following:
+
+  [pi]   2.2.4.4.6.6.8...
+  ---- = ----------------,
+    2    1.3.3.5.5.7.7...
+
+  [pi]-3  =   1       1       1
+  ------  = ----- - ----- + ----- - ...,
+    4       2.3.4   4.5.6   6.7.8
+
+  [pi]        1         1      1       1       1
+  ---- = sqrt - . (1 - --- + ----- - ----- + ----- - ...),
+    6         3        3.3   3^2.5   3^3.7   3^4.9
+
+  [pi]       1     1       1       1
+  ---- = 4 ( - - ----- + ----- - ----- + ...)
+   4         5   3.5^3   5.5^5   7.5^7
+
+              1       1         1
+         - ( --- - ------- + ------- - ...).
+             239   3.239^3   5.239^5
+
+[617] "To a privateer, a privateer and a half."
+
+[618] Joshua Milne (1776-1851) was actuary of the Sun Life Assurance
+Society. He wrote _A Treatise on the Valuation of Annuities and Assurances
+on Lives and Survivorships; on the Construction of tables of mortality; and
+on the Probabilities and Expectations of Life_, London, 1815. Upon the
+basis of the Carlisle bills of mortality of Dr. Heysham he reconstructed
+the mortality tables then in use and which were based upon the Northampton
+table of Dr. Price. His work revolutionized the actuarial science of the
+time. In later years he devoted his attention to natural history.
+
+[619] See note 576, page 252. He also wrote the _Theory of Parallels. The
+proof of Euclid's axiom looked for in the properties of the equiangular
+spiral_ (London, 1840), which went through four editions, and the _Theory
+of Parallels. The proof that the three angles of a triangle are equal to
+two right angles looked for in the inflation of the sphere_ (London, 1853),
+of which there were three editions.
+
+[620] For the latest summary, see W. B. Frankland, _Theories of
+Parallelism, an historical critique_, Cambridge, 1910.
+
+[621] Joseph Louis Lagrange (1736-1813), author of the _Mecanique
+analytique_ (1788), _Theorie des functions analytiques_ (1797), _Traite de
+la resolution des equations numeriques de tous degres_ (1798), _Lecons sur
+le calcul des fonctions_ (1806), and many memoirs. Although born in Turin
+and spending twenty of his best years in Germany, he is commonly looked
+upon as the great leader of French mathematicians. The last twenty-seven
+years of his life were spent in Paris, and his remarkable productivity
+continued to the time of his death. His genius in the theory of numbers was
+probably never excelled except by Fermat. He received very high honors at
+the hands of Napoleon and was on the first staff of the Ecole polytechnique
+(1797).
+
+[622] "I shall have to think it over again."
+
+[623] Henry Goulburn (1784-1856) held various government posts. He was
+under-secretary for war and the colonies (1813), commissioner to negotiate
+peace with America (1814), chief secretary to the Lord Lieutenant of
+Ireland (1821), and several times Chancellor of the Exchequer. On the
+occasion mentioned by De Morgan he was standing for parliament, and was
+successful.
+
+[624] On Drinkwater Bethune see note 165, page 99.
+
+[625] Charles Henry Cooper (1808-1866) was a biographer and antiquary. He
+was town clerk of Cambridge (1849-1866) and wrote the _Annals of Cambridge_
+(1842-1853). His _Memorials of Cambridge_ (1874) appeared after his death.
+Thompson Cooper was his son, and the two collaborated in the _Athenae
+Cantabrigiensis_ (1858).
+
+[626] William Yates Peel (1789-1858) was a brother of Sir Robert Peel, he
+whose name degenerated into the familiar title of the London "Bobby" or
+"Peeler." Yates Peel was a member of parliament almost continuously from
+1817 to 1852. He represented Cambridge at Westminster from 1831 to 1835.
+
+[627] Henry John Temple, third Viscount of Palmerston (1784-1865), was
+member for Cambridge in 1811, 1818, 1820, 1826 (defeating Goulburn), and
+1830. He failed of reelection in 1831 because of his advocacy of reform.
+This must have been the time when Goulburn defeated him. He was Foreign
+Secretary (1827) and Secretary of State for Foreign Affairs (1830-1841, and
+1846-1851). It is said of him that he "created Belgium, saved Portugal and
+Spain from absolutism, rescued Turkey from Russia and the highway to India
+from France." He was Prime Minister almost continuously from 1855 to 1865,
+a period covering the Indian Mutiny and the American Civil War.
+
+[628] William Cavendish, seventh Duke of Devonshire (1808-1891). He was
+member for Cambridge from 1829 to 1831, but was defeated in 1831 because he
+had favored parliamentary reform. He became Earl of Burlington in 1834, and
+Duke of Devonshire in 1858. He was much interested in the promotion of
+railroads and in the iron and steel industries.
+
+[629] Richard Sheepshanks (1794-1855) was a brother of John Sheepshanks the
+benefactor of art. (See note 314, p. 147.) He was a fellow of Trinity
+College, Cambridge, a fellow of the Royal Society and secretary of the
+Astronomical Society. Babbage (See note 469, p. 207) suspected him of
+advising against the government support of his calculating machine and
+attacked him severely in his _Exposition of 1851_, in the chapter on _The
+Intrigues of Science_. Babbage also showed that Sheepshanks got an
+astronomical instrument of French make through the custom house by having
+Troughton's (See note 332, page 152) name engraved on it. Sheepshanks
+admitted this second charge, but wrote a _Letter in Reply to the Calumnies
+of Mr. Babbage_, which was published in 1854. He had a highly controversial
+nature.
+
+[630] See note 469, page 207. The work referred to is _Passages from the
+Life of a Philosopher_, London, 1864.
+
+[631] Drinkwater Bethune. See note 165, page 99.
+
+[632] Simeon-Denis Poisson (1781-1840) was professor of calculus and
+mechanics at the Ecole polytechnique. He was made a baron by Napoleon, and
+was raised to the peerage in 1837. His chief works are the _Traite de
+mecanique_ (1811) and the _Traite mathematique de la chaleur_ (1835).
+
+[633] "As to M. Poisson, I really wish I had a thousandth part of his
+mathematical knowledge that I might prove my system to the incredulous."
+
+[634] This list includes most of the works of Antoine-Louis-Guenard
+Demonville. There was also the _Nouveau systeme du monde ... et hypotheses
+conformes aux experiences sur les vents, sur la lumiere et sur le fluide
+electro-magnetique_, Paris, 1830.
+
+[635] Paris, 1835.
+
+[636] Paris, 1833.
+
+[637] The second part appeared in 1837. There were also editions in 1850
+and 1852, and one edition appeared without date.
+
+[638] Paris, 1842.
+
+[639] Parsey also wrote _The Art of Miniature Painting on Ivory_ (1831),
+_Perspective Rectified_ (1836), and _The Science of Vision_ (1840), the
+third being a revision of the second.
+
+[640] William Ritchie (1790-1837) was a physicist who had studied at Paris
+under Biot and Gay-Lussac. He contributed several papers on electricity,
+heat, and elasticity, and was looked upon as a good experimenter. Besides
+the geometry he wrote the _Principles of the Differential and Integral
+Calculus_ (1836).
+
+[641] Alfred Day (1810-1849) was a man who was about fifty years ahead of
+his time in his attempt to get at the logical foundations of geometry. It
+is true that he laid himself open to criticism, but his work was by no
+means bad. He also wrote _A Treatise on Harmony_ (1849, second edition
+1885), _The Rotation of the Pendulum_ (1851), and several works on Greek
+and Latin Grammar.
+
+[642] Walter Forman wrote a number of controversial tracts. His first seems
+to have been _A plan for improving the Revenue without adding to the
+burdens of the people_, a letter to Canning in 1813. He also wrote _A New
+Theory of the Tides_ (1822). His _Letter to Lord John Russell, on Lord
+Brougham's most extraordinary conduct; and another to Sir J. Herschel, on
+the application of Kepler's third law_ appeared in 1832.
+
+[643] Lord John Russell (1792-1878) first Earl Russell, was one of the
+strongest supporters of the reform measures of the early Victorian period.
+He became prime minister in 1847, and again in 1865.
+
+[644] Lauder seems never to have written anything else.
+
+[645] See note 22, page 40.
+
+[646] The names of Alphonso Cano de Molina, Yvon, and Robert Sara have no
+standing in the history of the subject beyond what would be inferred from
+De Morgan's remark.
+
+[647] Claude Mydorge (1585-1647), an intimate friend of Descartes, was a
+dilletante in mathematics who read much but accomplished little. His
+_Recreations mathematiques_ is his chief work. Boncompagni published the
+"Problemes de Mydorge" in his _Bulletino_.
+
+[648] Claude Hardy was born towards the end of the 16th century and died at
+Paris in 1678. In 1625 he edited the _Data Euclidis_, publishing the Greek
+text with a Latin translation. He was a friend of Mydorge and Descartes,
+but an opponent of Fermat.
+
+[649] That is, in the _Bibliotheca Realis_ of Martin Lipen, or Lipenius
+(1630-1692), which appeared in six folio volumes, at Frankfort, 1675-1685.
+
+[650] See note 29, page 43.
+
+[651] Baldassare Boncompagni (1821-1894) was the greatest general collector
+of mathematical works that ever lived, possibly excepting Libri. His
+magnificent library was dispersed at his death. His _Bulletino_ (1868-1887)
+is one of the greatest source books on the history of mathematics that we
+have. He also edited the works of Leonardo of Pisa.
+
+[652] He seems to have attracted no attention since De Morgan's search, for
+he is not mentioned in recent bibliographies.
+
+[653] Joseph-Louis Vincens de Mouleon de Causans was born about the
+beginning of the l8th century. He was a Knight of Malta, colonel in the
+infantry, prince of Conti, and governor of the principality of Orange. His
+works on geometry are the _Prospectus apologetique pour la quadrature du
+cercle_ (1753), and _La vraie geometrie transcendante_ (1754).
+
+[654] See note 119, page 80.
+
+[655] See note 120, page 81.
+
+[656] Lieut. William Samuel Stratford (1791-1853), was in active service
+during the Napoleonic wars but retired from the army in 1815. He was first
+secretary of the Astronomical Society (1820) and became superintendent of
+the Nautical Almanac in 1831. With Francis Baily he compiled a star
+catalogue, and wrote on Halley's (1835-1836) and Encke's (1838) comets.
+
+[657] See Sir J. Herschel's _Astronomy_, p. 369.--A. De M.
+
+[658] Captain Ross had just stuck a bit of brass there.--A. De M.
+
+Sir James Clark Ross (1800-1862) was a rear admiral in the British navy and
+an arctic and antarctic explorer of prominence. De Morgan's reference is to
+Ross's discovery of the magnetic pole on June 1, 1831. In 1838 he was
+employed by the Admiralty on a magnetic survey of the United Kingdom. He
+was awarded the gold medal of the geographical societies of London and
+Paris in 1842.
+
+[659] John Partridge (1644-1715), the well-known astrologer and almanac
+maker. Although bound to a shoemaker in his early boyhood, he had acquired
+enough Latin at the age of eighteen to read the works of the astrologers.
+He then mastered Greek and Hebrew and studied medicine. In 1680 he began
+the publication of his almanac, the _Merlinus Liberatus_, a book that
+acquired literary celebrity largely through the witty comments upon it by
+such writers as Swift and Steele.
+
+[660] See note 642 on page 296.
+
+[661] William Woodley also published several almanacs (1838, 1839, 1840)
+after his rejection by the Astronomical Society in 1834.
+
+[662] It appeared at London.
+
+[663] The first edition appeared in 1830, also at London.
+
+[664] See note 441, page 196.
+
+[665] Thomas Kerigan wrote _The Young Navigator's Guide to the siderial and
+planetary parts of Nautical Astronomy_ (London, 1821, second edition 1828),
+a work on eclipses (London, 1844), and the work on tides (London, 1847) to
+which De Morgan refers.
+
+[666] Jean Sylvain Bailly, who was guillotined. See note 365, page 166.
+
+[667] See note 670, page 309.
+
+[668] Laurent seems to have had faint glimpses of the modern theory of
+matter. He is, however, unknown.
+
+[669] See note 133, page 87.
+
+[670] Francis Baily (1774-1844) was a London stockbroker. His interest in
+science in general and in astronomy in particular led to his membership in
+the Royal Society and to his presidency of the Astronomical Society. He
+wrote on interest and annuities (1808), but his chief works were on
+astronomy.
+
+[671] If the story is correctly told Baily must have enjoyed his statement
+that Gauss was "the oldest mathematician now living." As a matter of fact
+he was then only 58, three years the junior of Baily himself. Gauss was
+born in 1777 and died in 1855, and Baily was quite right in saying that he
+was "generally thought to be the greatest" mathematician then living.
+
+[672] Margaret Cooke, who married Flamsteed in 1692.
+
+[673] John Brinkley (1763-1835), senior wrangler, first Smith's prize-man
+(1788), Andrews professor of astronomy at Dublin, first Astronomer Royal
+for Ireland (1792), F.R.S. (1803), Copley medallist, president of the Royal
+Society and Bishop of Cloyne. His _Elements of Astronomy_ appeared in 1808.
+
+[674] See note 248, page 124.
+
+[675] See note 276, page 133.
+
+[676] See note 352, page 161.
+
+[677] "It becomes the doctors of the Sorbonne to dispute, the Pope to
+decree, and the mathematician to go to Paradise on a perpendicular line."
+
+[678] See note 124, page 83.
+
+[679] See note 621, page 288.
+
+[680] Sylvain van de Weyer, who was born at Louvain in 1802. He was a
+jurist and statesman, holding the portfolio for foreign affairs
+(1831-1833), and being at one time ambassador to England.
+
+[681] Henry Crabb Robinson (1775-1867), correspondent of the _Times_ at
+Altona and in the Peninsula, and later foreign editor. He was one of the
+founders of the Athenaeum Club and of University College, London. He seems
+to have known pretty much every one of his day, and his posthumous _Diary_
+attracted attention when it appeared.
+
+[682] Was this Whewell, who was at Trinity from 1812 to 1816 and became a
+fellow in 1817?
+
+[683] Tom Cribb (1781-1848) the champion pugilist. He had worked as a coal
+porter and hence received his nickname, the Black Diamond.
+
+[684] John Finleyson, or Finlayson, was born in Scotland in 1770 and died
+in London in 1854. He published a number of pamphlets that made a pretense
+to being scientific. Among his striking phrases and sentences are the
+statements that the stars were made "to amuse us in observing them"; that
+the earth is "not shaped like a garden turnip as the Newtonians make it,"
+and that the stars are "oval-shaped immense masses of frozen water." The
+first edition of the work here mentioned appeared at London in 1830.
+
+[685] Richard Brothers (1757-1824) was a native of Newfoundland. He went to
+London when he was about 30, and a little later set forth his claim to
+being a descendant of David, prince of the Hebrews, and ruler of the world.
+He was confined as a criminal lunatic in 1795 but was released in 1806.
+
+[686] Charles Grey (1764-1845), second Earl Grey, Viscount Howick, was then
+Prime Minister. The Reform Bill was introduced and defeated in 1831. The
+following year, with the Royal guarantees to allow him to create peers, he
+finally carried the bill in spite of "the number of the beast."
+
+[687] The letters of obscure men, the _Epistolae obscurorum virorum ad
+venerabilem virum Magistrum Ortuinum Gratium Dauentriensem_, by Joannes
+Crotus, Ulrich von Hutten, and others appeared at Venice about 1516.
+
+[688] The lamentations of obscure men, the _Lamentationes obscurorum
+virorum, non prohibete per sedem Apostolicam. Epistola D. Erasmi
+Roterodami: quid de obscuris sentiat_, by G. Ortwinus, appeared at Cologne
+in 1518.
+
+[689] The criticism was timely when De Morgan wrote it. At present it would
+have but little force with respect to the better class of algebras.
+
+[690] Thomas Ignatius Maria Forster (1789-1860) was more of a man than one
+would infer from this satire upon his theory. He was a naturalist,
+astronomer, and physiologist. In 1812 he published his _Researches about
+Atmospheric Phenomena_, and seven years later (July 3, 1819) he discovered
+a comet. With Sir Richard Phillips he founded a Meteorological Society, but
+it was short lived. He declined a fellowship in the Royal Society because
+he disapproved of certain of its rules, so that he had a recognized
+standing in his day. The work mentioned by De Morgan is the second edition,
+the first having appeared at Frankfort on the Main in 1835 under the title,
+_Recueil des ouvrages et des pensees d'un physicien et metaphysicien_.
+
+[691] Zadkiel, whose real name was Richard James Morrison (1795-1874), was
+in his early years an officer in the navy. In 1831 he began the publication
+of the _Herald of Astrology_, which was continued as _Zadkiel's Almanac_.
+His name became familiar throughout Great Britain as a result.
+
+[692] See note 566, page 246.
+
+[693] Sumner (1780-1862) was an Eton boy. He went to King's College,
+Cambridge, and was elected fellow in 1801. He took many honors, and in 1807
+became M.A. He was successively Canon of Durham (1820), Bishop of Chester
+(1828), and Archbishop of Canterbury (1848). Although he voted for the
+Catholic Relief Bill (1829) and the Reform Bill (1832), he opposed the
+removal of Jewish disabilities.
+
+[694] Charles Richard Sumner (1790-1874) was not only Bishop of Winchester
+(1827), but also Bishop of Llandaff and Dean of St. Paul's, London (1826).
+He lost the king's favor by voting for the Catholic Relief Bill.
+
+[695] John Bird Sumner, brother of Charles Richard.
+
+[696] Thomas Musgrave (1788-1860) became Fellow of Trinity in 1812, and
+senior proctor in 1831. He was also Dean of Bristol.
+
+[697] Charles Thomas Longley (1794-1868) was educated at Westminster School
+and at Christ Church, Oxford. He became M.A. in 1818 and D.D. in 1829.
+Besides the bishoprics mentioned he was Bishop of Ripon (1836-1856), and
+before that was headmaster of Harrow (1829-1836).
+
+[698] Thomson (1819-1890) was scholar and fellow of Queen's College,
+Oxford. He became chaplain to the Queen in 1859.
+
+[699] This is worthy of the statistical psychologists of the present day.
+
+[700] The famous Moon Hoax was written by Richard Adams Locke, who was born
+in New York in 1800 and died in Staten Island in 1871. He was at one time
+editor of the _Sun_, and the Hoax appeared in that journal in 1835. It was
+reprinted in London (1836) and Germany, and was accepted seriously by most
+readers. It was published in book form in New York in 1852 under the title
+_The Moon Hoax_. Locke also wrote another hoax, the _Lost Manuscript of
+Mungo Park_, but it attracted relatively little attention.
+
+[701] It is true that Jean-Nicolas Nicollet (1756-1843) was at that time in
+the United States, but there does not seem to be any very tangible evidence
+to connect him with the story. He was secretary and librarian of the Paris
+observatory (1817), member of the Bureau of Longitudes (1822), and teacher
+of mathematics in the Lycee Louis-le-Grand. Having lost his money through
+speculations he left France for the United States in 1831 and became
+connected with the government survey of the Mississippi Valley.
+
+[702] This was Alexis Bouvard (1767-1843), who made most of the
+computations for Laplace's _Mecanique celeste_ (1793). He discovered eight
+new comets and calculated their orbits. In his tables of Uranus (1821) he
+attributed certain perturbations to the presence of an undiscovered planet,
+but unlike Leverrier and Adams he did not follow up this clue and thus
+discover Neptune.
+
+[703] Patrick Murphy (1782-1847) awoke to find himself famous because of
+his natural guess that there would be very cold weather on January 20,
+although that is generally the season of lowest temperature. It turned out
+that his forecasts were partly right on 168 days and very wrong on 197
+days.
+
+[704] He seems to have written nothing else. If one wishes to enter into
+the subject of the mathematics of the Great Pyramid there is an extensive
+literature awaiting him. Richard William Howard Vyse (1784-1853) published
+in 1840 his _Operations carried on at the Pyramids of Gizeh in 1837_, and
+in this he made a beginning of a scientific metrical study of the subject.
+Charles Piazzi Smyth (1819-1900), astronomer Royal for Scotland (1845-1888)
+was much carried away with the number mysticism of the Great Pyramid, so
+much so that he published in 1864 a work entitled _Our Inheritance in the
+Great Pyramid_, in which his vagaries were set forth. Although he was then
+a Fellow of the Royal Society (1857), his work was so ill received that
+when he offered a paper on the subject it was rejected (1874) and he
+resigned in consequence of this action. The latest and perhaps the most
+scholarly of all investigators of the subject is William Matthew Flinders
+Petrie (born in 1853), Edwards professor of Egyptology at University
+College, London, whose _Pyramids and Temples of Gizeh_ (1883) and
+subsequent works are justly esteemed as authorities.
+
+[705] As De Morgan subsequently found, this name reversed becomes Oliver
+B...e, for Oliver Byrne, one of the odd characters among the minor
+mathematical writers of the middle of the last century. One of his most
+curious works is _The first six Books of the Elements of Euclid; in which
+coloured diagrams and symbols are used instead of letters_ (1847). There is
+some merit in speaking of the red triangle instead of the triangle ABC, but
+not enough to give the method any standing. His _Dual Arithmetic_
+(1863-1867) was also a curious work.
+
+[706] Brenan also wrote on English composition (1829), a work that went
+through fourteen editions by 1865; a work entitled _The Foreigner's English
+Conjugator_ (1831), and a work on the national debt.
+
+[707] See note 211, page 112.
+
+[708] See note 592, page 261.
+
+[709] Sir William Rowan Hamilton (1805-1865), the discoverer of quaternions
+(1852), was an infant prodigy, competing with Zerah Colburn as a child. He
+was a linguist of remarkable powers, being able, at thirteen years of age,
+to boast that he knew as many languages as he had lived years. When only
+sixteen he found an error in Laplace's _Mecanique celeste_. When only
+twenty-two he was appointed Andrews professor of astronomy, and he soon
+after became Astronomer Royal of Ireland. He was knighted in 1835. His
+earlier work was on optics, his _Theory of Systems of Rays_ appearing in
+1823. In 1827 he published a paper on the principle of _Varying Action_. He
+also wrote on dynamics.
+
+[710] "Let him not leave the kingdom,"--a legal phrase.
+
+[711] Probably De Morgan is referring to Johann Bernoulli III (1744-1807),
+who edited Lambert's _Logische und philosophische Abhandlungen_, Berlin,
+1782. He was astronomer of the Academy of Sciences at Berlin.
+
+[712] Jacob Bernoulli (1654-1705) was one of the two brothers who founded
+the famous Bernoulli family of mathematicians, the other being Johann I.
+His _Ars conjectandi_ (1713), published posthumously, was the first
+distinct treatise on probabilities.
+
+[713] Johann Heinrich Lambert (1728-1777) was one of the most learned men
+of his time. Although interested chiefly in mathematics, he wrote also on
+science, logic, and philosophy.
+
+[714] Joseph Diez Gergonne (1771-1859), a soldier under Napoleon, and
+founder of the _Annales de mathematiques_ (1810).
+
+[715] Gottfried Ploucquet (1716-1790) was at first a clergyman, but
+afterwards became professor of logic at Tuebingen.
+
+[716] "In the premises let the middle term be omitted; what remains
+indicates the conclusion."
+
+[717] Probably Sir William Edmond Logan (1789-1875), who became so
+interested in geology as to be placed at the head of the geological survey
+of Canada (1842). The University of Montreal conferred the title LL.D. upon
+him, and Napoleon III gave him the cross of the Legion of Honor.
+
+[718] "So strike that he may think himself to die."
+
+[719] "Witticism or piece of stupidity."
+
+[720] A very truculently unjust assertion: for Sir W. was as great a setter
+up of some as he was a puller down of others. His writings are a congeries
+of praises and blames, both _cruel smart_, as they say in the States. But
+the combined instigation of prose, rhyme, and retort would send Aristides
+himself to Tartarus, if it were not pretty certain that Minos would grant a
+_stet processus_ under the circumstances. The first two verses are
+exaggerations standing on a basis of truth. The fourth verse is quite true:
+Sir W. H. was an Edinburgh Aristotle, with the difference of ancient and
+modern Athens well marked, especially the _perfervidum ingenium
+Scotorum_.--A. De M.
+
+[721] See note 576, p. 252. There was also a _Theory of Parallels_ that
+differed from these, London, 1853, second edition 1856, third edition 1856.
+
+[722] The work was written by Robert Chambers (1802-1871), the Edinburgh
+publisher, a friend of Scott and of many of his contemporaries in the
+literary field. He published the _Vestiges of the Natural History of
+Creation_ in 1844, not 1840.
+
+[723] Everett (1784-1872) was at that time a good Wesleyan, but was
+expelled from the ministry in 1849 for having written _Wesleyan Takings_
+and as under suspicion for having started the _Fly Sheets_ in 1845. In 1857
+he established the United Methodist Free Church.
+
+[724] Smith was a Primitive Methodist preacher. He also wrote an _Earnest
+Address to the Methodists_ (1841) and _The Wealth Question_ (1840?).
+
+[725] He wrote the _Nouveau traite de Balistique_, Paris, 1837.
+
+[726] Joseph Denison, known to fame only through De Morgan. See also page
+353.
+
+[727] The radical (1784?-1858), advocate of the founding of London
+university (1826), of medical reform (1827-1834), and of the repeal of the
+duties on newspapers and corn, and an ardent champion of penny postage.
+
+[728] I. e., Roman Catholic Priest.
+
+[729] Murphy (1806-1843) showed extraordinary powers in mathematics even
+before the age of thirteen. He became a fellow of Caius College, Cambridge,
+in 1829, dean in 1831, and examiner in mathematics in London University in
+1838.
+
+[730] See note 442, page 196.
+
+[731] Sir John Bowring (1792-1872), the linguist, writer, and traveler,
+member of many learned societies and a writer of high reputation in his
+time. His works were not, however, of genuine merit.
+
+[732] Joseph Hume (1777-1855) served as a surgeon with the British army in
+India early in the nineteenth century. He returned to England in 1808 and
+entered parliament as a radical in 1812. He was much interested in all
+reform movements.
+
+[733] Sir Robert Harry Inglis (1786-1855), a strong Tory, known for his
+numerous addresses in the House of Commons rather than for any real
+ability.
+
+[734] Sir Robert Peel (1788-1850) began his parliamentary career in 1809
+and was twice prime minister. He was prominent in most of the great reforms
+of his time.
+
+[735] See note 627, page 290.
+
+[736] John Taylor (1781-1864) was a publisher, and published several
+pamphlets opposed to Peel's currency measures. De Morgan refers to his work
+on the Junius question. This was done early in his career, and resulted in
+_A Discovery of the author of the Letters of Junius_ (1813), and _The
+Identity of Junius with a distinguished living character established_
+(1816), this being Sir Philip Francis.
+
+[737] See note 665, page 308.
+
+[738] See page 348.
+
+[739] See note 348, page 160.
+
+[740] Sir Nicholas Harris Nicolas (1799-1848) was a reformer in various
+lines,--the Record Commission, the Society of Antiquaries, and the British
+Museum,--and his work was not without good results.
+
+[741] See note 98, page 69.
+
+[742] In the _Companion to the Almanac_ for 1845 is a paper by Prof. De
+Morgan, "On the Ecclesiastical Calendar," the statements of which, so far
+as concerns the Gregorian Calendar, are taken direct from the work of
+Clavius, the principal agent in the arrangement of the reformed reckoning.
+This was followed, in the _Companion to the Almanac_ for 1846, by a second
+paper, by the same author, headed "On the Earliest Printed Almanacs," much
+of which is written in direct supplement to the former article.--S. E. De
+Morgan.
+
+[743] It may be necessary to remind some English readers that in Latin and
+its derived European languages, what we call Easter is called the passover
+(_pascha_). The Quartadecimans had the _name_ on their side: a possession
+which often is, in this world, nine points of the law.--A. De M.
+
+[744] Socrates Scholasticus was born at Constantinople c. 379, and died
+after 439. His _Historia Ecclesiastica_ (in Greek) covers the period from
+Constantine the Great to about 439, and includes the Council of Nicaea. The
+work was printed in Paris 1544.
+
+[745] Theodoretus or Theodoritus was born at Antioch and died about 457. He
+was one of the greatest divines of the fifth century, a man of learning,
+piety, and judicial mind, and a champion of freedom of opinion in all
+religious matters.
+
+[746] He died in 417. He was a man of great energy and of high attainments.
+
+[747] He died in 461, having reigned as pope for twenty-one years. It was
+he who induced Attila to spare Rome in 452.
+
+[748] He succeeded Leo as pope in 461, and reigned for seven years.
+
+[749] Victorinus or Victorius Marianus seems to have been born at Limoges.
+He was a mathematician and astronomer, and the cycle mentioned by De Morgan
+is one of 532 years, a combination of the Metonic cycle of 19 years with
+the solar cycle of 28 years. His canon was published at Antwerp in 1633 or
+1634, _De doctrina temporum sive commentarius in Victorii Aquitani et
+aliorum canones paschales_.
+
+[750] He went to Rome about 497, and died there in 540. He wrote his _Liber
+de paschate_ in 525, and it was in this work that the Christian era was
+first used for calendar purposes.
+
+[751] See note 259, page 126.
+
+[752] Johannes de Sacrobosco (Holy wood), or John of Holywood. The name was
+often written, without regard to its etymology, Sacrobusto. He was educated
+at Oxford and taught in Paris until his death (1256). He did much to make
+the Hindu-Arabic numerals known to European scholars.
+
+[753] See note 36, page 44.
+
+[754] See note 45, page 48.
+
+[755] The Julian year is a year of the Julian Calendar, in which there is
+leap year every fourth year. Its average length is therefore 365 days and a
+quarter.--A. De M.
+
+[756] Ugo Buoncompagno (1502-1585) was elected pope in 1572.
+
+[757] He was a Calabrian, and as early as 1552 was professor of medicine at
+Perugia. In 1576 his manuscript on the reform of the calendar was presented
+to the Roman Curia by his brother, Antonius. The manuscript was not printed
+and it has not been preserved.
+
+[758] The title of this work, which is the authority on all points of the
+new Calendar, is _Kalendarium Gregorianum Perpetuum. Cum Privilegio Summi
+Pontificis Et Aliorum Principum. Romae, Ex Officina Dominici Basae. MDLXXXII.
+Cum Licentia Superiorum_ (quarto, pp. 60).--A. De M.
+
+[759] _Manuels-Roret. Theorie du Calendrier et collection de tous les
+Calendriers des Annees passees et futures_.... Par L. B. Francoeur,...
+Paris, a la librairie encyclopedique de Roret, rue Hautefeuille, 10 bis.
+1842. (12mo.) In this valuable manual, the 35 possible almanacs are given
+at length, with such preliminary tables as will enable any one to find, by
+mere inspection, which almanac he is to choose for any year, whether of old
+or new style. [1866. I may now refer to my own _Book of Almanacs_, for the
+same purpose].--A. De M.
+
+Louis Benjamin Francoeur (1773-1849), after holding positions in the Ecole
+polytechnique (1804) and the Lycee Charlemagne (1805), became professor of
+higher algebra in the University of Paris (1809). His _Cours complet des
+mathematiques pures_ was well received, and he also wrote on mechanics,
+astronomy, and geodesy.
+
+[760] Albertus Pighius, or Albert Pigghe, was born at Kempen c. 1490 and
+died at Utrecht in 1542. He was a mathematician and a firm defender of the
+faith, asserting the supremacy of the Pope and attacking both Luther and
+Calvin. He spent some time in Rome. His greatest work was his _Hierarchiae
+ecclesiasticae assertio_ (1538).
+
+[761] This was A. F. Vogel. The work was his translation from the German
+edition which appeared at Leipsic the same year, _Entdeckung einer
+numerischen General-Aufloesung aller hoeheren endlichen Gleichungen von jeder
+beliebigen algebraischen und transcendenten Form_.
+
+[762] The latest edition of Burnside and Panton's _Theory of Equations_ has
+this brief summary of the present status of the problem: "Demonstrations
+have been given by Abel and Wantzel (see Serret's _Cours d'Algebre
+Superieure_, Art. 516) of the impossibility of resolving algebraically
+equations unrestricted in form, of a degree higher than the fourth. A
+transcendental solution, however, of the quintic has been given by M.
+Hermite, in a form involving elliptic integrals."
+
+[763] There was a second edition of this work in 1846. The author's
+_Astronomy Simplified_ was published in 1838, and the _Thoughts on Physical
+Astronomy_ in 1840, with a second edition in 1842.
+
+[764] This was _The Science of the Weather, by several authors... edited by
+B._, Glasgow, 1867.
+
+[765] This was Y. Ramachandra, son of Sundara L[=a]la. He was a teacher of
+science in Delhi College, and the work to which De Morgan refers is _A
+Treatise on problems of Maxima and Minima solved by Algebra_, which
+appeared at Calcutta in 1850. De Morgan's edition was published at London
+nine years later.
+
+[766] Abraham de Moivre (1667-1754), French refugee in London, poor,
+studying under difficulties, was a man with tastes in some respects like
+those of De Morgan. For one thing, he was a lover of books, and he had a
+good deal of interest in the theory of probabilities to which De Morgan
+also gave much thought. His introduction of imaginary quantities into
+trigonometry was an event of importance in the history of mathematics, and
+the theorem that bears his name, (cos [phi] + i sin [phi])^{n} = cos n[phi]
++ i sin n[phi], is one of the most important ones in all analysis.
+
+[767] John Dolland (1706-1761), the silk weaver who became the greatest
+maker of optical instruments in his time.
+
+[768] Thomas Simpson (1710-1761), also a weaver, taking his leisure from
+his loom at Spitalfields to teach mathematics. His _New Treatise on
+Fluxions_ (1737) was written only two years after he began working in
+London, and six years later he was appointed professor of mathematics at
+Woolwich. He wrote many works on mathematics and Simpson's Formulas for
+computing trigonometric tables are still given in the text-books.
+
+[769] Nicholas Saunderson (1682-1739), the blind mathematician. He lost his
+eyesight through smallpox when only a year old. At the age of 25 he began
+lecturing at Cambridge on the principles of the Newtonian philosophy. His
+_Algebra_, in two large volumes, was long the standard treatise on the
+subject.
+
+[770] He was not in the class with the others mentioned.
+
+[771] Not known in the literature of mathematics.
+
+[772] Probably J. Butler Williams whose _Practical Geodesy_ appeared in
+1842, with a third edition in 1855.
+
+[773] Benjamin Gompertz (1779-1865) was debarred as a Jew from a university
+education. He studied mathematics privately and became president of the
+Mathematical Society. De Morgan knew him professionally through the fact
+that he was prominent in actuarial work.
+
+[774] Referring to the contributions of Archimedes (287-212 B.C.) to the
+mensuration of the sphere.
+
+[775] The famous Alexandrian astronomer (c. 87-c. 165 A.D.), author of the
+_Almagest_, a treatise founded on the works of Hipparchus.
+
+[776] Dr. Whewell, when I communicated this song to him, started the
+opinion, which I had before him, that this was a very good idea, of which
+too little was made.--A. De M.
+
+[777] See note 117, page 76.
+
+[778] The common epithet of rank: _nobilis Tycho_, as he was a nobleman.
+The writer had been at history.--A. De M.
+
+See note 117, page 76.
+
+[779] He lost it in a duel, with Manderupius Pasbergius. A contemporary,
+T. B. Laurus, insinuates that they fought to settle which was the best
+mathematician! This seems odd, but it must be remembered they fought in the
+dark, "_in tenebris densis_"; and it is a nice problem to shave off a nose
+in the dark, without any other harm.--A. De M.
+
+Was this T. B. Laurus Joannes Baptista Laurus or Giovanni Battista Lauro
+(1581-1621), the poet and writer?
+
+[780] See note 117, page 76.
+
+[781] Referring to Kepler's celebrated law of planetary motion. He had
+previously wasted his time on analogies between the planetary orbits and
+the polyhedrons.--A. De M.
+
+[782] See note 117, page 76.
+
+[783] "It does move though."
+
+[784] As great a lie as ever was told: but in 1800 a compliment to Newton
+without a fling at Descartes would have been held a lopsided structure.--A.
+De M.
+
+[785] Jean-le-Rond D'Alembert (1717-1783), the foundling who was left on
+the steps of Jean-le-Rond in Paris, and who became one of the greatest
+mathematical physicists and astronomers of his century.
+
+[786] Leonhard Euler (1707-1783), friend of the Bernoullis, the greatest of
+Swiss mathematicians, prominent in the theory of numbers, and known for
+discoveries in all lines of mathematics as then studied.
+
+[787] See notes 478, 479, page 219.
+
+[788] See note 621, page 288.
+
+[789] See note 584, page 255.
+
+[790] The _siderial_ day is about four minutes short of the solar; there
+are 366 sidereal days in the year.--A. De M.
+
+[791] The founding of the London Mathematical Society is discussed by Mrs.
+De Morgan in her _Memoir_ (p. 281). The idea came from a conversation
+between her brilliant son, George Campbell De Morgan, and his friend Arthur
+Cowper Ranyard in 1864. The meeting of organization was held on Nov. 7,
+1864, with Professor De Morgan in the chair, and the first regular meeting
+on January 16, 1865.
+
+[792] See note 33, page 43.
+
+[793] See note 119, page 80.
+
+[794] John Russell Hind (b. 1823), the astronomer. Between 1847 and 1854 he
+discovered ten planetoids.
+
+[795] Sir Roderick Impey Murchison (1792-1871), the great geologist. He was
+knighted in 1846 and devoted the latter part of his life to the work of the
+Royal Geographical Society and to the geology of Scotland.
+
+[796] Friedrich Wilhelm Bessel (1784-1846), the astronomer and physicist.
+He was professor of astronomy at Koenigsberg.
+
+[797] This was the _Reduction of the Observations of Planets made ... from
+1750 to 1830: computed ... under the superintendence of George Biddell
+Airy_ (1848). See note 129, page 85.
+
+[798] The expense of this magnificent work was defrayed by Government
+grants, obtained, at the instance of the British Association, in 1833--A.
+De M.
+
+[799] See note 32, page 43.
+
+[800] Franz Friedrich Ernst Bruennow (1821-1891) was at that time or shortly
+before director of the observatory at Dusseldorf. He then went to Berlin
+and thence (1854) to Ann Arbor, Michigan. He then went to Dublin and
+finally became Royal Astronomer of Ireland.
+
+[801] Johann Gottfried Galle (1812-1910), at that time connected with the
+Berlin observatory, and later professor of astronomy at Breslau.
+
+[802] George Bishop (1785-1861), in whose observatory in Regent's Park
+important observations were made by Dawes, Hind, and Marth.
+
+[803] James Challis (1803-1882), director of the Cambridge observatory, and
+successor of Airy as Plumian professor of astronomy.
+
+[804] On Leverrier and Arago see note 33, page 43, and note 561, page 243.
+
+[805] Robert Grant's (1814-1892) _History of Physical Astronomy from the
+Earliest Ages to the Middle of the Nineteenth Century_ appeared in 1852. He
+was professor of astronomy and director of the observatory at Glasgow.
+
+[806] John Debenham was more interested in religion than in astronomy. He
+wrote _The Strait Gate; or, the true scripture doctrine of salvation
+clearly explained_, London, 1843, and _Tractatus de magis et Bethlehemae
+stella et Christi in deserto tentatione_, privately printed at London in
+1845.
+
+[807] More properly the Sydney Smirke reading room, since it was built from
+his designs.
+
+[808] The Antinomians were followers of Johannes Agricola (1494-1566). They
+believed that Christians as such were released from all obligations to the
+Old Testament. Some went so far as to assert that, since all Christians
+were sanctified, they could not lose this sanctity even though they
+disobeyed God. The sect was prominent in England in the seventeenth
+century, and was transferred to New England. Here it suffered a check in
+the condemnation of Mrs. Ann Hutchinson (1636) by the Newton Synod.
+
+[809] Aside from this work and his publications on Reeve and Muggleton he
+wrote nothing. With Joseph Frost he published _A list_ _of Books and
+general index to J. Reeve and L. Muggleton's works_ (1846), _Divine Songs
+of the Muggletonians_ (1829), and the work mentioned on page 396. _The
+works of J. Reeve and L. Muggleton_ (1832).
+
+[810] About 1650 he and his cousin John Reeve (1608-1658) began to have
+visions. As part of their creed they taught that astronomy was opposed by
+the Bible. They asserted that the sun moves about the earth, and Reeve
+figured out that heaven was exactly six miles away. Both Muggleton and
+Reeve were imprisoned for their unitarian views. Muggleton wrote a
+_Transcendant Spirituall Treatise_ (1652). I have before me _A true
+Interpretation of All the Chief Texts ... of the whole Book of the
+Revelation of St. John.... By Lodowick Muggleton, one of the two last
+Commissioned Witnesses & Prophets of the onely high, immortal, glorious
+God, Christ Jesus_ (1665), in which the interpretation of the "number of
+the beast" occupies four pages without arriving anywhere.
+
+[811] In 1652 he was, in a vision, named as the Lord's "last messenger,"
+with Muggleton as his "mouth," and died six years later, probably of
+nervous tension resulting from his divine "illumination." He was the more
+spiritual of the two.
+
+[812] William Guthrie (1708-1770) was a historian and political writer. His
+_History of England_ (1744-1751) was the first attempt to base history on
+parliamentary records. He also wrote a _General History of Scotland_ in 10
+volumes (1767). The work to which Frost refers is the _Geographical,
+Historical, and Commercial Grammar_ (1770) which contained an astronomical
+part by J. Ferguson. By 1827 it had passed through 24 editions.
+
+[813] George Fox (1624-1691), founder of the Society of Friends; a mystic
+and a disciple of Boehme. He was eight times imprisoned for heresy.
+
+[814] If they were friends they were literary antagonists, for Muggleton
+wrote against Fox _The Neck of the Quakers Broken_ (1663), and Fox replied
+in 1667. Muggleton also wrote _A Looking Glass for George Fox_.
+
+[815] John Conduitt (1688-1737), who married (1717) Newton's half niece,
+Mrs. Katherine Barton. See note 284, page 136.
+
+[816] Probably Peter Mark Roget's (1779-1869) _Thesaurus of English Words_
+(1852) is not much used at present, but it went through 28 editions in his
+lifetime. Few who use the valuable work are aware that Roget was a
+professor of physiology at the Royal Institution (London), that he achieved
+his title of F. R. S. because of his work in perfecting the slide rule, and
+that he followed Sir John Herschel as secretary of the Royal Society.
+
+[817] See note 703, page 327. This work went into a second edition in the
+year of its first publication.
+
+[818] See note 398, page 177.
+
+[819] See note 528, page 233.
+
+[820] George Jacob Holyoake (1817-1906) entered into a controversial life
+at an early age. In 1841 he was imprisoned for six months for blasphemy. He
+founded and edited _The Reasoner_ (Vols. 1-26, 1846-1861). In his later
+life he did much to promote cooperation among the working class.
+
+[821] See note 176, page 102.
+
+[822] William Thomas Lowndes (1798-1843), whose _Bibliographer's Manual of
+English Literature_, 4 vols., London, 1834 (also 1857-1864, and 1869) is a
+classic in its line.
+
+[823] Jacques Charles Brunet (1780-1867), the author of the great French
+bibliography, the _Manuel du Libraire_ (1810).
+
+       *       *       *       *       *
+
+
+Corrections made to printed original.
+
+Page 5, "direct acquaintance with the whole of his mental ancestry":
+'acquantance' in original.
+
+Page 100, "The error is at the rate": 'it' (for 'is') in original.
+
+Page 192, "the lineal successor of the Repository association":
+'successsor' in original.
+
+Page 211, "the doctors had finished their compliments": 'docters' in
+original.
+
+Page 302, "causing mutual perturbations": 'peturbations' in original.
+
+Page 344, "The work itself is described": 'decribed' in original.
+
+Page 370, The entry for 1852 is printed as 19, it appears that the correct
+value should be 9.
+
+Page 392, "Sir John Herschel's previous communication": 'pervious' in
+original.
+
+Note 317, "he constructed a working model of a steam road carriage":
+'contructed' in original.
+
+Note 380, "the variation of the Earth's Diameters": 'Diaameters' in
+original.
+
+Note 550, "The first edition of the anonymous [Greek]": 'anonynous' in
+original.
+
+
+
+
+
+
+End of the Project Gutenberg EBook of A Budget of Paradoxes, Volume I (of II), by
+Augustus De Morgan
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