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diff --git a/23100-8.txt b/23100-8.txt new file mode 100644 index 0000000..8d0d3bb --- /dev/null +++ b/23100-8.txt @@ -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: 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 | 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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 *** + +***** This file should be named 23100-8.txt or 23100-8.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/2/3/1/0/23100/ + +Produced by David Starner, Keith Edkins and the Online +Distributed Proofreading Team at http://www.pgdp.net + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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