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You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: A Budget of Paradoxes, Volume I (of II) + +Author: Augustus De Morgan + +Editor: David Eugene Smith + +Release Date: October 20, 2007 [EBook #23100] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK A BUDGET OF PARADOXES *** + + + + +Produced by David Starner, Keith Edkins and the Online +Distributed Proofreading Team at http://www.pgdp.net + + + + + + +</pre> + + +<table border="0" cellpadding="10" style="background-color: #ccccff;"> +<tr> +<td style="width:25%; vertical-align:top"> +Transcriber's note: +</td> +<td> +A few typographical errors have been corrected. They +appear in the text <span class="correction" title="explanation will pop up">like this</span>, and the +explanation will appear when the mouse pointer is moved over the marked +passage. +</td> +</tr> +</table> + +<h3>BY AUGUSTUS DE MORGAN</h3> + +<h1>A BUDGET OF<br /> +PARADOXES</h1> + +<p class="cenhead"><span class="scac">REPRINTED WITH THE AUTHOR'S ADDITIONS FROM THE ATHENAEUM</span></p> + + <p> </p> + +<p class="cenhead">SECOND EDITION EDITED BY DAVID EUGENE SMITH</p> + +<p class="cenhead">WITH A NEW INTRODUCTION BY ERNEST NAGEL</p> + +<p class="cenhead">PROFESSOR OF PHILOSOPHY, COLUMBIA UNIVERSITY</p> + +<p class="cenhead">UNABRIDGED EDITION—TWO VOLUMES BOUND AS ONE</p> + + <p> </p> + +<h1>Volume I</h1> + + <p> </p> + +<p class="cenhead">DOVER PUBLICATIONS, INC., NEW YORK</p> + +<hr class="full" > + +<h3>PREFACE TO THE FIRST EDITION.</h3> + +<p class="cenhead">(1872)</p> + + <p>It is not without hesitation that I have taken upon myself the + editorship of a work left avowedly imperfect by the author, and, from its + miscellaneous and discursive character, difficult of completion with due + regard to editorial limitations by a less able hand.</p> + + <p>Had the author lived to carry out his purpose he would have looked + through his Budget again, amplifying and probably rearranging some of its + contents. He had collected materials for further illustration of Paradox + of the kind treated of in this book; and he meant to write a second part, + in which the contradictions and inconsistencies of orthodox learning + would have been subjected to the same scrutiny and castigation as + heterodox ignorance had already received.</p> + + <p>It will be seen that the present volume contains more than the + <i>Athenæum</i> Budget. Some of the additions formed a Supplement to the + original articles. These supplementary paragraphs were, by the author, + placed after those to which they respectively referred, being + distinguished from the rest of the text by brackets. I have omitted these + brackets as useless, except where they were needed to indicate subsequent + writing.</p> + + <p>Another and a larger portion of the work consists of discussion of + matters of contemporary interest, for the Budget was in some degree a + receptacle for the author's thoughts on any literary, scientific, or + social question. Having grown thus gradually to its present size, the + book as it was left was not quite in a fit condition for publication, but + the alterations which have been made are slight and few, being in most + cases verbal, and such as the sense absolutely required, or + transpositions of sentences to secure coherence with the rest, in places + where the author, in his more recent insertion of them, had overlooked + the connection in which they stood. In no case has the meaning been in + any degree modified or interfered with.</p> + + <p>One rather large omission must be mentioned here. It is an account of + the quarrel between Sir James South and Mr. Troughton on the mounting, + etc. of the equatorial telescope at Campden Hill. At some future time + when the affair has passed entirely out of the memory of living + Astronomers, the appreciative sketch, which is omitted in this edition of + the Budget, will be an interesting piece of history and study of + character.<a name="NtA_1" href="#Nt_1"><sup>[1]</sup></a></p> + + <p>A very small portion of Mr. James Smith's circle-squaring has been + left out, with a still smaller portion of Mr. De Morgan's answers to that + Cyclometrical Paradoxer.</p> + + <p>In more than one place repetitions, which would have disappeared under + the author's revision, have been allowed to remain, because they could + not have been taken away without leaving a hiatus, not easy to fill up + without damage to the author's meaning.</p> + + <p>I give these explanations in obedience to the rules laid down for the + guidance of editors at page <a href="#page15">15</a>.<a name="NtA_2" + href="#Nt_2"><sup>[2]</sup></a> If any apology for the fragmentary + character of the book be thought necessary, it may be found in the + author's own words at page 281 of the second volume.<a name="NtA_3" + href="#Nt_3"><sup>[3]</sup></a></p> + + <p>The publication of the Budget could not have been delayed without + lessening the interest attaching to the writer's thoughts upon questions + of our own day. I trust that, incomplete as the work is compared with + what it might have been, I shall not be held mistaken in giving it to the + world. Rather let me hope that it will be welcomed as an old friend + returning under great disadvantages, but bringing a pleasant remembrance + of the amusement which its weekly appearance in the <i>Athenæum</i> gave + to both writer and reader.</p> + + <p>The Paradoxes are dealt with in chronological order. This will be a + guide to the reader, and with the alphabetical Index of Names, etc., + will, I trust, obviate all difficulty of reference.</p> + + <p class="author"><span class="sc">Sophia De Morgan</span>. + +<blockquote class="b1n"> + + <p>6 <span class="sc">Merton Road, Primrose Hill</span>.</p> + +</blockquote> + +<hr class="full" > + +<h3>PREFACE TO THE SECOND EDITION.</h3> + + <p>If Mrs. De Morgan felt called upon to confess her hesitation at taking + upon herself the labor of editing these Paradoxes, much more should one + who was born two generations later, who lives in another land and who was + reared amid different influences, confess to the same feeling when + undertaking to revise this curious medley. But when we consider the + nature of the work, the fact that its present rarity deprives so many + readers of the enjoyment of its delicious satire, and the further fact + that allusions that were commonplace a half century ago are now + forgotten, it is evident that some one should take up the work and + perform it <i>con amore</i>.</p> + + <p>Having long been an admirer of De Morgan, having continued his work in + the bibliography of early arithmetics, and having worked in his library + among the books of which he was so fond, it is possible that the present + editor, whatever may be his other shortcomings, may undertake the labor + with as much of sympathy as any one who is in a position to perform it. + With this thought in mind, two definite rules were laid down at the + beginning of the task: (1) That no alteration in the text should be made, + save in slightly modernizing spelling and punctuation and in the case of + manifest typographical errors; (2) That whenever a note appeared it + should show at once its authorship, to the end that the material of the + original edition might appear intact.</p> + + <p>In considering, however, the unbroken sequence of items that form the + Budget, it seems clear that readers would be greatly aided if the various + leading topics were separated in some convenient manner. After + considerable thought it was decided to insert brief captions from time to + time that might aid the eye in selecting the larger subjects of the text. + In some parts of the work these could easily be taken from the original + folio heads, but usually they had to be written anew. While, therefore, + the present editor accepts the responsibility for the captions of the + various subdivisions, he has endeavored to insert them in harmony with + the original text.</p> + + <p>As to the footnotes, the first edition had only a few, some due to De + Morgan himself and others to Mrs. De Morgan. In the present edition those + due to the former are signed A. De M., and those due to Mrs. De Morgan + appear with her initials, S. E. De M. For all other footnotes the present + editor is responsible. In preparing them the effort has been made to + elucidate the text by supplying such information as the casual reader + might wish as he passes over the pages. Hundreds of names are referred to + in the text that were more or less known in England half a century ago, + but are now forgotten there and were never familiar elsewhere. Many books + that were then current have now passed out of memory, and much that + agitated England in De Morgan's prime seems now like ancient history. + Even with respect to well-known names, a little information as to dates + and publications will often be welcome, although the editor recognizes + that it will quite as often be superfluous. In order, therefore, to + derive the pleasure that should come from reading the Budget, the reader + should have easy access to the information that the notes are intended to + supply. That they furnish too much here and too little there is to be + expected. They are a human product, and if they fail to serve their + purpose in all respects it is hoped that this failure will not seriously + interfere with the reader's pleasure.</p> + + <p>In general the present editor has refrained from expressing any + opinions that would strike a discordant note in the reading of the text + as De Morgan left it. The temptation is great to add to the discussion at + various points, but it is a temptation to be resisted. To furnish such + information as shall make the reading more pleasant, rather than to + attempt to improve upon one of the most delicious bits of satire of the + nineteenth century, has been the editor's wish. It would have been an + agreeable task to review the history of circle squaring, of the + trisection problem, and of the duplication of the cube. This, however, + would be to go too far afield. For the benefit of those who wish to + investigate the subject the editor can only refer to such works and + articles as the following: F. Rudio, <i>Archimedes, Huygens, Lambert, + Legendre,—mit einer Uebersicht über die Geschichte des Problemes + von der Quadratur des Zirkels</i>, Leipsic, 1892; Thomas Muir, "Circle," + in the eleventh edition of the <i>Encyclopædia Britannica</i>; the + various histories of mathematics; and to his own article on "The + Incommensurability of <span class="grk">π</span>" in Prof. J. W. A. + Young's <i>Monographs on Topics of Modern Mathematics</i>, New York, + 1911.</p> + + <p>The editor wishes to express his appreciation and thanks to Dr. Paul + Carus, editor of <i>The Monist</i> and <i>The Open Court</i> for the + opportunity of undertaking this work; to James Earl Russell, LL.D., Dean + of Teachers College, Columbia University, for his encouragement in its + prosecution; to Miss Caroline Eustis Seely for her intelligent and + painstaking assistance in securing material for the notes; and to Miss + Lydia G. Robinson and Miss Anna A. Kugler for their aid and helpful + suggestions in connection with the proof-sheets. Without the generous + help of all five this work would have been impossible.</p> + + <p class="author"><span class="sc">David Eugene Smith</span>. + +<blockquote class="b1n"> + + <p><span class="sc">Teachers College, Columbia University</span>.</p> + +</blockquote> + +<hr class="full" > + +<h2>A BUDGET OF PARADOXES</h2> + +<p><!-- Page 1 --><span class="pagenum"><a name="page1"></a>[1]</span></p> + +<h3>INTRODUCTORY.</h3> + + <p>If I had before me a fly and an elephant, having never seen more than + one such magnitude of either kind; and if the fly were to endeavor to + persuade me that he was larger than the elephant, I might by possibility + be placed in a difficulty. The apparently little creature might use such + arguments about the effect of distance, and might appeal to such laws of + sight and hearing as I, if unlearned in those things, might be unable + wholly to reject. But if there were a thousand flies, all buzzing, to + appearance, about the great creature; and, to a fly, declaring, each one + for himself, that he was bigger than the quadruped; and all giving + different and frequently contradictory reasons; and each one despising + and opposing the reasons of the others—I should feel quite at my + ease. I should certainly say, My little friends, the case of each one of + you is destroyed by the rest. I intend to show flies in the swarm, with a + few larger animals, for reasons to be given.</p> + + <p>In every age of the world there has been an established system, which + has been opposed from time to time by isolated and dissentient reformers. + The established system has sometimes fallen, slowly and gradually: it has + either been upset by the rising influence of some one man, or it has been + sapped by gradual change of opinion in the many.</p> + + <p>I have insisted on the isolated character of the dissentients, as an + element of the <i>a priori</i> probabilities of the case. Show me a + schism, especially a growing schism, and it is another thing. The + homeopathists, for instance, shall be, if any one so think, as wrong as + St. John Long; but an <!-- Page 2 --><span class="pagenum"><a + name="page2"></a>[2]</span>organized opposition, supported by the efforts + of many acting in concert, appealing to common arguments and experience, + with perpetual succession and a common seal, as the Queen says in the + charter, is, be the merit of the schism what it may, a thing wholly + different from the case of the isolated opponent in the mode of + opposition to it which reason points out.</p> + + <p>During the last two centuries and a half, physical knowledge has been + gradually made to rest upon a basis which it had not before. It has + become <i>mathematical</i>. The question now is, not whether this or that + hypothesis is better or worse to the pure thought, but whether it accords + with observed phenomena in those consequences which can be shown + necessarily to follow from it, if it be true. Even in those sciences + which are not yet under the dominion of mathematics, and perhaps never + will be, a working copy of the mathematical process has been made. This + is not known to the followers of those sciences who are not themselves + mathematicians and who very often exalt their horns against the + mathematics in consequence. They might as well be squaring the circle, + for any sense they show in this particular.</p> + + <p>A great many individuals, ever since the rise of the mathematical + method, have, each for himself, attacked its direct and indirect + consequences. I shall not here stop to point out how the very accuracy of + exact science gives better aim than the preceding state of things could + give. I shall call each of these persons a <i>paradoxer</i>, and his + system a <i>paradox</i>. I use the word in the old sense: a paradox is + something which is apart from general opinion, either in subject-matter, + method, or conclusion.</p> + + <p>Many of the things brought forward would now be called + <i>crotchets</i>, which is the nearest word we have to old + <i>paradox</i>. But there is this difference, that by calling a thing a + <i>crotchet</i> we mean to speak lightly of it; which was not the + necessary sense of <i>paradox</i>. Thus in the sixteenth century many + spoke of the earth's motion as the <i>paradox of <!-- Page 3 --><span + class="pagenum"><a name="page3"></a>[3]</span>Copernicus</i>, who held + the ingenuity of that theory in very high esteem, and some, I think, who + even inclined towards it. In the seventeenth century, the depravation of + meaning took place, in England at least. Phillips says <i>paradox</i> is + "a thing which seemeth strange"—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.</p> + + <p>Some of my readers are hardly inclined to think that the word + <i>paradox</i> could once have had no disparagement in its meaning; still + less that persons could have applied it to themselves. I chance to have + met with a case in point against them. It is Spinoza's <i>Philosophia + Scripturæ Interpres, Exercitatio Paradoxa</i>, printed anonymously at + Eleutheropolis, in 1666. This place was one of several cities in the + clouds, to which the cuckoos resorted who were driven away by the other + birds; that is, a feigned place of printing, adopted by those who would + have caught it if orthodoxy could have caught them. Thus, in 1656, the + works of Socinus could only be printed at Irenopolis. The author deserves + his self-imposed title, as in the following:<a name="NtA_4" + href="#Nt_4"><sup>[4]</sup></a></p> + + <p>"Quanto sane satius fuisset illam [Trinitatem] pro mysterio non + habuisse, et Philosophiæ ope, antequam quod esset statuerent, secundum + veræ logices præcepta quid esset cum Cl. Kleckermanno investigasse; tanto + fervore ac labore in profundissimas speluncas et obscurissimos + metaphysicarum speculationum atque fictionum recessus se recipere ut ab + adversariorum telis sententiam suam in tuto collocarent. <!-- Page 4 + --><span class="pagenum"><a name="page4"></a>[4]</span>Profecto magnus + ille vir ... dogma illud, quamvis apud theologos eo nomine non multum + gratiæ iniverit, ita ex immotis Philosophiæ fundamentis explicat ac + demonstrat, ut paucis tantum immutatis, atque additis, nihil amplius + animus veritate sincere deditus desiderare possit."</p> + + <p>This is properly paradox, though also heterodox. It supposes, contrary + to all opinion, orthodox and heterodox, that philosophy can, with slight + changes, explain the Athanasian doctrine so as to be at least compatible + with orthodoxy. The author would stand almost alone, if not quite; and + this is what he meant. I have met with the counter-paradox. I have heard + it maintained that the doctrine as it stands, in all its mystery is <i>a + priori</i> more likely than any other to have been Revelation, if such a + thing were to be; and that it might almost have been predicted.</p> + + <p>After looking into books of paradoxes for more than thirty years, and + holding conversation with many persons who have written them, and many + who might have done so, there is one point on which my mind is fully made + up. The manner in which a paradoxer will show himself, as to sense or + nonsense, will not depend upon what he maintains, but upon whether he has + or has not made a sufficient knowledge of what has been done by others, + <i>especially as to the mode of doing it</i>, a preliminary to inventing + knowledge for himself. That a little knowledge is a dangerous thing is + one of the most fallacious of proverbs. A person of small knowledge is in + danger of trying to make his <i>little</i> do the work of <i>more</i>; + but a person without any is in more danger of making his <i>no</i> + knowledge do the work of <i>some</i>. Take the speculations on the tides + as an instance. Persons with nothing but a little geometry have certainly + exposed themselves in their modes of objecting to results which require + the higher mathematics to be known before an independent opinion can be + formed on sufficient grounds. But persons with no geometry at all have + done the same thing much more completely. <!-- Page 5 --><span + class="pagenum"><a name="page5"></a>[5]</span></p> + + <p>There is a line to be drawn which is constantly put aside in the + arguments held by paradoxers in favor of their right to instruct the + world. Most persons must, or at least will, like the lady in Cadogan + Place,<a name="NtA_5" href="#Nt_5"><sup>[5]</sup></a> form and express an + immense variety of opinions on an immense variety of subjects; and all + persons must be their own guides in many things. So far all is well. But + there are many who, in carrying the expression of their own opinions + beyond the usual tone of private conversation, whether they go no further + than attempts at oral proselytism, or whether they commit themselves to + the press, do not reflect that they have ceased to stand upon the ground + on which their process is defensible. Aspiring to lead <i>others</i>, + they have never given themselves the fair chance of being first led by + <i>other</i> others into something better than they can start for + themselves; and that they should first do this is what both those classes + of others have a fair right to expect. New knowledge, when to any + purpose, must come by contemplation of old knowledge in every matter + which concerns thought; mechanical contrivance sometimes, not very often, + escapes this rule. All the men who are now called discoverers, in every + matter ruled by thought, have been men versed in the minds of their + predecessors, and learned in what had been before them. There is not one + exception. I do not say that every man has made direct <span + class="correction" title="text reads `acquantance'">acquaintance</span> + with the whole of his mental ancestry; many have, as I may say, only + known their grandfathers by the report of their fathers. But even on this + point it is remarkable how many of the greatest names in all departments + of knowledge have been real antiquaries in their several subjects.</p> + + <p>I may cite, among those who have wrought strongly upon opinion or + practice in science, Aristotle, Plato, Ptolemy, Euclid, Archimedes, Roger + Bacon, Copernicus, Francis Bacon, Ramus, Tycho Brahé, Galileo, Napier, + Descartes, Leibnitz, Newton, Locke. I take none but names known out of + their <!-- Page 6 --><span class="pagenum"><a + name="page6"></a>[6]</span>fields of work; and all were learned as well + as sagacious. I have chosen my instances: if any one will undertake to + show a person of little or no knowledge who has established himself in a + great matter of pure thought, let him bring forward his man, and we shall + see.</p> + + <p>This is the true way of putting off those who plague others with their + great discoveries. The first demand made should be—Mr. Moses, + before I allow you to lead me over the Red Sea, I must have you show that + you are learned in all the wisdom of the Egyptians upon your own subject. + The plea that it is unlikely that this or that unknown person should + succeed where Newton, etc. have failed, or should show Newton, etc. to be + wrong, is utterly null and void. It was worthily versified by Sylvanus + Morgan (the great herald who in his <i>Sphere of Gentry</i> gave coat + armor to "Gentleman Jesus," as he said), who sang of Copernicus as + follows (1652):</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"If Tellus winged be,</p> + <p>The earth a motion round;</p> + <p>Then much deceived are they</p> + <p>Who nere before it found.</p> + <p>Solomon was the wisest,</p> + <p>His wit nere this attained;</p> + <p>Cease, then, Copernicus,</p> + <p>Thy hypothesis is vain."</p> + </div> + </div> + <p>Newton, etc. were once unknown; but they made themselves known by what + they knew, and then brought forward what they could do; which I see is as + good verse as that of Herald Sylvanus. The demand for previous knowledge + disposes of twenty-nine cases out of thirty, and the thirtieth is worth + listening to.</p> + + <p>I have not set down Copernicus, Galileo, etc. among the paradoxers, + merely because everybody knows them; if my list were quite complete, they + would have been in it. But the reader will find Gilbert, the great + precursor of sound magnetical theory; and several others on whom no + censure can be cast, though some of their paradoxes are inadmissible, + <!-- Page 7 --><span class="pagenum"><a name="page7"></a>[7]</span>some + unprovoked, and some capital jokes, true or false: the author of + <i>Vestiges of Creation</i> is an instance. I expect that my old + correspondent, General Perronet Thompson, will admit that his geometry is + part and parcel of my plan; and also that, if that plan embraced + politics, he would claim a place for his <i>Catechism on the Corn + Laws</i>, a work at one time paradoxical, but which had more to do with + the abolition of the bread-tax than Sir Robert Peel.</p> + + <p>My intention in publishing this Budget in the <i>Athenæum</i> is <i>to + enable those who have been puzzled by one or two discoverers to see how + they look in a lump</i>. The only question is, has the selection been + fairly made? To this my answer is, that no selection at all has been + made. The books are, without exception, those which I have in my own + library; and I have taken <i>all</i>—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 <i>undescribed</i> portion of + miscellaneous auction lots; I have received a few from friends who found + them among what they called their rubbish; and I have preserved books + sent to me for review. In not a few instances the books have been bound + up with others, unmentioned at the back; and for years I knew no more I + had them than I knew I had Lord Macclesfield's speech on moving the + change of Style, which, after I had searched shops, etc. for it in vain, + I found had been reposing on my own shelves for many years, at the end of + a summary of Leibnitz's philosophy. Consequently, I may positively affirm + that the following list is formed by accident and circumstance alone, and + that it truly represents the casualties of about a third of a century. + For instance, the large proportion of works <!-- Page 8 --><span + class="pagenum"><a name="page8"></a>[8]</span>on the quadrature of the + circle is not my doing: it is the natural share of this subject in the + actual run of events.</p> + + <p>[I keep to my plan of inserting only such books as I possessed in + 1863, except by casual notice in aid of my remarks. I have found several + books on my shelves which ought to have been inserted. These have their + titles set out at the commencement of their articles, in leading + paragraphs; the casuals are without this formality.<a name="NtA_6" + href="#Nt_6"><sup>[6]</sup></a>]</p> + + <p>Before proceeding to open the Budget, I say something on my personal + knowledge of the class of discoverers who square the circle, upset + Newton, etc. I suspect I know more of the English class than any man in + Britain. I never kept any reckoning; but I know that one year with + another—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 + <i>bona fide</i> 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.</p> + + <p>These discoverers despise one another: if there were the concert among + them which there is among foreign mendicants, a man who admitted one to a + conference would be plagued to death. I once gave something to a very + genteel French applicant, who overtook me in the street, at my own door, + saying he had picked up my handkerchief: whether he picked it up in my + pocket for an introduction, I know not. <!-- Page 9 --><span + class="pagenum"><a name="page9"></a>[9]</span>But that day week came + another Frenchman to my house, and that day fortnight a French lady; both + failed, and I had no more trouble. The same thing happened with Poles. It + is not so with circle-squarers, etc.: they know nothing of each other. + Some will read this list, and will say I am right enough, generally + speaking, but that there <i>is</i> an exception, if I could but see + it.</p> + + <p>I do not mean, by my confession of the manner in which I have sinned + against the twenty-four hours, to hold myself out as accessible to + personal explanation of new plans. Quite the contrary: I consider myself + as having made my report, and being discharged from further attendance on + the subject. I will not, from henceforward, talk to any squarer of the + circle, trisector of the angle, duplicator of the cube, constructor of + perpetual motion, subverter of gravitation, stagnator of the earth, + builder of the universe, etc. I will receive any writings or books which + require no answer, and read them when I please: I will certainly preserve + them—this list may be enlarged at some future time.</p> + + <p>There are three subjects which I have hardly anything upon; astrology, + mechanism, and the infallible way of winning at play. I have never cared + to preserve astrology. The mechanists make models, and not books. The + infallible winners—though I have seen a few—think their + secret too valuable, and prefer <i>mutare quadrata rotundis</i>—to + turn dice into coin—at the gaming-house: verily they have their + reward.</p> + + <p>I shall now select, to the mystic number seven, instances of my + personal knowledge of those who think they have discovered, in + illustration of as many misconceptions.</p> + + <p>1. <i>Attempt by help of the old philosophy, the discoverer not being + in possession of modern knowledge.</i> A poor schoolmaster, in rags, + introduced himself to a scientific friend with whom I was talking, and + announced that he had found out the composition of the sun. "How was that + done?"—"By consideration of the four elements."—"What are + <!-- Page 10 --><span class="pagenum"><a + name="page10"></a>[10]</span>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?"</p> + + <p>2. <i>The notion that difficulties are enigmas, to be overcome in a + moment by a lucky thought.</i> A nobleman of very high rank, now long + dead, read an article by me on the quadrature, in an early number of the + <i>Penny Magazine</i>. He had, I suppose, school recollections of + geometry. He put pencil to paper, drew a circle, and constructed what + seemed likely to answer, and, indeed, was—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.</p> + + <p>3. <i>Discovery at all hazards, to get on in the world.</i> Thirty + years ago, an officer of rank, just come from foreign service, and trying + for a decoration from the Crown, found that his claims were of doubtful + amount, and was told by a friend that so and so, who had got the order, + had the additional claim of scientific distinction. Now this officer, + while abroad, had bethought himself one day, that there really could be + no difficulty in finding the circumference of a circle: if a circle were + rolled upon a straight line until the undermost point came undermost + again, there would be the straight line equal to the circle. He came to + me, saying that he did not feel equal to the statement of his claim in + this respect, but that if some clever fellow would put the thing in a + proper light, he thought his affair might be managed. I was clever enough + to put the thing in a proper light to himself, to this extent at least, + that, though perhaps they were wrong, the advisers of the Crown would + never put the letters K.C.B. to such a circle as his.</p> + + <p>4. <i>The notion that mathematicians cannot find the circle for common + purposes.</i> A working man measured the altitude of a cylinder + accurately, and—I think the process of <!-- Page 11 --><span + class="pagenum"><a name="page11"></a>[11]</span>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 <i>Astronomical + Memoirs</i>, in which were a large number of observed places of the + planets compared with prediction, and asked him whether it could be + possible that persons who did not know the circle better than he had + found it could make the calculations, of which I gave him a notion, so + accurately? He was perfectly astonished, and took the titles of some + books which he said he would read.</p> + + <p>5. <i>Application for the reward from abroad.</i> Many years ago, + about twenty-eight, I think, a Jesuit came from South America, with a + quadrature, and a cutting from a newspaper announcing that a reward was + ready for the discovery in England. On this evidence he came over. After + satisfying him that nothing had ever been offered here, I discussed his + quadrature, which was of no use. I succeeded better when I told him of + Richard White, also a Jesuit, and author of a quadrature published before + 1648, under the name of <i>Chrysæspis</i>, of which I can give no + account, having never seen it. This White (<i>Albius</i>) is the only + quadrator who was ever convinced of his error. My Jesuit was struck by + the instance, and promised to read more geometry—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 <!-- Page 12 --><span class="pagenum"><a + name="page12"></a>[12]</span>Jesuit did not send me a copy, which he + ought to have done, after the hour I had given him.</p> + + <p>6. <i>Application for the reward at home.</i> An agricultural laborer + squared the circle, and brought the proceeds to London. He left his + papers with me, one of which was the copy of a letter to the Lord + Chancellor, desiring his Lordship to hand over forthwith 100,000 pounds, + the amount of the alleged offer of reward. He did not go quite so far as + M. de Vausenville, who, I think in 1778, brought an action against the + Academy of Sciences to recover a reward to which he held himself + entitled. I returned the papers, with a note, stating that he had not the + knowledge requisite to see in what the problem consisted. I got for + answer a letter in which I was told that a person who could not see that + he had done the thing should "change his business, and appropriate his + time and attention to a Sunday-school, to learn what he could, and keep + the <i>litle</i> children from <i>durting</i> their <i>close</i>." I also + received a letter from a friend of the quadrator, informing me that I + knew his friend had succeeded, and had been heard to say so. These + letters were printed—without the names of the writers—for the + amusement of the readers of <i>Notes and Queries</i>, First Series, xii. + 57, and they will appear again in the sequel.</p> + + <p>[There are many who have such a deep respect for any attempt at + thought that they are shocked at ridicule even of those who have made + themselves conspicuous by pretending to lead the world in matters which + they have not studied. Among my anonyms is a gentleman who is angry at my + treatment of the "poor but thoughtful" man who is described in my + introduction as recommending me to go to a Sunday-school because I + informed him that he did not know in what the difficulty of quadrature + consisted. My impugner quite forgets that this man's "thoughtfulness" + chiefly consisted in his demanding a hundred thousand pounds from the + Lord Chancellor for his discovery; and I may add, that his greatest + stretch of invention was finding out that "the clergy" <!-- Page 13 + --><span class="pagenum"><a name="page13"></a>[13]</span>were the means + of his modest request being unnoticed. I mention this letter because it + affords occasion to note a very common error, namely, that men unread in + their subjects have, by natural wisdom, been great benefactors of + mankind. My critic says, "Shakspeare, whom the Pro<sup>r</sup> + (<i>sic</i>) may admit to be a wisish man, though an object of contempt + as to learning ..." Shakespeare an object of contempt as to learning! + Though not myself a thoroughgoing Shakespearean—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 <i>some</i>, even when he was depreciating. To have any + Greek at all was in those days exceptional. In Shakespeare's youth St. + Paul's and Merchant Taylor's schools were to have masters learned in good + and clean Latin literature, <i>and also in Greek if such may be + gotten</i>. When Jonson spoke as above, he intended to put Shakespeare + low among the learned, but not out of their pale; and he spoke as a rival + dramatist, who was proud of his own learned sock; and it may be a subject + of inquiry how much Latin <i>he</i> would call <i>little</i>. If + Shakespeare's learning on certain points be very much less visible than + Jonson's, it is partly because Shakespeare's writings hold it in chemical + combination, Jonson's in mechanical aggregation.]</p> + + <p>7. An elderly man came to me to show me how the universe was created. + There was one molecule, which by vibration became—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 <!-- Page 14 + --><span class="pagenum"><a name="page14"></a>[14]</span>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.</p> + + <p>My list is given in chronological order. My readers will understand + that my general expressions, where slighting or contemptuous, refer to + the ignorant, who teach before they have learned. In every instance, + those of whom I am able to speak with respect, whether as right or wrong, + have sought knowledge in the subject they were to handle before they + completed their speculations. I shall further illustrate this at the + conclusion of my list.</p> + + <p>Before I begin the list, I give prominence to the following letter, + addressed by me to the <i>Correspondent</i> of October 28, 1865. Some of + my paradoxers attribute to me articles in this or that journal; and + others may think—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. <!-- Page 15 --><span class="pagenum"><a + name="page15"></a>[15]</span></p> + +<hr class="short" > + +<p class="cenhead">THE EDITORIAL SYSTEM.</p> + + <p>"Sir,—I have reason to think that many persons have a very + inaccurate notion of the <i>Editorial System</i>. What I call by this + name has grown up in the last <i>centenary</i>—a word I may use to + signify the hundred years now ending, and to avoid the ambiguity of + <i>century</i>. It cannot conveniently be explained by editors + themselves, and <i>edited</i> journals generally do not like to say much + about it. In <i>your</i> paper perhaps, in which editorial duties differ + somewhat from those of ordinary journals, the common system may be freely + spoken of.</p> + + <p>"When a reviewed author, as very often happens, writes to the editor + of the reviewing journal to complain of what has been said of him, he + frequently—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.</p> + + <p>"All that is in a journal, except what is marked as from a + correspondent, either by the editor himself or by the correspondent's + real or fictitious signature, is published entirely on editorial + responsibility, as much as if the editor had written it himself. The + editor, therefore, may claim, and does claim and exercise, unlimited + right of omission, addition, and alteration. This is so well understood + that the editor performs his last function on the last revise without the + 'contributor' knowing what is done. The word <i>contributor</i> is the + proper one; it implies that he furnishes materials without stating what + he furnishes or how much of it is accepted, or whether he be the only + contributor. All this applies both to political and literary journals. No + editor acknowledges <!-- Page 16 --><span class="pagenum"><a + name="page16"></a>[16]</span>the right of a contributor to withdraw an + article, if he should find alterations in the proof sent to him for + correction which would make him wish that the article should not appear. + If the <i>demand</i> for suppression were made—I say nothing about + what might be granted to <i>request</i>—the answer would be, 'It is + not your article, but mine; I have all the responsibility; if it should + contain a libel, I could not give you up, even at your own desire. You + have furnished me with materials, on the known and common understanding + that I was to use them at my discretion, and you have no right to impede + my operations by making the appearance of the article depend on your + approbation of my use of your materials.'</p> + + <p>"There is something to be said for this system, and something against + it—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 <!-- Page 17 --><span class="pagenum"><a + name="page17"></a>[17]</span>the contributor is likely to know his + business better than an editor can teach him; in fact, it is on that + principle that the selection is made. But he feels that he is more + competent than the writer to judge questions of strength and of tone, + especially when the general purpose of the journal is considered, of + which the editor is the judge without appeal. An editor who meddles with + substantive matter is likely to be wrong, even when he knows the subject; + but one who prunes what he deems excess, is likely to be right, even when + he does not know the subject. In the second place, a contributor knows + that he is supplying an editor, and learns, without suppressing truth or + suggesting falsehood, to make the tone of his communications suit the + periodical in which they are to appear. Hence it very often arises that a + reviewed author, who thinks he knows the name of his reviewer, and + proclaims it with expressions of dissatisfaction, is only wrong in + supposing that his critic has given all his mind. It has happened to + myself more than once, to be announced as the author of articles which I + could not have signed, because they did not go far enough to warrant my + affixing my name to them as to a sufficient expression of my own + opinion.</p> + + <p>"There are two other ways in which a reviewed author may be wrong + about his critic. An editor frequently makes slight insertions or + omissions—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 <!-- + Page 18 --><span class="pagenum"><a name="page18"></a>[18]</span>allowed + to remain in another part of the article; and sometimes, especially in + the case of omission, it renders other parts of the article + unintelligible. These are disadvantages of the system, and a judicious + editor is not very free with his <i>unus et alter pannus</i>. Next, + readers in general, when they see the pages of a journal with the + articles so nicely fitting, and so many ending with the page or column, + have very little notion of the cutting and carving which goes to the + process. At the very last moment arises the necessity of some trimming of + this kind; and the editor, who would gladly call the writer to counsel if + he could, is obliged to strike out ten or twelve lines. He must do his + best, but it may chance that the omission selected would take from the + writer the power of owning the article. A few years ago, an able opponent + of mine wrote to a journal some criticisms upon an article which he + expressly attributed to me. I replied as if I were the writer, which, in + a sense, I was. But if any one had required of me an unmodified 'Yes' or + 'No' to the question whether I wrote the article, I must, of two + falsehoods, have chosen 'No': for certain omissions, dictated by the + necessities of space and time, would have amounted, had my signature been + affixed, to a silent surrender of points which, in my own character, I + must have strongly insisted on, unless I had chosen to admit certain + inferences against what I had previously published in my own name. I may + here add that the forms of journalism obliged me in this case to remind + my opponent that it could not be permitted to me, <i>in that journal</i>, + either to acknowledge or deny the authorship of the articles. The + cautions derived from the above remarks are particularly wanted with + reference to the editorial comments upon letters of complaint. There is + often no time to send these letters to the contributor, and even when + this can be done, an editor is—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 <!-- Page 19 --><span class="pagenum"><a + name="page19"></a>[19]</span>critical position as to responsibility. Of + course, an editor never meddles, except under notice, with the letter of + a correspondent, whether of a complainant, of a casual informant, or of a + contributor who sees reason to become a correspondent. Omissions must + sometimes be made when a grievance is too highly spiced. It did once + happen to me that a waggish editor made an insertion without notice in a + letter signed by me with some fiction, which insertion contained the name + of a friend of mine, with a satire which I did not believe, and should + not have written if I had. To my strong rebuke, he replied—'I know + it was very wrong; but human nature could not resist.' But this was the + only occasion on which such a thing ever happened to me.</p> + + <p>"I daresay what I have written may give some of your readers to + understand some of the <i>pericula et commoda</i> of modern journalism. I + have known men of deep learning and science as ignorant of the prevailing + system as any uneducated reader of a newspaper in a country town. I may + perhaps induce some writers not to be too sure about this, that, or the + other person. They may detect their reviewer, and they may be safe in + attributing to him the general matter and tone of the article. But about + one and another point, especially if it be a short and stinging point, + they may very easily chance to be wrong. It has happened to myself, and + within a few weeks to publication, to be wrong in two ways in reading a + past article—to attribute to editorial insertion what was really my + own, and to attribute to myself what was really editorial insertion."</p> + + <p> </p> + + <p>What is a man to do who is asked whether he wrote an article? He may, + of course, refuse to answer; which is regarded as an admission. He may + say, as Swift did to Serjeant Bettesworth, "Sir, when I was a young man, + a friend of mine advised me, whenever I was asked whether I had written a + certain paper, to deny it; and I accordingly tell that I did <i>not</i> + write it." He may say, as I often do, <!-- Page 20 --><span + class="pagenum"><a name="page20"></a>[20]</span>when charged with having + invented a joke, story, or epigram, "I want all the credit I can get, and + therefore I always acknowledge all that is attributed to me, truly or + not; the story, etc. <i>is</i> mine." But for serious earnest, in the + matter of imputed criticism, the answer may be, "The article was of my + material, but the editor has not let it stand as I gave it; I cannot own + it as a whole." He may then refuse to be particular as to the amount of + the editor's interference. Of this there are two extreme cases. The + editor may have expunged nothing but a qualifying adverb. Or he may have + done as follows. We all remember the account of Adam which satirizes + woman, but eulogizes her if every second and third line be transposed. As + in:</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Adam could find no solid peace</p> + <p class="i2">When Eve was given him for a mate,</p> + <p>Till he beheld a woman's face,</p> + <p class="i2">Adam was in a happy state."</p> + </div> + </div> + <p>If this had been the article, and a gallant editor had made the + transpositions, the author could not with truth acknowledge. If the + alteration were only an omitted adverb, or a few things of the sort, the + author could not with truth deny. In all that comes between, every man + must be his own casuist. I stared, when I was a boy, to hear grave + persons approve of Sir Walter Scott's downright denial that he was the + author of Waverley, in answer to the Prince Regent's downright question. + If I remember rightly, Samuel Johnson would have approved of the same + course.</p> + + <p>It is known that, whatever the law gives, it also gives all that is + necessary to full possession; thus a man whose land is environed by land + of others has a right of way over the land of these others. By analogy, + it is argued that when a man has a right to his secret, he has a right to + all that is necessary to keep it, and that is not unlawful. If, then, he + can only keep his secret by denial, he has a right to denial. This I + admit to be an answer against all men except the denier himself; if + conscience and self-respect will allow <!-- Page 21 --><span + class="pagenum"><a name="page21"></a>[21]</span>it, no one can impeach + it. But the question cannot be solved on a case. That question is, A lie, + is it <i>malum in se</i>, without reference to meaning and circumstances? + This is a question with two sides to it. Cases may be invented in which a + lie is the only way of preventing a murder, or in which a lie may + otherwise save a life. In these cases it is difficult to acquit, and + almost impossible to blame; discretion introduced, the line becomes very + hard to draw.</p> + + <p>I know but one work which has precisely—as at first + appears—the character and object of my Budget. It is the <i>Review + of the Works of the Royal Society of London</i>, by Sir John Hill, M.D. + (1751 and 1780, 4to.). This man offended many: the Royal Society, by his + work, the medical profession, by inventing and selling + extra-pharmacopœian doses; Garrick, by resenting the rejection of a + play. So Garrick wrote:</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"For physic and farces his equal there scarce is;</p> + <p>His farces are physic; his physic a farce is."</p> + </div> + </div> + <p>I have fired at the Royal Society and at the medical profession, but I + have given a wide berth to the drama and its wits; so there is no epigram + out against me, as yet. He was very able and very eccentric. Dr. Thomson + (<i>Hist. Roy. Soc.</i>) says he has no humor, but Dr. Thomson was a man + who never would have discovered humor.</p> + + <p>Mr. Weld (<i>Hist. Roy. Soc.</i>) backs Dr. Thomson, but with a + remarkable addition. Having followed his predecessor in observing that + the <i>Transactions</i> in Martin Folkes's time have an unusual + proportion of trifling and puerile papers, he says that Hill's book is a + poor attempt at humor, and glaringly exhibits the feelings of a + disappointed man. It is probable, he adds, that the points told with some + effect on the Society; for shortly after its publication the + <i>Transactions</i> possess a much higher scientific value.</p> + + <p>I copy an account which I gave elsewhere.</p> + + <p>When the Royal Society was founded, the Fellows set <!-- Page 22 + --><span class="pagenum"><a name="page22"></a>[22]</span>to work to prove + all things, that they might hold fast that which was good. They bent + themselves to the question whether sprats were young herrings. They made + a circle of the powder of a unicorn's horn, and set a spider in the + middle of it; "but it immediately ran out." They tried several times, and + the spider "once made some stay in the powder." They inquired into Kenelm + Digby's sympathetic powder. "Magnetic cures being discoursed of, Sir + Gilbert Talbot promised to communicate what he knew of sympathetical + cures; and those members who had any of the powder of sympathy, were + desired to bring some of it at the next meeting."</p> + + <p>June 21, 1661, certain gentlemen were appointed "curators of the + proposal of tormenting a man with the sympathetic powder"; I cannot find + any record of the result. And so they went on until the time of Sir John + Hill's satire, in 1751. This once well-known work is, in my judgment, the + greatest compliment the Royal Society ever received. It brought forward a + number of what are now feeble and childish researches in the + Philosophical Transactions. It showed that the inquirers had actually + been inquiring; and that they did not pronounce decision about "natural + <i>knowledge</i>" by help of "<i>natural</i> knowledge." But for this, + Hill would neither have known what to assail, nor how. Matters are now + entirely changed. The scientific bodies are far too well established to + risk themselves. <i>Ibit qui zonam perdidit:</i></p> + +<blockquote class="b1n"> + + <p>"Let him take castles who has ne'er a groat."</p> + +</blockquote> + + <p>These great institutions are now without any collective purpose, + except that of promoting individual energy; they print for their + contributors, and guard themselves by a general declaration that they + will not be answerable for the things they print. Of course they will not + put forward anything for everybody; but a writer of a certain reputation, + or matter of a certain look of plausibility and safety, <!-- Page 23 + --><span class="pagenum"><a name="page23"></a>[23]</span>will find + admission. This is as it should be; the pasturer of flocks and herds and + the hunters of wild beasts are two very different bodies, with very + different policies. The scientific academies are what a spiritualist + might call "publishing mediums," and <i>their</i> spirits fall + occasionally into writing which looks as if minds in the higher state + were not always impervious to nonsense.</p> + + <p>The following joke is attributed to Sir John Hill. I cannot honestly + say I believe it; but it shows that his contemporaries did not believe he + had no humor. Good stories are always in some sort of keeping with the + characters on which they are fastened. Sir John Hill contrived a + communication to the Royal Society from Portsmouth, to the effect that a + sailor had broken his leg in a fall from the mast-head; that bandages and + a plentiful application of tarwater had made him, in three days, able to + use his leg as well as ever. While this communication was under grave + discussion—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.</p> + + <p>Sir John Hill's book is droll and cutting satire. Dr. Maty, (Sec. + Royal Society) wrote thus of it in the <i>Journal Britannique</i> (Feb. + 1751), of which he was editor:</p> + + <p>"Il est fâcheux que cet ingénieux Naturaliste, qui nous a déjà donné + et qui nous prépare encore des ouvrages plus utiles, emploie à cette + odieuse tâche une plume qu'il trempe dans le fiel et dans l'absinthe. Il + est vrai que plusieurs de ses remarques sont fondées, et qu'à l'erreur + qu'il indique, il joint en même tems la correction. Mais il n'est pas + toujours équitable, et ne manque jamais d'insulter. Que peut <!-- Page 24 + --><span class="pagenum"><a name="page24"></a>[24]</span>après tout + prouver son livre, si ce n'est que la quarante-cinquième partie d'un + très-ample et très-utile Recueil n'est pas exempte d'erreurs? Devoit-il + confondre avec des Ecrivains superficiels, dont la Liberté du Corps ne + permet pas de restreindre la fertilité, cette foule de savans du Premier + ordre, dont les Ecrits ont orné et ornent encore les Transactions? A-t-il + oublié qu'on y a vu fréquemment les noms des Boyle, des Newton, des + Halley, des De Moivres, des Hans Sloane, etc.? Et qu'on y trouve encore + ceux des Ward, des Bradley, des Graham, des Ellicot, des Watson, et d'un + Auteur que Mr. Hill préfère à tous les autres, je veux dire de Mr. Hill + lui-même?"<a name="NtA_7" href="#Nt_7"><sup>[7]</sup></a></p> + + <p>This was the only answer; but it was no answer at all. Hill's object + was to expose the absurdities; he therefore collected the absurdities. I + feel sure that Hill was a benefactor of the Royal Society; and much more + than he would have been if he had softened their errors and enhanced + their praises. No reviewer will object to me that I have omitted Young, + Laplace, etc. But then my book has a true title. Hill should not have + called his a review of the "Works."</p> + + <p>It was charged against Sir John Hill that he had tried to become a + Fellow of the Royal Society and had failed. This he denied, and + challenged the production of the certificate which a candidate always + sends in, and which is preserved. <!-- Page 25 --><span + class="pagenum"><a name="page25"></a>[25]</span>But perhaps he could not + get so far as a certificate—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! <i>Nullus liber + homo capiatur aut imprisonetur ... aut aliquo modo destruatur, nisi per + judicium parium</i> ....<a name="NtA_8" href="#Nt_8"><sup>[8]</sup></a> + <i>Liber homo: frank home</i>; a capital thing for him—but how + about the <i>villeins</i>? Oh, there are none <i>now</i>! But there were. + Who cares for villains, or barbarians, or helots? And so England, and + Athens, and Sparta, were free States; all the freemen in them were free. + Long after Magna Charta, villains were sold with their "chattels and + offspring," named in that order. Long after Magna Charta, it was law that + "Le Seigniour poit rob, naufrer, et chastiser son villein a son volunt, + salve que il ne poit luy maim."<a name="NtA_9" + href="#Nt_9"><sup>[9]</sup></a></p> + + <p>The Royal Society was founded as a co-operative body, and co-operation + was its purpose. The early charters, etc. do not contain a trace of the + intention to create a <i>scientific distinction</i>, a kind of Legion of + Honor. It is clear that the <!-- Page 26 --><span class="pagenum"><a + name="page26"></a>[26]</span>qualification was ability and willingness to + do good work for the promotion of natural knowledge, no matter in how + many persons, nor of what position in society. Charles II gave a smart + rebuke for exclusiveness, as elsewhere mentioned. In time arose, almost + of course, the idea of distinction attaching to the title; and when I + first began to know the Society, it was in this state. Gentlemen of good + social position were freely elected if they were really educated men; but + the moment a claimant was announced as resting on his science, there was + a disposition to inquire whether he was scientific enough. The maxim of + the poet was adopted; and the Fellows were practically divided into + <i>Drink-deeps</i> and <i>Taste-nots</i>.</p> + + <p>I was, in early life, much repelled by the tone taken by the Fellows + of the Society with respect to their very mixed body. A man high in + science—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.</p> + + <p>Of late years this pretension has been made by a President of the + Society. In 1855, Lord Rosse presented a confidential memorandum to the + Council on the expediency of enlarging their number. He says, "In a + Council so small it <!-- Page 27 --><span class="pagenum"><a + name="page27"></a>[27]</span>is impossible to secure a satisfactory + representation of the leading scientific Societies, and it is scarcely to + be expected that, under such circumstances, they will continue to publish + inferior papers while they send the best to our <i>Transactions</i>."</p> + + <p>And, again, with all the Societies represented on the Council, "even + if every Science had its Society, and if they published everything, + withholding their best papers [i.e., from the Royal Society], which they + would not be likely to do, still there would remain to the Royal Society + ...." Lord Rosse seems to imagine that the minor Societies themselves + transfer their best papers to the Royal Society; that if, for instance, + the Astronomical Society were to receive from A.B. a paper of unusual + merit, the Society would transfer it to the Royal Society. This is quite + wrong: any preference of the Royal to another Society is the work of the + contributor himself. But it shows how well hafted is the Royal Society's + claim, that a President should acquire the notion that it is acknowledged + and acted upon by the other Societies, in their joint and corporate + capacities. To the pretension thus made I never could give any sympathy. + When I first heard Mr. Christie, Sec. R. S., set it forth at the + anniversary dinner of the Astronomical Society, I remembered the Baron in + Walter Scott:</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Of Gilbert the Galliard a heriot he sought,</p> + <p>Saying, Give thy best steed as a vassal ought."</p> + </div> + </div> + <p>And I remembered the answer:</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Lord and Earl though thou be, I trow</p> + <p>I can rein Buck's-foot better than thou."</p> + </div> + </div> + <p>Fully conceding that the Royal Society is entitled to preeminent rank + and all the respect due to age and services, I could not, nor can I now, + see any more obligation in a contributor to send his best to that Society + than he can make out to be due to himself. This pretension, in my mind, + was hooked on, by my historical mode of viewing things already mentioned, + to my knowledge of the fact that the Royal <!-- Page 28 --><span + class="pagenum"><a name="page28"></a>[28]</span>Society—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 <i>a + priori philosophy</i>, the nibbling at the small end of omniscience, and + the effect it has had on common life, from the family parlor to the + jury-box, from the girls'-school to the vestry-meeting. There are in the + Society those who would, were there no others, prevent my criticism, be + its conclusions true or false, from having any basis; but they are in the + minority.</p> + + <p>There is no objection to be made to the principles of philosophy in + vogue at the Society, when they are stated as principles; but there is an + omniscience in daily practice which the principles repudiate. In like + manner, the most retaliatory Christians have a perfect form of round + words about behavior to those who injure them; none of them are as candid + as a little boy I knew, who, to his mother's admonition, You should love + your enemies, answered—Catch me at it!</p> + + <p>Years ago, a change took place which would alone have <!-- Page 29 + --><span class="pagenum"><a name="page29"></a>[29]</span>put a sufficient + difficulty in the way. The co-operative body got tired of getting funds + from and lending name to persons who had little or no science, and wanted + F.R.S. to be in every case a Fellow Really Scientific. Accordingly, the + number of yearly elections was limited to fifteen recommended by the + Council, unless the general body should choose to elect more; which it + does not do. The election is now a competitive examination: it is no + longer—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—<i>he could not afford it</i>. 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 <i>for + science</i>, 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, <!-- + Page 30 --><span class="pagenum"><a name="page30"></a>[30]</span>is, with + the mass, a very second-rate sort of Newton, whatever he may be in the + field of investigation. Even men of science, so called, have this + feeling. I know that the <i>scientific advisers</i> of the Admiralty, + who, years ago, received 100 pounds a year each for his trouble, were + sneered at by a wealthy pretender as "fellows to whom a hundred a year is + an object." Dr. Thomas Young was one of them. To a bookish man—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.</p> + + <p>So much for the Royal Society as concerns myself. I must add that + there is not a spark of party feeling against those who wilfully remain + outside. The better minds of course know better; and the smaller + <i>savants</i> look complacently on the idea of an outer world which + makes <i>élite</i> of them. I have done such a thing as serve on a + committee of the Society, and report on a paper: they had the sense to + ask, and I had the sense to see that none of my opinions were compromised + by compliance. And I will be of any use which does not involve the status + of <i>homo trium literarum</i>; as I have elsewhere explained, I would + gladly be <i>Fautor Realis Scientiæ</i>, but I would not be taken for + <i>Falsæ Rationis Sacerdos</i>.</p> + + <p>Nothing worse will ever happen to me than the smile which individuals + bestow on a man who does not <i>groove</i>. Wisdom, like religion, + belongs to majorities; who can <!-- Page 31 --><span class="pagenum"><a + name="page31"></a>[31]</span>wonder that it should be so thought, when it + is so clearly pictured in the New Testament from one end to the + other?</p> + + <p>The counterpart of <i>paradox</i>, the isolated opinion of one or of + few, is the general opinion held by all the rest; and the counterpart of + false and absurd paradox is what is called the "vulgar error," the + <i>pseudodox</i>. There is one great work on this last subject, the + <i>Pseudodoxia Epidemica</i> of Sir Thomas Browne, the famous author of + the <i>Religio Medici</i>; it usually goes by the name of Browne "On + Vulgar Errors" (1st ed. 1646; 6th, 1672). A careful analysis of this work + would show that vulgar errors are frequently opposed by scientific + errors; but good sense is always good sense, and Browne's book has a vast + quantity of it.</p> + + <p>As an example of bad philosophy brought against bad observation. The + Amphisbæna serpent was supposed to have two heads, one at each end; + partly from its shape, partly because it runs backwards as well as + forwards. On this Sir Thomas Browne makes the following remarks:</p> + + <p>"And were there any such species or natural kind of animal, it would + be hard to make good those six positions of body which, according to the + three dimensions, are ascribed unto every Animal; that is, <i>infra</i>, + <i>supra</i>, <i>ante</i>, <i>retro</i>, <i>dextrosum</i>, + <i>sinistrosum</i>: for if (as it is determined) that be the anterior and + upper part wherein the senses are placed, and that the posterior and + lower part which is opposite thereunto, there is no inferior or former + part in this Animal; for the senses, being placed at both extreams, doth + make both ends anterior, which is impossible; the terms being Relative, + which mutually subsist, and are not without each other. And therefore + this duplicity was ill contrived to place one head at both extreams, and + had been more tolerable to have settled three or four at one. And + therefore also Poets have been more reasonable than Philosophers, and + <i>Geryon</i> or <i>Cerberus</i> less monstrous than <i>Amphisbæna</i>." + <!-- Page 32 --><span class="pagenum"><a + name="page32"></a>[32]</span></p> + + <p>There may be paradox upon paradox: and there is a good instance in the + eighth century in the case of Virgil, an Irishman, Bishop of Salzburg and + afterwards Saint, and his quarrels with Boniface, an Englishman, + Archbishop of Mentz, also afterwards Saint. All we know about the matter + is, that there exists a letter of 748 from Pope Zachary, citing + Virgil—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 (<i>mundus</i>) under our earth + (<i>terra</i>), with another sun and another moon. Nothing more is known: + the letter contains threats in the event of the charge being true; and + there history drops the matter. Since Virgil was afterwards a Bishop and + a Saint, we may fairly conclude that he died in the full flower of his + orthodox reputation. It has been supposed—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 <i>them</i>, whether their wine and their water could be lawfully + used in the sacraments, etc.</p> + + <p>On so small a basis as the above has been constructed a companion case + to the persecution of Galileo. On one side the positive assertion, with + indignant comment, that Virgil was deposed for antipodal heresy, on the + other, serious attempts at justification, palliation, or mystification. + Some writers say that Virgil was found guilty; others that he gave + satisfactory explanation, and became very good friends with <!-- Page 33 + --><span class="pagenum"><a name="page33"></a>[33]</span>Boniface: for + all which see Bayle. Some have maintained that the antipodist was a + different person from the canonized bishop: there is a second Virgil, + made to order. When your shoes pinch, and will not stretch, always throw + them away and get another pair: the same with your facts. Baronius was + not up to the plan of a substitute: his commentator Pagi (probably + writing about 1690) argues for it in a manner which I think Baronius + would not have approved. This Virgil was perhaps a slippery fellow. The + Pope says he hears that Virgil pretended licence from him to claim one of + some new bishoprics: this he declares is totally false. It is part of the + argument that such a man as this could not have been created a Bishop and + a Saint: on this point there will be opinions and opinions.<a + name="NtA_10" href="#Nt_10"><sup>[10]</sup></a></p> + + <p>Lactantius, four centuries before, had laughed at the antipodes in a + manner which seems to be ridicule thrown on the idea of the earth's + roundness. Ptolemy, without reference to the antipodes, describes the + extent of the inhabited part of the globe in a way which shows that he + could have had no objection to men turned opposite ways. Probably, in the + eighth century, the roundness of the earth was matter of thought only to + astronomers. It should always be remembered, especially by those who + affirm persecution of a true opinion, that but for our knowing from + Lactantius that the antipodal notion had been matter of assertion and + denial among theologians, we could never have had any great confidence in + Virgil really having maintained the simple theory of the existence of + antipodes. And even now we are not entitled to affirm it as having + historical proof: the evidence <!-- Page 34 --><span class="pagenum"><a + name="page34"></a>[34]</span>goes to Virgil having been charged with very + absurd notions, which it seems more likely than not were the absurd + constructions which ignorant contemporaries put upon sensible opinions of + his.</p> + + <p>One curious part of this discussion is that neither side has allowed + Pope Zachary to produce evidence to character. He shall have been an + Urban, say the astronomers; an Urban he ought to have been, say the + theologians. What sort of man was Zachary? He was eminently sensible and + conciliatory; he contrived to make northern barbarians hear reason in a + way which puts him high among that section of the early popes who had the + knack of managing uneducated swordsmen. He kept the peace in Italy to an + extent which historians mention with admiration. Even Bale, that + Maharajah of pope-haters, allows himself to quote in favor of Zachary, + that "multa Papalem dignitatem decentia, eademque præclara (scilicet) + opera confecit."<a name="NtA_11" href="#Nt_11"><sup>[11]</sup></a> And + this, though so willing to find fault that, speaking of Zachary putting a + little geographical description of the earth on the portico of the + Lateran Church, he insinuates that it was intended to affirm that the + Pope was lord of the whole. Nor can he say how long Zachary held the see, + except by announcing his death in 752, "cum decem annis pestilentiæ sedi + præfuisset."<a name="NtA_12" href="#Nt_12"><sup>[12]</sup></a></p> + + <p>There was another quarrel between Virgil and Boniface which is an + illustration. An ignorant priest had baptized "in nomine Patri<i>a</i>, + et Fili<i>a</i> et Spiritu<i>a</i> Sanct<i>a</i>." Boniface declared the + rite null and void: Virgil maintained the contrary; and Zachary decided + in favor of Virgil, on the ground that the absurd form was only ignorance + of Latin, and not heresy. It is hard to believe that this man deposed a + priest for asserting the whole globe to be inhabited. To me the little + information that we have seems <!-- Page 35 --><span class="pagenum"><a + name="page35"></a>[35]</span>to indicate—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 <i>description</i> of the earth, + according to historians, was a <i>map</i>; this Pope may have been more + ready than another to prick up his ears at any rumor of geographical + heresy, from hope of information. And Virgil, who may have entered the + sacred presence as frightened as Jacquard, when Napoleon I sent for him + and said, with a stern voice and threatening gesture, "You are the man + who can tie a knot in a stretched string," may have departed as well + pleased as Jacquard with the riband and pension which the interview was + worth to him.</p> + + <p>A word more about Baronius. If he had been pope, as he would have been + but for the opposition of the Spaniards, and if he had lived ten years + longer than he did, and if Clavius, who would have been his astronomical + adviser, had lived five years longer than he did, it is probable, nay + almost certain, that the great exhibition, the proceeding against + Galileo, would not have furnished a joke against theology in all time to + come. For Baronius was sensible and witty enough to say that in the + Scriptures the Holy Spirit intended to teach how to go to Heaven, not how + Heaven goes; and Clavius, in his last years, confessed that the whole + system of the heavens had broken down, and must be mended.</p> + + <p>The manner in which the Galileo case, a reality, and the Virgil case, + a fiction, have been hawked against the Roman see are enough to show that + the Pope and his adherents have not cared much about physical philosophy. + In truth, orthodoxy has always had other fish to fry. Physics, which <!-- + Page 36 --><span class="pagenum"><a name="page36"></a>[36]</span>in + modern times has almost usurped the name <i>philosophy</i>, in England at + least, has felt a little disposed to clothe herself with all the honors + of persecution which belong to the real owner of the name. But the + bishops, etc. of the Middle Ages knew that the contest between nominalism + and realism, for instance, had a hundred times more bearing upon + orthodoxy than anything in astronomy, etc. A wrong notion about + <i>substance</i> might play the mischief with + <i>transubstantiation</i>.</p> + + <p>The question of the earth's motion was the single point in which + orthodoxy came into real contact with science. Many students of physics + were suspected of magic, many of atheism: but, stupid as the mistake may + have been, it was <i>bona fide</i> the magic or the atheism, not the + physics, which was assailed. In the astronomical case it was the very + doctrine, as a doctrine, independently of consequences, which was the + <i>corpus delicti</i>: and this because it contradicted the Bible. And so + it did; for the stability of the earth is as clearly assumed from one end + of the Old Testament to the other as the solidity of iron. Those who take + the Bible to be <i>totidem verbis</i> dictated by the God of Truth can + refuse to believe it; and they make strange reasons. They undertake, <i>a + priori</i>, to settle Divine intentions. The Holy Spirit did not + <i>mean</i> to teach natural philosophy: this they know beforehand; or + else they infer it from finding that the earth does move, and the Bible + says it does not. Of course, ignorance apart, every word is truth, or the + writer did not mean truth. But this puts the whole book on its trial: for + we never can find out what the writer meant, until we otherwise find out + what is true. Those who like may, of course, declare for an inspiration + over which they are to be viceroys; but common sense will either accept + verbal meaning or deny verbal inspiration.</p> + +<hr class="full" > + +<p><!-- Page 37 --><span class="pagenum"><a name="page37"></a>[37]</span></p> + +<h2>A BUDGET OF PARADOXES.</h2> + +<h3>VOLUME I.</h3> + +<p class="cenhead">THE STORY OF BURIDAN'S ASS.</p> + +<blockquote class="b1n"> + + <p>Questiones Morales, folio, 1489 [Paris]. By T. Buridan.</p> + +</blockquote> + + <p>This is the title from the Hartwell Catalogue of Law Books. I suppose + it is what is elsewhere called the "Commentary on the Ethics of + Aristotle," printed in 1489.<a name="NtA_13" + href="#Nt_13"><sup>[13]</sup></a> Buridan<a name="NtA_14" + href="#Nt_14"><sup>[14]</sup></a> (died about 1358) is the creator of the + famous ass which, as <i>Burdin's</i><a name="NtA_15" + href="#Nt_15"><sup>[15]</sup></a> ass, was current in Burgundy, perhaps + is, as a vulgar proverb. Spinoza<a name="NtA_16" + href="#Nt_16"><sup>[16]</sup></a> says it was a jenny ass, and that a man + would not have been so foolish; but whether the compliment is paid to + human or to masculine character does not appear—perhaps to both in + one. The story <i>told</i> about the famous paradox is very curious. The + Queen of France, Joanna or Jeanne, was in the habit of sewing her lovers + up in sacks, and throwing them into the Seine; not for blabbing, but that + they might not blab—certainly the safer plan. Buridan was exempted, + and, in gratitude, invented the sophism. What it has to do with the + matter <!-- Page 38 --><span class="pagenum"><a + name="page38"></a>[38]</span>has never been explained. Assuredly <i>qui + facit per alium facit per se</i> will convict Buridan of prating. The + argument is as follows, and is seldom told in full. Buridan was for + free-will—that is, will which determines conduct, let motives be + ever so evenly balanced. An ass is <i>equally</i> pressed by hunger and + by thirst; a bundle of hay is on one side, a pail of water on the other. + Surely, you will say, he will not be ass enough to die for want of food + or drink; he will then make a choice—that is, will choose between + alternatives of equal force. The problem became famous in the schools; + some allowed the poor donkey to die of indecision; some denied the + possibility of the balance, which was no answer at all.</p> + + <p> </p> + +<p class="cenhead">MICHAEL SCOTT'S DEVILS.</p> + + <p>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<a name="NtA_17" + href="#Nt_17"><sup>[17]</sup></a> devils. The wizard <!-- Page 39 + --><span class="pagenum"><a name="page39"></a>[39]</span>knew nothing + about squaring the circle, etc., so he set them to make ropes out of sea + sand, which puzzled them. Stupid devils; much of our glass is sea sand, + and it makes beautiful thread. Had Michael set them to square the circle + or to find a perpetual motion, he would have done his work much better. + But all this is conjecture: who knows that I have not hit on the very + plan he adopted? Perhaps the whole race of paradoxers on hopeless + subjects are Michael's subordinates, condemned to transmigration after + transmigration, until their task is done.</p> + + <p>The above was not a bad guess. A little after the time when the famous + Pascal papers<a name="NtA_18" href="#Nt_18"><sup>[18]</sup></a> were + produced, I came into possession of a correspondence which, but for these + papers, I should have held too incredible to be put before the world. But + when one sheep leaps the ditch, another will follow: so I gave the + following account in the <i>Athenæum</i> of October 5, 1867:</p> + + <p>"The recorded story is that Michael Scott, being bound by contract to + produce perpetual employment for a number of young demons, was worried + out of his life in inventing jobs for them, until at last he set them to + make ropes out of sea sand, which they never could do. We have obtained a + very curious correspondence between the wizard Michael and his + demon-slaves; but we do not feel at liberty to say how it came into our + hands. We much regret that we did not receive it in time for the British + Association. It appears that the story, true as far as it goes, was never + finished. The demons easily conquered the rope difficulty, by the simple + process of making the sand into glass, and spinning the glass into + thread, which they twisted. Michael, thoroughly disconcerted, hit upon + the plan of setting some to <!-- Page 40 --><span class="pagenum"><a + name="page40"></a>[40]</span>square the circle, others to find the + perpetual motion, etc. He commanded each of them to transmigrate from one + human body into another, until their tasks were done. This explains the + whole succession of cyclometers, and all the heroes of the Budget. Some + of this correspondence is very recent; it is much blotted, and we are not + quite sure of its meaning: it is full of figurative allusions to driving + something illegible down a steep into the sea. It looks like a humble + petition to be allowed some diversion in the intervals of transmigration; + and the answer is—</p> + + <div class="poem"> + <div class="stanza"> + <p>Rumpat et serpens iter institutum,<a name="NtA_19" href="#Nt_19"><sup>[19]</sup></a></p> + </div> + </div> + <p>—a line of Horace, which the demons interpret as a direction to + come athwart the proceedings of the Institute by a sly trick. Until we + saw this, we were suspicious of M. Libri,<a name="NtA_20" + href="#Nt_20"><sup>[20]</sup></a> the unvarying blunders of the + correspondence look like knowledge. To be always out of the road requires + a map: genuine ignorance occasionally lapses into truth. We thought it + possible M. Libri might have played the trick to show how easily the + French are deceived; but with our present information, our minds are at + rest on the subject. We see M. Chasles does not like to avow the real + source of information: he will not confess himself a spiritualist."</p> + + <p> </p> + +<p class="cenhead">PHILO OF GADARA.</p> + + <p>Philo of Gadara<a name="NtA_21" href="#Nt_21"><sup>[21]</sup></a> is + asserted by Montucla,<a name="NtA_22" href="#Nt_22"><sup>[22]</sup></a> + on the <!-- Page 41 --><span class="pagenum"><a + name="page41"></a>[41]</span>authority of Eutocius,<a name="NtA_23" + href="#Nt_23"><sup>[23]</sup></a> the commentator on Archimedes, to have + squared the circle within the <i>ten-thousandth</i> part of a unit, that + is, to <i>four</i> places of decimals. A modern classical dictionary + represents it as done by Philo to <i>ten thousand</i> places of decimals. + Lacroix comments on Montucla to the effect that <i>myriad</i> (in Greek + <i>ten thousand</i>) is here used as we use it, vaguely, for an immense + number. On looking into Eutocius, I find that not one definite word is + said about the extent to which Philo carried the matter. I give a + translation of the passage:</p> + + <p>"We ought to know that Apollonius Pergæus, in his Ocytocium [this work + is lost], demonstrated the same by other numbers, and came nearer, which + seems more accurate, but has nothing to do with Archimedes; for, as + before said, he aimed only at going near enough for the wants of life. + Neither is Porus of Nicæa fair when he takes Archimedes to task for not + giving a line accurately equal to the circumference. He says in his Cerii + that his teacher, Philo of Gadara, had given a more accurate + approximation (<span title="eis akribesterous arithmous agagein" class="grk" + >εἰς + ἀκριβεστέρους + ἀριθμοὺς + ἀγάγειν</span>) than that of + Archimedes, or than 7 to 22. But all these [the rest as well as Philo] + miss the intention. They multiply and divide by <i>tens of thousands</i>, + which no one can easily do, unless he be versed in the logistics + [fractional computation] of Magnus [now unknown]."</p> + + <p>Montucla, or his source, ought not to have made this mistake. He had + been at the Greek to correct Philo <i>Gadetanus</i>, as he had often been + called, and he had brought away <!-- Page 42 --><span class="pagenum"><a + name="page42"></a>[42]</span>and quoted <span title="apo Gadarôn" class="grk" + >ἀπὸ + Γάδαρων</span>. Had he read two + sentences further, he would have found the mistake.</p> + + <p>We here detect a person quite unnoticed hitherto by the moderns, + Magnus the arithmetician. The phrase is ironical; it is as if we should + say, "To do this a man must be deep in Cocker."<a name="NtA_24" + href="#Nt_24"><sup>[24]</sup></a> Accordingly, Magnus, Baveme,<a + name="NtA_25" href="#Nt_25"><sup>[25]</sup></a> and Cocker, are three + personifications of arithmetic; and there may be more.</p> + + <p> </p> + +<p class="cenhead">ON SQUARING THE CIRCLE.</p> + + <p>Aristotle, treating of the category of relation, denies that the + quadrature has been found, but appears to assume that it can be done. + Boethius,<a name="NtA_26" href="#Nt_26"><sup>[26]</sup></a> in his + comment on the passage, says that it has been done since Aristotle, but + that the demonstration is too long for him to give. Those who have no + notion of the quadrature question may look at the <i>English + Cyclopædia</i>, art. "Quadrature of the Circle."</p> + +<blockquote class="b1n"> + + <p>Tetragonismus. Id est circuli quadratura per Campanum, Archimedem + Syracusanum, atque Boetium mathematicæ perspicacissimos + adinventa.—At the end, Impressum Venetiis per Ioan. Bapti. Sessa. + Anno ab incarnatione Domini, 1503. Die 28 Augusti.</p> + +</blockquote> + +<p><!-- Page 43 --><span class="pagenum"><a name="page43"></a>[43]</span></p> + + <p>This book has never been noticed in the history of the subject, and I + cannot find any mention of it. The quadrature of Campanus<a name="NtA_27" + href="#Nt_27"><sup>[27]</sup></a> takes the ratio of Archimedes,<a + name="NtA_28" href="#Nt_28"><sup>[28]</sup></a> 7 to 22 to be absolutely + correct; the account given of Archimedes is not a translation of his + book; and that of Boetius has more than is in Boet<i>h</i>ius. This book + must stand, with the next, as the earliest in print on the subject, until + further showing: Murhard<a name="NtA_29" + href="#Nt_29"><sup>[29]</sup></a> and Kastner<a name="NtA_30" + href="#Nt_30"><sup>[30]</sup></a> have nothing so early. It is edited by + Lucas Gauricus,<a name="NtA_31" href="#Nt_31"><sup>[31]</sup></a> who has + given a short preface. Luca Gaurico, Bishop of Civita Ducale, an + astrologer of astrologers, published this work at about thirty years of + age, and lived to eighty-two. His works are collected in folios, but I do + not know whether they contain this production. The poor fellow could + never tell his own fortune, because his father neglected to note the hour + and minute of his birth. But if there had been anything in astrology, he + could have worked back, as Adams<a name="NtA_32" + href="#Nt_32"><sup>[32]</sup></a> and Leverrier<a name="NtA_33" + href="#Nt_33"><sup>[33]</sup></a> did when they caught <!-- Page 44 + --><span class="pagenum"><a name="page44"></a>[44]</span>Neptune: at + sixty he could have examined every minute of his day of birth, by the + events of his life, and so would have found the right minute. He could + then have gone on, by rules of prophecy. Gauricus was the mathematical + teacher of Joseph Scaliger,<a name="NtA_34" + href="#Nt_34"><sup>[34]</sup></a> who did him no credit, as we shall + see.</p> + + <p> </p> + +<p class="cenhead">BOVILLUS ON THE QUADRATURE PROBLEM.</p> + +<blockquote class="b1n"> + + <p>In hoc opere contenta Epitome.... Liber de quadratura Circuli.... + Paris, 1503, folio.</p> + +</blockquote> + + <p>The quadrator is Charles Bovillus,<a name="NtA_35" + href="#Nt_35"><sup>[35]</sup></a> who adopted the views of Cardinal + Cusa,<a name="NtA_36" href="#Nt_36"><sup>[36]</sup></a> presently + mentioned. Montucla is hard on his compatriot, who, he says, was only + saved from the laughter of geometers by his obscurity. Persons must guard + against most historians of mathematics in one point: they frequently + attribute to <i>his own</i> age the obscurity which a writer has in + <i>their own</i> time. This tract was printed by Henry Stephens,<a + name="NtA_37" href="#Nt_37"><sup>[37]</sup></a> at the instigation of + Faber Stapulensis,<a name="NtA_38" href="#Nt_38"><sup>[38]</sup></a> <!-- + Page 45 --><span class="pagenum"><a name="page45"></a>[45]</span>and is + recorded by Dechales,<a name="NtA_39" href="#Nt_39"><sup>[39]</sup></a> + etc. It was also introduced into the <i>Margarita Philosophica</i> of + 1815,<a name="NtA_40" href="#Nt_40"><sup>[40]</sup></a> in the same + appendix with the new perspective from Viator. This is not extreme + obscurity, by any means. The quadrature deserved it; but that is another + point.</p> + + <p>It is stated by Montucla that Bovillus makes <span + class="grk">π</span> = √10. But Montucla cites a work of 1507, + <i>Introductorium Geometricum</i>, which I have never seen.<a + name="NtA_41" href="#Nt_41"><sup>[41]</sup></a> He finds in it an account + which Bovillus gives of the quadrature of the peasant laborer, and + describes it as agreeing with his own. But the description makes <span + class="grk">π</span> = 3-1/8, which it thus appears Bovillus could not + distinguish from √10. It seems also that this 3-1/8, about which we + shall see so much in the sequel, takes its rise in the thoughtful head of + a poor laborer. It does him great honor, being so near the truth, and he + having no means of instruction. In our day, when an ignorant person + chooses to bring his fancy forward in opposition to demonstration which + he will not study, he is deservedly laughed at.</p> + +<p><!-- Page 46 --><span class="pagenum"><a name="page46"></a>[46]</span></p> + + <p> </p> + +<p class="cenhead">THE STORY OF LACOMME'S ATTEMPT AT QUADRATURE.</p> + + <p>Mr. James Smith,<a name="NtA_42" href="#Nt_42"><sup>[42]</sup></a> of + Liverpool—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:</p> + + <p>"In the year 1836, at which time Lacomme could neither read nor write, + he had constructed a circular reservoir and wished to know the quantity + of stone that would be required to pave the bottom, and for this purpose + called on a professor of mathematics. On putting his question and giving + the diameter, he was surprised at getting the following answer from the + Professor: <i>'Qu'il lui était impossible de le lui dire au juste, + attendu que personne n'avait encore pu trouver d'une manière exacte le + rapport de la circonférence au diametre.'</i><a name="NtA_43" + href="#Nt_43"><sup>[43]</sup></a> From this he was led to attempt the + solution of the problem. His first process was purely mechanical, and he + was so far convinced he had made the discovery that he took to educating + himself, and became an expert arithmetician, and then found that + arithmetical results agreed with his mechanical experiments. He appears + to have eked out a bare existence for many years by teaching arithmetic, + all the time struggling to get a hearing from some of the learned + societies, but without success. In the year 1855 he found his way to + Paris, where, as if by accident, he made the acquaintance of a young + gentleman, son of M. Winter, a commissioner of police, and taught him his + peculiar methods of calculation. The young man was so enchanted that he + strongly recommended Lacomme to his father, and <!-- Page 47 --><span + class="pagenum"><a name="page47"></a>[47]</span>subsequently through M. + Winter he obtained an introduction to the President of the Society of + Arts and Sciences of Paris. A committee of the society was appointed to + examine and report upon his discovery, and the society at its + <i>séance</i> of March 17, 1856, awarded a silver medal of the first + class to M. Joseph Lacomme for his discovery of the true ratio of + diameter to circumference in a circle. He subsequently received three + other medals from other societies. While writing this I have his likeness + before me, with his medals on his breast, which stands as a frontispiece + to a short biography of this extraordinary man, for which I am indebted + to the gentleman who did me the honor to publish a French translation of + the pamphlet I distributed at the meeting of the British Association for + the Advancement of Science, at Oxford, in + 1860."—<i>Correspondent</i>, May 3, 1866.</p> + + <p>My inquiries show that the story of the medals is not incredible. + There are at Paris little private societies which have not so much claim + to be exponents of scientific opinion as our own Mechanics' Institutes. + Some of them were intended to give a false lustre: as the "Institut + Historique," the members of which are "Membre de l'Institut Historique." + That M. Lacomme should have got four medals from societies of this class + is very possible: that he should have received one from any society at + Paris which has the least claim to give one is as yet simply + incredible.</p> + + <p> </p> + +<p class="cenhead">NICOLAUS OF CUSA'S ATTEMPT.</p> + +<blockquote class="b1n"> + + <p>Nicolai de Cusa Opera Omnia. Venice, 1514. 3 vols. folio.</p> + +</blockquote> + + <p>The real title is "Hæc accurata recognitio trium voluminum operum + clariss. P. Nicolai Cusæ ... proxime sequens pagina monstrat."<a + name="NtA_44" href="#Nt_44"><sup>[44]</sup></a> Cardinal Cusa, who died + in 1464, is one of the earliest modern attempters. His quadrature is + found in the second volume, and is now quite unreadable.</p> + +<p><!-- Page 48 --><span class="pagenum"><a name="page48"></a>[48]</span></p> + + <p>In these early days every quadrator found a geometrical opponent, who + finished him. Regimontanus<a name="NtA_45" + href="#Nt_45"><sup>[45]</sup></a> did this office for the Cardinal.</p> + + <p> </p> + +<p class="cenhead">HENRY CORNELIUS AGRIPPA.</p> + +<blockquote class="b1n"> + + <p>De Occulta Philosophia libri III. By Henry Cornelius Agrippa. Lyons, + 1550, 8vo.</p> + + <p>De incertitudine et vanitate scientiarum. By the same. Cologne, 1531, + 8vo.</p> + +</blockquote> + + <p>The first editions of these works were of 1530, as well as I can make + out; but the first was in progress in 1510.<a name="NtA_46" + href="#Nt_46"><sup>[46]</sup></a> In the second work Agrippa repents of + having wasted time on the magic of the first; but all those who actually + deal with demons are destined to eternal fire with Jamnes and Mambres and + Simon Magus. This means, as is the fact, that his occult philosophy did + not actually enter upon <i>black</i> magic, but confined itself to the + power of the stars, of numbers, etc. The fourth book, which appeared + after the death of Agrippa, and really concerns dealing with evil + spirits, is undoubtedly spurious. It is very difficult to make out what + Agrippa really believed on the subject. I have introduced his books as + the most marked specimens of treatises on magic, a paradox of our day, + though not far from orthodoxy in his; and here I should have ended my + notice, if I had not casually found something more interesting to the + reader of our day.</p> + +<p><!-- Page 49 --><span class="pagenum"><a name="page49"></a>[49]</span></p> + + <p> </p> + +<p class="cenhead">WHICH LEADS TO WALTER SCOTT.</p> + + <p>Walter Scott, it is well known, was curious on all matters connected + with magic, and has used them very widely. But it is hardly known how + much pains he has taken to be correct, and to give the real thing. The + most decided detail of a magical process which is found in his writings + is that of Dousterswivel in <i>The Antiquary</i>; and it is obvious, by + his accuracy of process, that he does not intend the adept for a mere + impostor, but for one who had a lurking belief in the efficacy of his own + processes, coupled with intent to make a fraudulent use of them. The + materials for the process are taken from Agrippa. I first quote Mr. + Dousterswivel:</p> + + <p>"... I take a silver plate when she [the moon] is in her fifteenth + mansion, which mansion is in de head of <i>Libra</i>, and I engrave upon + one side de worts <i>Schedbarschemoth Scharta</i>ch<i>an</i> [<i>ch</i> + should be <i>t</i>]—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...."</p> + + <p>In the <i>De Occulta Philosophia</i>, p. 290, we find that the + fifteenth mansion of the moon <i>incipit capite Libræ</i>, and is good + <i>pro extrahendis thesauris</i>, the object being to discover hidden + treasure. In p. 246, we learn that a <i>silver</i> plate must be used + with the moon. In p. 248, we have the words which denote the + Intelligence, etc. But, owing to the falling of a number into a wrong + line, or the misplacement of a line, one or other—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 <i>demon of the demons</i> of + the moon. Instead of the gibberish above, it should have been <i>Malcha + betarsisim hed beruah schenhakim</i>. In p. 253, we have the magic square + of the moon, with eighty-one numbers, and the symbol for the + Intelligence, which Scott likens to a flying <!-- Page 50 --><span + class="pagenum"><a name="page50"></a>[50]</span>serpent with a + turkey-cock's head. He was obliged to say something; but I will stake my + character—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<a name="NtA_47" + href="#Nt_47"><sup>[47]</sup></a> and Petrus Thyracus; but this last word + should be Thyræus.</p> + + <p>The tendency of Scott's mind towards prophecy is very marked, and it + is always fulfilled. Hyder, in his disguise, calls out to Tippoo: "Cursed + is the prince who barters justice for lust; he shall die in the gate by + the sword of the stranger." Tippoo was killed in a gateway at + Seringapatam.<a name="NtA_48" href="#Nt_48"><sup>[48]</sup></a></p> + + <p> </p> + +<p class="cenhead">FINAEUS ON CIRCLE SQUARING.</p> + +<blockquote class="b1n"> + + <p>Orontii Finaei ... Quadratura Circuli. Paris, 1544, 4to.</p> + +</blockquote> + + <p>Orontius<a name="NtA_49" href="#Nt_49"><sup>[49]</sup></a> squared the + circle out of all comprehension; but he was killed by a feather from his + own wing. His <!-- Page 51 --><span class="pagenum"><a + name="page51"></a>[51]</span>former pupil, John Buteo,<a name="NtA_50" + href="#Nt_50"><sup>[50]</sup></a> the same who—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<a name="NtA_51" + href="#Nt_51"><sup>[51]</sup></a> should be called Viète, because his + Latin name is Vieta. It is difficult to restore Buteo; for not only now + is <i>butor</i> a blockhead as well as a bird, but we really cannot know + what kind of bird Buteo stood for. We may be sure that Madame Fine was + Denise Blanche; for Dionysia Candida can mean nothing else. Let her shade + rejoice in the fame which Hubertus Sussannæus has given her.</p> + + <p>I ought to add that the quadrature of Orontius, and solutions of all + the other difficulties, were first published in <i>De Rebus Mathematicis + Hactenus Desideratis</i>,<a name="NtA_52" + href="#Nt_52"><sup>[52]</sup></a> of which I have not the date.</p> + + <p> </p> + +<p><!-- Page 52 --><span class="pagenum"><a name="page52"></a>[52]</span></p> + +<p class="cenhead">DUCHESNE, AND A DISQUISITION ON ETYMOLOGY.</p> + +<blockquote class="b1n"> + + <p>Nicolai Raymari Ursi Dithmarsi Fundamentum Astronomicum, id est, nova + doctrina sinuum et triangulorum.... Strasburg, 1588, 4to.<a name="NtA_53" + href="#Nt_53"><sup>[53]</sup></a></p> + +</blockquote> + + <p>People choose the name of this astronomer for themselves: I take + <i>Ursus</i>, because he <i>was</i> a bear. This book gave the quadrature + of Simon Duchesne,<a name="NtA_54" href="#Nt_54"><sup>[54]</sup></a> or à + Quercu, which excited Peter Metius,<a name="NtA_55" + href="#Nt_55"><sup>[55]</sup></a> as presently noticed. It also gave that + unintelligible reference to Justus Byrgius which has been used in the + discussion about the invention of logarithms.<a name="NtA_56" + href="#Nt_56"><sup>[56]</sup></a></p> + + <p>The real name of Duchesne is Van der Eycke. I have met with a tract in + Dutch, <i>Letterkundige Aanteekeningen</i>, upon Van Eycke, Van Ceulen,<a + name="NtA_57" href="#Nt_57"><sup>[57]</sup></a> etc., by J. J. Dodt van + Flensburg,<a name="NtA_58" href="#Nt_58"><sup>[58]</sup></a> which I make + out to be since 1841 in date. I should <!-- Page 53 --><span + class="pagenum"><a name="page53"></a>[53]</span>much like a translation + of this tract to be printed, say in the <i>Phil. Mag.</i> Dutch would be + clear English if it were properly spelt. For example, <i>learn-master</i> + would be seen at once to be <i>teacher</i>; but they will spell it + <i>leermeester</i>. <i>Of these</i> they write as <i>van deze</i>; + <i>widow</i> they make <i>weduwe</i>. All this is plain to me, who never + saw a Dutch dictionary in my life; but many of their misspellings are + quite unconquerable.</p> + + <p> </p> + +<p class="cenhead">FALCO'S RARE TRACT.</p> + +<blockquote class="b1n"> + + <p>Jacobus Falco Valentinus, miles Ordinis Montesiani, hanc circuli + quadraturam invenit. Antwerp, 1589, 4to.<a name="NtA_59" + href="#Nt_59"><sup>[59]</sup></a></p> + +</blockquote> + + <p>The attempt is more than commonly worthless; but as Montucla and + others have referred to the verses at the end, and as the tract is of the + rarest, I will quote them:</p> + + <div class="poem"> + <div class="stanza"> + <p class="i4"><i>Circulus loquitur.</i></p> + <p>Vocabar ante circulus</p> + <p>Eramque curvus undique</p> + <p>Ut alta solis orbita</p> + <p>Et arcus ille nubium.</p> + <p>Eram figura nobilis</p> + <p>Carensque sola origine</p> + <p>Carensque sola termino.</p> + <p>Modo indecora prodeo</p> + <p>Novisque fœdor angulis.</p> + <p>Nec hoc peregit Archytas<a name="NtA_60" href="#Nt_60"><sup>[60]</sup></a></p> + <p>Neque Icari pater neque</p> + <p>Tuus, Iapete, filius.</p> + <p>Quis ergo casus aut Deus</p> + <p>Meam quadravit aream?</p> + </div> + + <div class="stanza"> + <p class="i4"><i>Respondet auctor.</i></p> + <p>Ad alta Turiæ ostia</p> + <p>Lacumque limpidissimum</p> + <p>Sita est beata civitas</p> +<!-- Page 54 --><span class="pagenum"><a name="page54"></a>[54]</span> + <p>Parum Saguntus abfuit</p> + <p>Abestque Sucro plusculum.</p> + <p>Hic est poeta quispiam</p> + <p>Libenter astra consulens</p> + <p>Sibique semper arrogans</p> + <p>Negata doctioribus,</p> + <p>Senex ubique cogitans</p> + <p>Sui frequenter immemor</p> + <p>Nec explicare circinum</p> + <p>Nec exarare lineas</p> + <p>Sciens ut ipse prædicat.</p> + <p>Hic ergo bellus artifex</p> + <p>Tuam quadravit aream.<a name="NtA_61" href="#Nt_61"><sup>[61]</sup></a></p> + </div> + </div> + <p>Falco's verses are pretty, if the ˘-mysteries be correct; but of + these things I have forgotten—what I knew. [One mistake has been + pointed out to me: it is Arch<span class="over">y</span>tas].</p> + + <p>As a specimen of the way in which history is written, I copy the + account which Montucla—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.</p> + +<p><!-- Page 55 --><span class="pagenum"><a name="page55"></a>[55]</span></p> + + <p> </p> + +<p class="cenhead">BUNGUS ON THE MYSTERY OF NUMBER.</p> + +<blockquote class="b1n"> + + <p>Petri Bungi Bergomatis Numerorum mysteria. Bergomi [Bergamo], 1591, + 4to. Second Edition.</p> + +</blockquote> + + <p>The first edition is said to be of 1585;<a name="NtA_62" + href="#Nt_62"><sup>[62]</sup></a> the third, Paris, 1618. Bungus is not + for my purpose on his own score, but those who gave the numbers their + mysterious characters: he is but a collector. He quotes or uses 402 + authors, as we are informed by his list; this just beats Warburton,<a + name="NtA_63" href="#Nt_63"><sup>[63]</sup></a> whom some eulogist or + satirist, I forget which, holds up as having used 400 authors in some one + work. Bungus goes through 1, 2, 3, etc., and gives the account of + everything remarkable in which each number occurs; his accounts not being + always mysterious. The numbers which have nothing to say for themselves + are omitted: thus there is a gap between 50 and 60. In treating 666, + Bungus, a good Catholic, could not compliment the Pope with it, but he + fixes it on Martin Luther with a little forcing. If from A to I represent + 1-10, from K to S 10-90, and from T to Z 100-500, we see:</p> + +<table class="nobctr" width="50%" summary="Martin Lutera 666" title="Martin Lutera 666"> +<tr><td style="width:2%" align="center">M</td> +<td style="width:2%" align="center">A</td> +<td style="width:2%" align="center">R</td> +<td style="width:2%" align="center">T</td> +<td style="width:2%" align="center">I</td> +<td style="width:2%" align="center">N</td> +<td style="width:2%" align="center"> </td> +<td style="width:2%" align="center">L</td> +<td style="width:2%" align="center">U</td> +<td style="width:2%" align="center">T</td> +<td style="width:2%" align="center">E</td> +<td style="width:2%" align="center">R</td> +<td style="width:2%" align="center">A</td></tr> +<tr><td align="center">30</td> +<td align="center">1</td> +<td align="center">80</td> +<td align="center">100</td> +<td align="center">9</td> +<td align="center">40</td> +<td align="center"> </td> +<td align="center">20</td> +<td align="center">200</td> +<td align="center">100</td> +<td align="center">5</td> +<td align="center">80</td> +<td align="center">1</td></tr> +</table> + + <p>which gives 666. Again, in Hebrew, <i>Lulter</i> does the same:</p> + +<table class="nobctr" width="25%" summary="Hebrew Lulter 666" title="Hebrew Lulter 666"> +<tr> +<td style="width:2%" align="center"><span lang="he" class="heb" title="R" ><bdo dir="rtl">ר</bdo></span></td> +<td style="width:2%" align="center"><span lang="he" class="heb" title="T" ><bdo dir="rtl">ת</bdo></span></td> +<td style="width:2%" align="center"><span lang="he" class="heb" title="L" ><bdo dir="rtl">ל</bdo></span></td> +<td style="width:2%" align="center"><span lang="he" class="heb" title="W" ><bdo dir="rtl">ו</bdo></span></td> +<td style="width:2%" align="center"><span lang="he" class="heb" title="L" ><bdo dir="rtl">ל</bdo></span></td> +</tr> +<tr><td align="center">200</td> +<td align="center">400</td> +<td align="center">30</td> +<td align="center">6</td> +<td align="center">30</td></tr> +</table> + + <p>And thus two can play at any game. The second is better than the + first: to Latinize the surname and not the Christian <!-- Page 56 + --><span class="pagenum"><a name="page56"></a>[56]</span>name is very + unscholarlike. The last number mentioned is a thousand millions; all + greater numbers are dismissed in half a page. Then follows an accurate + distinction between <i>number</i> and <i>multitude</i>—a thing much + wanted both in arithmetic and logic.</p> + + <p> </p> + +<p class="cenhead">WHICH LEADS TO A STORY ABOUT THE ROYAL SOCIETY.</p> + + <p>What may be the use of such a book as this? The last occasion on which + it was used was the following. Fifteen or sixteen years ago the Royal + Society determined to restrict the number of yearly admissions to fifteen + men of science, and noblemen <i>ad libitum</i>; the men of science being + selected and recommended by the Council, with a power, since practically + surrendered, to the Society to elect more. This plan appears to me to be + directly against the spirit of their charter, the true intent of which + is, that all who are fit should be allowed to promote natural knowledge + in association, from and after the time at which they are both fit and + willing. It is also working more absurdly from year to year; the tariff + of fifteen per annum will soon amount to the practical exclusion of many + who would be very useful. This begins to be felt already, I suspect. But, + as appears above, the body of the Society has the remedy in its own + hands. When the alteration was discussed by the Council, my friend the + late Mr. Galloway,<a name="NtA_64" href="#Nt_64"><sup>[64]</sup></a> then + one of the body, opposed it strongly, and inquired particularly into the + reason why <i>fifteen</i>, of all numbers, was the one to be selected. + Was it because fifteen is seven and eight, typifying the Old Testament + Sabbath, and the New Testament day of the resurrection following? Was it + because Paul strove fifteen days against Peter, proving that he was a + doctor both of the Old and New Testament? Was it because the prophet + Hosea bought a lady <!-- Page 57 --><span class="pagenum"><a + name="page57"></a>[57]</span>for fifteen pieces of silver? Was it + because, according to Micah, seven shepherds and eight chiefs should + waste the Assyrians? Was it because Ecclesiastes commands equal reverence + to be given to both Testaments—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 <i>fifteen</i> of the + Royal Society.</p> + + <p> </p> + +<p class="cenhead">AND ALSO TO A QUESTION OF EVIDENCE.</p> + + <p>[I make a remark on the different colors which the same person gives + to one story, according to the bias under which he tells it. My friend + Galloway told me how he had quizzed the Council of the Royal Society, to + my great amusement. Whenever I am struck by the words of any one, I carry + away a vivid recollection of position, gestures, tones, etc. I do not + know whether this be common or uncommon. I never recall this joke without + seeing before me my friend, leaning against his bookcase, with Bungus + open in his hand, and a certain half-depreciatory tone which he often + used <!-- Page 58 --><span class="pagenum"><a + name="page58"></a>[58]</span>when speaking of himself. Long after his + death, an F.R.S. who was present at the discussion, told me the story. I + did not say I had heard it, but I watched him, with Galloway at the + bookcase before me. I wanted to see whether the two would agree as to the + fact of an enormous budget of fifteens having been fired at the Council, + and they did agree perfectly. But when the paragraph of the Budget + appeared in the <i>Athenæum</i>, my friend, who seemed rather to object + to the <i>showing-up</i>, assured me that the thing was grossly + exaggerated; there was indeed a fifteen or two, but nothing like the + number I had given. I had, however, taken sharp note of the previous + narration.</p> + + <p> </p> + +<p class="cenhead">AND TO ANOTHER QUESTION OF EVIDENCE.</p> + + <p>I will give another instance. An Indian officer gave me an account of + an elephant, as follows. A detachment was on the march, and one of the + gun-carriages got a wheel off the track, so that it was also off the + ground, and hanging over a precipice. If the bullocks had moved a step, + carriages, bullocks, and all must have been precipitated. No one knew + what could be done until some one proposed to bring up an elephant, and + let him manage it his own way. The elephant took a moment's survey of the + fix, put his trunk under the axle of the free wheel, and waited. The + surrounders, who saw what he meant, moved the bullocks gently forward, + the elephant followed, supporting the axle, until there was ground under + the wheel, when he let it quietly down. From all I had heard of the + elephant, this was not too much to believe. But when, years afterwards, I + reminded my friend of his story, he assured me that I had misunderstood + him, that the elephant was <i>directed</i> to put his trunk under the + wheel, and saw in a moment why. This is reasonable sagacity, and very + likely the correct account; but I am quite sure that, in the fit of + elephant-worship under which the story was first told, it was told as I + have first stated it.] <!-- Page 59 --><span class="pagenum"><a + name="page59"></a>[59]</span></p> + + <p> </p> + +<p class="cenhead">GIORDANO BRUNO AND HIS PARADOXES.</p> + +<blockquote class="b1n"> + + <p>[Jordani Bruni Nolani de Monade, Numero et Figura ... item de + Innumerabilibus, Immenso, et Infigurabili ... Frankfort, 1591, 8vo.<a + name="NtA_65" href="#Nt_65"><sup>[65]</sup></a></p> + +</blockquote> + + <p>I cannot imagine how I came to omit a writer whom I have known so many + years, unless the following story will explain it. The officer reproved + the boatswain for perpetual swearing; the boatswain answered that he + heard the officers swear. "Only in an emergency," said the officer. + "That's just it," replied the other; "a boatswain's life is a life of + 'mergency." Giordano Bruno was all paradox; and my mind was not alive to + his paradoxes, just as my ears might have become dead to the boatswain's + oaths. He was, as has been said, a vorticist before Descartes,<a + name="NtA_66" href="#Nt_66"><sup>[66]</sup></a> an optimist before + Leibnitz, a Copernican before Galileo. It would be easy to collect a + hundred strange opinions of his. He was born about 1550, and was roasted + alive at Rome, February 17, 1600, for the maintenance and defence of the + holy Church, and the rights and liberties of the same. These last words + are from the writ of our own good James I, under which Leggatt<a + name="NtA_67" href="#Nt_67"><sup>[67]</sup></a> was roasted at + Smithfield, in March 1612; and if I had a copy of the instrument under + which Wightman<a name="NtA_68" href="#Nt_68"><sup>[68]</sup></a> was + roasted at Lichfield, a month afterwards, I daresay I should <!-- Page 60 + --><span class="pagenum"><a name="page60"></a>[60]</span>find something + quite as edifying. I extract an account which I gave of Bruno in the + <i>Comp. Alm.</i> for 1855:</p> + + <p>"He was first a Dominican priest, then a Calvinist; and was roasted + alive at Rome, in 1600, for as many heresies of opinion, religious and + philosophical, as ever lit one fire. Some defenders of the papal cause + have at least worded their accusations so to be understood as imputing to + him villainous actions. But it is positively certain that his death was + due to opinions alone, and that retractation, even after sentence, would + have saved him. There exists a remarkable letter, written from Rome on + the very day of the murder, by Scioppius<a name="NtA_69" + href="#Nt_69"><sup>[69]</sup></a> (the celebrated scholar, a waspish + convert from Lutheranism, known by his hatred to Protestants and Jesuits) + to Rittershusius,<a name="NtA_70" href="#Nt_70"><sup>[70]</sup></a> a + well-known Lutheran writer on civil and canon law, whose works are in the + index of prohibited books. This letter has been reprinted by Libri (vol. + iv. p. 407). The writer informs his friend (whom he wished to convince + that even a Lutheran would have burnt Bruno) that all Rome would tell him + that Bruno died for Lutheranism; but this is because the Italians do not + know the difference between one heresy and another, in which simplicity + (says the writer) may God preserve them. That is to say, they knew the + difference between a live heretic and a roasted one by actual inspection, + but had no idea of the difference between a Lutheran and a Calvinist. The + countrymen of Boccaccio would have smiled at the idea which the German + scholar entertained of them. They said Bruno was burnt for Lutheranism, a + name under which they classed all Protestants: and they are better + witnesses than Schopp, or Scioppius. He then proceeds to describe to his + Protestant friend (to whom he would certainly not have omitted any act + which both their churches would have condemned) the mass of opinions with + which Bruno was charged; as that there <!-- Page 61 --><span + class="pagenum"><a name="page61"></a>[61]</span>are innumerable worlds, + that souls migrate, that Moses was a magician, that the Scriptures are a + dream, that only the Hebrews descended from Adam and Eve, that the devils + would be saved, that Christ was a magician and deservedly put to death, + etc. In fact, says he, Bruno has advanced all that was ever brought + forward by all heathen philosophers, and by all heretics, ancient and + modern. A time for retractation was given, both before sentence and + after, which should be noted, as well for the wretched palliation which + it may afford, as for the additional proof it gives that opinions, and + opinions only, brought him to the stake. In this medley of charges the + Scriptures are a dream, while Adam, Eve, devils, and salvation are + truths, and the Saviour a deceiver. We have examined no work of Bruno + except the <i>De Monade</i>, etc., mentioned in the text. A strong though + strange <i>theism</i> runs through the whole, and Moses, Christ, the + Fathers, etc., are cited in a manner which excites no remark either way. + Among the versions of the cause of Bruno's death is <i>atheism</i>: but + this word was very often used to denote rejection of revelation, not + merely in the common course of dispute, but by such writers, for + instance, as Brucker<a name="NtA_71" href="#Nt_71"><sup>[71]</sup></a> + and Morhof.<a name="NtA_72" href="#Nt_72"><sup>[72]</sup></a> Thus Morhof + says of the <i>De Monade, etc.</i>, that it exhibits no manifest signs of + atheism. What he means by the word is clear enough, when he thus speaks + of a work which acknowledges God in hundreds of places, and rejects + opinions as blasphemous in several. The work of Bruno in which his + astronomical opinions are contained is <i>De Monade, etc.</i> (Frankfort, + 1591, 8vo). He is the most thorough-going Copernican possible, and throws + out almost every opinion, true or false, which has ever been discussed by + astronomers, from the theory of innumerable inhabited worlds and systems + to that <!-- Page 62 --><span class="pagenum"><a + name="page62"></a>[62]</span>of the planetary nature of comets. Libri + (vol. iv)<a name="NtA_73" href="#Nt_73"><sup>[73]</sup></a> has reprinted + the most striking part of his expressions of Copernican opinion."</p> + + <p> </p> + +<p class="cenhead">THIS LEADS TO THE CHURCH QUESTION.</p> + + <p>The Satanic doctrine that a church may employ force in aid of its + dogma is supposed to be obsolete in England, except as an individual + paradox; but this is difficult to settle. Opinions are much divided as to + what the Roman Church would do in England, if she could: any one who + doubts that she claims the right does not deserve an answer. When the + hopes of the Tractarian section of the High Church were in bloom, before + the most conspicuous intellects among them had <i>transgressed</i> their + ministry, that they might go to their own place, I had the curiosity to + see how far it could be ascertained whether they held the only doctrine + which makes me the personal enemy of a sect. I found in one of their + tracts the assumption of a right to persecute, modified by an asserted + conviction that force was not efficient. I cannot now say that this tract + was one of the celebrated ninety; and on looking at the collection I find + it so poorly furnished with contents, etc., that nothing but searching + through three thick volumes would decide. In these volumes I find, + augmenting as we go on, declarations about the character and power of + "the Church" which have a suspicious appearance. The suspicion is + increased by that curious piece of sophistry, No. 87, on religious + reserve. The queer paradoxes of that tract leave us in doubt as to + everything but this, that the church(man) is not bound to give his whole + counsel in all things, and not bound to say what the things are in which + he does not give it. It is likely enough that some of the "rights and + liberties" are but scantily described. There is now no fear; but the time + was when, if not fear, there might be a looking for of fear to come; + nobody could then be so <!-- Page 63 --><span class="pagenum"><a + name="page63"></a>[63]</span>sure as we now are that the lion was only + asleep. There was every appearance of a harder fight at hand than was + really found needful.</p> + + <p>Among other exquisite quirks of interpretation in the No. 87 above + mentioned is the following. God himself employs reserve; he is said to be + decked with light as with a garment (the old or prayer-book version of + Psalm civ. 2). To an ordinary apprehension this would be a strong image + of display, manifestation, revelation; but there is something more. "Does + not a garment veil in some measure that which it clothes? Is not that + very light concealment?"</p> + + <p>This No. 87, admitted into a series, fixes upon the managers of the + series, who permitted its introduction, a strong presumption of that + underhand intent with which they were charged. At the same time it is + honorable to our liberty that this series could be published: though its + promoters were greatly shocked when the Essayists and Bishop Colenso<a + name="NtA_74" href="#Nt_74"><sup>[74]</sup></a> took a swing on the other + side. When No. 90 was under discussion, Dr. Maitland,<a name="NtA_75" + href="#Nt_75"><sup>[75]</sup></a> the librarian at Lambeth, asked + Archbishop Howley<a name="NtA_76" href="#Nt_76"><sup>[76]</sup></a> a + question about No. 89. "I did not so much as know there <i>was</i> a No. + 89," was the answer. I am almost sure I have seen this in print, and + quite sure that Dr. Maitland told it to me. It is creditable that there + was so much freedom; but No. 90 was <i>too bad</i>, and was stopped.</p> + + <p>The Tractarian mania has now (October 1866) settled down into a + chronic vestment disease, complicated with fits of transubstantiation, + which has taken the name of <!-- Page 64 --><span class="pagenum"><a + name="page64"></a>[64]</span><i>Ritualism</i>. The common sense of our + national character will not put up with a continuance of this grotesque + folly; millinery in all its branches will at last be advertised only over + the proper shops. I am told that the Ritualists give short and practical + sermons; if so, they may do good in the end. The English Establishment + has always contained those who want an excitement; the New Testament, in + its plain meaning, can do little for them. Since the Revolution, + Jacobitism, Wesleyanism, Evangelicism, Puseyism,<a name="NtA_77" + href="#Nt_77"><sup>[77]</sup></a> and Ritualism, have come on in turn, + and have furnished hot water for those who could not wash without it. If + the Ritualists should succeed in substituting short and practical + teaching for the high-spiced lectures of the doctrinalists, they will be + remembered with praise. John the Baptist would perhaps not have brought + all Jerusalem out into the wilderness by his plain and good sermons: it + was the camel's hair and the locusts which got him a congregation, and + which, perhaps, added force to his precepts. When at school I heard a + dialogue, between an usher and the man who cleaned the shoes, about Mr. + ——, a minister, a very corporate body with due area of + waistcoat. "He is a man of great erudition," said the first. "Ah, yes + sir," said Joe; "any one can see that who looks at that silk + waistcoat."]</p> + + <p> </p> + +<p class="cenhead">OF THOMAS GEPHYRANDER SALICETUS.</p> + + <p>[When I said at the outset that I had only taken books from my own + store, I should have added that I did not make any search for information + given as <i>part</i> of a work. Had I looked <i>through</i> all my books, + I might have made some curious additions. For instance, in Schott's + <i>Magia Naturalis</i><a name="NtA_78" href="#Nt_78"><sup>[78]</sup></a> + <!-- Page 65 --><span class="pagenum"><a + name="page65"></a>[65]</span>(vol. iii. pp. 756-778) is an account of the + quadrature of Gephyra<i>u</i>der, as he is misprinted in Montucla. He was + Thomas Gephyrander Salicetus; and he published two editions, in 1608 and + 1609.<a name="NtA_79" href="#Nt_79"><sup>[79]</sup></a> I never even + heard of a copy of either. His work is of the extreme of absurdity: he + makes a distinction between geometrical and arithmetical fractions, and + evolves theorems from it. More curious than his quadrature is his name; + what are we to make of it? If a German, he is probably a German form of + <i>Bridgeman</i>. and Salicetus refers him to <i>Weiden</i>. But + <i>Thomas</i> was hardly a German Christian name of his time; of 526 + German philosophers, physicians, lawyers, and theologians who were + biographed by Melchior Adam,<a name="NtA_80" + href="#Nt_80"><sup>[80]</sup></a> only two are of this name. Of these one + is Thomas Erastus,<a name="NtA_81" href="#Nt_81"><sup>[81]</sup></a> the + physician whose theological writings against the Church as a separate + power have given the name of Erastians to those who follow his doctrine, + whether they have heard of him or not. Erastus is little known; + accordingly, some have supposed that he must be Erastus, the friend of + St. Paul and Timothy (Acts xix. 22; 2 Tim. iv. 20; Rom. xvi. 23), but + what this gentleman did to earn the character is not hinted at. Few words + would have done: Gaius (Rom. xvi. 23) has an immortality which many more + noted men have missed, given by John Bunyan, out of seven words of St. + Paul. I was once told that the Erastians got their name from + <i>Blastus</i>, and I could not solve <i>bl = er</i>: at last I + remembered that Blastus was a <i>chamberlain</i><a name="NtA_82" + href="#Nt_82"><sup>[82]</sup></a> as well as Erastus; hence the + association which <!-- Page 66 --><span class="pagenum"><a + name="page66"></a>[66]</span>caused the mistake. The real heresiarch was + a physician who died in 1583; his heresy was promulgated in a work, + published immediately after his death by his widow, <i>De + Excommunicatione Ecclesiastica</i>. He denied the power of + excommunication on the principle above stated; and was answered by + Besa.<a name="NtA_83" href="#Nt_83"><sup>[83]</sup></a> The work was + translated by Dr. R. Lee<a name="NtA_84" + href="#Nt_84"><sup>[84]</sup></a> (Edinb. 1844, 8vo). The other is Thomas + Grynæus,<a name="NtA_85" href="#Nt_85"><sup>[85]</sup></a> a theologian, + nephew of Simon, who first printed Euclid in Greek; of him Adam says that + of works he published none, of learned sons four. If Gephyrander were a + Frenchman, his name is not so easily guessed at; but he must have been of + La Saussaye. The account given by Schott is taken from a certain Father + Philip Colbinus, who wrote against him.</p> + + <p>In some manuscripts lately given to the Royal Society, David + Gregory,<a name="NtA_86" href="#Nt_86"><sup>[86]</sup></a> who seems to + have seen Gephyrander's work, calls him Salicetus <i>Westphalus</i>, + which is probably on the title-page. But the only Weiden I can find is in + Bavaria. Murhard has both editions in his Catalogue, but had plainly + never seen the books: he gives the author as Thomas Gep. Hyandrus, + Salicettus Westphalus. Murhard is a very old referee of mine; but who the + <i>non nominandus</i> was to see Montucla's <i>Gephyrander</i> in + Murhard's <i>Gep. Hyandrus</i>, both writers being usually accurate?]</p> + + <p> </p> + +<p class="cenhead">NAPIER ON REVELATIONS.</p> + +<blockquote class="b1n"> + + <p>A plain discoverie of the whole Revelation of St. John ... whereunto + are annexed certain oracles of Sibylla.... Set Foorth by John Napeir L. + of Marchiston. London, 1611, 4to.<a name="NtA_87" + href="#Nt_87"><sup>[87]</sup></a></p> + +</blockquote> + +<p><!-- Page 67 --><span class="pagenum"><a name="page67"></a>[67]</span></p> + + <p>The first edition was Edinburgh, 1593,<a name="NtA_88" + href="#Nt_88"><sup>[88]</sup></a> 4to. Napier<a name="NtA_89" + href="#Nt_89"><sup>[89]</sup></a> always believed that his great mission + was to upset the Pope, and that logarithms, and such things, were merely + episodes and relaxations. It is a pity that so many books have been + written about this matter, while Napier, as good as any, is forgotten and + unread. He is one of the first who gave us the six thousand years. "There + is a sentence of the house of Elias reserved in all ages, bearing these + words: The world shall stand six thousand years, and then it shall be + consumed by fire: two thousand yeares voide or without lawe, two thousand + yeares under the law, and two thousand yeares shall be the daies of the + Messias...."</p> + + <p>I give Napier's parting salute: it is a killing dilemma:</p> + + <p>"In summar conclusion, if thou o <i>Rome</i> aledges thyselfe + reformed, and to beleeue true Christianisme, then beleeue Saint + <i>John</i> the Disciple, whome Christ loued, publikely here in this + Reuelation proclaiming thy wracke, but if thou remain Ethnick in thy + priuate thoghts, beleeuing<a name="NtA_90" + href="#Nt_90"><sup>[90]</sup></a> the old Oracles of the <i>Sibyls</i> + reuerently keeped somtime in thy <i>Capitol</i>: then doth here this + <i>Sibyll</i> proclame also thy wracke. Repent therefore alwayes, in this + thy latter breath, as thou louest thine Eternall salvation. + <i>Amen</i>."</p> + + <p>—Strange that Napier should not have seen that this appeal could + not succeed, unless the prophecies of the Apocalypse were no true + prophecies at all.</p> + +<p><!-- Page 68 --><span class="pagenum"><a name="page68"></a>[68]</span></p> + + <p> </p> + +<p class="cenhead">OF GILBERT'S DE MAGNETE.</p> + +<blockquote class="b1n"> + + <p>De Magnete magneticisque corporibus, et de magno magnete tellure. By + William Gilbert. London, 1600, folio.—There is a second edition; + and a third, according to Watt.<a name="NtA_91" + href="#Nt_91"><sup>[91]</sup></a></p> + +</blockquote> + + <p>Of the great work on the magnet there is no need to speak, though it + was a paradox in its day. The posthumous work of Gilbert, "De Mundo + nostro sublunari philosophia nova" (Amsterdam, 1651, 4to)<a name="NtA_92" + href="#Nt_92"><sup>[92]</sup></a> is, as the title indicates, confined to + the physics of the globe and its atmosphere. It has never excited + attention: I should hope it would be examined with our present + lights.</p> + + <p> </p> + +<p class="cenhead">OF GIOVANNI BATISTA PORTA.</p> + +<blockquote class="b1n"> + + <p>Elementorum Curvilineorium Libri tres. By John Baptista Porta. Rome, + 1610, 4to.<a name="NtA_93" href="#Nt_93"><sup>[93]</sup></a></p> + +</blockquote> + + <p>This is a ridiculous attempt, which defies description, except that it + is all about lunules. Porta was a voluminous writer. His printer + announces fourteen works printed, and four to come, besides thirteen + plays printed, and eleven waiting. His name is, and will be, current in + treatises on physics for more reasons than one.</p> + +<p><!-- Page 69 --><span class="pagenum"><a name="page69"></a>[69]</span></p> + + <p> </p> + +<p class="cenhead">CATALDI ON THE QUADRATURE.</p> + +<blockquote class="b1n"> + + <p>Trattato della quadratura del cerchio. Di Pietro Antonio Cataldi. + Bologna, 1612, folio.<a name="NtA_94" + href="#Nt_94"><sup>[94]</sup></a></p> + +</blockquote> + + <p>Rheticus,<a name="NtA_95" href="#Nt_95"><sup>[95]</sup></a> Vieta, and + Cataldi are the three untiring computers of Germany, France, and Italy; + Napier in Scotland, and Briggs<a name="NtA_96" + href="#Nt_96"><sup>[96]</sup></a> in England, come just after them. This + work claims a place as beginning with the quadrature of Pellegrino + Borello<a name="NtA_97" href="#Nt_97"><sup>[97]</sup></a> of Reggio, who + will have the circle to be exactly 3 diameters and 69/484 of a diameter. + Cataldi, taking Van Ceulen's approximation, works hard at the finding of + integers which nearly represent the ratio. He had not then the + <i>continued fraction</i>, a mode of representation which he gave the + next year in his work on the square root. He has but twenty of Van + Ceulen's thirty places, which he takes from Clavius<a name="NtA_98" + href="#Nt_98"><sup>[98]</sup></a>: and any one might be puzzled to know + whence the Italians got the result; Van Ceulen, in 1612, not having been + translated from Dutch. But Clavius names his comrade Gruenberger, and + attributes the approximation to them <!-- Page 70 --><span + class="pagenum"><a name="page70"></a>[70]</span>jointly; "Lud. a Collen + et Chr. Gruenbergerus<a name="NtA_99" href="#Nt_99"><sup>[99]</sup></a> + invenerunt," which he had no right to do, unless, to his private + knowledge, Gruenberger had verified Van Ceulen. And Gruenberger only + handed over twenty of the places. But here is one instance, out of many, + of the polyglot character of the Jesuit body, and its advantages in + literature.</p> + + <p> </p> + +<p class="cenhead">OF LANSBERGIUS.</p> + +<blockquote class="b1n"> + + <p>Philippi Lausbergii Cyclometriæ Novæ Libri Duo. Middleburg, 1616, + 4to.<a name="NtA_100" href="#Nt_100"><sup>[100]</sup></a></p> + +</blockquote> + + <p>This is one of the legitimate quadratures, on which I shall here only + remark that by candlelight it is quadrature under difficulties, for all + the diagrams are in red ink.</p> + + <p> </p> + +<p class="cenhead">A TEXT LEADING TO REMARKS ON PRESTER JOHN.</p> + +<blockquote class="b1n"> + + <p>Recherches Curieuses des Mesures du Monde. By S. C. de V. Paris, 1626, + 8vo (pp. 48).<a name="NtA_101" href="#Nt_101"><sup>[101]</sup></a></p> + +</blockquote> + + <p>It is written by some Count for his son; and if all the French + nobility would have given their sons the same kind of instruction about + rank, the old French aristocracy would have been as prosperous at this + moment as the English peerage and squireage. I sent the tract to Capt. + Speke,<a name="NtA_102" href="#Nt_102"><sup>[102]</sup></a> shortly after + his arrival in England, thinking he might like <!-- Page 71 --><span + class="pagenum"><a name="page71"></a>[71]</span>to see the old names of + the Ethiopian provinces. But I first made a copy of all that relates to + Prester John,<a name="NtA_103" href="#Nt_103"><sup>[103]</sup></a> + himself a paradox. The tract contains, <i>inter alia</i>, an account of + the four empires; of the great Turk, the great Tartar, the great Sophy, + and the great Prester John. This word <i>great</i> (<i>grand</i>), which + was long used in the phrase "the great Turk," is a generic adjunct to an + emperor. Of the Tartars it is said that "c'est vne nation prophane et + barbaresque, sale et vilaine, qui mangent la chair demie cruë, qui + boiuent du laict de jument, et qui n'vsent de nappes et seruiettes que + pour essuyer leurs bouches et leurs mains."<a name="NtA_104" + href="#Nt_104"><sup>[104]</sup></a> Many persons have heard of Prester + John, and have a very indistinct idea of him. I give all that is said + about him, since the recent discussions about the Nile may give an + interest to the old notions of geography.</p> + + <p>"Le grand Prestre Jean qui est le quatriesme en rang, est Empereur + d'Ethiopie, et des Abyssins, et se vante d'estre issu de la race de + Dauid, comme estant descendu de la Royne de Saba, Royne d'Ethiopie, + laquelle estant venuë en Hierusalem pour voir la sagesse de Salomon, + enuiron l'an du monde 2952, s'en retourna grosse d'vn fils qu'ils nomment + Moylech, duquel ils disent estre descendus en ligne directe. Et ainsi il + se glorifie d'estre le plus ancien Monarque de la terre, disant que son + Empire a duré plus de trois mil ans, ce que nul autre Empire ne peut + dire. Aussi met-il en ses tiltres ce qui s'ensuit: Nous, N. Souuerain en + mes Royaumes, vniquement aymé de Dieu, colomne de la foy, sorty de la + race de Inda, etc. Les limites de cet Empire touchent à la mer Rouge, et + aux montagnes d'Azuma vers <!-- Page 72 --><span class="pagenum"><a + name="page72"></a>[72]</span>l'Orient, et du costé de l'Occident, il est + borné du fleuue du Nil, qui le separe de la Nubie, vers le Septentrion il + a l'Ægypte, et au Midy les Royaumes de Congo, et de Mozambique, sa + longueur contenant quarante degré, qui font mille vingt cinq lieuës, et + ce depuis Congo ou Mozambique qui sont au Midy, iusqu'en Ægypte qui est + au Septentrion, et sa largeur contenant depuis le Nil qui est à + l'Occident, iusqu'aux montagnes d'Azuma, qui sont à l'Orient, sept cens + vingt cinq lieues, qui font vingt neuf degrez. Cét empire a sous soy + trente grandes Prouinces, sçavoir, Medra, Gaga, Alchy, Cedalon, Mantro, + Finazam, Barnaquez, Ambiam, Fungy, Angoté, Cigremaon, Gorga, Cafatez, + Zastanla, Zeth, Barly, Belangana, Tygra, Gorgany, Barganaza, d'Ancut, + Dargaly, Ambiacatina, Caracogly, Amara, Maon (<i>sic</i>), Guegiera, + Bally, Dobora et Macheda. Toutes ces Prouinces cy dessus sont situées + iustement sous la ligne equinoxiale, entres les Tropiques de Capricorne, + et de Cancer. Mais elles s'approchent de nostre Tropique, de deux cens + cinquante lieuës plus qu'elles ne font de l'autre Tropique. Ce mot de + Prestre Jean signifie grand Seigneur, et n'est pas Prestre comme + plusieurs pense, il a esté tousiours Chrestien, mais souuent + Schismatique: maintenant il est Catholique, et reconnaist le Pape pour + Souuerain Pontife. I'ay veu quelqu'vn des ses Euesques, estant en + Hierusalem, auec lequel i'ay conferé souuent par le moyen de nostre + trucheman: il estoit d'vn port graue et serieux, succiur (<i>sic</i>) en + son parler, mais subtil à merueilles en tout ce qu'il disoit. Il prenoit + grand plaisir au recit que je luy faisais de nos belles ceremonies, et de + la grauité de nos Prelats en leurs habits Pontificaux, et autres choses + que je laisse pour dire, que l'Ethiopien est ioyoux et gaillard, ne + ressemblant en rien a la saleté du Tartare, ny à l'affreux regard du + miserable Arabe, mais ils sont fins et cauteleux, et ne se fient en + personne, soupçonneux à merueilles, et fort devotieux, ils ne sont du + tout noirs comme l'on croit, i'entens parler de ceux qui ne sont pas sous + la ligne Equinoxiale, ny trop proches <!-- Page 73 --><span + class="pagenum"><a name="page73"></a>[73]</span>d'icelle, car ceux qui + sont dessous sont les Mores que nous voyons."<a name="NtA_105" + href="#Nt_105"><sup>[105]</sup></a></p> + + <p>It will be observed that the author speaks of his conversation with an + Ethiopian bishop, about that bishop's sovereign. Something must have + passed between the two which satisfied the writer that the bishop + acknowledged his own sovereign under some title answering to Prester + John.</p> + +<p><!-- Page 74 --><span class="pagenum"><a name="page74"></a>[74]</span></p> + + <p> </p> + +<p class="cenhead">CONCERNING A TRACT BY FIENUS.</p> + +<blockquote class="b1n"> + + <p>De Cometa anni 1618 dissertationes Thomæ Fieni<a name="NtA_106" + href="#Nt_106"><sup>[106]</sup></a> et Liberti Fromondi<a name="NtA_107" + href="#Nt_107"><sup>[107]</sup></a> ... Equidem Thomæ Fieni epistolica + quæstio, An verum sit Cœlum moveri et Terram quiescere? London, + 1670, 8vo.</p> + +</blockquote> + + <p>This tract of Fienus against the motion of the earth is a reprint of + one published in 1619.<a name="NtA_108" + href="#Nt_108"><sup>[108]</sup></a> I have given an account of it as a + good summary of arguments of the time, in the <i>Companion to the + Almanac</i> for 1836.</p> + +<p><!-- Page 75 --><span class="pagenum"><a name="page75"></a>[75]</span></p> + + <p> </p> + +<p class="cenhead">ON SNELL'S WORK.</p> + +<blockquote class="b1n"> + + <p>Willebrordi Snellii. R. F. Cyclometricus. Leyden, 1621, 4to.</p> + +</blockquote> + + <p>This is a celebrated work on the approximative quadrature, which, + having the suspicious word <i>cyclometricus</i>, must be noticed here for + distinction.<a name="NtA_109" href="#Nt_109"><sup>[109]</sup></a></p> + + <p> </p> + +<p class="cenhead">ON BACON'S NOVUM ORGANUM.</p> + + <p>1620. In this year, Francis Bacon<a name="NtA_110" + href="#Nt_110"><sup>[110]</sup></a> published his <i>Novum Organum</i>,<a + name="NtA_111" href="#Nt_111"><sup>[111]</sup></a> which was long held in + England—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.</p> + + <p>But old prepossession will find reason for anything. A learned friend + of mine wrote to me that he had discovered proof that Newton owned Bacon + for his master: the proof was that Newton, in some of his earlier + writings, used the <!-- Page 76 --><span class="pagenum"><a + name="page76"></a>[76]</span>phrase <i>experimentum crucis</i>, which is + Bacon's. Newton may have read some of Bacon, though no proof of it + appears. I have a dim idea that I once saw the two words attributed to + the alchemists: if so, there is another explanation; for Newton was + deeply read in the alchemists.</p> + + <p>I subjoin a review which I wrote of the splendid edition of Bacon by + Spedding,<a name="NtA_112" href="#Nt_112"><sup>[112]</sup></a> Ellis,<a + name="NtA_113" href="#Nt_113"><sup>[113]</sup></a> and Heath.<a + name="NtA_114" href="#Nt_114"><sup>[114]</sup></a> All the opinions + therein expressed had been formed by me long before: most of the + materials were collected for another purpose.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>The Works of Francis Bacon. Edited by James Spedding, R. Leslie Ellis, + and Douglas D. Heath. 5 vols.<a name="NtA_115" + href="#Nt_115"><sup>[115]</sup></a></p> + +</blockquote> + + <p>No knowledge of nature without experiment and observation: so said + Aristotle, so said Bacon, so acted Copernicus, Tycho Brahé,<a + name="NtA_116" href="#Nt_116"><sup>[116]</sup></a> Gilbert, Kepler, + Galileo, Harvey, etc., before Bacon wrote.<a name="NtA_117" + href="#Nt_117"><sup>[117]</sup></a> No derived knowledge <i>until</i> + experiment and observation are concluded: so said Bacon, and no one else. + We do not mean to say that he laid down his principle in these words, or + that he carried it to the utmost extreme: we mean that Bacon's ruling + idea was the <!-- Page 77 --><span class="pagenum"><a + name="page77"></a>[77]</span>collection of enormous masses of facts, and + then digested processes of arrangement and elimination, so artistically + contrived, that a man of common intelligence, without any unusual + sagacity, should be able to announce the truth sought for. Let Bacon + speak for himself, in his editor's English:</p> + + <p>"But the course I propose for the discovery of sciences is such as + leaves but little to the acuteness and strength of wits, but places all + wits and understandings nearly on a level. For, as in the drawing of a + straight line or a perfect circle, much depends on the steadiness and + practice of the hand, if it be done by aim of hand only, but if with the + aid of rule or compass little or nothing, so it is exactly with my + plan.... For my way of discovering sciences goes far to level men's wits, + and leaves but little to individual excellence; because it performs + everything by the surest rules and demonstrations."</p> + + <p>To show that we do not strain Bacon's meaning, we add what is said by + Hooke,<a name="NtA_118" href="#Nt_118"><sup>[118]</sup></a> whom we have + already mentioned as his professed disciple, and, we believe, his only + disciple of the day of Newton. We must, however, remind the reader that + Hooke was very little of a mathematician, and spoke of algebra from his + own idea of what others had told him:</p> + + <p>"The intellect is not to be suffered to act without its helps, but is + continually to be assisted by some method or engine, which shall be as a + guide to regulate its actions, so as that it shall not be able to act + amiss. Of this engine, no man except the incomparable Verulam hath had + any thoughts and he indeed hath promoted it to a very good pitch; but + there is yet somewhat more to be added, which he seemed to want time to + complete. By this, as by that <!-- Page 78 --><span class="pagenum"><a + name="page78"></a>[78]</span>art of algebra in geometry, 'twill be very + easy to proceed in any natural inquiry, regularly and certainly.... For + as 'tis very hard for the most acute wit to find out any difficult + problem in geometry without the help of algebra ... and altogether as + easy for the meanest capacity acting by that method to complete and + perfect it, so will it be in the inquiry after natural knowledge."</p> + + <p>Bacon did not live to mature the whole of this plan. Are we really to + believe that if he had completed the <i>Instauratio</i> we who write + this—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 <i>did</i> leave, and with its + consequences. Be it so. Mr. Ellis says: "That his method is impracticable + cannot, I think, be denied, if we reflect not only that it never has + produced any result, but also that the process by which scientific truths + have been established cannot be so presented as even to appear to be in + accordance with it." That this is very true is well known to all who have + studied the history of discovery: those who deny it are bound to + establish either that some great discovery has been made by Bacon's + method—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 <i>induction</i>: no reliance upon the mere + fact that certain experiments or observations have been made; let us see + where <i>Bacon's induction</i> has been actually used or can be used. + Mere induction, <i>enumeratio simplex</i>, is spoken of by himself with + contempt, as utterly incompetent. For Bacon knew well that a thousand + instances may be contradicted by the thousand and first: so that no + enumeration of instances, however large, is "sure demonstration," so long + any are left.</p> + + <p>The immortal Harvey, who was <i>inventing</i>—we use the word in + its old sense—the circulation of the blood, while <!-- Page 79 + --><span class="pagenum"><a name="page79"></a>[79]</span>Bacon was in the + full flow of thought upon his system, may be trusted to say whether, when + the system appeared, he found any likeness in it to his own processes, or + what would have been any help to him, if he had waited for the <i>Novum + Organum</i>. He said of Bacon, "He writes philosophy like a Lord + Chancellor." This has been generally supposed to be only a sneer at the + <i>sutor ultra crepidam</i>; but we cannot help suspecting that there was + more intended by it. To us, Bacon is eminently the philosopher of + <i>error prevented</i>, not of <i>progress facilitated</i>. When we throw + off the idea of being <i>led right</i>, and betake ourselves to that of + being <i>kept from going wrong</i>, we read his writings with a sense of + their usefulness, his genius, and their probable effect upon purely + experimental science, which we can be conscious of upon no other + supposition. It amuses us to have to add that the part of Aristotle's + logic of which he saw the value was the book on <i>refutation of + fallacies</i>. Now is this not the notion of things to which the bias of + a practised lawyer might lead him? In the case which is before the Court, + generally speaking, truth lurks somewhere about the facts, and the + elimination of all error will show it in the residuum. The two senses of + the word <i>law</i> come in so as to look almost like a play upon words. + The judge can apply the law so soon as the facts are settled: the + physical philosopher has to deduce the law from the facts. Wait, says the + judge, until the facts are determined: did the prisoner take the goods + with felonious intent? did the defendant give what amounts to a warranty? + or the like. Wait, says Bacon, until all the facts, or all the obtainable + facts, are brought in: apply my rules of separation to the facts, and the + result shall come out as easily as by ruler and compasses. We think it + possible that Harvey might allude to the legal character of Bacon's + notions: we can hardly conceive so acute a man, after seeing what manner + of writer Bacon was, meaning only that he was a lawyer and had better + stick to his business. We do ourselves believe that Bacon's philosophy + <!-- Page 80 --><span class="pagenum"><a + name="page80"></a>[80]</span>more resembles the action of mind of a + common-law judge—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.</p> + + <p>Let us take the well-known first aphorism of the <i>Novum + Organum</i>:</p> + + <p>"Man being the servant and interpreter of nature, can do and + understand so much, and so much only, as he has observed in fact or in + thought of the course of nature: beyond this he neither knows anything + nor can do anything."</p> + + <p>This aphorism is placed by Sir John Herschel<a name="NtA_119" + href="#Nt_119"><sup>[119]</sup></a> at the head of his <i>Discourse on + the Study of Natural Philosophy</i>: a book containing notions of + discovery far beyond any of which Bacon ever dreamed; and this because it + was written <!-- Page 81 --><span class="pagenum"><a + name="page81"></a>[81]</span>after discovery, instead of before. Sir John + Herschel, in his version, has avoided the translation of <i>re vel mente + observaverit</i>, and gives us only "by his observation of the order of + nature." In making this the opening of an excellent sermon, he has + imitated the theologians, who often employ the whole time of the + discourse in stuffing matter into the text, instead of drawing matter out + of it. By <i>observation</i> he (Herschel) means the whole course of + discovery, observation, hypothesis, deduction, comparison, etc. The type + of the Baconian philosopher as it stood in his mind, had been derived + from a noble example, his own father, William Herschel,<a name="NtA_120" + href="#Nt_120"><sup>[120]</sup></a> an inquirer whose processes would + have been held by Bacon to have been vague, insufficient, compounded of + chance work and sagacity, and too meagre of facts to deserve the name of + induction. In another work, his treatise on Astronomy,<a name="NtA_121" + href="#Nt_121"><sup>[121]</sup></a> Sir John Herschel, after noting that + a popular account can only place the reader on the threshold, proceeds to + speak as follows of all the higher departments of science. The italics + are his own:</p> + + <p>"Admission to its sanctuary, and to the privileges and feelings of a + votary, is only to be gained by one means—<i>sound and sufficient + knowledge of mathematics, the great instrument of all exact inquiry, + without which no man can ever make such advances in this or any other of + the higher departments of science as can entitle him to form an + independent opinion on any subject of discussion within their + range</i>."</p> + + <p>How is this? Man can know no more than he gets from observation, and + yet mathematics is the great instrument of all exact inquiry. Are the + results of mathematical deduction results of observation? We think it + likely that <!-- Page 82 --><span class="pagenum"><a + name="page82"></a>[82]</span>Sir John Herschel would reply that Bacon, in + coupling together <i>observare re</i> and <i>observare mente</i>, has + done what some wags said Newton afterwards did in his + study-door—cut a large hole of exit for the large cat, and a little + hole for the little cat.<a name="NtA_122" + href="#Nt_122"><sup>[122]</sup></a> But Bacon did no such thing: he never + included any deduction under observation. To mathematics he had a + dislike. He averred that logic and mathematics should be the handmaids, + not the mistresses, of philosophy. He meant that they should play a + subordinate and subsequent part in the dressing of the vast mass of facts + by which discovery was to be rendered equally accessible to Newton and to + us. Bacon himself was very ignorant of all that had been done by + mathematics; and, strange to say, he especially objected to astronomy + being handed over to the mathematicians. Leverrier and Adams, calculating + an unknown planet into visible existence by enormous heaps of algebra, + furnish the last comment of note on this specimen of the goodness of + Bacon's views. The following account of his knowledge of what had been + done in his own day or before it, is Mr. Spedding's collection of casual + remarks in Mr. Ellis's several prefaces:</p> + + <p>"Though he paid great attention to astronomy, discussed carefully the + methods in which it ought to be studied, constructed for the satisfaction + of his own mind an elaborate theory of the heavens, and listened eagerly + for the news from the stars brought by Galileo's telescope, he appears to + have been utterly ignorant of the discoveries which had just been made by + Kepler's calculations. Though he complained in 1623 of the want of + compendious methods for facilitating arithmetical computations, + especially with regard to the doctrine of Series, and fully recognized + the importance of them as an aid to physical inquiries—he does not + say a word about Napier's Logarithms, which had been published only nine + years before and reprinted more than once in the <!-- Page 83 --><span + class="pagenum"><a name="page83"></a>[83]</span>interval. He complained + that no considerable advance had made in geometry beyond Euclid, without + taking any notice of what had been done by Archimedes and Apollonius. He + saw the importance of determining accurately the specific gravity of + different substances, and himself attempted to form a table of them by a + rude process of his own, without knowing of the more scientific though + still imperfect methods previously employed by Archimedes, Ghetaldus,<a + name="NtA_123" href="#Nt_123"><sup>[123]</sup></a> and Porta. He speaks + of the <span title="heurêka" class="grk" + >εὕρηκα</span> of Archimedes in a + manner which implies that he did not clearly apprehend either the nature + of the problem to be solved or the principles upon which the solution + depended. In reviewing the progress of mechanics, he makes no mention of + Archimedes himself, or of Stevinus,<a name="NtA_124" + href="#Nt_124"><sup>[124]</sup></a> Galileo, Guldinus,<a name="NtA_125" + href="#Nt_125"><sup>[125]</sup></a> or Ghetaldus. He makes no allusion to + the theory of equilibrium. He observes that a ball of one pound weight + will fall nearly as fast through the air as a ball of two, without + alluding to the theory of the acceleration of falling bodies, which had + been made known by Galileo more than thirty years before. He proposes an + inquiry with regard to the lever—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 <!-- Page 84 --><span class="pagenum"><a + name="page84"></a>[84]</span>of his own to ascertain the cause of the + motion of a windmill, he overlooks an obvious circumstance which makes + the experiment inconclusive, and an equally obvious variation of the same + experiment which would have shown him that his theory was false. He + speaks of the poles of the earth as fixed, in a manner which seems to + imply that he was not acquainted with the precession of the equinoxes; + and in another place, of the north pole being above and the south pole + below, as a reason why in our hemisphere the north winds predominate over + the south."</p> + + <p>Much of this was known before, but such a summary of Bacon's want of + knowledge of the science of his own time was never yet collected in one + place. We may add, that Bacon seems to have been as ignorant of + Wright's<a name="NtA_126" href="#Nt_126"><sup>[126]</sup></a> memorable + addition to the resources of navigation as of Napier's addition to the + means of calculation. Mathematics was beginning to be the great + instrument of exact inquiry: Bacon threw the science aside, from + ignorance, just at the time when his enormous sagacity, applied to + knowledge, would have made him see the part it was to play. If Newton had + taken Bacon for his master, not he, but somebody else, would have been + Newton.<a name="NtA_127" href="#Nt_127"><sup>[127]</sup></a></p> + + <p> </p> + +<p class="cenhead">ON METEOROLOGICAL OBSERVATORIES.</p> + + <p>There is an attempt at induction going on, which has yielded little or + no fruit, the observations made in the meteorological observatories. This + attempt is carried on in a manner which would have caused Bacon to dance + for joy; for he lived in times when Chancellors did dance. <!-- Page 85 + --><span class="pagenum"><a name="page85"></a>[85]</span>Russia, says M. + Biot,<a name="NtA_128" href="#Nt_128"><sup>[128]</sup></a> is covered by + an army of meteorographs, with generals, high officers, subalterns, and + privates with fixed and defined duties of observation. Other countries + have also their systematic observations. And what has come of it? + Nothing, says M. Biot, and nothing will ever come of it; the veteran + mathematician and experimental philosopher declares, as does Mr. Ellis, + that no single branch of science has ever been fruitfully explored in + this way. There is no <i>special object</i>, he says. Any one would + suppose that M. Biot's opinion, given to the French Government upon the + proposal to construct meteorological observatories in Algeria (<i>Comptes + Rendus</i>, vol. xli, Dec. 31, 1855), was written to support the mythical + Bacon, modern physics, against the real Bacon of the <i>Novum + Organum</i>. There is no <i>special object</i>. In these words lies the + difference between the two methods.</p> + + <p> </p> + + <p>[In the report to the Greenwich Board of Visitors for 1867 Mr. Airy,<a + name="NtA_129" href="#Nt_129"><sup>[129]</sup></a> speaking of the + increase of meteorological observatories, remarks, "Whether the effect of + this movement will be that millions of useless observations will be added + to the millions that already exist, or whether something may be expected + to result which will lead to a meteorological theory, I cannot hazard a + conjecture." This <i>is</i> a conjecture, and a very obvious one: if Mr. + Airy would have given 2-3/4<i>d.</i> for the chance of a meteorological + theory formed by masses of observations, he would never have said what I + have quoted.]</p> + + <p> </p> + +<p class="cenhead">BASIS OF MODERN DISCOVERY.</p> + + <p>Modern discoveries have not been made by large collections of facts, + with subsequent discussion, separation, and <!-- Page 86 --><span + class="pagenum"><a name="page86"></a>[86]</span>resulting deduction of a + truth thus rendered perceptible. A few facts have suggested an + <i>hypothesis</i>, which means a <i>supposition</i>, proper to explain + them. The necessary results of this supposition are worked out, and then, + and not till then, other facts are examined to see if these ulterior + results are found in nature. The trial of the hypothesis is the + <i>special object</i>: prior to which, hypothesis must have been started, + not by rule, but by that sagacity of which no description can be given, + precisely because the very owners of it do not act under laws perceptible + to themselves.<a name="NtA_130" href="#Nt_130"><sup>[130]</sup></a> The + inventor of hypothesis, if pressed to explain his method, must answer as + did Zerah Colburn,<a name="NtA_131" href="#Nt_131"><sup>[131]</sup></a> + when asked for his mode of instantaneous calculation. When the poor boy + had been bothered for some time in this manner, he cried out in a huff, + "God put it into my head, and I can't put it into yours."<a + name="NtA_132" href="#Nt_132"><sup>[132]</sup></a> <!-- Page 87 --><span + class="pagenum"><a name="page87"></a>[87]</span>Wrong hypotheses, rightly + worked from, have produced more useful results than unguided observation. + But this is not the Baconian plan. Charles the Second, when informed of + the state of navigation, founded a Baconian observatory at Greenwich, to + observe, observe, observe away at the moon, until her motions were known + sufficiently well to render her useful in guiding the seaman. And no + doubt Flamsteed's<a name="NtA_133" href="#Nt_133"><sup>[133]</sup></a> + observations, twenty or thirty of them at least, were of signal use. But + how? A somewhat fanciful thinker, one Kepler, had hit upon the + approximate orbits of the planets by trying one hypothesis after another: + he found the <i>ellipse</i>, which the Platonists, well despised of + Bacon, and who would have despised him as heartily if they had known him, + had investigated and put ready to hand nearly 2000 years before.<a + name="NtA_134" href="#Nt_134"><sup>[134]</sup></a> The sun in the focus, + the motions of the planet more and more rapid as they approach the sun, + led Kepler—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,<a name="NtA_135" + href="#Nt_135"><sup>[135]</sup></a> upon a fanciful analogy, rejected the + inverse distance, <!-- Page 88 --><span class="pagenum"><a + name="page88"></a>[88]</span>and, rejecting the force altogether, + declared that if such a thing there were, it would be as the inverse + <i>square</i> of the distance. Newton, ready prepared with the + mathematics of the subject, tried the fall of the moon towards the earth, + away from her tangent, and found that, as compared with the fall of a + stone, the law of the inverse square did hold for the moon. He deduced + the ellipse, he proceeded to deduce the effect of the disturbance of the + sun upon the moon, upon the assumed theory of <i>universal</i> + gravitation. He found result after result of his theory in conformity + with observed fact: and, by aid of Flamsteed's observations, which + amended what mathematicians call his <i>constants</i>, he constructed his + lunar theory. Had it not been for Newton, the whole dynasty of Greenwich + astronomers, from Flamsteed of happy memory, to Airy whom Heaven + preserve,<a name="NtA_136" href="#Nt_136"><sup>[136]</sup></a> might have + worked away at nightly observation and daily reduction, without any + remarkable result: looking forward, as to a millennium, to the time when + any man of moderate intelligence was to see the whole explanation. What + are large collections of facts for? To make theories <i>from</i>, says + Bacon: to try ready-made theories <i>by</i>, says the history of + discovery: it's all the same, says the idolater: nonsense, say we!</p> + + <p>Time and space run short: how odd it is that of the three leading + ideas of mechanics, time, space, and matter, the first two should always + fail a reviewer before the third. We might dwell upon many points, + especially if we attempted a more descriptive account of the valuable + edition before us. No one need imagine that the editors, by their + uncompromising attack upon the notion of Bacon's influence common even + among mathematicians and experimental philosophers, have lowered the + glory of the great man whom it was, many will think, their business to + defend through thick and thin. They have given a clearer notion of his + <!-- Page 89 --><span class="pagenum"><a + name="page89"></a>[89]</span>excellencies, and a better idea of the power + of his mind, than ever we saw given before. Such a correction as theirs + must have come, and soon, for as Hallam says—after noting that the + <i>Novum Organum</i> was <i>never published separately in England</i>, + Bacon has probably been more read in the last thirty years—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.</p> + + <p> </p> + +<p class="cenhead">THE REAL VALUE OF BACON'S WORKS.</p> + + <p>Passing over the success of Bacon's own endeavors to improve the + details of physical science, which was next to nothing, and of his method + as a whole, which has never been practised, we might say much of the good + influence of his writings. Sound wisdom, set in sparkling wit, must + instruct and amuse to the end of time: and, as against error, we repeat + that Bacon is soundly wise, so far as he goes. There is hardly a form of + human error within his scope which he did not detect, expose, and attach + to a satirical metaphor which never ceases to sting. He is largely + indebted to a very extensive reading; but the thoughts of others fall + into his text with such a close-fitting compactness that he can make even + the words of the Sacred Writers pass for his own. A saying of the prophet + Daniel, rather a hackneyed quotation in our day, <i>Multi pertransibunt, + et augebitur scientia</i>, stands in the title-page of the first edition + <!-- Page 90 --><span class="pagenum"><a name="page90"></a>[90]</span>of + Montucla's <i>History of Mathematics</i> as a quotation from + Bacon—and it is not the only place in which this mistake occurs. + When the truth of the matter, as to Bacon's system, is fully recognized, + we have little fear that there will be a reaction against the man. First, + because Bacon will always live to speak for himself, for he will not + cease to be read: secondly, because those who seek the truth will find it + in the best edition of his works, and will be most ably led to know what + Bacon was, in the very books which first showed at large what he <i>was + not</i>.</p> + + <p> </p> + +<p class="cenhead">THE CONGREGATION OF THE INDEX, ON COPERNICUS.</p> + + <p>In this year (1620) appeared the corrections under which the + Congregation of the Index—i.e., the Committee of Cardinals which + superintended the <i>Index</i> 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.</p> + + <p>By a decree of the Congregation of the Index, dated March 5, 1616, the + work of Copernicus, and another of Didacus Astunica,<a name="NtA_137" + href="#Nt_137"><sup>[137]</sup></a> are suspended <i>donec + corrigantur</i>, as teaching:</p> + + <p>"Falsam illam doctrinam Pythagoricam, divinæ que Scripturæ omnino + adversantem, de mobilitate Terræ et immobilitate Solis."<a name="NtA_138" + href="#Nt_138"><sup>[138]</sup></a></p> + + <p>But a work of the Carmelite Foscarini<a name="NtA_139" + href="#Nt_139"><sup>[139]</sup></a> is:</p> + +<p><!-- Page 91 --><span class="pagenum"><a name="page91"></a>[91]</span></p> + + <p>"Omnino prohibendum atque damnandum," because "ostendere conatur + præfatam doctrinam ... consonam esse veritati et non adversari Sacræ + Scripturæ."<a name="NtA_140" href="#Nt_140"><sup>[140]</sup></a></p> + + <p>Works which teach the false doctrine of the earth's motion are to be + corrected; those which declare the doctrine conformable to Scripture are + to be utterly prohibited.</p> + + <p>In a "Monitum ad Nicolai Copernici lectorem, ejusque emendatio, + permissio, et correctio," dated 1620 without the month or day, permission + is given to reprint the work of Copernicus with certain alterations; and, + by implication, to read existing copies after correction in writing. In + the preamble the author is called <i>nobilis astrologus</i>; not a + compliment to his birth, which was humble, but to his fame. The + suspension was because:</p> + + <p>"Sacræ Scripturæ, ejusque veræ et Catholicæ interpretationi + repugnantia (quod in homine Christiano minime tolerandum) non <i>per + hypothesin</i> tractare, sed <i>ut verissima</i> adstruere non + dubitat!"<a name="NtA_141" href="#Nt_141"><sup>[141]</sup></a></p> + + <p>And the corrections relate:</p> + + <p>"Locis in quibus non <i>ex hypothesi</i>, sed <i>asserendo</i> de situ + et motu Terræ disputat."<a name="NtA_142" + href="#Nt_142"><sup>[142]</sup></a></p> + + <p>That is, the earth's motion may be an hypothesis for elucidation of + the heavenly motions, but must not be asserted as a fact.</p> + + <p> </p> + + <p>(In Pref. circa finem.) "<i>Copernicus.</i> Si fortasse erunt <span + title="mataiologoi" class="grk" + >ματαιόλογοι</span>, + qui cum omnium Mathematum ignari sint, tamen de illis judicium sibi + summunt, propter aliquem locum scripturæ, male ad suum propositum + detortum, ausi fuerint meum <!-- Page 92 --><span class="pagenum"><a + name="page92"></a>[92]</span>hoc institutum reprehendere ac insectari: + illos nihil moror adeo ut etiam illorum judicium tanquam temerarium + contemnam. Non enim obscurum est Lactantium, celebrem alioqui scriptorem, + sed Mathematicum parum, admodum pueriliter de forma terræ loqui, cum + deridet eos, qui terram globi formam habere prodiderunt. Itaque non debet + mirum videri studiosis, si qui tales nos etiam videbunt. Mathemata + Mathematicis scribuntur, quibus et hi nostri labores, si me non fallit + opinio, videbuntur etiam Reipub. ecclesiasticæ conducere aliquid.... + <i>Emend.</i> Ibi <i>si fortasse</i> dele omnia, usque ad verbum <i>hi + nostri labores</i> et sic accommoda—<i>Cœterum hi nostri + labores</i>."<a name="NtA_143" href="#Nt_143"><sup>[143]</sup></a></p> + + <p>All the allusion to Lactantius, who laughed at the notion of the earth + being round, which was afterwards found true, is to be struck out.</p> + + <p> </p> + + <p>(Cap. 5. lib. i. p. 3) "<i>Copernicus.</i> Si tamen attentius rem + consideremus, videbitur hæc quæstio nondum absoluta, et ideireo minime + contemnenda. <i>Emend.</i> Si tamen attentius rem consideremus, nihil + refert an Terram in medio Mundi, an extra Medium existere, quoad + solvendas cœlestium motuum apparentias existimemus."<a + name="NtA_144" href="#Nt_144"><sup>[144]</sup></a></p> + +<p><!-- Page 93 --><span class="pagenum"><a name="page93"></a>[93]</span></p> + + <p>We must not say the question is not yet settled, but only that it may + be settled either way, so far as mere explanation of the celestial + motions is concerned.</p> + + <p> </p> + + <p>(Cap. 8. lib. i.) "Totum hoc caput potest expungi, quia ex professo + tractat de veritate motus Terræ, dum solvit veterum rationes probantes + ejus quietem. Cum tamen problematice videatur loqui; ut studiosis + satisfiat, seriesque et ordo libri integer maneat; emendetur ut infra."<a + name="NtA_145" href="#Nt_145"><sup>[145]</sup></a></p> + + <p>A chapter which seems to assert the motion should perhaps be expunged; + but it may perhaps be problematical; and, not to break up the book, must + be amended as below.</p> + + <p> </p> + + <p>(p. 6.) "<i>Copernicus.</i> Cur ergo hesitamus adhuc, mobilitatem illi + formæ suæ a natura congruentem concedere, magisquam quod totus labatur + mundus, cujus finis ignoratur, scirique nequit, neque fateamur ipsius + cotidianæ revolutionis in cœlo apparentiam esse, et in terra + veritatem? Et hæc perinde se habere, ac si diceret Virgilianus Æneas: + Provehimur portu ... <i>Emend.</i> Cur ergo non possum mobilitatem illi + formæ suæ concedere, magisque quod totus labatur mundus, cujus finis + ignoratur scirique nequit, et quæ apparent in cœlo, perinde se + habere ac si ..."<a name="NtA_146" + href="#Nt_146"><sup>[146]</sup></a></p> + +<p><!-- Page 94 --><span class="pagenum"><a name="page94"></a>[94]</span></p> + + <p>"Why should we hesitate to allow the earth's motion," must be altered + into "I cannot concede the earth's motion."</p> + + <p> </p> + + <p>(p. 7.) "<i>Copernicus.</i> Addo etiam, quod satis absurdum videretur, + continenti sive locanti motum adscribi, et non potius contento et locato, + quod est terra. <i>Emend.</i> Addo etiam difficilius non esse contento et + locato, quod est Terra, motum adscribere, quam continenti."<a + name="NtA_147" href="#Nt_147"><sup>[147]</sup></a></p> + + <p>We must not say it is absurd to refuse motion to the <i>contained</i> + and <i>located</i>, and to give it to the containing and locating; say + that neither is more difficult than the other.</p> + + <p> </p> + + <p>(p. 7.) "<i>Copernicus.</i> Vides ergo quod ex his omnibus probabilior + sit mobilitas Terræ, quam ejus quies, præsertim in cotidiana revolutione, + tanquam terræ maxime propria. <i>Emend.</i> <i>Vides</i> ... delendus est + usque ad finem capitis."<a name="NtA_148" + href="#Nt_148"><sup>[148]</sup></a></p> + + <p>Strike out the whole of the chapter from this to the end; it says that + the motion of the earth is the most probable hypothesis.</p> + + <p> </p> + + <p>(Cap. 9. lib. i. p. 7.) "<i>Copernicus.</i> Cum igitur nihil prohibeat + mobilitatem Terræ, videndum nunc arbitror, an etiam plures illi motus + conveniant, ut possit una errantium syderum existimari. <i>Emend.</i> Cum + igitur Terram moveri assumpserim, videndum nunc arbitror, an etiam illi + plures possint convenire motus."<a name="NtA_149" + href="#Nt_149"><sup>[149]</sup></a></p> + +<p><!-- Page 95 --><span class="pagenum"><a name="page95"></a>[95]</span></p> + + <p>We must not say that nothing prohibits the motion of the earth, only + that having <i>assumed</i> it, we may inquire whether our explanations + require several motions.</p> + + <p> </p> + + <p>(Cap. 10. lib. i. p. 9.) "<i>Copernicus.</i> Non pudet nos fateri ... + hoc potius in mobilitate terræ verificari. <i>Emend.</i> Non pudet nos + assumere ... hoc consequenter in mobilitate verificari."<a name="NtA_150" + href="#Nt_150"><sup>[150]</sup></a></p> + + <p>(Cap. 10. lib. i. p. 10.) "<i>Copernicus.</i> Tanta nimirum est divina + hæc. Opt. Max. fabrica. <i>Emend.</i> Dele illa verba postrema."<a + name="NtA_151" href="#Nt_151"><sup>[151]</sup></a></p> + + <p>(Cap. ii. lib. i.<a name="NtA_152" + href="#Nt_152"><sup>[152]</sup></a>) "<i>Copernicus.</i> De triplici motu + telluris demonstratio. <i>Emend.</i> De hypothesi triplicis motus Terræ, + ejusque demonstratione."<a name="NtA_153" + href="#Nt_153"><sup>[153]</sup></a></p> + + <p>(Cap. 10. lib. iv. p. 122.<a name="NtA_154" + href="#Nt_154"><sup>[154]</sup></a>) "<i>Copernicus.</i> De magnitudine + horum trium siderum, Solis, Lunæ, et Terræ. <i>Emend.</i> Dele verba + <i>horum trium siderum</i>, quia terra non est sidus, ut facit eam + Copernicus."<a name="NtA_155" href="#Nt_155"><sup>[155]</sup></a></p> + + <p>We must not say we are not ashamed to <i>acknowledge</i>; + <i>assume</i> is the word. We must not call this assumption a <i>Divine + work</i>. A chapter must not be headed <i>demonstration</i>, but + <i>hypothesis</i>. The earth must not be called a <i>star</i>; the word + implies motion.</p> + + <p>It will be seen that it does not take much to reduce Copernicus to + pure hypothesis. No personal injury being done to the author—who + indeed had been 17 years out of <!-- Page 96 --><span class="pagenum"><a + name="page96"></a>[96]</span>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 <i>problematice + videtur loqui, ut studiosis satisfiat</i>,<a name="NtA_156" + href="#Nt_156"><sup>[156]</sup></a> is an excuse to avoid corrections. + But they struck out the stinging allusion to Lactantius<a name="NtA_157" + href="#Nt_157"><sup>[157]</sup></a> in the preface, little thinking, + honest men, for they really believed what they said—that the light + of Lactantius would grow dark before the brightness of their own.</p> + + <p> </p> + +<p class="cenhead">THE CONVOCATION AT OXFORD EQUALLY AT FAULT.</p> + + <p>1622. I make no reference to the case of Galileo, except this. I have + pointed out (<i>Penny Cycl. Suppl.</i> "Galileo"; <i>Engl. Cycl.</i> + "Motion of the Earth") that it is clear the absurdity was the act of the + <i>Italian</i> Inquisition—for the private and personal pleasure of + the Pope, who <i>knew</i> that the course he took would not commit him as + <i>Pope</i>—and not of the body which calls itself the + <i>Church</i>. Let the dirty proceeding have its right name. The Jesuit + Riccioli,<a name="NtA_158" href="#Nt_158"><sup>[158]</sup></a> the + stoutest and most learned Anti-Copernican in Europe, and the Puritan + Wilkins, a strong Copernican and Pope-hater, are equally positive that + the Roman <i>Church</i> never pronounced any decision: and this in the + time immediately following the ridiculous proceeding of the Inquisition. + In like manner a decision of the Convocation of Oxford is not a law of + the <i>English</i> Church; which is fortunate, for that Convocation, in + 1622, came to a decision quite as absurd, and a great deal <!-- Page 97 + --><span class="pagenum"><a name="page97"></a>[97]</span>more wicked than + the declaration against the motion of the earth. The second was a foolish + mistake; the first was a disgusting surrender of right feeling. The story + is told without disapprobation by Anthony Wood, who never exaggerated + anything against the university of which he is writing eulogistic + history.</p> + + <p>In 1622, one William Knight<a name="NtA_159" + href="#Nt_159"><sup>[159]</sup></a> put forward in a sermon preached + before the University certain theses which, looking at the state of the + times, may have been improper and possibly of seditious intent. One of + them was that the bishop might excommunicate the civil magistrate: this + proposition the clerical body could not approve, and designated it by the + term <i>erronea</i>,<a name="NtA_160" href="#Nt_160"><sup>[160]</sup></a> + the mildest going. But Knight also declared as follows:</p> + + <p>"Subditis mere privatis, si Tyrannus tanquam latro aut stuprator in + ipsos faciat impetum, et ipsi nec potestatem ordinariam implorare, nec + alia ratione effugere periculum possint, in presenti periculo se et suos + contra tyrannum, sicut contra privatum grassatorem, defendere licet."<a + name="NtA_161" href="#Nt_161"><sup>[161]</sup></a></p> + + <p>That is, a man may defend his purse or a woman her honor, against the + personal attack of a king, as against that of a private person, if no + other means of safety can be found. The Convocation sent Knight to + prison, declared the proposition <i>"falsa</i>, periculosa, et + <i>impia</i>," and enacted that all applicants for degrees should + subscribe this censure, and make oath that they would neither hold, + teach, nor defend Knight's opinions.</p> + + <p>The thesis, in the form given, was unnecessary and improper. Though + strong opinions of the king's rights were advanced at the time, yet no + one ventured to say that, <!-- Page 98 --><span class="pagenum"><a + name="page98"></a>[98]</span>ministers and advisers apart, the king might + <i>personally</i> break the law; and we know that the first and only + attempt which his successor made brought on the crisis which cost him his + throne and his head. But the declaration that the proposition was + <i>false</i> far exceeds in all that is disreputable the decision of the + Inquisition against the earth's motion. We do not mention this little + matter in England. Knight was a Puritan, and Neal<a name="NtA_162" + href="#Nt_162"><sup>[162]</sup></a> gives a short account of his sermon. + From comparison with Wood,<a name="NtA_163" + href="#Nt_163"><sup>[163]</sup></a> I judge that the theses, as given, + were not Knight's words, but the digest which it was customary to make in + criminal proceedings against opinion. This heightens the joke, for it + appears that the qualifiers of the Convocation took pains to present + their condemnation of Knight in the terms which would most unequivocally + make their censure condemn themselves. This proceeding took place in the + interval between the two proceedings against Galileo: it is left + undetermined whether we must say pot-kettle-pot or kettle-pot-kettle.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Liberti Fromondi.... Ant-Aristarchus, sive orbis terræ immobilis. + Antwerp, 1631, 8vo.<a name="NtA_164" + href="#Nt_164"><sup>[164]</sup></a></p> + +</blockquote> + + <p>This book contains the evidence of an ardent opponent of Galileo to + the fact, that Roman Catholics of the day did not consider the decree of + the <i>Index</i> or of the <i>Inquisition</i> as a declaration of their + <i>Church</i>. Fromond would have been glad to say as much, and tries to + come near it, but confesses he must abstain. See <i>Penny Cyclop. + Suppl.</i> "Galileo," and <i>Eng. Cycl.</i> "Motion of the Earth." The + author of a celebrated article in the <i>Dublin Review</i>, in defence of + the <!-- Page 99 --><span class="pagenum"><a + name="page99"></a>[99]</span>Church of Rome, seeing that Drinkwater + Bethune<a name="NtA_165" href="#Nt_165"><sup>[165]</sup></a> makes use of + the authority of Fromondus, but for another purpose, sneers at him for + bringing up a "musty old Professor." If he had known Fromondus, and used + him he would have helped his own case, which is very meagre for want of + knowledge.<a name="NtA_166" href="#Nt_166"><sup>[166]</sup></a></p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Advis à Monseigneur l'eminentissime Cardinal Duc de Richelieu, sur la + Proposition faicte par le Sieur Morin pour l'invention des longitudes. + Paris, 1634, 8vo.<a name="NtA_167" + href="#Nt_167"><sup>[167]</sup></a></p> + +</blockquote> + + <p>This is the Official Report of the Commissioners appointed by the + Cardinal, of whom Pascal is the one now best known, to consider Morin's + plan. See the full account in Delambre, <i>Hist. Astr. Mod.</i> ii. 236, + etc.</p> + + <p> </p> + +<p class="cenhead">THE METIUS APPROXIMATION.</p> + +<blockquote class="b1n"> + + <p>Arithmetica et Geometria practica. By Adrian Metius. Leyden, 1640, + 4to.<a name="NtA_168" href="#Nt_168"><sup>[168]</sup></a></p> + +</blockquote> + + <p>This book contains the celebrated approximation <i>guessed at</i> by + his father, Peter Metius,<a name="NtA_169" + href="#Nt_169"><sup>[169]</sup></a> namely that the diameter is <!-- Page + 100 --><span class="pagenum"><a name="page100"></a>[100]</span>to the + circumference as 113 to 355. The error <span class="correction" + title="text reads `it'">is</span> at the rate of about a foot in 2,000 + miles. Peter Metius, having his attention called to the subject by the + false quadrature of Duchesne, found that the ratio lay between 333/106 + and 377/120. He then took the liberty of taking the mean of both + numerators and denominators, giving 355/113. He had no right to presume + that this mean was better than either of the extremes; nor does it appear + positively that he did so. He published nothing; but his son Adrian,<a + name="NtA_170" href="#Nt_170"><sup>[170]</sup></a> when Van Ceulen's work + showed how near his father's result came to the truth, first made it + known in the work above. (See <i>Eng. Cyclop.</i>, art. + "Quadrature.")</p> + + <p> </p> + +<p class="cenhead">ON INHABITABLE PLANETS.</p> + +<blockquote class="b1n"> + + <p>A discourse concerning a new world and another planet, in two books. + London, 1640, 8vo.<a name="NtA_171" + href="#Nt_171"><sup>[171]</sup></a></p> + + <p>Cosmotheoros: or conjectures concerning the planetary worlds and their + inhabitants. Written in Latin, by Christianus Huyghens. This translation + was first published in 1698. Glasgow, 1757, 8vo. [The original is also of + 1698.]<a name="NtA_172" href="#Nt_172"><sup>[172]</sup></a></p> + +</blockquote> + + <p>The first work is by Bishop Wilkins, being the third edition, [first + in 1638] of the first book, "That the Moon may be a Planet"; and the + first edition of the second work, <!-- Page 101 --><span + class="pagenum"><a name="page101"></a>[101]</span>"That the Earth may be + a Planet." [See more under the reprint of 1802.] Whether other planets be + inhabited or not, that is, crowded with organisations some of them having + consciousness, is not for me to decide; but I should be much surprised + if, on going to one of them, I should find it otherwise. The whole + dispute tacitly assumes that, if the stars and planets be inhabited, it + must be by things of which we can form some idea. But for aught we know, + what number of such bodies there are, so many organisms may there be, of + which we have no way of thinking nor of speaking. This is seldom + remembered. In like manner it is usually forgotten that the <i>matter</i> + of other planets may be of different chemistry from ours. There may be no + oxygen and hydrogen in Jupiter, which may have <i>gens</i> of its own.<a + name="NtA_173" href="#Nt_173"><sup>[173]</sup></a> But this must not be + said: it would limit the omniscience of the <i>a priori</i> school of + physical inquirers, the larger half of the whole, and would be very + <i>unphilosophical</i>. Nine-tenths of my best paradoxers come out from + among this larger half, because they are just a little more than of it at + their entrance.</p> + + <p>There was a discussion on the subject some years ago, which began + with</p> + +<blockquote class="b1n"> + + <p>The plurality of worlds: an Essay. London, 1853, 8vo. [By Dr. Wm. + Whewell, Master of Trinity College, Cambridge]. A dialogue on the + plurality of worlds, being a supplement to the Essay on that subject. + [First found in the second edition, 1854; removed to the end in + subsequent editions, and separate copies issued.]<a name="NtA_174" + href="#Nt_174"><sup>[174]</sup></a></p> + +</blockquote> + + <p>A work of skeptical character, insisting on analogies which prohibit + the positive conclusion that the planets, stars, etc., are what we should + call <i>inhabited</i> worlds. It produced <!-- Page 102 --><span + class="pagenum"><a name="page102"></a>[102]</span>several works and a + large amount of controversy in reviews. The last predecessor of whom I + know was</p> + +<blockquote class="b1n"> + + <p>Plurality of Worlds.... By Alexander Maxwell. Second Edition. London, + 1820, 8vo.</p> + +</blockquote> + + <p>This work is directed against the plurality by an author who does not + admit modern astronomy. It was occasioned by Dr. Chalmers's<a + name="NtA_175" href="#Nt_175"><sup>[175]</sup></a> celebrated discourses + on religion in connection with astronomy. The notes contain many + citations on the gravity controversy, from authors now very little read: + and this is its present value. I find no mention of Maxwell, not even in + Watt.<a name="NtA_176" href="#Nt_176"><sup>[176]</sup></a> He + communicated with mankind without the medium of a publisher; and, from + Vieta till now, this method has always been favorable to loss of + books.</p> + + <p>A correspondent informs me that Alex. Maxwell, who wrote on the + plurality of worlds, in 1820, was a law-bookseller and publisher + (probably his own publisher) in Bell Yard. He had peculiar notions, which + he was fond of discussing with his customers. He was a bit of a + Swedenborgian.</p> + + <p> </p> + +<p class="cenhead">INHABITED PLANETS IN FICTION.</p> + + <p>There is a class of hypothetical creations which do not belong to my + subject, because they are <i>acknowledged</i> to be fictions, as those of + Lucian,<a name="NtA_177" href="#Nt_177"><sup>[177]</sup></a> Rabelais,<a + name="NtA_178" href="#Nt_178"><sup>[178]</sup></a> Swift, Francis <!-- + Page 103 --><span class="pagenum"><a + name="page103"></a>[103]</span>Godwin,<a name="NtA_179" + href="#Nt_179"><sup>[179]</sup></a> Voltaire, etc. All who have more + positive notions as to either the composition or organization of other + worlds, than the reasonable conclusion that our Architect must be quite + able to construct millions of other buildings on millions of other plans, + ought to rank with the writers just mentioned, in all but self-knowledge. + Of every one of their systems I say, as the Irish Bishop said of + Gulliver's book,—I don't believe half of it. Huyghens had been + preceded by Fontenelle,<a name="NtA_180" + href="#Nt_180"><sup>[180]</sup></a> who attracted more attention. + Huyghens is very fanciful and very positive; but he gives a true account + of his method. "But since there's no hopes of a Mercury to carry us such + a journey, we shall e'en be contented with what's in our power: we shall + suppose ourselves there...." And yet he says, "We have proved that they + live in societies, have hands and feet...." Kircher<a name="NtA_181" + href="#Nt_181"><sup>[181]</sup></a> had gone to the stars before him, but + would not find any life in them, either animal or vegetable.</p> + + <p>The question of the inhabitants of a particular planet is one which + has truth on one side or the other: either there are some inhabitants, or + there are none. Fortunately, it is of no consequence which is true. But + there are many cases where the balance is equally one of truth and + falsehood, in which the choice is a matter of importance. My work + selects, for the most part, sins against demonstration: but the world is + full of questions of fact or opinion, in which a struggling minority will + become a majority, or else will <!-- Page 104 --><span class="pagenum"><a + name="page104"></a>[104]</span>be gradually annihilated: and each of the + cases subdivides into results of good, and results of evil. What is to be + done?</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Periculosum est credere et non credere;</p> + <p>Hippolitus obiit quia novercæ creditum est;</p> + <p>Cassandræ quia non creditum ruit Ilium:</p> + <p>Ergo exploranda est veritas multum prius</p> + <p>Quam stulta prove judicet sententia."<a name="NtA_182" href="#Nt_182"><sup>[182]</sup></a></p> + </div> + </div> + <p> </p> + +<blockquote class="b1n"> + + <p>Nova Demonstratio immobilitatis terræ petita ex virtute magnetica. By + Jacobus Grandamicus. Flexiae (La Flèche), 1645, 4to.<a name="NtA_183" + href="#Nt_183"><sup>[183]</sup></a></p> + +</blockquote> + + <p>No magnetic body can move about its poles: the earth is a magnetic + body, therefore, etc. The iron and its magnetism are typical of two + natures in one person; so it is said, "Si exaltatus fuero à terra, omnia + traham ad me ipsum."<a name="NtA_184" + href="#Nt_184"><sup>[184]</sup></a></p> + + <p> </p> + +<p class="cenhead">A VENETIAN BUDGET OF PARADOXES.</p> + +<blockquote class="b1n"> + + <p>Le glorie degli incogniti, o vero gli huomini illustri dell' accademia + de' signori incogniti di Venetia. Venice, 1647, 4to.</p> + +</blockquote> + + <p>This work is somewhat like a part of my own: it is a budget of + Venetian nobodies who wished to be somebodies; but paradox is not the + only means employed. It is of a serio-comic character, gives genuine + portraits in copperplate, and grave lists of works; but satirical + accounts. The astrologer Andrew Argoli<a name="NtA_185" + href="#Nt_185"><sup>[185]</sup></a> is there, and his son; both of whom, + with some of the others, have place in modern works <!-- Page 105 + --><span class="pagenum"><a name="page105"></a>[105]</span>on biography. + Argoli's discovery that logarithms facilitate easy processes, but + increase the labor of difficult ones, is worth recording.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Controversiæ de vera circuli mensura ... inter ... C. S. Longomontanum + et Jo. Pellium.<a name="NtA_186" href="#Nt_186"><sup>[186]</sup></a> + Amsterdam, 1647, 4to.</p> + +</blockquote> + + <p>Longomontanus,<a name="NtA_187" href="#Nt_187"><sup>[187]</sup></a> a + Danish astronomer of merit, squared the circle in 1644: he found out that + the diameter 43 gives the square root of 18252 for the circumference; + which gives 3.14185... for the ratio. Pell answered him, and being a kind + of circulating medium, managed to engage in the controversy names known + and unknown, as Roberval, Hobbes, Carcavi, Lord Charles Cavendish, + Pallieur, Mersenne, Tassius, Baron Wolzogen, Descartes, Cavalieri and + Golius.<a name="NtA_188" href="#Nt_188"><sup>[188]</sup></a> Among them, + of course, Longomontanus was made <!-- Page 106 --><span + class="pagenum"><a name="page106"></a>[106]</span>mincemeat: but he is + said to have insisted on the discovery of his epitaph.<a name="NtA_189" + href="#Nt_189"><sup>[189]</sup></a></p> + +<p><!-- Page 107 --><span class="pagenum"><a name="page107"></a>[107]</span></p> + + <p> </p> + +<p class="cenhead">THE CIRCULATING MEDIA OF MATHEMATICS.</p> + + <p>The great circulating mediums, who wrote to everybody, heard from + everybody, and sent extracts to everybody else, have been Father + Mersenne, John Collins, and the late Professor Schumacher: all "late" no + doubt, but only the last recent enough to be so styled. If M.C.S. should + ever again stand for "Member of the Corresponding Society," it should + raise an acrostic thought of the three. There is an allusion to + Mersenne's occupation in Hobbes's reply to him. He wanted to give Hobbes, + who was very ill at Paris, the Roman Eucharist: but Hobbes said, "I have + settled all that long ago; when did you hear from Gassendi?" We are + reminded of William's answer to Burnet. John Collins disseminated Newton, + among others. Schumacher ought to have been called the postmaster-general + of astronomy, as Collins was called the attorney-general of + mathematics.<a name="NtA_190" href="#Nt_190"><sup>[190]</sup></a></p> + +<p><!-- Page 108 --><span class="pagenum"><a name="page108"></a>[108]</span></p> + + <p> </p> + +<p class="cenhead">THE SYMPATHETIC POWDER.</p> + +<blockquote class="b1n"> + + <p>A late discourse ... by Sir Kenelme Digby.... Rendered into English by + R. White. London, 1658, 12mo.</p> + +</blockquote> + + <p>On this work see <i>Notes and Queries</i>, 2d series, vii. 231, 299, + 445, viii. 190. It contains the celebrated sympathetic powder. I am still + in much doubt as to the connection of Digby with this tract.<a + name="NtA_191" href="#Nt_191"><sup>[191]</sup></a> Without entering on + the subject here, I observe that in Birch's <i>History of the Royal + Society</i>,<a name="NtA_192" href="#Nt_192"><sup>[192]</sup></a> to + which both Digby and White belonged, Digby, though he brought many things + before the Society, never mentioned the powder, which is connected only + with the names of Evelyn<a name="NtA_193" + href="#Nt_193"><sup>[193]</sup></a> and Sir Gilbert Talbot.<a + name="NtA_194" href="#Nt_194"><sup>[194]</sup></a> The sympathetic powder + was that which cured by anointing the weapon with its salve instead of + the wound. I have long been convinced that it was efficacious. The + directions were to keep the <!-- Page 109 --><span class="pagenum"><a + name="page109"></a>[109]</span>wound clean and cool, and to take care of + diet, rubbing the salve on the knife or sword.<a name="NtA_195" + href="#Nt_195"><sup>[195]</sup></a> If we remember the dreadful notions + upon drugs which prevailed, both as to quantity and quality, we shall + readily see that any way of <i>not</i> dressing the wound would have been + useful. If the physicians had taken the hint, had been careful of diet + etc., and had poured the little barrels of medicine down the throat of a + practicable doll, <i>they</i> would have had their magical cures as well + as the surgeons.<a name="NtA_196" href="#Nt_196"><sup>[196]</sup></a> + Matters are much improved now; the quantity of medicine given, even by + orthodox physicians, would have been called infinitesimal by their + professional ancestors. Accordingly, the College of Physicians has a + right to abandon its motto, which is <i>Ars longa, vita brevis</i>, + meaning <i>Practice is long, so life is short</i>.</p> + + <p> </p> + +<p class="cenhead">HOBBES AS A MATHEMATICIAN.</p> + +<blockquote class="b1n"> + + <p>Examinatio et emendatio Mathematicæ Hodiernæ. By Thomas Hobbes. + London, 1666, 4to.</p> + +</blockquote> + + <p>In six dialogues: the sixth contains a quadrature of the circle.<a + name="NtA_197" href="#Nt_197"><sup>[197]</sup></a> But there is another + edition of this work, without place or date on the title-page, in which + the quadrature is omitted. This seems to be connected with the + publication <!-- Page 110 --><span class="pagenum"><a + name="page110"></a>[110]</span>of another quadrature, without date, but + about 1670, as may be judged from its professing to answer a tract of + Wallis, printed in 1669.<a name="NtA_198" + href="#Nt_198"><sup>[198]</sup></a> The title is "Quadratura circuli, + cubatio sphæræ, duplicatio cubi," 4to.<a name="NtA_199" + href="#Nt_199"><sup>[199]</sup></a> Hobbes, who began in 1655, was very + wrong in his quadrature; but, though not a Gregory St. Vincent,<a + name="NtA_200" href="#Nt_200"><sup>[200]</sup></a> he was not the + ignoramus in geometry that he is sometimes supposed. His writings, + erroneous as they are in many things, contain acute remarks on points of + principle. He is wronged by being coupled with Joseph Scaliger, as the + two great instances of men of letters who have come into geometry to help + the mathematicians out of their difficulty. I have never seen Scaliger's + quadrature,<a name="NtA_201" href="#Nt_201"><sup>[201]</sup></a> except + in the answers of Adrianus Romanus,<a name="NtA_202" + href="#Nt_202"><sup>[202]</sup></a> Vieta and Clavius, and in the + extracts of Kastner.<a name="NtA_203" href="#Nt_203"><sup>[203]</sup></a> + Scaliger had no right to such strong opponents: Erasmus or Bentley might + just as well have tried the problem, and either would have done much + better in any twenty minutes of his life.<a name="NtA_204" + href="#Nt_204"><sup>[204]</sup></a></p> + + <p> </p> + +<p class="cenhead">AN ESTIMATE OF SCALIGER.</p> + + <p>Scaliger inspired some mathematicians with great respect for his + geometrical knowledge. Vieta, the first man of his time, who answered + him, had such regard for his opponent <!-- Page 111 --><span + class="pagenum"><a name="page111"></a>[111]</span>as made him conceal + Scaliger's name. Not that he is very respectful in his manner of + proceeding: the following dry quiz on his opponent's logic must have been + very cutting, being true. "In grammaticis, dare navibus Austros, et dare + naves Austris, sunt æque significantia. Sed in Geometricis, aliud est + adsumpsisse circulum <span class="scac">BCD</span> non esse majorem + triginta sex segmentis <span class="scac">BCDF</span>, aliud circulo + <span class="scac">BCD</span> non esse majora triginta sex segmenta <span + class="scac">BCDF</span>. Illa adsumptiuncula vera est, hæc falsa."<a + name="NtA_205" href="#Nt_205"><sup>[205]</sup></a> Isaac Casaubon,<a + name="NtA_206" href="#Nt_206"><sup>[206]</sup></a> in one of his letters + to De Thou,<a name="NtA_207" href="#Nt_207"><sup>[207]</sup></a> relates + that, he and another paying a visit to Vieta, the conversation fell upon + Scaliger, of whom the host said that he believed Scaliger was the only + man who perfectly understood mathematical writers, especially the Greek + ones: and that he thought more of Scaliger when wrong than of many others + when right; "pluris se Scaligerum vel errantem facere quam multos <span + title="katorthountas" class="grk" + >κατορθούντας</span>."<a + name="NtA_208" href="#Nt_208"><sup>[208]</sup></a> This must have been + before Scaliger's quadrature (1594). There is an old story of some one + saying, "Mallem cum Scaligero errare, quam cum Clavio recte sapere."<a + name="NtA_209" href="#Nt_209"><sup>[209]</sup></a> This I cannot help + suspecting to have been a version of Vieta's speech with Clavius + satirically inserted, on account of the great hostility which Vieta + showed towards Clavius in the latter years of his life.</p> + + <p>Montucla could not have read with care either Scaliger's quadrature or + Clavius's refutation. He gives the first a wrong date: he assures the + world that there is no question about Scaliger's quadrature being wrong, + in the eyes of geometers at least: and he states that Clavius mortified + him <!-- Page 112 --><span class="pagenum"><a + name="page112"></a>[112]</span>extremely by showing that it made the + circle less than its inscribed dodecagon, which is, of course, equivalent + to asserting that a straight line is not always the shortest distance + between two points. Did <i>Clavius</i> show this? No, it was Scaliger + himself who showed it, boasted of it, and declared it to be a "noble + paradox" that a theorem false in geometry is true in arithmetic; a thing, + he says with great triumph, not noticed by Archimedes himself! He says in + so many words that the periphery of the dodecagon is greater than that of + the circle; and that the more sides there are to the inscribed figure, + the more does it exceed the circle in which it is. And here <i>are</i> + the words, on the independent testimonies of Clavius and Kastner:</p> + + <p>"Ambitus dodecagoni circulo inscribendi plus potest quam circuli + ambitus. Et quanto deinceps plurium laterum fuerit polygonum circulo + inscribendum, tanto plus poterit ambitus polygoni quam ambitus + circuli."<a name="NtA_210" href="#Nt_210"><sup>[210]</sup></a></p> + + <p>There is much resemblance between Joseph Scaliger and William + Hamilton,<a name="NtA_211" href="#Nt_211"><sup>[211]</sup></a> in a + certain impetuousity of character, and inaptitude to think of quantity. + Scaliger maintained that the arc of a circle is less than its chord in + arithmetic, though greater in geometry; Hamilton arrived at two + quantities which are identical, but the greater the one the less the + other. But, on the whole, I liken Hamilton rather to Julius than to + Joseph. On this last hero of literature I repeat Thomas Edwards,<a + name="NtA_212" href="#Nt_212"><sup>[212]</sup></a> who says that a man is + unlearned who, be his other knowledge what it may, does not <!-- Page 113 + --><span class="pagenum"><a name="page113"></a>[113]</span>understand the + subject he writes about. And now one of many instances in which + literature gives to literature character in science. Anthony Teissier,<a + name="NtA_213" href="#Nt_213"><sup>[213]</sup></a> the learned annotator + of De Thou's biographies, says of Finæus, "Il se vanta sans raison avoir + trouvé la quadrature du cercle; la gloire de cette admirable découverte + était réservée à Joseph Scalinger, comme l'a écrit Scévole de St. + Marthe."<a name="NtA_214" href="#Nt_214"><sup>[214]</sup></a></p> + + <p> </p> + +<p class="cenhead">JOHN GRAUNT AS A PARADOXER.</p> + +<blockquote class="b1n"> + + <p>Natural and Political Observations ... upon the Bills of Mortality. By + John Graunt, citizen of London. London, 1662, 4to.<a name="NtA_215" + href="#Nt_215"><sup>[215]</sup></a></p> + +</blockquote> + + <p>This is a celebrated book, the first great work upon mortality. But + the author, going <i>ultra crepidam</i>, has attributed to the motion of + the moon in her orbit all the tremors which she gets from a shaky + telescope.<a name="NtA_216" href="#Nt_216"><sup>[216]</sup></a> But there + is another paradox about this book: the above absurd opinion is + attributed to that excellent mechanist, Sir William Petty, who passed his + days among the astronomers. Graunt did not write his own book! Anthony + Wood<a name="NtA_217" href="#Nt_217"><sup>[217]</sup></a> hints that + Petty "assisted, or put into a way" his old benefactor: no doubt the two + friends talked the matter over many a time. Burnet and Pepys<a + name="NtA_218" href="#Nt_218"><sup>[218]</sup></a> state that Petty wrote + the book. It is enough for me that <!-- Page 114 --><span + class="pagenum"><a name="page114"></a>[114]</span>Graunt, whose honesty + was never impeached, uses the plainest incidental professions of + authorship throughout; that he was elected into the Royal Society because + he was the author; that Petty refers to him as author in scores of + places, and published an edition, as editor, after Graunt's death, with + Graunt's name of course. The note on Graunt in the <i>Biographia + Britannica</i> may be consulted; it seems to me decisive. Mr. C. B. + Hodge, an able actuary, has done the best that can be done on the other + side in the <i>Assurance Magazine</i>, viii. 234. If I may say what is in + my mind, without imputation of disrespect, I suspect some actuaries have + a bias: they would rather have Petty the greater for their Coryphæus than + Graunt the less.<a name="NtA_219" href="#Nt_219"><sup>[219]</sup></a></p> + + <p>Pepys is an ordinary gossip: but Burnet's account has an animus which + is of a worse kind. He talks of "one Graunt, a Papist, under whose name + Sir William Petty<a name="NtA_220" href="#Nt_220"><sup>[220]</sup></a> + published his observations on the bills of mortality." He then gives the + cock without a bull story of Graunt being a trustee of the New River + Company, and shutting up the cocks and carrying off their keys, just + before the fire of London, by which a supply of water was delayed.<a + name="NtA_221" href="#Nt_221"><sup>[221]</sup></a> It was one of the + first objections made to Burnet's work, that Graunt was <i>not</i> a + trustee at the time; and Maitland, the historian of London, ascertained + from the books of the Company that he was not admitted until twenty-three + days after the breaking out of the fire. Graunt's first admission <!-- + Page 115 --><span class="pagenum"><a name="page115"></a>[115]</span>to + the Company took place on the very day on which a committee was appointed + to inquire into the cause of the fire. So much for Burnet. I incline to + the view that Graunt's setting London on fire strongly corroborates his + having written on the bills of mortality: every practical man takes stock + before he commences a grand operation in business.</p> + + <p> </p> + +<p class="cenhead">MANKIND A GULLIBLE LOT.</p> + +<blockquote class="b1n"> + + <p>De Cometis: or a discourse of the natures and effects of Comets, as + they are philosophically, historically, and astrologically considered. + With a brief (yet full) account of the III late Comets, or blazing stars, + visible to all Europe. And what (in a natural way of judicature) they + portend. Together with some observations on the nativity of the Grand + Seignior. By John Gadbury, <span title="Philomathêmatikos" class="grk" + >Φιλομαθηματικός</span>. + London, 1665, 4to.</p> + +</blockquote> + + <p>Gadbury, though his name descends only in astrology, was a + well-informed astronomer.<a name="NtA_222" + href="#Nt_222"><sup>[222]</sup></a> D'Israeli<a name="NtA_223" + href="#Nt_223"><sup>[223]</sup></a> sets down Gadbury, Lilly, Wharton, + Booker, etc., as rank rogues: I think him quite wrong. The easy belief in + roguery and intentional imposture which prevails in educated society is, + to my mind, a greater presumption against the honesty of mankind than all + the roguery and imposture itself. Putting aside mere swindling for the + sake of gain, and looking at speculation and paradox, I find very little + reason to suspect wilful deceit.<a name="NtA_224" + href="#Nt_224"><sup>[224]</sup></a> My opinion of mankind is founded upon + the <!-- Page 116 --><span class="pagenum"><a + name="page116"></a>[116]</span>mournful fact that, so far as I can see, + they find within themselves the means of believing in a thousand times as + much as there is to believe in, judging by experience. I do not say + anything against Isaac D'Israeli for talking his time. We are all in the + team, and we all go the road, but we do not all draw.</p> + + <p> </p> + +<p class="cenhead">A FORERUNNER OF A WRITTEN ESPERANTO.</p> + +<blockquote class="b1n"> + + <p>An essay towards a real character and a philosophical language. By + John Wilkins [Dean of Ripon, afterwards Bishop of Chester].<a + name="NtA_225" href="#Nt_225"><sup>[225]</sup></a> London, 1668, + folio.</p> + +</blockquote> + + <p>This work is celebrated, but little known. Its object gives it a right + to a place among paradoxes. It proposes a language—if that be the + proper name—in which <i>things</i> and their relations shall be + denoted by signs, not <i>words</i>: so that any person, whatever may be + his mother tongue, may read it in his own words. This is an obvious + possibility, and, I am afraid, an obvious impracticability. One man may + construct such a system—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 <i>Biographia + Britannica</i>, except discussion of Anthony Wood's statement that the + hint was derived from Dalgarno's book, <!-- Page 117 --><span + class="pagenum"><a name="page117"></a>[117]</span><i>De Signis</i>, + 1661.<a name="NtA_226" href="#Nt_226"><sup>[226]</sup></a> Hamilton + (<i>Discussions</i>, Art. 5, "Dalgarno") does not say a word on this + point, beyond quoting Wood; and Hamilton, though he did now and then + write about his countrymen with a rough-nibbed pen, knew perfectly well + how to protect their priorities.</p> + + <p> </p> + +<p class="cenhead">GREGOIRE DE ST. VINCENT.</p> + +<blockquote class="b1n"> + + <p>Problema Austriacum. Plus ultra Quadratura Circuli. Auctore P. + Gregorio a Sancto Vincentio Soc. Jesu., Antwerp, 1647, folio.—Opus + Geometricum posthumum ad Mesolabium. By the same. Gandavi [Ghent], 1668, + folio.<a name="NtA_227" href="#Nt_227"><sup>[227]</sup></a></p> + +</blockquote> + + <p>The first book has more than 1200 pages, on all kinds of geometry. + Gregory St. Vincent is the greatest of circle-squarers, and his + investigations led him into many truths: he found the property of the + area of the hyperbola<a name="NtA_228" + href="#Nt_228"><sup>[228]</sup></a> which led to Napier's logarithms + being called <i>hyperbolic</i>. Montucla says of him, with sly truth, + that no one has ever squared the circle with so much genius, or, + excepting his principal object, with so much success.<a name="NtA_229" + href="#Nt_229"><sup>[229]</sup></a> His reputation, and the many merits + of his work, led to a sharp controversy on his quadrature, which ended in + its complete exposure by Huyghens and others. He had a small school of + followers, who defended him in print.</p> + +<p><!-- Page 118 --><span class="pagenum"><a name="page118"></a>[118]</span></p> + + <p> </p> + +<p class="cenhead">RENE DE SLUSE.</p> + +<blockquote class="b1n"> + + <p>Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liège], 1668, + 4to.<a name="NtA_230" href="#Nt_230"><sup>[230]</sup></a></p> + +</blockquote> + + <p>The Mesolabum is the solution of the problem of finding two mean + proportionals, which Euclid's geometry does not attain. Slusius is a true + geometer, and uses the ellipse, etc.: but he is sometimes ranked with the + trisecters, for which reason I place him here, with this explanation.</p> + + <p>The finding of two mean proportionals is the preliminary to the famous + old problem of the duplication of the cube, proposed by Apollo (not + Apollonius) himself. D'Israeli speaks of the "six follies of + science,"—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!</p> + + <p> </p> + +<p class="cenhead">JAMES GREGORY.</p> + + <p>1668. In this year James Gregory, in his <i>Vera Circuli et Hyperbolæ + Quadratura</i>,<a name="NtA_231" href="#Nt_231"><sup>[231]</sup></a> held + himself to have proved that <!-- Page 119 --><span class="pagenum"><a + name="page119"></a>[119]</span>the <i>geometrical</i> quadrature of the + circle is impossible. Few mathematicians read this very abstruse + speculation, and opinion is somewhat divided. The regular circle-squarers + attempt the <i>arithmetical</i> quadrature, which has long been proved to + be impossible. Very few attempt the geometrical quadrature. One of the + last is Malacarne, an Italian, who published his <i>Solution + Géométrique</i>, at Paris, in 1825. His method would make the + circumference less than three times the diameter.</p> + + <p> </p> + +<p class="cenhead">BEAULIEU'S QUADRATURE.</p> + +<blockquote class="b1n"> + + <p>La Géométrie Françoise, ou la Pratique aisée.... La quadracture du + cercle. Par le Sieur de Beaulieu, Ingénieur, Géographe du Roi ... Paris, + 1676, 8vo. [not Pontault de Beaulieu, the celebrated topographer; he died + in 1674].<a name="NtA_232" href="#Nt_232"><sup>[232]</sup></a></p> + +</blockquote> + + <p>If this book had been a fair specimen, I might have pointed to it in + connection with contemporary English works, and made a scornful + comparison. But it is not a fair specimen. Beaulieu was attached to the + Royal Household, and throughout the century it may be suspected that the + household forced a royal road to geometry. Fifty years before, Beaugrand, + the king's secretary, made a fool of himself, and [so?] contrived to pass + for a geometer. He had interest enough to get Desargues, the most + powerful geometer of his time,<a name="NtA_233" + href="#Nt_233"><sup>[233]</sup></a> the teacher and friend of Pascal, + prohibited from <!-- Page 120 --><span class="pagenum"><a + name="page120"></a>[120]</span>lecturing. See some letters on the History + of Perspective, which I wrote in the <i>Athenæum</i>, in October and + November, 1861. Montucla, who does not seem to know the true secret of + Beaugrand's greatness, describes him as "un certain M. de Beaugrand, + mathématicien, fort mal traité par Descartes, et à ce qu'il paroit avec + justice."<a name="NtA_234" href="#Nt_234"><sup>[234]</sup></a></p> + + <p>Beaulieu's quadrature amounts to a geometrical construction<a + name="NtA_235" href="#Nt_235"><sup>[235]</sup></a> which gives <span + class="grk">π</span> = √10. His depth may be ascertained from + the following extracts. First on Copernicus:</p> + + <p>"Copernic, Allemand, ne s'est pas moins rendu illustre par ses doctes + écrits; et nous pourrions dire de luy, qu'il seroit le seul et unique en + la force de ses Problèmes, si sa trop grande présomption ne l'avoit porté + à avancer en cette Science une proposition aussi absurde, qu'elle est + contre la Foy et raison, en faisant la circonférence d'un Cercle fixe, + immobile, et le centre mobile, sur lequel principe Géométrique, il a + avancé en son Traitté Astrologique le Soleil fixe, et la Terre mobile."<a + name="NtA_236" href="#Nt_236"><sup>[236]</sup></a></p> + + <p>I digress here to point out that though our quadrators, etc., very + often, and our historians sometimes, assert that men of the character of + Copernicus, etc., were treated with contempt and abuse until their day of + ascendancy came, nothing can be more incorrect. From Tycho Brahé<a + name="NtA_237" href="#Nt_237"><sup>[237]</sup></a> to Beaulieu, there is + but one expression of admiration for the genius of Copernicus. There is + an exception, which, I <!-- Page 121 --><span class="pagenum"><a + name="page121"></a>[121]</span>believe, has been quite misunderstood. + Maurolycus,<a name="NtA_238" href="#Nt_238"><sup>[238]</sup></a> in his + <i>De Sphæra</i>, written many years before its posthumous publication in + 1575, and which it is not certain he would have published, speaking of + the safety with which various authors may be read after his cautions, + says, "Toleratur et Nicolaus Copernicus qui Solem fixum et Terram <i>in + girum circumverti</i> posuit: et scutica potius, aut flagello, quam + reprehensione dignus est."<a name="NtA_239" + href="#Nt_239"><sup>[239]</sup></a> Maurolycus was a mild and somewhat + contemptuous satirist, when expressing disapproval: as we should now say, + he pooh-poohed his opponents; but, unless the above be an instance, he + was never savage nor impetuous. I am fully satisfied that the meaning of + the sentence is, that Copernicus, who turned the earth like a boy's top, + ought rather to have a whip given him wherewith to keep up his plaything + than a serious refutation. To speak of <i>tolerating</i> a person <i>as + being</i> more worthy of a flogging than an argument, is almost a + contradiction.</p> + + <p>I will now extract Beaulieu's treatise on algebra, entire.</p> + + <p>"L'Algebre est la science curieuse des Sçavans et specialement d'un + General d'Armée ou Capitaine, pour promptement ranger une Armée en + bataille, et nombre de Mousquetaires et Piquiers qui composent les + bataillons d'icelle, outre les figures de l'Arithmetique. Cette science a + 5 figures particulieres en cette sorte. P signifie <i>plus</i> au + commerce, et à l'Armée <i>Piquiers</i>. M signifie <i>moins</i>, et + <i>Mousquetaire</i> en l'Art des bataillons. [It is quite true that P and + M were used for <i>plus</i> and <i>minus</i> in a great many old works.] + R signifie <i>racine</i> en la mesure du Cube, et en l'Armée <i>rang</i>. + Q signifie <i>quaré</i> en l'un et l'autre usage. C signifie <i>cube</i> + en la mesure, et <i>Cavallerie</i> en la composition des bataillons et + escadrons. Quant à l'operation de cette science, c'est <!-- Page 122 + --><span class="pagenum"><a name="page122"></a>[122]</span>d'additionner + un <i>plus</i> d'avec <i>plus</i>, la somme sera <i>plus</i>, et + <i>moins</i> d'avec <i>plus</i>, on soustrait le moindre du <i>plus</i>, + et la reste est la somme requise ou nombre trouvé. Je dis seulement cecy + en passant pour ceux qui n'en sçavent rien du tout."<a name="NtA_240" + href="#Nt_240"><sup>[240]</sup></a></p> + + <p>This is the algebra of the Royal Household, seventy-three years after + the death of Vieta. Quære, is it possible that the fame of Vieta, who + himself held very high stations in the household all his life, could have + given people the notion that when such an officer chose to declare + himself an algebraist, he must be one indeed? This would explain + Beaugrand, Beaulieu, and all the <i>beaux</i>. Beaugrand—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 + <i>Geostatique</i>, published about 1638.<a name="NtA_241" + href="#Nt_241"><sup>[241]</sup></a> He makes bodies diminish in weight as + they approach the earth, because the effect of a weight on a lever is + less as it approaches the fulcrum.</p> + +<p><!-- Page 123 --><span class="pagenum"><a name="page123"></a>[123]</span></p> + + <p> </p> + +<p class="cenhead">SIR MATTHEW HALE.</p> + +<blockquote class="b1n"> + + <p>Remarks upon two late ingenious discourses.... By Dr. Henry More.<a + name="NtA_242" href="#Nt_242"><sup>[242]</sup></a> London, 1676, 8vo.</p> + +</blockquote> + + <p>In 1673 and 1675, Matthew Hale,<a name="NtA_243" + href="#Nt_243"><sup>[243]</sup></a> then Chief Justice, published two + tracts, an "Essay touching Gravitation," and "Difficiles Nugæ" on the + Torricellian experiment. Here are the answers by the learned and + voluminous Henry More. The whole would be useful to any one engaged in + research about ante-Newtonian notions of gravitation.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Observations touching the principles of natural motions; and + especially touching rarefaction and condensation.... By the author of + <i>Difficiles Nugæ</i>. London, 1677, 8vo.</p> + +</blockquote> + + <p>This is another tract of Chief Justice Hale, published the year after + his death. The reader will remember that <i>motion</i>, in old + philosophy, meant any change from state to state: what we now describe as + <i>motion</i> was <i>local motion</i>. This is a very philosophical book, + about <i>flux</i> and <i>materia prima</i>, <i>virtus activa</i> and + <i>essentialis</i>, and other fundamentals. I think Stephen Hales, the + author of the "Vegetable Statics," has the writings of the Chief Justice + sometimes attributed to him, which is very puny justice indeed.<a + name="NtA_244" href="#Nt_244"><sup>[244]</sup></a> Matthew Hale died in + 1676, and from his devotion to science it probably arose that his famous + <i>Pleas of the Crown</i><a name="NtA_245" + href="#Nt_245"><sup>[245]</sup></a> and other law works did not appear + until after his death. One of his <!-- Page 124 --><span + class="pagenum"><a name="page124"></a>[124]</span>contemporaries was the + astronomer Thomas Street, whose <i>Caroline Tables</i><a name="NtA_246" + href="#Nt_246"><sup>[246]</sup></a> were several times printed: another + contemporary was his brother judge, Sir Thomas Street.<a name="NtA_247" + href="#Nt_247"><sup>[247]</sup></a> But of the astronomer absolutely + nothing is known: it is very unlikely that he and the judge were the same + person, but there is not a bit of positive evidence either for or + against, so far as can be ascertained. Halley<a name="NtA_248" + href="#Nt_248"><sup>[248]</sup></a>—no less a + person—published two editions of the <i>Caroline Tables</i>, no + doubt after the death of the author: strange indeed that neither Halley + nor any one else should leave evidence that Street was born or died.</p> + + <p>Matthew Hale gave rise to an instance of the lengths a lawyer will go + when before a jury who cannot detect him. Sir Samuel Shepherd,<a + name="NtA_249" href="#Nt_249"><sup>[249]</sup></a> the Attorney General, + in opening Hone's<a name="NtA_250" href="#Nt_250"><sup>[250]</sup></a> + first trial, calls him "one who was the most learned man that ever + adorned the Bench, the most even man that ever blessed domestic life, the + <i>most eminent man that ever advanced the progress of science</i>, and + one of the [very moderate] best and most purely religious men that ever + lived."</p> + +<p><!-- Page 125 --><span class="pagenum"><a name="page125"></a>[125]</span></p> + + <p> </p> + +<p class="cenhead">ON THE DISCOVERY OF ANTIMONY.</p> + +<blockquote class="b1n"> + + <p>Basil Valentine his triumphant Chariot of Antimony, with annotations + of Theodore Kirkringius, M.D. With the true book of the learned Synesius, + a Greek abbot, taken out of the Emperour's library, concerning the + Philosopher's Stone. London, 1678, 8vo.<a name="NtA_251" + href="#Nt_251"><sup>[251]</sup></a></p> + +</blockquote> + + <p>There are said to be three Hamburg editions of the collected works of + Valentine, who discovered the common antimony, and is said to have given + the name <i>antimoine</i>, in a curious way. Finding that the pigs of his + convent throve upon it, he gave it to his brethren, who died of it.<a + name="NtA_252" href="#Nt_252"><sup>[252]</sup></a> The impulse given to + chemistry by R. Boyle<a name="NtA_253" + href="#Nt_253"><sup>[253]</sup></a> seems to have brought out a vast + number of translations, as in the following tract:</p> + + <p> </p> + +<p class="cenhead">ON ALCHEMY.</p> + +<blockquote class="b1n"> + + <p><i>Collectanea Chymica</i>: A collection of ten several treatises in + chymistry, concerning the liquor Alkehest, the Mercury of Philosophers, + and other curiosities worthy the perusal. Written by Eir. Philaletha,<a + name="NtA_254" href="#Nt_254"><sup>[254]</sup></a> Anonymus, J. B. + Van-Helmont,<a name="NtA_255" href="#Nt_255"><sup>[255]</sup></a> Dr. Fr. + <!-- Page 126 --><span class="pagenum"><a + name="page126"></a>[126]</span>Antonie,<a name="NtA_256" + href="#Nt_256"><sup>[256]</sup></a> Bernhard Earl of Trevisan,<a + name="NtA_257" href="#Nt_257"><sup>[257]</sup></a> Sir Geo. Ripley,<a + name="NtA_258" href="#Nt_258"><sup>[258]</sup></a> Rog. Bacon,<a + name="NtA_259" href="#Nt_259"><sup>[259]</sup></a> Geo. Starkie,<a + name="NtA_260" href="#Nt_260"><sup>[260]</sup></a> Sir Hugh Platt,<a + name="NtA_261" href="#Nt_261"><sup>[261]</sup></a> and the Tomb of + Semiramis. See more in the contents. London, 1684, 8vo.</p> + +</blockquote> + + <p>In the advertisements at the ends of these tracts there are upwards of + a hundred English tracts, nearly all of the period, and most of them + translations. Alchemy looks up since the chemists have found perfectly + different substances composed of the same elements and proportions. It is + true the chemists cannot yet <i>transmute</i>; but they may in time: they + poke about most assiduously. It seems, then, that the conviction that + alchemy <i>must</i> be impossible was a delusion: but we do not mention + it.</p> + +<p><!-- Page 127 --><span class="pagenum"><a name="page127"></a>[127]</span></p> + + <p>The astrologers and the alchemists caught it in company in the + following, of which I have an unreferenced note.</p> + + <p>"Mendacem et futilem hominem nominare qui volunt, calendariographum + dicunt; at qui sceleratum simul ac impostorem, chimicum.<a name="NtA_262" + href="#Nt_262"><sup>[262]</sup></a></p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Crede ratem ventis corpus ne crede chimistis;</p> + <p class="i4">Est quævis chimica tutior aura fide."<a name="NtA_263" href="#Nt_263"><sup>[263]</sup></a></p> + </div> + </div> + <p>Among the smaller paradoxes of the day is that of the <i>Times</i> + newspaper, which always spells it <i>chymistry</i>: but so, I believe, do + Johnson, Walker, and others. The Arabic work is very likely formed from + the Greek: but it may be connected either with <span title="chêmeia" class="grk" + >χημεια</span> or with <span + title="chumeia" class="grk" + >χυμεια</span>.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Lettre d'un gentil-homme de province à une dame de qualité, sur le + sujet de la Comète. Paris, 1681, 4to.</p> + +</blockquote> + + <p>An opponent of astrology, whom I strongly suspect to have been one of + the members of the Academy of Sciences under the name of a country + gentleman,<a name="NtA_264" href="#Nt_264"><sup>[264]</sup></a> writes + very good sense on the tremors excited by comets.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>The Petitioning-Comet: or a brief Chronology of all the famous Comets + and their events, that have happened from the birth of Christ to this + very day. Together with a modest enquiry into this present comet, London, + 1681, 4to.</p> + +</blockquote> + + <p>A satirical tract against the cometic prophecy:</p> + + <p>"This present comet (it's true) is of a menacing aspect, but if the + <i>new parliament</i> (for whose convention so many good men pray) + continue long to sit, I fear not but the star will lose its virulence and + malignancy, or at least its portent be averted from this our nation; + which being the humble request to God of all good men, makes me thus + entitle it, a Petitioning-Comet."</p> + +<p><!-- Page 128 --><span class="pagenum"><a name="page128"></a>[128]</span></p> + + <p>The following anecdote is new to me:</p> + + <p>"Queen Elizabeth (1558) being then at Richmond, and being disswaded + from looking on a comet which did then appear, made answer, <i>jacta est + alea</i>, the dice are thrown; thereby intimating that the pre-order'd + providence of God was above the influence of any star or comet."</p> + + <p>The argument was worth nothing: for the comet might have been <i>on + the dice</i> with the event; the astrologers said no more, at least the + more rational ones, who were about half of the whole.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>An astrological and theological discourse upon this present great + conjunction (the like whereof hath not (likely) been in some ages) + ushered in by a great comet. London, 1682, 4to. By C. N.<a name="NtA_265" + href="#Nt_265"><sup>[265]</sup></a></p> + +</blockquote> + + <p>The author foretells the approaching "sabbatical jubilee," but will + not fix the date: he recounts the failures of his predecessors.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>A judgment of the comet which became first generally visible to us in + Dublin, December 13, about 15 minutes before 5 in the evening, <span + class="scac">A.D.</span> 1680. By a person of quality. Dublin, 1682, + 4to.</p> + +</blockquote> + + <p>The author argues against cometic astrology with great ability.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>A prophecy on the conjunction of Saturn and Jupiter in this present + year 1682. With some prophetical predictions of what is likely to ensue + therefrom in the year 1684. By John Case, Student in physic and + astrology.<a name="NtA_266" href="#Nt_266"><sup>[266]</sup></a> London, + 1682, 4to.</p> + +</blockquote> + +<p><!-- Page 129 --><span class="pagenum"><a name="page129"></a>[129]</span></p> + + <p>According to this writer, great conjunctions of Jupiter and Saturn + occur "in the fiery trigon," about once in 800 years. Of these there are + to be seven: six happened in the several times of Enoch, Noah, Moses, + Solomon, Christ, Charlemagne. The seventh, which is to happen at "the + lamb's marriage with the bride," seems to be that of 1682; but this is + only vaguely hinted.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>De Quadrature van de Circkel. By Jacob Marcelis. Amsterdam, 1698, + 4to.</p> + + <p>Ampliatie en demonstratie wegens de Quadrature ... By Jacob Marcelis. + Amsterdam, 1699, 4to.</p> + + <p>Eenvoudig vertoog briev-wys geschrevem am J. Marcelis ... Amsterdam, + 1702, 4to.</p> + + <p>De sleutel en openinge van de quadrature ... Amsterdam, 1704, 4to.</p> + +</blockquote> + + <p>Who shall contradict Jacob Marcelis?<a name="NtA_267" + href="#Nt_267"><sup>[267]</sup></a> He says the circumference contains + the diameter exactly times</p> + + <div class="poem"> + <div class="stanza"> + <p class="i2">1008449087377541679894282184894</p> + <p>3 ————————————————</p> + <p class="i2">6997183637540819440035239271702</p> + </div> + </div> + <p>But he does not come very near, as the young arithmetician will + find.</p> + + <p> </p> + +<p class="cenhead">MATHEMATICAL THEOLOGY.</p> + +<blockquote class="b1n"> + + <p>Theologiæ Christianæ Principia Mathematica. Auctore Johanne Craig.<a + name="NtA_268" href="#Nt_268"><sup>[268]</sup></a> London, 1699, 4to.</p> + +</blockquote> + + <p>This is a celebrated speculation, and has been reprinted abroad, and + seriously answered. Craig is known in the early history of fluxions, and + was a good mathematician. <!-- Page 130 --><span class="pagenum"><a + name="page130"></a>[130]</span>He professed to calculate, on the + hypothesis that the suspicions against historical evidence increase with + the square of the time, how long it will take the evidence of + Christianity to die out. He finds, by formulæ, that had it been oral + only, it would have gone out A.D. 800; but, by aid of the written + evidence, it will last till A.D. 3150. At this period he places the + second coming, which is deferred until the extinction of evidence, on the + authority of the question "When the Son of Man cometh, shall he find + faith on the earth?" It is a pity that Craig's theory was not adopted: it + would have spared a hundred treatises on the end of the world, founded on + no better knowledge than his, and many of them falsified by the event. + The most recent (October, 1863) is a tract in proof of Louis Napoleon + being Antichrist, the Beast, the eighth Head, etc.; and the present + dispensation is to close soon after 1864.</p> + + <p>In order rightly to judge Craig, who added speculations on the + variations of pleasure and pain treated as functions of time, it is + necessary to remember that in Newton's day the idea of force, as a + quantity to be measured, and as following a law of variation, was very + new: so likewise was that of probability, or belief, as an object of + measurement.<a name="NtA_269" href="#Nt_269"><sup>[269]</sup></a> The + success of the <i>Principia</i> of Newton put it into many heads to + speculate about applying notions of quantity to other things not then + brought under measurement. Craig imitated Newton's title, and evidently + thought he was making a step in advance: but it is not every one who can + plough with Samson's heifer.</p> + + <p>It is likely enough that Craig took a hint, directly or indirectly, + from Mohammedan writers, who make a reply to the argument that the Koran + has not the evidence derived <!-- Page 131 --><span class="pagenum"><a + name="page131"></a>[131]</span>from miracles. They say that, as evidence + of Christian miracles is daily becoming weaker, a time must at last + arrive when it will fail of affording assurance that they were miracles + at all: whence would arise the necessity of another prophet and other + miracles. Lee,<a name="NtA_270" href="#Nt_270"><sup>[270]</sup></a> the + Cambridge Orientalist, from whom the above words are taken, almost + certainly never heard of Craig or his theory.</p> + + <p> </p> + +<p class="cenhead">THE ARISTOCRAT AS A SCIENTIST.</p> + +<blockquote class="b1n"> + + <p>Copernicans of all sorts convicted ... to which is added a Treatise of + the Magnet. By the Hon. Edw. Howard, of Berks. London, 1705, 8vo.</p> + +</blockquote> + + <p>Not all the blood of all the Howards will gain respect for a writer + who maintains that eclipses admit no possible explanation under the + Copernican hypothesis, and who asks how a man can "go 200 yards to any + place if the moving superficies of the earth does carry it from him?" + Horace Walpole, at the beginning of his <i>Royal and Noble Authors</i>, + has mottoed his book with the Cardinal's address to Ariosto, "Dove + diavolo, Messer Ludovico, avete pigliato tante coglionerie?"<a + name="NtA_271" href="#Nt_271"><sup>[271]</sup></a> Walter Scott says you + could hardly pick out, on any principle of selection—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, <!-- Page 132 + --><span class="pagenum"><a name="page132"></a>[132]</span>for instance, + Lord Brounker's<a name="NtA_272" href="#Nt_272"><sup>[272]</sup></a> + translation of Descartes on Music. Secondly, Walpole only takes the heads + of houses: this cuts both ways; he equally eliminates the Hon. Robert + Boyle and the precious Edward Howard. The last writer is hardly out of + the time in which aristocracy suppressed its names; the avowal was then + usually meant to make the author's greatness useful to the book. In our + day, literary peers and honorables are very favorably known, and contain + an eminent class.<a name="NtA_273" href="#Nt_273"><sup>[273]</sup></a> + They rough it like others, and if such a specimen as Edw. Howard were now + to appear, he would be greeted with</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Hereditary noodle! knowest thou not</p> + <p>Who would be wise, himself must make him so?"</p> + </div> + </div> + <p> </p> + +<p class="cenhead">THE LONGITUDE PROBLEM.</p> + +<blockquote class="b1n"> + + <p>A new and easy method to find the longitude at land or sea. London, + 1710, 4to.</p> + +</blockquote> + + <p>This tract is a little earlier than the great epoch of such + publications (1714), and professes to find the longitude by the observed + altitudes of the moon and two stars.<a name="NtA_274" + href="#Nt_274"><sup>[274]</sup></a> <!-- Page 133 --><span + class="pagenum"><a name="page133"></a>[133]</span></p> + + <p> </p> + +<blockquote class="b1n"> + + <p>A new method for discovering the longitude both at sea and land, + humbly proposed to the consideration of the public.<a name="NtA_275" + href="#Nt_275"><sup>[275]</sup></a> By Wm. Whiston<a name="NtA_276" + href="#Nt_276"><sup>[276]</sup></a> and Humphry Ditton.<a name="NtA_277" + href="#Nt_277"><sup>[277]</sup></a> London, 1714, 8vo.</p> + +</blockquote> + + <p>This is the celebrated tract, written by the two Arian heretics. + Swift, whose orthodoxy was as undoubted as his meekness, wrote upon it + the epigram—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<a + name="NtA_278" href="#Nt_278"><sup>[278]</sup></a> writes as follows to + Swift:</p> + + <p>"Whiston has at last published his project of the longitude; the most + ridiculous thing that ever was thought on. But a pox on him! he has + spoiled one of my papers of Scriblerus, which was a proposition for the + longitude not very unlike his, to this purpose; that since there was no + pole for east and west, that all the princes of Europe should join and + build two prodigious poles, upon high mountains, <!-- Page 134 --><span + class="pagenum"><a name="page134"></a>[134]</span>with a vast lighthouse + to serve for a polestar. I was thinking of a calculation of the time, + charges, and dimensions. Now you must understand his project is by + lighthouses, and explosion of bombs at a certain hour."</p> + + <p>The plan was certainly impracticable; but Whiston and Ditton might + have retorted that they were nearer to the longitude than their satirist + to the kingdom of heaven, or even to a bishopric. Arbuthnot, I think, + here and elsewhere, reveals himself as the calculator who kept Swift + right in his proportions in the matter of the Lilliputians, + Brobdingnagians, etc. Swift was very ignorant about things connected with + number. He writes to Stella that he has discovered that leap-year comes + every four years, and that all his life he had thought it came every + three years. Did he begin with the mistake of Cæsar's priests? Whether or + no, when I find the person who did not understand leap-year inventing + satellites of Mars in correct accordance with Kepler's third law, I feel + sure he must have had help.</p> + + <p> </p> + +<p class="cenhead">THE AURORA BOREALIS.</p> + +<blockquote class="b1n"> + + <p>An essay concerning the late apparition in the heavens on the 6th of + March. Proving by mathematical, logical, and moral arguments, that it + cou'd not have been produced meerly by the ordinary course of nature, but + must of necessity be a prodigy. Humbly offered to the consideration of + the Royal Society. London, 1716, 8vo.</p> + +</blockquote> + + <p>The prodigy, as described, was what we should call a very decided and + unusual aurora borealis. The inference was, that men's sins were bringing + on the end of the world. The author thinks that if one of the old + "threatening prophets" were then alive, he would give "something like the + following." I quote a few sentences of the notion which the author had of + the way in which Ezekiel, for instance, would have addressed his Maker in + the reign of George the First:</p> + + <p>"Begin! Begin! O Sovereign, for once, with an <!-- Page 135 --><span + class="pagenum"><a name="page135"></a>[135]</span>effectual clap of + thunder.... O Deity! either thunder to us no more, or when you thunder, + do it home, and strike with vengeance to the mark.... 'Tis not enough to + raise a storm, unless you follow it with a blow, and the thunder without + the bolt, signifies just nothing at all.... Are then your lightnings of + so short a sight, that they don't know how to hit, unless a mountain + stands like a barrier in their way? Or perhaps so many eyes open in the + firmament make you lose your aim when you shoot the arrow? Is it this? + No! but, my dear Lord, it is your custom never to take hold of your arms + till you have first bound round your majestic countenance with gathered + mists and clouds."</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>The principles of the Philosophy of the Expansive and Contractive + Forces ... By Robert Greene,<a name="NtA_279" + href="#Nt_279"><sup>[279]</sup></a> M.A., Fellow of Clare Hall. + Cambridge, 1727, folio.</p> + +</blockquote> + + <p>Sanderson<a name="NtA_280" href="#Nt_280"><sup>[280]</sup></a> writes + to Jones,<a name="NtA_281" href="#Nt_281"><sup>[281]</sup></a> "The + gentleman has been reputed mad for these two years last past, but never + gave the world such ample testimony of it before." This was said of a + former work of Greene's, on solid geometry, published in 1712, in which + he gives a quadrature.<a name="NtA_282" + href="#Nt_282"><sup>[282]</sup></a> He gives the same or another, I do + not know which, in the present work, in which the circle is 3-1/5 + diameters. This volume is of 981 good folio pages, and treats of all + things, mental and material. The author is not at all mad, only wrong on + <!-- Page 136 --><span class="pagenum"><a + name="page136"></a>[136]</span>many points. It is the weakness of the + orthodox follower of any received system to impute insanity to the + solitary dissentient: which is voted (in due time) a very wrong opinion + about Copernicus, Columbus, or Galileo, but quite right about Robert + Greene. If misconceptions, acted on by too much self-opinion, be + sufficient evidence of madness, it would be a curious inquiry what is the + least per-centage of the reigning school which has been insane at any one + time. Greene is one of the sources for Newton being led to think of + gravitation by the fall of an apple: his authority is the gossip of + Martin Folkes.<a name="NtA_283" href="#Nt_283"><sup>[283]</sup></a> + Probably Folkes had it from Newton's niece, Mrs. Conduitt, whom Voltaire + acknowledges as <i>his authority</i>.<a name="NtA_284" + href="#Nt_284"><sup>[284]</sup></a> It is in the draft found among + Conduitt's papers of memoranda to be sent to Fontenelle. But Fontenelle, + though a great retailer of anecdote, does not mention it in his + <i>éloge</i> of Newton; whence it may be suspected that it was left out + in the copy forwarded to France. D'Israeli has got an improvement on the + story: the apple "struck him a smart blow on the head": no doubt taking + him just on the organ of causality. He was "surprised at the force of the + stroke" from so small an apple: but then the apple had a mission; Homer + would have said <!-- Page 137 --><span class="pagenum"><a + name="page137"></a>[137]</span>it was Minerva in the form of an apple. + "This led him to consider the accelerating motion of falling bodies," + which Galileo had settled long before: "from whence he deduced the + principle of gravity," which many had considered before him, but no one + had <i>deduced anything from it</i>. I cannot imagine whence D'Israeli + got the rap on the head, I mean got it for Newton: this is very unlike + his usual accounts of things. The story is pleasant and possible: its + only defect is that various writings, well known to Newton, a very + <i>learned</i> mathematician, had given more suggestion than a whole sack + of apples could have done, if they had tumbled on that mighty head all at + once. And Pemberton, speaking from Newton himself, says nothing more than + that the idea of the moon being retained by the same force which causes + the fall of bodies struck him for the first time while meditating in a + garden. One particular tree at Woolsthorpe has been selected as the + gallows of the appleshaped goddess: it died in 1820, and Mr. Turnor<a + name="NtA_285" href="#Nt_285"><sup>[285]</sup></a> kept the wood; but Sir + D. Brewster<a name="NtA_286" href="#Nt_286"><sup>[286]</sup></a> brought + away a bit of root in 1814, and must have had it on his conscience for 43 + years that he may have killed the tree. Kepler's suggestion of + gravitation with the inverse distance, and Bouillaud's proposed + substitution of the inverse square of the distance, are things which + Newton knew better than his modern readers. I discovered two anagrams on + his name, which are quite conclusive; the notion of gravitation was + <i>not new</i>; but Newton <i>went on</i>. Some wandering spirit, + probably whose business it was to resent any liberty taken with Newton's + name, put into the head of a friend of mine <i>eighty-one</i> anagrams on + my own pair, some of which hit harder than any apple.</p> + +<p><!-- Page 138 --><span class="pagenum"><a name="page138"></a>[138]</span></p> + + <p> </p> + +<p class="cenhead">DE MORGAN ANAGRAMS.</p> + + <p>This friend, whom I must not name, has since made it up to about 800 + anagrams on my name, of which I have seen about 650. Two of them I have + joined in the title-page: the reader may find the sense. A few of the + others are personal remarks.</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Great gun! do us a sum!"</p> + </div> + </div> + <p>is a sneer at my pursuits: but,</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Go! great sum! ∫<i>a u<sup><i>n</i></sup> du</i>"</p> + </div> + </div> + <p>is more dignified.</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Sunt agro! gaudemus,"<a name="NtA_287" href="#Nt_287"><sup>[287]</sup></a></p> + </div> + </div> + <p>is happy as applied to one of whom it may be said:</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Ne'er out of town; 'tis such a horrid life;</p> + <p class="i1">But duly sends his family and wife."</p> + </div> + </div> + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Adsum, nugator, suge!"<a name="NtA_288" href="#Nt_288"><sup>[288]</sup></a></p> + </div> + </div> + <p>is addressed to a student who continues talking after the lecture has + commenced: oh! the rascal!</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Graduatus sum! nego"<a name="NtA_289" href="#Nt_289"><sup>[289]</sup></a></p> + </div> + </div> + <p>applies to one who declined to subscribe for an M.A. degree.</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Usage mounts guard"</p> + </div> + </div> + <p>symbolizes a person of very fixed habits.</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Gus! Gus! a mature don!</p> + <p class="i2">August man! sure, god!</p> + <p>And Gus must argue, O!</p> + <p class="i2">Snug as mud to argue,</p> + <p>Must argue on gauds.</p> + <p class="i2">A mad rogue stung us.</p> + <p>Gag a numerous stud</p> + <p class="i2">Go! turn us! damage us!</p> + <p>Tug us! O drag us! Amen.</p> + <p class="i2">Grudge us! moan at us!</p> +<!-- Page 139 --><span class="pagenum"><a name="page139"></a>[139]</span> + <p>Daunt us! gag us more!</p> + <p class="i2">Dog-ear us, man! gut us!</p> + <p>D—— us! a rogue tugs!"</p> + </div> + </div> + <p>are addressed to me by the circle-squarers; and,</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"O! Gus! tug a mean surd!"</p> + </div> + </div> + <p>is smart upon my preference of an incommensurable value of <span + class="grk">π</span> to 3-1/5, or some such simple substitute. + While,</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Gus! Gus! at 'em a' round!"</p> + </div> + </div> + <p>ought to be the backing of the scientific world to the author of the + <i>Budget of Paradoxes</i>.</p> + + <p>The whole collection commenced existence in the head of a powerful + mathematician during some sleepless nights. Seeing how large a number was + practicable, he amused himself by inventing a digested plan of finding + more.</p> + + <p>Is there any one whose name cannot be twisted into either praise or + satire? I have had given to me,</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Thomas Babington Macaulay</p> + <p class="i1">Mouths big: a Cantab anomaly."</p> + </div> + </div> + <p> </p> + +<p class="cenhead">NEWTON'S DE MUNDI SYSTEMATE LIBER.</p> + +<blockquote class="b1n"> + + <p>A treatise of the system of the world. By Sir Isaac Newton. Translated + into English. London, 1728, 8vo.</p> + +</blockquote> + + <p>I think I have a right to one little paradox of my own: I greatly + doubt that Newton wrote this book. Castiglione,<a name="NtA_290" + href="#Nt_290"><sup>[290]</sup></a> in his <i>Newtoni Opuscula</i>,<a + name="NtA_291" href="#Nt_291"><sup>[291]</sup></a> gives it in the Latin + which appeared in 1731,<a name="NtA_292" + href="#Nt_292"><sup>[292]</sup></a> not for the first time; he says + <i>Angli omnes Newtono tribuunt</i>.<a name="NtA_293" + href="#Nt_293"><sup>[293]</sup></a> It appeared just after Newton's + death, without the name of any editor, or any allusion to Newton's <!-- + Page 140 --><span class="pagenum"><a + name="page140"></a>[140]</span>recent departure, purporting to be that + popular treatise which Newton, at the beginning of the third book of the + <i>Principia</i>, says he wrote, intending it to be the third book. It is + very possible that some observant turnpenny might construct such a + treatise as this from the third book, that it might be ready for + publication the moment Newton could not disown it. It has been treated + with singular silence: the name of the editor has never been given. + Rigaud<a name="NtA_294" href="#Nt_294"><sup>[294]</sup></a> mentions it + without a word: I cannot find it in Brewster's <i>Newton</i>, nor in the + <i>Biographia Britannica</i>. There is no copy in the Catalogue of the + Royal Society's Library, either in English or Latin, except in + Castiglione. I am open to correction; but I think nothing from Newton's + acknowledged works will prove—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.<a name="NtA_295" + href="#Nt_295"><sup>[295]</sup></a></p> + + <p>Mr. Edleston<a name="NtA_296" href="#Nt_296"><sup>[296]</sup></a> + gives an account of the <i>lectures</i> "de motu corporum," and gives the + corresponding pages of the <i>Latin</i> "De Systemate Mundi" of 1731. But + no one mentions the <i>English</i> of 1728. This English seems to agree + with the Latin; but there is a mystery about it. The preface says, "That + this work as here published is genuine will so clearly appear by the + intrinsic marks it bears, that it will be but losing words and the + reader's time to take pains in giving him any other satisfaction." Surely + fewer words would have been lost if the prefator had said at once that + the work was from the manuscript preserved at Cambridge. Perhaps it was a + mangled copy clandestinely taken and interpreted. <!-- Page 141 --><span + class="pagenum"><a name="page141"></a>[141]</span></p> + + <p> </p> + +<p class="cenhead">A BACONIAN CONTROVERSY.</p> + +<blockquote class="b1n"> + + <p>Lord Bacon not the author of "The Christian Paradoxes," being a + reprint of "Memorials of Godliness and Christianity," by Herbert Palmer, + B.D.<a name="NtA_297" href="#Nt_297"><sup>[297]</sup></a> With + Introduction, Memoir, and Notes, by the Rev. Alexander B. Grosart,<a + name="NtA_298" href="#Nt_298"><sup>[298]</sup></a> Kenross. (Private + circulation, 1864).</p> + +</blockquote> + + <p>I insert the above in this place on account of a slight connection + with the last. Bacon's Paradoxes,—so attributed—were first + published as his in some asserted "Remains," 1648.<a name="NtA_299" + href="#Nt_299"><sup>[299]</sup></a> They were admitted into his works in + 1730, and remain there to this day. The title is "The Character of a + believing Christian, set forth in paradoxes and seeming contradictions." + The following is a specimen:</p> + + <p>"He believes three to be one and one to be three; a father not to be + older than his son; a son to be equal with his father; and one proceeding + from both to be equal with both: he believes three persons in one nature, + and two natures in one person.... He believes the God of all grace to + have been angry with one that never offended Him; and that God that hates + sin to be reconciled to himself though sinning continually, and never + making or being able to make Him any satisfaction. He believes a most + just God to have punished a most just person, and to have justified + himself, though a most ungodly sinner. He believes himself freely + pardoned, and yet a sufficient satisfaction was made for him."</p> + + <p>Who can doubt that if Bacon had written this it must have been wrong? + Many writers, especially on the <!-- Page 142 --><span class="pagenum"><a + name="page142"></a>[142]</span>Continent, have taken him as sneering at + (Athanasian) Christianity right and left. Many Englishmen have taken him + to be quite in earnest, and to have produced a body of edifying doctrine. + More than a century ago the Paradoxes were published as a penny tract; + and, again, at the same price, in the <i>Penny Sunday Reader</i>, vol. + vi, No. 148, a few passages were omitted, as <i>too strong</i>. But all + did not agree: in my copy of Peter Shaw's <a name="NtA_300" + href="#Nt_300"><sup>[300]</sup></a> edition (vol. ii, p. 283) the + Paradoxes have been cut out by the binder, who has left the backs of the + leaves. I never had the curiosity to see whether other copies of the + edition have been served in the same way. The Religious Tract Society + republished them recently in <i>Selections from the Writings of Lord + Bacon</i>, (no date; bad plan; about 1863, I suppose). No omissions were + made, so far as I find.</p> + + <p>I never believed that Bacon wrote this paper; it has neither his + <i>sparkle</i> nor his idiom. I stated my doubts even before I heard that + Mr. Spedding, one of Bacon's editors, was of the same mind. + (<i>Athenæum</i>, July 16, 1864). I was little moved by the wide consent + of orthodox men: for I knew how Bacon, Milton, Newton, Locke, etc., were + always claimed as orthodox until almost the present day. Of this there is + a remarkable instance.</p> + + <p> </p> + +<p class="cenhead">LOCKE AND SOCINIANISM.</p> + + <p>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 <a name="NtA_301" + href="#Nt_301"><sup>[301]</sup></a> "Reasonableness of Christianity." It + seems to have come down from the eighteenth century, when the battle was + belief in Christ against unbelief, <i>simpliciter</i>, as the <!-- Page + 143 --><span class="pagenum"><a name="page143"></a>[143]</span>logicians + say. Now, if ever there was a Socinian<a name="NtA_302" + href="#Nt_302"><sup>[302]</sup></a> book in the world, it is this work of + Locke. "These two," says Locke, "faith and repentance, i.e., believing + Jesus to be the Messiah, and a good life, are the indispensable + conditions of the new covenant, to be performed by all those who would + obtain eternal life." All the book is amplification of this doctrine. + Locke, in this and many other things, followed Hobbes, whose doctrine, in + the Leviathan, is <i>fidem, quanta ad salutem necessaria est, contineri + in hoc articulo, Jesus est Christus</i>.<a name="NtA_303" + href="#Nt_303"><sup>[303]</sup></a> For this Hobbes was called an + atheist, which <!-- Page 144 --><span class="pagenum"><a + name="page144"></a>[144]</span>many still believe him to have been: some + of his contemporaries called him, rightly, a Socinian. Locke was known + for a Socinian as soon as his work appeared: Dr. John Edwards,<a + name="NtA_304" href="#Nt_304"><sup>[304]</sup></a> his assailant, says he + is "Socinianized all over." Locke, in his reply, says "there is not one + word of Socinianism in it:" and he was right: the positive Socinian + doctrine has <i>not one word of Socinianism in it</i>; Socinianism + consists in omissions. Locke and Hobbes did not dare <i>deny</i> the + Trinity: for such a thing Hobbes might have been roasted, and Locke might + have been strangled. Accordingly, the well-known way of teaching + Unitarian doctrine was the collection of the asserted essentials of + Christianity, without naming the Trinity, etc. This is the plan Newton + followed, in the papers which have at last been published.<a + name="NtA_305" href="#Nt_305"><sup>[305]</sup></a></p> + + <p>So I, for one, thought little about the general tendency of orthodox + writers to claim Bacon by means of the Paradoxes. I knew that, in his + "Confession of Faith"<a name="NtA_306" + href="#Nt_306"><sup>[306]</sup></a> he is a Trinitarian of a heterodox + stamp. His second Person takes human nature before he took flesh, not for + redemption, but as a condition precedent of creation. "God is so holy, + pure, and jealous, that it is impossible for him to be pleased in any + creature, though the work of his own hands.... [Gen. i. 10, 12, 18, 21, + 25, 31, freely rendered]. But—purposing to become a Creator, and to + communicate to his creatures, he ordained in his eternal counsel that one + person of the Godhead should be united to one nature, and to one + particular of his creatures; that so, in the person of the Mediator, the + true ladder might be fixed, whereby God might <!-- Page 145 --><span + class="pagenum"><a name="page145"></a>[145]</span>descend to his + creatures and his creatures might ascend to God...."</p> + + <p>This is republished by the Religious Tract Society, and seems to suit + their theology, for they confess to having omitted some things of which + they disapprove.</p> + + <p>In 1864, Mr. Grosart published his discovery that the Paradoxes are by + Herbert Palmer; that they were first published surreptitiously, and + immediately afterwards by himself, both in 1645; that the "Remains" of + Bacon did not appear until 1648; that from 1645 to 1708, thirteen + editions of the "Memorials" were published, all containing the Paradoxes. + In spite of this, the Paradoxes were introduced into Bacon's works in + 1730, where they have remained.</p> + + <p>Herbert Palmer was of good descent, and educated as a Puritan. He was + an accomplished man, one of the few of his day who could speak French as + well as English. He went into the Church, and was beneficed by Laud,<a + name="NtA_307" href="#Nt_307"><sup>[307]</sup></a> in spite of his + puritanism; he sat in the Assembly of Divines, and was finally President + of Queens' College, Cambridge, in which post he died, August 13, 1647, in + the 46th year of his age.</p> + + <p>Mr. Grosart says, speaking of Bacon's "Remains," "All who have had + occasion to examine our early literature are aware that it was a common + trick to issue imperfect, false, and unauthorized writings under any + recently deceased name that might be expected to take. The Puritans, down + to John Bunyan, were perpetually expostulating and protesting against + such procedure." I have met with instances of all this; but I did not + know that there was so much of it: a good collection would be very + useful. The work of 1728, attributed to Newton, is likely enough to be + one of the class.</p> + +<p><!-- Page 146 --><span class="pagenum"><a name="page146"></a>[146]</span></p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Demonstration de l'immobilitez de la Terre.... Par M. de la + Jonchere,<a name="NtA_308" href="#Nt_308"><sup>[308]</sup></a> Ingénieur + Français. Londres, 1728, 8vo.</p> + +</blockquote> + + <p>A synopsis which is of a line of argument belonging to the beginning + of the preceding century.</p> + + <p> </p> + +<p class="cenhead">TWO FORGOTTEN CIRCLE SQUARERS.</p> + +<blockquote class="b1n"> + + <p>The Circle squared; together with the Ellipsis and several reflections + on it. The finding two geometrical mean proportionals, or doubling the + cube geometrically. By Richard Locke<a name="NtA_309" + href="#Nt_309"><sup>[309]</sup></a>.... London, no date, probably about + 1730, 8vo.</p> + +</blockquote> + + <p>According to Mr. Locke, the circumference is three diameters, + three-fourths the difference of the diameter and the side of the + inscribed equilateral triangle, and three-fourths the difference between + seven-eighths of the diameter and the side of the same triangle. This + gives, he says, 3.18897. There is an addition to this tract, being an + appendix to a book on the longitude.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>The Circle squar'd. By Thos. Baxter, Crathorn, Cleaveland, Yorkshire. + London, 1732, 8vo.</p> + +</blockquote> + + <p>Here <span class="grk">π</span> = 3.0625. No proof is offered.<a + name="NtA_310" href="#Nt_310"><sup>[310]</sup></a></p> + + <p> </p> + +<blockquote class="b1n"> + + <p>The longitude discovered by the Eclipses, Occultations, and + Conjunctions of Jupiter's planets. By William Whiston. London, 1738.</p> + +</blockquote> + + <p>This tract has, in some copies, the celebrated preface containing the + account of Newton's appearance before the Parliamentary Committee on the + longitude question, in 1714 <!-- Page 147 --><span class="pagenum"><a + name="page147"></a>[147]</span>(Brewster, ii. 257-266). This "historical + preface," is an insertion and is dated April 28, 1741, with four + additional pages dated August 10, 1741. The short "preface" is by the + publisher, John Whiston,<a name="NtA_311" + href="#Nt_311"><sup>[311]</sup></a> the author's son.</p> + + <p> </p> + +<p class="cenhead">THE STEAMSHIP SUGGESTED.</p> + +<blockquote class="b1n"> + + <p>A description and draught of a new-invented machine for carrying + vessels or ships out of, or into any harbour, port, or river, against + wind and tide, or in a calm. For which, His Majesty has granted letters + patent, for the sole benefit of the author, for the space of fourteen + years. By Jonathan Hulls.<a name="NtA_312" + href="#Nt_312"><sup>[312]</sup></a> London: printed for the author, 1737. + Price sixpence (folding plate and pp. 48, beginning from title).</p> + +</blockquote> + + <p>(I ought to have entered this tract in its place. It is so rare that + its existence was once doubted. It is the earliest description of + steam-power applied to navigation. The plate shows a barge, with smoking + funnel, and paddles at the stem, towing a ship of war. The engine, as + described, is Newcomen's.<a name="NtA_313" + href="#Nt_313"><sup>[313]</sup></a></p> + + <p>In 1855, John Sheepshanks,<a name="NtA_314" + href="#Nt_314"><sup>[314]</sup></a> so well known as a friend of Art and + a public donor, reprinted this tract, in fac-simile, from his own copy; + twenty-seven copies of the original 12mo size, and twelve on old paper, + small 4to. I have an original copy, wanting the plate, and with "Price + sixpence" carefully erased, to the honor of the book.<a name="NtA_315" + href="#Nt_315"><sup>[315]</sup></a></p> + +<p><!-- Page 148 --><span class="pagenum"><a name="page148"></a>[148]</span></p> + + <p>It is not known whether Hulls actually constructed a boat.<a + name="NtA_316" href="#Nt_316"><sup>[316]</sup></a> In all probability his + tract suggested to Symington, as Symington<a name="NtA_317" + href="#Nt_317"><sup>[317]</sup></a> did to Fulton.)</p> + + <p> </p> + +<p class="cenhead">THE NEWTONIANS ATTACKED.</p> + +<blockquote class="b1n"> + + <p>Le vrai système de physique générale de M. Isaac Newton exposé et + analysé en parallèle avec celui de Descartes. By Louis Castel<a + name="NtA_318" href="#Nt_318"><sup>[318]</sup></a> [Jesuit and F.R.S.] + Paris, 1743, 4to.</p> + +</blockquote> + + <p>This is an elaborate correction of Newton's followers, and of Newton + himself, who it seems did not give his own views with perfect fidelity. + Father Castel, for instance, assures us that Newton placed the sun <i>at + rest</i> in the center of the system. Newton left the sun to arrange that + matter with the planets and the rest of the universe. In this volume of + 500 pages there is right and wrong, both clever.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>A dissertation on the Æther of Sir Isaac Newton. By Bryan Robinson,<a + name="NtA_319" href="#Nt_319"><sup>[319]</sup></a> M.D. Dublin, 1743, + 8vo.<a name="NtA_320" href="#Nt_320"><sup>[320]</sup></a></p> + +</blockquote> + +<p><!-- Page 149 --><span class="pagenum"><a name="page149"></a>[149]</span></p> + + <p>A mathematical work professing to prove that the assumed ether causes + gravitation.</p> + + <p> </p> + +<p class="cenhead">MATHEMATICAL THEOLOGY.</p> + +<blockquote class="b1n"> + + <p>Mathematical principles of theology, or the existence of God + geometrically demonstrated. By Richard Jack, teacher of Mathematics. + London, 1747, 8vo.<a name="NtA_321" + href="#Nt_321"><sup>[321]</sup></a></p> + +</blockquote> + + <p>Propositions arranged after the manner of Euclid, with beings + represented by circles and squares. But these circles and squares are + logical symbols, not geometrical ones. I brought this book forward to the + Royal Commission on the British Museum as an instance of the absurdity of + attempting a <i>classed</i> catalogue from the <i>titles</i> of books. + The title of this book sends it either to theology or geometry: when, in + fact, it is a logical vagary. Some of the houses which Jack built were + destroyed by the fortune of war in 1745, at Edinburgh: who will say the + rebels did no good whatever? I suspect that Jack copied the ideas of J.B. + Morinus, "Quod Deus sit," Paris, 1636,<a name="NtA_322" + href="#Nt_322"><sup>[322]</sup></a> 4to, containing an attempt of the + same kind, but not stultified with diagrams.</p> + + <p> </p> + +<p class="cenhead">TWO MODEL INDORSEMENTS.</p> + +<blockquote class="b1n"> + + <p>Dissertation, découverte, et démonstrations de la quadrature + mathématique du cercle. Par M. de Fauré, géomètre. [<i>s. l.</i>, + probably Geneva] 1747, 8vo.</p> + + <p>Analyse de la Quadrature du Cercle. Par M. de Fauré, Gentilhomme + Suisse. Hague, 1749,<a name="NtA_323" href="#Nt_323"><sup>[323]</sup></a> + 4to.</p> + +</blockquote> + + <p>According to this octavo geometer and quarto gentleman, a diameter of + 81 gives a circumference of 256. There is an amusing circumstance about + the quarto which has been overlooked, if indeed the book has ever been + <!-- Page 150 --><span class="pagenum"><a + name="page150"></a>[150]</span>examined. John Bernoulli (the one of the + day)<a name="NtA_324" href="#Nt_324"><sup>[324]</sup></a> and Koenig<a + name="NtA_325" href="#Nt_325"><sup>[325]</sup></a> have both given an + attestation: my mathematical readers may stare as they please, such is + the fact. But, on examination, there will be reason to think the two sly + Swiss played their countryman the same trick as the medical man played + Miss Pickle, in the novel of that name. The lady only wanted to get his + authority against sousing her little nephew, and said, "Pray, doctor, is + it not both dangerous and cruel to be the means of letting a poor tender + infant perish by sousing it in water as cold as ice?"—"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:</p> + +<blockquote class="b1n"> + + <p>"Suivant les suppositions posées dans ce Mémoire, il est si évident + que <i>t</i> doit être = 34, <i>y</i> = 1, et <i>z</i> = 1, que cela n'a + besoin ni de preuve ni d'autorité pour être reconnu par tout le monde.<a + name="NtA_326" href="#Nt_326"><sup>[326]</sup></a></p> + + <p class="author">"à Basle le 7e Mai 1749. <span class="sc">Jean Bernoulli.</span>" + + <p>"Je souscris au jugement de Mr. Bernoulli, en conséquence de ces + suppositions.<a name="NtA_327" href="#Nt_327"><sup>[327]</sup></a></p> + + <p class="author">"à la Haye le 21 Juin 1749. <span class="sc">S. Koenig.</span>" + +</blockquote> + + <p>On which de Fauré remarks with triumph—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 <!-- Page 151 --><span + class="pagenum"><a name="page151"></a>[151]</span>reconnu et approuvé + parfaitement que la quadrature du cercle est mathématiquement + démontrée."<a name="NtA_328" href="#Nt_328"><sup>[328]</sup></a> It + should seem that it is easier to square the circle than to get round a + mathematician.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>An attempt to demonstrate that all the Phenomena in Nature may be + explained by two simple active principles, Attraction and Repulsion, + wherein the attraction of Cohesion, Gravity and Magnetism are shown to be + one the same. By Gowin Knight. London, 1748, 4to.</p> + +</blockquote> + + <p>Dr. Knight<a name="NtA_329" href="#Nt_329"><sup>[329]</sup></a> was + Mr. Panizzi's<a name="NtA_330" href="#Nt_330"><sup>[330]</sup></a> + archetype, the first Principal Librarian of the British Museum. He was + celebrated for his magnetical experiments. This work was long neglected; + but is now recognized as of remarkable resemblance to modern + speculations.</p> + + <p> </p> + +<p class="cenhead">THOMAS WRIGHT OF DURHAM.</p> + +<blockquote class="b1n"> + + <p>An original theory or Hypothesis of the Universe. By Thomas Wright<a + name="NtA_331" href="#Nt_331"><sup>[331]</sup></a> of Durham. London, + 4to, 1750.</p> + +</blockquote> + + <p>Wright is a speculator whose thoughts are now part of our current + astronomy. He took that view—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 <i>Philosophical Magazine</i> for + April, 1848.</p> + + <p>Wright was mathematical instrument maker to the King, <!-- Page 152 + --><span class="pagenum"><a name="page152"></a>[152]</span>and kept a + shop in Fleet Street. Is the celebrated business of Troughton & + 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,<a name="NtA_332" + href="#Nt_332"><sup>[332]</sup></a> Troughton & Simms.<a + name="NtA_333" href="#Nt_333"><sup>[333]</sup></a></p> + + <p> </p> + +<p class="cenhead">BISHOP HORNE ON NEWTON.</p> + +<blockquote class="b1n"> + + <p>The theology and philosophy in Cicero's <i>Somnium Scipionis</i> + explained. Or, a brief attempt to demonstrate, that the Newtonian system + is perfectly agreeable to the notions of the wisest ancients: and that + mathematical principles are the only sure ones. [By Bishop Horne,<a + name="NtA_334" href="#Nt_334"><sup>[334]</sup></a> at the age of + nineteen.] London, 1751, 8vo.</p> + +</blockquote> + + <p>This tract, which was not printed in the collected works, and is now + excessively rare, is mentioned in <i>Notes and Queries</i>, 1st S., v, + 490, 573; 2d S., ix, 15. The boyish satire on Newton is amusing. Speaking + of old Benjamin Martin,<a name="NtA_335" + href="#Nt_335"><sup>[335]</sup></a> he goes on as follows:</p> + +<p><!-- Page 153 --><span class="pagenum"><a name="page153"></a>[153]</span></p> + + <p>"But the most elegant account of the matter [attraction] is by that + hominiform animal, Mr. Benjamin Martin, who having attended Dr. + Desaguliers'<a name="NtA_336" href="#Nt_336"><sup>[336]</sup></a> fine, + raree, gallanty shew for some years [Desaguliers was one of the first who + gave public experimental lectures, before the saucy boy was born] in the + capacity of a turnspit, has, it seems, taken it into his head to set up + for a philosopher."</p> + + <p>Thus is preserved the fact, unknown to his biographers, that Benj. + Martin was an assistant to Desaguliers in his lectures. Hutton<a + name="NtA_337" href="#Nt_337"><sup>[337]</sup></a> says of him, that "he + was well skilled in the whole circle of the mathematical and + philosophical sciences, and wrote useful books on every one of them": + this is quite true; and even at this day he is read by twenty where Horne + is read by one; see the stalls, <i>passim</i>. All that I say of him, + indeed my knowledge of the tract, is due to this contemptuous mention of + a more durable man than himself. My assistant secretary at the + Astronomical Society, the late Mr. Epps,<a name="NtA_338" + href="#Nt_338"><sup>[338]</sup></a> bought the copy at a stall because + his eye was caught by the notice of "Old Ben Martin," of whom he was a + great reader. Old Ben could not be a Fellow of the Royal Society, because + he kept a shop: even though the shop sold nothing but philosophical + instruments. Thomas Wright, similarly situated as to shop and goods, + never was a Fellow. The Society of our day has greatly degenerated: those + of the old time would be pleased, no doubt, that the glories of their day + <!-- Page 154 --><span class="pagenum"><a + name="page154"></a>[154]</span>should be commemorated. In the early days + of the Society, there was a similar difficulty about Graunt, the author + of the celebrated work on mortality. But their royal patron, "who never + said a foolish thing," sent them a sharp message, and charged them if + they found any more such tradesmen, they should "elect them without more + ado."</p> + + <p>Horne's first pamphlet was published when he was but twenty-one years + old. Two years afterwards, being then a Fellow of his college, and having + seen more of the world, he seems to have felt that his manner was a + little too pert. He endeavored, it is said, to suppress his first tract: + and copies are certainly of extreme rarity. He published the following as + his maturer view:</p> + +<blockquote class="b1n"> + + <p>A fair, candid, and impartial state of the case between Sir Isaac + Newton and Mr. Hutchinson.<a name="NtA_339" + href="#Nt_339"><sup>[339]</sup></a> In which is shown how far a system of + physics is capable of mathematical demonstration; how far Sir Isaac's, as + such a system, has that demonstration; and consequently, what regard Mr. + Hutchinson's claim may deserve to have paid to it. By George Horne, M.A. + Oxford, 1753, 8vo.</p> + +</blockquote> + + <p>It must be remembered that the successors of Newton were very apt to + declare that Newton had demonstrated attraction as a <i>physical</i> + cause: he had taken reasonable pains to show that he did not pretend to + this. If any one had said to Newton, I hold that every particle of matter + is a responsible being of vast intellect, ordered by the Creator to move + as it would do if every other particle attracted it, and gifted with + power to make its way in true accordance with that law, as easily as a + lady picks her way across the street; what have you to say against + it?—Newton must have replied, Sir! if you really undertake to + maintain this as <i>demonstrable</i>, your soul had better borrow a + little power <!-- Page 155 --><span class="pagenum"><a + name="page155"></a>[155]</span>from the particles of which your body is + made: if you merely ask me to refute it, I tell you that I neither can + nor need do it; for whether attraction comes in this way or in any other, + <i>it comes</i>, and that is all I have to do with it.</p> + + <p>The reader should remember that the word attraction, as used by Newton + and the best of his followers, only meant a <i>drawing towards</i>, + without any implication as to the cause. Thus whether they said that + matter attracts matter, or that young lady attracts young gentleman, they + were using one word in one sense. Newton found that the law of the first + is the inverse square of the distance: I am not aware that the law of the + second has been discovered; if there be any chance, we shall see it at + the year 1856 in this list.</p> + + <p>In this point young Horne made a hit. He justly censures those who + fixed upon Newton a more positive knowledge of what attraction is than he + pretended to have. "He has owned over and over he did not know what he + meant by it—it might be this, or it might be that, or it might be + anything, or it might be nothing." With the exception of the + <i>nothing</i> clause, this is true, though Newton might have answered + Horne by "Thou hast said it."</p> + + <p>(I thought everybody knew the meaning of "Thou hast said it": but I + was mistaken. In three of the evangelists <span title="Su legeis" class="grk" + >Σὺ λέγεις</span> is + the answer to "Art thou a king?" The force of this answer, as always + understood, is "That is your way of putting it." The Puritans, who lived + in Bible phrases, so understood it: and Walter Scott, who caught all + peculiarities of language with great effect, makes a marked instance, + "Were you armed?—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. <i>Thou + hast spoken it</i>, replied the prisoner.")</p> + + <p>Again, Horne quotes Rowning<a name="NtA_340" + href="#Nt_340"><sup>[340]</sup></a> as follows:</p> + +<p><!-- Page 156 --><span class="pagenum"><a name="page156"></a>[156]</span></p> + + <p>"Mr. Rowning, pt. 2, p. 5 in a note, has a very pretty conceit upon + this same subject of attraction, about every particle of a fluid being + intrenched in three spheres of attraction and repulsion, one within + another, 'the innermost of which (he says) is a sphere of repulsion, + which keeps them from approaching into contact; the next, a sphere of + attraction, diffused around this of repulsion, by which the particles are + disposed to run together into drops; and the outermost of all, a sphere + of repulsion, whereby they repel each other, when removed out of the + attraction.' So that between the <i>urgings</i>, and + <i>solicitations</i>, of one and t'other, a poor unhappy particle must + ever be at his wit's end, not knowing which way to turn, or whom to obey + first."</p> + + <p>Rowning has here started the notion which Boscovich<a name="NtA_341" + href="#Nt_341"><sup>[341]</sup></a> afterwards developed.</p> + + <p>I may add to what precedes that it cannot be settled that, as + Granger<a name="NtA_342" href="#Nt_342"><sup>[342]</sup></a> says, + Desaguliers was the first who gave experimental lectures in London. + William Whiston gave some, and Francis Hauksbee<a name="NtA_343" + href="#Nt_343"><sup>[343]</sup></a> made the experiments. The prospectus, + as we should now call it, is extant, a quarto tract of plates and + descriptions, without date. Whiston, in his life, <!-- Page 157 --><span + class="pagenum"><a name="page157"></a>[157]</span>gives 1714 as the first + date of publication, and therefore, no doubt, of the lectures. + Desaguliers removed to London soon after 1712, and commenced his lectures + soon after that. It will be rather a nice point to settle which lectured + first; probabilities seem to go in favor of Whiston.</p> + + <p> </p> + +<p class="cenhead">FALLACIES IN A THEORY OF ANNUITIES.</p> + +<blockquote class="b1n"> + + <p>An Essay to ascertain the value of leases, and annuities for years and + lives. By W[eyman] L[ee]. London, 1737, 8vo.</p> + + <p>A valuation of Annuities and Leases certain, for a single life. By + Weyman Lee, Esq. of the Inner Temple. London, 1751, 8vo. Third edition, + 1773.</p> + +</blockquote> + + <p>Every branch of exact science has its paradoxer. The world at large + cannot tell with certainty who is right in such questions as squaring the + circle, etc. Mr. Weyman Lee<a name="NtA_344" + href="#Nt_344"><sup>[344]</sup></a> was the assailant of what all who had + studied called demonstration in the question of annuities. He can be + exposed to the world: for his error arose out of his not being able to + see that the whole is the sum of all its parts.</p> + + <p>By an annuity, say of £100, now bought, is meant that the buyer is to + have for his money £100 in a year, if he be then alive, £100 at the end + of two years, if then alive, and so on. It is clear that he would buy a + life annuity if he should buy the first £100 in one office, the second in + another, and so on. All the difference between buying the whole from one + office and buying all the separate contingent payments at different + offices, is immaterial to calculation. Mr. Lee would have agreed with the + rest of the world about the payments to be made to the several different + offices, in consideration of their several contracts: but he differed + from every one else about the sum to be paid to <i>one</i> office. He + contended that the way to value an annuity is to find out the term of + years which the individual has an even chance of surviving, and to charge + for the life annuity the value of an annuity certain for that term.</p> + +<p><!-- Page 158 --><span class="pagenum"><a name="page158"></a>[158]</span></p> + + <p>It is very common to say that Lee took the average life, or + expectation, as it is wrongly called, for his term: and this I have done + myself, taking the common story. Having exposed the absurdity of this + second supposition, taking it for Lee's, in my <i>Formal Logic</i>,<a + name="NtA_345" href="#Nt_345"><sup>[345]</sup></a> I will now do the same + with the first.</p> + + <p>A mathematical truth is true in its extreme cases. Lee's principle is + that an annuity on a life is the annuity made certain for the term within + which it is an even chance the life drops. If, then, of a thousand + persons, 500 be sure to die within a year, and the other 500 be immortal, + Lee's price of an annuity to any one of these persons is the present + value of one payment: for one year is the term which each one has an even + chance of surviving and not surviving. But the true value is obviously + half that of a perpetual annuity: so that at 5 percent Lee's rule would + give less than the tenth of the true value. It must be said for the poor + circle-squarers, that they never err so much as this.</p> + + <p>Lee would have said, if alive, that I have put an <i>extreme case</i>: + but any <i>universal</i> truth is true in its extreme cases. It is not + fair to bring forward an extreme case against a person who is speaking as + of usual occurrences: but it is quite fair when, as frequently happens, + the proposer insists upon a perfectly general acceptance of his + assertion. And yet many who go the whole hog protest against being + tickled with the tail. Counsel in court are good instances: they are + paradoxers by trade. June 13, 1849, at Hertford, there was an action + about a ship, insured against a <i>total</i> loss: some planks were + saved, and the underwriters refused to pay. Mr. 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 <!-- Page 159 --><span + class="pagenum"><a name="page159"></a>[159]</span>would go that length." + What would <i>Judge</i> Z.—as he now is—say to the extreme + case beginning somewhere between six planks and a bit of rope?</p> + + <p> </p> + +<p class="cenhead">MONTUCLA'S WORK ON THE QUADRATURE.</p> + +<blockquote class="b1n"> + + <p>Histoire des recherches sur la quadrature du cercle ... avec une + addition concernant les problèmes de la duplication du cube et de la + trisection de l'angle. Paris, 1754, 12mo. [By Montucla.]</p> + +</blockquote> + + <p>This is <i>the</i> history of the subject.<a name="NtA_346" + href="#Nt_346"><sup>[346]</sup></a> It was a little episode to the great + history of mathematics by Montucla, of which the first edition appeared + in 1758. There was much addition at the end of the fourth volume of the + second edition; this is clearly by Montucla, though the bulk of the + volume is put together, with help from Montucla's papers, by Lalande.<a + name="NtA_347" href="#Nt_347"><sup>[347]</sup></a> There is also a second + edition of the history of the quadrature, Paris, 1831, 8vo, edited, I + think, by Lacroix; of which it is the great fault that it makes hardly + any use of the additional matter just mentioned.</p> + + <p>Montucla is an admirable historian when he is writing from his own + direct knowledge: it is a sad pity that he did not tell us when he was + depending on others. We are not to trust a quarter of his book, and we + must read many other books to know which quarter. The fault is common + enough, but Montucla's good three-quarters is so good that the fault is + greater in him than in most others: I mean the fault of not + acknowledging; for an historian cannot read everything. But it must be + said that mankind give little encouragement to candor on this point. + Hallam, in his <!-- Page 160 --><span class="pagenum"><a + name="page160"></a>[160]</span><i>History of Literature</i>, states with + his own usual instinct of honesty every case in which he depends upon + others: Montucla does not. And what is the consequence?—Montucla is + trusted, and believed in, and cried up in the bulk; while the smallest + talker can lament that Hallam should be so unequal and apt to depend on + others, without remembering to mention that Hallam himself gives the + information. As to a universal history of any great subject being written + entirely upon primary knowledge, it is a thing of which the possibility + is not yet proved by an example. Delambre attempted it with astronomy, + and was removed by death before it was finished,<a name="NtA_348" + href="#Nt_348"><sup>[348]</sup></a> to say nothing of the gaps he + left.</p> + + <p>Montucla was nothing of a bibliographer, and his descriptions of books + in the first edition were insufficient. The Abbé Rive<a name="NtA_349" + href="#Nt_349"><sup>[349]</sup></a> fell foul of him, and as the phrase + is, gave it him. Montucla took it with great good humor, tried to mend, + and, in his second edition, wished his critic had lived to see the + <i>vernis de bibliographe</i> which he had given himself.</p> + + <p>I have seen Montucla set down as an <i>esprit fort</i>, more than + once: wrongly, I think. When he mentions Barrow's<a name="NtA_350" + href="#Nt_350"><sup>[350]</sup></a> address to the Almighty, he adds, "On + voit, au reste, par là, que Barrow étoit un pauvre philosophe; car il + croyait en l'immortalité de l'âme, et en une Divinité autre que la nature + <!-- Page 161 --><span class="pagenum"><a + name="page161"></a>[161]</span>universelle."<a name="NtA_351" + href="#Nt_351"><sup>[351]</sup></a> This is irony, not an expression of + opinion. In the book of mathematical recreations which Montucla + constructed upon that of Ozanam,<a name="NtA_352" + href="#Nt_352"><sup>[352]</sup></a> and Ozanam upon that of Van Etten,<a + name="NtA_353" href="#Nt_353"><sup>[353]</sup></a> now best known in + England by Hutton's similar treatment of Montucla, there is an amusing + chapter on the quadrators. Montucla refers to his own anonymous book of + 1754 as a curious book published by Jombert.<a name="NtA_354" + href="#Nt_354"><sup>[354]</sup></a> He seems to have been a little + ashamed of writing about circle-squarers: what a slap on the face for an + unborn Budgeteer!</p> + + <p>Montucla says, speaking of France, that he finds three notions + prevalent among the cyclometers: (1) that there is a large reward offered + for success; (2) that the longitude problem depends on that success; (3) + that the solution is the great end and object of geometry. The same three + <!-- Page 162 --><span class="pagenum"><a + name="page162"></a>[162]</span>notions are equally prevalent among the + same class in England. No reward has ever been offered by the government + of either country. The longitude problem in no way depends upon perfect + solution; existing approximations are sufficient to a point of accuracy + far beyond what can be wanted.<a name="NtA_355" + href="#Nt_355"><sup>[355]</sup></a> And geometry, content with what + exists, has long passed on to other matters. Sometimes a cyclometer + persuades a skipper who has made land in the wrong place that the + astronomers are in fault, for using a wrong measure of the circle; and + the skipper thinks it a very comfortable solution! And this is the utmost + that the problem ever has to do with longitude.</p> + + <p> </p> + +<p class="cenhead">ANTINEWTONIANISMUS.</p> + +<blockquote class="b1n"> + + <p>Antinewtonianismus.<a name="NtA_356" + href="#Nt_356"><sup>[356]</sup></a> By Cælestino Cominale,<a + name="NtA_357" href="#Nt_357"><sup>[357]</sup></a> M.D. Naples, 1754 and + 1756, 2 vols. 4to.</p> + +</blockquote> + + <p>The first volume upsets the theory of light; the second vacuum, vis + inertiæ, gravitation, and attraction. I confess I never attempted these + big Latin volumes, numbering 450 closely-printed quarto pages. The man + who slays Newton in a pamphlet is the man for me. But I will lend them to + anybody who will give security, himself in £500, and two sureties in £250 + each, that he will read them through, and give a full abstract; and I + will not exact security for their return. I have never seen any mention + of this book: it has a printer, but not a publisher, as happens with so + many unrecorded books.</p> + +<p><!-- Page 163 --><span class="pagenum"><a name="page163"></a>[163]</span></p> + + <p> </p> + +<p class="cenhead">OFFICIAL BLOW TO CIRCLE SQUARERS.</p> + + <p>1755. The French Academy of Sciences came to the determination not to + examine any more quadratures or kindred problems. This was the + consequence, no doubt, of the publication of Montucla's book: the time + was well chosen; for that book was a full justification of the + resolution. The Royal Society followed the same course, I believe, a few + years afterwards. When our Board of Longitude was in existence, most of + its time was consumed in listening to schemes, many of which included the + quadrature of the circle. It is certain that many quadrators have + imagined the longitude problem to be connected with theirs: and no doubt + the notion of a reward offered by Government for a true quadrature is a + result of the reward offered for the longitude. Let it also be noted that + this longitude reward was not a premium upon excogitation of a mysterious + difficulty. The legislature was made to know that the rational hopes of + the problem were centered in the improvement of the lunar tables and the + improvement of chronometers. To these objects alone, and by name, the + offer was directed: several persons gained rewards for both; and the + offer was finally repealed.</p> + + <p> </p> + +<p class="cenhead">AN INTERESTING HOAX.</p> + +<blockquote class="b1n"> + + <p>Fundamentalis Figura Geometrica, primas tantum lineas circuli + quadraturæ possibilitatis ostendens. By Niels Erichsen (Nicolaus + Ericius), shipbuilder, of Copenhagen. Copenhagen, 1755, 12mo.</p> + +</blockquote> + + <p>This was a gift from my oldest friend who was not a relative, Dr. + Samuel Maitland of the "Dark Ages."<a name="NtA_358" + href="#Nt_358"><sup>[358]</sup></a> He found it among his books, and + could not imagine how he came by it: I could have told him. He once + collected interpretations of the Apocalypse: and auction lots of such + <!-- Page 164 --><span class="pagenum"><a + name="page164"></a>[164]</span>books often contain quadratures. The + wonder is he never found more than one.</p> + + <p>The quadrature is not worth notice. Erichsen is the only squarer I + have met with who has distinctly asserted the particulars of that reward + which has been so frequently thought to have been offered in England. He + says that in 1747 the Royal Society on the 2d of June, offered to give a + large reward for the quadrature of the circle and a true explanation of + magnetism, in addition to £30,000 previously promised for the same. I + need hardly say that the Royal Society had not £30,000 at that time, and + would not, if it had had such a sum, have spent it on the circle, nor on + magnetic theory; nor would it have coupled the two things. On this book, + see <i>Notes and Queries</i>, 1st S., xii, 306. Perhaps Erichsen meant + that the £30,000 had been promised by the Government, and the addition by + the Royal Society.</p> + + <p>October 8, 1866. I receive a letter from a cyclometer who understands + that a reward is offered to any one who will square the circle, and that + all competitors are to send their plans to me. The hoaxers have not yet + failed out of the land.</p> + + <p> </p> + +<p class="cenhead">TWO JESUIT CONTRIBUTIONS.</p> + +<blockquote class="b1n"> + + <p>Theoria Philosophiæ Naturalis redacta ad unicam legem virium in natura + existentium. Editio <i>Veneta</i> prima. By Roger Joseph Boscovich. + Venice, 1763, 4to.</p> + +</blockquote> + + <p>The first edition is said to be of Vienna, 1758.<a name="NtA_359" + href="#Nt_359"><sup>[359]</sup></a> This is a celebrated work on the + molecular theory of matter, grounded on the hypothesis of spheres of + alternate attraction and repulsion. Boscovich was a Jesuit of varied + pursuit. During his measurement of a degree of the meridian, while on + horseback or waiting for his observations, he composed a Latin poem of + about five thousand verses on eclipses, <!-- Page 165 --><span + class="pagenum"><a name="page165"></a>[165]</span>with notes, which he + dedicated to the Royal Society: <i>De Solis et Lunæ defectibus</i>,<a + name="NtA_360" href="#Nt_360"><sup>[360]</sup></a> London, Millar and + Dodsley, 1760, 4to.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Traité de paix entre Des Cartes et Newton, <i>précédé</i> des vies + littéraires de ces deux chefs de la physique moderne.... By Aimé Henri + Paulian.<a name="NtA_361" href="#Nt_361"><sup>[361]</sup></a> Avignon, + 1763, 12mo.</p> + +</blockquote> + + <p>I have had these books for many years without feeling the least desire + to see how a lettered Jesuit would atone Descartes and Newton. On looking + at my two volumes, I find that one contains nothing but the literary life + of Descartes; the other nothing but the literary life of Newton. The + preface indicates more: and Watt mentions <i>three</i> volumes.<a + name="NtA_362" href="#Nt_362"><sup>[362]</sup></a> I dare say the first + two contain all that is valuable. On looking more attentively at the two + volumes, I find them both readable and instructive; the account of Newton + is far above that of Voltaire, but not so popular. But he should not have + said that Newton's family came from Newton in Ireland. Sir Rowland Hill + gives fourteen <i>Newtons</i> in Ireland;<a name="NtA_363" + href="#Nt_363"><sup>[363]</sup></a> twice the number of the cities that + contended for the birth of Homer may now contend for the origin of + Newton, on the word of Father Paulian.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Philosophical Essays, in three parts. By R. Lovett, Lay Clerk of the + Cathedral Church of Worcester. Worcester, 1766, 8vo.</p> + + <p>The Electrical Philosopher: containing a new system of physics <!-- + Page 166 --><span class="pagenum"><a + name="page166"></a>[166]</span>founded upon the principle of an universal + Plenum of elementary fire.... By R. Lovett, Worcester, 1774, 8vo.</p> + +</blockquote> + + <p>Mr. Lovett<a name="NtA_364" href="#Nt_364"><sup>[364]</sup></a> was + one of those ether philosophers who bring in elastic fluid as an + explanation by imposition of words, without deducing any one phenomenon + from what we know of it. And yet he says that attraction has received no + support from geometry; though geometry, applied to a particular law of + attraction, had shown how to predict the motions of the bodies of the + solar system. He, and many of his stamp, have not the least idea of the + confirmation of a theory by accordance of deduced results with + observation posterior to the theory.</p> + + <p> </p> + +<p class="cenhead">BAILLY'S EXAGGERATED VIEW OF ASTRONOMY.</p> + +<blockquote class="b1n"> + + <p>Lettres sur l'Atlantide de Platon, et sur l'ancien Histoire de l'Asie, + pour servir de suite aux lettres sur l'origine des Sciences, adressées à + M. de Voltaire, par M. Bailly.<a name="NtA_365" + href="#Nt_365"><sup>[365]</sup></a> London and Paris, 1779, 8vo.</p> + +</blockquote> + + <p>I might enter here all Bailly's histories of astronomy.<a + name="NtA_366" href="#Nt_366"><sup>[366]</sup></a> The paradox which runs + through them all more or less, is the doctrine that astronomy is of + immense antiquity, coming from some forgotten source, probably the + drowned island of Plato, peopled by a race whom Bailly makes, as has <!-- + Page 167 --><span class="pagenum"><a name="page167"></a>[167]</span>been + said, to teach us everything except their existence and their name. These + books, the first scientific histories which belong to readable + literature, made a great impression by power of style: Delambre created a + strong reaction, of injurious amount, in favor of history founded on + contemporary documents, which early astronomy cannot furnish. These + letters are addressed to Voltaire, and continue the discussion. There is + one letter of Voltaire, being the fourth, dated Feb. 27, 1777, and signed + "le vieux malade de Ferney, V. puer centum annorum."<a name="NtA_367" + href="#Nt_367"><sup>[367]</sup></a> Then begin Bailly's letters, from + January 16 to May 12, 1778. From some ambiguous expressions in the + Preface, it would seem that these are fictitious letters, supposed to be + addressed to Voltaire at their dates. Voltaire went to Paris February 10, + 1778, and died there May 30. Nearly all this interval was his closing + scene, and it is very unlikely that Bailly would have troubled him with + these letters.<a name="NtA_368" href="#Nt_368"><sup>[368]</sup></a></p> + + <p> </p> + +<blockquote class="b1n"> + + <p>An inquiry into the cause of motion, or a general theory of physics. + By S. Miller. London, 1781, 4to</p> + +</blockquote> + + <p>Newton all wrong: matter consists of two kinds of particles, one + inert, the other elastic and capable of expanding themselves <i>ad + infinitum</i>.</p> + + <p> </p> + +<p class="cenhead">SAINT-MARTIN ON ERRORS AND TRUTH.</p> + +<blockquote class="b1n"> + + <p>Des Erreurs et de la Vérité, ou les hommes rappelés au principe + universel de la science; ouvrage dans lequel, en faisant remarquer aux + observateurs l'incertitude de leurs recherches, et leurs méprises + continuelles, on leur indique la route qu'ils auroient dû suivre, pour + acquérir l'évidence physique sur l'origine du bien et du mal, sur + l'homme, sur la nature matérielle, et la nature sacrée; sur la base des + gouvernements <!-- Page 168 --><span class="pagenum"><a + name="page168"></a>[168]</span>politiques, sur l'autorité des souverains, + sur la justice civile et criminelle, sur les sciences, les langues, et + les arts. Par un Ph.... Inc.... A Edimbourg. 1782.<a name="NtA_369" + href="#Nt_369"><sup>[369]</sup></a> Two vols. 8vo.</p> + +</blockquote> + + <p>This is the famous work of Louis Claude de Saint-Martin<a + name="NtA_370" href="#Nt_370"><sup>[370]</sup></a> (1743-1803), for whose + other works, vagaries included, the reader must look elsewhere: among + other things, he was a translator of Jacob Behmen.<a name="NtA_371" + href="#Nt_371"><sup>[371]</sup></a> The title promises much, and the + writer has smart thoughts now and then; but the whole is the wearisome + omniscience of the author's day and country, which no reader of our time + can tolerate. Not that we dislike omniscience; but we have it of our own + country, both home-made and imported; and fashions vary. But surely there + can be but one omniscience? Must a man have but one wife? Nay, may not a + man have a new wife while the old one is living? There was a famous + instrumental professor forty years ago, who presented a friend to Madame + ——. 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.</p> + + <p>The book was printed at Lyons, but it was a trick of French authors to + pretend to be afraid of prosecution: it <!-- Page 169 --><span + class="pagenum"><a name="page169"></a>[169]</span>made a book look + wicked-like to have a feigned place of printing, and stimulated readers. + A Government which had undergone Voltaire would never have drawn its + sword upon quiet Saint-Martin. To make himself look still worse, he was + only ph[ilosophe] Inc...., which is generally read <i>Inconnu</i><a + name="NtA_372" href="#Nt_372"><sup>[372]</sup></a> but sometimes + <i>Incrédule</i>; <a name="NtA_373" href="#Nt_373"><sup>[373]</sup></a> + most likely the ambiguity was intended. There is an awful paradox about + the book, which explains, in part, its leaden sameness. It is all about + <i>l'homme</i>, <i>l'homme</i>, <i>l'homme</i>,<a name="NtA_374" + href="#Nt_374"><sup>[374]</sup></a> except as much as treats of <i>les + hommes</i>, <i>les hommes</i>, <i>les hommes</i>;<a name="NtA_375" + href="#Nt_375"><sup>[375]</sup></a> but not one single man is mentioned + by name in its 500 pages. It reminds one of</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Water, water everywhere,</p> + <p>And not a drop to drink."</p> + </div> + </div> + <p>Not one opinion of any other man is referred to, in the way of + agreement or of opposition. Not even a town is mentioned: there is + nothing which brings a capital letter into the middle of a sentence, + except, by the rarest accident, such a personification as <i>Justice</i>. + A likely book to want an <i>Edimbourg</i> godfather!</p> + + <p>Saint-Martin is great in mathematics. The number <i>four</i> + essentially belongs to straight lines, and <i>nine</i> to curves. The + object of a straight line is to perpetuate <i>ad infinitum</i> the + production of a point from which it emanates. A circle <a + href="images/adem_177.png"><img src="images/adem_177.png" class="middle" + style="height:2ex" alt="circle" /></a> bounds the production of all its + radii, tends to destroy them, and is in some sort their enemy. How is it + possible that things so distinct should not be distinguished in their + <i>number</i> as well as in their action? If this important observation + had been made earlier, immense trouble would have been saved to the + mathematicians, who would have been prevented from searching for a common + measure to lines which have nothing in common. But, though all straight + lines have the number <i>four</i>, it must not be supposed that they are + all equal, for a line is the result of its law and <!-- Page 170 --><span + class="pagenum"><a name="page170"></a>[170]</span>its number; but though + both are the same for all lines of a sort, they act differently, as to + force, energy, and duration, in different individuals; which explains all + differences of length, etc. I congratulate the reader who understands + this; and I do not pity the one who does not.</p> + + <p>Saint-Martin and his works are now as completely forgotten as if they + had never been born, except so far as this, that some one may take up one + of the works as of heretical character, and lay it down in + disappointment, with the reflection that it is as dull as orthodoxy. For + a person who was once in some vogue, it would be difficult to pick out a + more fossil writer, from Aa to Zypœus, 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 + <i>Des Erreurs</i> ... published a book in two parts with the same + fictitious place of printing;</p> + +<blockquote class="b1n"> + + <p>Tableau Naturel des Rapports qui existent entre Dieu, l'Homme, et + l'Univers. A Edimbourg, 1782, 8vo.<a name="NtA_376" + href="#Nt_376"><sup>[376]</sup></a></p> + +</blockquote> + + <p>There is a motto from the <i>Des Erreurs</i> itself, "Expliquer les + choses par l'homme, et non l'homme par les choses. <i>Des Erreurs et de + la Vérité</i>, par un PH.... INC...., p. 9."<a name="NtA_377" + href="#Nt_377"><sup>[377]</sup></a> This work is set down in various + catalogues and biographies as written by the PH.... INC.... himself. But + it is not usual for a writer to publish two works in the same year, one + of which takes a motto from the other. And the second work is profuse in + capitals and italics, and uses Hebrew learning: its style differs much + from the first work. The first work sets out from man, and has nothing to + do with God: the second is religious and raps the knuckles of the first + as follows: "Si nous voulons nous préserver de toutes <!-- Page 171 + --><span class="pagenum"><a name="page171"></a>[171]</span>les illusions, + et surtout des amorces de l'orgueil par lesquelles l'homme est si souvent + séduit, ne prenons jamais les hommes, mais toujours <i>Dieu</i> pour + notre terme de comparaison."<a name="NtA_378" + href="#Nt_378"><sup>[378]</sup></a> The first uses <i>four</i> and + <i>nine</i> in various ways, of which I have quoted one: the second says, + "Et ici se trouve déjà une explication des nombres <i>quatre</i> et + <i>neuf</i>, qui ont peu embarrassé dans l'ouvrage déjà cité. L'homme + s'est égaré en allant de <i>quatre</i> à <i>neuf</i>...."<a + name="NtA_379" href="#Nt_379"><sup>[379]</sup></a> The work cited is the + <i>Erreurs</i>, etc., and the citation is in the motto, which is the text + of the opposition sermon.</p> + + <p> </p> + +<p class="cenhead">A FORERUNNER OF THE METRIC SYSTEM.</p> + +<blockquote class="b1n"> + + <p>Method to discover the difference of the earth's diameters; proving + its true ratio to be not less variable than as 45 is to 46, and shortest + in its pole's axis 174 miles.... likewise a method for fixing an + universal standard for weights and measures. By Thomas Williams.<a + name="NtA_380" href="#Nt_380"><sup>[380]</sup></a> London, 1788, 8vo.</p> + +</blockquote> + + <p>Mr. Williams was a paradoxer in his day, and proposed what was, no + doubt, laughed at by some. He proposed the sort of plan which the + French—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.</p> + + <p>I was beginning to look up those who had made similar proposals, when + a learned article on the proposal of a <!-- Page 172 --><span + class="pagenum"><a name="page172"></a>[172]</span>metrical system came + under my eye in the <i>Times</i> of Sept. 15, 1863. The author cites + Mouton,<a name="NtA_381" href="#Nt_381"><sup>[381]</sup></a> who would + have the minute of a degree divided into 10,000 <i>virgulæ</i>; James + Cassini,<a name="NtA_382" href="#Nt_382"><sup>[382]</sup></a> whose foot + was to be six thousandths of a minute; and Paucton,<a name="NtA_383" + href="#Nt_383"><sup>[383]</sup></a> whose foot was the 400,000th of a + degree. I have verified the first and third statements; surely the second + ought to be the <i>six-thousandth</i>.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>An inquiry into the Copernican system ... wherein it is proved, in the + clearest manner, that the earth has only her diurnal motion ... with an + attempt to point out the only true way whereby mankind can receive any + real benefit from the study of the heavenly bodies. By John Cunningham.<a + name="NtA_384" href="#Nt_384"><sup>[384]</sup></a> London, 1789, 8vo.</p> + +</blockquote> + + <p>The "true way" appears to be the treatment of heaven and earth as + emblematical of the Trinity.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Cosmology. An inquiry into the cause of what is called gravitation or + attraction, in which the motions of the heavenly bodies, and the + preservation and operations of all nature, are deduced from an universal + principle of efflux and reflux. By T. Vivian,<a name="NtA_385" + href="#Nt_385"><sup>[385]</sup></a> vicar of Cornwood, Devon. Bath, 1792, + 12mo.</p> + +</blockquote> + +<p><!-- Page 173 --><span class="pagenum"><a name="page173"></a>[173]</span></p> + + <p>Attraction, an influx of matter to the sun; centrifugal force, the + solar rays; cohesion, the pressure of the atmosphere. The confusion about + centrifugal <i>force</i>, so called, as demanding an external agent, is + very common.</p> + + <p> </p> + +<p class="cenhead">THOMAS PAINE'S RIGHTS OF MAN.</p> + +<blockquote class="b1n"> + + <p>The rights of <span class="sc">Man</span>, being an answer to Mr. + Burke's attack on the French Revolution.<a name="NtA_386" + href="#Nt_386"><sup>[386]</sup></a> By Thomas Paine.<a name="NtA_387" + href="#Nt_387"><sup>[387]</sup></a> In two parts. 1791-1792. 8vo. + (Various editions.)<a name="NtA_388" + href="#Nt_388"><sup>[388]</sup></a></p> + + <p>A vindication of the rights of <span class="sc">Woman</span>, with + strictures on political and moral subjects. By Mary Wollstonecraft.<a + name="NtA_389" href="#Nt_389"><sup>[389]</sup></a> 1792. 8vo.</p> + + <p>A sketch of the rights of <span class="sc">Boys</span> and <span + class="sc">Girls</span>. By Launcelot Light, of Westminster School; and + Lætitia Lookabout, of Queen's Square, Bloomsbury. [By the Rev. Samuel + Parr,<a name="NtA_390" href="#Nt_390"><sup>[390]</sup></a> LL.D.] 1792. + 8vo. (pp.64).</p> + +</blockquote> + + <p>When did we three meet before? The first work has sunk into oblivion: + had it merited its title, it might have <!-- Page 174 --><span + class="pagenum"><a name="page174"></a>[174]</span>lived. It is what the + French call a <i>pièce de circonstance</i>; it belongs in time to the + French Revolution, and in matter to Burke's opinion of that movement. + Those who only know its name think it was really an attempt to write a + philosophical treatise on what we now call socialism. Silly government + prosecutions gave it what it never could have got for itself.</p> + + <p>Mary Wollstonecraft seldom has her name spelled right. I suppose the + O! O! character she got made her W<i>oo</i>lstonecraft. Watt gives double + insinuation, for his cross-reference sends us to G<i>oo</i>dwin.<a + name="NtA_391" href="#Nt_391"><sup>[391]</sup></a> No doubt the title of + the book was an act of discipleship to Paine's <i>Rights of Man</i>; but + this title is very badly chosen. The book was marred by it, especially + when the authoress and her husband assumed the right of dispensing with + legal sanction until the approach of offspring brought them to a sense of + their child's interest.<a name="NtA_392" + href="#Nt_392"><sup>[392]</sup></a> Not a hint of such a claim is found + in the book, which is mostly about female education. The right claimed + for woman is to have the education of a rational human being, and not to + be considered as nothing but woman throughout youthful training. The + maxims of Mary Wollstonecraft are now, though not derived from her, + largely followed in the education of girls, especially in home education: + just as many of the political principles of Tom Paine, again not derived + from him, are the guides of our actual legislation. I remember, forty + years ago, an old lady used to declare that she disliked girls from the + age of sixteen to five-and-twenty. "They are full," said she, "of + <i>femalities</i>." She spoke of their behavior to women as well as to + men. She <!-- Page 175 --><span class="pagenum"><a + name="page175"></a>[175]</span>would have been shocked to know that she + was a follower of Mary Wollstonecraft, and had packed half her book into + one sentence.</p> + + <p>The third work is a satirical attack on Mary Wollstonecraft and Tom + Paine. The details of the attack would convince any one that neither has + anything which would now excite reprobation. It is utterly unworthy of + Dr. Parr, and has quite disappeared from lists of his works, if it were + ever there. That it was written by him I take to be evident, as follows. + Nichols,<a name="NtA_393" href="#Nt_393"><sup>[393]</sup></a> who could + not fail to know, says (<i>Anecd.</i>, vol. ix, p. 120): "This is a + playful essay by a first-rate scholar, who is elsewhere noticed in this + volume, but whose name I shall not bring forward on so trifling an + occasion." Who the scholar was is made obvious by Master Launcelot being + made to talk of Bellendenus.<a name="NtA_394" + href="#Nt_394"><sup>[394]</sup></a> Further, the same boy is made to say, + "Let Dr. Parr lay his hand upon his heart, if his conscience will let + him, and ask himself how many thousands of wagon-loads of this article + [birch] he has cruelly misapplied." How could this apply to Parr, with + his handful of private pupils,<a name="NtA_395" + href="#Nt_395"><sup>[395]</sup></a> and no reputation for severity? Any + one except himself would have called on the head-master of Westminster or + Eton. I doubt whether the name of Parr could be connected with the rod by + anything in print, except the above and an anecdote of his pupil, Tom + Sheridan.<a name="NtA_396" href="#Nt_396"><sup>[396]</sup></a> The Doctor + had dressed for a dinner visit, and <!-- Page 176 --><span + class="pagenum"><a name="page176"></a>[176]</span>was ready a quarter of + an hour too soon to set off. "Tom," said he, "I think I had better whip + you now; you are sure to do something while I am out."—"I wish you + would, sir!" said the boy; "it would be a letter of licence for the whole + evening." The Doctor saw the force of the retort: my two tutelaries will + see it by this time. They paid in advance; and I have given liberal + interpretation to the order.</p> + + <p>The following story of Dr. Parr was told me and others, about 1829, by + the late Leonard Horner,<a name="NtA_397" + href="#Nt_397"><sup>[397]</sup></a> who knew him intimately. Parr was + staying in a house full of company, I think in the north of England. Some + gentlemen from America were among the guests, and after dinner they + disputed some of Parr's assertions or arguments. So the Doctor broke out + with "Do you know what country you come from? You come from the place to + which we used to send our thieves!" This made the host angry, and he gave + Parr such a severe rebuke as sent him from the room in ill-humor. The + rest walked on the lawn, amusing the Americans with sketches of the + Doctor. There was a dark cloud overhead, and from that cloud presently + came a voice which called <i>Tham</i> (Parr-lisp for <i>Sam</i>). The + company were astonished for a moment, but thought the Doctor was calling + his servant in the house, and that the apparent direction was an illusion + arising out of inattention. But presently the sound was repeated, + certainly from the cloud,</p> + +<blockquote class="b1n"> + + <p>"And nearer, clearer, deadlier than before."</p> + +</blockquote> + + <p>There was now a little alarm: where could the Doctor have got to? They + ran to his bedroom, and there they discovered a sufficient rather than + satisfactory explanation. The Doctor had taken his pipe into his bedroom, + and had seated himself, in sulky mood, upon the higher bar of a large and + deep old-fashioned grate with a high mantelshelf. Here he had <!-- Page + 177 --><span class="pagenum"><a name="page177"></a>[177]</span>tumbled + backwards, and doubled himself up between the bars and the back of the + grate. He was fixed tight, and when he called for help, he could only + throw his voice up the chimney. The echo from the cloud was the warning + which brought his friends to the rescue.</p> + + <p> </p> + +<p class="cenhead">ATTACKS ON RELIGIOUS CUSTOMS.</p> + + <p>Days of political paradox were coming, at which we now stare. + Cobbett<a name="NtA_398" href="#Nt_398"><sup>[398]</sup></a> said, about + 1830, in earnest, that in the country every man who did not take off his + hat to the clergyman was suspected, and ran a fair chance of having + something brought against him. I heard this assertion canvassed, when it + was made, in a party of elderly persons. The Radicals backed it, the old + Tories rather denied it, but in a way which satisfied me they ought to + have denied it less if they could not deny it more. But it must be said + that the Governments stopped far short of what their partisans would have + had them do. All who know Robert Robinson's<a name="NtA_399" + href="#Nt_399"><sup>[399]</sup></a> very quiet assault on church-made + festivals in his <i>History and Mystery of Good Friday</i> (1777)<a + name="NtA_400" href="#Nt_400"><sup>[400]</sup></a> will hear or remember + with surprise that the <i>British Critic</i> pronounced it a direct, + unprovoked, and malicious libel on the most <!-- Page 178 --><span + class="pagenum"><a name="page178"></a>[178]</span>sacred institutions of + the national Church. It was reprinted again and again: in 1811 it was in + a cheap form at 6s. 6d. a hundred. When the Jacobin day came, the State + was really in a fright: people thought twice before they published what + would now be quite disregarded. I examined a quantity of letters + addressed to George Dyer<a name="NtA_401" + href="#Nt_401"><sup>[401]</sup></a> (Charles Lamb's G.D.) and what + between the autographs of Thelwall, Hardy, Horne Tooke, and all the + rebels,<a name="NtA_402" href="#Nt_402"><sup>[402]</sup></a> put together + a packet which produced five guineas, or thereabouts, for the widow. + Among them were the following verses, sent by the author—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 <i>not</i> sent. The occasion was the public + thanksgiving at St. Paul's for the naval victories, December 19, + 1797.</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"God bless me! what a thing!</p> + <p>Have you heard that the King</p> + <p class="i2">Goes to St. Paul's?</p> +<!-- Page 179 --><span class="pagenum"><a name="page179"></a>[179]</span> + <p>Good Lord! and when he's there,</p> + <p>He'll roll his eyes in prayer,</p> + <p>To make poor Johnny stare</p> + <p class="i2">At this fine thing.</p> + </div> + + <div class="stanza"> + <p class="hg3">"No doubt the plan is wise</p> + <p>To blind poor Johnny's eyes</p> + <p class="i2">By this grand show;</p> + <p>For should he once suppose</p> + <p>That he's led by the nose,</p> + <p>Down the whole fabric goes,</p> + <p class="i2">Church, lords, and king.</p> + </div> + + <div class="stanza"> + <p class="hg3">"As he shouts Duncan's<a name="NtA_403" href="#Nt_403"><sup>[403]</sup></a> praise,</p> + <p>Mind how supplies they'll raise</p> + <p class="i2">In wondrous haste.</p> + <p>For while upon the sea</p> + <p>We gain one victory,</p> + <p>John still a dupe will be</p> + <p class="i2">And taxes pay.</p> + </div> + + <div class="stanza"> + <p class="hg3">"Till from his little store</p> + <p>Three-fourths or even more</p> + <p class="i2">Goes to the Crown.</p> + <p>Ah, John! you little think</p> + <p>How fast we downward sink</p> + <p>And touch the fatal brink</p> + <p class="i2">At which we're slaves."</p> + </div> + </div> + <p>I would have indicted the author for not making his thirds and + sevenths rhyme. As to the rhythm, it is not much better than what the + French sang in the Calais theater when the Duke of Clarence<a + name="NtA_404" href="#Nt_404"><sup>[404]</sup></a> took over Louis XVIII + in 1814.</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"God save noble Clarence,</p> + <p>Who brings our king to France;</p> + <p class="i2">God save Clarence!</p> + <p>He maintains the glory</p> + <p>Of the British navy,</p> + <p class="i2">etc., etc."</p> + </div> + </div> +<p><!-- Page 180 --><span class="pagenum"><a name="page180"></a>[180]</span></p> + + <p>Perhaps had this been published, the Government would have assailed it + as a libel on the church service. They got into the way of defending + themselves by making libels on the Church, of what were libels, if on + anything, on the rulers of the State; until the celebrated trials of Hone + settled the point for ever, and established that juries will not convict + for one offence, even though it have been committed, when they know the + prosecution is directed at another offence and another intent.</p> + + <p> </p> + +<p class="cenhead">HONE'S FAMOUS TRIALS.</p> + + <p>The results of Hone's trials (William Hone, 1779-1842) are among the + important constitutional victories of our century. He published parodies + on the Creeds, the Lord's Prayer, the Catechism, etc., with intent to + bring the Ministry into contempt: everybody knew that was his + <i>purpose</i>. The Government indicted him for impious, profane, + blasphemous intent, but not for seditious intent. They hoped to wear him + out by proceeding day by day. December 18, 1817, they hid themselves + under the Lord's Prayer, the Creed, and the Commandments; December 19, + under the Litany; December 20, under the Athanasian Creed, an odd place + for shelter when they could not find it in the previous places. Hone + defended himself for six, seven, and eight hours on the several days: and + the jury acquitted him in 15, 105, and 20 minutes. In the second trial + the offense was laid both as profanity and as sedition, which seems to + have made the jury hesitate. And they probably came to think that the + second count was false pretence: but the length of their deliberation is + a satisfactory addition to the value of the whole. In the first trial the + Attorney-General (Shepherd) had the impudence to say that the libel had + nothing of a political tendency about it, but was <i>avowedly</i> set off + against the religion and worship of the Church of England. The whole <!-- + Page 181 --><span class="pagenum"><a name="page181"></a>[181]</span>is + political in every sentence; neither more nor less political than the + following, which is part of the parody on the Catechism: "What is thy + duty towards the Minister? My duty towards the Minister is, to trust him + as much as I can; to honor him with all my words, with all my bows, with + all my scrapes, and with all my cringes; to flatter him; to give him + thanks; to give up my whole soul to him; to idolize his name, and obey + his word, and serve him blindly all the days of his political life." And + the parody on the Creed begins, "I believe in George, the Regent + almighty, maker of new streets and Knights of the Bath." This is what the + Attorney-General said had nothing of a political tendency about it. But + this was <i>on the first trial</i>: Hone was not known. The first day's + trial was under Justice Abbott (afterwards C. J. Tenterden).<a + name="NtA_405" href="#Nt_405"><sup>[405]</sup></a> It was perfectly + understood, when Chief Justice Ellenborough<a name="NtA_406" + href="#Nt_406"><sup>[406]</sup></a> appeared in Court on the second day, + that he was very angry at the first result, and put his junior aside to + try his own rougher dealing. But Hone tamed the lion. An eye-witness told + me that when he implored of Hone not to detail his own father Bishop + Law's<a name="NtA_407" href="#Nt_407"><sup>[407]</sup></a> views on the + Athanasian Creed, which humble petition Hone kindly granted, he held by + the desk for support. And the same when—which is not + reported—the Attorney-General appealed to the Court for protection + against a <!-- Page 182 --><span class="pagenum"><a + name="page182"></a>[182]</span>stinging attack which Hone made on the + Bar: he <i>held on</i>, and said, "Mr. Attorney, what <i>can</i> I do!" I + was a boy of twelve years old, but so strong was the feeling of + exultation at the verdicts that boys at school were not prohibited from + seeing the parodies, which would have been held at any other time quite + unfit to meet their eyes. I was not able to comprehend all about the Lord + Chief Justice until I read and heard again in after years. In the + meantime, Joe Miller had given me the story of the leopard which was sent + home on board a ship of war, and was in two days made as docile as a cat + by the sailors.<a name="NtA_408" href="#Nt_408"><sup>[408]</sup></a> "You + have got that fellow well under," said an officer. "Lord bless your + Honor!" said Jack, "if the Emperor of Marocky would send us a cock + rhinoceros, we'd bring him to his bearings in no time!" When I came to + the subject again, it pleased me to entertain the question whether, if + the Emperor had sent a cock rhinoceros to preside on the third day in the + King's Bench, Hone would have mastered <i>him</i>: I forget how I settled + it. There grew up a story that Hone caused Lord Ellenborough's death, but + this could not have been true. Lord Ellenborough resigned his seat in a + few months, and died just a year after the trials; but sixty-eight years + may have had more to do with it than his defeat.</p> + + <p>A large subscription was raised for Hone, headed by the Duke of + Bedford<a name="NtA_409" href="#Nt_409"><sup>[409]</sup></a> for £105. + Many of the leading anti-ministerialists joined: but there were many of + the other side who avowed their disapprobation of the false pretense. + Many could not venture their names. In the list I find: <!-- Page 183 + --><span class="pagenum"><a name="page183"></a>[183]</span>A member of + the House of Lords, an enemy to persecution, and especially to religious + persecution employed for political purposes—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<a name="NtA_410" + href="#Nt_410"><sup>[410]</sup></a> 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 <!-- Page 184 --><span class="pagenum"><a + name="page184"></a>[184]</span>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!</p> + + <p>These are specimens of a great many allusive mottoes. The subscription + was very large, and would have bought a handsome annuity, but Hone + employed it in the bookselling trade, and did not thrive. His <i>Everyday + Book</i><a name="NtA_411" href="#Nt_411"><sup>[411]</sup></a> and his + <i>Apocryphal New Testament</i>,<a name="NtA_412" + href="#Nt_412"><sup>[412]</sup></a> are useful books. On an annuity he + would have thriven as an antiquarian writer and collector. It is well + that the attack upon the right to ridicule Ministers roused a dormant + power which was equal to the occasion. Hone declared, on his honor, that + he had never addressed a meeting in his life, nor spoken a word before + more than twelve persons. Had he—which however could not then be + done—employed counsel and had a <i>guilty defense</i> made for him, + he would very likely have been convicted, and the work would have been + left to be done by another. No question that the parodies disgusted all + who reverenced Christianity, and who could not separate the serious and + the ludicrous, and prevent their existence in combination.</p> + + <p>My extracts, etc., are from the nineteenth, seventeenth, and sixteenth + editions of the three trials, which seem to have been contemporaneous + (all in 1818) as they are made up into one book, with additional title + over all, and the motto "Thrice the brindled cat hath mew'd." They are + published by Hone himself, who I should have said was a publisher <!-- + Page 185 --><span class="pagenum"><a name="page185"></a>[185]</span>as + well as was to be. And though the trials only ended Dec. 20, 1817, the + preface attached to this common title is dated Jan. 23, 1818.<a + name="NtA_413" href="#Nt_413"><sup>[413]</sup></a></p> + + <p>The spirit which was roused against the false dealing of the + Government, i.e., the pretense of prosecuting for impiety when all the + world knew the real offense was, if anything, sedition—was not got + up at the moment: there had been previous exhibitions of it. For example, + in the spring of 1818 Mr. Russell, a little printer in Birmingham, was + indicted for publishing the Political Litany<a name="NtA_414" + href="#Nt_414"><sup>[414]</sup></a> on which Hone was afterwards tried. + He took his witnesses to the summer Warwick assizes, and was told that + the indictment had been removed by certiorari into the King's Bench. He + had notice of trial for the spring assizes at Warwick: he took his + witnesses there, and the trial was postponed by the Crown. He then had + notice for the summer assizes at Warwick; and so on. The policy seems to + have been to wear out the obnoxious parties, either by delays or by + heaping on trials. The Government was odious, and knew it could + <i>not</i> get verdicts against ridicule, and <i>could</i> get verdicts + against impiety. No difficulty was found in convicting the sellers of + Paine's works, and the like. When Hone was held to bail it was seen that + a crisis was at hand. All parties in politics furnished him with parodies + in proof of religious persons having made instruments of them. The + parodies by Addison and Luther were contributed by a Tory lawyer, who was + afterwards a judge.</p> + + <p>Hone had published, in 1817, tracts of purely political ridicule: + <i>Official Account of the Noble Lord's Bite,</i><a name="NtA_415" + href="#Nt_415"><sup>[415]</sup></a> <i>Trial of the Dog for Biting the + Noble Lord</i>, etc. These were not touched. After the trials, it is + manifest that Hone was <!-- Page 186 --><span class="pagenum"><a + name="page186"></a>[186]</span>to be unassailed, do what he might. <i>The + Political House that Jack built</i>, in 1819; <i>The Man in the Moon</i>, + 1820; <i>The Queen's Matrimonial Ladder</i>, <i>Non mi ricordo</i>, + <i>The R—l Fowls</i>, 1820; <i>The Political Showman at Home</i>, + with plates by G. Cruickshank,<a name="NtA_416" + href="#Nt_416"><sup>[416]</sup></a> 1821 [he did all the plates]; <i>The + Spirit of Despotism</i>, 1821—would have been legitimate marks for + prosecution in previous years. The biting caricature of several of these + works are remembered to this day. <i>The Spirit of Despotism</i> was a + tract of 1795, of which a few copies had been privately circulated with + great secrecy. Hone reprinted it, and prefixed the following address to + "Robert Stewart, <i>alias</i> Lord Castlereagh"<a name="NtA_417" + href="#Nt_417"><sup>[417]</sup></a>: "It appears to me that if, + unhappily, your counsels are allowed much longer to prevail in the + Brunswick Cabinet, they will bring on a crisis, in which the king may be + dethroned or the people enslaved. Experience has shown that the people + will not be enslaved—the alternative is the affair of your + employers." Hone might say this without notice.</p> + + <p>In 1819 Mr. Murray<a name="NtA_418" + href="#Nt_418"><sup>[418]</sup></a> published Lord Byron's <i>Don + Juan</i>,<a name="NtA_419" href="#Nt_419"><sup>[419]</sup></a> and Hone + followed it with <i>Don John, or Don Juan Unmasked</i>, a little account + of what the publisher to the Admiralty was allowed to issue without + prosecution. The parody on the Commandments was a case very much in + point: and Hone makes a stinging allusion to the use of the + "<i>unutterable Name</i>, with a profane levity unsurpassed by <!-- Page + 187 --><span class="pagenum"><a name="page187"></a>[187]</span>any other + two lines in the English language." The lines are</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"'Tis strange—the Hebrew noun which means 'I am,'</p> + <p>The English always use to govern d——n."</p> + </div> + </div> + <p>Hone ends with: "Lord Byron's dedication of 'Don Juan' to Lord + Castlereagh was suppressed by Mr. Murray from delicacy to Ministers. Q. + Why did not Mr. Murray suppress Lord Byron's <i>parody</i> on the Ten + Commandments? <i>A.</i> Because it contains nothing in ridicule of + Ministers, and therefore nothing that <i>they</i> could suppose would + lead to the displeasure of Almighty God."</p> + + <p>The little matters on which I have dwelt will never appear in history + from their political importance, except in a few words of result. As a + mode of thought, silly evasions of all kinds belong to such a work as the + present. Ignorance, which seats itself in the chair of knowledge, is a + mother of revolutions in politics, and of unread pamphlets in + circle-squaring. From 1815 to 1830 the question of revolution or no + revolution lurked in all our English discussions. The high classes must + govern; the high classes shall not govern; and thereupon issue was to be + joined. In 1828-33 the question came to issue; and it was, Revolution + with or without civil war; choose. The choice was wisely made; and the + Reform Bill started a new system so well dovetailed into the old that the + joinings are hardly visible. And now, in 1867, the thing is repeated with + a marked subsidence of symptoms; and the party which has taken the place + of the extinct Tories is carrying through Parliament a wider extension of + the franchise than their opponents would have ventured. Napoleon used to + say that a decided nose was a sign of power: on which it has been + remarked that he had good reason to say so before the play was done. And + so had our country; it was saved from a religious war, and from a civil + war, by the power of that nose over its colleagues. <!-- Page 188 + --><span class="pagenum"><a name="page188"></a>[188]</span></p> + + <p> </p> + +<p class="cenhead">THOMAS TAYLOR, THE PLATONIST.</p> + +<blockquote class="b1n"> + + <p>The Commentaries of Proclus.<a name="NtA_420" + href="#Nt_420"><sup>[420]</sup></a> Translated by Thomas Taylor.<a + name="NtA_421" href="#Nt_421"><sup>[421]</sup></a> London, 1792, 2 vols. + 4to.<a name="NtA_422" href="#Nt_422"><sup>[422]</sup></a></p> + +</blockquote> + + <p>The reputation of "the Platonist" begins to grow, and will continue to + grow. The most authentic account is in the <i>Penny Cyclopædia</i>, + written by one of the few persons who knew him well, and one of the fewer + who possess all his works. At page lvi of the Introduction is Taylor's + notion of the way to find the circumference. It is not geometrical, for + it proceeds on the motion of a point: the words "on account of the + simplicity of the impulsive motion, such a line must be either straight + or circular" will suffice to show how Platonic it is. Taylor certainly + professed a kind of heathenism. D'lsraeli said, "Mr. T. Taylor, the + Platonic philosopher and the modern Plethon,<a name="NtA_423" + href="#Nt_423"><sup>[423]</sup></a> consonant to that philosophy, + professes polytheism." Taylor printed this in large type, in a page by + itself after the dedication, without any disavowal. I have seen the + following, Greek and translation both, in his handwriting: "<span + title="Pas agathos hêi agathos ethnikos; kai pas christianos hêi christianos kakos." class="grk" + >Πᾶς ἀγαθὸς + ᾗ ἀγαθὸς + ἐθνικός· + καὶ πᾶς + χριστιανὸς ᾗ + χριστιανὸς + κακός.</span> Every good man, so far as + he is a good man, is a heathen; and every Christian, so far as he is a + Christian, is a bad man." Whether Taylor had in his head the Christian of + the New Testament, or whether he drew from those members of the + "religious world" who make manifest the religious flesh and the religious + devil, <!-- Page 189 --><span class="pagenum"><a + name="page189"></a>[189]</span>cannot be decided by us, and perhaps was + not known to himself. If a heathen, he was a virtuous one.</p> + + <p> </p> + +<p class="cenhead">A NEW ERA IN FICTION.</p> + + <p>(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 + <i>poor children</i>. In 1795, a benevolent association began to + circulate the works of a lady who had been herself a dramatist, and had + nourished a pleasant vein of satire in the society of Garrick and his + friends; all which is carefully suppressed in some biographies. Hannah + More's<a name="NtA_424" href="#Nt_424"><sup>[424]</sup></a> <i>Cheap + Repository Tracts</i>,<a name="NtA_425" + href="#Nt_425"><sup>[425]</sup></a> which were bought by millions of + copies, destroyed the vicious publications with which the hawkers deluged + the country, by the simple process of furnishing the hawkers with + something more saleable.</p> + + <p><i>Dramatic fiction</i>, in which the <i>characters</i> are drawn by + themselves, was, at the middle of the last century, the monopoly of + writers who required indecorum, such as Fielding and Smollett. All, or + nearly all, which could be permitted to the young, was dry narrative, + written by people who could not make their personages <i>talk + character</i>; they all spoke <!-- Page 190 --><span class="pagenum"><a + name="page190"></a>[190]</span>alike. The author of the <i>Rambler</i><a + name="NtA_426" href="#Nt_426"><sup>[426]</sup></a> is ridiculed, because + his young ladies talk Johnsonese; but the satirists forget that all the + presentable novel-writers were equally incompetent; even the author of + <i>Zeluco</i> (1789)<a name="NtA_427" href="#Nt_427"><sup>[427]</sup></a> + is the strongest possible case in point.</p> + + <p>Dr. Moore,<a name="NtA_428" href="#Nt_428"><sup>[428]</sup></a> the + father of the hero of Corunna,<a name="NtA_429" + href="#Nt_429"><sup>[429]</sup></a> with good narrative power, some sly + humor, and much observation of character, would have been, in our day, a + writer of the <i>Peacock</i><a name="NtA_430" + href="#Nt_430"><sup>[430]</sup></a> family. Nevertheless, to one who is + accustomed to our style of things, it is comic to read the dialogue of a + jealous husband, a suspected wife, a faithless maid-servant, a tool of a + nurse, a wrong-headed pomposity of a priest, and a sensible physician, + all talking Dr. Moore through their masks. Certainly an Irish soldier + does say "by Jasus," and a cockney footman "this here" and "that there"; + and this and the like is all the painting of characters which is effected + out of the mouths of the bearers by a narrator of great power. I suspect + that some novelists repressed their power under a rule that a narrative + should narrate, and that the dramatic should be confined to the + drama.</p> + + <p>I make no exception in favor of Miss Burney;<a name="NtA_431" + href="#Nt_431"><sup>[431]</sup></a> though she was the forerunner of a + new era. Suppose a country <!-- Page 191 --><span class="pagenum"><a + name="page191"></a>[191]</span>in which dress is always of one color; + suppose an importer who brings in cargoes of blue stuff, red stuff, green + stuff, etc., and exhibits dresses of these several colors, that person is + the similitude of Miss Burney. It would be a delightful change from a + universal dull brown, to see one person all red, another all blue, etc.; + but the real inventor of pleasant dress would be the one who could mix + his colors and keep down the bright and gaudy. Miss Burney's introduction + was so charming, by contrast, that she nailed such men as Johnson, Burke, + Garrick, etc., to her books. But when a person who has read them with + keen pleasure in boyhood, as I did, comes back to them after a long + period, during which he has made acquaintance with the great novelists of + our century, three-quarters of the pleasure is replaced by wonder that he + had not seen he was at a puppet-show, not at a drama. Take some + <i>labeled</i> characters out of our humorists, let them be put together + into one piece, to speak only as labeled: let there be a Dominie with + nothing but "Prodigious!" a Dick Swiveller with nothing but adapted + quotations; a Dr. Folliott with nothing but sneers at Lord Brougham;<a + name="NtA_432" href="#Nt_432"><sup>[432]</sup></a> and the whole will + pack up into one of Miss Burney's novels.</p> + + <p>Maria Edgeworth,<a name="NtA_433" href="#Nt_433"><sup>[433]</sup></a> + Sydney Owenson (Lady Morgan),<a name="NtA_434" + href="#Nt_434"><sup>[434]</sup></a> Jane Austen,<a name="NtA_435" + href="#Nt_435"><sup>[435]</sup></a> Walter Scott,<a name="NtA_436" + href="#Nt_436"><sup>[436]</sup></a> etc., are all of our century; as <!-- + Page 192 --><span class="pagenum"><a name="page192"></a>[192]</span>are, + I believe, all the Minerva Press novels, as they were called, which show + some of the power in question. Perhaps dramatic talent found its best + encouragement in the drama itself. But I cannot ascertain that any such + power was directed at the multitude, whether educated or uneducated, with + natural mixture of character, under the restraints of decorum, until the + use of it by two religious writers of the school called "evangelical," + Hannah More and Rowland Hill.<a name="NtA_437" + href="#Nt_437"><sup>[437]</sup></a> The <i>Village Dialogues</i>, though + not equal to the <i>Repository Tracts</i>, are in many parts an approach, + and perhaps a copy; there is frequently humorous satire, in that most + effective form, self-display. They were published in 1800, and, partly at + least, by the Religious Tract Society, the lineal <span + class="correction" title="text reads `successsor'">successor</span> of + the <i>Repository</i> association, though knowing nothing about its + predecessor. I think it right to add that Rowland Hill here mentioned is + not the regenerator of the Post Office.<a name="NtA_438" + href="#Nt_438"><sup>[438]</sup></a> Some do not distinguish accurately; I + have heard of more than one who took me to have had a logical controversy + with a diplomatist who died some years before I was born.</p> + + <p> </p> + +<p class="cenhead">THE RELIGIOUS TRACT SOCIETY.</p> + + <p>A few years ago, an attempt was made by myself and others to collect + some information about the <i>Cheap Repository</i> (see <i>Notes and + Queries</i>, 3d Series, vi. 241, 290, 353; <i>Christian Observer</i>, + Dec. 1864, pp. 944-49). It appeared that after the Religious Tract + Society had existed more than fifty years, a friend presented it with a + copy of the original prospectus of the <i>Repository</i>, a thing the + existence of which was not known. In this prospectus it is announced that + from the plan "will be carefully excluded whatever is enthusiastic, + absurd, or superstitious." The "evangelical" <!-- Page 193 --><span + class="pagenum"><a name="page193"></a>[193]</span>party had, from the + foundation of the Religious Tract Society, regretted that the + <i>Repository Tracts</i> "did not contain a fuller statement of the great + evangelical principles"; while in the prospectus it is also stated that + "no cause of any particular party is intended to be served by it, but + general Christianity will be promoted upon practical principles." This + explains what has often been noticed, that the tracts contain a mild form + of "evangelical" doctrine, free from that more fervid dogmatism which + appears in the <i>Village Dialogues</i>; and such as H. More's friend, + Bishop Porteus<a name="NtA_439" + href="#Nt_439"><sup>[439]</sup></a>—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 <i>ad libitum</i>. This is an improper way of dealing with the + works of the dead; especially when the reprints are of popular works. A + small type addition to the preface contains: "Some alterations and + abridgements have been made to adapt them to the present times and the + aim of the Religious Tract Society." I think every publicity ought to be + given to the existence of such a practice; and I reprint what I said on + the subject in <i>Notes and Queries</i>.</p> + + <p>Alterations in works which the Society republishes are a necessary + part of their plan, though such notes as they should judge to be + corrective would be the best way of proceeding. But the fact of + alteration should be very distinctly announced on the title of the work + itself, not left to a little bit of small type at the end of the preface, + in the place where trade advertisements, or directions to the binder, are + often found. And the places in which alteration has been made should be + pointed out, either by marks of omission, when omission is the + alteration, or by putting the altered sentences in brackets, when change + has been made. May any one alter the works of the dead at his own + discretion? <!-- Page 194 --><span class="pagenum"><a + name="page194"></a>[194]</span>We all know that readers in general will + take each sentence to be that of the author whose name is on the title; + so that a correcting republisher <i>makes use of his author's name to + teach his own variation</i>. The tortuous logic of "the trade," which is + content when "the world" is satisfied, is not easily answered, any more + than an eel is easily caught; but the Religious Tract Society may be + <i>convinced</i> [in the old sense] in a sentence. On which course would + they feel most safe in giving their account to the God of truth? "In your + own conscience, now?"</p> + + <p>I have tracked out a good many of the variations made by the Religious + Tract Society in the recently published volume of <i>Repository + Tracts</i>. Most of them are doctrinal insertions or amplifications, to + the matter of which Hannah More would not have objected—all that + can be brought against them is the want of notice. But I have found two + which the respect I have for the Religious Tract Society, in spite of + much difference on various points, must not prevent my designating as + paltry. In the story of Mary Wood, a kind-hearted clergyman converses + with the poor girl who has ruined herself by lying. In the original, he + "assisted her in the great work of repentance;" in the reprint it is to + be shown in some detail how he did this. He is to begin by pointing out + that "the heart is deceitful above all things and desperately wicked." + Now the clergyman's name is <i>Heartwell</i>: so to prevent his name from + contradicting his doctrine, he is actually cut down to <i>Harwell</i>. + Hannah Moore meant this good man for one of those described in Acts xv. + 8, 9, and his name was appropriate.</p> + + <p>Again, Mr. Flatterwell, in persuasion of Parley the porter to let him + into the castle, declares that the worst he will do is to "play an + innocent game of cards just to keep you awake, or sing a cheerful song + with the maids." Oh fie! Miss Hannah More! and you a single lady too, and + a contemporary of the virtuous Bowdler!<a name="NtA_440" + href="#Nt_440"><sup>[440]</sup></a> Though Flatterwell be an <!-- Page + 195 --><span class="pagenum"><a name="page195"></a>[195]</span>allegory + of the devil, this is really too indecorous, even for him. Out with the + three last words! and out it is.</p> + + <p>The Society cuts a poor figure before a literary tribunal. Nothing was + wanted except an admission that the remarks made by me were unanswerable, + and this was immediately furnished by the Secretary (<i>N. and Q.</i>, 3d + S., vi. 290). In a reply of which six parts out of seven are a very + amplified statement that the Society did not intend to reprint <i>all</i> + Hannah More's tracts, the remaining seventh is as follows:</p> + + <p>"I am not careful [perhaps this should be <i>careful not</i>] to + notice Professor De Morgan's objections to the changes in 'Mary Wood' or + 'Parley the Porter,' but would merely reiterate that the tracts were + neither designed nor announced to be 'reprints' of the originals [design + is only known to the designers; as to announcement, the title is ''Tis + all for the best, The Shepherd of Salisbury Plain, and other narratives + by Hannah More']; and much less [this must be <i>careful not</i>; further + removed from answer than <i>not careful</i>] can I occupy your space by a + treatise on the Professor's question: 'May any one alter the works of the + dead at his own discretion?'"</p> + + <p>To which I say: Thanks for help!</p> + + <p>I predict that Hannah More's <i>Cheap Repository Tracts</i> will + somewhat resemble the <i>Pilgrim's Progress</i> in their fate. Written + for the cottage, and long remaining in their original position, they will + become classical works of their kind. Most assuredly this will happen if + my assertion cannot be upset, namely, that they contain the first + specimens of fiction addressed to the world at large, and widely + circulated, in which dramatic—as distinguished from + puppet—power is shown, and without indecorum.</p> + +<p><!-- Page 196 --><span class="pagenum"><a name="page196"></a>[196]</span></p> + + <p>According to some statements I have seen, but which I have not + verified, other publishing bodies, such as the Christian Knowledge + Society, have taken the same liberty with the names of the dead as the + Religious Tract Society. If it be so, the impropriety is the work of the + smaller spirits who have not been sufficiently overlooked. There must be + an overwhelming majority in the higher councils to feel that, whenever + <i>altered</i> works are published, <i>the fact of alteration should be + made as prominent as the name of the author</i>. Everything short of this + is suppression of truth, and will ultimately destroy the credit of the + Society. Equally necessary is it that the alterations should be noted. + When it comes to be known that the author before him is altered, he knows + not where nor how nor by whom, the lowest reader will lose his + interest.</p> + + <p> </p> + +<p class="cenhead">A TRIBUTE TO WILLIAM FREND.</p> + +<blockquote class="b1n"> + + <p>The principles of Algebra. By William Frend.<a name="NtA_441" + href="#Nt_441"><sup>[441]</sup></a> London, 1796, 8vo. Second Part, + 1799.</p> + +</blockquote> + + <p>This Algebra, says Dr. Peacock,<a name="NtA_442" + href="#Nt_442"><sup>[442]</sup></a> shows "great distrust <!-- Page 197 + --><span class="pagenum"><a name="page197"></a>[197]</span>of the results + of algebraical science which were in existence at the time when it was + written." Truly it does; for, as Dr. Peacock had shown by full citation, + it makes war of extermination upon all that distinguishes algebra from + arithmetic. Robert Simson<a name="NtA_443" + href="#Nt_443"><sup>[443]</sup></a> and Baron Maseres<a name="NtA_444" + href="#Nt_444"><sup>[444]</sup></a> were Mr. Frend's predecessors in this + opinion.</p> + + <p>The genuine respect which I entertained for my father-in-law did not + prevent my canvassing with perfect freedom his anti-algebraical and + anti-Newtonian opinions, in a long obituary memoir read at the + Astronomical Society in February 1842, which was written by me. It was + copied into the <i>Athenæum</i> of March 19. It must be said that if the + manner in which algebra <i>was</i> presented to the learner had been true + algebra, he would have been right: and if he had confined himself to + protesting against the imposition of attraction as a fundamental part of + the existence of matter, he would have been in unity with a great many, + including Newton himself. I wish he had preferred amendment to rejection + when he was a college tutor: he wrote and spoke English with a clearness + which is seldom equaled.</p> + + <p>His anti-Newtonian discussions are confined to the preliminary + chapters of his <i>Evening Amusements</i>,<a name="NtA_445" + href="#Nt_445"><sup>[445]</sup></a> a series of astronomical lessons in + nineteen volumes, following the moon through a period of the golden + numbers.</p> + + <p>There is a mistake about him which can never be destroyed. It is + constantly said that, at his celebrated trial in 1792, for sedition and + opposition to the Liturgy, etc., he was <i>expelled</i> from the + University. He was <i>banished</i>. People cannot see the difference; but + it made all the difference to <!-- Page 198 --><span class="pagenum"><a + name="page198"></a>[198]</span>Mr. Frend. He held his fellowship and its + profits till his marriage in 1808, and was a member of the University and + of its Senate till his death in 1841, as any Cambridge Calendar up to + 1841 will show. That they would have expelled him if they could, is + perfectly true; and there is a funny story—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.</p> + + <p>There is an absurd mistake in Gunning's<a name="NtA_446" + href="#Nt_446"><sup>[446]</sup></a> <i>Reminiscences of Cambridge</i>. In + quoting a passage of Mr. Frend's pamphlet, which was very obnoxious to + the existing Government, it is printed that the poor market-women + complained that they were to be <i>scotched</i> a quarter of their wages + by taxation; and attention is called to the word by its being three times + printed in italics. In the pamphlet it is "sconced"; that very common old + word for fined or mulcted.</p> + + <p>Lord Lyndhurst,<a name="NtA_447" href="#Nt_447"><sup>[447]</sup></a> + who has [1863] just passed away under a load of years and honors, was Mr. + Frend's private pupil at Cambridge. At the time of the celebrated trial, + he and two others amused themselves, and vented the feeling which was + very strong among the undergraduates, by chalking the walls of Cambridge + with "Frend for ever!" While thus engaged in what, using the term + legally, we are probably to call his first publication, he and his + friends were surprised by the proctors. Flight and chase followed of + course: Copley and one of the others, Serjeant Rough,<a name="NtA_448" + href="#Nt_448"><sup>[448]</sup></a> escaped: the <!-- Page 199 --><span + class="pagenum"><a name="page199"></a>[199]</span>third, whose name I + forget, but who afterwards, I have been told was a bishop,<a + name="NtA_449" href="#Nt_449"><sup>[449]</sup></a> being lame, was + captured and impositioned. Looking at the Cambridge Calendar to verify + the fact that Copley was an undergraduate at the time, I find that there + are but two other men in the list of honors of his year whose names are + now widely remembered. And they were both celebrated schoolmasters; + Butler<a name="NtA_450" href="#Nt_450"><sup>[450]</sup></a> of Harrow, + and Tate<a name="NtA_451" href="#Nt_451"><sup>[451]</sup></a> of + Richmond.</p> + + <p>But Mr. Frend had another noted pupil. I once had a conversation with + a very remarkable man, who was generally called "Place,<a name="NtA_452" + href="#Nt_452"><sup>[452]</sup></a> the tailor," but who was politician, + political economist, etc., etc. He sat in the room above his + shop—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 <!-- Page 200 + --><span class="pagenum"><a name="page200"></a>[200]</span>now and then + to give me instruction, while I was sitting on the board, working for my + living, you know."</p> + + <p>Place, who really was a sound economist, is joined with Cobbett, + because they were together at one time, and because he was, in 1800, + etc., a great Radical. But for Cobbett he had a great contempt. He told + me the following story. He and others were advising with Cobbett about + the defense he was to make on a trial for seditious libel which was + coming on. Said Place, "You must put in the letters you have received + from Ministers, members of the Commons from the Speaker downwards, etc., + about your Register, and their wish to have subjects noted. You must then + ask the jury whether a person so addressed must be considered as a common + sower of sedition, etc. You will be acquitted; nay, if your intention + should get about, very likely they will manage to stop proceedings." + Cobbett was too much disturbed to listen; he walked about the room + ejaculating "D—— the prison!" and the like. He had not the + sense to follow the advice, and was convicted.</p> + + <p>Cobbett, to go on with the chain, was a political acrobat, ready for + any kind of posture. A friend of mine gave me several times an account of + a mission to him. A Tory member—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!" <!-- Page 201 --><span class="pagenum"><a + name="page201"></a>[201]</span></p> + + <p>To return to Place. He is a noted instance of the advantage of our + jury system, which never asks a man's politics, etc. The late King of + Hanover, when Duke of Cumberland, being unpopular, was brought under + unjust suspicions by the suicide of his valet: he must have seduced the + wife and murdered the husband. The charges were as absurd as those + brought against the Englishman in the Frenchman's attempt at satirical + verses upon him:</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"The Englishman is a very bad man;</p> + <p>He drink the beer and he steal the can:</p> + <p>He kiss the wife and he beat the man;</p> + <p>And the Englishman is a very G—— d——."</p> + </div> + </div> + <p>The charges were revived in a much later day, and the defense might + have given some trouble. But Place, who had been the foreman at the + inquest, came forward, and settled the question in a few lines. Every one + knew that the old Radical was quite free of all disposition to suppress + truth from wish to curry favor with royalty.</p> + + <p>John Speed,<a name="NtA_453" href="#Nt_453"><sup>[453]</sup></a> the + author of the <i>English History</i>,<a name="NtA_454" + href="#Nt_454"><sup>[454]</sup></a> (1632) which Bishop Nicolson<a + name="NtA_455" href="#Nt_455"><sup>[455]</sup></a> calls the best + chronicle extant, was a man, like Place, of no education, but what he + gave himself. The bishop says he would have done better if he had a + better training: but what, he adds, could have been expected from a + tailor! This Speed was, as well as Place. But he was <!-- Page 202 + --><span class="pagenum"><a name="page202"></a>[202]</span>released from + manual labor by Sir Fulk Grevil,<a name="NtA_456" + href="#Nt_456"><sup>[456]</sup></a> who enabled him to study.</p> + + <p> </p> + +<p class="cenhead">A STORY ON SIMSON.</p> + + <p>I have elsewhere noticed that those who oppose the mysteries of + algebra do not ridicule them; this I want the cyclometers to do. Of the + three who wrote against the great point, the negative quantity, and the + uses of 0 which are connected with it, only one could fire a squib. That + Robert Simson<a name="NtA_457" href="#Nt_457"><sup>[457]</sup></a> should + do such a thing will be judged impossible by all who admit tradition. I + do not vouch for the following; I give it as a proof of the impression + which prevailed about him:</p> + + <p>He used to sit at his open window on the ground floor, as deep in + geometry as a Robert Simson ought to be. Here he would be accosted by + beggars, to whom he generally gave a trifle, he roused himself to hear a + few words of the story, made his donation, and instantly dropped down + into his depths. Some wags one day stopped a mendicant who was on his way + to the window with "Now, my man, do as we tell you, and you will get + something from that gentleman, and a shilling from us besides. You will + go and say you are in distress, he will ask you who you are, and you will + say you are Robert Simson, son of John Simson of Kirktonhill." The man + did as he was told; Simson quietly gave him a coin, and dropped off. The + wags watched a little, and saw him rouse himself again, and exclaim + "Robert Simson, son of John Simson of Kirktonhill! why, that is myself. + That man must be an impostor." Lord Brougham tells the same story, with + some difference of details.</p> + +<p><!-- Page 203 --><span class="pagenum"><a name="page203"></a>[203]</span></p> + + <p> </p> + +<p class="cenhead">BARON MASERES.</p> + + <p>Baron Maseres<a name="NtA_458" href="#Nt_458"><sup>[458]</sup></a> + was, as a writer, dry; those who knew his writings will feel that he + seldom could have taken in a joke or issued a pun. Maseres was the fourth + wrangler of 1752, and first Chancellor's medallist (or highest in + classics); his second was Porteus<a name="NtA_459" + href="#Nt_459"><sup>[459]</sup></a> (afterward Bishop of London). + Waring<a name="NtA_460" href="#Nt_460"><sup>[460]</sup></a> came five + years after him: he could not get Maseres through the second page of his + first book on algebra; a negative quantity stood like a lion in the way. + In 1758 he published his <i>Dissertation on the Use of the Negative + Sign</i>,<a name="NtA_461" href="#Nt_461"><sup>[461]</sup></a> 4to. There + are some who care little about + and -, who would give it house-room for + the sake of the four words "Printed by Samuel Richardson."</p> + + <p>Maseres speaks as follows: "A single quantity can never be marked with + either of those signs, or considered as either affirmative or negative; + for if any single quantity, as <i>b</i>, is marked either with the sign + + or with the sign - without assigning some other quantity, as <i>a</i>, to + which it is to be added, or from which it is to be subtracted, the mark + will have no meaning or signification: thus if it be said that the square + of -5, or the product of -5 into -5, is equal to +25, such an assertion + must either signify no more than that 5 times 5 is equal to 25 without + any regard to the signs, or it must be mere nonsense and unintelligible + jargon. I speak according to the foregoing definition, by which the + affirmativeness or negativeness of any quantity implies a relation to + another quantity of the same kind to which it <!-- Page 204 --><span + class="pagenum"><a name="page204"></a>[204]</span>is added, or from which + it is subtracted; for it may perhaps be very clear and intelligible to + those who have formed to themselves some other idea of affirmative and + negative quantities different from that above defined."</p> + + <p>Nothing can be more correct, or more identically logical: +5 and -5, + standing alone, are jargon if +5 and -5 are to be understood as without + reference to another quantity. But those who have "formed to themselves + some other idea" see meaning enough. The great difficulty of the + opponents of algebra lay in want of power or will to see extension of + terms. Maseres is right when he implies that extension, accompanied by + its refusal, makes jargon. One of my paradoxers was present at a meeting + of the Royal Society (in 1864, I think) and asked permission to make some + remarks upon a paper. He rambled into other things, and, naming me, said + that I had written a book in which two sides of a triangle are pronounced + <i>equal</i> to the third.<a name="NtA_462" + href="#Nt_462"><sup>[462]</sup></a> So they are, in the sense in which + the word is used in complete algebra; in which A + B = C makes A, B, C, + three sides of a triangle, and declares that going over A and B, one + after the other, is equivalent, in change of place, to going over C at + once. My critic, who might, if he pleased, have objected to extension, + insisted upon reading me in unextended meaning.</p> + + <p>On the other hand, it must be said that those who wrote on the other + idea wrote very obscurely about it and justified Des Cartes (<i>De + Methodo</i>)<a name="NtA_463" href="#Nt_463"><sup>[463]</sup></a> when he + said: "Algebram vero, ut solet doceri, animadverti certis regulis et + numerandi formulis ita esse contentam, ut videatur potius ars quædam + confusa, cujus usu ingenium quodam modo turbatur et obscuratur, quam + scientia qua excolatur et perspicacius <!-- Page 205 --><span + class="pagenum"><a name="page205"></a>[205]</span>reddatur."<a + name="NtA_464" href="#Nt_464"><sup>[464]</sup></a> Maseres wrote this + sentence on the title of his own work, now before me; he would have made + it his motto if he had found it earlier.</p> + + <p>There is, I believe, in Cobbett's <i>Annual Register</i>,<a + name="NtA_465" href="#Nt_465"><sup>[465]</sup></a> an account of an + interview between Maseres and Cobbett when in prison.</p> + + <p>The conversation of Maseres was lively, and full of serious anecdote: + but only one attempt at humorous satire is recorded of him; it is an + instructive one. He was born in 1731 (Dec. 15), and his father was a + refugee. French was the language of the house, with the pronunciation of + the time of Louis XIV. He lived until 1824 (May 19), and saw the race of + refugees who were driven out by the first Revolution. Their pronunciation + differed greatly from his own; and he used to amuse himself by mimicking + them. Those who heard him and them had the two schools of pronunciation + before them at once; a thing which seldom happens. It might even yet be + worth while to examine the Canadian pronunciation.</p> + + <p>Maseres went as Attorney-General to Quebec; and was appointed Cursitor + Baron of our Exchequer in 1773. There is a curious story about his + mission to Canada, which I have heard as good tradition, but have never + seen in print. The reader shall have it as cheap as I; and I confess I + rather believe it. Maseres was inveterately honest; he could not, at the + bar, bear to see his own client victorious, when he knew his cause was a + bad one. On a certain occasion he was in a cause which he knew would go + against him if a certain case were quoted. Neither the judge nor the + opposite counsel seemed to remember this case, and Maseres could not help + dropping an allusion which brought it out. <!-- Page 206 --><span + class="pagenum"><a name="page206"></a>[206]</span>His business as a + barrister fell off, of course. Some time after, Mr. Pitt (Chatham) wanted + a lawyer to send to Canada on a private mission, and wanted a <i>very + honest man</i>. Some one mentioned Maseres, and told the above story: + Pitt saw that he had got the man he wanted. The mission was + satisfactorily performed, and Maseres remained as Attorney-General.</p> + + <p>The <i>Doctrine of Life Annuities</i><a name="NtA_466" + href="#Nt_466"><sup>[466]</sup></a> (4to, 726 pages, 1783) is a strange + paradox. Its size, the heavy dissertations on the national debt, and the + depth of algebra supposed known, put it out of the question as an + elementary work, and it is unfitted for the higher student by its + elaborate attempt at elementary character, shown in its rejection of + forms derived from chances in favor of <i>the average</i>, and its + exhibition of the separate values of the years of an annuity, as + arithmetical illustrations. It is a climax of unsaleability, + unreadability, and inutility. For intrinsic nullity of interest, and + dilution of little matter with much ink, I can compare this book to + nothing but that of Claude de St. Martin, elsewhere mentioned, or the + lectures <i>On the Nature and Properties of Logarithms</i>, by James + Little,<a name="NtA_467" href="#Nt_467"><sup>[467]</sup></a> Dublin, + 1830, 8vo. (254 heavy pages of many words and few symbols), a wonderful + weight of weariness.</p> + + <p>The stock of this work on annuities, very little diminished, was given + by the author to William Frend, who paid warehouse room for it until + about 1835, when he consulted me as to its disposal. As no publisher + could be found who would take it as a gift, for any purpose of sale, it + was consigned, all but a few copies, to a buyer of waste paper.</p> + + <p>Baron Maseres's republications are well known: the <i>Scriptores + Logarithmici</i><a name="NtA_468" href="#Nt_468"><sup>[468]</sup></a> is + a set of valuable reprints, mixed <!-- Page 207 --><span + class="pagenum"><a name="page207"></a>[207]</span>with much which might + better have entered into another collection. It is not so well known that + there is a volume of optical reprints, <i>Scriptores Optici</i>, London, + 1823, 4to, edited for the veteran of ninety-two by Mr. Babbage<a + name="NtA_469" href="#Nt_469"><sup>[469]</sup></a> at twenty-nine. This + excellent volume contains James Gregory, Des Cartes, Halley, Barrow, and + the optical writings of Huyghens, the <i>Principia</i> of the undulatory + theory. It also contains, by the sort of whim in which such men as + Maseres, myself, and some others are apt to indulge, a reprint of "The + great new Art of weighing Vanity,"<a name="NtA_470" + href="#Nt_470"><sup>[470]</sup></a> by M. Patrick Mathers, Arch-Bedel to + the University of St. Andrews, Glasgow, 1672. Professor Sinclair,<a + name="NtA_471" href="#Nt_471"><sup>[471]</sup></a> of Glasgow, a good man + at clearing mines of the water which they did not want, and furnishing + cities with water which they did want, seems to have written absurdly + about hydrostatics, and to have attacked a certain Sanders,<a + name="NtA_472" href="#Nt_472"><sup>[472]</sup></a> M.A. So Sanders, + assisted by James Gregory, published a heavy bit of jocosity about him. + This story of the authorship rested on a note made in his <!-- Page 208 + --><span class="pagenum"><a name="page208"></a>[208]</span>copy by Robert + Gray, M.D.; but it has since been fully confirmed by a letter of James + Gregory to Collins, in the Macclesfield Correspondence. "There is one + Master Sinclair, who did write the <i>Ars Magna et Nova</i>,<a + name="NtA_473" href="#Nt_473"><sup>[473]</sup></a> a pitiful ignorant + fellow, who hath lately written horrid nonsense in the hydrostatics, and + hath abused a master in the University, one Mr. Sanders, in print. This + Mr. Sanders ... is resolved to cause the Bedel of the University to write + against him.... We resolve to make excellent sport with him."</p> + + <p>On this I make two remarks: First, I have learned from experience that + old notes, made in books by their possessors, are statements of high + authority: they are almost always confirmed. I do not receive them + without hesitation; but I believe that of all the statements about books + which rest on one authority, there is a larger percentage of truth in the + written word than in the printed word. Secondly, I mourn to think that + when the New Zealander picks up his old copy of this book, and reads it + by the associations of his own day, he may, in spite of the many + assurances I have received that my <i>Athenæum Budget</i> was amusing, + feel me to be as heavy as I feel James Gregory and Sanders. But he will + see that I knew what was coming, which Gregory did not.</p> + + <p> </p> + +<p class="cenhead">MR. FREND'S BURLESQUE.</p> + + <p>It was left for Mr. Frend to prove that an impugner of algebra could + attempt ridicule. He was, in 1803, editor of a periodical <i>The + Gentleman's Monthly Miscellany</i>, which lasted a few months.<a + name="NtA_474" href="#Nt_474"><sup>[474]</sup></a> To this, among other + things, he contributed the following, in burlesque of the use made of 0, + to which he objected.<a name="NtA_475" + href="#Nt_475"><sup>[475]</sup></a> The imitation of Rabelais, a writer + <!-- Page 209 --><span class="pagenum"><a + name="page209"></a>[209]</span>in whom he delighted, is good: to those + who have never dipped, it may give such a notion as they would not easily + get elsewhere. The point of the satire is not so good. But in truth it is + not easy to make pungent scoffs upon what is common sense to all mankind. + Who can laugh with effect at six times nothing is nothing, as false or + unintelligible? In an article intended for that undistinguishing know-0 + the "general reader," there would have been no force of satire, if + <i>division</i> by 0 had been separated from multiplication by the + same.</p> + + <p>I have followed the above by another squib, by the same author, on the + English language. The satire is covertly aimed at theological + phraseology; and any one who watches this subject will see that it is a + very just observation that the Greek words are not boiled enough.</p> + +<p class="cenhead"><span class="sc">Pantagruel's Decision</span> <i>of the</i> <span class="sc">Question</span> <i>about</i> <span class="sc">Nothing</span>.</p> + + <p>"Pantagruel determined to have a snug afternoon with Epistemon and + Panurge. Dinner was ordered to be set in a small parlor, and a particular + batch of Hermitage with some choice Burgundy to be drawn from a remote + corner of the cellar upon the occasion. By way of lunch, about an hour + before dinner, Pantagruel was composing his stomach with German sausages, + reindeer's tongues, oysters, brawn, and half a dozen different sorts of + English beer just come into fashion, when a most thundering knocking was + heard at the great gate, and from the noise they expected it to announce + the arrival at least of the First Consul, or king Gargantua. Panurge was + sent to reconnoiter, and after a quarter of an hour's absence, returned + with the news that the University of Pontemaca was waiting his highness's + leisure in the great hall, to propound a question which <!-- Page 210 + --><span class="pagenum"><a name="page210"></a>[210]</span>had turned the + brains of thirty-nine students, and had flung twenty-seven more into a + high fever. With all my heart, says Pantagruel, and swallowed down three + quarts of Burton ale; but remember, it wants but an hour of dinner time, + and the question must be asked in as few words as possible; for I cannot + deprive myself of the pleasure I expected to enjoy in the company of my + good friends for a set of mad-headed masters. I wish brother John was + here to settle these matters with the black gentry.</p> + + <p>"Having said or rather growled this, he proceeded to the hall of + ceremony, and mounted his throne; Epistemon and Panurge standing on each + side, but two steps below him. Then advanced to the throne the three + beadles of the University of Pontemaca with their silver staves on their + shoulders, and velvet caps on their heads, and they were followed by + three times three doctors, and thrice three times three masters of art; + for everything was done in Pontemaca by the number three, and on this + account the address was written on parchment, one foot in breadth, and + thrice three times thrice three feet in length. The beadles struck the + ground with their heads and their staves three times in approaching the + throne; the doctors struck the ground with their heads thrice three + times, and the masters did the same thrice each time, beating the ground + with their heads thrice three times. This was the accustomed form of + approaching the throne, time out of mind, and it was said to be + emblematic of the usual prostration of science to the throne of + greatness.</p> + + <p>"The mathematical professor, after having spit, and hawked, and + cleared his throat, and blown his nose on a handkerchief lent to him, for + he had forgotten to bring his own, began to read the address. In this he + was assisted by three masters of arts, one of whom, with a silver pen, + pointed out the stops; the second with a small stick rapped his knuckles + when he was to raise or lower his voice; and a third pulled his hair + behind when he was to look Pantagruel in the face. Pantagruel began to + chafe like a lion: <!-- Page 211 --><span class="pagenum"><a + name="page211"></a>[211]</span>he turned first on one side, then on the + other: he listened and groaned, and groaned and listened, and was in the + utmost cogitabundity of cogitation. His countenance began to brighten, + when, at the end of an hour, the reader stammered out these words:</p> + + <p>"'It has therefore been most clearly proved that as all matter may be + divided into parts infinitely smaller than the infinitely smallest part + of the infinitesimal of nothing, so nothing has all the properties of + something, and may become, by just and lawful right, susceptible of + addition, subtraction, multiplication, division, squaring, and cubing: + that it is to all intents and purposes as good as anything that has been, + is, or can be taught in the nine universities of the land, and to deprive + it of its rights is a most cruel innovation and usurpation, tending to + destroy all just subordination in the world, making all universities + superfluous, leveling vice-chancellors, doctors, and proctors, masters, + bachelors, and scholars, to the mean and contemptible state of butchers + and tallow-chandlers, bricklayers and chimney-sweepers, who, if it were + not for these learned mysteries, might think that they knew as much as + their betters. Every one then, who has the good of science at heart, must + pray for the interference of his highness to put a stop to all the + disputes about nothing, and by his decision to convince all gainsayers + that the science of nothing is taught in the best manner in the + universities, to the great edification and improvement of all the youth + in the land.'</p> + + <p>"Here Pantagruel whispered in the ear of Panurge, who nodded to + Epistemon, and they two left the assembly, and did not return for an + hour, till the orator had finished his task. The three beadles had thrice + struck the ground with their heads and staves, the <span + class="correction" title="text reads `docters'">doctors</span> had + finished their compliments, and the masters were making their + twenty-seven prostrations. Epistemon and Panurge went up to Pantagruel, + whom they found fast asleep and snoring; nor could he be roused but by as + many tugs as there had been <!-- Page 212 --><span class="pagenum"><a + name="page212"></a>[212]</span>bowings from the corps of learning. At + last he opened his eyes, gave a good stretch, made half a dozen yawns, + and called for a stoup of wine. I thank you, my masters, says he; so + sound a nap I have not had since I came from the island of Priestfolly. + Have you dined, my masters? They answered the question by as many bows as + at entrance; but his highness left them to the care of Panurge, and + retired to the little parlor with Epistemon, where they burst into a fit + of laughter, declaring that this learned Baragouin about nothing was just + as intelligible as the lawyer's Galimathias. Panurge conducted the + learned body into a large saloon, and each in his way hearing a + clattering of plates and glasses, congratulated himself on his + approaching good cheer. There they were left by Panurge, who took his + chair by Pantagruel just as the soup was removed, but he made up for the + want of that part of his dinner by a pint of champagne. The learning of + the university had whetted their appetites; what they each ate it is + needless to recite; good wine, good stories, and hearty laughs went + round, and three hours elapsed before one soul of them recollected the + hungry students of Pontemaca.</p> + + <p>"Epistemon reminded them of the business in hand, and orders were + given for a fresh dozen of hermitage to be put upon table, and the royal + attendants to get ready. As soon as the dozen bottles were emptied, + Pantagruel rose from table, the royal trumpets sounded, and he was + accompanied by the great officers of his court into the large dining + hall, where was a table with forty-two covers. Pantagruel sat at the + head, Epistemon at the bottom, and Panurge in the middle, opposite an + immense silver tureen, which would hold fifty gallons of soup. The wise + men of Pontemaca then took their seats according to seniority. Every + countenance glistened with delight; the music struck up; the dishes were + uncovered. Panurge had enough to do to handle the immense silver ladle: + Pantagruel and Epistemon had no time for eating, they were fully employed + in carving. The bill <!-- Page 213 --><span class="pagenum"><a + name="page213"></a>[213]</span>of fare announced the names of a hundred + different dishes. From Panurge's ladle came into the soup plate as much + as he took every time out of the tureen; and as it was the rule of the + court that every one should appear to eat, as long as he sat at table, + there was the clattering of nine and thirty spoons against the silver + soup-plates for a quarter of an hour. They were then removed, and knives + and forks were in motion for half an hour. Glasses were continually + handed round in the mean time, and then everything was removed, except + the great tureen of soup. The second course was now served up, in + dispatching which half an hour was consumed; and at the conclusion the + wise men of Pontemaca had just as much in their stomachs as Pantagruel in + his head from their address: for nothing was cooked up for them in every + possible shape that Panurge could devise.</p> + + <p>"Wine-glasses, large decanters, fruit dishes, and plates were now set + on. Pantagruel and Epistemon alternately gave bumper toasts: the + University of Pontemaca, the eye of the world, the mother of taste and + good sense and universal learning, the patroness of utility, and the + second only to Pantagruel in wisdom and virtue (for these were her + titles), was drank standing with thrice three times three, and huzzas and + clattering of glasses; but to such wine the wise men of Pontemaca had not + been accustomed; and though Pantagruel did not suffer one to rise from + table till the eighty-first glass had been emptied, not even the weakest + headed master of arts felt his head in the least indisposed. The + decanters indeed were often removed, but they were brought back + replenished, filled always with nothing.</p> + + <p>"Silence was now proclaimed, and in a trice Panurge leaped into the + large silver tureen. Thence he made his bows to Pantagruel and the whole + company, and commenced an oration of signs, which lasted an hour and a + half, and in which he went over all the matter contained in the Pontemaca + address; and though the wise men looked very serious during the whole + time, Pantagruel himself and his whole <!-- Page 214 --><span + class="pagenum"><a name="page214"></a>[214]</span>court could not help + indulging in repeated bursts of laughter. It was universally acknowledged + that he excelled himself, and that the arguments by which he beat the + English masters of arts at Paris were nothing to the exquisite selection + of attitudes which he this day assumed. The greatest shouts of applause + were excited when he was running thrice round the tureen on its rim, with + his left hand holding his nose, and the other exercising itself nine and + thirty times on his back. In this attitude he concluded with his back to + the professor of mathematics; and at the instant he gave his last flap, + by a sudden jump, and turning heels over head in the air, he presented + himself face to face to the professor, and standing on his left leg, with + his left hand holding his nose, he presented to him, in a white satin + bag, Pantagruel's royal decree. Then advancing his right leg, he fixed it + on the professor's head, and after three turns, in which he clapped his + sides with both hands thrice three times, down he leaped, and Pantagruel, + Epistemon, and himself took their leaves of the wise men of + Pontemaca.</p> + + <p>"The wise men now retired, and by royal orders were accompanied by a + guard, and according to the etiquette of the court, no one having a royal + order could stop at any public house till it was delivered. The + procession arrived at Pontemaca at nine o'clock the next morning, and the + sound of bells from every church and college announced their arrival. The + congregation was assembled; the royal decree was saluted in the same + manner as if his highness had been there in person; and after the proper + ceremonies had been performed, the satin bag was opened exactly at twelve + o'clock. A finely emblazoned roll was drawn forth, and the public orator + read to the gaping assembly the following words:</p> + + <p>"'They who can make something out of nothing shall have nothing to eat + at the court of—<span class="sc">Pantagruel</span>.'" <!-- Page 215 + --><span class="pagenum"><a name="page215"></a>[215]</span></p> + +<p class="cenhead"><span class="sc">Origin</span> <i>of the</i> <span class="sc">English Language</span>, <i>related by a</i> <span class="sc">Swede</span>.</p> + + <p>"Some months ago in a party in Holland, consisting of natives of + various countries, the merit of their respective languages became a topic + of conversation. A Swede, who had been a great traveler, and could + converse in most of the modern languages of Europe, laughed very heartily + at an Englishman, who had ventured to speak in praise of the tongue of + his dear country. I never had any trouble, says he, in learning English. + To my very great surprise, the moment I sat foot on shore at Gravesend, I + found out, that I could understand, with very little trouble, every word + that was said. It was a mere jargon, made up of German, French, and + Italian, with now and then a word from the Spanish, Latin or Greek. I had + only to bring my mouth to their mode of speaking, which was done with + ease in less than a week, and I was everywhere taken for a true-born + Englishman; a privilege by the way of no small importance in a country, + where each man, God knows why, thinks his foggy island superior to any + other part of the world: and though his door is never free from some dun + or other coming for a tax, and if he steps out of it he is sure to be + knocked down or to have his pocket picked, yet he has the insolence to + think every foreigner a miserable slave, and his country the seat of + everything wretched. They may talk of liberty as they please, but Spain + or Turkey for my money: barring the bowstring and the inquisition, they + are the most comfortable countries under heaven, and you need not be + afraid of either, if you do not talk of religion and politics. I do not + see much difference too in this respect in England, for when I was there, + one of their most eminent men for learning was put in prison for a couple + of years, and got his death for translating one of Æsop's fables into + English, which every child in Spain and Turkey is taught, as soon as he + comes out of his leading strings. Here all the company unanimously cried + out against the Swede, that it was <!-- Page 216 --><span + class="pagenum"><a name="page216"></a>[216]</span>impossible: for in + England, the land of liberty, the only thing its worst enemies could say + against it, was, that they paid for their liberty a much greater price + than it was worth.—Every man there had a fair trial according to + laws, which everybody could understand; and the judges were cool, + patient, discerning men, who never took the part of the crown against the + prisoner, but gave him every assistance possible for his defense.</p> + + <p>"The Swede was borne down, but not convinced; and he seemed determined + to spit out all his venom. Well, says he, at any rate you will not deny + that the English have not got a language of their own, and that they came + by it in a very odd way. Of this at least I am certain, for the whole + history was related to me by a witch in Lapland, whilst I was bargaining + for a wind. Here the company were all in unison again for the story.</p> + + <p>"In ancient times, said the old hag, the English occupied a spot in + Tartary, where they lived sulkily by themselves, unknowing and unknown. + By a great convulsion that took place in China, the inhabitants of that + and the adjoining parts of Tartary were driven from their seats, and + after various wanderings took up their abode in Germany. During this time + nobody could understand the English, for they did not talk, but hissed + like so many snakes. The poor people felt uneasy under this circumstance, + and in one of their parliaments, or rather hissing meetings, it was + determined to seek a remedy: and an embassy was sent to some of our + sisterhood then living on Mount Hecla. They were put to a nonplus, and + summoned the Devil to their relief. To him the English presented their + petitions, and explained their sad case; and he, upon certain conditions, + promised to befriend them, and to give them a language. The poor Devil + was little aware of what he had promised; but he is, as all the world + knows, a man of too much honor to break his word. Up and down the world + then he went in quest of this new language: visited all the universities, + and all <!-- Page 217 --><span class="pagenum"><a + name="page217"></a>[217]</span>the schools, and all the courts of law, + and all the play-houses, and all the prisons; never was poor devil so + fagged. It would have made your heart bleed to see him. Thrice did he go + round the earth in every parallel of latitude; and at last, wearied and + jaded out, back came he to Hecla in despair, and would have thrown + himself into the volcano, if he had been made of combustible materials. + Luckily at that time our sisters were engaged in settling the balance of + Europe; and whilst they were looking over projects, and counter-projects, + and ultimatums, and post ultimatums, the poor Devil, unable to assist + them was groaning in a corner and ruminating over his sad condition.</p> + + <p>"On a sudden, a hellish joy overspread his countenance; up he jumped, + and, like Archimedes of old, ran like a madman amongst the throng, + turning over tables, and papers, and witches, roaring out for a full hour + together nothing else but 'tis found, 'tis found! Away were sent the + sisterhood in every direction, some to traverse all the corners of the + earth, and others to prepare a larger caldron than had ever yet been set + upon Hecla. The affairs of Europe were at a stand: its balance was thrown + aside; prime ministers and ambassadors were everywhere in the utmost + confusion; and, by the way, they have never been able to find the balance + since that time, and all the fine speeches upon the subject, with which + your newspapers are every now and then filled, are all mere hocus-pocus + and rhodomontade. However, the caldron was soon set on, and the air was + darkened by witches riding on broomsticks, bringing a couple of folios + under each arm, and across each shoulder. I remember the time exactly: it + was just as the council of Nice had broken up, so that they got books and + papers there dog cheap; but it was a bad thing for the poor English, as + these were the worst materials that entered into the caldron. Besides, as + the Devil wanted some amusement, and had not seen an account of the + transactions of this famous council, he had all the books brought from it + laid before him, and split his sides almost <!-- Page 218 --><span + class="pagenum"><a name="page218"></a>[218]</span>with laughing, whilst + he was reading the speeches and decrees of so many of his old friends and + acquaintances. All this while the witches were depositing their loads in + the great caldron. There were books from the Dalai Lama, and from China: + there were books from the Hindoos, and tallies from the Caffres: there + were paintings from Mexico, and rocks of hieroglyphics from Egypt: the + last country supplied besides the swathings of two thousand mummies, and + four-fifths of the famed library of Alexandria. Bubble! bubble! toil and + trouble! never was a day of more labor and anxiety; and if our good + master had but flung in the Greek books at the proper time, they would + have made a complete job of it. He was a little too impatient: as the + caldron frothed up, he skimmed it off with a great ladle, and filled some + thousands of our wind-bags with the froth, which the English with great + joy carried back to their own country. These bags were sent to every + district: the chiefs first took their fill, and then the common people; + hence they now speak a language which no foreigner can understand, unless + he has learned half a dozen other languages; and the poor people, not one + in ten, understand a third part of what is said to them. The hissing, + however, they have not entirely got rid of, and every seven years, when + the Devil, according to agreement, pays them a visit, they entertain him + at their common halls and county meetings with their original + language.</p> + + <p>"The good-natured old hag told me several other circumstances, + relative to this curious transaction, which, as there is an Englishman in + company, it will be prudent to pass over in silence: but I cannot help + mentioning one thing which she told me as a very great secret. You know, + says she to me, that the English have more religions among them than any + other nation in Europe, and that there is more teaching and sermonizing + with them than in any other country. The fact is this; it matters not who + gets up to teach them, the hard words of the Greek were not sufficiently + <!-- Page 219 --><span class="pagenum"><a + name="page219"></a>[219]</span>boiled, and whenever they get into a + sentence, the poor people's brains are turned, and they know no more what + the preacher is talking about, than if he harangued them in Arabic. Take + my word for it if you please; but if not, when you get to England, desire + the bettermost sort of people that you are acquainted with to read to you + an act of parliament, which of course is written in the clearest and + plainest style in which anything can be written, and you will find that + not one in ten will be able to make tolerable sense of it. The language + would have been an excellent language, if it had not been for the council + of Nice, and the words had been well boiled.</p> + + <p>"Here the company burst out into a fit of laughter. The Englishman got + up and shook hands with the Swede: <i>si non è vero</i>, said he, <i>è + ben trovato</i>.<a name="NtA_476" href="#Nt_476"><sup>[476]</sup></a> + But, however I may laugh at it here, I would not advise you to tell this + story on the other side of the water. So here's a bumper to Old England + for ever, and God save the king."</p> + + <p> </p> + +<p class="cenhead">ON YOUTHFUL PRODIGIES.</p> + + <p>The accounts given of extraordinary children and adolescents + frequently defy credence.<a name="NtA_477" + href="#Nt_477"><sup>[477]</sup></a> I will give two well-attested + instances.</p> + + <p>The celebrated mathematician Alexis Claude Clairault (now Clairaut)<a + name="NtA_478" href="#Nt_478"><sup>[478]</sup></a> was certainly born in + May, 1713. His treatise on curves of double curvature (printed in 1731)<a + name="NtA_479" href="#Nt_479"><sup>[479]</sup></a> received <!-- Page 220 + --><span class="pagenum"><a name="page220"></a>[220]</span>the + approbation of the Academy of Sciences, August 23, 1729. Fontenelle, in + his certificate of this, calls the author sixteen years of age, and does + not strive to exaggerate the wonder, as he might have done, by reminding + his readers that this work, of original and sustained mathematical + investigation, must have been coming from the pen at the ages of fourteen + and fifteen. The truth was, as attested by De Molières,<a name="NtA_480" + href="#Nt_480"><sup>[480]</sup></a> Clairaut had given public proofs of + his power at twelve years old. His age being thus publicly certified, all + doubt is removed: say he had been—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 <i>Garde des Sceaux</i>, is transported beyond the bounds of + official gravity, and says that it "ne mérite pas seulement d'être + imprimé, mais d'être admiré comme un prodige d'imagination, de + conception, et de capacité."<a name="NtA_481" + href="#Nt_481"><sup>[481]</sup></a></p> + + <p>That Blaise Pascal was born in June, 1623, is perfectly well + established and uncontested.<a name="NtA_482" + href="#Nt_482"><sup>[482]</sup></a> That he wrote his conic sections at + the age of sixteen might be difficult to establish, though tolerably well + attested, if it were not for <!-- Page 221 --><span class="pagenum"><a + name="page221"></a>[221]</span>one circumstance, for the book was not + published. The celebrated theorem, "Pascal's hexagram,"<a name="NtA_483" + href="#Nt_483"><sup>[483]</sup></a> makes all the rest come very easy. + Now Curabelle,<a name="NtA_484" href="#Nt_484"><sup>[484]</sup></a> in a + work published in 1644, sneers at Desargues,<a name="NtA_485" + href="#Nt_485"><sup>[485]</sup></a> whom he quotes, for having, in 1642, + deferred a discussion until "cette grande proposition nommée le Pascale + verra le jour."<a name="NtA_486" href="#Nt_486"><sup>[486]</sup></a> That + is, by the time Pascal was nineteen, the <i>hexagram</i> was circulating + under a name derived from the author. The common story about Pascal, + given by his sister,<a name="NtA_487" href="#Nt_487"><sup>[487]</sup></a> + is an absurdity which no doubt has prejudiced many against tales of early + proficiency. He is made, when quite a boy, to invent geometry <i>in the + order of Euclid's propositions</i>: as if that order were natural + sequence of investigation. The hexagram at ten years old would be a + hundred times less unlikely.</p> + + <p>The instances named are painfully astonishing: I give one which has + fallen out of sight, because it will preserve an imperfect biography. + John Wilson<a name="NtA_488" href="#Nt_488"><sup>[488]</sup></a> is + Wilson of that <!-- Page 222 --><span class="pagenum"><a + name="page222"></a>[222]</span>Ilk, that is, of "Wilson's Theorem." It is + this: if <i>p</i> be a prime number, the product of all the numbers up to + <i>p</i>-1, increased by 1, is divisible without remainder by <i>p</i>. + All mathematicians know this as Wilson's theorem, but few know who Wilson + was. He was born August 6, 1741, at the Howe in Applethwaite, and he was + heir to a small estate at Troutbeck in Westmoreland. He was sent to + Peterhouse, at Cambridge, and while an undergraduate was considered + stronger in algebra than any one in the University, except Professor + Waring, one of the most powerful algebraists of the century.<a + name="NtA_489" href="#Nt_489"><sup>[489]</sup></a> He was the senior + wrangler of 1761, and was then for some time a private tutor. When + Paley,<a name="NtA_490" href="#Nt_490"><sup>[490]</sup></a> then in his + third year, determined to make a push for the senior wranglership, which + he got, Wilson was recommended to him as a tutor. Both were ardent in + their work, except that sometimes Paley, when he came for his lesson, + would find "Gone a fishing" written on his tutor's outer door: which was + insult added to injury, for Paley was very fond of fishing. Wilson soon + left Cambridge, and went to the bar. He practised on the northern circuit + with great success; and, one day, while passing his vacation on his + little property at Troutbeck, he received information, to his great + surprise, that Lord Thurlow,<a name="NtA_491" + href="#Nt_491"><sup>[491]</sup></a> with whom he had <!-- Page 223 + --><span class="pagenum"><a name="page223"></a>[223]</span>no + acquaintance, had recommended him to be a Judge of the Court of Common + Pleas. He died, Oct. 18, 1793, with a very high reputation as a lawyer + and a Judge. These facts are partly from Meadley's <i>Life of + Paley</i>,<a name="NtA_492" href="#Nt_492"><sup>[492]</sup></a> no doubt + from Paley himself, partly from the <i>Gentleman's Magazine</i>, and from + an epitaph written by Bishop Watson.<a name="NtA_493" + href="#Nt_493"><sup>[493]</sup></a> Wilson did not publish anything: the + theorem by which he has cut his name in the theory of numbers was + communicated to Waring, by whom it was published. He married, in 1788, a + daughter of Serjeant Adair,<a name="NtA_494" + href="#Nt_494"><sup>[494]</sup></a> and left issue. <i>Had a family</i>, + many will say: but a man and his wife are a family, even without + children. An actuary may be allowed to be accurate in this matter, of + which I was reminded by what an actuary wrote of another actuary. William + Morgan,<a name="NtA_495" href="#Nt_495"><sup>[495]</sup></a> in the life + of his uncle Dr. Richard Price,<a name="NtA_496" + href="#Nt_496"><sup>[496]</sup></a> says that the Doctor and his <!-- + Page 224 --><span class="pagenum"><a name="page224"></a>[224]</span>wife + were "never blessed with an addition to their family." I never met with + such accuracy elsewhere. Of William Morgan I add that my surname and + pursuits have sometimes, to my credit be it said, made a confusion + between him and me. Dates are nothing to the mistaken; the last three + years of Morgan's life were the first three years of my actuary-life + (1830-33). The mistake was to my advantage as well as to my credit. I owe + to it the acquaintance of one of the noblest of the human race, I mean + Elizabeth Fry,<a name="NtA_497" href="#Nt_497"><sup>[497]</sup></a> who + came to me for advice about a philanthropic design, which involved life + questions, under a general impression that some Morgan had attended to + such things.<a name="NtA_498" href="#Nt_498"><sup>[498]</sup></a></p> + +<p><!-- Page 225 --><span class="pagenum"><a name="page225"></a>[225]</span></p> + + <p> </p> + +<p class="cenhead">NEWTON AGAIN OVERTHROWN.</p> + +<blockquote class="b1n"> + + <p>A treatise on the sublime science of heliography, satisfactorily + demonstrating our great orb of light, the sun, to be absolutely no other + than a body of ice! Overturning all the received systems of the universe + hitherto extant; proving the celebrated and indefatigable Sir Isaac + Newton, in his theory of the solar system, to be as far distant from the + truth, as many of the heathen authors of Greece and Rome. By Charles + Palmer,<a name="NtA_499" href="#Nt_499"><sup>[499]</sup></a> Gent. + London, 1798, 8vo.</p> + +</blockquote> + + <p>Mr. Palmer burned some tobacco with a burning glass, saw that a lens + of ice would do as well, and then says:</p> + + <p>"If we admit that the sun could be removed, and a terrestrial body of + ice placed in its stead, it would produce the same effect. The sun is a + crystaline body receiving the radiance of God, and operates on this earth + in a similar manner as the light of the sun does when applied to a convex + mirror or glass."</p> + + <p>Nov. 10, 1801. The Rev. Thomas Cormouls,<a name="NtA_500" + href="#Nt_500"><sup>[500]</sup></a> minister of Tettenhall, addressed a + letter to Sir Wm. Herschel, from which I extract the following:</p> + + <p>"Here it may be asked, then, how came the doctrines of Newton to solve + all astronomic Phenomina, and all problems concerning the same, both <i>a + parte ante</i> and <i>a parte post</i>.<a name="NtA_501" + href="#Nt_501"><sup>[501]</sup></a> It is answered that he certainly + wrought the principles he made use of into strickt analogy with the real + Phenomina of the heavens, and that the rules and results arizing from + them <!-- Page 226 --><span class="pagenum"><a + name="page226"></a>[226]</span>agree with them and resolve accurately all + questions concerning them. Though they are not fact and true, or nature, + but analogous to it, in the manner of the artificial numbers of + logarithms, sines, &c. A very important question arises here, Did + Newton mean to impose upon the world? By no means: he received and used + the doctrines reddy formed; he did a little extend and contract his + principles when wanted, and commit a few oversights of consequences. But + when he was very much advanced in life, he suspected the fundamental + nullity of them: but I have from a certain anecdote strong ground to + believe that he knew it before his decease and intended to have retracted + his error. But, however, somebody did deceive, if not wilfully, + negligently at least. That was a man to whom the world has great + obligations too. It was no less a philosopher than Galileo."</p> + + <p>That Newton wanted to retract before his death, is a notion not + uncommon among paradoxers. Nevertheless, there is no retraction in the + third edition of the <i>Principia</i>, published when Newton was + eighty-four years old! The moral of the above is, that a gentleman who + prefers instructing William Herschel to learning how to spell, may find a + proper niche in a proper place, for warning to others. It seems that + gravitation is not truth, but only the logarithm of it.</p> + + <p> </p> + +<p class="cenhead">BISHOPS AS PARADOXERS.</p> + +<blockquote class="b1n"> + + <p>The mathematical and philosophical works of the Right Rev. John + Wilkins<a name="NtA_502" href="#Nt_502"><sup>[502]</sup></a>.... In two + volumes. London, 1802, 8vo.</p> + +</blockquote> + + <p>This work, or at least part of the edition—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 <!-- + Page 227 --><span class="pagenum"><a name="page227"></a>[227]</span>life + prefixed, and a mention by D'Israeli, I should suppose that it had + originally a separate title-page, and some circulation as a separate + tract. Wilkins treats this subject half seriously, half jocosely; he has + evidently not quite made up his mind. He is clear that "arts are not yet + come to their solstice," and that posterity will bring hidden things to + light. As to the difficulty of carrying food, he thinks, scoffing Puritan + that he is, the Papists may be trained to fast the voyage, or may find + the bread of their Eucharist "serve well enough for their + <i>viaticum</i>."<a name="NtA_503" href="#Nt_503"><sup>[503]</sup></a> He + also puts the case that the story of Domingo Gonsales may be realized, + namely, that wild geese find their way to the moon. It will be + remembered—to use the usual substitute for, It has been + forgotten—that the posthumous work of Bishop Francis Godwin<a + name="NtA_504" href="#Nt_504"><sup>[504]</sup></a> of Llandaff was + published in 1638, the very year of Wilkins's first edition, in time for + him to mention it at the end. Godwin makes Domingo Gonsales get to the + moon in a chariot drawn by wild geese, and, as old books would say, + discourses fully on that head. It is not a little amusing that Wilkins + should have been seriously accused of plagiarizing Godwin, Wilkins + writing in earnest, or nearly so, and Godwin writing fiction. It may + serve to show philosophers how very near pure speculation comes to fable. + From the sublime to the ridiculous is but a step: which is the sublime, + and which the ridiculous, every one must settle for himself. With me, + good fiction is the sublime, and bad speculation the ridiculous. The + number of bishops in my list is small. I might, had I possessed the book, + have opened the list of quadrators with an Archbishop of Canterbury, or + at least with a divine who was not wholly not archbishop. Thomas + Bradwardine<a name="NtA_505" href="#Nt_505"><sup>[505]</sup></a> + (Bragvardinus, Bragadinus) was elected in <!-- Page 228 --><span + class="pagenum"><a name="page228"></a>[228]</span>1348; the Pope put in + another, who died unconsecrated; and Bradwardine was again elected in + 1349, and lived five weeks longer, dying, I suppose, unconfirmed and + unconsecrated.<a name="NtA_506" href="#Nt_506"><sup>[506]</sup></a> + Leland says he held the see a year, <i>unus tantum annulus</i>,<a + name="NtA_507" href="#Nt_507"><sup>[507]</sup></a> which seems to be a + confusion: the whole business, from the first election, took about a + year. He squared the circle, and his performance was printed at Paris in + 1494. I have never seen it, nor any work of the author, except a tract on + proportion.</p> + + <p>As Bradwardine's works are very scarce indeed, I give two titles from + one of the Libri catalogues.</p> + +<blockquote class="b1n"> + + <p>"<span class="sc">Arithmetic. Brauardini</span> (Thomæ) Arithmetica + speculativa revisa et correcta a Petro Sanchez Ciruelo Aragonesi, black + letter, <i>elegant woodcut title-page</i>, <span class="scac">VERY + RARE</span>, <i>folio. Parisiis, per Thomam Anguelast (pro Olivier + Senant), s. a. circa 1510</i>.<a name="NtA_508" + href="#Nt_508"><sup>[508]</sup></a></p> + +</blockquote> + + <p>"This book, by Thomas Bradwardine, Archbishop of Canterbury must be + exceedingly scarce as it has escaped the notice of Professor De Morgan, + who, in his <i>Arithmetical Books</i>, speaks of a treatise of the same + author on proportions,<a name="NtA_509" + href="#Nt_509"><sup>[509]</sup></a> printed at Vienna in 1515, but does + not mention the present work.</p> + +<p><!-- Page 229 --><span class="pagenum"><a name="page229"></a>[229]</span></p> + +<blockquote class="b1n"> + + <p>"Bradwardine (Archbp. T.). Brauardini (Thomæ) Geometria speculativa, + com Tractato de Quadratura Circuli bene revisa a Petro Sanchez Ciruelo, + <span class="scac">SCARCE</span>, <i>folio. Parisiis, J. Petit</i>, + 1511.<a name="NtA_510" href="#Nt_510"><sup>[510]</sup></a></p> + +</blockquote> + + <p>"In this work we find the <i>polygones étoilés</i>,<a name="NtA_511" + href="#Nt_511"><sup>[511]</sup></a> see Chasles (<i>Aperçu</i>, pp. 480, + 487, 521, 523, &c.) on the merit of the discoveries of this English + mathematician, who was Archbishop of Canterbury in the <span + class="scac">XIV</span>th Century (<i>tempore</i> Edward III. <span + class="scac">A.D.</span> 1349); and who applied geometry to theology. M. + Chasles says that the present work of Bradwardine contains 'Une théorie + nouvelle qui doit faire honneur au <span class="scac">XIV</span>e + Siècle.'"<a name="NtA_512" href="#Nt_512"><sup>[512]</sup></a></p> + + <p>The titles do not make it quite sure that Bradwardine is the + quadrator; it may be Peter Sanchez after all.<a name="NtA_513" + href="#Nt_513"><sup>[513]</sup></a></p> + + <p> </p> + +<p class="cenhead">THE QUESTION OF PARALLELS.</p> + +<blockquote class="b1n"> + + <p>Nouvelle théorie des parallèles. Par Adolphe Kircher<a name="NtA_514" + href="#Nt_514"><sup>[514]</sup></a> [so signed at the end of the + appendix]. Paris, 1803, 8vo.</p> + +</blockquote> + + <p>An alleged emendation of Legendre.<a name="NtA_515" + href="#Nt_515"><sup>[515]</sup></a> The author refers <!-- Page 230 + --><span class="pagenum"><a name="page230"></a>[230]</span>to attempts by + Hoffman,<a name="NtA_516" href="#Nt_516"><sup>[516]</sup></a> 1801, by + Hauff,<a name="NtA_517" href="#Nt_517"><sup>[517]</sup></a> 1799, and to + a work of Karsten,<a name="NtA_518" href="#Nt_518"><sup>[518]</sup></a> + or at least a theory of Karsten, contained in "Tentamen novæ parallelarum + theoriæ notione situs fundatæ; auctore G. C. Schwal,<a name="NtA_519" + href="#Nt_519"><sup>[519]</sup></a> Stuttgardæ, 1801, en 8 volumes." + Surely this is a misprint; <i>eight</i> volumes on the theory of + parallels? If there be such a work, I trust I and it may never meet, + though ever so far produced.</p> + +<p><!-- Page 231 --><span class="pagenum"><a name="page231"></a>[231]</span></p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Soluzione ... della quadratura del Circolo. By Gaetano Rossi.<a + name="NtA_520" href="#Nt_520"><sup>[520]</sup></a> London, 1804, 8vo.</p> + +</blockquote> + + <p>The three remarkable points of this book are, that the household of + the Prince of Wales took ten copies, Signora Grassini<a name="NtA_521" + href="#Nt_521"><sup>[521]</sup></a> sixteen, and that the circumference + is 3-1/5 diameters. That is, the appetite of Grassini for quadrature + exceeded that of the whole household (<i>loggia</i>) of the Prince of + Wales in the ratio in which the semi-circumference exceeds the diameter. + And these are the first two in the list of subscribers. Did the author + see this theorem?</p> + + <p> </p> + +<p class="cenhead">A PATRIOTIC PARADOX.</p> + +<blockquote class="b1n"> + + <p>Britain independent of commerce; or proofs, deduced from an + investigation into the true cause of the wealth of nations, that our + riches, prosperity, and power are derived from sources inherent in + ourselves, and would not be affected, even though our commerce were + annihilated. By Wm. Spence.<a name="NtA_522" + href="#Nt_522"><sup>[522]</sup></a> 4th edition, 1808, 8vo.</p> + +</blockquote> + + <p>A patriotic paradox, being in alleviation of the Commerce panic which + the measures of Napoleon I.—who <i>felt</i> our Commerce, while Mr. + Spence only <i>saw</i> 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 <!-- Page + 232 --><span class="pagenum"><a name="page232"></a>[232]</span>a solemn + embassy to the Americans, to beg them not to whittle, would be desirable. + There was a gold panic beginning, before the new fields were discovered. + For myself, I am the unknown and unpitied victim of a chronic + gutta-percha panic: I never could get on without it; to me, gutta percha + and Rowland Hill are the great discoveries of our day; and not + unconnected either, gutta percha being to the submarine post what Rowland + Hill is to the superterrene. I should be sorry to lose cow-choke—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): "<i>Cela était autrefois ainsi, mais + nous avons changé tout cela.</i>"<a name="NtA_523" + href="#Nt_523"><sup>[523]</sup></a> A great many people think that if the + coal be used up, it will be announced some unexpected morning by all the + yards being shut up and written notice outside, "Coal all gone!" just + like the "Please, ma'am, there ain't no more sugar," with which the maid + servant damps her mistress just at breakfast-time. But these persons + should be informed that there is every reason to think that there will be + time, as the city gentleman said, to <i>venienti</i> the <i>occurrite + morbo</i>.<a name="NtA_524" href="#Nt_524"><sup>[524]</sup></a></p> + + <p> </p> + +<p class="cenhead">SOME SCIENTIFIC PARADOXES.</p> + +<blockquote class="b1n"> + + <p>An appeal to the republic of letters in behalf of injured science, + from the opinions and proceedings of some modern authors of elements of + geometry. By George Douglas.<a name="NtA_525" + href="#Nt_525"><sup>[525]</sup></a> Edinburgh, 1810, 8vo.</p> + +</blockquote> + + <p>Mr. Douglas was the author of a very good set of <!-- Page 233 + --><span class="pagenum"><a name="page233"></a>[233]</span>mathematical + tables, and of other works. He criticizes Simson,<a name="NtA_526" + href="#Nt_526"><sup>[526]</sup></a> Playfair,<a name="NtA_527" + href="#Nt_527"><sup>[527]</sup></a> and others,—sometimes, I think, + very justly. There is a curious phrase which occurs more than once. When + he wants to say that something or other was done before Simson or another + was born, he says "before he existed, at least as an author." He seems to + reserve the possibility of Simson's <i>pre-existence</i>, but at the same + time to assume that he never wrote anything in his previous state. Tell + me that Simson pre-existed in any other way than as editor of some + pre-existent Euclid? Tell Apella!<a name="NtA_528" + href="#Nt_528"><sup>[528]</sup></a></p> + + <p>1810. In this year Jean Wood, Professor of Mathematics in the + University of Virginia (Richmond),<a name="NtA_529" + href="#Nt_529"><sup>[529]</sup></a> addressed a printed circular to "Dr. + Herschel, Astronomer, Greenwich Observatory." No mistake was more common + than the natural one of imagining that the <i>Private Astronomer</i> of + the king was the <i>Astronomer Royal</i>. The letter was on the <!-- Page + 234 --><span class="pagenum"><a name="page234"></a>[234]</span>difference + of velocities of the two sides of the earth, arising from the composition + of the rotation and the orbital motion. The <i>paradox</i> is a fair one, + and deserving of investigation; but, perhaps it would not be easy to + deduce from it tides, trade-winds, aerolithes, &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.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>The Elements of Geometry. In 2 vols. [By the Rev. J. Dobson,<a + name="NtA_530" href="#Nt_530"><sup>[530]</sup></a> B.D.] Cambridge, 1815. + 4to.</p> + +</blockquote> + + <p>Of this unpunctuating paradoxer I shall give an account in his own + way: he would not stop for any one; why should I stop for him? It is + worth while to try how unpunctuated sentences will read.</p> + + <p>The reverend J Dobson BD late fellow of saint Johns college Cambridge + was rector of Brandesburton in Yorkshire he was seventh wrangler in 1798 + and died in 1847 he was of that sort of eccentricity which permits + account of his private life if we may not rather say that in such cases + private life becomes public there is a tradition that he was called Death + Dobson on account of his head and aspect of countenance being not very + unlike the ordinary pictures of a human skull his mode of life is + reported to have been very singular whenever he visited Cambridge he was + never known to go twice to the same inn he never would sleep at the + rectory with another person in the house some ancient charwoman used to + attend to the house but never slept in it he has been known in the time + of coach travelling to have <!-- Page 235 --><span class="pagenum"><a + name="page235"></a>[235]</span>deferred his return to Yorkshire on + account of his disinclination to travel with a lady in the coach he + continued his mathematical studies until his death and till his executors + sold the type all his tracts to the number of five were kept in type at + the university press none of these tracts had any stops except full stops + at the end of paragraphs only neither had they capitals except one at the + beginning of a paragraph so that a full stop was generally followed by + some white as there is not a single proper name in the whole of the book + I have I am not able to say whether he would have used capitals before + proper names I have inserted them as usual for which I hope his spirit + will forgive me if I be wrong he also published the elements of geometry + in two volumes quarto Cambridge 1815 this book had also no stops except + when a comma was wanted between letters as in the straight lines AB, BC I + should also say that though the title is unpunctuated in the author's + part it seems the publishers would not stand it in their imprint this + imprint is punctuated as usual and Deighton and Sons to prove the + completeness of their allegiance have managed that comma semicolon and + period shall all appear in it why could they not have contrived + interrogation and exclamation this is a good precedent to establish the + separate right of the publisher over the imprint it is said that only + twenty of the tracts were printed and very few indeed of the book on + geometry it is doubtful whether any were sold there is a copy of the + geometry in the university library at Cambridge and I have one myself the + matter of the geometry differs entirely from Euclid and is so fearfully + prolix that I am sure no mortal except the author ever read it the man + went on without stops and without stop save for a period at the end of a + paragraph this is the unpunctuated account of the unpunctuating geometer + <i>suum cuique tribuito</i><a name="NtA_531" + href="#Nt_531"><sup>[531]</sup></a> Mrs Thrale<a name="NtA_532" + href="#Nt_532"><sup>[532]</sup></a> would have been amused <!-- Page 236 + --><span class="pagenum"><a name="page236"></a>[236]</span>at a Dobson + who managed to come to a full stop without either of the three + warnings.</p> + + <p>I do not find any difficulty in reading Dobson's geometry; and I have + read more of it to try reading without stops than I should have done had + it been printed in the usual way. Those who dip into the middle of my + paragraph may be surprised for a moment to see "on account of his + disinclination to travel with a lady in the coach he continued his + mathematical studies until his death and [further, of course] until his + executors sold the type." But a person reading straight through would + hardly take it so. I should add that, in order to give a fair trial, I + did not compose as I wrote, but copied the words of the correspondent who + gave me the facts, so far as they went.</p> + + <p> </p> + +<p class="cenhead">A RELIGIOUS PARADOX.</p> + +<blockquote class="b1n"> + + <p><i>Philosophia Sacra, or the principles of natural Philosophy. + Extracted from Divine Revelation.</i> By the Rev. Samuel Pike.<a + name="NtA_533" href="#Nt_533"><sup>[533]</sup></a> Edited by the Rev. + Samuel Kittle.<a name="NtA_534" href="#Nt_534"><sup>[534]</sup></a> + Edinburgh, 1815, 8vo.</p> + +</blockquote> + + <p>This is a work of modified Hutchinsonianism, which I have seen cited + by several. Though rather dark on the subject, it seems not to contradict + the motion of the earth, or the doctrine of gravitation. Mr. Kittle gives + a list of some Hutchinsonians,—as Bishop Horne;<a name="NtA_535" + href="#Nt_535"><sup>[535]</sup></a> Dr. Stukeley;<a name="NtA_536" + href="#Nt_536"><sup>[536]</sup></a> the Rev. <!-- Page 237 --><span + class="pagenum"><a name="page237"></a>[237]</span>W. Jones,<a + name="NtA_537" href="#Nt_537"><sup>[537]</sup></a> author of + <i>Physiological Disquisitions</i>; Mr. Spearman,<a name="NtA_538" + href="#Nt_538"><sup>[538]</sup></a> author of <i>Letters on the + Septuagint</i> and editor of Hutchinson; Mr. Barker,<a name="NtA_539" + href="#Nt_539"><sup>[539]</sup></a> author of <i>Reflexions on + Learning</i>; Dr. Catcott,<a name="NtA_540" + href="#Nt_540"><sup>[540]</sup></a> author of a work on the creation, + &c.; Dr. Robertson,<a name="NtA_541" + href="#Nt_541"><sup>[541]</sup></a> author of a <i>Treatise on the Hebrew + Language</i>; <i>Dr. Holloway</i>,<a name="NtA_542" + href="#Nt_542"><sup>[542]</sup></a> author of <i>Originals, Physical and + Theological</i>; Dr. Walter Hodges,<a name="NtA_543" + href="#Nt_543"><sup>[543]</sup></a> author of a work on <i>Elohim</i>; + Lord President Forbes (<i>ob.</i> 1747).<a name="NtA_544" + href="#Nt_544"><sup>[544]</sup></a></p> + + <p>The Rev. William Jones, above mentioned (1726-1800), the friend and + biographer of Bishop Horne and his stout <!-- Page 238 --><span + class="pagenum"><a name="page238"></a>[238]</span>defender, is best known + as William Jones of Nayland, who (1757)<a name="NtA_545" + href="#Nt_545"><sup>[545]</sup></a> published the <i>Catholic Doctrine of + the Trinity</i>; he was also strong for the Hutchinsonian physical + trinity of fire, light, and spirit. This well-known work was generally + recommended, as the defence of the orthodox system, to those who could + not go into the learning of the subject. There is now a work more suited + to our time: <i>The Rock of Ages</i>, by the Rev. E. H. Bickersteth,<a + name="NtA_546" href="#Nt_546"><sup>[546]</sup></a> now published by the + Religious Tract Society, without date, answered by the Rev. Dr. Sadler,<a + name="NtA_547" href="#Nt_547"><sup>[547]</sup></a> in a work (1859) + entitled <i>Gloria Patri</i>, in which, says Mr. Bickersteth, "the author + has not even attempted to grapple with my main propositions." I have read + largely on the controversy, and I think I know what this means. Moreover, + when I see the note "There are two other passages to which Unitarians + sometimes refer, but the deduction they draw from them is, in each case, + refuted by the context"—I think I see why the two texts are not + named. Nevertheless, the author is a little more disposed to yield to + criticism than his foregoers; he does not insist on texts and readings + which the greatest editors have rejected. And he writes with courtesy, + both direct and oblique, towards his antagonists; which, on his side of + this subject, is like letting in fresh air. So that I suspect the two + books will together make a tolerably good introduction to the subject for + those who cannot go deep. Mr. Bickersteth's book is well arranged and + indexed, which is a point of superiority to Jones of Nayland. There is a + point which I should gravely recommend to writers on the orthodox side. + The Unitarians in <!-- Page 239 --><span class="pagenum"><a + name="page239"></a>[239]</span>England have frequently contended that the + method of proving the divinity of Jesus Christ from the New Testament + would equally prove the divinity of Moses. I have not fallen in the way + of any orthodox answers specially directed at the repeated tracts written + by Unitarians in proof of their assertion. If there be any, they should + be more known; if there be none, some should be written. Which ever side + may be right, the treatment of this point would be indeed coming to close + quarters. The heterodox assertion was first supported, it is said, by + John Bidle or Biddle (1615-1662) of Magdalen College, Oxford, the + earliest of the English Unitarian writers, previously known by a + translation of part of Virgil and part of Juvenal.<a name="NtA_548" + href="#Nt_548"><sup>[548]</sup></a> But I cannot find that he wrote on + it.<a name="NtA_549" href="#Nt_549"><sup>[549]</sup></a> It is the + subject of "<span title="haireseôn anastasis" class="grk" + >αἱρεσεων + ἀναστασις</span>, or a + new way of deciding old controversies. By Basanistes. Third edition, + enlarged," London, 1815, 8vo.<a name="NtA_550" + href="#Nt_550"><sup>[550]</sup></a> It is the appendix to the amusing, + "Six more letters to Granville Sharp, Esq., ... By Gregory Blunt, Esq." + London, 8vo., 1803.<a name="NtA_551" href="#Nt_551"><sup>[551]</sup></a> + This much I can confidently say, that the study of these tracts would + prevent orthodox writers from some curious slips, which are slips obvious + to all sides of opinion. The lower defenders of orthodoxy frequently vex + the spirits of the higher ones.</p> + + <p>Since writing the above I have procured Dr. Sadler's answer. I thought + I knew what the challenger meant when he said the respondent had not + grappled with his main <!-- Page 240 --><span class="pagenum"><a + name="page240"></a>[240]</span>propositions. I should say that he is + clung on to from beginning to end. But perhaps Mr. B. has his own meaning + of logical terms, such as "proposition": he certainly has his own meaning + of "cumulative." He says his evidence is cumulative; not a catena, the + strength of which is in its weakest part, but distinct and independent + lines, each of which corroborates the other. This is the very opposite of + <i>cumulative</i>: it is <i>distributive</i>. When different arguments + are each necessary to a conclusion, the evidence is <i>cumulative</i>; + when any one will do, even though they strengthen each other, it is + <i>distributive</i>. The word "cumulative" is a synonym of the law word + "constructive"; a whole which will do made out of parts which separately + will not. Lord Strafford <a name="NtA_552" + href="#Nt_552"><sup>[552]</sup></a> opens his defence with the use of + both words: "They have invented a kind of <i>accumulated</i> or + <i>constructive</i> evidence; by which many actions, either totally + innocent in themselves, or criminal in a much inferior degree, shall, + when united, <i>amount</i> to treason." The conclusion is, that Mr. B. is + a Cambridge man; the Oxford men do not confuse the elementary terms of + logic. O dear old Cambridge! when the New Zealander comes let him find + among the relics of your later sons some proof of attention to the + elementary laws of thought. A little-go of logic, please!</p> + + <p>Mr. B., though apparently not a Hutchinsonian, has a nibble at a + physical Trinity. "If, as we gaze on the sun shining in the firmament, we + see any faint adumbration of the doctrine of the Trinity in the fontal + orb, the light ever generated, and the heat proceeding from the sun and + its beams—threefold and yet one, the sun, its light, and its <!-- + Page 241 --><span class="pagenum"><a + name="page241"></a>[241]</span>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."</p> + + <p>We shall see how Revilo<a name="NtA_553" + href="#Nt_553"><sup>[553]</sup></a> illustrates orthodoxy by mathematics. + It was my duty to have found one of the many illustrations from physics; + but perhaps I should have forgotten it if this instance had not come in + my way. It is very bad physics. The sun, apart from its light, evident to + the eye! Heat more self-demonstrating than light, because <i>felt</i>! + Heat only manifested by the life it diffuses! Light implied not necessary + to life! But the theology is worse than Sabellianism<a name="NtA_554" + href="#Nt_554"><sup>[554]</sup></a>. To adumbrate—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 <i>properties</i>, and these properties have a parallel not in the + second and third persons of the Trinity, but in the attributes of + Deity."</p> + + <p>The letting light alone, as self-evident, and making heat + self-demonstrating, because felt—i.e., perceptible now and + then—has the character of the Irishman's astronomy:</p> + +<p><!-- Page 242 --><span class="pagenum"><a name="page242"></a>[242]</span></p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Long life to the moon, for a dear noble cratur,</p> + <p>Which serves us for lamplight all night in the dark,</p> + <p>While the sun only shines in the day, which by natur,</p> + <p>Wants no light at all, as ye all may remark."</p> + </div> + </div> + <p> </p> + +<p class="cenhead">SIR RICHARD PHILLIPS.</p> + + <p><i>Sir Richard Phillips</i><a name="NtA_555" + href="#Nt_555"><sup>[555]</sup></a> (born 1768) was conspicuous in 1793, + when he was sentenced to a year's imprisonment<a name="NtA_556" + href="#Nt_556"><sup>[556]</sup></a> for selling Paine's <i>Rights of + Man</i>; and again when, in 1807<a name="NtA_557" + href="#Nt_557"><sup>[557]</sup></a>, he was knighted as Sheriff of + London. As a bookseller, he was able to enforce his opinions in more ways + than others. For instance, in James Mitchell's<a name="NtA_558" + href="#Nt_558"><sup>[558]</sup></a> <i>Dictionary of the Mathematical and + Physical Sciences</i>, 1823, 12mo, which, though he was not technically a + publisher, was printed for him—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<a name="NtA_559" href="#Nt_559"><sup>[559]</sup></a> pension, + and in Mrs. Somerville's<a name="NtA_560" + href="#Nt_560"><sup>[560]</sup></a>. In 1836, he <!-- Page 243 --><span + class="pagenum"><a name="page243"></a>[243]</span>did me the honor to + attempt my conversion. In his first letter he says:</p> + + <p>"Sir Richard Phillips has an inveterate abhorrence of all the + pretended wisdom of philosophy derived from the monks and doctors of the + middle ages, and not less of those of higher name who merely sought to + make the monkish philosophy more plausible, or so to disguise it as to + mystify the mob of small thinkers."</p> + + <p>So little did his writings show any knowledge of antiquity, that I + strongly suspect, if required to name one of the monkish doctors, he + would have answered—Aristotle. These schoolmen, and the + "philosophical trinity of gravitating force, projectile force, and void + space," were the bogies of his life.</p> + + <p>I think he began to publish speculations in the <i>Monthly + Magazine</i> (of which he was editor) in July 1817: these he republished + separately in 1818. In the Preface, perhaps judging the feelings of + others by his own, he says that he "fully expects to be vilified, + reviled, and anathematized, for many years to come." Poor man! he was let + alone. He appeals with confidence to the "impartial decision of + posterity"; but posterity does not appoint a hearing for one per cent. of + the appeals which are made; and it is much to be feared that an article + in such a work of reference as this will furnish nearly all her materials + fifty years hence. The following, addressed to M. Arago,<a name="NtA_561" + href="#Nt_561"><sup>[561]</sup></a> in 1835, will give posterity as good + a notion as she will probably need:</p> + + <p>"Even the present year has afforded <span + class="scac">EVER-MEMORABLE</span> examples, paralleled only by that of + the Romish Conclave which persecuted Galileo. Policy has adopted that + maxim of Machiavel which teaches that it is <i>more prudent</i> to + <i>reward</i> <!-- Page 244 --><span class="pagenum"><a + name="page244"></a>[244]</span>partisans than to <i>persecute</i> + opponents. Hence, a bigotted party had influence enough with the late + short-lived administration [I think he is wrong as to the administration] + of Wellington, Peel, &c., to confer munificent royal pensions on + three writers whose sole distinction was their advocacy of the Newtonian + philosophy. A Cambridge professor last year published an elaborate volume + in illustration of <i>Gravitation</i>, and on him has been conferred a + pension of 300<i>l.</i> per annum. A lady has written a light popular + view of the Newtonian Dogmas, and she has been complimented by a pension + of 200<i>l.</i> per annum. And another writer, who has recently published + a volume to prove that the only true philosophy is that of Moses, has + been endowed with a pension of 200<i>l.</i> per annum. Neither of them + were needy persons, and the political and ecclesiastical bearing of the + whole was indicated by another pension of 300<i>l.</i> bestowed on a + political writer, the advocate of all abuses and prejudices. Whether the + conduct of the Romish Conclave was more base for visiting with legal + penalties the promulgation of the doctrines that the Earth turns on its + axis and revolves around the Sun; or that of the British Court, for its + craft in conferring pensions on the opponents of the plain corollary, + that all the motions of the Earth are 'part and parcel' of these great + motions, and those again and all like them consecutive displays of still + greater motions in equality of action and reaction, is <span + class="scac">A QUESTION</span> which must be reserved for the casuists of + other generations.... I cannot expect that on a sudden you and your + friends will come to my conclusion, that the present philosophy of the + Schools and Universities of Europe, based on faith in witchcraft, magic, + &c., is a system of execrable nonsense, <i>by which quacks live on + the faith of fools</i>; but I desire a free and fair examination of my + Aphorisms, and if a few are admitted to be true, merely as courteous + concessions to arithmetic, my purpose will be effected, for men will thus + be led to think; and if they think, then the fabric <!-- Page 245 + --><span class="pagenum"><a name="page245"></a>[245]</span>of false + assumptions, and degrading superstitions will soon tumble in ruins."</p> + + <p>This for posterity. For the present time I ground the fame of Sir R. + Phillips on his having squared the circle without knowing it, or + intending to do it. In the <i>Protest</i> presently noted he discovered + that "the force taken as 1 is equal to the sum of all its fractions ... + thus 1 = 1/4 + 1/9 + 1/16 + 1/25, &c., carried to infinity." This the + mathematician instantly sees is equivalent to the theorem that the + circumference of any circle is double of the diagonal of the cube on its + diameter.<a name="NtA_562" href="#Nt_562"><sup>[562]</sup></a></p> + + <p>I have examined the following works of Sir R. Phillips, and heard of + many others:</p> + +<blockquote class="b1n"> + + <p>Essays on the proximate mechanical causes of the general phenomena of + the Universe, 1818, 12mo.<a name="NtA_563" + href="#Nt_563"><sup>[563]</sup></a></p> + + <p>Protest against the prevailing principles of natural philosophy, with + the development of a common sense system (no date, 8vo, pp. 16).<a + name="NtA_564" href="#Nt_564"><sup>[564]</sup></a></p> + + <p>Four dialogues between an Oxford Tutor and a disciple of the + common-sense philosophy, relative to the proximate causes of material + phenomena. 8vo, 1824.</p> + + <p>A century of original aphorisms on the proximate causes of the + phenomena of nature, 1835, 12mo.</p> + +</blockquote> + + <p>Sir Richard Phillips had four valuable qualities; honesty, zeal, + ability, and courage. He applied them all to teaching <!-- Page 246 + --><span class="pagenum"><a name="page246"></a>[246]</span>matters about + which he knew nothing; and gained himself an uncomfortable life and a + ridiculous memory.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Astronomy made plain; or only way the true perpendicular distance of + the Sun, Moon, or Stars, from this earth, can be obtained. By Wm. Wood.<a + name="NtA_565" href="#Nt_565"><sup>[565]</sup></a> Chatham, 1819, + 12mo.</p> + +</blockquote> + + <p>If this theory be true, it will follow, of course, that this earth is + the only one God made, and that it does not whirl round the sun, but + <i>vice versa</i>, the sun round it.</p> + + <p> </p> + +<p class="cenhead">WHATELY'S FAMOUS PARADOX.</p> + +<blockquote class="b1n"> + + <p>Historic doubts relative to Napoleon Buonaparte. London, 1819, + 8vo.</p> + +</blockquote> + + <p>This tract has since been acknowledged by Archbishop Whately<a + name="NtA_566" href="#Nt_566"><sup>[566]</sup></a> and reprinted. It is + certainly a paradox: but differs from most of those in my list as being a + joke, and a satire upon the reasoning of those who cannot receive + narrative, no matter what the evidence, which is to them utterly + improbable <i>a priori</i>. But had it been serious earnest, it would not + have been so absurd as many of those which I have brought forward. The + next on the list is not a joke.</p> + + <p>The idea of the satire is not new. Dr. King,<a name="NtA_567" + href="#Nt_567"><sup>[567]</sup></a> in the dispute on the genuineness of + Phalaris, proved with humor that Bentley did not write his own + dissertation. An attempt has lately been made, for the honor of Moses, to + prove, <!-- Page 247 --><span class="pagenum"><a + name="page247"></a>[247]</span>without humor, that Bishop Colenso did not + write his own book. This is intolerable: anybody who tries to use such a + weapon without banter, plenty and good, and of form suited to the + subject, should get the drubbing which the poor man got in the Oriental + tale for striking the dervishes with the wrong hand.</p> + + <p>The excellent and distinguished author of this tract has ceased to + live. I call him the Paley of our day: with more learning and more + purpose than his predecessor; but perhaps they might have changed places + if they had changed centuries. The clever satire above named is not the + only work which he published without his name. The following was + attributed to him, I believe rightly: "Considerations on the Law of + Libel, as relating to Publications on the subject of Religion, by John + Search." London, 1833, 8vo. This tract excited little attention: for + those who should have answered, could not. Moreover, it wanted a + prosecution to call attention to it: the fear of calling such attention + may have prevented prosecutions. Those who have read it will have seen + why.</p> + + <p>The theological review elsewhere mentioned attributes the pamphlet of + John Search on blasphemous libel to Lord Brougham. This is quite absurd: + the writer states points of law on credence where the judge must have + spoken with authority. Besides which, a hundred points of style are + decisive between the two. I think any one who knows Whately's writing + will soon arrive at my conclusion. Lord Brougham himself informs me that + he has no knowledge whatever of the pamphlet.</p> + + <p>It is stated in <i>Notes and Queries</i> (3 S. xi. 511) that Search + was answered by the Bishop of Ferns<a name="NtA_568" + href="#Nt_568"><sup>[568]</sup></a> as S. N., with <!-- Page 248 --><span + class="pagenum"><a name="page248"></a>[248]</span>a rejoinder by Blanco + White.<a name="NtA_569" href="#Nt_569"><sup>[569]</sup></a> These + circumstances increase the probability that Whately was written against + and for.</p> + +<blockquote class="b1n"> + + <p> </p> + +<p class="cenhead">VOLTAIRE A CHRISTIAN.</p> + + <p>Voltaire Chrétien; preuves tirées de ses ouvrages. Paris, 1820, + 12mo.</p> + +</blockquote> + + <p>If Voltaire have not succeeded in proving himself a strong theist and + a strong anti-revelationist, who is to succeed in proving himself one + thing or the other in any matter whatsoever? By occasional confusion + between theism and Christianity; by taking advantage of the formal + phrases of adhesion to the Roman Church, which very often occur, and are + often the happiest bits of irony in an ironical production; by citations + of his morality, which is decidedly Christian, though often attributed to + Brahmins; and so on—the author makes a fair case for his paradox, + in the eyes of those who know no more than he tells them. If he had said + that Voltaire was a better Christian than himself knew of, towards all + mankind except men of letters, I for one should have agreed with him.</p> + + <p><i>Christian!</i> the word has degenerated into a synonym of + <i>man</i>, in what are called Christian countries. So we have the parrot + who "swore for all the world like a Christian," and the two dogs who + "hated each other just like Christians." When the Irish duellist of the + last century, whose name may be spared in consideration of its historic + fame <!-- Page 249 --><span class="pagenum"><a + name="page249"></a>[249]</span>and the worthy people who bear it, was + (June 12, 1786) about to take the consequence of his last brutal murder, + the rope broke, and the criminal got up, and exclaimed, "By + —— Mr. Sheriff, you ought to be ashamed of yourself! this + rope is not strong enough to hang a dog, far less a Christian!" But such + things as this are far from the worst depravations. As to a word so + defiled by usage, it is well to know that there is a way of escape from + it, without renouncing the New Testament. I suppose any one may assume + for himself what I have sometimes heard contended for, that no New + Testament word is to be used in religion in any sense except that of the + New Testament. This granted, the question is settled. The word + <i>Christian</i>, which occurs three times, is never recognized as + anything but a term of contempt from those without the pale to those + within. Thus, Herod Agrippa, who was deep in Jewish literature, and a + correspondent of Josephus, says to Paul (Acts xxvi. 28), "Almost thou + persuadest me to be (what I and other followers of the state religion + despise under the name) a Christian." Again (Acts xi. 26), "The disciples + (as they called <i>themselves</i>) were called (by the surrounding + heathens) Christians first in Antioch." Thirdly (1 Peter iv. 16), "Let + none of you suffer as a <i>murderer</i>.... But if as a <i>Christian</i> + (as the heathen call it by whom the suffering comes), let him not be + ashamed." That is to say, no <i>disciple</i> ever called <i>himself</i> a + Christian, or applied the name, as from himself, to another disciple, + from one end of the New Testament to the other; and no disciple need + apply that name to himself in our day, if he dislike the associations + with which the conduct of Christians has clothed it.</p> + + <p> </p> + +<p class="cenhead">WRONSKI ON THE LONGITUDE PROBLEM.</p> + +<blockquote class="b1n"> + + <p>Address of M. Hoene Wronski to the British Board of Longitude, upon + the actual state of the mathematics, their reform, <!-- Page 250 --><span + class="pagenum"><a name="page250"></a>[250]</span>and upon the new + celestial mechanics, giving the definitive solution of the problem of + longitude.<a name="NtA_570" href="#Nt_570"><sup>[570]</sup></a> London, + 1820, 8vo.</p> + +</blockquote> + + <p>M. Wronski<a name="NtA_571" href="#Nt_571"><sup>[571]</sup></a> was + the author of seven quartos on mathematics, showing very great power of + generalization. He was also deep in the transcendental philosophy,<a + name="NtA_572" href="#Nt_572"><sup>[572]</sup></a> and had the Absolute + at his fingers' ends. All this knowledge was rendered useless by a + persuasion that he had greatly advanced beyond the whole world, with many + hints that the Absolute would not be forthcoming, unless prepaid. He was + a man of the widest extremes. At one time he desired people to see all + possible mathematics in</p> + + <div class="poem"> + <div class="stanza"> + <p>F<i>x</i> = A<sub>0</sub><span class="grk">Ω</span><sub>0</sub> + A<sub>1</sub><span class="grk">Ω</span><sub>1</sub> + A<sub>2</sub><span class="grk">Ω</span><sub>2</sub> + A<sub>3</sub><span class="grk">Ω</span><sub>3</sub> + &c.</p> + </div> + </div> + <p>which he did not explain, though there is meaning to it in the + quartos. At another time he was proposing the general solution of the<a + name="NtA_573" href="#Nt_573"><sup>[573]</sup></a> fifth degree by help + of 625 independent equations of one form and 125 of another. The first + separate memoir from any Transactions that I ever possessed was given to + me when at Cambridge; the refutation (1819) of this asserted solution, + presented to the Academy of Lisbon by Evangelista Torriano. I cannot say + I read it. The tract above is an attack on modern mathematicians in + general, and on the Board of Longitude, and Dr. Young.<a name="NtA_574" + href="#Nt_574"><sup>[574]</sup></a></p> + +<p><!-- Page 251 --><span class="pagenum"><a name="page251"></a>[251]</span></p> + + <p> </p> + +<p class="cenhead">DR. MILNER'S PARADOXES.</p> + + <p>1820. In this year died Dr. Isaac Milner,<a name="NtA_575" + href="#Nt_575"><sup>[575]</sup></a> President of Queens' College, + Cambridge, one of the class of rational paradoxers. Under this name I + include all who, in private life, and in matters which concern + themselves, take their own course, and suit their own notions, no matter + what other people may think of them. These men will put things to uses + they were never intended for, to the great distress and disgust of their + gregarious friends. I am one of the class, and I could write a little + book of cases in which I have incurred absolute reproach for not "doing + as other people do." I will name two of my atrocities: I took one of + those butter-dishes which have for a top a dome with holes in it, which + is turned inward, out of reach of accident, when not in use. Turning the + dome inwards, I filled the dish with water, and put a sponge in the dome: + the holes let it fill with water, and I had a penwiper, always moist, and + worth its price five times over. "Why! what do you mean? It was made to + hold butter. You are always at some queer thing or other!" I bought a + leaden comb, intended to dye the hair, it being supposed that the + application of lead will have this effect. I did not try: but I divided + the comb into two, separated the part of closed prongs from the other; + and thus I had two ruling machines. The lead marks paper, and by drawing + the end of one of the machines along a ruler, I could rule twenty lines + at a time, quite fit to write on. I thought I should have killed a friend + to whom I explained it: he could not for the life of him understand how + leaden <i>lines</i> on paper would dye the hair.</p> + + <p>But Dr. Milner went beyond me. He wanted a seat suited to his shape, + and he defied opinion to a fearful point. <!-- Page 252 --><span + class="pagenum"><a name="page252"></a>[252]</span>He spread a thick block + of putty over a wooden chair and sat in it until it had taken a ceroplast + copy of the proper seat. This he gave to a carpenter to be imitated in + wood. One of the few now living who knew him—my friend, General + Perronet Thompson<a name="NtA_576" + href="#Nt_576"><sup>[576]</sup></a>—answers for the wood, which was + shown him by Milner himself; but he does not vouch for the material being + putty, which was in the story told me at Cambridge; William Frend<a + name="NtA_577" href="#Nt_577"><sup>[577]</sup></a> also remembered it. + Perhaps the Doctor took off his great seal in green wax, like the Crown; + but some soft material he certainly adopted; and very comfortable he + found the wooden copy.</p> + + <div class="figleft" style="width:10%;"> + <a href="images/adem_260.png"><img style="width:100%" src="images/adem_260.png" + alt="Milner's lamp" title="Milner's lamp" /></a> + </div> + <p>The same gentleman vouches for Milner's lamp: but this had visible + <i>science</i> in it; the vulgar see no science in the construction of + the chair. A hollow semi-cylinder, but not with a circular curve, + revolved on pivots. The curve was calculated on the law that, whatever + quantity of oil might be in the lamp, the position of equilibrium just + brought the oil up to the edge of the cylinder, at which a bit of wick + was placed. As the wick exhausted the oil, the cylinder slowly revolved + about the pivots so as to keep the oil always touching the wick.</p> + + <p>Great discoveries are always laughed at; but it is very often not the + laugh of incredulity; it is a mode of distorting the sense of inferiority + into a sense of superiority, or a mimicry of superiority interposed + between the laugher and his feeling of inferiority. Two persons in + conversation <!-- Page 253 --><span class="pagenum"><a + name="page253"></a>[253]</span>agreed that it was often a nuisance not to + be able to lay hands on a bit of paper to mark the place in a book, every + bit of paper on the table was sure to contain something not to be spared. + I very quietly said that I always had a stock of bookmarkers ready cut, + with a proper place for them: my readers owe many of my anecdotes to this + absurd practice. My two colloquials burst into a fit of laughter; about + what? Incredulity was out of the question; and there could be nothing + foolish in my taking measures to avoid what they knew was an + inconvenience. I was in this matter obviously their superior, and so they + laughed at me. Much more candid was the Royal Duke of the last century, + who was noted for slow ideas. "The rain comes into my mouth," said he, + while riding. "Had not your Royal Highness better shut your mouth?" said + the equerry. The Prince did so, and ought, by rule, to have laughed + heartily at his adviser; instead of this, he said quietly, "It doesn't + come in now."</p> + + <p> </p> + +<p class="cenhead">HERBART'S MATHEMATICAL PSYCHOLOGY.</p> + +<blockquote class="b1n"> + + <p>De Attentionis mensura causisque primariis. By J. F. Herbart.<a + name="NtA_578" href="#Nt_578"><sup>[578]</sup></a> Kœnigsberg, + 1822, 4to.</p> + +</blockquote> + +<p><!-- Page 254 --><span class="pagenum"><a name="page254"></a>[254]</span></p> + + <p>This celebrated philosopher maintained that mathematics ought to be + applied to psychology, in a separate tract, published also in 1822: the + one above seems, therefore, to be his challenge on the subject. It is on + <i>attention</i>, and I think it will hardly support Herbart's thesis. As + a specimen of his formula, let <i>t</i> be the time elapsed since the + consideration began, <span class="grk">β</span> the whole perceptive + intensity of the individual, <span class="grk">φ</span> the whole of + his mental force, and <i>z</i> the force given to a notion by attention + during the time <i>t</i>. Then,</p> + +<p class="cenhead"><i>z</i> = <span class="grk">φ</span> (1 - <span class="grk">ε</span><sup>-<span class="grk">β</span><i>t</i></sup>)</p> + + <p>Now for a test. There is a <i>jactura</i>, <i>v</i>, the meaning of + which I do not comprehend. If there be anything in it, my mathematical + readers ought to interpret it from the formula</p> + +<p class="cenhead"><i>v</i> = <span class="grk">π</span><span class="grk">φ</span><span class="grk">β</span>/(1 - <span class="grk">β</span>)<span class="grk">ε</span><sup>-<span class="grk">β</span><i>t</i></sup> + C<span class="grk">ε</span><sup>-t</sup></p> + + <p>and to this task I leave them, wishing them better luck than mine. The + time may come when other manifestations of mind, besides <i>belief</i>, + shall be submitted to calculation: at that time, should it arrive, a + final decision may be passed upon Herbart.</p> + + <p> </p> + +<p class="cenhead">ON THE WHIZGIG.</p> + +<blockquote class="b1n"> + + <p>The theory of the Whizgig considered; in as much as it mechanically + exemplifies the three working properties of nature; which are now set + forth under the guise of this toy, for children of all ages. London, + 1822, 12mo (pp. 24, B. McMillan, Bow Street, Covent Garden).</p> + +</blockquote> + + <p>The toy called the <i>whizgig</i> will be remembered by many. The + writer is a follower of Jacob Behmen,<a name="NtA_579" + href="#Nt_579"><sup>[579]</sup></a> William Law,<a name="NtA_580" + href="#Nt_580"><sup>[580]</sup></a> <!-- Page 255 --><span + class="pagenum"><a name="page255"></a>[255]</span>Richard Clarke,<a + name="NtA_581" href="#Nt_581"><sup>[581]</sup></a> and Eugenius + Philalethes.<a name="NtA_582" href="#Nt_582"><sup>[582]</sup></a> Jacob + Behmen first announced the three working properties of nature, which + Newton stole, as described in the <i>Gentleman's Magazine</i>, July, + 1782, p. 329. These laws are illustrated in the whizgig. There is the + harsh astringent, attractive compression; the bitter compunction, + repulsive expansion; and the stinging anguish, duplex motion. The author + hints that he has written other works, to which he gives no clue. I have + heard that Behmen was pillaged by Newton, and Swedenborg<a name="NtA_583" + href="#Nt_583"><sup>[583]</sup></a> by Laplace,<a name="NtA_584" + href="#Nt_584"><sup>[584]</sup></a> and Pythagoras by Copernicus,<a + name="NtA_585" href="#Nt_585"><sup>[585]</sup></a> and Epicurus by + Dalton,<a name="NtA_586" href="#Nt_586"><sup>[586]</sup></a> &c. I do + not think this mention will revive Behmen; but it may the whizgig, a very + pretty toy, and philosophical withal, for few of those who used it could + explain it.</p> + +<p><!-- Page 256 --><span class="pagenum"><a name="page256"></a>[256]</span></p> + + <p> </p> + +<p class="cenhead">SOME MYTHOLOGICAL PARADOXES.</p> + +<blockquote class="b1n"> + + <p>A Grammar of infinite forms; or the mathematical elements of ancient + philosophy and mythology. By Wm. Howison.<a name="NtA_587" + href="#Nt_587"><sup>[587]</sup></a> Edinburgh, 1823, 8vo.</p> + +</blockquote> + + <p>A curius combination of geometry and mythology. Perseus, for instance, + is treated under the head, "the evolution of diminishing hyperbolic + branches."</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>The Mythological Astronomy of the Ancients; part the second: or the + key of Urania, the words of which will unlock all the mysteries of + antiquity. Norwich, 1823, 12mo.</p> + + <p>A Companion to the Mythological Astronomy, &c., containing remarks + on recent publications.... Norwich, 1824, 12mo.</p> + + <p>A new Theory of the Earth and of planetary motion; in which it is + demonstrated that the Sun is vicegerent of his own system. Norwich, 1825, + 12mo.</p> + + <p>The analyzation of the writings of the Jews, so far as they are found + to have any connection with the sublime science of astronomy. [This is + pp. 97-180 of some other work, being all I have seen.]</p> + +</blockquote> + + <p>These works are all by Sampson Arnold Mackey,<a name="NtA_588" + href="#Nt_588"><sup>[588]</sup></a> for whom see <i>Notes and + Queries</i>, 1st S. viii. 468, 565, ix. 89, 179. Had it not been for + actual quotations given by one correspondent only (1st S. viii. 565), + that journal would have handed him down as a man of some real learning. + An extraordinary man he certainly was: it is not one illiterate shoemaker + in a thousand who could work upon such a singular mass of Sanskrit and + Greek words, without showing <!-- Page 257 --><span class="pagenum"><a + name="page257"></a>[257]</span>evidence of being able to read a line in + any language but his own, or to spell that correctly. He was an + uneducated Godfrey Higgins.<a name="NtA_589" + href="#Nt_589"><sup>[589]</sup></a> A few extracts will put this in a + strong light: one for history of science, one for astronomy, and one for + philology:</p> + + <p>"Sir Isaac Newton was of opinion that 'the atmosphere of the earth was + the sensory of God; by which he was enabled to see quite round the + earth:' which proves that Sir Isaac had no idea that God could see + through the earth.</p> + + <p>"Sir Richard [Phillips] has given the most rational explanation of the + cause of the earth's elliptical orbit that I have ever seen in print. It + is because the earth presents its watery hemisphere to the sun at one + time and that of solid land the other; but why has he made his Oxonian + astonished at the coincidence? It is what I taught in my attic twelve + years before.</p> + + <p>"Again, admitting that the Eloim were powerful and intelligent beings + that managed these things, we would accuse <i>them</i> of being the + authors of all the sufferings of Chrisna. And as they and the + constellation of Leo were below the horizon, and consequently cut off + from the end of the zodiac, there were but eleven constellations of the + zodiac to be seen; the three at the end were wanted, but those three + would be accused of bringing Chrisna into the troubles which at last + ended in his death. All this would be expressed in the Eastern language + by saying that Chrisna was persecuted by those Judoth Ishcarioth!!!!! + [the five notes of exclamation are the author's]. But the astronomy of + those distant ages, when the sun was at the south pole in winter, would + leave five of those Decans cut off from our view, in the latitude of + twenty-eight degrees; hence Chrisna died of <!-- Page 258 --><span + class="pagenum"><a name="page258"></a>[258]</span>wounds from five + Decans, but the whole five may be included in Judoth Ishcarioth! for the + phrase means 'the men that are wanted at the extreme parts.' Ishcarioth + is a compound of <i>ish</i>, a man, and <i>carat</i> wanted or taken + away, and oth the plural termination, more ancient than + <i>im</i>...."</p> + + <p>I might show at length how Michael is the sun, and the D'-ev-'l in + French Di-ob-al, also 'L-evi-ath-an—the evi being the radical part + both of d<i>evi</i>l and l<i>evi</i>athan—is the Nile, which the + sun dried up for Moses to pass: a battle celebrated by Jude. Also how + <i>Moses</i>, the same name as <i>Muses</i>, is from <i>mesha</i>, drawn + out of the water, "and hence we called our land which is saved from the + water by the name of <i>marsh</i>." But it will be of more use to collect + the character of S. A. M. from such correspondents of <i>Notes and + Queries</i> as have written after superficial examination. Great + astronomical and philological attainments, much ability and learning; had + evidently read and studied deeply; remarkable for the originality of his + views upon the very abstruse subject of mythological astronomy, in which + he exhibited great sagacity. Certainly his views were <i>original</i>; + but their sagacity, if it be allowable to copy his own mode of + etymologizing, is of an <i>ori-gin-ale</i> cast, resembling that of a + person who puts to his mouth liquors both distilled and fermented.</p> + + <p> </p> + +<p class="cenhead">A KANTESIAN JEWELER.</p> + +<blockquote class="b1n"> + + <p>Principles of the Kantesian, or transcendental philosophy. By Thomas + Wirgman.<a name="NtA_590" href="#Nt_590"><sup>[590]</sup></a> London, + 1824, 8vo.</p> + +</blockquote> + + <p>Mr. Wirgman's mind was somewhat attuned to psychology; but he was + cracky and vagarious. He had been a fashionable jeweler in St. James's + Street, no doubt the son or grandson of Wirgman at "the well-known + toy-shop in <!-- Page 259 --><span class="pagenum"><a + name="page259"></a>[259]</span>St. James's Street," where Sam Johnson + smartened himself with silver buckles. (Boswell, <i>æt.</i> 69). He would + not have the ridiculous large ones in fashion; and he would give no more + than a guinea a pair; such, says Boswell, in Italics, were the + <i>principles</i> of the business: and I think this may be the first + place in which the philosophical word was brought down from heaven to mix + with men. However this may be, <i>my</i> Wirgman sold snuff-boxes, among + other things, and fifty years ago a fashionable snuff-boxer would be + under inducement, if not positively obliged, to have a stock with very + objectionable pictures. So it happened that Wirgman—by reason of a + trifle too much candor—came under the notice of the + <i>Suppression</i> Society, and ran considerable risk. Mr. Brougham was + his counsel; and managed to get him acquitted. Years and years after + this, when Mr. Brougham was deep in the formation of the London + University (now University College), Mr. Wirgman called on him. "What + now?" said Mr. B. with his most sarcastic look—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!</p> + + <p>Mr. Wirgman, an itinerant paradoxer, called on me in 1831: he came to + convert me. "I assure you," said he, "I am nothing but an old brute of a + jeweler;" and his eye and manner were of the extreme of jocosity, as good + in their way, as the satire of his former counsel. I mention him as one + of that class who go away quite satisfied that they have wrought + conviction. "Now," said he, "I'll make it clear to you! Suppose a number + of gold-fishes in a glass bowl,—you understand? Well! I come with + my cigar and go puff, puff, puff, over the bowl, until there is a little + cloud of smoke: now, tell me, what will the gold-fishes say to that?" "I + should imagine," said I, "That they would not know what to make of it." + "By Jove! you're a Kantian;" said he, and with this and the like, he left + me, vowing that <!-- Page 260 --><span class="pagenum"><a + name="page260"></a>[260]</span>it was delightful to talk to so + intelligent a person. The greatest compliment Wirgman ever received was + from James Mill, who used to say he did not <i>understand</i> Kant. That + such a man as Mill should think this worth saying is a feather in the cap + of the jocose jeweler.</p> + + <p>Some of my readers will stare at my supposing that Boswell may have + been the first down-bringer of the word <i>principles</i> into common + life; the best answer will be a prior instance of the word as true + vernacular; it has never happened to me to notice one. Many words have + very common uses which are not old. Take the following from Nichols + (<i>Anecd.</i> ix. 263): "Lord Thurlow presents his best respects to Mr. + and Mrs. Thicknesse, and assures them that he knows of no cause to + complain of any part of Mr. Thicknesse's carriage; least of all the + circumstance of sending the head to Ormond Street." Surely Mr. T. had + lent Lord T. a satisfactory carriage with a movable head, and the above + is a polite answer to inquiries. Not a bit of it! <i>carriage</i> is here + <i>conduct</i>, and the <i>head</i> is a <i>bust</i>. The vehicles of the + rich, at the time, were coaches, chariots, chaises, etc., never + carriages, which were rather <i>carts</i>. Gibbon has the word for + baggage-wagons. In Jane Austen's novels the word carriage is + established.</p> + + <p> </p> + +<p class="cenhead">WALSH'S DELUSIONS.</p> + + <p><i>John Walsh</i>,<a name="NtA_591" + href="#Nt_591"><sup>[591]</sup></a> of Cork (1786-1847). This discoverer + has had the honor of a biography from Professor Boole, who, at my + request, collected information about him on the scene of his labors. It + is in the <i>Philosophical Magazine</i> for November, 1851, and will, I + hope, be transferred to some biographical collection where it may find a + larger class of readers. It is the best biography of a single hero of the + kind that I know. Mr. Walsh introduced himself to me, <!-- Page 261 + --><span class="pagenum"><a name="page261"></a>[261]</span>as he did to + many others, in the anterowlandian days of the Post-office; his unpaid + letters were double, treble, &c. They contained his pamphlets, and + cost their weight in silver: all have the name of the author, and all are + in octavo or in quarto letter-form: most are in four pages, and all dated + from Cork. I have the following by me:</p> + +<blockquote class="b1n"> + + <p>The Geometric Base, 1825.—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.</p> + +</blockquote> + + <p>Besides these, there is a <i>Metalogia</i>, and I know not how many + others.</p> + + <p>Mr. Boole,<a name="NtA_592" href="#Nt_592"><sup>[592]</sup></a> who + has taken the moral and social features of Walsh's delusions from the + commiserating point of view, which makes ridicule out of place, has been + obliged to treat Walsh as Scott's Alan Fairford treated his client Peter + Peebles; namely, keep the scarecrow out of court while the case was + argued. My plan requires me to bring him in: and when he comes in at the + door, pity and sympathy fly out at the window. Let the reader remember + that he was not an ignoramus in mathematics: he might have won his spurs + if he could have first served as an esquire. Though so illiterate that + even in Ireland he never picked up anything more Latin than + <i>Irelandus</i>, he was a very pretty mathematician spoiled in the + making by intense self-opinion.</p> + + <p>This is part of a private letter to me at the back of a page of print: + I had never addressed a word to him:</p> + +<p><!-- Page 262 --><span class="pagenum"><a name="page262"></a>[262]</span></p> + + <p>"There are no limits in mathematics, and those that assert there are, + are infinite ruffians, ignorant, lying blackguards. There is no + differential calculus, no Taylor's theorem, no calculus of variations, + &c. in mathematics. There is no quackery whatever in mathematics; no + % equal to anything. What sheer ignorant blackguardism that!</p> + + <p>"In mechanics the parallelogram of forces is quackery, and is + dangerous; for nothing is at rest, or in uniform, or in rectilinear + motion, in the universe. Variable motion is an essential property of + matter. Laplace's demonstration of the parallelogram of forces is a + begging of the question; and the attempts of them all to show that the + difference of twenty minutes between the sidereal and actual revolution + of the earth round the sun arises from the tugging of the Sun and Moon at + the pot-belly of the earth, without being sure even that the earth has a + pot-belly at all, is perfect quackery. The said difference arising from + and demonstrating the revolution of the Sun itself round some distant + center."</p> + + <p>In the letter to Lord Brougham we read as follows:</p> + + <p>"I ask the Royal Society of London, I ask the Saxon crew of that crazy + hulk, where is the dogma of their philosophic god now?... When the Royal + Society of London, and the Academy of Sciences of Paris, shall have read + this memorandum, how will they appear? Like two cur dogs in the paws of + the noblest beast of the forest.... Just as this note was going to press, + a volume lately published by you was put into my hands, wherein you + attempt to defend the fluxions and <i>Principia</i> of Newton. Man! what + are you about? You come forward now with your special pleading, and + fraught with national prejudice, to defend, like the philosopher + Grassi,<a name="NtA_593" href="#Nt_593"><sup>[593]</sup></a> the + persecutor of Galileo, principles <!-- Page 263 --><span + class="pagenum"><a name="page263"></a>[263]</span>and reasoning which, + unless you are actually insane, or an ignorant quack in mathematics, you + know are mathematically false. What a moral lesson this for the students + of the University of London from its head! Man! demonstrate corollary 3, + in this note, by the lying dogma of Newton, or turn your thoughts to + something you understand.</p> + + <p class="author">"<span class="sc">Walsh Irelandus.</span>" + + <p>Mr. Walsh—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:</p> + + <p>(1838.) "Mr. Walsh takes leave to send the enclosed corrected copy to + Mr. Hutton as one of the Council of the University of London, and to save + postage for the Professor of Mathematics there. He will find in it + geometry more deep and subtle, and at the same time more simple and + elegant, than it was ever contemplated human genius could invent."</p> + + <p>He then proceeds to set forth that a certain "tomfoolery lemma," with + its "tomfoolery" superstructure, "never had existence outside the shallow + brains of its inventor," Euclid. He then proceeds thus:</p> + + <p>"The same spirit that animated those philosophers who sent Galileo to + the Inquisition animates all the philosophers of the present day without + exception. If anything can free them from the yoke of error, it is the + [Walsh] problem of double tangence. But free them it will, how deeply + soever they may be sunk into mental slavery—and God knows that is + deeply enough; and they bear it with an admirable grace; for none bear + slavery with a better grace than tyrants. The lads must adopt my + theory.... It will be a sad reverse for all our great professors to be + compelled to become schoolboys in their gray years. But the sore scratch + is to be compelled, as they had before been compelled one thousand years + ago, to have recourse to Ireland for instruction." <!-- Page 264 --><span + class="pagenum"><a name="page264"></a>[264]</span></p> + + <p>The following "Impromptu" is no doubt by Walsh himself: he was more of + a poet than of an astronomer:</p> + + <div class="poem"> + <div class="stanza"> + <p class="i2hg3">"Through ages unfriended,</p> + <p class="i2">With sophistry blended,</p> + <p>Deep science in Chaos had slept;</p> + <p class="i2">Its limits were fettered,</p> + <p class="i2">Its voters unlettered,</p> + <p>Its students in movements but crept.</p> + <p class="i2">Till, despite of great foes,</p> + <p class="i2">Great <span class="sc">Walsh</span> first arose,</p> + <p>And with logical might did unravel</p> + <p class="i2">Those mazes of knowledge,</p> + <p class="i2">Ne'er known in a college,</p> + <p>Though sought for with unceasing travail.</p> + <p class="i2">With cheers we now hail him,</p> + <p class="i2">May success never fail him,</p> + <p>In Polar Geometrical mining;</p> + <p class="i2">Till his foes be as tamed</p> + <p class="i2">As his works are far-famed</p> + <p>For true philosophic refining."</p> + </div> + </div> + <p>Walsh's system is, that all mathematics and physics are wrong: there + is hardly one proposition in Euclid which is demonstrated. His example + ought to warn all who rely on their own evidence to their own success. He + was not, properly speaking, insane; he only spoke his mind more freely + than many others of his class. The poor fellow died in the Cork union, + during the famine. He had lived a happy life, contemplating his own + perfections, like Brahma on the lotus-leaf.<a name="NtA_594" + href="#Nt_594"><sup>[594]</sup></a></p> + +<p><!-- Page 265 --><span class="pagenum"><a name="page265"></a>[265]</span></p> + + <p> </p> + +<p class="cenhead">GROWTH OF FREEDOM OF OPINION.</p> + + <p>The year 1825 brings me to about the middle of my <i>Athenæum</i> + list: that is, so far as mere number of names mentioned is concerned. + Freedom of opinion, beyond a doubt, is gaining ground, for good or for + evil, according to what the speaker happens to think: admission of + authority is no longer made in the old way. If we take soul-cure and + body-cure, divinity and medicine, it is manifest that a change has come + over us. Time was when it was enough that dose or dogma should be + certified by "Il a été ordonné, Monsieur, il a été ordonné,"<a + name="NtA_595" href="#Nt_595"><sup>[595]</sup></a> as the apothecary said + when he wanted to operate upon poor de Porceaugnac. Very much changed: + but whether for good or for evil does not now matter; the question is, + whether contempt of <i>demonstration</i> such as our paradoxers show has + augmented with the rejection of <i>dogmatic authority</i>. It ought to be + just the other way: for the worship of reason is the system on which, if + we trust them, the deniers of guidance ground their plan of life. The + following attempt at an experiment on this point is the best which I can + make; and, so far as I know, the first that ever was made.</p> + + <p>Say that my list of paradoxers divides in 1825: this of itself proves + nothing, because so many of the earlier books are lost, or not likely to + be come at. It would be a fearful rate of increase which would make the + number of paradoxes since 1825 equal to the whole number before that + date. Let us turn now to another collection of mine, arithmetical books, + of which I have published a list. The two collections are similarly + circumstanced as to new and old books; the paradoxes had no care given to + the collection of either; the arithmetical books equal care to both. The + list of arithmetical books, published in 1847, divides at 1735; the + paradoxes, up to 1863, divide at 1825. If we take the process which is + most against the distinction, and allow every year <!-- Page 266 --><span + class="pagenum"><a name="page266"></a>[266]</span>from 1847 to 1863 to + add a year to 1735, we should say that the arithmetical writers divide at + 1751. This rough process may serve, with sufficient certainty, to show + that the proportion of paradoxes to books of sober demonstration is on + the increase; and probably, quite as much as the proportion of + heterodoxes to books of orthodox adherence. So that divinity and medicine + may say to geometry, Don't <i>you</i> sneer: if rationalism, + homœopathy, 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 <i>even</i> yourselves to me: remember that you, Dame Divinity, + have inflicted every kind of penalty, from the stake to the stocks, in + aid of your reasoning; remember that you, Mother Medicine, have not many + years ago applied to Parliament for increase of forcible hindrance of + antipharmacopœal drenches, pills, and powders. Who ever heard of my + asking the legislature to fine blundering circle-squarers? Remember that + the D in dogma is the D in decay; but the D in demonstration is the D in + durability.</p> + + <p> </p> + +<p class="cenhead">THE STATUS OF MEDICINE.</p> + + <p>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 (<i>Examiner</i>, April 5, 1856); which, to my surprise, + I saw reprinted in a medical journal, as a <!-- Page 267 --><span + class="pagenum"><a name="page267"></a>[267]</span>plan not absolutely to + be rejected. I am perfectly satisfied that it would greatly promote true + medical orthodoxy, the predominance of well educated thinkers, and the + development of their desirable differences.</p> + + <p> </p> + + <p>"<span class="sc">Sir.</span> The Medical Bill and the medical + question generally is one on which experience would teach, if people + would be taught.</p> + + <p>"The great soul question took three hundred years to settle: the + little body question might be settled in thirty years, if the decisions + in the former question were studied.</p> + + <p>"Time was when the State believed, as honestly as ever it believed + anything, that it <i>might</i>, <i>could</i>, and <i>should</i> find out + the true doctrine for the poor ignorant community; to which, like a + worthy honest state, it added <i>would</i>. Accordingly, by the + assistance of the Church, which undertook the physic, the surgery, and + the pharmacy of sound doctrine all by itself, it sent forth its legally + qualified teachers into every parish, and woe to the man who called in + any other. They burnt that man, they whipped him, they imprisoned him, + they did everything but what was Christian to him, all for his soul's + health and the amendment of his excesses.</p> + + <p>"But men would not submit. To the argument that the State was a father + to the ignorant, they replied that it was at best the ignorant father of + an ignorant son, and that a blind man could find his way into a ditch + without another blind man to help him. And when the State said—But + here we have the Church, which knows all about it, the ignorant community + declared that it had a right to judge that question, and that it would + judge it. It also said that the Church was never one thing long, and that + it progressed, on the whole, rather more slowly than the ignorant + community.</p> + + <p>"The end of it was, in this country, that every one who chose taught + all who chose to let him teach, on condition only of an open and true + registration. The State was <!-- Page 268 --><span class="pagenum"><a + name="page268"></a>[268]</span>allowed to patronize one particular + Church, so that no one need trouble himself to choose a pastor from the + mere necessity of choosing. But every church is allowed its colleges, its + studies, its diplomas; and every man is allowed his choice. There is no + proof that our souls are worse off than in the sixteenth century; and, + judging by fruits, there is much reason to hope they are better off.</p> + + <p>"Now the little body question is a perfect parallel to the great soul + question in all its circumstances. The only things in which the parallel + fails are the following: Every one who believes in a future state sees + that the soul question is incomparably more important than the body + question, and every one can try the body question by experiment to a + larger extent than the soul question. The proverb, which always has a + spark of truth at the bottom, says that every man of forty is either a + fool or a physician; but did even the proverb maker ever dare to say that + every man is at any age either a fool or a fit teacher of religion?</p> + + <p>"Common sense points out the following settlement of the medical + question: and to this it will come sooner or later.</p> + + <p>"Let every man who chooses—subject to one common law of + manslaughter for all the <i>crass</i> 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.</p> + + <p>"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 <!-- Page 269 --><span + class="pagenum"><a name="page269"></a>[269]</span>which of its own nature + admits of proof be proved, as by the diploma or certificate, &c., + leaving things which cannot be proved, as asserted private study, + intuition, inspiration, &c., to work their own way.</p> + + <p>"Let it be highly penal to assert to the patient any qualification + which is not in the register, and let the register be sold very cheap. + Let the registrar give each registered practitioner a copy of the + register in his own case; let any patient have the power to demand a + sight of this copy; and let no money for attendance be recoverable in any + case in which there has been false representation.</p> + + <p>"Let any party in any suit have a right to produce what medical + testimony he pleases. Let the medical witness produce his register, and + let his evidence be for the jury, as is that of an engineer or a + practitioner of any art which is not attested by diplomas.</p> + + <p>"Let any man who practises without venturing to put his name on the + register be liable to fine and imprisonment.</p> + + <p>"The consequence would be that, as now, anybody who pleases might + practise; for the medical world is well aware that there is no power of + preventing what they call quacks from practising. But very different from + what is now, every man who practises would be obliged to tell the whole + world what his claim is, and would run a great risk if he dared to tell + his patient in private anything different from what he had told the whole + world.</p> + + <p>"The consequence would be that a real education in anatomy, + physiology, chemistry, surgery, and what is known of the thing called + medicine, would acquire more importance than it now has.</p> + + <p>"It is curious to see how completely the medical man of the nineteenth + century squares with the priest of the sixteenth century. The clergy of + all sects are now better divines and better men than they ever were. They + have lost Bacon's reproach that they took a smaller measure of things + than any other educated men; and the physicians are now <!-- Page 270 + --><span class="pagenum"><a name="page270"></a>[270]</span>in this + particular the rearguard of the learned world; though it may be true that + the rear in our day is further on in the march than the van of Bacon's + day. Nor will they ever recover the lost position until medicine is as + free as religion.</p> + + <p>"To this it must come. To this the public, which will decide for + itself, has determined it shall come. To this the public has, in fact, + brought it, but on a plan which it is not desirable to make permanent. We + will be as free to take care of our bodies as of our souls and of our + goods. This is the profession of all who sign as I do, and the practice + of most of those who would not like the name</p> + + <p class="author">"<span class="sc">Heteropath</span>." + + <p> </p> + +<blockquote class="b1n"> + + <p>The motion of the Sun in the Ecliptic, proved to be uniform in a + circular orbit ... with preliminary observations on the fallacy of the + Solar System. By Bartholomew Prescott,<a name="NtA_596" + href="#Nt_596"><sup>[596]</sup></a> 1825, 8vo.</p> + +</blockquote> + + <p>The author had published, in 1803, a <i>Defence of the Divine + System</i>, which I never saw; also, <i>On the inverted scheme of + Copernicus</i>. The above work is clever in its satire.</p> + + <p> </p> + +<p class="cenhead">THE CHRISTIAN EVIDENCE SOCIETY.</p> + +<blockquote class="b1n"> + + <p>Manifesto of the Christian Evidence Society, established Nov. 12, + 1824. Twenty-four plain questions to honest men.</p> + +</blockquote> + + <p>These are two broadsides of August and November, 1826, signed by + Robert Taylor,<a name="NtA_597" href="#Nt_597"><sup>[597]</sup></a> A.B., + Orator of the Christian Evidence Society. This gentleman was a clergyman, + <!-- Page 271 --><span class="pagenum"><a + name="page271"></a>[271]</span>and was convicted of blasphemy in 1827, + for which he suffered imprisonment, and got the name of the <i>Devil's + Chaplain</i>. The following are quotations:</p> + + <p>"For the book of Revelation, there was no original Greek at all, but + <i>Erasmus</i> wrote it himself in Switzerland, in the year 1516. Bishop + Marsh,<a name="NtA_598" href="#Nt_598"><sup>[598]</sup></a> vol. i. p. + 320."—"Is not God the author of your reason? Can he then be the + author of anything which is contrary to your reason? If reason be a + sufficient guide, why should God give you any other? if it be not a + sufficient guide, why has he given you <i>that</i>?"</p> + + <p>I remember a votary of the Society being asked to substitute for + <i>reason</i> "the right leg," and for <i>guide</i> "support," and to + answer the two last questions: he said there must be a quibble, but he + did not see what. It is pleasant to reflect that the <i>argumentum à + carcere</i><a name="NtA_599" href="#Nt_599"><sup>[599]</sup></a> is + obsolete. One great defect of it was that it did not go far enough: there + should have been laws against subscriptions for blasphemers, against + dealing at their shops, and against rich widows marrying them.</p> + + <p>Had I taken in theology, I must have entered books against + Christianity. I mention the above, and Paine's <i>Age of Reason</i>, + simply because they are the only English modern works that ever came in + my way without my asking for them. The three parts of the <i>Age of + Reason</i> were published in Paris 1793, Paris 1795, and New York 1807. + Carlile's<a name="NtA_600" href="#Nt_600"><sup>[600]</sup></a> edition is + of London, 1818, 8vo. It must be republished when the time comes, to show + what stuff governments and clergy were afraid of at the beginning of this + century. I should never have seen the book, if it <!-- Page 272 --><span + class="pagenum"><a name="page272"></a>[272]</span>had not been + prohibited: a bookseller put it under my nose with a fearful look round + him; and I could do no less, in common curiosity, than buy a work which + had been so complimented by church and state. And when I had read it, I + said in my mind to church and state,—Confound you! you have taken + me in worse than any reviewer I ever met with. I forget what I gave for + the book, but I ought to have been able to claim compensation + somewhere.</p> + + <p> </p> + +<p class="cenhead">THE CABBALA.</p> + +<blockquote class="b1n"> + + <p>Cabbala Algebraica. Auctore Gul. Lud. Christmann.<a name="NtA_601" + href="#Nt_601"><sup>[601]</sup></a> Stuttgard, 1827, 4to.</p> + +</blockquote> + + <p>Eighty closely printed pages of an attempt to solve equations of every + degree, which has a process called by the author <i>cabbala</i>. An + anonymous correspondent spells <i>cabbala</i> as follows, <span + title="chabball" class="grk" + >χαββαλλ</span>, and makes 666 + out of its letters. This gentleman has sent me since my Budget commenced, + a little heap of satirical communications, each having a 666 or two; for + instance, alluding to my remarks on the spelling of <i>chemistry</i>, he + finds the fated number in <span title="chimeia" class="grk" + >χιμεια</span>. With these are challenges + to explain them, and hints about the end of the world. All these letters + have different fantastic seals; one of them with the legend "keep your + temper,"—another bearing "bank token five pence." The only + signature is a triangle with a little circle in it, which I interpret to + mean that the writer confesses himself to be the round man stuck in the + three-cornered hole, to be explained as in Sydney Smith's joke.</p> + +<p><!-- Page 273 --><span class="pagenum"><a name="page273"></a>[273]</span></p> + + <p>There is a kind of Cabbala Alphabetica which the investigators of the + numerals in words would do well to take up: it is the formation of + sentences which contain all the letters of the alphabet, and each only + once. No one has done it with <i>v</i> and <i>j</i> treated as + consonants; but you and I can do it. Dr. Whewell<a name="NtA_602" + href="#Nt_602"><sup>[602]</sup></a> and I amused ourselves, some years + ago, with attempts. He could not make sense, though he joined words: he + gave me</p> + + <div class="poem"> + <div class="stanza"> + <p>Phiz, styx, wrong, buck, flame, quid.</p> + </div> + </div> + <p>I gave him the following, which he agreed was "admirable sense": I + certainly think the words would never have come together except in this + way:</p> + + <div class="poem"> + <div class="stanza"> + <p>I, quartz pyx, who fling muck beds.</p> + </div> + </div> + <p>I long thought that no human being could say this under any + circumstances. At last I happened to be reading a religious + writer—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.</p> + + <p>I can find no circumstances for the following, which I received from + another:</p> + + <div class="poem"> + <div class="stanza"> + <p>Fritz! quick! land! hew gypsum box.</p> + </div> + </div> + <p>From other quarters I have the following:</p> + + <div class="poem"> + <div class="stanza"> + <p>Dumpy quiz! whirl back fogs next.</p> + </div> + </div> + <p>This might be said in time of haze to the queer little figure in the + Dutch weather-toy, which comes out or goes in with the change in the + atmosphere. Again,</p> + +<p><!-- Page 274 --><span class="pagenum"><a name="page274"></a>[274]</span></p> + + <div class="poem"> + <div class="stanza"> + <p>Export my fund! Quiz black whigs.</p> + </div> + </div> + <p>This Squire Western might have said, who was always afraid of the + whigs sending the sinking-fund over to Hanover. But the following is the + best: it is good advice to a young man, very well expressed under the + circumstances:</p> + + <div class="poem"> + <div class="stanza"> + <p>Get nymph; quiz sad brow; fix luck.</p> + </div> + </div> + <p>Which in more sober English would be, Marry; be cheerful; watch your + business. There is more edification, more religion in this than in all + the 666-interpretations put together.</p> + + <p>Such things would make excellent writing copies, for they secure + attention to every letter; <i>v</i> and <i>j</i> might be placed at the + end.</p> + + <p> </p> + +<p class="cenhead">ON GODFREY HIGGINS.</p> + +<blockquote class="b1n"> + + <p>The Celtic Druids. By Godfrey Higgins,<a name="NtA_603" + href="#Nt_603"><sup>[603]</sup></a> Esq. of Skellow Grange, near + Doncaster. London, 1827, 4to.</p> + + <p>Anacalypsis, or an attempt to draw aside the veil of the Saitic Isis: + or an inquiry into the origin of languages, nations, and religions. By + Godfrey Higgins, &c..., London, 1836, 2 vols. 4to.</p> + +</blockquote> + + <p>The first work had an additional preface and a new index in 1829. + Possibly, in future time, will be found bound up with copies of the + second work two sheets which Mr. Higgins circulated among his friends in + 1831: the first a "Recapitulation," the second "Book vi. ch. 1."</p> + + <p>The system of these works is that—</p> + + <p>"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."</p> + +<p><!-- Page 275 --><span class="pagenum"><a name="page275"></a>[275]</span></p> + + <p>These works contain an immense quantity of learning, very honestly put + together. I presume the enormous number of facts, and the goodness of the + index, to be the reasons why the <i>Anacalypsis</i> found a permanent + place in the <i>old</i> reading-room of the British Museum, even before + the change which greatly increased the number of books left free to the + reader in that room.</p> + + <p>Mr. Higgins, whom I knew well in the last six years of his life, and + respected as a good, learned, and (in his own way) <i>pious</i> man, was + thoroughly and completely the man of a system. He had that sort of mental + connection with his theory that made his statements of his authorities + trustworthy: for, besides perfect integrity, he had no bias towards + alteration of facts: he saw his system in the way the fact was presented + to him by his authority, be that what it might.</p> + + <p>He was very sure of a fact which he got from any of his authorities: + nothing could shake him. Imagine a conversation between him and an Indian + officer who had paid long attention to Hindoo antiquities and their + remains: a third person was present, <i>ego qui scribo</i>. <i>G. H.</i> + "You know that in the temples of I-forget-who the Ceres is always + sculptured precisely as in Greece." <i>Col.</i> ——, "I really + do not remember it, and I have seen most of these temples." <i>G. H.</i> + "It is so, I assure you, especially at I-forget-where." <i>Col.</i> + ——, "Well, I am sure! I was encamped for six weeks at the + gate of that very temple, and, except a little shooting, had nothing to + do but to examine its details, which I did, day after day, and I found + nothing of the kind." It was of no use at all.</p> + + <p>Godfrey Higgins began life by exposing and conquering, at the expense + of two years of his studies, some shocking abuses which existed in the + York Lunatic Asylum. This was a proceeding which called much attention to + the treatment of the insane, and produced much good effect. He was very + resolute and energetic. The magistracy of his <!-- Page 276 --><span + class="pagenum"><a name="page276"></a>[276]</span>time had such scruples + about using the severity of law to people of such station as well-to-do + farmers, &c.: they would allow a great deal of resistance, and + endeavor to mollify the rebels into obedience. A young farmer flatly + refused to pay under an order of affiliation made upon him by Godfrey + Higgins. He was duly warned; and persisted: he shortly found himself in + gaol. He went there sure to conquer the Justice, and the first thing he + did was to demand to see his lawyer. He was told, to his horror, that as + soon as he had been cropped and prison-dressed, he might see as many + lawyers as he pleased, to be looked at, laughed at, and advised that + there was but one way out of the scrape. Higgins was, in his + speculations, a regular counterpart of Bailly; but the celebrated Mayor + of Paris had not his nerve. It was impossible to say, if their characters + had been changed, whether the unfortunate crisis in which Bailly was not + equal to the occasion would have led to very different results if Higgins + had been in his place: but assuredly constitutional liberty would have + had one chance more. There are two works of his by which he was known, + apart from his paradoxes. First, <i>An apology for the life and character + of the celebrated prophet of Arabia, called Mohamed, or the + Illustrious</i>. London, 8vo. 1829. The reader will look at this writing + of our English Buddhist with suspicious eye, but he will not be able to + avoid confessing that the Arabian prophet has some reparation to demand + at the hands of Christians. Next, <i>Horæ Sabaticæ; or an attempt to + correct certain superstitions and vulgar errors respecting the + Sabbath</i>. Second edition, with a large appendix. London, 12mo. 1833. + This book was very heterodox at the time, but it has furnished material + for some of the clergy of our day.</p> + + <p>I never could quite make out whether Godfrey Higgins took that system + which he traced to the Buddhists to have a Divine origin, or to be the + result of good men's meditations. Himself a strong theist, and believer + in a future <!-- Page 277 --><span class="pagenum"><a + name="page277"></a>[277]</span>state, one would suppose that he would + refer a <i>universal</i> religion, spread in different forms over the + whole earth from one source, directly to the universal Parent. And this I + suspect he did, whether he knew it or not. The external evidence is + balanced. In his preface he says:</p> + + <p>"I cannot help smiling when I consider that the priests have objected + to admit my former book, <i>The Celtic Druids</i>, into libraries, + because it was antichristian; and it has been attacked by Deists, because + it was superfluously religious. The learned Deist, the Rev. R. Taylor + [already mentioned], has designated me as the <i>religious</i> Mr. + Higgins."</p> + + <p>The time will come when some profound historian of literature will + make himself much clearer on the point than I am.</p> + + <p> </p> + +<p class="cenhead">ON POPE'S DIPPING NEEDLE.</p> + +<blockquote class="b1n"> + + <p>The triumphal Chariot of Friction: or a familiar elucidation of the + origin of magnetic attraction, &c. &c. By William Pope.<a + name="NtA_604" href="#Nt_604"><sup>[604]</sup></a> London, 1829, 4to.</p> + +</blockquote> + + <p>Part of this work is on a dipping-needle of the author's construction. + It must have been under the impression that a book of naval magnetism was + proposed, that a great many officers, the Royal Naval Club, etc. lent + their names to the subscription list. How must they have been surprised + to find, right opposite to the list of subscribers, the plate presenting + "the three emphatic letters, J. 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 <i>moral</i>, until Lucifer <i>churned</i> it into + <i>physical</i> "as far as the third circle in Deity": this Lucifer, + called Leviathan in Job, being thus the moving cause of <!-- Page 278 + --><span class="pagenum"><a name="page278"></a>[278]</span>chaos. I shall + say no more, except that the friction of the air is the cause of + magnetism.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Remarks on the Architecture, Sculpture, and Zodiac of Palmyra; with a + Key to the Inscriptions. By B. Prescot.<a name="NtA_605" + href="#Nt_605"><sup>[605]</sup></a> London, 1830, 8vo.</p> + +</blockquote> + + <p>Mr. Prescot gives the signs of the zodiac a Hebrew origin.</p> + + <p> </p> + +<p class="cenhead">THE JACOTOT METHOD.</p> + +<blockquote class="b1n"> + + <p>Epitomé de mathématiques. Par F. Jacotot,<a name="NtA_606" + href="#Nt_606"><sup>[606]</sup></a> Avocat. 3ième edition, Paris, 1830, + 8vo. (pp. 18).</p> + + <p>Méthode Jacotot. Choix de propositions mathématiques. Par P. Y. + Séprés.<a name="NtA_607" href="#Nt_607"><sup>[607]</sup></a> 2nde + édition. Paris, 1830, 8vo. (pp. 82).</p> + +</blockquote> + + <p>Of Jacotot's method, which had some vogue in Paris, the principle was + <i>Tout est dans tout</i>,<a name="NtA_608" + href="#Nt_608"><sup>[608]</sup></a> and the process <i>Apprendre quelque + chose, et à y rapporter tout le reste</i>.<a name="NtA_609" + href="#Nt_609"><sup>[609]</sup></a> The first tract has a proposition in + conic sections and its preliminaries: the second has twenty exercises, of + which the first is finding the greatest common measure of two numbers, + and the last is the motion of a point on a surface, acted on by given + forces. This is topped up with the problem of sound in a tube, and a + slice of Laplace's theory of the tides. All to be studied until known by + heart, and all the rest will come, or at least join on easily when it + comes. There is much truth in the assertion that new knowledge <!-- Page + 279 --><span class="pagenum"><a name="page279"></a>[279]</span>hooks on + easily to a little of the old, thoroughly mastered. The day is coming + when it will be found out that crammed erudition, got up for + examinations, does not cast out any hooks for more.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Lettre à MM. les Membres de l'Académie Royale des Sciences, contenant + un développement de la réfutation du système de la gravitation + universelle, qui leur a été présentée le 30 août, 1830. Par Félix + Passot.<a name="NtA_610" href="#Nt_610"><sup>[610]</sup></a> Paris, 1830, + 8vo.</p> + +</blockquote> + + <p>Works of this sort are less common in France than in England. In + France there is only the Academy of Sciences to go to: in England there + is a reading public out of the Royal Society, &c.</p> + + <p> </p> + +<p class="cenhead">A DISCOURSE ON PROBABILITY.</p> + + <p>About 1830 was published, in the <i>Library of Useful Knowledge</i>, + the tract on <i>Probability</i>, the joint work of the late Sir John + Lubbock<a name="NtA_611" href="#Nt_611"><sup>[611]</sup></a> and Mr. + Drinkwater (Bethune).<a name="NtA_612" + href="#Nt_612"><sup>[612]</sup></a> It is one of the best elementary + openings of the subject. A binder put my name on the outside (the work + was anonymous) and the consequence was that nothing could drive out of + people's heads that it was written by me. I do not know how many denials + I have made, from a passage in one of my own works to a letter in the + <i>Times</i>: and I am not sure that I have succeeded in establishing the + truth, even now. I accordingly note the fact once more. But as a book has + no right here unless it contain a paradox—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 <i>probability</i>, should be used; and I hold him quite + right.</p> + +<p><!-- Page 280 --><span class="pagenum"><a name="page280"></a>[280]</span></p> + + <p>The second case was this: My friend Sir J. L., with a large cluster of + intellectual qualities, and another of social qualities, had one point of + character which I will not call bad and cannot call good; he never used a + slang expression. To such a length did he carry his dislike, that he + could not bear <i>head</i> and <i>tail</i>, even in a work on games of + chance: so he used <i>obverse</i> and <i>reverse</i>. I stared when I + first saw this: but, to my delight, I found that the force of + circumstances beat him at last. He was obliged to take an example from + the race-course, and the name of one of the horses was <i>Bessy + Bedlam</i>! And he did not put her down as <i>Elizabeth Bethlehem</i>, + but forced himself to follow the jockeys.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>[Almanach Romain sur la Loterie Royale de France, ou les Etrennes + nécessaires aux Actionnaires et Receveurs de la dite Loterie. Par M. + Menut de St.-Mesmin. Paris, 1830. 12mo.</p> + +</blockquote> + + <p>This book contains all the drawings of the French lottery (two or + three, each month) from 1758 to 1830. It is intended for those who + thought they could predict the future drawings from the past: and various + sets of <i>sympathetic</i> numbers are given to help them. The principle + is, that anything which has not happened for a long time must be soon to + come. At <i>rouge et noir</i>, for example, when the red has won five + times running, sagacious gamblers stake on the black, for they think the + turn which must come at last is nearer than it was. So it is: but + observation would have shown that if a large number of those cases had + been registered which show a run of five for the red, the next game would + just as often have made the run into six as have turned in favor of the + black. But the gambling reasoner is incorrigible: if he would but take to + squaring the circle, what a load of misery would be saved. A writer of + 1823, who appeared to be thoroughly acquainted with the gambling of Paris + and London, says that the gamesters by <!-- Page 281 --><span + class="pagenum"><a name="page281"></a>[281]</span>profession are haunted + by a secret foreboding of their future destruction, and seem as if they + said to the banker at the table, as the gladiators said to the emperor, + <i>Morituri te salutant</i>.<a name="NtA_613" + href="#Nt_613"><sup>[613]</sup></a></p> + + <p>In the French lottery, five numbers out of ninety were drawn at a + time. Any person, in any part of the country, might stake any sum upon + any event he pleased, as that 27 should be drawn; that 42 and 81 should + be drawn; that 42 and 81 should be drawn, and 42 first; and so on up to a + <i>quine déterminé</i>, if he chose, which is betting on five given + numbers in a given order. Thus, in July, 1821, one of the drawings + was</p> + + <div class="poem"> + <div class="stanza"> + <p>8 46 16 64 13.</p> + </div> + </div> + <p>A gambler had actually predicted the five numbers (but not their + order), and won 131,350 francs on a trifling stake. M. Menut seems to + insinuate that the hint what numbers to choose was given at his own + office. Another won 20,852 francs on the quaterne, 8, 16, 46, 64, in this + very drawing. These gains, of course, were widely advertised: of the + multitudes who lost nothing was said. The enormous number of those who + played is proved to all who have studied chances arithmetically by the + numbers of simple quaternes which were gained: in 1822, fourteen; in + 1823, six; in 1824, sixteen; in 1825, nine, &c.</p> + + <p>The paradoxes of what is called chance, or hazard, might themselves + make a small volume. All the world understands that there is a long run, + a general average; but great part of the world is surprised that this + general average should be computed and predicted. There are many + remarkable cases of verification; and one of them relates to the + quadrature of the circle. I give some account of this and another. Throw + a penny time after time until <i>head</i> arrives, which it will do + before long: let this be called a <i>set</i>. Accordingly, H is the + smallest set, TH the next smallest, then TTH, &c. For abbreviation, + let a set in which seven <i>tails</i> <!-- Page 282 --><span + class="pagenum"><a name="page282"></a>[282]</span>occur before + <i>head</i> turns up be T<sup>7</sup>H. In an immense number of trials of + sets, about half will be H; about a quarter TH; about an eighth, + T<sup>2</sup>H. Buffon<a name="NtA_614" + href="#Nt_614"><sup>[614]</sup></a> tried 2,048 sets; and several have + followed him. It will tend to illustrate the principle if I give all the + results; namely, that many trials will with moral certainty show an + approach—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.</p> + +<table class="nobctr" summary="Coin tossing trials" title="Coin tossing trials"> +<tr><td>H</td><td align="right">1,024</td><td align="right">1,061</td><td align="right">1,048</td><td align="right">1,017</td><td align="right">1,039</td></tr> +<tr><td>TH</td><td align="right">512</td><td align="right">494</td><td align="right">507</td><td align="right">547</td><td align="right">480</td></tr> +<tr><td>T<sup>2</sup>H</td><td align="right">256</td><td align="right">232</td><td align="right">248</td><td align="right">235</td><td align="right">267</td></tr> +<tr><td>T<sup>3</sup>H</td><td align="right">128</td><td align="right">137</td><td align="right">99</td><td align="right">118</td><td align="right">126</td></tr> +<tr><td>T<sup>4</sup>H</td><td align="right">64</td><td align="right">56</td><td align="right">71</td><td align="right">72</td><td align="right">67</td></tr> +<tr><td>T<sup>5</sup>H</td><td align="right">32</td><td align="right">29</td><td align="right">38</td><td align="right">32</td><td align="right">33</td></tr> +<tr><td>T<sup>6</sup>H</td><td align="right">16</td><td align="right">25</td><td align="right">17</td><td align="right">10</td><td align="right">19</td></tr> +<tr><td>T<sup>7</sup>H</td><td align="right">8</td><td align="right">8</td><td align="right">9</td><td align="right">9</td><td align="right">10</td></tr> +<tr><td>T<sup>8</sup>H</td><td align="right">4</td><td align="right">6</td><td align="right">5</td><td align="right">3</td><td align="right">3</td></tr> +<tr><td>T<sup>9</sup>H</td><td align="right">2</td><td align="right"> </td><td align="right">3</td><td align="right">2</td><td align="right">4</td></tr> +<tr><td>T<sup>10</sup>H</td><td align="right">1</td><td align="right"> </td><td align="right">1</td><td align="right">1</td></tr> +<tr><td>T<sup>11</sup>H</td><td align="right"> </td><td align="right"> </td><td align="right">0</td><td align="right">1</td></tr> +<tr><td>T<sup>12</sup>H</td><td align="right"> </td><td align="right"> </td><td align="right">0</td><td align="right">0</td></tr> +<tr><td>T<sup>13</sup>H</td><td align="right">1</td><td align="right"> </td><td align="right">1</td><td align="right">0</td></tr> +<tr><td>T<sup>14</sup>H</td><td align="right"> </td><td align="right"> </td><td align="right">0</td><td align="right">0</td></tr> +<tr><td>T<sup>15</sup>H</td><td align="right"> </td><td align="right"> </td><td align="right">1</td><td align="right">1</td></tr> +<tr><td>&c.</td><td align="right"> </td><td align="right"> </td><td align="right">0</td><td align="right">0</td></tr> +<tr><td> </td><td align="right">——</td><td align="right">——</td><td align="right">——</td><td align="right">——</td><td align="right">——</td></tr> +<tr><td> </td><td align="right"> 2,048</td><td align="right"> 2,048</td><td align="right"> 2,048</td><td align="right"> 2,048</td><td align="right"> 2,048</td></tr> +</table> + +<p><!-- Page 283 --><span class="pagenum"><a name="page283"></a>[283]</span></p> + + <p>In very many trials, then, we may depend upon something like the + predicted average. Conversely, from many trials we may form a guess at + what the average will be. Thus, in Buffon's experiment the 2,048 first + throws of the sets gave <i>head</i> in 1,061 cases: we have a right to + infer that in the long run something like 1,061 out of 2,048 is the + proportion of heads, even before we know the reasons for the equality of + chance, which tell us that 1,024 out of 2,048 is the real truth. I now + come to the way in which such considerations have led to a mode in which + mere pitch-and-toss has given a more accurate approach to the quadrature + of the circle than has been reached by some of my paradoxers. What would + my friend<a name="NtA_615" href="#Nt_615"><sup>[615]</sup></a> in No. 14 + have said to this? The method is as follows: Suppose a planked floor of + the usual kind, with thin visible seams between the planks. Let there be + a thin straight rod, or wire, not so long as the breadth of the plank. + This rod, being tossed up at hazard, will either fall quite clear of the + seams, or will lay across one seam. Now Buffon, and after him Laplace, + proved the following: That in the long run the fraction of the whole + number of trials in which a seam is intersected will be the fraction + which twice the length of the rod is of the circumference of the circle + having the breadth of a plank for its diameter. In 1855 Mr. + <i>Ambrose</i> Smith, of Aberdeen, made 3,204 trials with a rod + three-fifths of the distance between the planks: there were 1,213 clear + intersections, and 11 contacts on which it was difficult to decide. + Divide these contacts equally, and we have 1,218½ to 3,204 for the ratio + of 6 to 5<span class="grk">π</span>, presuming that the greatness of + the number of trials gives something near to the final average, or result + in the long run: this gives <span class="grk">π</span> = 3.1553. If + all the 11 contacts had been treated as intersections, the result would + have been <!-- Page 284 --><span class="pagenum"><a + name="page284"></a>[284]</span><span class="grk">π</span> = 3.1412, + exceedingly near. A pupil of mine made 600 trials with a rod of the + length between the seams, and got <span class="grk">π</span> = + 3.137.</p> + + <p>This method will hardly be believed until it has been repeated so + often that "there never could have been any doubt about it."</p> + + <p>The first experiment strongly illustrates a truth of the theory, well + confirmed by practice: whatever can happen will happen if we make trials + enough. Who would undertake to throw tail eight times running? + Nevertheless, in the 8,192 sets tail 8 times running occurred 17 times; 9 + times running, 9 times; 10 times running, twice; 11 times and 13 times, + each once; and 15 times twice.]</p> + + <p> </p> + +<p class="cenhead">ON CURIOSITIES OF <span class="grk">π</span>.</p> + + <p>1830. The celebrated interminable fraction 3.14159..., which the + mathematician calls <span class="grk">π</span>, is the ratio of the + circumference to the diameter. But it is thousands of things besides. It + is constantly turning up in mathematics: and if arithmetic and algebra + had been studied without geometry, <span class="grk">π</span> must + have come in somehow, though at what stage or under what name must have + depended upon the casualties of algebraical invention. This will readily + be seen when it is stated that <span class="grk">π</span> is nothing + but four times the series</p> + + <div class="poem"> + <div class="stanza"> + <p>1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...</p> + </div> + </div> + <p><i>ad infinitum</i>.<a name="NtA_616" + href="#Nt_616"><sup>[616]</sup></a> It would be wonderful if so simple a + series <!-- Page 285 --><span class="pagenum"><a + name="page285"></a>[285]</span>had but one kind of occurrence. As it is, + our trigonometry being founded on the circle, <span + class="grk">π</span> first appears as the ratio stated. If, for + instance, a deep study of probable fluctuation from average had preceded, + <span class="grk">π</span> might have emerged as a number perfectly + indispensable in such problems as: What is the chance of the number of + aces lying between a million + <i>x</i> and a million - <i>x</i>, when + six million of throws are made with a die? I have not gone into any + detail of all those cases in which the paradoxer finds out, by his + unassisted acumen, that results of mathematical investigation <i>cannot + be</i>: in fact, this discovery is only an accompaniment, though a + necessary one, of his paradoxical statement of that which <i>must be</i>. + Logicians are beginning to see that the notion of <i>horse</i> is + inseparably connected with that of <i>non-horse</i>: that the first + without the second would be no notion at all. And it is clear that the + positive affirmation of that which contradicts mathematical demonstration + cannot but be accompanied by a declaration, mostly overtly made, that + demonstration is false. If the mathematician were interested in punishing + this indiscretion, he could make his denier ridiculous by inventing + asserted results which would completely take him in.</p> + + <p>More than thirty years ago I had a friend, now long gone, who was a + mathematician, but not of the higher branches: he was, <i>inter alia</i>, + thoroughly up in all that relates to mortality, life assurance, &c. + One day, explaining to him how it should be ascertained what the chance + is of the survivors of a large number of persons now alive lying between + given limits of number at the end of a certain time, I came, of course + upon the introduction of <span class="grk">π</span>, which I could + only describe as the ratio of the circumference of a circle to its + diameter. "Oh, my dear friend! that must be a delusion; what can the + circle have to do with the numbers alive at the end of a given + time?"—"I cannot demonstrate it to you; but it is + demonstrated."—"Oh! stuff! I think you can prove anything with your + differential calculus: figment, <!-- Page 286 --><span class="pagenum"><a + name="page286"></a>[286]</span>depend upon it." I said no more; but, a + few days afterwards, I went to him and very gravely told him that I had + discovered the law of human mortality in the Carlisle Table, of which he + thought very highly. I told him that the law was involved in this + circumstance. Take the table of expectation of life, choose any age, take + its expectation and make the nearest integer a new age, do the same with + that, and so on; begin at what age you like, you are sure to end at the + place where the age past is equal, or most nearly equal, to the + expectation to come. "You don't mean that this always + happens?"—"Try it." He did try, again and again; and found it as I + said. "This is, indeed, a curious thing; this <i>is</i> a discovery." I + might have sent him about trumpeting the law of life: but I contented + myself with informing him that the same thing would happen with any table + whatsoever in which the first column goes up and the second goes down; + and that if a proficient in the higher mathematics chose to palm a + figment upon him, he could do without the circle: <i>à corsaire, corsaire + et demi</i>,<a name="NtA_617" href="#Nt_617"><sup>[617]</sup></a> the + French proverb says. "Oh!" it was remarked, "I see, this was Milne!"<a + name="NtA_618" href="#Nt_618"><sup>[618]</sup></a> It was <i>not</i> + Milne: I remember well showing the formula to him some time afterwards. + He raised no difficulty about <span class="grk">π</span>; he knew the + forms of Laplace's results, and he was much interested. Besides, Milne + never said stuff! and figment! And he would not have been taken in: he + would have quietly tried it with the Northampton and all the other + tables, and would have got at the truth.</p> + +<p><!-- Page 287 --><span class="pagenum"><a name="page287"></a>[287]</span></p> + + <p> </p> + +<p class="cenhead">EUCLID WITHOUT AXIOMS.</p> + +<blockquote class="b1n"> + + <p>The first book of Euclid's Elements. With alterations and familiar + notes. Being an attempt to get rid of axioms altogether; and to establish + the theory of parallel lines, without the introduction of any principle + not common to other parts of the elements. By a member of the University + of Cambridge. Third edition. In usum serenissimæ filiolæ. London, + 1830.</p> + +</blockquote> + + <p>The author was Lieut. Col. (now General) Perronet Thompson,<a + name="NtA_619" href="#Nt_619"><sup>[619]</sup></a> the author of the + "Catechism on the Corn Laws." I reviewed the fourth edition—which + had the name of "Geometry without Axioms," 1833—in the quarterly + <i>Journal of Education</i> for January, 1834. Col. Thompson, who then + was a contributor to—if not editor of—the <i>Westminster + Review</i>, replied in an article the authorship of which could not be + mistaken.</p> + + <p>Some more attempts upon the problem, by the same author, will be found + in the sequel. They are all of acute and legitimate speculation; but they + do not conquer the difficulty in the manner demanded by the conditions of + the problem. The paradox of parallels does not contribute much to my + pages: its cases are to be found for the most part in geometrical + systems, or in notes to them. Most of them consist in the proposal of + additional postulates; some are attempts to do without any new postulate. + Gen. Perronet Thompson, whose paradoxes are always constructed on much + study of previous writers, has collected in the work above named, a + budget of attempts, the heads of which are in the <i>Penny</i> and + <i>English Cyclopædias</i>, at "Parallels." He has given thirty + instances, selected from what he had found.<a name="NtA_620" + href="#Nt_620"><sup>[620]</sup></a></p> + +<p><!-- Page 288 --><span class="pagenum"><a name="page288"></a>[288]</span></p> + + <p>Lagrange,<a name="NtA_621" href="#Nt_621"><sup>[621]</sup></a> in one + of the later years of his life, imagined that he had overcome the + difficulty. He went so far as to write a paper, which he took with him to + the Institute, and began to read it. But in the first paragraph something + struck him which he had not observed: he muttered <i>Il faut que j'y + songe encore</i>,<a name="NtA_622" href="#Nt_622"><sup>[622]</sup></a> + and put the paper in his pocket.</p> + + <p> </p> + +<p class="cenhead">THE LUNAR CAUSTIC JOKE.</p> + + <p>The following paragraph appeared in the <i>Morning Post</i>, May 4, + 1831:</p> + + <p>"We understand that although, owing to circumstances with which the + public are not concerned, Mr. Goulburn<a name="NtA_623" + href="#Nt_623"><sup>[623]</sup></a> declined becoming a candidate for + University honors, that his scientific attainments are far from + inconsiderable. He is well known to be the author of an essay in the + Philosophical Transactions on the accurate rectification of a circular + arc, and of an investigation of the equation of a lunar caustic—a + problem likely to become of great use in nautical astronomy."</p> + +<p><!-- Page 289 --><span class="pagenum"><a name="page289"></a>[289]</span></p> + + <p>This hoax—which would probably have succeeded with any + journal—was palmed upon the <i>Morning Post</i>, which supported + Mr. Goulburn, by some Cambridge wags who supported Mr. Lubbock, the other + candidate for the University of Cambridge. Putting on the usual + concealment, I may say that I always suspected Dr-nkw-t-r B-th-n-<a + name="NtA_624" href="#Nt_624"><sup>[624]</sup></a> of having a share in + the matter. The skill of the hoax lies in avoiding the words "quadrature + of the circle," which all know, and speaking of "the accurate + rectification of a circular arc," which all do not know for its synonyme. + The <i>Morning Post</i> next day gave a reproof to hoaxers in general, + without referring to any particular case. It must be added, that although + there are <i>caustics</i> in mathematics, there is no <i>lunar</i> + caustic.</p> + + <p>So far as Mr. Goulburn was concerned, the above was poetic justice. He + was the minister who, in old time, told a deputation from the + Astronomical Society that the Government "did not care twopence for all + the science in the country." There may be some still alive who remember + this: I heard it from more than one of those who were present, and are + now gone. Matters are much changed. I was thirty years in office at the + Astronomical Society; and, to my certain knowledge, every Government of + that period, Whig and Tory, showed itself ready to help with influence + when wanted, and with money whenever there was an answer for the House of + Commons. The following correction subsequently appeared. Referring to the + hoax about Mr. Goulburn, Messrs. C. H. and Thompson Cooper<a + name="NtA_625" href="#Nt_625"><sup>[625]</sup></a> have corrected an + error, by stating that the election which gave rise to the hoax was that + in which Messrs. Goulburn <!-- Page 290 --><span class="pagenum"><a + name="page290"></a>[290]</span>and Yates Peel<a name="NtA_626" + href="#Nt_626"><sup>[626]</sup></a> defeated Lord Palmerston<a + name="NtA_627" href="#Nt_627"><sup>[627]</sup></a> and Mr. Cavendish.<a + name="NtA_628" href="#Nt_628"><sup>[628]</sup></a> They add that Mr. + Gunning, the well-known Esquire Bedell of the University, attributed the + hoax to the late Rev. R. Sheepshanks, to whom, they state, are also + attributed certain clever fictitious biographies—of public men, as + I understand it—which were palmed upon the editor of the + <i>Cambridge Chronicle</i>, who never suspected their genuineness to the + day of his death. Being in most confidential intercourse with Mr. + Sheepshanks,<a name="NtA_629" href="#Nt_629"><sup>[629]</sup></a> both at + the time and all the rest of his life (twenty-five years), and never + heard him allude to any such things—which were not in his line, + though he had satirical power of quite another <!-- Page 291 --><span + class="pagenum"><a name="page291"></a>[291]</span>kind—I feel + satisfied he had nothing to do with them. I may add that others, his + nearest friends, and also members of his family, never heard him allude + to these hoaxes as their author, and disbelieve his authorship as much as + I do myself. I say this not as imputing any blame to the true author, + such hoaxes being fair election jokes in all time, but merely to put the + saddle off the wrong horse, and to give one more instance of the + insecurity of imputed authorship. Had Mr. Sheepshanks ever told me that + he had perpetrated the hoax, I should have had no hesitation in giving it + to him. I consider all clever election squibs, free from bitterness and + personal imputation, as giving the multitude good channels for the vent + of feelings which but for them would certainly find bad ones.</p> + + <p>[But I now suspect that Mr. Babbage<a name="NtA_630" + href="#Nt_630"><sup>[630]</sup></a> had some hand in the hoax. He gives + it in his "Passages, &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.<a + name="NtA_631" href="#Nt_631"><sup>[631]</sup></a> Both were on + Cavendish's committee. Mr. Babbage adds, that "late one evening a cab + drove up in hot haste to the office of the <i>Morning Post</i>, delivered + the copy as coming from Mr. Goulburn's committee, and at the same time + ordered fifty extra copies of the <i>Post</i> to be sent next morning to + their committee-room." I think the man—the only one I ever heard + of—who knew all about the cab and the extra copies must have known + more.]</p> + + <p> </p> + +<p class="cenhead">ON M. DEMONVILLE.</p> + + <p><i>Demonville.</i>—A Frenchman's Christian name is his own + secret, unless there be two of the surname. M. Demonville is a very good + instance of the difference between a <!-- Page 292 --><span + class="pagenum"><a name="page292"></a>[292]</span>French and English + discoverer. In England there is a public to listen to discoveries in + mathematical subjects made without mathematics: a public which will hear, + and wonder, and think it possible that the pretensions of the discoverer + have some foundation. The unnoticed man may possibly be right: and the + old country-town reputation which I once heard of, attaching to a man who + "had written a book about the signs of the zodiac which all the + philosophers in London could not answer," is fame as far as it goes. + Accordingly, we have plenty of discoverers who, even in astronomy, + pronounce the learned in error because of mathematics. In France, beyond + the sphere of influence of the Academy of Sciences, there is no one to + cast a thought upon the matter: all who take the least interest repose + entire faith in the Institute. Hence the French discoverer turns all his + thoughts to the Institute, and looks for his only hearing in that + quarter. He therefore throws no slur upon the means of knowledge, but + would say, with M. Demonville: "A l'égard de M. Poisson,<a name="NtA_632" + href="#Nt_632"><sup>[632]</sup></a> j'envie loyalement la millième partie + de ses connaissances mathématiques, pour prouver mon systême d'astronomie + aux plus incrédules."<a name="NtA_633" + href="#Nt_633"><sup>[633]</sup></a> This system is that the only bodies + of our system are the earth, the sun, and the moon; all the others being + illusions, caused by reflection of the sun and moon from the ice of the + polar regions. In mathematics, addition and subtraction are for men; + multiplication and division, which are in truth creation and destruction, + are prerogatives of deity. But <i>nothing</i> multiplied by + <i>nothing</i> is <i>one</i>. M. Demonville obtained an introduction to + William the Fourth, who desired the opinion of the Royal Society upon his + system: the <!-- Page 293 --><span class="pagenum"><a + name="page293"></a>[293]</span>answer was very brief. The King was quite + right; so was the Society: the fault lay with those who advised His + Majesty on a matter they knew nothing about. The writings of M. + Demonville in my possession are as follows.<a name="NtA_634" + href="#Nt_634"><sup>[634]</sup></a> The dates—which were only on + covers torn off in binding—were about 1831-34:</p> + + <p><i>Petit cours d'astronomie</i><a name="NtA_635" + href="#Nt_635"><sup>[635]</sup></a> followed by <i>Sur l'unité + mathématique.</i>—<i>Principes de la physique de la création + implicitement admis dans la notice sur le tonnerre par M. + Arago.</i>—<i>Question de longitude sur mer.</i><a name="NtA_636" + href="#Nt_636"><sup>[636]</sup></a>—<i>Vrai système du monde</i><a + name="NtA_637" href="#Nt_637"><sup>[637]</sup></a> (pp. 92). Same title, + four pages, small type. Same title, four pages, addressed to the British + Association. Same title, four pages, addressed to M. Mathieu. Same title, + four pages, on M. Bouvard's report.—<i>Résumé de la physique de la + création; troisième partie du vrai système du monde.</i><a name="NtA_638" + href="#Nt_638"><sup>[638]</sup></a></p> + + <p> </p> + +<p class="cenhead">PARSEY'S PARADOX.</p> + +<blockquote class="b1n"> + + <p>The quadrature of the circle discovered, by Arthur Parsey,<a + name="NtA_639" href="#Nt_639"><sup>[639]</sup></a> author of the 'art of + miniature painting.' Submitted to the consideration of the Royal Society, + on whose protection the author humbly throws himself. London, 1832, + 8vo.</p> + +</blockquote> + + <p>Mr. Parsey was an artist, who also made himself conspicuous by a new + view of perspective. Seeing that the sides of a tower, for instance, + would appear to meet in a point if the tower were high enough, he thought + that these sides ought to slope to one another in the picture. On this + <!-- Page 294 --><span class="pagenum"><a + name="page294"></a>[294]</span>theory he published a small work, of which + I have not the title, with a Grecian temple in the frontispiece, stated, + if I remember rightly, to be the first picture which had ever been drawn + in true perspective. Of course the building looked very Egyptian, with + its sloping sides. The answer to his notion is easy enough. What is + called the picture is not the picture from which the mind takes its + perception; that picture is on the retina. The <i>intermediate</i> + picture, as it may be called—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 <i>picture-sides</i>, though parallel, would appear to meet + in a point. I never saw this answer given, though I have seen and heard + the remarks of artists on Mr. Parsey's work. I am inclined to think it is + commonly supposed that the artist's picture is the representation which + comes before the mind: this is not true; we might as well say the same of + the object itself. In July 1831, reading an article on squaring the + circle, and finding that there was a difficulty, he set to work, got a + light denied to all mathematicians in—some would say + through—a crack, and advertised in the <i>Times</i> that he had + done the trick. He then prepared this work, in which, those who read it + will see how, he showed that 3.14159... should be 3.0625. He might have + found out his error by <i>stepping</i> a draughtsman's circle with the + compasses.</p> + + <p>Perspective has not had many paradoxes. The only other one I remember + is that of a writer on perspective, whose name I forget, and whose four + pages I do not possess. He circulated remarks on my notes on the subject, + published in the <i>Athenæum</i>, in which he denies that the + stereographic projection is a case of perspective, the reason being that + the whole hemisphere makes too large a picture for the eye conveniently + to grasp at once. That is to say, it is no perspective because there is + too much perspective. <!-- Page 295 --><span class="pagenum"><a + name="page295"></a>[295]</span></p> + + <p> </p> + +<p class="cenhead">ON A COUPLE OF GEOMETRIES.</p> + +<blockquote class="b1n"> + + <p>Principles of Geometry familiarly illustrated. By the Rev. W. + Ritchie,<a name="NtA_640" href="#Nt_640"><sup>[640]</sup></a> LL.D. + London, 1833, 12mo.</p> + + <p>A new Exposition of the system of Euclid's Elements, being an attempt + to establish his work on a different basis. By Alfred Day,<a + name="NtA_641" href="#Nt_641"><sup>[641]</sup></a> LL.D. London, 1839, + 12mo.</p> + +</blockquote> + + <p>These works belong to a small class which have the peculiarity of + insisting that in the general propositions of geometry a proposition + gives its converse: that "Every B is A" follows from "Every A is B." Dr. + Ritchie says, "If it be proved that the equality of two of the angles of + a triangle depends <i>essentially</i> upon the equality of the opposite + sides, it follows that the equality of opposite sides depends + <i>essentially</i> on the equality of the angles." Dr. Day puts it as + follows:</p> + + <p>"That the converses of Euclid, so called, where no particular + limitation is specified or implied in the leading proposition, more than + in the converse, must be necessarily true; for as by the nature of the + reasoning the leading proposition must be universally true, should the + converse be not so, it cannot be so universally, but has at least all the + exceptions conveyed in the leading proposition, and the case is therefore + unadapted to geometric reasoning; or, what is the same thing, by the very + nature of geometric reasoning, the particular exceptions to the extended + converse must be identical with some one or other of the cases under the + universal affirmative proposition with which we set forth, which is + absurd."</p> + +<p><!-- Page 296 --><span class="pagenum"><a name="page296"></a>[296]</span></p> + + <p>On this I cannot help transferring to my reader the words of the Pacha + when he orders the bastinado,—May it do you good! A rational study + of logic is much wanted to show many mathematicians, of all degrees of + proficiency, that there is nothing in the <i>reasoning</i> of mathematics + which differs from other reasoning. Dr. Day repeated his argument in <i>A + Treatise on Proportion</i>, London, 1840, 8vo. Dr. Ritchie was a very + clear-headed man. He published, in 1818, a work on arithmetic, with + rational explanations. This was too early for such an improvement, and + nearly the whole of his excellent work was sold as waste paper. His + elementary introduction to the Differential Calculus was drawn up while + he was learning the subject late in life. Books of this sort are often + very effective on points of difficulty.</p> + + <p> </p> + +<p class="cenhead">NEWTON AGAIN OBLITERATED.</p> + +<blockquote class="b1n"> + + <p>Letter to the Royal Astronomical Society in refutation of Mistaken + Notions held in common, by the Society, and by all the Newtonian + philosophers. By Capt. Forman,<a name="NtA_642" + href="#Nt_642"><sup>[642]</sup></a> R.N. Shepton-Mallet, 1833, 8vo.</p> + +</blockquote> + + <p>Capt. Forman wrote against the whole system of gravitation, and got no + notice. He then wrote to Lord Brougham, Sir J. Herschel, and others I + suppose, desiring them to procure notice of his books in the reviews: + this not being acceded to, he wrote (in print) to Lord John Russell<a + name="NtA_643" href="#Nt_643"><sup>[643]</sup></a> to complain of their + "dishonest" conduct. He then sent a manuscript letter to the Astronomical + Society, inviting controversy: he was answered by a recommendation to + study <!-- Page 297 --><span class="pagenum"><a + name="page297"></a>[297]</span>dynamics. The above pamphlet was the + consequence, in which, calling the Council of the Society "craven + dunghill cocks," he set them right about their doctrines. From all I can + learn, the life of a worthy man and a creditable officer was completely + embittered by his want of power to see that no person is bound in reason + to enter into controversy with every one who chooses to invite him to the + field. This mistake is not peculiar to philosophers, whether of orthodoxy + or paradoxy; a majority of educated persons imply, by their modes of + proceeding, that no one has a right to any opinion which he is not + prepared to defend against all comers.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>David and Goliath, or an attempt to prove that the Newtonian system of + Astronomy is directly opposed to the Scriptures. By Wm. Lauder,<a + name="NtA_644" href="#Nt_644"><sup>[644]</sup></a> Sen., Mere, Wilts. + Mere, 1833, 12mo.</p> + +</blockquote> + + <p>Newton is Goliath; Mr. Lauder is David. David took five pebbles; Mr. + Lauder takes five arguments. He expects opposition; for Paul and Jesus + both met with it.</p> + + <p>Mr. Lauder, in his comparison, seems to put himself in the divinely + inspired class. This would not be a fair inference in every case; but we + know not what to think when we remember that a tolerable number of + cyclometers have attributed their knowledge to direct revelation. The + works of this class are very scarce; I can only mention one or two from + Montucla.<a name="NtA_645" href="#Nt_645"><sup>[645]</sup></a> Alphonso + Cano de Molina,<a name="NtA_646" href="#Nt_646"><sup>[646]</sup></a> in + the last century, upset all Euclid, and squared the circle upon the + ruins; he found a follower, Janson, who translated him from Spanish into + Latin. He declared that he believed in Euclid, until God, who humbles the + proud, taught him better. One Paul Yvon, called from his estate de la + Leu, a merchant at Rochelle, supported by his book-keeper, M. Pujos, and + a <!-- Page 298 --><span class="pagenum"><a + name="page298"></a>[298]</span>Scotchman, John Dunbar, solved the problem + by divine grace, in a manner which was to convert all Jews, Infidels, + etc. There seem to have been editions of his work in 1619 and 1628, and a + controversial "Examen" in 1630, by Robert Sara. There was a noted + discussion, in which Mydorge,<a name="NtA_647" + href="#Nt_647"><sup>[647]</sup></a> Hardy,<a name="NtA_648" + href="#Nt_648"><sup>[648]</sup></a> and others took part against de la + Leu. I cannot find this name either in Lipenius<a name="NtA_649" + href="#Nt_649"><sup>[649]</sup></a> or Murhard,<a name="NtA_650" + href="#Nt_650"><sup>[650]</sup></a> and I should not have known the dates + if it had not been for one of the keenest bibliographers of any time, my + friend Prince Balthasar Boncompagni,<a name="NtA_651" + href="#Nt_651"><sup>[651]</sup></a> who is trying to find copies of the + works, and has managed to find copies of the titles. In 1750, Henry + Sullamar, an Englishman, squared the circle by the number of the Beast: + he published a pamphlet every two or three years; but I cannot find any + mention of him in English works.<a name="NtA_652" + href="#Nt_652"><sup>[652]</sup></a> In France, in 1753, M. de Causans,<a + name="NtA_653" href="#Nt_653"><sup>[653]</sup></a> of the Guards, cut a + circular piece of turf, squared it, and <!-- Page 299 --><span + class="pagenum"><a name="page299"></a>[299]</span>deduced original sin + and the Trinity. He found out that the circle was equal to the square in + which it is inscribed; and he offered a reward for detection of any + error, and actually deposited 10,000 francs as earnest of 300,000. But + the courts would not allow any one to recover.</p> + + <p> </p> + +<p class="cenhead">SIR JOHN HERSCHEL.</p> + + <p>1834. In this year Sir John Herschel<a name="NtA_654" + href="#Nt_654"><sup>[654]</sup></a> set up his telescope at Feldhausen, + Cape of Good Hope. He did much for astronomy, but not much for the + <i>Budget of Paradoxes</i>. He gives me, however, the following story. He + showed a resident a remarkable blood-red star, and some little time after + he heard of a sermon preached in those parts in which it was asserted + that the statements of the Bible must be true, for that Sir J. H. had + seen in his telescope "the very place where wicked people go."</p> + + <p>But red is not always the color. Sir J. Herschel has in his possession + a letter written to his father, Sir W. H.,<a name="NtA_655" + href="#Nt_655"><sup>[655]</sup></a> dated April 3, 1787, and signed + "Eliza Cumyns," begging to know if any of the stars be <i>indigo</i> in + color, "because, if there be, I think it may be deemed a strong + conjectural illustration of the expression, so often used by our Saviour + in the Holy Gospels, that 'the disobedient shall be cast into outer + darkness'; for as the Almighty Being can doubtless confine any of his + creatures, whether corporeal or spiritual, to what part of his creation + He pleases, if therefore any of the stars (which are beyond all doubt so + many suns to other systems) be of so dark a color as that above + mentioned, they may be calculated to give the most insufferable heat to + those dolorous systems dependent upon them (and to reprobate spirits + placed there), without one ray of cheerful light; and may therefore be + the scenes of future punishments." This letter is addressed to Dr. + Heirschel at Slow. Some have placed the infernal regions inside the + earth, but <!-- Page 300 --><span class="pagenum"><a + name="page300"></a>[300]</span>others have filled this internal + cavity—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!"</p> + + <p> </p> + +<p class="cenhead">THE NAUTICAL ALMANAC.</p> + + <p>1834. From 1769 to 1834 the <i>Nautical Almanac</i> was published on a + plan which gradually fell behind what was wanted. In 1834 the new series + began, under a new superintendent (Lieut. W. S. Stratford).<a + name="NtA_656" href="#Nt_656"><sup>[656]</sup></a> There had been a long + scientific controversy, which would not be generally intelligible. To set + some of the points before the reader, I reprint a cutting which I have by + me. It is from the Nautical <i>Magazine</i>, but I did hear that some had + an idea that it was in the Nautical <i>Almanac</i> itself. It certainly + was not, and I feel satisfied the Lords of the Admiralty would not have + permitted the insertion; they are never in advance of their age. The + Almanac for 1834 was published in July 1833.</p> + +<blockquote class="b1n"> + + <p><span class="sc">The New Nautical Almanac</span>—Extract from + the 'Primum Mobile,' and 'Milky Way Gazette.' Communicated by <span + class="sc">Aerolith</span>.</p> + +</blockquote> + + <p>A meeting of the different bodies composing the Solar System was this + day held at the Dragon's Tail, for the purpose of taking into + consideration the alterations and amendments introduced into the New + Nautical Almanac. The honorable luminaries had been individually summoned + <!-- Page 301 --><span class="pagenum"><a + name="page301"></a>[301]</span>by fast-sailing comets, and there was a + remarkably full attendance. Among the visitors we <i>observed</i> several + nebulæ, and almost all the stars whose proper motions would admit of + their being present.</p> + + <p>The <span class="sc">Sun</span> was unanimously called to the focus. + The small planets took the oaths, and their places, after a short + discussion, in which it was decided that the places should be those of + the Almanac itself, with leave reserved to move for corrections.</p> + + <p>Petitions were presented from <span class="grk">α</span> and + <span class="grk">δ</span> Ursæ Minoris, complaining of being put + on daily duty, and praying for an increase of salary.—Laid on the + plane of the ecliptic.</p> + + <p>The trustees of the eccentricity<a name="NtA_657" + href="#Nt_657"><sup>[657]</sup></a> and inclination funds reported a + balance of .00001 in the former, and a deficit of 0".009 in the latter. + This announcement caused considerable surprise, and a committee was moved + for, to ascertain which of the bodies had more or less than his share. + After some discussion, in which the small planets offered to consent to a + reduction, if necessary, the motion was carried.</p> + + <p>The <span class="sc">Focal Body</span> then rose to address the + meeting. He remarked that the subject on which they were assembled was + one of great importance to the routes and revolutions of the heavenly + bodies. For himself, though a private arrangement between two of his + honourable neighbours (here he looked hard at the Earth and Venus) had + prevented his hitherto paying that close attention to the predictions of + the Nautical Almanac which he declared he always had wished to do; yet he + felt consoled by knowing that the conductors of that work had every + disposition to take his peculiar circumstances into consideration. He + declared that he had never passed the wires of a transit without deeply + feeling his inability to adapt himself to the present state of his + theory; a feeling which he was afraid had sometimes caused a slight + tremor in his limb. Before <!-- Page 302 --><span class="pagenum"><a + name="page302"></a>[302]</span>he sat down, he expressed a hope that + honourable luminaries would refrain as much as possible from eclipsing + each other, or causing mutual <span class="correction" title="text reads `peturbations'" + >perturbations</span>. Indeed, he should be very sorry to see any + interruption of the harmony of the spheres. (Applause.)</p> + + <p>The several articles of the New Nautical Almanac were then read over + without any comment; only we observed that Saturn shook his ring at every + novelty, and Jupiter gave his belt a hitch, and winked at the satellites + at page 21 of each month.</p> + + <p>The <span class="sc">Moon</span> rose to propose a resolution. No one, + he said, would be surprised at his bringing this matter forward in the + way he did, when it was considered in how complete and satisfactory a + manner his motions were now represented. He must own he had trembled when + the Lords of the Admiralty dissolved the Board of Longitude, but his + tranquillity was more than reestablished by the adoption of the new + system. He did not know but that any little assistance he could give in + Nautical Astronomy was becoming of less and less value every day, owing + to the improvement of chronometers. But there was one thing, of which + nothing could deprive him—he meant the regulation of the tides. + And, perhaps, when his attention was not occupied by more than the + latter, he should be able to introduce a little more regularity into the + phenomena. (Here the honourable luminary gave a sort of modest libration, + which convulsed the meeting with laughter.) They might laugh at his + natural infirmity if they pleased, but he could assure them it arose only + from the necessity he was under, when young, of watching the motions of + his worthy primary. He then moved a resolution highly laudatory of the + alterations which appeared in the New Nautical Almanac.</p> + + <p>The <span class="sc">Earth</span> rose, to second the motion. His + honourable satellite had fully expressed his opinions on the subject. He + joined his honourable friend in the focus in wishing to pay every + attention to the Nautical Almanac, but, <!-- Page 303 --><span + class="pagenum"><a name="page303"></a>[303]</span>really, when so + important an alteration had taken place in his magnetic pole<a + name="NtA_658" href="#Nt_658"><sup>[658]</sup></a> (hear) and there + might, for aught he knew, be a successful attempt to reach his pole of + rotation, he thought he could not answer for the preservation of the + precession in its present state. (Here the hon. luminary, scratching his + side, exclaimed, as he sat down, "More steamboats—confound + 'em!")</p> + + <p>An honourable satellite (whose name we could not learn) proposed that + the resolution should be immediately despatched, corrected for + refraction, when he was called to order by the Focal Body, who reminded + him that it was contrary to the moving orders of the system to take + cognizance of what passed inside the atmosphere of any planet.</p> + + <p><span class="sc">Saturn</span> and <span class="sc">Pallas</span> rose + together. (Cries of "New member!" and the former gave way.) The latter, + in a long and eloquent speech, praised the liberality with which he and + his colleagues had at length been relieved from astronomical + disqualifications. He thought that it was contrary to the spirit of the + laws of gravitation to exclude any planet from office on account of the + eccentricity or inclination of his orbit. Honourable luminaries need not + talk of the want of convergency of his series. What had they to do with + any private arrangements between him and the general equations of the + system? (Murmurs from the opposition.) So long as he obeyed the laws of + motion, to which he had that day taken a solemn oath, he would ask, were + old planets, which were now so well known that nobody trusted them, + to....</p> + + <p>The <span class="sc">Focal Body</span> said he was sorry to break the + continuity of the proceedings, but he thought that remarks upon + character, with a negative sign, would introduce <!-- Page 304 --><span + class="pagenum"><a name="page304"></a>[304]</span>differences of too high + an order. The honourable luminary must eliminate the expression which he + had brought out, in finite terms, and use smaller inequalities in future. + (Hear, hear.)</p> + + <p><span class="sc">Pallas</span> explained, that he was far from meaning + to reflect upon the orbital character of any planet present. He only + meant to protest against being judged by any laws but those of + gravitation, and the differential calculus: he thought it most unjust + that astronomers should prevent the small planets from being observed, + and then reproach them with the imperfections of the tables, which were + the result of their own narrow-minded policy. (Cheers.)</p> + + <p><span class="sc">Saturn</span> thought that, as an old planet, he had + not been treated with due respect. (Hear, from his satellites.) He had + long foretold the wreck of the system from the friends of innovation. + Why, he might ask, were his satellites to be excluded, when small + planets, trumpery comets, which could not keep their mean distances + (cries of oh! oh!), double stars, with graphical approximations, and such + obscure riff-raff of the heavens (great uproar) found room enough. So + help him Arithmetic, nothing could come of it, but a stoppage of all + revolution. His hon. friend in the focus might smile, for he would be a + gainer by such an event; but as for him (Saturn), he had something to + lose, and hon. luminaries well knew that, whatever they might think + <i>under</i> an atmosphere, <i>above</i> it continual revolution was the + only way of preventing perpetual anarchy. As to the hon. luminary who had + risen before him, he was not surprised at his remarks, for he had + invariably observed that he and his colleagues allowed themselves <i>too + much latitude</i>. The stability of the system required that they should + be brought down, and he, for one, would exert all his powers of + attraction to accomplish that end. If other bodies would cordially unite + with him, particularly his noble friend next him, than whom no luminary + possessed greater weight—</p> + + <p><span class="sc">Jupiter</span> rose to order. He conceived his noble + friend <!-- Page 305 --><span class="pagenum"><a + name="page305"></a>[305]</span>had no right to allude to him in that + manner, and was much surprised at his proposal, considering the matters + which remained in dispute between them. In the present state of affairs, + he would take care never to be in conjunction with his hon. neighbour one + moment longer than he could help. (Cries of "Order, order, no long + inequalities," during which he sat down.)</p> + + <p><span class="sc">Saturn</span> proceeded to say, that he did not know + till then that a planet with a ring could affront one who had only a + belt, by proposing mutual co-operation. He would now come to the subject + under discussion. He should think meanly of his hon. colleagues if they + consented to bestow their approbation upon a mere astronomical + production. Had they forgotten that they once were considered the + arbiters of fate, and the prognosticators of man's destiny? What had lost + them that proud position? Was it not the infernal march of intellect, + which, after having turned the earth topsy-turvy, was now disturbing the + very universe? For himself (others might do as they pleased), but he + stuck to the venerable Partridge,<a name="NtA_659" + href="#Nt_659"><sup>[659]</sup></a> and the Stationers' Company, and + trusted that they would outlive infidels and anarchists, whether of + Astronomical or Diffusion of Knowledge Societies. (Cries of oh! oh!)</p> + + <p><span class="sc">Mars</span> said he had been told, for he must + confess he had not seen the work, that the places of the planets were + given for Sundays. This, he must be allowed to say, was an indecorum he + had not expected; and he was convinced the Lords of the Admiralty had + given no orders to that effect. He hoped this point would be considered + in the measure which had been introduced in another place, and that some + <!-- Page 306 --><span class="pagenum"><a + name="page306"></a>[306]</span>one would move that the prohibition + against travelling on Sundays extend to the heavenly as well as earthly + bodies.</p> + + <p>Several of the stars here declared, that they had been much annoyed by + being observed on Sunday evenings, during the hours of divine + service.</p> + + <p>The room was then cleared for a division, but we are unable to state + what took place. Several comets-at-arms were sent for, and we heard + rumors of a personal collision having taken place between two luminaries + in opposition. We were afterwards told that the resolution was carried by + a majority, and the luminaries elongated at 2 h. 15 m. 33,41 s. sidereal + time.</p> + + <p>* * * It is reported, but we hope without foundation, that Saturn, and + several other discontented planets, have accepted an invitation from + Sirius to join his system, on the most liberal appointments. We believe + the report to have originated in nothing more than the discovery of the + annual parallax of Sirius from the orbit of Saturn; but we may safely + assure our readers that no steps have as yet been taken to open any + communication.</p> + + <p>We are also happy to state, that there is no truth in the rumor of the + laws of gravitation being about to be repealed. We have traced this + report, and find it originated with a gentleman living near Bath (Captain + Forman, R.N),<a name="NtA_660" href="#Nt_660"><sup>[660]</sup></a> whose + name we forbear to mention.</p> + + <p>A great excitement has been observed among the nebulæ, visible to the + earth's southern hemisphere, particularly among those which have not yet + been discovered from thence. We are at a loss to conjecture the cause, + but we shall not fail to report to our readers the news of any movement + which may take place. (Sir J. Herschel's visit. He could just see this + before he went out.)</p> + +<p><!-- Page 307 --><span class="pagenum"><a name="page307"></a>[307]</span></p> + + <p> </p> + +<p class="cenhead">WOODLEY'S DIVINE SYSTEM.</p> + +<blockquote class="b1n"> + + <p>A Treatise on the Divine System of the Universe, by Captain Woodley, + R.N.,<a name="NtA_661" href="#Nt_661"><sup>[661]</sup></a> and as + demonstrated by his Universal Time-piece, and universal method of + determining a ship's longitude by the apparent true place of the moon; + with an introduction refuting the solar system of Copernicus, the + Newtonian philosophy, and mathematics. 1834.<a name="NtA_662" + href="#Nt_662"><sup>[662]</sup></a> 8vo.</p> + + <p>Description of the Universal Time-piece. (4pp. 12mo.)</p> + +</blockquote> + + <p>I think this divine system was published several years before, and was + republished with an introduction in 1834.<a name="NtA_663" + href="#Nt_663"><sup>[663]</sup></a> Capt. Woodley was very sure that the + earth does not move: he pointed out to me, in a conversation I had with + him, something—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:</p> + + <p>"The north pole of the Earth's axis deserts, they say, the north star + or pole of the Heavens, at the rate of 1° in 71¾ years.... The fact is, + nothing can be more certain than that the Stars have not changed their + latitudes or declinations <i>one degree</i> in the last 71¾ years."</p> + + <p>This is a strong specimen of a class of men by whom all accessible + persons who have made any name in science are hunted. It is a pity that + they cannot be admitted into scientific societies, and allowed fairly to + state their cases, and stand quiet cross-examination, being kept in their + answers very close to the questions, and the answers written down. I am + perfectly satisfied that if one meeting in the year were devoted to the + hearing of those who chose to come forward on such conditions, much good + would be done. But I strongly suspect few would come forward <!-- Page + 308 --><span class="pagenum"><a name="page308"></a>[308]</span>at first, + and none in a little while: and I have had some experience of the method + I recommend, privately tried. Capt. Woodley was proposed, a little after + 1834, as a Fellow of the Astronomical Society; and, not caring whether he + moved the sun or the earth, or both—I could not have stood + <i>neither</i>—I signed the proposal. I always had a sneaking + kindness for paradoxers, such a one, perhaps, as Petit André had for his + <i>lambs</i>, as he called them. There was so little feeling against his + opinions, that he only failed by a fraction of a ball. Had I myself + voted, he would have been elected; but being engaged in conversation, and + not having heard the slightest objection to him, I did not think it worth + while to cross the room for the purpose. I regretted this at the time, + but had I known how ignorant he was I should not have supported him. + Probably those who voted against him knew more of his book than I + did.</p> + + <p>I remember no other instance of exclusion from a scientific society on + the ground of opinion, even if this be one; of which it may be that + ignorance had more to do with it than paradoxy. Mr. Frend,<a + name="NtA_664" href="#Nt_664"><sup>[664]</sup></a> a strong + anti-Newtonian, was a Fellow of the Astronomical Society, and for some + years in the Council. Lieut. Kerigan<a name="NtA_665" + href="#Nt_665"><sup>[665]</sup></a> was elected to the Royal Society at a + time when his proposers must have known that his immediate object was to + put F.R.S. on the title-page of a work against the tides. To give all I + know, I may add that the editor of some very ignorant bombast about the + "forehead of the solar sky," who did not know the difference between + <i>Bailly</i><a name="NtA_666" href="#Nt_666"><sup>[666]</sup></a> and + <i>Baily</i>,<a name="NtA_667" href="#Nt_667"><sup>[667]</sup></a> + received hints which induced him to withdraw his proposal for election + into the Astronomical Society. But this was an act of kindness; <!-- Page + 309 --><span class="pagenum"><a name="page309"></a>[309]</span>for if he + had seen Mr. Baily in the chair, with his head on, he might have been + political historian enough to faint away.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>De la formation des Corps. Par Paul Laurent.<a name="NtA_668" + href="#Nt_668"><sup>[668]</sup></a> Nancy, 1834, 8vo.</p> + +</blockquote> + + <p>Atoms, and ether, and ovules or eggs, which are planets, and their + eggs, which are satellites. These speculators can create worlds, in which + they cannot be refuted; but none of them dare attack the problem of a + grain of wheat, and its passage from a seed to a plant, bearing scores of + seeds like what it was itself.</p> + + <p> </p> + +<p class="cenhead">ON JOHN FLAMSTEED.</p> + +<blockquote class="b1n"> + + <p>An account of the Rev. John Flamsteed,<a name="NtA_669" + href="#Nt_669"><sup>[669]</sup></a> the First Astronomer-Royal.... By + Francis Baily,<a name="NtA_670" href="#Nt_670"><sup>[670]</sup></a> Esq. + London, 1835, 4to. Supplement, London, 1837, 4to.</p> + +</blockquote> + + <p>My friend Francis Baily was a paradoxer: he brought forward things + counter to universal opinion. That Newton was impeccable in every point + was the national creed; and failings of temper and conduct would have + been utterly disbelieved, if the paradox had not come supported by very + unusual evidence. Anybody who impeached Newton on existing evidence might + as well have been squaring the circle, for any attention he would have + got. About this book I will tell a story. It was published by the + Admiralty for distribution; and the distribution was entrusted to Mr. + Baily. On the eve of its appearance, rumors of its extraordinary + revelations got about, and persons of influence applied to the Admiralty + for copies. The Lords were in a difficulty: but on looking at the list + they saw names, as they <!-- Page 310 --><span class="pagenum"><a + name="page310"></a>[310]</span>thought, which were so obscure that they + had a right to assume Mr. Baily had included persons who had no claim to + such a compliment as presentation from the Admiralty. The Secretary + requested Mr. Baily to call upon him. "Mr. Baily, my Lords are inclined + to think that some of the persons in this list are perhaps not of that + note which would justify their Lordships in presenting this + work."—"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<a + name="NtA_671" href="#Nt_671"><sup>[671]</sup></a>—<i>who's + Gauss</i>?"—"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.</p> + + <p>There was a controversy about the revelations made in this work; but + as the eccentric anomalies took no part in it, there is nothing for my + purpose. The following valentine from Mrs. Flamsteed,<a name="NtA_672" + href="#Nt_672"><sup>[672]</sup></a> which I found among Baily's papers, + illustrates some of the points:</p> + + <p class="author">"3 Astronomers' Row, Paradise: February 14, 1836. + + <p>"Dear Sir,—I suppose you hardly expected to receive a letter + from me, dated from this place; but the truth is, a gentleman from our + street was appointed guardian angel to the American Treaty, in which + there is some astronomical question about boundaries. He has got leave to + go back to fetch some instruments which he left behind, and I take this + opportunity of making your acquaintance. That America has become a + wonderful place since I was down among you; you have no idea how grand + the fire at New York <!-- Page 311 --><span class="pagenum"><a + name="page311"></a>[311]</span>looked up here. Poor dear Mr. Flamsteed + does not know I am writing a letter to a gentleman on Valentine's day; he + is walked out with Sir Isaac Newton (they are pretty good friends now, + though they do squabble a little sometimes) and Sir William Herschel, to + see a new nebula. Sir Isaac says he can't make out at all how it is + managed; and I am sure I cannot help him. I never bothered my head about + those things down below, and I don't intend to begin here.</p> + + <p>"I have just received the news of your having written a book about my + poor dear man. It's a chance that I heard it at all; for the truth is, + the scientific gentlemen are somehow or other become so wicked, and go so + little to church, that very few of them are considered fit company for + this place. If it had not been for Dr. Brinkley,<a name="NtA_673" + href="#Nt_673"><sup>[673]</sup></a> who came here of course, I should not + have heard about it. He seems a nice man, but is not yet used to our + ways. As to Mr. Halley,<a name="NtA_674" + href="#Nt_674"><sup>[674]</sup></a> he is of course not here; which is + lucky for him, for Mr. Flamsteed swore the moment he caught him in a + place where there are no magistrates, he would make a sacrifice of him to + heavenly truth. It was very generous in Mr. F. not appearing against Sir + Isaac when he came up, for I am told that if he had, Sir Isaac would not + have been allowed to come in at all. I should have been sorry for that, + for he is a companionable man enough, only holds his head rather higher + than he should do. I met him the other day walking with Mr. Whiston,<a + name="NtA_675" href="#Nt_675"><sup>[675]</sup></a> and disputing about + the deluge. 'Well, Mrs. Flamsteed,' says he, 'does old Poke-the-Stars + understand gravitation yet?' Now you must know that is rather a sore + point with poor dear Mr. Flamsteed. He says that Sir Isaac is as + crochetty about the moon as ever; and as to <!-- Page 312 --><span + class="pagenum"><a name="page312"></a>[312]</span>what some people say + about what has been done since his time, he says he should like to see + somebody who knows something about it of himself. For it is very singular + that none of the people who have carried on Sir Isaac's notions have been + allowed to come here.</p> + + <p>"I hope you have not forgotten to tell how badly Sir Isaac used Mr. + Flamsteed about that book. I have never quite forgiven him; as for Mr. + Flamsteed, he says that as long as he does not come for observations, he + does not care about it, and that he will never trust him with any papers + again as long as he lives. I shall never forget what a rage he came home + in when Sir Isaac had called him a puppy. He struck the stairs all the + way up with his crutch, and said puppy at every step, and all the + evening, as soon as ever a star appeared in the telescope, he called it + puppy. I could not think what was the matter, and when I asked, he only + called me puppy.</p> + + <p>"I shall be very glad to see you if you come our way. Pray keep up + some appearances, and go to church a little. St. Peter is always + uncommonly civil to astronomers, and indeed to all scientific persons, + and never bothers them with many questions. If they can make anything out + of the case, he is sure to let them in. Indeed, he says, it is perfectly + out of the question expecting a mathematician to be as religious as an + apostle, but that it is as much as his place is worth to let in the + greater number of those who come. So try if you cannot manage it, for I + am very curious to know whether you found all the letters. I remain, dear + sir, your faithful servant,</p> + + <p class="author">"<span class="sc">Margaret Flamsteed.</span> + + <div class="poem"> + <div class="stanza"> + <p>Francis Baily, Esq.</p> + </div> + </div> + <p>"P.S. Mr. Flamsteed has come in, and says he left Sir Isaac riding + cockhorse upon the nebula, and poring over it as if it were a book. He + has brought in his old acquaintance Ozanam,<a name="NtA_676" + href="#Nt_676"><sup>[676]</sup></a> who says that it was always his maxim + on <!-- Page 313 --><span class="pagenum"><a + name="page313"></a>[313]</span>earth, that 'il appartient aux docteurs de + Sorbonne de disputer, au Pape de prononcer, et au mathématicien d'aller + en Paradis en ligne perpendiculaire.'"<a name="NtA_677" + href="#Nt_677"><sup>[677]</sup></a></p> + + <p> </p> + +<p class="cenhead">ON STEVIN.</p> + + <p>The Secretary of the Admiralty was completely extinguished. I can + recall but two instances of demolition as complete, though no doubt there + are many others. The first is in</p> + + <div class="poem"> + <div class="stanza"> + <p>Simon Stevin<a name="NtA_678" href="#Nt_678"><sup>[678]</sup></a> and M. Dumortier. Nieuport, 1845, 12mo.</p> + </div> + </div> + <p>M. Dumortier was a member of the Academy of Brussels: there was a + discussion, I believe, about a national Pantheon for Belgium. The name of + Stevinus suggested itself as naturally as that of Newton to an + Englishman; probably no Belgian is better known to foreigners as + illustrious in science. Stevinus is great in the <i>Mécanique + Analytique</i> of Lagrange;<a name="NtA_679" + href="#Nt_679"><sup>[679]</sup></a> Stevinus is great in the <i>Tristram + Shandy</i> of Sterne. M. Dumortier, who believed that not one Belgian in + a thousand knew Stevinus, and who confesses with ironical shame that he + was not the odd man, protested against placing the statue of an obscure + man in the Pantheon, to give foreigners the notion that Belgium could + show nothing greater. The work above named is a slashing retort: any one + who knows the history of science ever so little may imagine what a + dressing was given, by mere extract from foreign writers. The tract is a + letter signed J. du Fan, but this is a pseudonym of Mr. Van de Weyer.<a + name="NtA_680" href="#Nt_680"><sup>[680]</sup></a> The Academician says + Stevinus was a man who was not <!-- Page 314 --><span class="pagenum"><a + name="page314"></a>[314]</span>without merit for the time at which he + lived: Sir! is the answer, he was as much before his own time as you are + behind yours. How came a man who had never heard of Stevinus to be a + member of the Brussels Academy?</p> + + <p>The second story was told me by Mr. Crabb Robinson,<a name="NtA_681" + href="#Nt_681"><sup>[681]</sup></a> who was long connected with the + <i>Times</i>, and intimately acquainted with Mr. W***.<a name="NtA_682" + href="#Nt_682"><sup>[682]</sup></a> When W*** was an undergraduate at + Cambridge, taking a walk, he came to a stile, on which sat a bumpkin who + did not make way for him: the gown in that day looked down on the town. + "Why do you not make way for a gentleman?"—"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."<a name="NtA_683" href="#Nt_683"><sup>[683]</sup></a> W*** + seized the great pugilist's hand, and shook it warmly, got him to his own + rooms in college, collected some friends, and had a symposium which + lasted until the large end of the small hours.</p> + + <p> </p> + +<p class="cenhead">FINLEYSON AS A PARADOXER.</p> + +<blockquote class="b1n"> + + <p>God's Creation of the Universe as it is, in support of the Scriptures. + By Mr. Finleyson.<a name="NtA_684" href="#Nt_684"><sup>[684]</sup></a> + Sixth Edition, 1835, 8vo.</p> + +</blockquote> + +<p><!-- Page 315 --><span class="pagenum"><a name="page315"></a>[315]</span></p> + + <p>This writer, by his own account, succeeded in delivering the famous + Lieut. Richard Brothers<a name="NtA_685" + href="#Nt_685"><sup>[685]</sup></a> from the lunatic asylum, and tending + him, not as a keeper but as a disciple, till he died. Brothers was, by + his own account, the nephew of the Almighty, and Finleyson ought to have + been the nephew of Brothers. For Napoleon came to him in a vision, with a + broken sword and an arrow in his side, beseeching help: Finleyson pulled + out the arrow, but refused to give a new sword; whereby poor Napoleon, + though he got off with life, lost the battle of Waterloo. This story was + written to the Duke of Wellington, ending with "I pulled out the arrow, + but left the broken sword. Your Grace can supply the rest, and what + followed is amply recorded in history." The book contains a long account + of applications to Government to do three things: to pay 2,000<i>l.</i> + for care taken of Brothers, to pay 10,000<i>l.</i> for discovery of the + longitude, and to prohibit the teaching of the Newtonian system, which + makes God a liar. The successive administrations were threatened that + they would have to turn out if they refused, which, it is remarked, came + to pass in every case. I have heard of a joke of Lord Macaulay, that the + House of Commons must be the Beast of the Revelations, since 658 members, + with the officers necessary for the action of the House, make 666. + Macaulay read most things, and the greater part of the rest: so that he + might be suspected of having appropriated as a joke one of Finleyson's + serious points—"I wrote Earl Grey<a name="NtA_686" + href="#Nt_686"><sup>[686]</sup></a> upon the 13th of July, 1831, + informing him that his Reform <!-- Page 316 --><span class="pagenum"><a + name="page316"></a>[316]</span>Bill could not be carried, as it reduced + the members below the present amount of 658, which, with the eight + principal clerks or officers of the House, make the number 666." But a + witness has informed me that Macaulay's joke was made in his hearing a + great many years before the Reform Bill was proposed; in fact, when both + were students at Cambridge. Earl Grey was, according to Finleyson, a + descendant of Uriah the Hittite. For a specimen of Lieut. Brothers, this + book would be worth picking up. Perhaps a specimen of the Lieutenant's + poetry may be acceptable: Brothers <i>loquitur</i>, remember:</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Jerusalem ! Jerusalem! shall be built again!</p> + <p class="i2">More rich, more grand then ever;</p> + <p>And through it shall Jordan flow!(!)</p> + <p class="i2">My people's favourite river.</p> + <p>There I'll erect a splendid throne,</p> + <p class="i2">And build on the wasted place;</p> + <p>To fulfil my ancient covenant</p> + <p class="i2">To King David and his race.</p> + <p> * * * * * *</p> + <p class="hg3">"Euphrates' stream shall flow with ships,</p> + <p class="i2">And also my wedded Nile;</p> + <p>And on my coast shall cities rise,</p> + <p class="i2">Each one distant but a mile.</p> + <p> * * * * * *</p> + <p class="hg3">"My friends the Russians on the north</p> + <p class="i2">With Persees and Arabs round,</p> + <p>Do show the limits of my land,</p> + <p class="i2">Here! Here! then I mark the ground."</p> + </div> + </div> + <p> </p> + +<p class="cenhead">ON THEOLOGICAL PARADOXERS.</p> + + <p>Among the paradoxers are some of the theologians who in their own + organs of the press venture to criticise science. These may hold their + ground when they confine themselves to the geology of long past periods + and to general cosmogony: for it is the tug of Greek against Greek; and + both sides deal much in what is grand when called <i>hypothesis</i>, + petty when called <i>supposition</i>. And very often they are not + conspicuous when they venture upon things within knowledge; <!-- Page 317 + --><span class="pagenum"><a name="page317"></a>[317]</span>wrong, but not + quite wrong enough for a Budget of Paradoxes. One case, however, is + destined to live, as an instance of a school which finds writers, + editors, and readers. The double stars have been seen from the + seventeenth century, and diligently observed by many from the time of Wm. + Herschel, who first devoted continuous attention to them. The year 1836 + was that of a remarkable triumph of astronomical prediction. The theory + of gravitation had been applied to the motion of binary stars about each + other, in elliptic orbits, and in that year the two stars of <span + class="grk">γ</span> 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 <i>Church of England + Quarterly Review</i> for April 1837, written against the Useful Knowledge + Society. The notion that there are any such things as double stars is (p. + 460) implied to be imposture or delusion, as in the following extract. I + suspect that I myself am the <i>Sidrophel</i>, and that my companion to + the maps of the stars, written for the Society and published in 1836, is + the work to which the writer refers:</p> + + <p>"We have forgotten the name of that Sidrophel who lately discovered + that the fixed stars were not single stars, but appear in the heavens + like soles at Billingsgate, in pairs; while a second astronomer, under + the influence of that competition in trade which the political economists + tell us is so advantageous to the public, professes to show us, through + his superior telescope, that the apparently single stars are really + three. Before such wondrous mandarins of science, how continually must + <i>homunculi</i> like ourselves keep in the background, lest we come + between the wind and their nobility."</p> + + <p>If the <i>homunculus</i> who wrote this be still above ground, <!-- + Page 318 --><span class="pagenum"><a name="page318"></a>[318]</span>how + devoutly must he hope he may be able to keep in the background! But the + chief blame falls on the editor. The title of the article is:</p> + + <p>"The new school of superficial pantology; a speech intended to be + delivered before a defunct Mechanics' Institute. By Swallow Swift, late + M.P. for the Borough of Cockney-Cloud, Witsbury: reprinted Balloon + Island, Bubble year, month <i>Ventose</i>. Long live Charlatan!"</p> + + <p>As a rule, orthodox theologians should avoid humor, a weapon which all + history shows to be very difficult to employ in favor of establishment, + and which, nine times out of ten, leaves its wielder fighting on the side + of heterodoxy. Theological argument, when not enlivened by bigotry, is + seldom worse than narcotic: but theological fun, when not covert heresy, + is almost always sialagogue. The article in question is a craze, which no + editor should have admitted, except after severe inspection by qualified + persons. The author of this wit committed a mistake which occurs now and + then in old satire, the confusion between himself and the party aimed at. + He ought to be reviewing this fictitious book, but every now and then the + article becomes the book itself; not by quotation, but by the writer + forgetting that <i>he</i> is not Mr. Swallow Swift, but his reviewer. In + fact he and Mr. S. Swift had each had a dose of the <i>Devil's + Elixir</i>. A novel so called, published about forty years ago, proceeds + upon a legend of this kind. If two parties both drink of the elixir, + their identities get curiously intermingled; each turns up in the + character of the other throughout the three volumes, without having his + ideas clear as to whether he be himself or the other. There is a similar + confusion in the answer made to the famous <i>Epistolæ Obscurorum + Virorum</i>:<a name="NtA_687" href="#Nt_687"><sup>[687]</sup></a> it is + headed <i>Lamentationes Obscurorum Virorum</i>.<a name="NtA_688" + href="#Nt_688"><sup>[688]</sup></a> <!-- Page 319 --><span + class="pagenum"><a name="page319"></a>[319]</span>This is not a retort of + the writer, throwing back the imputation: the obscure men who had been + satirized are themselves made, by name, to wince under the disapprobation + which the Pope had expressed at the satire upon themselves.</p> + + <p>Of course the book here reviewed is a transparent forgery. But I do + not know how often it may have happened that the book, in the journals + which always put a title at the head, may have been written after the + review. About the year 1830 a friend showed me the proof of an article of + his on the malt tax, for the next number of the <i>Edinburgh Review</i>. + Nothing was wanting except the title of the book reviewed; I asked what + it was. He sat down, and wrote as follows at the head, "The Maltster's + Guide (pp. 124)," and said that would do as well as anything.</p> + + <p>But I myself, it will be remarked, have employed such humor as I can + command "in favor of establishment." What it is worth I am not to judge; + as usual in such cases, those who are of my cabal pronounce it good, but + cyclometers and other paradoxers either call it very poor, or commend it + as sheer buffoonery. Be it one or the other, I observe that all the + effective ridicule is, in this subject, on the side of establishment. + This is partly due to the difficulty of quizzing plain and sober + demonstration; but so much, if not more, to the ignorance of the + paradoxers. For that which cannot be <i>ridiculed</i>, can be <i>turned + into ridicule</i> by those who know how. But by the time a person is deep + enough in <i>negative</i> quantities, and <i>impossible</i> quantities, + to be able to satirize them, he is caught, and being inclined to become a + <i>user</i>, shrinks from being an <i>abuser</i>. Imagine a person with a + gift of ridicule, and knowledge enough, trying his hand on the junction + of the assertions which he will find in various books of algebra. First, + that a negative quantity has no logarithm; secondly, that a <!-- Page 320 + --><span class="pagenum"><a name="page320"></a>[320]</span>negative + quantity has no square root; thirdly, that the first non-existent is to + the second as the circumference of a circle to its diameter. One great + reason of the allowance of such unsound modes of expression is the + confidence felt by the writers that √-1 and log(-1) will make their + way, however inaccurately described. I heartily wish that the cyclometers + had knowledge enough to attack the weak points of algebraical diction: + they would soon work a beneficial change.<a name="NtA_689" + href="#Nt_689"><sup>[689]</sup></a></p> + + <p> </p> + +<p class="cenhead">AN EARLY METEOROLOGIST.</p> + +<blockquote class="b1n"> + + <p>Recueil de ma vie, mes ouvrages et mes pensées. Par Thomas Ignace + Marie Forster.<a name="NtA_690" href="#Nt_690"><sup>[690]</sup></a> + Brussels, 1836, 12mo.</p> + +</blockquote> + + <p>Mr. Forster, an Englishman settled at Bruges, was an observer in many + subjects, but especially in meteorology. He communicated to the + Astronomical Society, in 1848, the information that, in the registers + kept by his grandfather, his father, and himself, beginning in 1767, new + moon on Saturday was followed, nineteen times out of twenty, by twenty + days of rain and wind. This statement being published in the + <i>Athenæum</i>, a cluster of correspondents averred that the belief is + common among seamen, in all parts of the world, and among landsmen too. + Some one quoted a distich:</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Saturday's moon and Sunday's full</p> + <p>Never were fine and never <i>wull</i>."</p> + </div> + </div> +<p><!-- Page 321 --><span class="pagenum"><a name="page321"></a>[321]</span></p> + + <p>Another brought forward:</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"If a Saturday's moon</p> + <p>Comes once in seven years it comes too soon."</p> + </div> + </div> + <p>Mr. Forster did not say he was aware of the proverbial character of + the phenomenon. He was a very eccentric man. He treated his dogs as + friends, and buried them with ceremony. He quarrelled with the + <i>curé</i> of his parish, who remarked that he could not take his dogs + to heaven with him. I will go nowhere, said he, where I cannot take my + dog. He was a sincere Catholic: but there is a point beyond which even + churches have no influence.</p> + + <p>The following is some account of the announcement of 1849. The + <i>Athenæum</i> (Feb. 17), giving an account of the meeting of the + Astronomical Society in December, 1858, says:</p> + + <p>"Dr. Forster of Bruges, who is well known as a meteorologist, made a + communication at which our readers will stare: he declares that by + journals of the weather kept by his grandfather, father, and himself, + ever since 1767, to the present time, <i>whenever the new moon has fallen + on a Saturday, the following twenty days have been wet and windy</i>, in + nineteen cases out of twenty. In spite of our friend Zadkiel<a + name="NtA_691" href="#Nt_691"><sup>[691]</sup></a> and the others who + declare that we would smother every truth that does not happen to agree + with us, we are glad to see that the Society had the sense to publish + this communication, coming, as it does, from a veteran observer, and one + whose love of truth is undoubted. It must be that the fact is so set down + in the journals, because Dr. Forster says it: and whether it be only a + fact of the journals, or one of the heavens, can soon be tried. The new + moon of March next, falls on <i>Saturday</i> the 24th, at 2 in the + afternoon. We shall certainly look out."</p> + +<p><!-- Page 322 --><span class="pagenum"><a name="page322"></a>[322]</span></p> + + <p>The following appeared in the number of March 31:</p> + + <p>"The first <i>Saturday Moon</i> since Dr. Forster's announcement came + off a week ago. We had previously received a number of letters from + different correspondents—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 <!-- Page 323 + --><span class="pagenum"><a name="page323"></a>[323]</span>cannot, when + he puts down a long series of results, detect any weather cycles at all? + One of our correspondents wrote us something of a lecture for + encouraging, he said, the notion that <i>names</i> could influence the + weather. He mistakes the question. If there be any weather cycles + depending on the moon, it is possible that one of them may be so related + to the week cycle of seven days, as to show recurrences which are of the + kind stated, or any other. For example, we know that if the new moon of + March fall on a Saturday in this year, it will most probably fall on a + Saturday nineteen years hence. This is not connected with the spelling of + Saturday—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."</p> + + <p>How many coincidences are required to establish a law of connection? + It depends on the way in which the mind views the matter in question. + Many of the paradoxers are quite set up by a very few instances. I will + now tell a story about myself, and then ask them a question.</p> + + <p>So far as instances can prove a law, the following is proved: no + failure has occurred. Let a clergyman be known to me, whether by personal + acquaintance or correspondence, or by being frequently brought before me + by those with whom I am connected in private life: that clergyman does + not, except in few cases, become a bishop; but <i>if</i> he become a + bishop, he is sure, first or last, to become an arch-bishop. This has + happened in every case. As follows:</p> + + <p>1. My last schoolmaster, a former Fellow of Oriel, was <!-- Page 324 + --><span class="pagenum"><a name="page324"></a>[324]</span>a very + intimate college friend of Richard Whately<a name="NtA_692" + href="#Nt_692"><sup>[692]</sup></a>, a younger man. Struck by his + friend's talents, he used to talk of him perpetually, and predict his + future eminence. Before I was sixteen, and before Whately had even given + his Bampton Lectures, I was very familiar with his name, and some of his + sayings. I need not say that he became Archbishop of Dublin.</p> + + <p>2. When I was a child, a first cousin of John Bird Sumner<a + name="NtA_693" href="#Nt_693"><sup>[693]</sup></a> married a sister of my + mother. I cannot remember the time when I first heard his name, but it + was made very familiar to me. In time he became Bishop of Chester, and + then, Archbishop of Canterbury. My reader may say that Dr. C. R. + Sumner,<a name="NtA_694" href="#Nt_694"><sup>[694]</sup></a> Bishop of + Winchester, has just as good a claim: but it is not so: those connected + with me had more knowledge of Dr. J. B. Sumner;<a name="NtA_695" + href="#Nt_695"><sup>[695]</sup></a> and said nothing, or next to nothing, + of the other. Rumor says that the Bishop of Winchester has + <i>declined</i> an Archbishopric: if so, my rule is a rule of + gradations.</p> + + <p>3. Thomas Musgrave,<a name="NtA_696" + href="#Nt_696"><sup>[696]</sup></a> Fellow of Trinity College, Cambridge, + was <i>Dean</i> of the college when I was an undergraduate: this brought + me into connection with him, he giving impositions for not going to + chapel, I writing them out according. We had also friendly intercourse in + after life; I forgiving, he probably forgetting. Honest Tom <!-- Page 325 + --><span class="pagenum"><a name="page325"></a>[325]</span>Musgrave, as + he used to be called, became Bishop of Hereford, and Archbishop of + York.</p> + + <p>4. About the time when I went to Cambridge, I heard a great deal about + Mr. C. T. Longley,<a name="NtA_697" href="#Nt_697"><sup>[697]</sup></a> + of Christchurch, from a cousin of my own of the same college, long since + deceased, who spoke of him much, and most affectionately. Dr. Longley + passed from Durham to York, and thence to Canterbury. I cannot quite make + out the two Archbishoprics; I do not remember any other private channel + through which the name came to me: perhaps Dr. Longley, having two + strings to his bow, would have been one archbishop if I had never heard + of him.</p> + + <p>5. When Dr. Wm. Thomson<a name="NtA_698" + href="#Nt_698"><sup>[698]</sup></a> was appointed to the see of + Gloucester in 1861, he and I had been correspondents on the subject of + logic—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.</p> + + <p>Here are five cases; and there is no opposing instance. I have + searched the almanacs since 1828, and can find no instance of a Bishop + not finally Archbishop of whom I had known through private sources, + direct or indirect. Now what do my paradoxers say? Is this a + pre-established harmony, or a chain of coincidences? And how many + instances will it require to establish a law?<a name="NtA_699" + href="#Nt_699"><sup>[699]</sup></a></p> + +<p><!-- Page 326 --><span class="pagenum"><a name="page326"></a>[326]</span></p> + + <p> </p> + +<p class="cenhead">THE HERSCHEL HOAX.</p> + +<blockquote class="b1n"> + + <p>Some account of the great astronomical discoveries lately made by Sir + John Herschel at the Cape of Good Hope. Second Edition. London, 12mo. + 1836.</p> + +</blockquote> + + <p>This is a curious hoax, evidently written by a person versed in + astronomy and clever at introducing probable circumstances and undesigned + coincidences.<a name="NtA_700" href="#Nt_700"><sup>[700]</sup></a> It + first appeared in a newspaper. It makes Sir J. Herschel discover men, + animals, etc. in the moon, of which much detail is given. There seems to + have been a French edition, the original, and English editions in + America, whence the work came into Britain: but whether the French was + published in America or at Paris I do not know. There is no doubt that it + was produced in the United States, by M. Nicollet,<a name="NtA_701" + href="#Nt_701"><sup>[701]</sup></a> an astronomer, once of Paris, and a + fugitive of some kind. About him I have heard two stories. First that he + fled to America with funds not his own, and that this book was a mere + device to raise the wind. Secondly, that he was a protégé of Laplace, and + of the Polignac party, and also an outspoken man. That after the + revolution he was so obnoxious to the republican party that he judged it + prudent to quit France; which he did in debt, leaving money for his + creditors, but not enough, with M. Bouvard. In America he connected + himself with an assurance office. <!-- Page 327 --><span + class="pagenum"><a name="page327"></a>[327]</span>The moon-story was + written, and sent to France, chiefly with the intention of entrapping M. + Arago, Nicollet's especial foe, into the belief of it. And those who + narrate this version of the story wind up by saying that M. Arago + <i>was</i> entrapped, and circulated the wonders through Paris, until a + letter from Nicollet to M. Bouvard<a name="NtA_702" + href="#Nt_702"><sup>[702]</sup></a> explained the hoax. I have no + personal knowledge of either story: but as the poor man had to endure the + first, it is but right that the second should be told with it.</p> + + <p> </p> + +<p class="cenhead">SOME MORE METEOROLOGY.</p> + +<blockquote class="b1n"> + + <p>The Weather Almanac for the Year 1838. By P. Murphy,<a name="NtA_703" + href="#Nt_703"><sup>[703]</sup></a> Esq., M.N.S.</p> + +</blockquote> + + <p>By M. N. S. is meant <i>member of no society.</i>. This almanac bears + on the title-page two recommendations. The <i>Morning Post</i> calls it + one of the most important-if-true publications of our generation. The + <i>Times</i> says: "If the basis of his theory prove sound, and its + principles be sanctioned by a more extended experience, it is not too + much to say that the importance of the discovery is equal to that of the + longitude." Cautious journalist! Three times that of the longitude would + have been too little to say. That the landsman might predict the weather + of all the year, at its beginning, Jack would cheerfully give up + astronomical longitude—<i>the</i> 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 <!-- Page 328 + --><span class="pagenum"><a name="page328"></a>[328]</span>bore + Changeable; Rain; Rain; Rain-<i>wind</i>; Changeable; Fair; Changeable. + To aim at such precision as to put a fair day between two changeable ones + by weather theory was going very near the wind and weather too. Murphy + opened the year with cold and frost; and the weather did the same. But + Murphy, opposite to Saturday, January 20, put down "Fair, Probable lowest + degree of winter temperature." When this Saturday came, it was not merely + the probably coldest of 1838, but certainly the coldest of many + consecutive years. Without knowing anything of Murphy, I felt it prudent + to cover my nose with my glove as I walked the street at eight in the + morning. The fortune of the Almanac was made. Nobody waited to see + whether the future would dement the prophecy: the shop was beset in a + manner which brought the police to keep order; and it was said that the + Almanac for 1838 was a gain of 5,000<i>l.</i> to the owners. It very soon + appeared that this was only a lucky hit: the weather-prophet had a + modified reputation for a few years; and is now no more heard of. A work + of his will presently appear in the list.</p> + + <p> </p> + +<p class="cenhead">THE GREAT PYRAMIDS.</p> + +<blockquote class="b1n"> + + <p>Letter from Alexandria on the evidence of the practical application of + the quadrature of the circle in the great pyramids of Gizeh. By H. C. + Agnew,<a name="NtA_704" href="#Nt_704"><sup>[704]</sup></a> Esq. London, + 1838, 4to.</p> + +</blockquote> + +<p><!-- Page 329 --><span class="pagenum"><a name="page329"></a>[329]</span></p> + + <p>Mr. Agnew detects proportions which he thinks were suggested by those + of the circumference and diameter of a circle.</p> + + <p> </p> + +<p class="cenhead">THE MATHEMATICS OF A CREED.</p> + +<blockquote class="b1n"> + + <p>The creed of St. Athanasius proved by a mathematical parallel. Before + you censure, condemn, or approve; read, examine, and understand. <span + class="sc">E. B. Revilo</span>.<a name="NtA_705" + href="#Nt_705"><sup>[705]</sup></a> London, 1839, 8vo.</p> + +</blockquote> + + <p>This author really believed himself, and was in earnest. He is not the + only person who has written nonsense by confounding the mathematical + infinite (of quantity) with what speculators now more correctly express + by the unlimited, the unconditioned, or the absolute. This tract is worth + preserving, as the extreme case of a particular kind. The following is a + specimen. Infinity being represented by ∞, as usual, and <i>f</i>, + <i>s</i>, <i>g</i>, being finite integers, the three Persons are denoted + by ∞<sup><i>f</i></sup>, (<i>m</i> ∞)<sup><i>s</i></sup>, + ∞<sup><i>g</i></sup>, the finite fraction <i>m</i> representing + human nature, as opposed to ∞. The clauses of the Creed are then + given with their mathematical parallels. I extract a couple:</p> + +<table class="nobctr" width="80%" summary="Credal Mathematics" title="Credal Mathematics"><tr><td valign="top" style="width:50%" class="spac"> +"But the Godhead of the +Father, of the Son, and of +the Holy Ghost, is all one: +the glory equal, the Majesty +co-eternal. +</td><td valign="top" style="width:50%" class="spac"> +"It has been shown that +∞<sup><i>f</i></sup>, ∞<sup><i>g</i></sup>, and (<i>m</i> ∞)<sup><i>s</i></sup>, together, +are but ∞, and that +each is ∞, and any magnitude +in existence represented +by ∞ always was and always +will be: for it cannot +be made, or destroyed, and +yet exists. +</td></tr></table> + +<p><!-- Page 330 --><span class="pagenum"><a name="page330"></a>[330]</span></p> + +<table class="nobctr" width="80%" summary="Credal Mathematics" title="Credal Mathematics"><tr><td valign="top" style="width:50%" class="spac"> +"Equal to the Father, as +touching his Godhead: and +inferior to the Father, +touching his Manhood." +</td><td valign="top" style="width:50%" class="spac"> +"(<i>m</i> ∞)<sup><i>s</i></sup> is equal to ∞<sup><i>f</i></sup> as +touching ∞, but inferior to +∞<sup><i>f</i></sup> as touching <i>m</i>: because +<i>m</i> is not infinite." +</td></tr></table> + + <p>I might have passed this over, as beneath even my present subject, but + for the way in which I became acquainted with it. A bookseller, <i>not + the publisher</i>, handed it to me over his counter: one who had + published mathematical works. He said, with an air of important + communication, Have you seen <i>this</i>, Sir! In reply, I recommended + him to show it to my friend Mr.——, for whom he had published + mathematics. Educated men, used to books and to the converse of learned + men, look with mysterious wonder on such productions as this: for which + reason I have made a quotation which many will judge had better have been + omitted. But it would have been an imposition on the public if I were, + omitting this and some other uses of the Bible and Common Prayer, to + pretend that I had given a true picture of my school.</p> + + <p>[Since the publication of the above, it has been stated that the + author is Mr. Oliver Byrne, the author of the <i>Dual Arithmetic</i> + mentioned further on: E. B. Revilo seems to be obviously a reversal.]</p> + + <p> </p> + +<p class="cenhead">LOGIC HAS NO PARADOXERS.</p> + +<blockquote class="b1n"> + + <p>Old and new logic contrasted: being an attempt to elucidate, for + ordinary comprehension, how Lord Bacon delivered the human mind from its + 2,000 years' enslavement under Aristotle. By Justin Brenan.<a + name="NtA_706" href="#Nt_706"><sup>[706]</sup></a> London, 1839, + 12mo.</p> + +</blockquote> + + <p>Logic, though the other exact science, has not had the sort of + assailants who have clustered about mathematics. There is a sect which + disputes the utility of logic, but there are no special points, like the + quadrature of the circle, which <!-- Page 331 --><span class="pagenum"><a + name="page331"></a>[331]</span>excite dispute among those who admit other + things. The old story about Aristotle having one logic to trammel us, and + Bacon another to set us free,—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:</p> + + <p>"The basis of this system is the syllogism. This is a form of couching + the substance of your argument or investigation into one short line or + sentence—then corroborating or supporting it in another, and + drawing your conclusion or proof in a third."</p> + + <p>On this definition he gives an example, as follows: "Every sin + deserves death," the substance of the "argument or investigation." Then + comes, "Every unlawful wish is a sin," which "corroborates or supports" + the preceding: and, lastly, "therefore every unlawful wish deserves + death," which is the "conclusion or proof." We learn, also, that + "sometimes the first is called the premises (<i>sic</i>), and sometimes + the first premiss"; as also that "the first is sometimes called the + proposition, or subject, or affirmative, and the next the predicate, and + sometimes the middle term." To which is added, with a mark of exclamation + at the end, "but in analyzing the syllogism, there is a middle term, and + a predicate too, in each of the lines!" It is clear that Aristotle never + enslaved this mind.</p> + + <p>I have said that logic has no paradoxers, but I was speaking of old + time. This science has slept until our own day: Hamilton<a name="NtA_707" + href="#Nt_707"><sup>[707]</sup></a> says there has been "no progress made + in <!-- Page 332 --><span class="pagenum"><a + name="page332"></a>[332]</span>the <i>general</i> development of the + syllogism since the time of Aristotle; and in regard to the few + <i>partial</i> improvements, the professed historians seem altogether + ignorant." But in our time, the paradoxer, the opponent of common + opinion, has appeared in this field. I do not refer to Prof. Boole,<a + name="NtA_708" href="#Nt_708"><sup>[708]</sup></a> who is not a + <i>paradoxer</i>, but a <i>discoverer</i>: his system could neither + oppose nor support common opinion, for its grounds were not in the + conception of any one. I speak especially of two others, who fought like + cat and dog: one was dogmatical, the other categorical. The first was + Hamilton himself—Sir William Hamilton of Edinburgh, the + metaphysician, not Sir William <i>Rowan</i> Hamilton<a name="NtA_709" + href="#Nt_709"><sup>[709]</sup></a> of Dublin, the mathematician, a + combination of peculiar genius with unprecedented learning, erudite in + all he could want except mathematics, for which he had no turn, and in + which he had not even a schoolboy's knowledge, thanks to the Oxford of + his younger day. The other was the author of this work, so fully + described in Hamilton's writings that there is no occasion to describe + him here. I shall try to say a few words in common language about the + paradoxers.</p> + + <p>Hamilton's great paradox was the <i>quantification of the + predicate</i>; a fearful phrase, easily explained. We all know that when + we say "Men are animals," a form wholly unquantified in phrase, we speak + of <i>all</i> men, but not of all animals: it is <i>some or all</i>, some + may be all for aught the proposition says. This + some-may-be-all-for-aught-we-say, or <i>not-none,</i> is the logician's + <i>some</i>. One would suppose <!-- Page 333 --><span class="pagenum"><a + name="page333"></a>[333]</span>that "all men are some animals," would + have been the logical phrase in all time: but the predicate never was + quantified. The few who alluded to the possibility of such a thing found + reasons for not adopting it over and above the great reason, that + Aristotle did not adopt it. For Aristotle never ruled in physics or + metaphysics <i>in the old time</i> with near so much of absolute sway as + he has ruled in logic <i>down to our own time</i>. The logicians knew + that in the proposition "all men are animals" the "animal" is not + <i>universal</i>, but <i>particular</i> yet no one dared to say that + <i>all</i> men are <i>some</i> animals, and to invent the phrase, + "<i>some</i> animals are <i>all</i> men" until Hamilton leaped the ditch, + and not only completed a system of enunciation, but applied it to + syllogism.</p> + + <p>My own case is as peculiar as his: I have proposed to introduce + mathematical <i>thought</i> into logic to an extent which makes the old + stagers cry:</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"St. Aristotle! what wild notions!</p> + <p>Serve a <i>ne exeat regno</i><a name="NtA_710" href="#Nt_710"><sup>[710]</sup></a> on him!"</p> + </div> + </div> + <p>Hard upon twenty years ago, a friend and opponent who stands high in + these matters, and who is not nearly such a sectary of Aristotle and + establishment as most, wrote to me as follows: "It is said that next to + the man who forms the taste of the nation, the greatest genius is the man + who corrupts it. I mean therefore no disrespect, but very much the + reverse, when I say that I have hitherto always considered you as a great + logical heresiarch." Coleridge says he thinks that it was Sir Joshua + Reynolds who made the remark: which, to copy a bull I once heard, I + cannot deny, because I was not there when he said it. My friend did not + call me to repentance and reconciliation with the church: I think he had + a guess that I was a reprobate sinner. My offences at that time were but + small: I went on spinning syllogism systems, all alien from the common + logic, until I had six, the initial letters of which, put together, from + the <!-- Page 334 --><span class="pagenum"><a + name="page334"></a>[334]</span>names I gave before I saw what they would + make, bar all repentance by the words</p> + + <div class="poem"> + <div class="stanza"> + <p>RUE NOT!</p> + </div> + </div> + <p>leaving to the followers of the old school the comfortable option of + placing the letters thus:</p> + + <div class="poem"> + <div class="stanza"> + <p>TRUE? NO!</p> + </div> + </div> + <p>It should however be stated that the question is not about absolute + truth or falsehood. No one denies that anything I call an inference is an + inference: they say that my alterations are <i>extra-logical</i>; that + they are <i>material</i>, not <i>formal</i>; and that logic is a + <i>formal</i> science.</p> + + <p>The distinction between material and formal is easily made, where the + usual perversions are not required. A <i>form</i> is an empty machine, + such as "Every X is Y"; it may be supplied with <i>matter</i>, as in + "Every <i>man</i> is <i>animal</i>." The logicians will not see that + their <i>formal</i> proposition, "Every X is Y," is material in three + points, the degree of assertion, the quantity of the proposition, and the + copula. The purely formal proposition is "There is the probability <span + class="grk">α</span> that X stands in the relation L to Y." The + time will come when it will be regretted that logic went without + paradoxers for two thousand years: and when much that has been said on + the distinction of form and matter will breed jokes.</p> + + <p>I give one instance of one mood of each of the systems, in the order + of the letters first written above.</p> + + <p><i>Relative.</i>—In this system the formal relation is taken, + that is, the copula may be any whatever. As a material instance, in which + the <i>relations</i> are those of consanguinity (of men understood), take + the following: X is the brother of Y; X is not the uncle of Z; therefore, + Z is not the child of Y. The discussion of relation, and of the + objections to the extension, is in the <i>Cambridge Transactions</i>, + Vol. X, Part 2; a crabbed conglomerate.</p> + + <p><i>Undecided.</i>—In this system one premise, and want of power + over another, infer want of power over a conclusion. <!-- Page 335 + --><span class="pagenum"><a name="page335"></a>[335]</span>As "Some men + are not capable of tracing consequences; we cannot be sure that there are + beings responsible for consequences who are incapable of tracing + consequences; therefore, we cannot be sure that all men are responsible + for the consequences of their actions."</p> + + <p><i>Exemplar.</i>—This, long after it suggested itself to me as a + means of correcting a defect in Hamilton's system, I saw to be the very + system of Aristotle himself, though his followers have drifted into + another. It makes its subject and predicate examples, thus: Any one man + is an animal; any one animal is a mortal; therefore, any one man is a + mortal.</p> + + <p><i>Numerical.</i>—Suppose 100 Ys to exist: then if 70 Xs be Ys, + and 40 Zs be Ys, it follows that 10 Xs (at least) are Zs. Hamilton, whose + mind could not generalize on symbols, saw that the word <i>most</i> would + come under this system, and admitted, as valid, such a syllogism as "most + Ys are Xs; most Ys are Zs; therefore, some Xs are Zs."</p> + + <p><i>Onymatic.</i>—This is the ordinary system much enlarged in + propositional forms. It is fully discussed in my <i>Syllabus of + Logic</i>.</p> + + <p><i>Transposed.</i>—In this syllogism the quantity in one premise + is transposed into the other. As, some Xs are not Ys; for every X there + is a Y which is Z; therefore, some Zs are not Xs.</p> + + <p>Sir William Hamilton of Edinburgh was one of the best friends and + allies I ever had. When I first began to publish speculation on this + subject, he introduced me to the logical world as having plagiarized from + him. This drew their attention: a mathematician might have written about + logic under forms which had something of mathematical look long enough + before the Aristotelians would have troubled themselves with him: as was + done by John Bernoulli,<a name="NtA_711" + href="#Nt_711"><sup>[711]</sup></a> <!-- Page 336 --><span + class="pagenum"><a name="page336"></a>[336]</span>James Bernoulli,<a + name="NtA_712" href="#Nt_712"><sup>[712]</sup></a> Lambert,<a + name="NtA_713" href="#Nt_713"><sup>[713]</sup></a> and Gergonne;<a + name="NtA_714" href="#Nt_714"><sup>[714]</sup></a> who, when our + discussion began, were not known even to omnilegent Hamilton. He + retracted his accusation of <i>wilful</i> theft in a manly way when he + found it untenable; but on this point he wavered a little, and was + convinced to the last that I had taken his principle unconsciously. He + thought I had done the same with Ploucquet<a name="NtA_715" + href="#Nt_715"><sup>[715]</sup></a> and Lambert. It was his pet notion + that I did not understand the commonest principles of logic, that I did + not always know the difference between the middle term of a syllogism and + its conclusion. It went against his grain to imagine that a mathematician + could be a logician. So long as he took me to be riding my own hobby, he + laughed consumedly: but when he thought he could make out that I was + mounted behind Ploucquet or Lambert, the current ran thus: "It would + indeed have been little short of a miracle had he, ignorant even of the + common principles of logic, been able of himself to rise to + generalization so lofty and so accurate as are supposed in the peculiar + doctrines of both the rival logicians, Lambert and Ploucquet—how + useless soever these may in practice prove to be." All this has been + sufficiently discussed elsewhere: "but, masters, remember that I am an + ass."</p> + + <p>I know that I never saw Lambert's work until after all Hamilton + supposed me to have taken was written: he himself, who read almost + everything, knew nothing about it until after I did. I cannot prove what + I say about my knowledge of Lambert: but the means of doing it may turn + up. For, by the casual turning up of an old letter, I <i>have</i> <!-- + Page 337 --><span class="pagenum"><a name="page337"></a>[337]</span>found + the means of clearing myself as to Ploucquet. Hamilton assumed that + (unconsciously) I took from Ploucquet the notion of a logical notation in + which the symbol of the conclusion is seen in the joint symbols of the + premises. For example, in my own fashion I write down ( . ) ( . ), two + symbols of premises. By these symbols I see that there is a valid + conclusion, and that it may be written in symbol by striking out the two + middle parentheses, which gives ( . . ) and reading the two negative dots + as an affirmative. And so I see in ( . ) ( . ) that ( ) is the + conclusion. This, in full, is the perception that "all are either Xs or + Ys" and "all are either Ys or Zs" necessitates "some Xs are Zs." Now in + Ploucquet's book of 1763, is found, "Deleatur in præmissis medius; id + quod restat indicat conclusionem."<a name="NtA_716" + href="#Nt_716"><sup>[716]</sup></a> In the paper in which I explain my + symbols—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 + <i>Formal Logic</i> what part of Ploucquet's book I had used: and a fair + disputant would either have strengthened his point by showing that I had + been at his part of the book, or allowed me the advantage of it being + apparent that I had not given evidence of having seen that part of the + book. My good friend, though an honest man, was sometimes unwilling to + allow due advantage to controversial opponents.</p> + + <p>But to my point. The only work of Ploucquet I ever saw was lent me by + my friend Dr. Logan,<a name="NtA_717" href="#Nt_717"><sup>[717]</sup></a> + with whom I have often corresponded on logic, etc. I chanced (in 1865) + <!-- Page 338 --><span class="pagenum"><a + name="page338"></a>[338]</span>to turn up the letter which he sent me + (Sept. 12, 1847) <i>with the book</i>. Part of it runs thus: "I + congratulate you on your success in your logical researches [that is, in + asking for the book, I had described some results]. Since the reading of + your first paper I have been satisfied as to the possibility of inventing + a logical notation in which the rationale of the inference is contained + in the symbol, though I never attempted to verify it [what I + communicated, then, satisfied the writer that I had done and communicated + what he, from my previous paper, suspected to be practicable]. I send you + Ploucquet's dissertation....'</p> + + <p>It now being manifest that I cannot be souring grapes which have been + taken from me, I will say what I never said in print before. There is not + the slightest merit in making the symbols of the premises yield that of + the conclusion by erasure: <i>the thing must do itself in every system + which symbolises quantities</i>. For in every syllogism (except the + inverted <i>Bramantip</i> of the Aristotelians) the conclusion is + manifest in this way without symbols. This <i>Bramantip</i> destroys + system in the Aristotelian lot: and circumstances which I have pointed + out destroy it in Hamilton's own collection. But in that enlargement of + the reputed Aristotelian system which I have called <i>onymatic</i>, and + in that correction of Hamilton's system which I have called + <i>exemplar</i>, the rule of erasure is universal, and may be seen + without symbols.</p> + + <p>Our first controversy was in 1846. In 1847, in my <i>Formal Logic</i>, + I gave him back a little satire for satire, just to show, as I stated, + that I could employ ridicule if I pleased. He was so offended with the + appendix in which this was contained, that he would not accept the copy + of the book I sent him, but returned it. Copies of controversial works, + sent from opponent to opponent, are not <i>presents</i>, in the usual + sense: it was a marked success to make him angry enough to forget this. + It had some effect however: during the rest of his life I wished to avoid + provocation; for I <!-- Page 339 --><span class="pagenum"><a + name="page339"></a>[339]</span>could not feel sure that excitement might + not produce consequences. I allowed his slashing account of me in the + <i>Discussions</i> to pass unanswered: and before that, when he proposed + to open a controversy in the <i>Athenæum</i> upon my second Cambridge + paper, I merely deferred the dispute until the next edition of my + <i>Formal Logic</i>. I cannot expect the account in the + <i>Discussions</i> to amuse an unconcerned reader as much as it amused + myself: but for a cut-and-thrust, might-and-main, tooth-and-nail, + hammer-and-tongs assault, I can particularly recommend it. I never knew, + until I read it, how much I should enjoy a thundering onslought on + myself, done with racy insolence by a master hand, to whom my good genius + had whispered <i>Ita feri ut se sentiat emori</i>.<a name="NtA_718" + href="#Nt_718"><sup>[718]</sup></a> Since that time I have, as the + Irishman said, become "dry moulded for want of a bating." Some of my + paradoxers have done their best: but theirs is mere twopenny—"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 <i>objective</i> 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'.</p> + + <p>Sir W. H. was suffering under local paralysis before our controversy + commenced: and though his mind was quite unaffected, a retort of as + downright a character as the attack might have produced serious effect + upon a person who had shown himself sensible of ridicule. Had a second + attack of his disorder followed an answer from me, I should have been + held to have caused it: though, looking at Hamilton's genial love of + combat, I strongly suspected that a retort in kind</p> + +<p><!-- Page 340 --><span class="pagenum"><a name="page340"></a>[340]</span></p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Would cheer his heart, and warm his blood,</p> + <p>And make him fight, and do him good."</p> + </div> + </div> + <p>But I could not venture to risk it. So all I did, in reply to the + article in the <i>Discussions</i>, was to write to him the following + note: which, as illustrating an etiquette of controversy, I insert.</p> + + <p>"I beg to acknowledge and thank you for.... It is necessary that I + should say a word on my retention of this work, with reference to your + return of the copy of my <i>Formal Logic</i>, which I presented to you on + its publication: a return made on the ground of your disapproval of the + account of our controversy which that work contained. According to my + view of the subject, any one whose dealing with the author of a book is + specially attacked in it, has a right to expect from the author that part + of the book in which the attack is made, together with so much of the + remaining part as is fairly context. And I hold that the acceptance by + the party assailed of such work or part of a work does not imply any + amount of approval of the contents, or of want of disapproval. On this + principle (though I am not prepared to add the word <i>alone</i>) I + forwarded to you the whole of my work on <i>Formal Logic</i> and my + second Cambridge Memoir. And on this principle I should have held you + wanting in due regard to my literary rights if you had not forwarded to + me your asterisked pages, with all else that was necessary to a full + understanding of their scope and meaning, so far as the contents of the + book would furnish it. For the remaining portion, which it would be a + hundred pities to separate from the pages in which I am directly + concerned, I am your debtor on another principle; and shall be glad to + remain so if you will allow me to make a feint of balancing the account + by the offer of two small works on subjects as little connected with our + discussion as the <i>Epistolæ Obscurorum Virorum</i>, or the Lutheran + dispute. I trust that by accepting my <i>Opuscula</i> you will enable me + to avoid the <!-- Page 341 --><span class="pagenum"><a + name="page341"></a>[341]</span>use of the knife, and leave me to cut you + up with the pen as occasion shall serve, I remain, etc. (April 21, + 1852)."</p> + + <p>I received polite thanks, but not a word about the body of the letter: + my argument, I suppose, was admitted.</p> + + <p> </p> + +<p class="cenhead">SOME DOGGEREL AND COUNTER DOGGEREL.</p> + + <p>I find among my miscellaneous papers the following <i>jeu + d'esprit</i>, or <i>jeu de bêtise</i>,<a name="NtA_719" + href="#Nt_719"><sup>[719]</sup></a> whichever the reader pleases—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 <i>in memoriam</i> [<i>technicam</i>] of the way in which + A E I O are used in logic: he added U, Y, for the addition of + <i>meet</i>, etc., to the system. I took the liberty of concocting some + counter-doggerel, just to show that a mathematician may have + architectonic power as well as a metaphysician.</p> + + <p> </p> + + <div class="poem"> + <div class="stanza"> + <p class="i8">DOGGEREL.</p> + <p class="i4"><span class="scac">BY SIR W. HAMILTON.</span></p> + <p>A it affirms of <i>this</i>, <i>these</i>, <i>all</i>,</p> + <p class="i2">Whilst E denies of <i>any</i>;</p> + <p>I it affirms (whilst O denies)</p> + <p class="i2">Of some (or few, or many).</p> + </div> + + <div class="stanza"> + <p>Thus A affirms, as E denies,</p> + <p class="i2">And definitely either;</p> + <p>Thus I affirms, as O denies,</p> + <p class="i2">And definitely neither.</p> + </div> + + <div class="stanza"> + <p>A half, left semidefinite,</p> + <p class="i2">Is worthy of its score;</p> + <p>U, then, affirms, as Y denies,</p> + <p class="i2">This, neither less nor more.</p> + </div> + + <div class="stanza"> + <p>Indefinito-definites,</p> + <p class="i2">I, UI, YO, last we come;</p> +<!-- Page 342 --><span class="pagenum"><a name="page342"></a>[342]</span> + <p>And this affirms, as that denies</p> + <p class="i2">Of <i>more</i>, <i>most</i> (<i>half</i>, <i>plus</i>, <i>some</i>).</p> + </div> + + <div class="stanza"> + <p class="i2">COUNTER DOGGEREL.</p> + <p class="i4"><span class="scac">BY PROF. DE MORGAN.</span></p> + <p class="i8">(1847.)</p> + <p>Great A affirms of all;</p> + <p class="i2">Sir William does so too:</p> + <p>When the subject is "my suspicion,"</p> + <p class="i2">And the predicate "must be true."</p> + </div> + + <div class="stanza"> + <p>Great E denies of all;</p> + <p class="i2">Sir William of all but one:</p> + <p>When he speaks about this present time,</p> + <p class="i2">And of those who in logic have done.</p> + </div> + + <div class="stanza"> + <p>Great I takes up but <i>some</i>;</p> + <p class="i2">Sir William! my dear soul!</p> + <p>Why then in all your writings,</p> + <p class="i2">Does "Great I" fill<a name="NtA_720" href="#Nt_720"><sup>[720]</sup></a> the whole!</p> + </div> + + <div class="stanza"> + <p>Great O says some are not;</p> + <p class="i2">Sir William's readers catch,</p> + <p>That some (modern) Athens is not without</p> + <p class="i2">An Aristotle to match.</p> + </div> + + <div class="stanza"> + <p class="hg3">"A half, left semi-definite,</p> + <p class="i2">Is worthy of its score:"</p> + <p>This looked very much like balderdash,</p> + <p class="i2">And neither less nor more.</p> + </div> + + <div class="stanza"> + <p>It puzzled me like anything;</p> + <p class="i2">In fact, it puzzled me worse:</p> + <p>Isn't schoolman's logic hard enough,</p> + <p class="i2">Without being in Sibyl's verse?</p> + </div> + + <div class="stanza"> +<!-- Page 343 --><span class="pagenum"><a name="page343"></a>[343]</span> + <p>At last, thinks I, 'tis German;</p> + <p class="i2">And I'll try it with some beer!</p> + <p>The landlord asked what bothered me so,</p> + <p class="i2">And at once he made it clear.</p> + </div> + + <div class="stanza"> + <p>It's <i>half-and-half</i>, the gentleman means;</p> + <p class="i2">Don't you see he talks of <i>score</i>?</p> + <p>That's the bit of memorandum</p> + <p class="i2">That we chalk behind the door.</p> + </div> + + <div class="stanza"> + <p><i>Semi-definite</i>'s outlandish;</p> + <p class="i2">But I see, in half a squint,</p> + <p>That he speaks of the lubbers who call for a quart,</p> + <p class="i2">When they can't manage more than a pint.</p> + </div> + + <div class="stanza"> + <p>Now I'll read it into English,</p> + <p class="i2">And then you'll answer me this:</p> + <p>If it isn't good logic all the world round,</p> + <p class="i2">I should like to know what is?</p> + </div> + + <div class="stanza"> + <p>When you call for a pot of half-and-half,</p> + <p class="i2">If you're lost to sense of shame,</p> + <p>You may leave it <i>semi-definite</i>,</p> + <p class="i2">But you pay for it all just the same.</p> + <p> * * * * * *</p> + </div> + </div> + <p>I am unspeakably comforted when I look over the above in remembering + that the question is not whether it be Pindaric or Horatian, but whether + the copy be as good as the original. And I say it is: and will take no + denial.</p> + + <p>Long live—long will live—the glad memory of William + Hamilton, Good, Learned, Acute, and Disputatious! He fought upon + principle: the motto of his book is:</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Truth, like a torch, the more it's shook it shines."</p> + </div> + </div> + <p>There is something in this; but metaphors, like puddings, quarrels, + rivers, and arguments, always have two sides to them. For instance,</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Truth, like a torch, the more it's shook it shines;</p> + <p class="i2">But those who want to use it, hold it steady.</p> + <p>They shake the flame who like a glare to gaze at,</p> + <p class="i2">They keep it still who want a light to see by."</p> + </div> + </div> +<p><!-- Page 344 --><span class="pagenum"><a name="page344"></a>[344]</span></p> + + <p> </p> + +<p class="cenhead">ANOTHER THEORY OF PARALLELS.</p> + +<blockquote class="b1n"> + + <p>Theory of Parallels. The proof of Euclid's axiom looked for in the + properties of the Equiangular Spiral. By Lieut-Col. G. Perronet + Thompson.<a name="NtA_721" href="#Nt_721"><sup>[721]</sup></a> The same, + second edition, revised and corrected. The same, third edition, + shortened, and freed from dependence on the theory of limits. The same, + fourth edition, ditto, ditto. All London, 1840, 8vo.</p> + +</blockquote> + + <p>To explain these editions it should be noted that General Thompson + rapidly modified his notions, and republished his tracts accordingly.</p> + + <p> </p> + +<p class="cenhead">SOME PRIMITIVE DARWINISM.</p> + +<blockquote class="b1n"> + + <p>Vestiges of the Natural History of Creation.<a name="NtA_722" + href="#Nt_722"><sup>[722]</sup></a> London, 1840, 12mo.</p> + +</blockquote> + + <p>This is the first edition of this celebrated work. Its form is a case + of the theory: the book is an undeniable duodecimo, but the size of its + paper gives it the look of not the smallest of octavos. Does not this + illustrate the law of development, the gradation of families, the + transference of species, and so on? If so, I claim the discovery of this + esoteric testimony of the book to its own contents; I defy any one to + point out the reviewer who has mentioned it. The work itself is <span + class="correction" title="text reads `decribed'">described</span> by its + author as "the first attempt to connect the natural sciences into a + history of creation." The attempt was commenced, and has been carried on, + both with marked talent, and will be continued. Great advantage will + result: at the worst we are but in the alchemy of some new chemistry, or + the astrology of some new astronomy. Perhaps it would be as well not to + be too sure on the matter, until we have an antidote to possible + consequences as exhibited under another theory, on which <!-- Page 345 + --><span class="pagenum"><a name="page345"></a>[345]</span>it is as + reasonable to speculate as on that of the <i>Vestiges</i>. I met long ago + with a splendid player on the guitar, who assured me, and was confirmed + by his friends, that he <i>never practised</i>, except in thought, and + did not possess an instrument: he kept his fingers acting in his mind, + until they got their habits; and thus he learnt the most difficult + novelties of execution. Now what if this should be a minor segment of a + higher law? What if, by constantly thinking of ourselves as descended + from primeval monkeys, we should—if it be true—actually + <i>get our tails again</i>? What if the first man who was detected with + such an appendage should be obliged to confess himself the author of the + <i>Vestiges</i>—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,</p> + + <div class="poem"> + <div class="stanza"> + <p>With a hole behind which his tail peeped through.</p> + </div> + </div> + <p>The first sentence of this book (1840) is a cast of the log, which + shows our rate of progress. "It is familiar knowledge that the earth + which we inhabit is a globe of somewhat less than 8,000 miles in + diameter, being one of a series of eleven which revolve at different + distances around the sun." The <i>eleven</i>! Not to mention the Iscariot + which Le Verrier and Adams calculated into existence, there is more than + a septuagint of <i>new</i> planetoids.</p> + + <p> </p> + +<p class="cenhead">ON RELIGIOUS INSURANCE.</p> + +<blockquote class="b1n"> + + <p>The Constitution and Rules of the Ancient and Universal 'Benefit + Society' established by Jesus Christ, exhibited, and its advantages and + claims maintained, against all Modern and <!-- Page 346 --><span + class="pagenum"><a name="page346"></a>[346]</span>merely Human + Institutions of the kind: A Letter very respectfully addressed to the + Rev. James Everett,<a name="NtA_723" href="#Nt_723"><sup>[723]</sup></a> + and occasioned by certain remarks made by him, in a speech to the Members + of the 'Wesleyan Centenary Institute' Benefit Society. Dated York, Dec. + 7, 1840. By Thomas Smith.<a name="NtA_724" + href="#Nt_724"><sup>[724]</sup></a> 12mo, (pp. 8.)</p> + +</blockquote> + + <p>The Wesleyan minister addressed had advocated provision against old + age, etc.: the writer declares all <i>private</i> provision un-Christian. + After decent maintenance and relief of family claims of indigence, he + holds that all the rest is to go to the "Benefit Society," of which he + draws up the rules, in technical form, with chapters of "Officers," + "Contributors" etc., from the Acts of the Apostles, etc., and some of the + early Fathers. He holds that a Christian may not "make a <i>private</i> + provision against the contingencies of the future": and that the great + "Benefit Society" is the divinely-ordained recipient of all the surplus + of his income; capital, beyond what is necessary for business, he is to + have none. A real good speculator shuts his eyes by instinct, when + opening them would not serve the purpose: he has the vizor of the Irish + fairy tale, which fell of itself over the eyes of the wearer the moment + he turned them upon the enchanted light which would have destroyed him if + he had caught sight of it. "Whiles it remained, was it not thine own? and + after it was sold, was it (the purchase-money) not in thine own power?" + would have been awkward to quote, and accordingly nothing is stated + except the well-known result, which is rule 3, cap. 5, "Prevention of + Abuses." By putting his principles together, the author can be made, + logically, to mean that the successors of the apostles should put to + death all contributors who are detected in not paying their full + premiums.</p> + +<p><!-- Page 347 --><span class="pagenum"><a name="page347"></a>[347]</span></p> + + <p>I have known one or two cases in which policy-holders have surrendered + their policies through having arrived at a conviction that direct + provision is unlawful. So far as I could make it out, these parties did + not think it unlawful to lay by out of income, except when this was done + in a manner which involved calculation of death-chances. It is singular + they did not see that the entrance of chance of death was the entrance of + the very principle of the benefit society described in the Acts of the + Apostles. The family of the one who died young received more in + proportion to <i>premiums</i> paid than the family of one who died old. + Every one who understands life assurance sees that—<i>bonus</i> + apart—the difference between an assurance office and a savings bank + consists in the adoption, <i>pro tanto</i>, of the principle of community + of goods. In the original constitution of the oldest assurance office, + the <i>Amicable Society</i>, the plan with which they started was nothing + but this: persons of all ages under forty-five paid one common premium, + and the proceeds were divided among the representatives of those who died + within the year.</p> + + <p> </p> + +<p class="cenhead">THE TWO OLD PARADOXES AGAIN.</p> + + <p>[I omitted from its proper place a manuscript quadrature (3.1416 + exactly) addressed to an eminent mathematician, dated in 1842 from the + debtor's ward of a country gaol. The unfortunate speculator says, "I have + labored many years to find the precise ratio." I have heard of several + cases in which squaring the circle has produced an inability to square + accounts. I remind those who feel a kind of inspiration to employ native + genius upon difficulties, without gradual progression from elements, that + the call is one which becomes stronger and stronger, and may lead, as it + has led, to abandonment of the duties of life, and all the consequences.] + <!-- Page 348 --><span class="pagenum"><a + name="page348"></a>[348]</span></p> + + <p> </p> + +<blockquote class="b1n"> + + <p>1842. Provisional Prospectus of the Double Acting Rotary Engine + Company. Also Mechanic's Magazine, March 26, 1842.</p> + +</blockquote> + + <p>Perpetual motion by a drum with one vertical half in mercury, the + other in a vacuum: the drum, I suppose, working round forever to find an + easy position. Steam to be superseded: steam and electricity convulsions + of nature never intended by Providence for the use of man. The price of + the present engines, as old iron, will buy new engines that will work + without fuel and at no expense. Guaranteed by the Count de Predaval,<a + name="NtA_725" href="#Nt_725"><sup>[725]</sup></a> the discoverer. I was + to have been a Director, but my name got no further than ink, and not so + far as official notification of the honor, partly owing to my having + communicated to the <i>Mechanic's Magazine</i> information privately + given to me, which gave premature publicity, and knocked up the plan.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>An Exposition of the Nature, Force, Action, and other properties of + Gravitation on the Planets. London, 1842, 12mo.</p> + + <p>An Investigation of the principles of the Rules for determining the + Measures of the Areas and Circumferences of Circular Plane Surfaces ... + London, 1844, 8vo.</p> + +</blockquote> + + <p>These are anonymous; but the author (whom I believe to be Mr. + Denison,<a name="NtA_726" href="#Nt_726"><sup>[726]</sup></a> presently + noted) is described as author of a new system of mathematics, and also of + mechanics. He had need have both, for he shows that the line which has a + square equal to a given circle, has a cube equal to the sphere on the + same diameter: that is, in old mathematics, the diameter is to the + circumference as 9 to 16! Again, admitting that the velocities of planets + in circular orbits are inversely as the square roots of their distances, + that is, admitting Kepler's law, he manages to prove that gravitation is + inversely as the square <i>root</i> of the distance: and suspects + magnetism of doing the difference between this and Newton's law. <!-- + Page 349 --><span class="pagenum"><a + name="page349"></a>[349]</span>Magnetism and electricity are, in physics, + the member of parliament and the cabman—at every man's bidding, as + Henry Warburton<a name="NtA_727" href="#Nt_727"><sup>[727]</sup></a> + said.</p> + + <p>The above is an outrageous quadrature. In the preceding year, 1841, + was published what I suppose at first to be a Maori quadrature, by + Maccook. But I get it from a cutting out of some French periodical, and I + incline to think that it must be by a Mr. M<sup>c</sup>Cook. He makes + <span class="grk">π</span> to be 2 + 2√(8√2 - 11).</p> + + <p> </p> + +<p class="cenhead">THE DUPLICATION PROBLEM.</p> + +<blockquote class="b1n"> + + <p>Refutation of a Pamphlet written by the Rev. John Mackey, R.C.P.,<a + name="NtA_728" href="#Nt_728"><sup>[728]</sup></a> entitled "A method of + making a cube double of a cube, founded on the principles of elementary + geometry," wherein his principles are proved erroneous, and the required + solution not yet obtained. By Robert Murphy.<a name="NtA_729" + href="#Nt_729"><sup>[729]</sup></a> Mallow, 1824, 12mo.</p> + +</blockquote> + + <p>This refutation was the production of an Irish boy of eighteen years + old, self-educated in mathematics, the son of a shoemaker at Mallow. He + died in 1843, leaving a name which is well known among mathematicians. + His works on the theory of equations and on electricity, and his papers + in the <i>Cambridge Transactions</i>, are all of high genius. The only + account of him which I know of is that which I wrote for the + <i>Supplement</i> of the <i>Penny Cyclopædia</i>. He was thrown by his + talents into a good income at Cambridge, with no social training except + penury, and very little intellectual training except mathematics. He fell + into dissipation, and his scientific career was almost arrested: but he + had great good in him, to my knowledge. A sentence in <!-- Page 350 + --><span class="pagenum"><a name="page350"></a>[350]</span>a letter from + the late Dean Peacock<a name="NtA_730" + href="#Nt_730"><sup>[730]</sup></a> to me—giving some advice about + the means of serving Murphy—sets out the old case: "Murphy is a man + whose <i>special</i> education is in advance of his <i>general</i>; and + such men are almost always difficult subjects to manage." This article + having been omitted in its proper place, I put it at 1843, the date of + Murphy's death.</p> + + <p> </p> + +<p class="cenhead">A NEW VALUE OF <span class="grk">π</span>.</p> + +<blockquote class="b1n"> + + <p>The Invisible Universe disclosed; or, the real Plan and Government of + the Universe. By Henry Coleman Johnson, Esq. London, 1843, 8vo.</p> + +</blockquote> + + <p>The book opens abruptly with:</p> + + <p>"First demonstration. Concerning the centre: showing that, because the + centre is an innermost point at an equal distance between two extreme + points of a right line, and from every two relative and opposite + intermediate points, it is composed of the two extreme internal points of + each half of the line; each extreme internal point attracting towards + itself all parts of that half to which it belongs...."</p> + + <p>Of course the circle is squared: and the circumference is 3-1/21 + diameters.</p> + + <p> </p> + +<p class="cenhead">SOME MODERN ASTROLOGY.</p> + +<blockquote class="b1n"> + + <p>Combination of the Zodiacal and Cometical Systems. Printed for the + London Society, Exeter Hall. Price Sixpence. (n. d. 1843.)</p> + +</blockquote> + + <p>What this London Society was, or the "combination," did not appear. + There was a remarkable comet in 1843, the tail of which was at first + confounded with what is called the <i>zodiacal light</i>. This + nicely-printed little tract, evidently got up with less care for expense + than is usual in such works, brings together all the announcements of the + astronomers, and adds a short head and tail piece, which I shall quote + entire. As the announcements are very ordinary <!-- Page 351 --><span + class="pagenum"><a name="page351"></a>[351]</span>astronomy, the reader + will be able to detect, if detection be possible, what is the meaning and + force of the "Combination of the Zodiacal and Cometical Systems":</p> + + <p>"<i>Premonition.</i> It has pleased the <span class="sc">Author</span> + <i>of</i> <span class="sc">Creation</span> to cause (to His <i>human and + reasoning</i> Creatures of this generation, by a '<i>combined</i>' + appearance in His <i>Zodiacal</i> and <i>Cometical</i> system) a + '<i>warning Crisis</i>' of universal concernment to this our <span + class="sc">Globe</span>. It is this '<i>Crisis</i>' that has so generally + '<span class="scac">ROUSED</span>' at this moment the '<i>nations + throughout the Earth</i>' that no equal interest has ever before been + excited by <span class="sc">Man</span>; unless it be in that caused by + the '<span class="sc">Pagan-Temple in Rome</span>,' which is recorded by + the elder Pliny, '<i>Nat. Hist.</i>' i. 23. iii. 3. <span + class="sc">Hardouin</span>."</p> + + <p>After the accounts given by the unperceiving astronomers, comes what + follows:</p> + + <p>"Such has been (<i>hitherto</i>) the only object discerned by the + '<i>Wise of this World</i>,' in this <i>twofold union</i> of the + '<i>Zodiacal</i>' and '<i>Cometical</i>' systems: yet it is nevertheless + a most '<i>Thrilling Warning</i>,' to <i>all</i> the inhabitants of this + precarious and transitory <span class="sc">Earth</span>. We have no + authorized intimation or reasonable prospective contemplation, of + '<i>current time</i>' beyond a year 1860, of the present century; or + rather, except '<i>the interval which may now remain from the present + year 1843, to a year 1860</i>' (<span title="hêmeras HEXÊKONTA" class="grk" + >ἡμέρας + ἙΞΗΚΟΝΤΑ</span>—'<i>threescore + or sixty days</i>'—'<i>I have appointed each</i> "<span + class="sc">Day</span>" <i>for a</i> "<span class="sc">Year</span>,"' + <i>Ezek.</i> iv. 6): and we know, from our '<i>common experience</i>,' + how speedily such a measure of time will pass away.</p> + + <p>"No words can be '<i>more explicit</i>' than these of <span + class="sc">our blessed Lord</span>: viz. '<span class="sc">This + Gospel</span> <i>of the Kingdom shall be preached in</i> <span + class="scac">ALL</span> the <span class="sc">Earth</span>, <i>for a + Witness to</i> <span class="sc">all Nations; and then</span>, <i>shall + the</i> <span class="sc">End come</span>.' The '<i>next 18 years</i>' + must therefore supply the interval of the '<i>special Episcopal + forerunners</i>.'</p> + +<p class="cenhead">(Matt. xxiv. 14.)</p> + + <p>"See the '<span class="sc">Jewish Intelligencer</span>' of the present + month (<i>April</i>), p. 153, for the '<i>Debates in Parliament</i>,' + respecting <!-- Page 352 --><span class="pagenum"><a + name="page352"></a>[352]</span>the <span class="sc">Bishop of + Jerusalem</span>, <i>viz.</i> Dr. Bowring,<a name="NtA_731" + href="#Nt_731"><sup>[731]</sup></a> Mr. Hume,<a name="NtA_732" + href="#Nt_732"><sup>[732]</sup></a> Sir R. Inglis,<a name="NtA_733" + href="#Nt_733"><sup>[733]</sup></a> Sir R. Peel,<a name="NtA_734" + href="#Nt_734"><sup>[734]</sup></a> Viscount Palmerston.<a name="NtA_735" + href="#Nt_735"><sup>[735]</sup></a>"</p> + + <p>I have quoted this at length, to show the awful threats which were + published at a time of some little excitement about the phenomenon, under + the name of the <i>London Society</i>. The assumption of a corporate + appearance is a very unfair trick: and there are junctures at which harm + might be done by it.</p> + + <p> </p> + +<p class="cenhead">THE NUMBER OF THE BEAST.</p> + +<blockquote class="b1n"> + + <p><i>Wealth</i> the name and number of the Beast, 666, in the Book of + Revelation. [by John Taylor.<a name="NtA_736" + href="#Nt_736"><sup>[736]</sup></a>] London, 1844, 8vo.</p> + +</blockquote> + + <p>Whether Junius or the Beast be the more difficult to identify, must be + referred to Mr. Taylor, the only person who has attempted both. His + cogent argument on the political secret is not unworthily matched in his + treatment of the theological riddle. He sees the solution in <span + title="euporia" class="grk" + >εὐπορία</span>, which occurs + in the Acts of the Apostles as the word for wealth in one of its most + disgusting forms, and makes 666 in the most straightforward way. This + explanation has as good a chance as any other. The work contains a + general <!-- Page 353 --><span class="pagenum"><a + name="page353"></a>[353]</span>attempt at explanation of the Apocalypse, + and some history of opinion on the subject. It has not the prolixity + which is so common a fault of apocalyptic commentators.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>A practical Treatise on Eclipses ... with remarks on the anomalies of + the present Theory of the Tides. By T. Kerigan,<a name="NtA_737" + href="#Nt_737"><sup>[737]</sup></a> F.R.S. 1844, 8vo.</p> + +</blockquote> + + <p>Containing also a refutation of the theory of the tides, and + afterwards increased by a supplement, "Additional facts and arguments + against the theory of the tides," in answer to a short notice in the + <i>Athenæum</i> journal. Mr. Kerigan was a lieutenant in the Navy: he + obtained admission to the Royal Society just before the publication of + his book.</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>A new theory of Gravitation. By Joseph Denison,<a name="NtA_738" + href="#Nt_738"><sup>[738]</sup></a> Esq. London, 1844, 12mo.</p> + + <p>Commentaries on the Principia. By the author of 'A new theory of + Gravitation.' London, 1846, 8vo.</p> + +</blockquote> + + <p>Honor to the speculator who can be put in his proper place by one + sentence, be that place where it may.</p> + + <p>"But we have shown that the velocities are inversely as the square + roots of the mean distances from the sun; wherefore, by equality of + ratios, the forces of the sun's gravitation upon them are also inversely + as the square roots of their distances from the sun."</p> + + <p> </p> + +<p class="cenhead">EASTER DAY PARADOXERS.</p> + + <p>In the years 1818 and 1845 the full moon fell on Easter Day, having + been particularly directed to fall before it in the act for the change of + style and in the English missals and prayer-books of all time: perhaps it + would be more correct to say that Easter Day was directed to fall after + the full moon; "but the principle is the same." No explanation was given + in 1818, but Easter was kept by the tables, <!-- Page 354 --><span + class="pagenum"><a name="page354"></a>[354]</span>in defiance of the + rule, and of several protests. A chronological panic was beginning in + December 1844, which was stopped by the <i>Times</i> newspaper printing + extracts from an article of mine in the <i>Companion to the Almanac</i> + for 1845, which had then just appeared. No one had guessed the true + reason, which is that the thing called the moon in the Gregorian Calendar + is not the moon of the heavens, but a fictitious imitation put wrong on + purpose, as will presently appear, partly to keep Easter out of the way + of the Jews' Passover, partly for convenience of calculation. The + apparent error happens but rarely; and all the work will perhaps have to + be gone over next time. I now give two bits of paradox.</p> + + <p>Some theologians were angry at this explanation. A review called the + <i>Christian Observer</i> (of which Christianity I do not know) got up a + crushing article against me. I did not look at it, feeling sure that an + article on such a subject which appeared on January 1, 1845, against a + publication made in December 1844, must be a second-hand job. But some + years afterwards (Sept. 10, 1850), the reviews, etc. having been just + placed at the disposal of readers in the <i>old</i> reading-room of the + Museum, I made a tour of inspection, came upon my critic on his perch, + and took a look at him. I was very glad to remember this, for, though + expecting only second-hand, yet even of this there is good and bad; and I + expected to find some hints in the good second-hand of a respectable + clerical publication. I read on, therefore, attentively, but not long: I + soon came to the information that some additions to Delambre's<a + name="NtA_739" href="#Nt_739"><sup>[739]</sup></a> statement of the rule + for finding Easter, belonging to distant years, had been made by Sir + Harris Nicolas!<a name="NtA_740" href="#Nt_740"><sup>[740]</sup></a> Now + as I myself furnished my friend Sir H. N. with Delambre's digest of <!-- + Page 355 --><span class="pagenum"><a + name="page355"></a>[355]</span>Clavius's<a name="NtA_741" + href="#Nt_741"><sup>[741]</sup></a> rule, which I translated out of + algebra into common language for the purpose, I was pretty sure this was + the ignorant reading of a person to whom Sir H. N. was the highest + <i>arithmetical</i> 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.</p> + + <p>The second case is this. Shortly after the publication of my article, + a gentleman called at my house, and, finding I was not at home, sent up + his card—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 <!-- + Page 356 --><span class="pagenum"><a name="page356"></a>[356]</span>would + not be ready to run if it were altered the wrong way. A doubt comes over + him: would Mrs. De M., in the event of her being mistaken, give him the + very earliest information? Promise given; profusion of thanks; more + apologies; and departure.</p> + + <p>Now, candid reader!—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.</p> + + <p>To give a better chance of the explanation being at once produced, + next time the real full moon and Easter Day shall fall together, I insert + here a summary which was printed in the Irish Prayer-book of the + Ecclesiastical Society. If the amusement given by paradoxers should + prevent a useless discussion some years hence, I and the paradoxers shall + have done a little good between us—at any rate, I have done my best + to keep the heavy weight afloat by tying bladders to it. I think the next + occurrence will be in 1875.</p> + +<p class="cenhead"><span class="scac">EASTER DAY.</span></p> + + <p>In the years 1818 and 1845, Easter Day, as given by the <i>rules + in</i> 24 Geo. II cap. 23. (known as the act for the <i>change of + style</i>) contradicted the <i>precept</i> given in the preliminary + explanations. The precept is as follows:</p> + + <p>"<i>Easter Day</i>, on which the rest" of the moveable feasts "depend, + is always the First Sunday after the Full Moon, which happens upon or + next after the Twenty-first Day of <!-- Page 357 --><span + class="pagenum"><a name="page357"></a>[357]</span><i>March</i>; and if + the Full Moon happens upon a Sunday, <i>Easter Day</i> is the Sunday + after."</p> + + <p>But in 1818 and 1845, the full moon fell on a Sunday, and yet the + rules gave <i>that same Sunday</i> for Easter Day. Much discussion was + produced by this circumstance in 1818: but a repetition of it in 1845 was + nearly altogether prevented by a timely<a name="NtA_742" + href="#Nt_742"><sup>[742]</sup></a> reference to the intention of those + who conducted the Gregorian reformation of the Calendar. Nevertheless, + seeing that the apparent error of the Calendar is due to the precept in + the Act of Parliament, which is both erroneous and insufficient, and that + the difficulty will recur so often as Easter Day falls on the day of full + moon, it may be advisable to select from the two articles cited in the + note such of their conclusions and rules, without proof or controversy, + as will enable the reader to understand the main points of the Easter + question, and, should he desire it, to calculate for himself the Easter + of the old or new style, for any given year.</p> + + <p>1. In the very earliest age of Christianity, a controversy arose as to + the mode of keeping Easter, some desiring to perpetuate the + <i>Passover</i>, others to keep the <i>festival of the Resurrection</i>. + The first afterwards obtained the name of <i>Quartadecimans</i>, from + their Easter being always kept on the <i>fourteenth day</i> of the moon + (Exod. xii. 18, Levit. xxiii. 5.). But though it is unquestionable that a + Judaizing party existed, it is also likely that many dissented on + chronological grounds. It is clear that no <i>perfect</i> anniversary can + take place, except when the fourteenth of the moon, and with it the + passover, falls on a Friday. Suppose, for instance, it falls on a + Tuesday: one of three things must be <!-- Page 358 --><span + class="pagenum"><a name="page358"></a>[358]</span>done. Either (which + seems never to have been proposed) the crucifixion and resurrection must + be celebrated on Tuesday and Sunday, with a wrong interval; or the former + on Tuesday, the latter on Thursday, abandoning the first day of the week; + or the former on Friday, and the latter on Sunday, abandoning the paschal + commemoration of the crucifixion.</p> + + <p>The last mode has been, as every one knows, finally adopted. The + disputes of the first three centuries did not turn on any <i>calendar</i> + questions. The Easter question was merely the symbol of the struggle + between what we may call the Jewish and Gentile sects of Christians: and + it nearly divided the Christian world, the Easterns, for the most part, + being <i>Quartadecimans</i>. It is very important to note that there is + no recorded dispute about a method of predicting the new moon, that is, + no general dispute leading to formation of sects: there may have been + difficulties, and discussions about them. The Metonic cycle, presently + mentioned, must have been used by many, perhaps most, churches.</p> + + <p>2. The question came before the Nicene Council (A.D. 325) not as an + astronomical, but as a doctrinal, question: it was, in fact, this, Shall + the <i>passover</i><a name="NtA_743" href="#Nt_743"><sup>[743]</sup></a> + be treated as a part of Christianity? The Council resolved this question + in the negative, and the only information on its premises and conclusion, + or either, which comes from itself, is contained in the following + sentence of the synodical epistle, which epistle is preserved by + Socrates<a name="NtA_744" href="#Nt_744"><sup>[744]</sup></a> and + Theodoret.<a name="NtA_745" href="#Nt_745"><sup>[745]</sup></a> "We also + send <!-- Page 359 --><span class="pagenum"><a + name="page359"></a>[359]</span>you the good news concerning the unanimous + consent of all in reference to the celebration of the most solemn feast + of Easter, for this difference also has been made up by the assistance of + your prayers: so that all the brethren in the East, who formerly + celebrated this festival <i>at the same time as the Jews</i>, will in + future conform <i>to the Romans and to us</i>, and to all who have of old + observed <i>our manner</i> of celebrating Easter." This is all that can + be found on the subject: none of the stories about the Council ordaining + the astronomical mode of finding Easter, and introducing the Metonic + cycle into ecclesiastical reckoning, have any contemporary evidence: the + canons which purport to be those of the Nicene Council do not contain a + word about Easter; and this is evidence, whether we suppose those canons + to be genuine or spurious.</p> + + <p>3. The astronomical dispute about a lunar cycle for the prediction of + Easter either commenced, or became prominent, by the extinction of + greater ones, soon after the time of the Nicene Council. Pope Innocent + I<a name="NtA_746" href="#Nt_746"><sup>[746]</sup></a> met with + difficulty in 414. S. Leo,<a name="NtA_747" + href="#Nt_747"><sup>[747]</sup></a> in 454, ordained that Easter of 455 + should be April 24; which is right. It is useless to record details of + these disputes in a summary: the result was, that in the year 463, Pope + Hilarius<a name="NtA_748" href="#Nt_748"><sup>[748]</sup></a> employed + Victorinus<a name="NtA_749" href="#Nt_749"><sup>[749]</sup></a> of + Aquitaine to correct the Calendar, and Victorinus formed a rule which + lasted until the sixteenth century. He combined the Metonic cycle and the + solar cycle presently described. But <!-- Page 360 --><span + class="pagenum"><a name="page360"></a>[360]</span>this cycle bears the + name of Dionysius Exiguus,<a name="NtA_750" + href="#Nt_750"><sup>[750]</sup></a> a Scythian settled at Rome, about + A.D. 530, who adapted it to his new yearly reckoning, when he abandoned + the era of Diocletian as a commencement, and constructed that which is + now in common use.</p> + + <p>4. With Dionysius, if not before, terminated all difference as to the + mode of keeping Easter which is of historical note: the increasing + defects of the Easter Cycle produced in time the remonstrance of persons + versed in astronomy, among whom may be mentioned Roger Bacon,<a + name="NtA_751" href="#Nt_751"><sup>[751]</sup></a> Sacrobosco,<a + name="NtA_752" href="#Nt_752"><sup>[752]</sup></a> Cardinal Cusa,<a + name="NtA_753" href="#Nt_753"><sup>[753]</sup></a> Regiomontanus,<a + name="NtA_754" href="#Nt_754"><sup>[754]</sup></a> etc. From the middle + of the sixth to that of the sixteenth century, one rule was observed.</p> + + <p>5. The mode of applying astronomy to chronology has always involved + these two principles. First, the actual position of the heavenly body is + not the object of consideration, but what astronomers call its <i>mean + place</i>, which may be described thus. Let a fictitious sun or moon move + in the heavens, in such manner as to revolve among the fixed stars at an + average rate, avoiding the alternate accelerations and retardations which + take place in every planetary motion. Thus the fictitious (say + <i>mean</i>) sun and moon are always very near to the real sun and moon. + The ordinary clocks show time by the mean, not the real, sun: and it was + always laid down that Easter depends on the opposition (or full moon) of + the mean sun and moon, not of the real ones. Thus we see that, were the + Calendar ever so correct <!-- Page 361 --><span class="pagenum"><a + name="page361"></a>[361]</span>as to the <i>mean</i> moon, it would be + occasionally false as to the <i>true</i> one: if, for instance, the + opposition of the mean sun and moon took place at one second before + midnight, and that of the real bodies only two seconds afterwards, the + calendar day of full moon would be one day before that of the common + almanacs. Here is a way in which the discussions of 1818 and 1845 might + have arisen: the British legislature has defined <i>the moon</i> as the + regulator of the paschal calendar. But this was only a part of the + mistake.</p> + + <p>6. Secondly, in the absence of perfectly accurate knowledge of the + solar and lunar motion (and for convenience, even if such knowledge + existed), cycles are, and always have been taken, which serve to + represent those motions nearly. The famous Metonic cycle, which is + introduced into ecclesiastical chronology under the name of the cycle of + the golden numbers, is a period of 19 Julian<a name="NtA_755" + href="#Nt_755"><sup>[755]</sup></a> years. This period, in the old + Calendar, was taken to contain exactly 235 <i>lunations</i>, or intervals + between new moons, of the mean moon. Now the state of the case is:</p> + + <p>19 average Julian years make 6939 days 18 hours.</p> + + <p>235 average lunations make 6939 days 16 hours 31 minutes.</p> + + <p>So that successive cycles of golden numbers, supposing the first to + start right, amount to making the new moons fall too late, gradually, so + that the mean moon <i>of this cycle</i> gains 1 hour 29 minutes in 19 + years upon the mean moon of the heavens, or about a day in 300 years. + When the Calendar was reformed, the calendar new moons were four days in + advance of the mean moon of the heavens: so that, for instance, calendar + full moon on the 18th usually meant real full moon on the 14th.</p> + + <p>7. If the difference above had not existed, the moon of the heavens + (the mean moon at least), would have returned <!-- Page 362 --><span + class="pagenum"><a name="page362"></a>[362]</span>permanently to the same + days of the month in 19 years; with an occasional slip arising from the + unequal distribution of the leap years, of which a period contains + sometimes five and sometimes four. As a general rule, the days of new and + full moon in any one year would have been also the days of new and full + moon of a year having 19 more units in its date. Again, if there had been + no leap years, the days of the month would have returned to the same days + of the week every seven years. The introduction of occasional 29ths of + February disturbs this, and makes the permanent return of month days to + week days occur only after 28 years. If all had been true, the lapse of + 28 times 19, or 532 years, would have restored the year in every point: + that is, A.D. 1, for instance, and A.D. 533, would have had the same + almanac in every matter relating to week days, month days, sun, and moon + (mean sun and moon at least). And on the supposition of its truth, the + old system of Dionysius was framed. Its errors, are, first, that the + moments of mean new moon advance too much by 1 h. 29 m. in 19 average + Julian years; secondly, that the average Julian year of 365¼ days is too + long by 11 m. 10 s.</p> + + <p>8. The Council of Trent, moved by the representations made on the + state of the Calendar, referred the consideration of it to the Pope. In + 1577, Gregory XIII<a name="NtA_756" href="#Nt_756"><sup>[756]</sup></a> + submitted to the Roman Catholic Princes and Universities a plan presented + to him by the representatives of Aloysius Lilius,<a name="NtA_757" + href="#Nt_757"><sup>[757]</sup></a> then deceased. This plan being + approved of, the Pope nominated a commission to consider its details, the + working member of which was the Jesuit Clavius. A short work was prepared + by Clavius, descriptive of the new Calendar: this <!-- Page 363 --><span + class="pagenum"><a name="page363"></a>[363]</span>was published<a + name="NtA_758" href="#Nt_758"><sup>[758]</sup></a> in 1582, with the + Pope's bull (dated February 24, 1581) prefixed. A larger work was + prepared by Clavius, containing fuller explanation, and entitled + <i>Romani Calendarii a Gregorio XIII. Pontifice Maximo restituti + Explicatio</i>. This was published at Rome in 1603, and again in the + collection of the works of Clavius in 1612.</p> + + <p>9. The following extracts from Clavius settle the question of the + meaning of the term <i>moon</i>, as used in the Calendar:</p> + + <p>"Who, except a few who think they are very sharp-sighted in this + matter, is so blind as not to see that the 14th of the moon and the full + moon are not the same things in the Church of God?... Although the + Church, in finding the new moon, and from it the 14th day, <i>uses + neither the true nor the mean motion of the moon</i>, but measures only + according to the order of a cycle, it is nevertheless undeniable that the + mean full moons found from astronomical tables are of the greatest use in + determining the cycle which is to be preferred ... the new moons of which + cycle, in order to the due celebration of Easter, should be so arranged + that the 14th days of those moons, reckoning from the day of new moon + <i>inclusive</i>, should not fall two or more days before the mean full + moon, but only one day, or else on the very day itself, or not long + after. And even thus far the Church need not take very great pains ... + for it is sufficient that all should reckon by the 14th day of the moon + in the cycle, even though sometimes it <i>should be more than one day + before or after</i> the mean full moon.... We have taken pains that in + our cycle the new moons should <i>follow</i> the real new moons, so that + the 14th of the moon should fall either the day before the mean full + moon, or on that day, or not long after; and this was done on purpose, + for if the new moon of the cycle fell on the same day as the mean new + moon of the <!-- Page 364 --><span class="pagenum"><a + name="page364"></a>[364]</span>astronomers, it might chance that we + should celebrate Easter on the same day as the Jews or the Quartadeciman + heretics, which would be absurd, or else before them, which would be + still more absurd."</p> + + <p>From this it appears that Clavius continued the Calendar of his + predecessors in the choice of the <i>fourteenth</i> day of the moon. Our + legislature lays down the day of the <i>full moon</i>: and this mistake + appears to be rather English than Protestant; for it occurs in missals + published in the reign of Queen Mary. The calendar lunation being 29½ + days, the middle day is the <i>fifteenth</i> day, and this is and was + reckoned as the day of the full moon. There is every right to presume + that the original passover was a feast of the <i>real full moon</i>: but + it is most probable that the moons were then reckoned, not from the + astronomical conjunction with the sun, which nobody sees except at an + eclipse, but from the day of <i>first visibility</i> of the new moon. In + fine climates this would be the day or two days after conjunction; and + the fourteenth day from that of first visibility inclusive, would very + often be the day of full moon. The following is then the proper + correction of the precept in the Act of Parliament:</p> + + <p>Easter Day, on which the rest depend, is always the First Sunday after + the <i>fourteenth day</i> of the <i>calendar</i> moon which happens upon + or next after the Twenty-first day of March, <i>according to the rules + laid down for the construction of the Calendar</i>; and if the + <i>fourteenth day</i> happens upon a Sunday, Easter Day is the Sunday + after.</p> + + <p>10. Further, it appears that Clavius valued the celebration of the + festival after the Jews, etc., more than astronomical correctness. He + gives comparison tables which would startle a believer in the + astronomical intention of his Calendar: they are to show that a calendar + in which the moon is always made a day older than by him, <i>represents + the heavens better than he has done, or meant to do</i>. But it must be + observed that this diminution of the real moon's age has <!-- Page 365 + --><span class="pagenum"><a name="page365"></a>[365]</span>a tendency to + make the English explanation often practically accordant with the + Calendar. For the fourteenth day of Clavius <i>is</i> generally the + fifteenth day of the mean moon of the heavens, and therefore most often + that of the real moon. But for this, 1818 and 1845 would not have been + the only instances of our day in which the English precept would have + contradicted the Calendar.</p> + + <p>11. In the construction of the Calendar, Clavius adopted the ancient + cycle of 532 years, but, we may say, without ever allowing it to run out. + At certain periods, a shift is made from one part of the cycle into + another. This is done whenever what should be Julian leap year is made a + common year, as in 1700, 1800, 1900, 2100, etc. It is also done at + certain times to correct the error of 1 h. 19 m., before referred to, in + each cycle of golden numbers: Clavius, to meet his view of the amount of + that error, put forward the moon's age a day 8 times in 2,500 years. As + we cannot enter at full length into the explanation, we must content + ourselves with giving a set of rules, independent of tables, by which the + reader may find Easter for himself in any year, either by the old + Calendar or the new. Any one who has much occasion to find Easters and + movable feasts should procure Francœur's<a name="NtA_759" + href="#Nt_759"><sup>[759]</sup></a> tables.</p> + + <p>12. <i>Rule for determining Easter Day of the Gregorian Calendar in + any year of the new style.</i> To the several parts <!-- Page 366 + --><span class="pagenum"><a name="page366"></a>[366]</span>of the rule + are annexed, by way of example, the results for the year 1849.</p> + + <p>I. Add 1 to the given year. (1850).</p> + + <p>II. Take the quotient of the given year divided by 4, neglecting the + remainder. (462).</p> + + <p>III. Take 16 from the centurial figures of the given year, if it can + be done, and take the remainder. (2).</p> + + <p>IV. Take the quotient of III. divided by 4, neglecting the remainder. + (0).</p> + + <p>V. From the sum of I, II, and IV., subtract III. (2310).</p> + + <p>VI. Find the remainder of V. divided by 7. (0).</p> + + <p>VII. Subtract VI. from 7; this is the number of the dominical + letter</p> + +<table class="nob" summary="Dominical letters" title="Dominical letters"> +<tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td valign="middle">(7; dominical letter G).</td></tr> +<tr><td>A</td><td>B</td><td>C</td><td>D</td><td>E</td><td>F</td><td>G</td></tr> +</table> + + <p>VIII. Divide I. by 19, the remainder (or 19, if no remainder) is the + <i>golden number</i>. (7).</p> + + <p>IX. From the centurial figures of the year subtract 17, divide by 25, + and keep the quotient. (0).</p> + + <p>X. Subtract IX. and 15 from the centurial figures, divide by 3, and + keep the quotient. (1).</p> + + <p>XI. To VIII. add ten times the next less number, divide by 30, and + keep the remainder. (7).</p> + + <p>XII. To XI. add X. and IV., and take away III., throwing out thirties, + if any. If this give 24, change it into 25. If 25, change it into 26, + whenever the golden number is greater than 11. If 0, change it into 30. + Thus we have the epact, or age of the <i>Calendar</i> moon at the + beginning of the year. (6).</p> + +<table width="100%" summary="Epacts" title="Epacts"><tr><td valign="top" class="spac" style="width:50%"> +<i>When the Epact is 23, or less.</i> + + <p>XIII. Subtract XII., the epact, from 45. (39).</p> + + <p>XIV. Subtract the epact from 27, divide by 7, and keep the remainder, + or 7, if there be no remainder. (7)</p> + +</td><td valign="top" class="spac" style="width:50%"> +<i>When the Epact is greater than 23.</i> + + <p>XIII. Subtract XII., the epact, from 75.</p> + + <p>XIV. Subtract the epact from 57, divide by 7, and keep the remainder, + or 7, if there be no remainder.</p> + +</td></tr></table> + + <p>XV. To XIII. add VII., the dominical number, (and 7 besides, if XIV. + be greater than VII.,) and subtract XIV., the result is the day of March, + or if more than 31, subtract 31, and <!-- Page 367 --><span + class="pagenum"><a name="page367"></a>[367]</span>the result is the day + of April, on which Easter Sunday falls. (39; Easter Day is April 8).</p> + + <p>In the following examples, the several results leading to the final + conclusion are tabulated.</p> + +<table class="allbctr" summary="Easter calculations" title="Easter calculations"> +<tr><td class="allb"><span class="sc">Given Year</span></td><td class="allb" align="right">1592</td><td class="allb" align="right">1637</td><td class="allb" align="right">1723</td><td class="allb" align="right">1853</td><td class="allb" align="right">2018</td><td class="allb" align="right">4686</td></tr> +<tr><td class="vertb" align="right">I.</td><td class="vertb" align="right">1593</td><td class="vertb" align="right">1638</td><td class="vertb" align="right">1724</td><td class="vertb" align="right">1854</td><td class="vertb" align="right">2019</td><td class="vertb" align="right">4687</td></tr> +<tr><td class="vertb" align="right">II.</td><td class="vertb" align="right">398</td><td class="vertb" align="right">409</td><td class="vertb" align="right">430</td><td class="vertb" align="right">463</td><td class="vertb" align="right">504</td><td class="vertb" align="right">1171</td></tr> +<tr><td class="vertb" align="right">III.</td><td class="vertb" align="right">—</td><td class="vertb" align="right">0</td><td class="vertb" align="right">1</td><td class="vertb" align="right">2</td><td class="vertb" align="right">4</td><td class="vertb" align="right">30</td></tr> +<tr><td class="vertb" align="right">IV.</td><td class="vertb" align="right">—</td><td class="vertb" align="right">0</td><td class="vertb" align="right">0</td><td class="vertb" align="right">0</td><td class="vertb" align="right">1</td><td class="vertb" align="right">7</td></tr> +<tr><td class="vertb" align="right">V.</td><td class="vertb" align="right">1991</td><td class="vertb" align="right">2047</td><td class="vertb" align="right">2153</td><td class="vertb" align="right">2315</td><td class="vertb" align="right">2520</td><td class="vertb" align="right">5835</td></tr> +<tr><td class="vertb" align="right">VI.</td><td class="vertb" align="right">3</td><td class="vertb" align="right">3</td><td class="vertb" align="right">4</td><td class="vertb" align="right">5</td><td class="vertb" align="right">0</td><td class="vertb" align="right">4</td></tr> +<tr><td class="vertb" align="right">VII.</td><td class="vertb" align="right">4</td><td class="vertb" align="right">4</td><td class="vertb" align="right">3</td><td class="vertb" align="right">2</td><td class="vertb" align="right">7</td><td class="vertb" align="right">3</td></tr> +<tr><td class="vertb" align="right">VIII.</td><td class="vertb" align="right">16</td><td class="vertb" align="right">4</td><td class="vertb" align="right">14</td><td class="vertb" align="right">11</td><td class="vertb" align="right">5</td><td class="vertb" align="right">13</td></tr> +<tr><td class="vertb" align="right">IX.</td><td class="vertb" align="right">—</td><td class="vertb" align="right">—</td><td class="vertb" align="right">0</td><td class="vertb" align="right">0</td><td class="vertb" align="right">0</td><td class="vertb" align="right">1</td></tr> +<tr><td class="vertb" align="right">X.</td><td class="vertb" align="right">0</td><td class="vertb" align="right">0</td><td class="vertb" align="right">0</td><td class="vertb" align="right">1</td><td class="vertb" align="right">1</td><td class="vertb" align="right">10</td></tr> +<tr><td class="vertb" align="right">XI.</td><td class="vertb" align="right">16</td><td class="vertb" align="right">4</td><td class="vertb" align="right">24</td><td class="vertb" align="right">21</td><td class="vertb" align="right">15</td><td class="vertb" align="right">13</td></tr> +<tr><td class="vertb" align="right">XII.</td><td class="vertb" align="right">16</td><td class="vertb" align="right">4</td><td class="vertb" align="right">23</td><td class="vertb" align="right">20</td><td class="vertb" align="right">13</td><td class="vertb" align="right">0 say 30</td></tr> +<tr><td class="vertb" align="right">XIII.</td><td class="vertb" align="right">29</td><td class="vertb" align="right">41</td><td class="vertb" align="right">22</td><td class="vertb" align="right">25</td><td class="vertb" align="right">32</td><td class="vertb" align="right">45</td></tr> +<tr><td class="vertb" align="right">XIV.</td><td class="vertb" align="right">4</td><td class="vertb" align="right">2</td><td class="vertb" align="right">4</td><td class="vertb" align="right">7</td><td class="vertb" align="right">7</td><td class="vertb" align="right">6</td></tr> +<tr><td class="vertb" align="right">XV.</td><td class="vertb" align="right">29</td><td class="vertb" align="right">43</td><td class="vertb" align="right">28</td><td class="vertb" align="right">27</td><td class="vertb" align="right">32</td><td class="vertb" align="right">49</td></tr> +<tr><td class="vertb" align="right">Easter Day</td><td class="vertb" align="right">Mar.29</td><td class="vertb" align="right">Apr.12</td><td class="vertb" align="right">Mar.28</td><td class="vertb" align="right">Mar.27</td><td class="vertb" align="right">Apr.1</td><td class="vertb" align="right">Apr.18</td></tr> +</table> + + <p>13. <i>Rule for determining Easter Day of the Antegregorian Calendar + in any year of the old style.</i> To the several parts of the rule are + annexed, by way of example, the results for the year 1287. The steps are + numbered to correspond with the steps of the Gregorian rule, so that it + can be seen what augmentations the latter requires.</p> + + <p>I. Set down the given year. (1287).</p> + + <p>II. Take the quotient of the given year divided by 4, neglecting the + remainder (321).</p> + + <p>V. Take 4 more than the sum of I. and II. (1612).</p> + + <p>VI. Find the remainder of V. divided by 7. (2).</p> + + <p>VII. Subtract VI. from 7; this is the number of the dominical + letter</p> + +<table class="nob" summary="Dominical letters" title="Dominical letters"> +<tr><td>1</td><td>2</td><td>3</td><td>4</td><td>5</td><td>6</td><td>7</td><td valign="middle">(5; dominical letter E).</td></tr> +<tr><td>A</td><td>B</td><td>C</td><td>D</td><td>E</td><td>F</td><td>G</td></tr> +</table> + + <p>VIII. Divide one more than the given year by 19, the remainder (or 19 + if no remainder) is the golden number. (15).</p> + + <p>XII. Divide 3 less than 11 times VIII. by 30; the remainder (or 30 if + there be no remainder) is the epact. (12).</p> + +<p><!-- Page 368 --><span class="pagenum"><a name="page368"></a>[368]</span></p> + +<table width="100%" summary="Epacts" title="Epacts"><tr><td valign="top" class="spac" style="width:50%"> +<i>When the Epact is 23, or less.</i> + + <p>XIII. Subtract XII., the epact, from 45. (33).</p> + + <p>XIV. Subtract the epact from 27, divide by 7, and keep the remainder, + or 7, if there be no remainder, (1).</p> + +</td><td valign="top" class="spac" style="width:50%"> +<i>When the Epact is greater than 23.</i> + + <p>XIII. Subtract XII., the epact, from 75.</p> + + <p>XIV. Subtract the epact from 57, divide by 7, and keep the remainder, + or 7, if there be no remainder.</p> + +</td></tr></table> + + <p>XV. To XIII. add VII., the dominical number, (and 7 besides if XIV. be + greater than VII.,) and subtract XIV., the result is the day of March, or + if more than 31, subtract 31, and the result is the day of April, on + which Easter Sunday (old style) falls. (37; Easter Day is April 6).</p> + + <p>These rules completely represent the old and new Calendars, so far as + Easter is concerned. For further explanation we must refer to the + articles cited at the commencement.</p> + + <p>The annexed is the table of new and full moons of the Gregorian + Calendar, cleared of the errors made for the purpose of preventing Easter + from coinciding with the Jewish Passover.</p> + + <p>The second table (page <a href="#page370">370</a>) contains + <i>epacts</i>, or ages of the moon at the beginning of the year: thus in + 1913, the epact is 22, in 1868 it is 6. This table goes from 1850 to + 1999: should the New Zealander not have arrived by that time, and should + the churches of England and Rome then survive, the epact table may be + continued from their liturgy-books. The way of using the table is as + follows: Take the epact of the required year, and find it in the first or + last column of the first table, in line with it are seen the calendar + days of new and full moon. Thus, when the epact is 17, the new and full + moons of March fall on the 13th and 28th. The result is, for the most + part, correct: but in a minority of cases there is an error of a day. + When this happens, the error is almost always a fraction of a day much + less than twelve hours. Thus, when the table gives full moon on the 27th, + and the real truth is the 28th, we may be sure it is early on the + 28th.</p> + +<p><!-- Page 369 --><span class="pagenum"><a name="page369"></a>[369]</span></p> + +<table class="allbctr" summary="True table of moons" title="True table of moons"> +<tr><td class="allb" align="center"> </td><td class="allb" align="center">Jan.</td><td class="allb" align="center">Feb.</td><td class="allb" align="center">Mar.</td><td class="allb" align="center">Apr.</td><td class="allb" align="center">May </td><td class="allb" align="center">June</td><td class="allb" align="center">July</td><td class="allb" align="center">Aug.</td><td class="allb" align="center">Sep.</td><td class="allb" align="center">Oct.</td><td class="allb" align="center">Nov.</td><td class="allb" align="center">Dec.</td><td class="allb" align="center"> </td></tr> +<tr><td class="vertb" align="center">1</td><td class="vertb" align="center">29</td><td class="vertb" align="center">27</td><td class="vertb" align="center">29</td><td class="vertb" align="center">27</td><td class="vertb" align="center">27</td><td class="vertb" align="center">25</td><td class="vertb" align="center">25</td><td class="vertb" align="center">23</td><td class="vertb" align="center">22</td><td class="vertb" align="center">21</td><td class="vertb" align="center">20</td><td class="vertb" align="center">19</td><td class="vertb" align="center">1</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">14</td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">14</td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">2</td><td class="vertb" align="center">28</td><td class="vertb" align="center">26</td><td class="vertb" align="center">28</td><td class="vertb" align="center">26</td><td class="vertb" align="center">26</td><td class="vertb" align="center">24</td><td class="vertb" align="center">24</td><td class="vertb" align="center">22</td><td class="vertb" align="center">21</td><td class="vertb" align="center">20</td><td class="vertb" align="center">19</td><td class="vertb" align="center">18</td><td class="vertb" align="center">2</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">3</td><td class="vertb" align="center">27</td><td class="vertb" align="center">25</td><td class="vertb" align="center">27</td><td class="vertb" align="center">25</td><td class="vertb" align="center">25</td><td class="vertb" align="center">23</td><td class="vertb" align="center">23</td><td class="vertb" align="center">21</td><td class="vertb" align="center">20</td><td class="vertb" align="center">19</td><td class="vertb" align="center">18</td><td class="vertb" align="center">17</td><td class="vertb" align="center">3</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">4</td><td class="vertb" align="center">26</td><td class="vertb" align="center">24</td><td class="vertb" align="center">26</td><td class="vertb" align="center">24</td><td class="vertb" align="center">24</td><td class="vertb" align="center">22</td><td class="vertb" align="center">22</td><td class="vertb" align="center">20</td><td class="vertb" align="center">19</td><td class="vertb" align="center">18</td><td class="vertb" align="center">17</td><td class="vertb" align="center">16</td><td class="vertb" align="center">4</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">2</td><td class="vertbotb" align="center">2,31</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">5</td><td class="vertb" align="center">25</td><td class="vertb" align="center">23</td><td class="vertb" align="center">25</td><td class="vertb" align="center">23</td><td class="vertb" align="center">23</td><td class="vertb" align="center">21</td><td class="vertb" align="center">21</td><td class="vertb" align="center">19</td><td class="vertb" align="center">18</td><td class="vertb" align="center">17</td><td class="vertb" align="center">16</td><td class="vertb" align="center">15</td><td class="vertb" align="center">5</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">1</td><td class="vertbotb" align="center">1,30</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">6</td><td class="vertb" align="center">24</td><td class="vertb" align="center">22</td><td class="vertb" align="center">24</td><td class="vertb" align="center">22</td><td class="vertb" align="center">22</td><td class="vertb" align="center">20</td><td class="vertb" align="center">20</td><td class="vertb" align="center">18</td><td class="vertb" align="center">17</td><td class="vertb" align="center">16</td><td class="vertb" align="center">15</td><td class="vertb" align="center">14</td><td class="vertb" align="center">6</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">9</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">2</td><td class="vertbotb" align="center">2,31</td><td class="vertbotb" align="center">30</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">7</td><td class="vertb" align="center">23</td><td class="vertb" align="center">21</td><td class="vertb" align="center">23</td><td class="vertb" align="center">21</td><td class="vertb" align="center">21</td><td class="vertb" align="center">19</td><td class="vertb" align="center">19</td><td class="vertb" align="center">17</td><td class="vertb" align="center">16</td><td class="vertb" align="center">15</td><td class="vertb" align="center">14</td><td class="vertb" align="center">13</td><td class="vertb" align="center">7</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">1</td><td class="vertbotb" align="center">1,30</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">8</td><td class="vertb" align="center">22</td><td class="vertb" align="center">20</td><td class="vertb" align="center">22</td><td class="vertb" align="center">20</td><td class="vertb" align="center">20</td><td class="vertb" align="center">18</td><td class="vertb" align="center">18</td><td class="vertb" align="center">16</td><td class="vertb" align="center">15</td><td class="vertb" align="center">14</td><td class="vertb" align="center">13</td><td class="vertb" align="center">12</td><td class="vertb" align="center">8</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">7</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">2,31</td><td class="vertbotb" align="center">30</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">9</td><td class="vertb" align="center">21</td><td class="vertb" align="center">19</td><td class="vertb" align="center">21</td><td class="vertb" align="center">19</td><td class="vertb" align="center">19</td><td class="vertb" align="center">17</td><td class="vertb" align="center">17</td><td class="vertb" align="center">15</td><td class="vertb" align="center">14</td><td class="vertb" align="center">13</td><td class="vertb" align="center">12</td><td class="vertb" align="center">11</td><td class="vertb" align="center">9</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">2</td><td class="vertbotb" align="center">1,30</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center">26</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">10</td><td class="vertb" align="center">20</td><td class="vertb" align="center">18</td><td class="vertb" align="center">20</td><td class="vertb" align="center">18</td><td class="vertb" align="center">18</td><td class="vertb" align="center">16</td><td class="vertb" align="center">16</td><td class="vertb" align="center">14</td><td class="vertb" align="center">13</td><td class="vertb" align="center">12</td><td class="vertb" align="center">11</td><td class="vertb" align="center">10</td><td class="vertb" align="center">10</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">5</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">2</td><td class="vertbotb" align="center">1,31</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center">26</td><td class="vertbotb" align="center">25</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">11</td><td class="vertb" align="center">19</td><td class="vertb" align="center">17</td><td class="vertb" align="center">19</td><td class="vertb" align="center">17</td><td class="vertb" align="center">17</td><td class="vertb" align="center">15</td><td class="vertb" align="center">15</td><td class="vertb" align="center">13</td><td class="vertb" align="center">12</td><td class="vertb" align="center">11</td><td class="vertb" align="center">10</td><td class="vertb" align="center">9</td><td class="vertb" align="center">11</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">4</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">2</td><td class="vertbotb" align="center">1,30</td><td class="vertbotb" align="center">30</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center">26</td><td class="vertbotb" align="center">25</td><td class="vertbotb" align="center">24</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">12</td><td class="vertb" align="center">18</td><td class="vertb" align="center">16</td><td class="vertb" align="center">18</td><td class="vertb" align="center">16</td><td class="vertb" align="center">16</td><td class="vertb" align="center">14</td><td class="vertb" align="center">14</td><td class="vertb" align="center">12</td><td class="vertb" align="center">11</td><td class="vertb" align="center">10</td><td class="vertb" align="center">9</td><td class="vertb" align="center">8</td><td class="vertb" align="center">12</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">2</td><td class="vertbotb" align="center">3</td><td class="vertbotb" align="center">2</td><td class="vertbotb" align="center">1,31</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center">26</td><td class="vertbotb" align="center">25</td><td class="vertbotb" align="center">24</td><td class="vertbotb" align="center">23</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">13</td><td class="vertb" align="center">17</td><td class="vertb" align="center">15</td><td class="vertb" align="center">17</td><td class="vertb" align="center">15</td><td class="vertb" align="center">15</td><td class="vertb" align="center">13</td><td class="vertb" align="center">13</td><td class="vertb" align="center">11</td><td class="vertb" align="center">10</td><td class="vertb" align="center">9</td><td class="vertb" align="center">8</td><td class="vertb" align="center">7</td><td class="vertb" align="center">13</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">2</td><td class="vertbotb" align="center">1</td><td class="vertbotb" align="center">2</td><td class="vertbotb" align="center">1,30</td><td class="vertbotb" align="center">30</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center">26</td><td class="vertbotb" align="center">25</td><td class="vertbotb" align="center">24</td><td class="vertbotb" align="center">23</td><td class="vertbotb" align="center">22</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">14</td><td class="vertb" align="center">16</td><td class="vertb" align="center">14</td><td class="vertb" align="center">16</td><td class="vertb" align="center">14</td><td class="vertb" align="center">14</td><td class="vertb" align="center">12</td><td class="vertb" align="center">12</td><td class="vertb" align="center">10</td><td class="vertb" align="center">9</td><td class="vertb" align="center">8</td><td class="vertb" align="center">7</td><td class="vertb" align="center">6</td><td class="vertb" align="center">14</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">1,31</td><td class="vertbotb" align="center">—</td><td class="vertbotb" align="center">1,31</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center">25</td><td class="vertbotb" align="center">24</td><td class="vertbotb" align="center">23</td><td class="vertbotb" align="center">22</td><td class="vertbotb" align="center">21</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">15</td><td class="vertb" align="center">15</td><td class="vertb" align="center">13</td><td class="vertb" align="center">15</td><td class="vertb" align="center">13</td><td class="vertb" align="center">13</td><td class="vertb" align="center">11</td><td class="vertb" align="center">11</td><td class="vertb" align="center">9</td><td class="vertb" align="center">8</td><td class="vertb" align="center">7</td><td class="vertb" align="center">6</td><td class="vertb" align="center">5</td><td class="vertb" align="center">15</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">30</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center">30</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center">26</td><td class="vertbotb" align="center">26</td><td class="vertbotb" align="center">24</td><td class="vertbotb" align="center">23</td><td class="vertbotb" align="center">22</td><td class="vertbotb" align="center">21</td><td class="vertbotb" align="center">20</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">16</td><td class="vertb" align="center">14</td><td class="vertb" align="center">12</td><td class="vertb" align="center">14</td><td class="vertb" align="center">12</td><td class="vertb" align="center">12</td><td class="vertb" align="center">10</td><td class="vertb" align="center">10</td><td class="vertb" align="center">8</td><td class="vertb" align="center">7</td><td class="vertb" align="center">6</td><td class="vertb" align="center">5</td><td class="vertb" align="center">4</td><td class="vertb" align="center">16</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center">29</td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center">25</td><td class="vertbotb" align="center">25</td><td class="vertbotb" align="center">23</td><td class="vertbotb" align="center">22</td><td class="vertbotb" align="center">21</td><td class="vertbotb" align="center">20</td><td class="vertbotb" align="center">19</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">17</td><td class="vertb" align="center">13</td><td class="vertb" align="center">11</td><td class="vertb" align="center">13</td><td class="vertb" align="center">11</td><td class="vertb" align="center">11</td><td class="vertb" align="center">9</td><td class="vertb" align="center">9</td><td class="vertb" align="center">7</td><td class="vertb" align="center">6</td><td class="vertb" align="center">5</td><td class="vertb" align="center">4</td><td class="vertb" align="center">3</td><td class="vertb" align="center">17</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center">26</td><td class="vertbotb" align="center">28</td><td class="vertbotb" align="center">26</td><td class="vertbotb" align="center">26</td><td class="vertbotb" align="center">24</td><td class="vertbotb" align="center">24</td><td class="vertbotb" align="center">22</td><td class="vertbotb" align="center">21</td><td class="vertbotb" align="center">20</td><td class="vertbotb" align="center">19</td><td class="vertbotb" align="center">18</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">18</td><td class="vertb" align="center">12</td><td class="vertb" align="center">10</td><td class="vertb" align="center">12</td><td class="vertb" align="center">10</td><td class="vertb" align="center">10</td><td class="vertb" align="center">8</td><td class="vertb" align="center">8</td><td class="vertb" align="center">6</td><td class="vertb" align="center">5</td><td class="vertb" align="center">4</td><td class="vertb" align="center">3</td><td class="vertb" align="center">2</td><td class="vertb" align="center">18</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center">25</td><td class="vertbotb" align="center">27</td><td class="vertbotb" align="center">25</td><td class="vertbotb" align="center">25</td><td class="vertbotb" align="center">23</td><td class="vertbotb" align="center">23</td><td class="vertbotb" align="center">21</td><td class="vertbotb" align="center">20</td><td class="vertbotb" align="center">19</td><td class="vertbotb" align="center">18</td><td class="vertbotb" align="center">17</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="vertb" align="center">19</td><td class="vertb" align="center">11</td><td class="vertb" align="center">9</td><td class="vertb" align="center">11</td><td class="vertb" align="center">9</td><td class="vertb" align="center">9</td><td class="vertb" align="center">7</td><td class="vertb" align="center">7</td><td class="vertb" align="center">5</td><td class="vertb" align="center">4</td><td class="vertb" align="center">3</td><td class="vertb" align="center">2</td><td class="vertb" align="center">1,31</td><td class="vertb" align="center">19</td></tr> +<tr><td class="vertbotb" align="center"> </td><td class="vertbotb" align="center">26</td><td class="vertbotb" 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</td><td class="vertbotb" align="center">15</td><td class="vertbotb" align="center">14</td><td class="vertbotb" align="center">15</td><td class="vertbotb" align="center">14</td><td class="vertbotb" align="center">13</td><td class="vertbotb" align="center">12</td><td class="vertbotb" align="center">11</td><td class="vertbotb" align="center">10</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">8</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center">6</td><td class="vertbotb" align="center"></td></tr> +<tr><td class="allb" align="center"> </td><td class="allb" align="center">Jan.</td><td class="allb" align="center">Feb.</td><td class="allb" align="center">Mar.</td><td class="allb" align="center">Apr.</td><td class="allb" align="center">May</td><td class="allb" align="center">June</td><td class="allb" align="center">July</td><td class="allb" align="center">Aug.</td><td class="allb" align="center">Sep.</td><td class="allb" align="center">Oct.</td><td class="allb" align="center">Nov.</td><td class="allb" align="center">Dec.</td><td class="allb" align="center"> </td></tr> +</table> + +<p><!-- Page 370 --><span class="pagenum"><a name="page370"></a>[370]</span></p> + +<table class="allbctr" summary="True table of epacts" title="True table of epacts"> +<tr><td class="allb" align="center"> </td><td class="allb" align="center">0</td><td class="allb" align="center">1</td><td class="allb" align="center">2</td><td class="allb" align="center">3</td><td class="allb" align="center">4</td><td class="allb" align="center">5</td><td class="allb" align="center">6</td><td class="allb" align="center">7</td><td class="allb" align="center">8</td><td class="allb" align="center">9</td></tr> +<tr><td class="allb" align="center">185</td><td class="allb" align="center">17</td><td class="allb" align="center">28</td><td class="allb" align="center"><span class="correction" title="text reads `19'">9</span></td><td class="allb" align="center">20</td><td class="allb" align="center">2</td><td class="allb" align="center">12</td><td class="allb" align="center">23</td><td class="allb" align="center">4</td><td class="allb" align="center">15</td><td class="allb" align="center">26</td></tr> +<tr><td class="allb" align="center">186</td><td class="allb" align="center">7</td><td class="allb" align="center">18</td><td class="allb" align="center">30</td><td class="allb" align="center">11</td><td class="allb" align="center">22</td><td class="allb" align="center">3</td><td class="allb" align="center">14</td><td class="allb" align="center">25</td><td class="allb" align="center">6</td><td class="allb" align="center">17</td></tr> +<tr><td class="allb" align="center">187</td><td class="allb" align="center">28</td><td class="allb" align="center">9</td><td class="allb" align="center">20</td><td class="allb" align="center">1</td><td class="allb" align="center">12</td><td class="allb" align="center">23</td><td class="allb" 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class="allb" align="center">5</td><td class="allb" align="center">16</td><td class="allb" align="center">27</td><td class="allb" align="center">8</td><td class="allb" align="center">19</td><td class="allb" align="center">30</td></tr> +<tr><td class="allb" align="center">195</td><td class="allb" align="center">11</td><td class="allb" align="center">22</td><td class="allb" align="center">3</td><td class="allb" align="center">14</td><td class="allb" align="center">26</td><td class="allb" align="center">6</td><td class="allb" align="center">17</td><td class="allb" align="center">29</td><td class="allb" align="center">10</td><td class="allb" align="center">21</td></tr> +<tr><td class="allb" align="center">196</td><td class="allb" align="center">2</td><td class="allb" align="center">13</td><td class="allb" align="center">24</td><td class="allb" align="center">5</td><td class="allb" align="center">16</td><td class="allb" align="center">27</td><td class="allb" align="center">8</td><td class="allb" align="center">19</td><td class="allb" align="center">30</td><td class="allb" align="center">11</td></tr> +<tr><td class="allb" align="center">197</td><td class="allb" align="center">22</td><td class="allb" align="center">3</td><td class="allb" align="center">14</td><td class="allb" align="center">26</td><td class="allb" align="center">6</td><td class="allb" align="center">17</td><td class="allb" align="center">29</td><td class="allb" align="center">10</td><td class="allb" align="center">21</td><td class="allb" align="center">2</td></tr> +<tr><td class="allb" align="center">198</td><td class="allb" align="center">13</td><td class="allb" align="center">24</td><td class="allb" align="center">5</td><td class="allb" align="center">16</td><td class="allb" align="center">27</td><td class="allb" align="center">8</td><td class="allb" align="center">19</td><td class="allb" align="center">30</td><td class="allb" align="center">11</td><td class="allb" align="center">22</td></tr> +<tr><td class="allb" align="center">199</td><td class="allb" align="center">3</td><td class="allb" align="center">14</td><td class="allb" align="center">26</td><td class="allb" align="center">6</td><td class="allb" align="center">17</td><td class="allb" align="center">29</td><td class="allb" align="center">10</td><td class="allb" align="center">21</td><td class="allb" align="center">2</td><td class="allb" align="center">13</td></tr> +</table> + + <p>For example, the year 1867. The epact is 25, and we find in the + table:</p> + +<table class="nobctr" summary="Moons for 1867" title="Moons for 1867"> +<tr><td class="spac"> </td><td class="spac" align="center">J.</td><td class="spac" align="center">F.</td><td class="spac" align="center">M.</td><td class="spac" align="center">AP.</td><td class="spac" align="center">M.</td><td class="spac" align="center">JU.</td><td class="spac" align="center">JL.</td><td class="spac" align="center">AU.</td><td class="spac" align="center">S.</td><td class="spac" align="center">O.</td><td class="spac" align="center">N.</td><td class="spac" align="center">D.</td></tr> +<tr><td class="spac">New</td><td class="spac" align="center">5+</td><td class="spac" align="center">4</td><td class="spac" align="center">5+</td><td class="spac" align="center">4</td><td class="spac" align="center">3+</td><td class="spac" align="center">2</td><td class="spac" align="center">1,31</td><td class="spac" align="center">29</td><td class="spac" align="center">28-</td><td class="spac" align="center">27</td><td class="spac" align="center">26</td><td class="spac" align="center">25</td></tr> +<tr><td class="spac">Full</td><td class="spac" align="center">20</td><td class="spac" align="center">19-</td><td class="spac" align="center">20</td><td class="spac" align="center">19-</td><td class="spac" align="center">18</td><td class="spac" align="center">17</td><td class="spac" align="center">16</td><td class="spac" align="center">15</td><td class="spac" align="center">13-</td><td class="spac" align="center">13</td><td class="spac" align="center">11+</td><td class="spac" align="center">11</td></tr> +</table> + + <p>When the truth is the day after + is written after the date; when the + day before, -. Thus, the new moon of March is on the 6th; the full moon + of April is on the 18th. <!-- Page 371 --><span class="pagenum"><a + name="page371"></a>[371]</span></p> + + <p>I now introduce a small paradox of my own; and as I am not able to + prove it, I am compelled to declare that any one who shall dissent must + be either very foolish or very dishonest, and will make me quite + uncomfortable about the state of his soul. This being settled once for + all, I proceed to say that the necessity of arriving at the truth about + the assertions that the Nicene Council laid down astronomical tests led + me to look at Fathers, Church histories, etc. to an extent which I never + dreamed of before. One conclusion which I arrived at was, that the Nicene + Fathers had a knack of sticking to the question which many later councils + could not acquire. In our own day, it is not permitted to Convocation + seriously to discuss any one of the points which are bearing so hard upon + their resources of defence—the cursing clauses of the Athanasian + Creed, for example. And it may be collected that the prohibition arises + partly from fear that there is no saying where a beginning, if allowed, + would end. There seems to be a suspicion that debate, once let loose, + would play up old Trent with the liturgy, and bring the whole book to + book. But if any one will examine the real Nicene Creed, without the + augmentation, he will admire the way in which the framers stuck to the + point, and settled what they had to decide, according to their view of + it. With such a presumption of good sense in their favor, it becomes + easier to believe in any claim which may be made on their behalf to tact + or sagacity in settling any other matter. And I strongly suspect such a + claim may be made for them on the Easter question.</p> + + <p>I collect from many little indications, both before and after the + Council, that the division of the Christian world into Judaical and + Gentile, though not giving rise to a sectarian distinction expressed by + names, was of far greater force and meaning than historians prominently + admit. I took <i>note</i> of many indications of this, but not + <i>notes</i>, as it was not to my purpose. If it were so, we must admire + the discretion of the Council. The Easter question was the <!-- Page 372 + --><span class="pagenum"><a name="page372"></a>[372]</span>fighting + ground of the struggle: the Eastern or Judaical Christians, with some + varieties of usage and meaning, would have the Passover itself to be the + great feast, but taken in a Christian sense; the Western or Gentile + Christians, would have the commemoration of the Resurrection, connected + with the Passover only by chronology. To shift the Passover in time, + under its name, <i>Pascha</i>, without allusion to any of the force of + the change, was gently cutting away the ground from under the feet of the + Conservatives. And it was done in a very quiet way: no allusion to the + precise character of the change; no hint that the question was about two + different festivals: "all the brethren in the East, who formerly + celebrated this festival at the same time as the Jews, will in future + conform to the Romans and to us." The Judaizers meant to be keeping the + Passover <i>as</i> a Christian feast: they are gently assumed to be + keeping, <i>not</i> the Passover, <i>but</i> a Christian feast; and a + doctrinal decision is quietly, but efficiently, announced under the form + of a chronological ordinance. Had the Council issued theses of doctrine, + and excommunicated all dissentients, the rupture of the East and West + would have taken place earlier by centuries than it did. The only place + in which I ever saw any part of my paradox advanced, was in an article in + the <i>Examiner</i> newspaper, towards the end of 1866, after the above + was written.</p> + + <p>A story about Christopher Clavius, the workman of the new Calendar. I + chanced to pick up "Albertus Pighius Campensis de æquinoctiorum + solsticiorumque inventione... Ejusdem de ratione Paschalis celebrationis, + De que Restitutione ecclesiastici Kalendarii," Paris, 1520, folio.<a + name="NtA_760" href="#Nt_760"><sup>[760]</sup></a> On the title-page were + decayed words followed by "..<i>hristophor.. C..ii</i>, 1556 (or 8)," the + last blank not entirely erased by time, but showing the lower halves of + an <i>l</i> and of an <i>a</i>, and <!-- Page 373 --><span + class="pagenum"><a name="page373"></a>[373]</span>rather too much room + for a <i>v</i>. It looked very like <i>E Libris Christophori Clavii</i> + 1556. By the courtesy of some members of the Jesuit body in London, I + procured a tracing of the signature of Clavius from Rome, and the shapes + of the letters, and the modes of junction and disjunction, put the matter + beyond question. Even the extra space was explained; he wrote himself + Cla<i>u</i>ius. Now in 1556, Clavius was nineteen years old: it thus + appears probable that the framer of the Gregorian Calendar was selected, + not merely as a learned astronomer, but as one who had attended to the + calendar, and to works on its reformation, from early youth. When on the + subject I found reason to think that Clavius had really read this work, + and taken from it a phrase or two and a notion or two. Observe the + advantage of writing the baptismal name at full length.</p> + + <p> </p> + +<p class="cenhead">A COUPLE OF MINOR PARADOXES.</p> + +<blockquote class="b1n"> + + <p>The discovery of a general resolution of all superior finite + equations, of every numerical both algebraick and transcendent form. By + A. P. Vogel,<a name="NtA_761" href="#Nt_761"><sup>[761]</sup></a> + mathematician at Leipzick. Leipzick and London, 1845, 8vo.</p> + +</blockquote> + + <p>This work is written in the English of a German who has not mastered + the idiom: but it is always intelligible. It professes to solve equations + of every degree "in a more extent sense, and till to every degree of + exactness." The general solution of equations of <i>all</i> degrees is a + vexed question, which cannot have the mysterious interest of the circle + problem, and is of a comparatively modern date.<a name="NtA_762" + href="#Nt_762"><sup>[762]</sup></a> Mr. Vogel <!-- Page 374 --><span + class="pagenum"><a name="page374"></a>[374]</span>announces a forthcoming + treatise in which are resolved the "last impossibilities of pure + mathematics."</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Elective Polarity the Universal Agent. By Frances Barbara Burton, + authoress of 'Astronomy familiarized,' 'Physical Astronomy,' &c. + London, 1845, 8vo.<a name="NtA_763" + href="#Nt_763"><sup>[763]</sup></a></p> + +</blockquote> + + <p>The title gives a notion of the theory. The first sentence states, + that 12,500 years ago <span class="grk">α</span> Lyræ was the + pole-star, and attributes the immense magnitude of the now fossil animals + to a star of such "polaric intensity as Vega pouring its magnetic streams + through our planet." Miss Burton was a lady of property, and of very + respectable acquirements, especially in Hebrew; she was eccentric in all + things.</p> + + <p>1867.—Miss Burton is revived by the writer of a book on + meteorology which makes use of the planets: she is one of his leading + minds.<a name="NtA_764" href="#Nt_764"><sup>[764]</sup></a></p> + + <p> </p> + +<p class="cenhead">SPECULATIVE THOUGHT IN ENGLAND.</p> + + <p>In the year 1845 the old <i>Mathematical Society</i> was merged in the + Astronomical Society. The circle-squarers, etc., thrive more in England + than in any other country: there are most weeds where there is the + largest crop. Speculation, though not encouraged by our Government so + much as by those of the Continent, has had, not indeed such forcing, but + much wider diffusion: few tanks, but many rivulets. On this point I quote + from the preface to the reprint of the work of Ramchundra,<a + name="NtA_765" href="#Nt_765"><sup>[765]</sup></a> which I superintended + for the late Court of Directors of the East India Company.</p> + +<p><!-- Page 375 --><span class="pagenum"><a name="page375"></a>[375]</span></p> + + <p>"That sound judgment which gives men well to know what is best for + them, as well as that faculty of invention which leads to development of + resources and to the increase of wealth and comfort, are both materially + advanced, perhaps cannot rapidly be advanced without, a great taste for + pure speculation among the general mass of the people, down to the lowest + of those who can read and write. England is a marked example. Many + persons will be surprised at this assertion. They imagine that our + country is the great instance of the refusal of all <i>unpractical</i> + knowledge in favor of what is <i>useful</i>. I affirm, on the contrary, + that there is no country in Europe in which there has been so wide a + diffusion of speculation, theory, or what other unpractical word the + reader pleases. In our country, the scientific <i>society</i> is always + formed and maintained by the people; in every other, the scientific + <i>academy</i>—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 + <i>Principia</i> of Newton; in no other country has the man of weekly + wages maintained his own scientific periodical. With us, since the + beginning of the last century, scores upon scores—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 <!-- Page 376 --><span class="pagenum"><a + name="page376"></a>[376]</span>state of things; I speak of the time + during which the present system took its rise, and of the circumstances + under which many of its most effective promoters were trained. In all + this there is nothing which stands out, like the state-nourished academy, + with its few great names and brilliant single achievements. This country + has differed from all others in the wide diffusion of the disposition to + speculate, which disposition has found its place among the ordinary + habits of life, moderate in its action, healthy in its amount."</p> + + <p> </p> + +<p class="cenhead">THE OLD MATHEMATICAL SOCIETY.</p> + + <p>Among the most remarkable proofs of the diffusion of speculation was + the Mathematical Society, which flourished from 1717 to 1845. Its habitat + was Spitalfields, and I think most of its existence was passed in Crispin + Street. It was originally a plain society, belonging to the studious + artisan. The members met for discussion once a week; and I believe I am + correct in saying that each man had his pipe, his pot, and his problem. + One of their old rules was that, "If any member shall so far forget + himself and the respect due to the Society as in the warmth of debate to + threaten or offer personal violence to any other member, he shall be + liable to immediate expulsion, or to pay such fine as the majority of the + members present shall decide." But their great rule, printed large on the + back of the title page of their last book of regulations, was "By the + constitution of the Society, it is the duty of every member, if he be + asked any mathematical or philosophical question by another member, to + instruct him in the plainest and easiest manner he is able." We shall + presently see that, in old time, the rule had a more homely form.</p> + + <p>I have been told that De Moivre<a name="NtA_766" + href="#Nt_766"><sup>[766]</sup></a> was a member of this <!-- Page 377 + --><span class="pagenum"><a name="page377"></a>[377]</span>Society. This + I cannot verify: circumstances render it unlikely; even though the French + refugees clustered in Spitalfields; many of them were of the Society, + which there is some reason to think was founded by them. But Dolland,<a + name="NtA_767" href="#Nt_767"><sup>[767]</sup></a> Thomas Simpson,<a + name="NtA_768" href="#Nt_768"><sup>[768]</sup></a> Saunderson,<a + name="NtA_769" href="#Nt_769"><sup>[769]</sup></a> Crossley,<a + name="NtA_770" href="#Nt_770"><sup>[770]</sup></a> and others of known + name, were certainly members. The Society gradually declined, and in 1845 + was reduced to nineteen members. An arrangement was made by which sixteen + of these members, who where not already in the Astronomical Society + became Fellows without contribution, all the books and other property of + the old Society being transferred to the new one. I was one of the + committee which made the preliminary inquiries, and the reason of the + decline was soon manifest. The only question which could arise was + whether the members of the society of working men—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 <!-- Page 378 + --><span class="pagenum"><a name="page378"></a>[378]</span>only live from + hand to mouth, and not up to the brain. The material of the old Society + no longer existed.</p> + + <p>In 1798, experimental lectures were given, a small charge for + admission being taken at the door: by this hangs a tale—and a song. + Many years ago, I found among papers of a deceased friend, who certainly + never had anything to do with the Society, and who passed all his life + far from London, a song, headed "Song sung by the Mathematical Society in + London, at a dinner given Mr. Fletcher,<a name="NtA_771" + href="#Nt_771"><sup>[771]</sup></a> a solicitor, who had defended the + Society gratis." Mr. Williams,<a name="NtA_772" + href="#Nt_772"><sup>[772]</sup></a> the Assistant Secretary of the + Astronomical Society, formerly Secretary of the Mathematical Society, + remembered that the Society had had a solicitor named Fletcher among the + members. Some years elapsed before it struck me that my old friend + Benjamin Gompertz,<a name="NtA_773" href="#Nt_773"><sup>[773]</sup></a> + who had long been a member, might have some recollection of the matter. + The following is an extract of a letter from him (July 9, 1861):</p> + + <p>"As to the Mathematical Society, of which I was a member when only 18 + years of age, [Mr. G. was born in 1779], having been, contrary to the + rules, elected under the age of 21. How I came to be a member of that + Society—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 <!-- + Page 379 --><span class="pagenum"><a name="page379"></a>[379]</span>one + of the rules was, if a member asked for information, and applied to any + one who could give it, he was obliged to give it, or fine one penny. + Though I might say much with respect to the Society which would be + interesting, I will for the present reply only to your question. I well + knew Mr. Fletcher, who was a very clever and very scientific person. He + did, as solicitor, defend an action brought by an informer against the + Society—I think for 5,000<i>l.</i>—for giving lectures to the + public in philosophical subjects [i.e., for unlicensed public exhibition + with money taken at the doors]. I think the price for admission was one + shilling, and we used to have, if I rightly recollect, from two to three + hundred visitors. Mr. Fletcher was successful in his defence, and we got + out of our trouble. There was a collection made to reward his services, + but he did not accept of any reward: and I think we gave him a dinner, as + you state, and enjoyed ourselves; no doubt with astronomical songs and + other songs; but my recollection does not enable me to say if the + astronomical song was a drinking song. I think the anxiety caused by that + action was the cause of some of the members' death. [They had, no doubt, + broken the law in ignorance; and by the sum named, the informer must have + been present, and sued for a penalty on every shilling he could prove to + have been taken]."</p> + + <p>I by no means guarantee that the whole song I proceed to give is what + was sung at the dinner: I suspect, by the completeness of the chain, that + augmentations have been made. My deceased friend was just the man to add + some verses, or the addition may have been made before it came into his + hands, or since his decease, for the scraps containing the verses passed + through several hands before they came into mine. We may, however, be + pretty sure that the original is substantially contained in what is + given, and that the character is therefore preserved. I have had myself + to repair damages every now and then, in the way of conjectural + restoration of defects caused by ill-usage. <!-- Page 380 --><span + class="pagenum"><a name="page380"></a>[380]</span></p> + + <p> </p> + +<p class="cenhead">THE ASTRONOMER'S DRINKING SONG.</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"Whoe'er would search the starry sky,</p> + <p class="i2">Its secrets to divine, sir,</p> + <p>Should take his glass—I mean, should try</p> + <p class="i2">A glass or two of wine, sir!</p> + <p>True virtue lies in golden mean,</p> + <p class="i2">And man must wet his clay, sir;</p> + <p>Join these two maxims, and 'tis seen</p> + <p class="i2">He should drink his bottle a day, sir!</p> + </div> + + <div class="stanza"> + <p class="hg3">"Old Archimedes, reverend sage!</p> + <p class="i2">By trump of fame renowned, sir,</p> + <p>Deep problems solved in every page,</p> + <p class="i2">And the sphere's curved surface found,<a name="NtA_774" href="#Nt_774"><sup>[774]</sup></a> sir:</p> + <p>Himself he would have far outshone,</p> + <p class="i2">And borne a wider sway, sir,</p> + <p>Had he our modern secret known,</p> + <p class="i2">And drank a bottle a day, sir!</p> + </div> + + <div class="stanza"> + <p class="hg3">"When Ptolemy,<a name="NtA_775" href="#Nt_775"><sup>[775]</sup></a> now long ago,</p> + <p class="i2">Believed the earth stood still, sir,</p> + <p>He never would have blundered so,</p> + <p class="i2">Had he but drunk his fill, sir:</p> + <p>He'd then have felt<a name="NtA_776" href="#Nt_776"><sup>[776]</sup></a> it circulate,</p> + <p class="i2">And would have learnt to say, sir,</p> + <p>The true way to investigate</p> + <p class="i2">Is to drink your bottle a day, sir!</p> + </div> + + <div class="stanza"> + <p class="hg3">"Copernicus,<a name="NtA_777" href="#Nt_777"><sup>[777]</sup></a> that learned wight,</p> + <p class="i2">The glory of his nation,</p> + <p>With draughts of wine refreshed his sight,</p> + <p class="i2">And saw the earth's rotation;</p> +<!-- Page 381 --><span class="pagenum"><a name="page381"></a>[381]</span> + <p>Each planet then its orb described,</p> + <p class="i2">The moon got under way, sir;</p> + <p>These truths from nature he imbibed</p> + <p class="i2">For he drank his bottle a day, sir!</p> + </div> + + <div class="stanza"> + <p class="hg3">"The noble<a name="NtA_778" href="#Nt_778"><sup>[778]</sup></a> Tycho placed the stars,</p> + <p class="i2">Each in its due location;</p> + <p>He lost his nose<a name="NtA_779" href="#Nt_779"><sup>[779]</sup></a> by spite of Mars,</p> + <p class="i2">But that was no privation:</p> + <p>Had he but lost his mouth, I grant</p> + <p class="i2">He would have felt dismay, sir,</p> + <p>Bless you! <i>he</i> knew what he should want</p> + <p class="i2">To drink his bottle a day, sir!</p> + </div> + + <div class="stanza"> + <p class="hg3">"Cold water makes no lucky hits;</p> + <p class="i2">On mysteries the head runs:</p> + <p>Small drink let Kepler<a name="NtA_780" href="#Nt_780"><sup>[780]</sup></a> time his wits</p> + <p class="i2">On the regular polyhedrons:</p> + <p>He took to wine, and it changed the chime,</p> + <p class="i2">His genius swept away, sir,</p> + <p>Through area varying<a name="NtA_781" href="#Nt_781"><sup>[781]</sup></a> as the time</p> + <p class="i2">At the rate of a bottle a day, sir!</p> + </div> + + <div class="stanza"> + <p class="hg3">"Poor Galileo,<a name="NtA_782" href="#Nt_782"><sup>[782]</sup></a> forced to rat</p> + <p class="i2">Before the Inquisition,</p> + <p><i>E pur si muove</i><a name="NtA_783" href="#Nt_783"><sup>[783]</sup></a> was the pat</p> + <p class="i2">He gave them in addition:</p> +<!-- Page 382 --><span class="pagenum"><a name="page382"></a>[382]</span> + <p>He meant, whate'er you think you prove,</p> + <p class="i2">The earth must go its way, sirs;</p> + <p>Spite of your teeth I'll make it move,</p> + <p class="i2">For I'll drink my bottle a day, sirs!</p> + </div> + + <div class="stanza"> + <p class="hg3">"Great Newton, who was never beat</p> + <p class="i2">Whatever fools may think, sir;</p> + <p>Though sometimes he forgot to eat,</p> + <p class="i2">He never forgot to drink, sir:</p> + <p>Descartes<a name="NtA_784" href="#Nt_784"><sup>[784]</sup></a> took nought but lemonade,</p> + <p class="i2">To conquer him was play, sir;</p> + <p>The first advance that Newton made</p> + <p class="i2">Was to drink his bottle a day, sir!</p> + </div> + + <div class="stanza"> + <p class="hg3">"D'Alembert,<a name="NtA_785" href="#Nt_785"><sup>[785]</sup></a> Euler,<a name="NtA_786" href="#Nt_786"><sup>[786]</sup></a> and Clairaut,<a name="NtA_787" href="#Nt_787"><sup>[787]</sup></a></p> + <p class="i2">Though they increased our store, sir,</p> + <p>Much further had been seen to go</p> + <p class="i2">Had they tippled a little more, sir!</p> + <p>Lagrange<a name="NtA_788" href="#Nt_788"><sup>[788]</sup></a> gets mellow with Laplace,<a name="NtA_789" href="#Nt_789"><sup>[789]</sup></a></p> + <p class="i2">And both are wont to say, sir,</p> + <p>The <i>philosophe</i> who's not an ass</p> + <p class="i2">Will drink his bottle a day, sir!</p> + </div> + + <div class="stanza"> + <p class="hg3">"Astronomers! what can avail</p> + <p class="i2">Those who calumniate us;</p> + <p>Experiment can never fail</p> + <p class="i2">With such an apparatus:</p> + <p>Let him who'd have his merits known</p> + <p class="i2">Remember what I say, sir;</p> + <p>Fair science shines on him alone</p> + <p class="i2">Who drinks his bottle a day, sir!</p> + </div> + + <div class="stanza"> +<!-- Page 383 --><span class="pagenum"><a name="page383"></a>[383]</span> + <p class="hg3">"How light we reck of those who mock</p> + <p class="i2">By this we'll make to appear, sir,</p> + <p>We'll dine by the sidereal<a name="NtA_790" href="#Nt_790"><sup>[790]</sup></a> clock</p> + <p class="i2">For one more bottle a year, sir:</p> + <p>But choose which pendulum you will,</p> + <p class="i2">You'll never make your way, sir,</p> + <p>Unless you drink—and drink your fill,—</p> + <p class="i2">At least a bottle a day, sir!"</p> + </div> + </div> + <p>Old times are changed, old manners gone!</p> + + <p>There is a new Mathematical Society,<a name="NtA_791" + href="#Nt_791"><sup>[791]</sup></a> and I am, at this present writing + (1866), its first President. We are very high in the newest developments, + and bid fair to take a place among the scientific establishments. + Benjamin Gompertz, who was President of the old Society when it expired, + was the link between the old and new body: he was a member of <i>ours</i> + at his death. But not a drop of liquor is seen at our meetings, except a + decanter of water: all our heavy is a fermentation of symbols; and we do + not draw it mild. There is no penny fine for reticence or occult science; + and as to a song! not the ghost of a chance.</p> + + <p> </p> + + <p>1826. The time may have come when the original documents connected + with the discovery of Neptune may be worth revising. The following are + extracts from the <i>Athenæum</i> of October 3 and October 17:</p> + + <p> </p> + +<p class="cenhead">LE VERRIER'S<a name="NtA_792" href="#Nt_792"><sup>[792]</sup></a> PLANET.</p> + + <p>We have received, at the last moment before making up for press, the + following letter from Sir John Herschel,<a name="NtA_793" + href="#Nt_793"><sup>[793]</sup></a> <!-- Page 384 --><span + class="pagenum"><a name="page384"></a>[384]</span>in reference to the + matter referred to in the communication from Mr. Hind<a name="NtA_794" + href="#Nt_794"><sup>[794]</sup></a> given below:</p> + + <p class="author">"Collingwood, Oct. 1. + + <p>"In my address to the British Association assembled at Southampton, on + the occasion of my resigning the chair to Sir R. Murchison,<a + name="NtA_795" href="#Nt_795"><sup>[795]</sup></a> I stated, among the + remarkable astronomical events of the last twelvemonth, that it had added + a new planet to our list,—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.</p> + + <p>"Give me leave to state my reasons for this confidence; and, in so + doing, to call attention to some facts which deserve to be put on record + in the history of this noble discovery. On July 12, 1842, the late + illustrious astronomer, Bessel,<a name="NtA_796" + href="#Nt_796"><sup>[796]</sup></a> honored me with a visit at my present + residence. On the evening of that day, conversing on the great work of + the planetary reductions undertaken by the Astronomer Royal<a + name="NtA_797" href="#Nt_797"><sup>[797]</sup></a>—then in + progress, and since published,<a name="NtA_798" + href="#Nt_798"><sup>[798]</sup></a>—M. Bessel remarked that the + motions of Uranus, as he had satisfied <!-- Page 385 --><span + class="pagenum"><a name="page385"></a>[385]</span>himself by careful + examination of the recorded observations, could not be accounted for by + the perturbations of the known planets; and that the deviations far + exceeded any possible limits of error of observation. In reply to the + question, Whether the deviations in question might not be due to the + action of an unknown planet?—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 + <i>announce</i> to you (<i>melde</i> ich Ihnen) that Uranus is not + forgotten.' Doubtless, therefore, among his papers will be found some + researches on the subject.</p> + + <p>"The remarkable calculations of M. Le Verrier—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;<a name="NtA_799" + href="#Nt_799"><sup>[799]</sup></a>—who will, I hope, <!-- Page 386 + --><span class="pagenum"><a name="page386"></a>[386]</span>pardon this + mention of his name (the matter being one of great historical + moment),—and who will, doubtless, in his own good time and manner, + place his calculations before the public.</p> + + <p class="author">"J. F. W. HERSCHEL." + +<p class="cenhead"><i>Discovery of Le Verrier's Planet.</i></p> + + <p>Mr. Hind announces to the <i>Times</i> that he has received a letter + from Dr. Brünnow, of the Royal Observatory at Berlin, giving the very + important information that Le Verrier's planet was found by M. Galle, on + the night of September 23. "In announcing this grand discovery," he says, + "I think it better to copy Dr. Brünnow's<a name="NtA_800" + href="#Nt_800"><sup>[800]</sup></a> letter."</p> + + <p> </p> + + <p class="author">"Berlin, Sept. 25. + + <p>"My dear Sir—M. Le Verrier's planet was discovered here the 23d + of September, by M. Galle.<a name="NtA_801" + href="#Nt_801"><sup>[801]</sup></a> It is a star of the 8th magnitude, + but with a diameter of two or three seconds. Here are its places:</p> + +<table class="nobctr" summary="Locations of Neptune" title="Locations of Neptune"> +<tr><td> </td><td>h.</td><td>m.</td><td>s.</td><td> </td><td align="center" colspan="4">R. A.</td><td> </td><td align="center" colspan="4">Declination.</td></tr> +<tr><td>Sept. 23,</td><td align="right">12</td><td align="right">0</td><td align="right">14.6 M.T.</td><td> </td><td align="right">328°</td><td align="right">19'</td><td align="right">16.0"</td><td> </td><td align="right">-13°</td><td align="right">24'</td><td align="right">8.2"</td></tr> +<tr><td>Sept. 24,</td><td align="right">8</td><td align="right">54</td><td align="right">40.9 M.T.</td><td> </td><td align="right">328°</td><td align="right">18'</td><td align="right">14.3"</td><td> </td><td align="right">-13°</td><td align="right">24'</td><td align="right">29.7"</td></tr> +</table> + + <p>The planet is now retrograde, its motion amounting daily to four + seconds of time.</p> + +<p class="cenhead">"Yours most respectfully, <span class="sc">Brünnow</span>."</p> + + <p>"This discovery," Mr. Hind says, "may be justly considered one of the + greatest triumphs of theoretical astronomy;" and he adds, in a + postscript, that the planet was observed at Mr. Bishop's<a name="NtA_802" + href="#Nt_802"><sup>[802]</sup></a> Observatory, in the Regent's Park, + <!-- Page 387 --><span class="pagenum"><a + name="page387"></a>[387]</span>on Wednesday night, notwithstanding the + moonlight and hazy sky. "It appears bright," he says, "and with a power + of 320 I can see the disc. The following position is the result of + instrumental comparisons with 33 Aquarii:</p> + + <p>Sept. 30, at 8h. 16m. 21s. Greenwich mean time—</p> + +<table class="nob" summary="Location of Neptune" title="Location of Neptune"> +<tr><td class="spac">Right ascension of planet</td><td>21h.</td><td>52m.</td><td>47.15s.</td></tr> +<tr><td class="spac">South declination</td><td>13°</td><td>27'</td><td>20"."</td></tr> +</table> + + <p> </p> + +<p class="cenhead">THE NEW PLANET.</p> + + <p class="author">"Cambridge Observatory, Oct. 15. + + <p>"The allusion made by Sir John Herschel, in his letter contained in + the <i>Athenæum</i> of October 3, to the theoretical researches of Mr. + Adams, respecting the newly-discovered planet, has induced me to request + that you would make the following communication public. It is right that + I should first say that I have Mr. Adams's permission to make the + statements that follow, so far as they relate to his labors. I do not + propose to enter into a detail of the steps by which Mr. Adams was led, + by his spontaneous and independent researches, to a conclusion that a + planet must exist more distant than Uranus. The matter is of too great + historical moment not to receive a more formal record than it would be + proper to give here. My immediate object is to show, while the attention + of the scientific public is more particularly directed to the subject, + that, with respect to this remarkable discovery, English astronomers may + lay claim to some merit.</p> + + <p>"Mr. Adams formed the resolution of trying, by calculation, to account + for the anomalies in the motion of Uranus on the hypothesis of a more + distant planet, when he was an undergraduate in this university, and when + his exertions for the academical distinction, which he obtained in + January 1843, left him no time for pursuing the research. In the course + of that year, he arrived at an approximation to the position of the + supposed planet; which, however, he did not consider to be worthy of + confidence, on account of his not <!-- Page 388 --><span + class="pagenum"><a name="page388"></a>[388]</span>having employed a + sufficient number of observations of Uranus. Accordingly, he requested my + intervention to obtain for him the early Greenwich observations, then in + course of reduction;—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 <!-- Page 389 --><span class="pagenum"><a + name="page389"></a>[389]</span>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 <i>secured</i>, 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.</p> + +<table class="nob" summary="Locations of Neptune" title="Locations of Neptune"> +<tr><td>Greenwich mean time.</td></tr> +<tr><td rowspan="2" valign="middle">Aug. 4, 13h. 36m. 25s. ...</td><td rowspan="2" valign="middle"><img src="images/$lbrace.png" style="height:4ex; width:0.5em" alt="left brace" /></td><td>R.A.</td><td>21h.</td><td>58m.</td><td>14.70s.</td></tr> +<tr><td>N.P.D.</td><td>102°</td><td>57'</td><td>32.2"</td></tr> +<tr><td rowspan="2" valign="middle">Aug. 12, 13h. 3m. 26s. ...</td><td rowspan="2" valign="middle"><img src="images/$lbrace.png" style="height:4ex; width:0.5em" alt="left brace" /></td><td>R.A.</td><td>21h.</td><td>57m.</td><td>26.13s.</td></tr> +<tr><td>N.P.D.</td><td>103°</td><td>2'</td><td> 0.2"</td></tr> +</table> + + <p>"From these places compared with recent observations Mr. Adams has + obtained the following results:</p> + +<table class="nob" summary="Orbital elements of Neptune" title="Orbital elements of Neptune"> +<tr><td>Distance of the planet from the sun ...</td><td align="right">30.05</td></tr> +<tr><td>Inclination of the orbit ...</td><td align="right">1° 45'</td></tr> +<tr><td>Longitude of the descending node ...</td><td align="right">309° 43'</td></tr> +<tr><td>Heliocentric longitude, Aug. 4 ...</td><td align="right">326° 39'</td></tr> +</table> + + <p>"The present distance from the sun is, therefore, thirty times the + earth's mean distance;—which is somewhat less than the theory had + indicated. The other elements of the orbit cannot be approximated to till + the observations shall have been continued for a longer period.</p> + + <p>"The part taken by Mr. Adams in the theoretical search after this + planet will, perhaps, be considered to justify the suggesting of a name. + With his consent, I mention <i>Oceanus</i> as one which may possibly + receive the votes of astronomers.—I <!-- Page 390 --><span + class="pagenum"><a name="page390"></a>[390]</span>have authority to state + that Mr. Adams's investigations will in a short time, be published in + detail.</p> + + <p class="author">"<span class="sc">J. Challis</span>."<a name="NtA_803" href="#Nt_803"><sup>[803]</sup></a> + + <p> </p> + +<p class="cenhead">ASTRONOMICAL POLICE REPORT.</p> + + <p>"An ill-looking kind of a body, who declined to give any name, was + brought before the Academy of Sciences, charged with having assaulted a + gentleman of the name of Uranus in the public highway. The prosecutor was + a youngish looking person, wrapped up in two or three great coats; and + looked chillier than anything imaginable, except the + prisoner,—whose teeth absolutely shook, all the time.</p> + + <p>Policeman Le Verrier<a name="NtA_804" + href="#Nt_804"><sup>[804]</sup></a> stated that he saw the prosecutor + walking along the pavement,—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.</p> + + <p><i>M. Arago.</i>—Was the prosecutor sober?</p> + + <p><i>Le Verrier.</i>—Lord, yes, your worship; no man who had a + drop in him ever looks so cold as he did.</p> + + <p><i>M. Arago.</i>—Did you see the assault?</p> + + <p><i>Le Verrier.</i>—I can't say I did; but I told Brünnow exactly + how he'd be crouched down;—just as he was.</p> + +<p><!-- Page 391 --><span class="pagenum"><a name="page391"></a>[391]</span></p> + + <p><i>M. Arago (to Brünnow).</i>—Did <i>you</i> see the + assault?</p> + + <p><i>Brünnow.</i>—No, your worship; but I caught the prisoner.</p> + + <p><i>M. Arago.</i>—How did you know there was any assault at + all?</p> + + <p><i>Le Verrier.</i>—I reckoned it couldn't be otherwise, when I + saw the prosecutor making those odd turns on the pavement.</p> + + <p><i>M. Arago.</i>—You reckon and you calculate! Why, you'll tell + me, next, that you policemen may sit at home and find out all that's + going on in the streets by arithmetic. Did you ever bring a case of this + kind before me till now?</p> + + <p><i>Le Verrier.</i>—Why, you see, your worship, the police are + growing cleverer and cleverer every day. We can't help it:—it grows + upon us.</p> + + <p><i>M. Arago.</i>—You're getting too clever for me. What does the + prosecutor know about the matter?</p> + + <p>The prosecutor said, all he knew was that he was pulled behind by + somebody several times. On being further examined, he said that he had + seen the prisoner often, but did not know his name, nor how he got his + living; but had understood he was called Neptune. He himself had paid + rates and taxes a good many years now. Had a family of six,—two of + whom got their own living.</p> + + <p>The prisoner being called on for his defence, said that it was a + quarrel. He had pushed the prosecutor—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.</p> + + <p>The prosecutor, on being asked, admitted, after a little hesitation, + that he had pushed and pulled the prisoner too. <!-- Page 392 --><span + class="pagenum"><a name="page392"></a>[392]</span>In the altercation + which followed, it was found very difficult to make out which + began:—and the worthy magistrate seemed to think they must have + begun together.</p> + + <p><i>M. Arago.</i>—Prisoner, have you any family?</p> + + <p>The prisoner declined answering that question at present. He said he + thought the police might as well reckon it out whether he had or not.</p> + + <p><i>M. Arago</i> said he didn't much differ from that opinion.—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."</p> + + <p> </p> + + <p>This quib was written by a person who was among the astronomers: and + it illustrates the fact that Le Verrier had sole possession of the field + until Mr. Challis's letter appeared. Sir John Herschel's <span + class="correction" title="text reads `pervious'">previous</span> + communication should have paved the way: but the wonder of the discovery + drove it out of many heads. There is an excellent account of the whole + matter in Professor Grant's<a name="NtA_805" + href="#Nt_805"><sup>[805]</sup></a> <i>History of Physical Astronomy</i>. + The squib scandalized some grave people, who wrote severe admonitions to + the editor. There are formalists who spend much time in writing propriety + to journals, to which they serve as foolometers. In a letter to the + <i>Athenæum</i>, speaking of the way in which people hawk fine terms for + common things, I said that these people ought to have a new translation + of the Bible, which should contain the verse "gentleman and lady, created + He them." The editor was handsomely fired and brimstoned!</p> + +<p><!-- Page 393 --><span class="pagenum"><a name="page393"></a>[393]</span></p> + + <p> </p> + +<p class="cenhead">A NEW THEORY OF TIDES.</p> + +<blockquote class="b1n"> + + <p>A new theory of the tides: in which the errors of the usual theory are + demonstrated; and proof shewn that the full moon is not the cause of a + concomitant spring tide, but actually the cause of the neaps.... By + Comm<sup>r</sup>. Debenham,<a name="NtA_806" + href="#Nt_806"><sup>[806]</sup></a> R.N. London, 1846, 8vo.</p> + +</blockquote> + + <p>The author replied to a criticism in the <i>Athenæum</i>, and I + remember how, in a very few words, he showed that he had read nothing on + the subject. The reviewer spoke of the forces of the planets (i.e., the + Sun and Moon) on the ocean, on which the author remarks, "But N.B. the + Sun is no planet, Mr. Critic." Had he read any of the actual + investigations on the usual theory, he would have known that to this day + the sun and moon continue to be called <i>planets</i>—though the + phrase is disappearing—in speaking of the tides; the sense, of + course, being the old one, wandering bodies.</p> + + <p>A large class of the paradoxers, when they meet with something which + taken in their sense is absurd, do not take the trouble to find out the + intended meaning, but walk off with the words laden with their own first + construction. Such men are hardly fit to walk the streets without an + interpreter. I was startled for a moment, at the time when a recent + happy—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 <!-- Page 394 --><span class="pagenum"><a + name="page394"></a>[394]</span>savage explanation. A paradoxer should not + stop at reading the advertisements of Newton or Laplace; he should learn + to look at the stock of goods.</p> + + <p>I think I must have an eye for double readings, when presented: though + I never guess riddles. On the day on which I first walked into the + <i>Panizzi</i> reading room<a name="NtA_807" + href="#Nt_807"><sup>[807]</sup></a>—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!"<a name="NtA_808" + href="#Nt_808"><sup>[808]</sup></a> If a line had been drawn below the + first word, Dr. Blast's history of the Antinomians would not have been so + fearfully misinterpreted. It seems that neither the binder nor the + arranger of the room had caught my reading. The book was removed before + the catalogue of books of reference was printed.</p> + + <p> </p> + +<p class="cenhead">AN ASTRONOMICAL PARADOXER.</p> + +<blockquote class="b1n"> + + <p>Two systems of astronomy: first, the Newtonian system, showing the + rise and progress thereof, with a short historical account; the general + theory with a variety of remarks thereon: second, the system in + accordance with the Holy Scriptures, showing the rise and progress from + Enoch, the seventh from Adam, the prophets, Moses, and others, in the + first Testament; our Lord Jesus Christ, and his apostles, in the new or + second Testament; Reeve and Muggleton, in the third and last Testament; + with a variety of remarks thereon. By Isaac Frost.<a name="NtA_809" + href="#Nt_809"><sup>[809]</sup></a> London, 1846, 4to.</p> + +</blockquote> + +<p><!-- Page 395 --><span class="pagenum"><a name="page395"></a>[395]</span></p> + + <p>A very handsomely printed volume, with beautiful plates. Many readers + who have heard of Muggletonians have never had any distinct idea of + Lodowick Muggleton,<a name="NtA_810" href="#Nt_810"><sup>[810]</sup></a> + the inspired tailor, (1608-1698) who about 1650 received his commission + from heaven, wrote a Testament, founded a sect, and descended to + posterity. Of Reeve<a name="NtA_811" href="#Nt_811"><sup>[811]</sup></a> + less is usually said; according to Mr. Frost, he and Muggleton are the + two "witnesses." I shall content myself with one specimen of Mr. Frost's + science:</p> + + <p>"I was once invited to hear read over 'Guthrie<a name="NtA_812" + href="#Nt_812"><sup>[812]</sup></a> on Astronomy,' and when the reading + was concluded I was asked my opinion thereon; when I said, 'Doctor, it + appears to me that Sir I. Newton has only given two proofs in support of + his theory of the earth revolving round the sun: all the rest is + assertion without any proofs.'—'What are they?' inquired the + Doctor.—'Well,' I said, 'they are, first, the power of <!-- Page + 396 --><span class="pagenum"><a name="page396"></a>[396]</span>attraction + to keep the earth to the sun; the second is the power of repulsion, by + virtue of the centrifugal motion of the earth: all the rest appears to me + assertion without proof.' The Doctor considered a short time and then + said, 'It certainly did appear so.' I said, 'Sir Isaac has certainly + obtained the credit of completing the system, but really he has only half + done his work.'—'How is that,' inquired my friend the Doctor. My + reply was this: 'You will observe his system shows the earth traverses + round the sun on an inclined plane; the consequence is, there are four + powers required to make his system complete:</p> + + <div class="poem"> + <div class="stanza"> + <p>1st. The power of <i>attraction</i>.</p> + <p>2ndly. The power of <i>repulsion</i>.</p> + <p>3rdly. The power of <i>ascending</i> the inclined plane.</p> + <p>4thly. The power of <i>descending</i> the inclined plane.</p> + </div> + </div> + <p>You will thus easily see the <i>four</i> powers required, and Newton + has only accounted for <i>two</i>; the work is therefore only half done.' + Upon due reflection the Doctor said, 'It certainly was necessary to have + these <i>four</i> points cleared up before the system could be said to be + complete.'"</p> + + <p> </p> + + <p>I have no doubt that Mr. Frost, and many others on my list, have + really encountered doctors who could be puzzled by such stuff as this, or + nearly as bad, among the votaries of existing systems, and have been + encouraged thereby to print their objections. But justice requires me to + say that from the words "power of repulsion by virtue of the centrifugal + motion of the earth," Mr. Frost may be suspected of having something more + like a notion of the much-mistaken term "centrifugal force" than many + paradoxers of greater fame. The Muggletonian sect is not altogether + friendless: over and above this handsome volume, the works of Reeve and + Muggleton were printed, in 1832, in three quarto volumes. See <i>Notes + and Queries, 1st Series</i>, v, 80; 3d Series, iii, 303. <!-- Page 397 + --><span class="pagenum"><a name="page397"></a>[397]</span></p> + + <p>[The system laid down by Mr. Frost, though intended to be + substantially that of Lodowick Muggleton, is not so vagarious. It is + worthy of note how very different have been the fates of two contemporary + paradoxers, Muggleton and George Fox.<a name="NtA_813" + href="#Nt_813"><sup>[813]</sup></a> They were friends and associates,<a + name="NtA_814" href="#Nt_814"><sup>[814]</sup></a> and commenced their + careers about the same time, 1647-1650. The followers of Fox have made + their sect an institution, and deserve to be called the pioneers of + philanthropy. But though there must still be Muggletonians, since + expensive books are published by men who take the name, no sect of that + name is known to the world. Nevertheless, Fox and Muggleton are men of + one type, developed by the same circumstances: it is for those who + investigate such men to point out why their teachings have had fates so + different. Macaulay says it was because Fox found followers of more sense + than himself. True enough: but why did Fox find such followers and not + Muggleton? The two were equally crazy, to all appearance: and the + difference required must be sought in the doctrines themselves.</p> + + <p>Fox was not a <i>rational</i> man: but the success of his sect and + doctrines entitles him to a letter of alteration of the phrase which I am + surprised has not become current. When Conduitt,<a name="NtA_815" + href="#Nt_815"><sup>[815]</sup></a> the husband of Newton's half-niece, + wrote a circular to Newton's friends, just after his death, inviting them + to bear their parts in a proper biography, he said, "As Sir I. Newton was + a <i>national</i> man, I think every one ought to contribute to a work + intended to do him justice." Here is the very phrase which is often + wanted to signify that <!-- Page 398 --><span class="pagenum"><a + name="page398"></a>[398]</span>celebrity which puts its mark, good or + bad, on the national history, in a manner which cannot be asserted of + many notorious or famous historical characters. Thus George Fox and + Newton are both <i>national</i> men. Dr. Roget's<a name="NtA_816" + href="#Nt_816"><sup>[816]</sup></a> <i>Thesaurus</i> gives more than + fifty synonyms—<i>colleagues</i> would be the better word—of + "<i>celebrated</i>," any one of which might be applied, either in prose + or poetry, to Newton or to his works, no one of which comes near to the + meaning which Conduitt's adjective immediately suggests.</p> + + <p>The truth is, that we are too <i>monarchical</i> to be + <i>national</i>. We have the Queen's army, the Queen's navy, the Queen's + highway, the Queen's English, etc.; nothing is national except the + <i>debt</i>. That this remark is not new is an addition to its force; it + has hardly been repeated since it was first made. It is some excuse that + <i>nation</i> is not vernacular English: the <i>country</i> is our word, + and <i>country man</i> is appropriated.]</p> + + <p> </p> + +<blockquote class="b1n"> + + <p>Astronomical Aphorisms, or Theory of Nature; founded on the immutable + basis of Meteoric Action. By P. Murphy,<a name="NtA_817" + href="#Nt_817"><sup>[817]</sup></a> Esq. London, 1847, 12mo.</p> + +</blockquote> + + <p>This is by the framer of the Weather Almanac, who appeals to that work + as corroborative of his theory of planetary temperature, years after all + the world knew by experience that this meteorological theory was just as + good as the others.</p> + +<p><!-- Page 399 --><span class="pagenum"><a name="page399"></a>[399]</span></p> + + <p> </p> + +<blockquote class="b1n"> + + <p>The conspiracy of the Bullionists as it affects the present system of + the money laws. By Caleb Quotem. Birmingham, 1847, 8vo. (pp. 16).</p> + +</blockquote> + + <p>This pamphlet is one of a class of which I know very little, in which + the effects of the laws relating to this or that political bone of + contention are imputed to deliberate conspiracy of one class to rob + another of what the one knew ought to belong to the other. The success of + such writers in believing what they have a bias to believe, would, if + they knew themselves, make them think it equally likely that the + inculpated classes might really believe what it is <i>their</i> interest + to believe. The idea of a <i>guilty</i> understanding existing among + fundholders, or landholders, or any holders, all the country over, and + never detected except by bouncing pamphleteers, is a theory which should + have been left for Cobbett<a name="NtA_818" + href="#Nt_818"><sup>[818]</sup></a> to propose, and for Apella to + believe.<a name="NtA_819" href="#Nt_819"><sup>[819]</sup></a></p> + + <p>[<i>August</i>, 1866. A pamphlet shows how to pay the National Debt. + Advance paper to railways, etc., receivable in payment of taxes. The + railways pay interest and principal in money, with which you pay your + national debt, and redeem your notes. Twenty-five years of interest + redeems the notes, and then the principal pays the debt. Notes to be kept + up to value by penalties.]</p> + + <p> </p> + +<p class="cenhead">THEISM INDEPENDENT OF REVELATION.</p> + +<blockquote class="b1n"> + + <p>The Reasoner. No. 45. Edited by G.J. Holyoake.<a name="NtA_820" + href="#Nt_820"><sup>[820]</sup></a> Price <i>2d.</i> Is there sufficient + proof of the existence of God? 8vo. 1847.</p> + +</blockquote> + + <p>This acorn of the holy oak was forwarded to me with a manuscript note, + signed by the editor, on the part of the <!-- Page 400 --><span + class="pagenum"><a name="page400"></a>[400]</span>"London Society of + Theological Utilitarians," who say, "they trust you may be induced to + give this momentous subject your consideration." The supposition that a + middle-aged person, known as a student of thought on more subjects than + one, had that particular subject yet to begin, is a specimen of what I + will call the <i>assumption-trick</i> of controversy, a habit which + pervades all sides of all subjects. The tract is a proof of the good + policy of letting opinions find their level, without any assistance from + the Court of Queen's Bench. Twenty years earlier the thesis would have + been positive, "There is sufficient proof of the non-existence of God," + and bitter in its tone. As it stands, we have a moderate and respectful + treatment—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 <i>The Reasoner</i> announces the secession of one of its + correspondents, and his adoption of the Christian faith. This would not + have happened twenty years before: nor, had it happened, would it have + been respectfully announced.</p> + + <p>There are people who are very unfortunate in the expression of their + meaning. Mr. Holyoake, in the name of the "London Society" etc., + forwarded a pamphlet on the existence of God, and said that the Society + trusted I "may be induced to give" the subject my "consideration." How + could I know the Society was one person, who supposed I had arrived at a + conclusion and wanted a "<i>guiding word</i>"? But so it seems it was: + Mr. Holyoake, in the <i>English <!-- Page 401 --><span class="pagenum"><a + name="page401"></a>[401]</span>Leader</i> of October 15, 1864, and in a + private letter to me, writes as follows:</p> + + <p>"The gentleman who was the author of the argument, and who asked me to + send it to Mr. De Morgan, never assumed that that gentleman had 'that + particular subject to begin'—on the contrary, he supposed that one + whom we all knew to be eminent as a thinker <i>had</i> come to a + conclusion upon it, and would perhaps vouchsafe a guiding word to one who + was, as yet, seeking the solution of the Great Problem of Theology. I + told my friend that 'Mr. De Morgan was doubtless preoccupied, and that he + must be content to wait. On some day of courtesy and leisure he might + have the kindness to write.' Nor was I wrong—the answer appears in + your pages at the lapse of seventeen years."</p> + + <p>I suppose Mr. Holyoake's way of putting his request was the <i>stylus + curiæ</i> of the Society. A worthy Quaker who was sued for debt in the + King's Bench was horrified to find himself charged in the declaration + with detaining his creditor's money by force and arms, contrary to the + peace of our Lord the King, etc. It's only the <i>stylus curiæ</i>, said + a friend: I don't know <i>curiæ</i>, said the Quaker, but he shouldn't + style us peace-breakers.</p> + + <p>The notion that the <i>non</i>-existence of God can be <i>proved</i>, + has died out under the light of discussion: had the only lights shone + from the pulpit and the prison, so great a step would never have been + made. The question now is as above. The dictum that Christianity is "part + and parcel of the law of the land" is also abrogated: at the same time, + and the coincidence is not an accident, it is becoming somewhat nearer + the truth that the law of the land is part and parcel of Christianity. It + must also be noticed that <i>Christianity</i> was part and parcel of the + articles of <i>war</i>; and so was <i>duelling</i>. Any officer speaking + against religion was to be cashiered; and any officer receiving an + affront without, in the last resort, attempting to kill his opponent, was + also to be cashiered. Though somewhat of a book-hunter, I <!-- Page 402 + --><span class="pagenum"><a name="page402"></a>[402]</span>have never + been able to ascertain the date of the collected remonstrances of the + prelates in the House of Lords against this overt inculcation of murder, + under the soft name of <i>satisfaction</i>: it is neither in Watt,<a + name="NtA_821" href="#Nt_821"><sup>[821]</sup></a> nor in Lowndes,<a + name="NtA_822" href="#Nt_822"><sup>[822]</sup></a> nor in any edition of + Brunet;<a name="NtA_823" href="#Nt_823"><sup>[823]</sup></a> and there is + no copy in the British Museum. Was the collected edition really + published?</p> + + <p>[The publication of the above in the <i>Athenæum</i> has not produced + reference to a single copy. The collected edition seems to be doubted. I + have even met one or two persons who doubt the fact of the Bishops having + remonstrated at all: but their doubt was founded on an absurd + supposition, namely, that it was <i>no business of theirs</i>; that it + was not the business of the prelates of the church in union with the + state to remonstrate against the Crown commanding murder! Some say that + the edition was published, but under an irrelevant title, which prevented + people from knowing what it was about. Such things have happened: for + example, arranged extracts from Wellington's general orders, which would + have attracted attention, fell dead under the title of "Principles of + War." It is surmised that the book I am looking for also contains the + protests of the Reverend bench against other things besides the + Thou-shalt-do-murder of the Articles (of war), and is called "First + Elements of Religion" or some similar title. Time clears up all + things.]</p> + +<hr class="full" > + +<h3>Notes</h3> + +<div class="note"> + <p><a name="Nt_1" href="#NtA_1">[1]</a> See Mrs. De Morgan's <i>Memoir of + Augustus De Morgan</i>, London, 1882, p 61.</p> + + <p><a name="Nt_2" href="#NtA_2">[2]</a> In the first edition this + reference was to page 11.</p> + + <p><a name="Nt_3" href="#NtA_3">[3]</a> In the first edition this read + "at page 438," the work then appearing in a single volume.</p> + + <p><a name="Nt_4" href="#NtA_4">[4]</a> "Just as it would surely have + been better not to have considered it (i.e., the trinity) as a mystery, + and with Cl. Kleckermann to have investigated by the aid of philosophy + according to the teaching of true logic what it might be, before they + determined what it was; just so would it have been better to withdraw + zealously and industriously into the deepest caverns and darkest recesses + of metaphysical speculations and suppositions in order to establish their + opinion beyond danger from the weapons of their adversaries.... Indeed + that great man so explains and demonstrates this dogma (although to + theologians the word has not much charm) from the immovable foundations + of philosophy, that with but few changes and additions a mind sincerely + devoted to truth can desire nothing more."</p> + + <p><a name="Nt_5" href="#NtA_5">[5]</a> Mrs. Wititterly, in <i>Nicholas + Nickleby</i>.—A. De M.</p> + + <p><a name="Nt_6" href="#NtA_6">[6]</a> The brackets mean that the + paragraph is substantially from some one of the <i>Athenæum + Supplements</i>.—S. E. De M.</p> + + <p><a name="Nt_7" href="#NtA_7">[7]</a> "It is annoying that this + ingenious naturalist who has already given us more useful works and has + still others in preparation, uses for this odious task, a pen dipped in + gall and wormwood. It is true that many of his remarks have some + foundation, and that to each error that he points out he at the same time + adds its correction. But he is not always just and never fails to insult. + After all, what does his book prove except that a forty-fifth part of a + very useful review is not free from mistakes? Must we confuse him with + those superficial writers whose liberty of body does not permit them to + restrain their fruitfulness, that crowd of savants of the highest rank + whose writings have adorned and still adorn the <i>Transactions</i>? Has + he forgotten that the names of the Boyles, Newtons, Halleys, De Moivres, + Hans Sloanes, etc. have been seen frequently? and that still are found + those of the Wards, Bradleys, Grahams, Ellicots, Watsons, and of an + author whom Mr. Hill prefers to all others, I mean Mr. Hill himself?"</p> + + <p><a name="Nt_8" href="#NtA_8">[8]</a> "Let no free man be seized or + imprisoned or in any way harmed except by trial of his peers."</p> + + <p><a name="Nt_9" href="#NtA_9">[9]</a> "The master can rob, wreck and + punish his slave according to his pleasure save only that he may not maim + him."</p> + + <p><a name="Nt_10" href="#NtA_10">[10]</a> An Irish antiquary informs me + that Virgil is mentioned in annals at A.D. 784, as "Verghil, i.e., the + geometer, Abbot of Achadhbo [and Bishop of Saltzburg] died in Germany in + the thirteenth year of his bishoprick." No allusion is made to his + opinions; but it seems he was, by tradition, a mathematician. The Abbot + of Aghabo (Queen's County) was canonized by Gregory IX, in 1233. The + story of the second, or scapegoat, Virgil would be much damaged by the + character given to the real bishop, if there were anything in it to + dilapidate.—A. De M.</p> + + <p><a name="Nt_11" href="#NtA_11">[11]</a> "He performed many acts + befitting the Papal dignity, and likewise many excellent (to be sure!) + works."</p> + + <p><a name="Nt_12" href="#NtA_12">[12]</a> "After having been on the + throne during ten years of pestilence."</p> + + <p><a name="Nt_13" href="#NtA_13">[13]</a> The work is the <i>Questiones + Joannis Buridani super X libros Aristotelis ad Nicomachum, curante Egidio + Delfo</i> ... Parisiis, 1489, folio. It also appeared at Paris in + editions of 1499, 1513, and 1518, and at Oxford in 1637.</p> + + <p><a name="Nt_14" href="#NtA_14">[14]</a> Jean Buridan was born at + Béthune about 1298, and died at Paris about 1358. He was professor of + philosophy at the University of Paris and several times held the office + of Rector. As a philosopher he was classed among the nominalists.</p> + + <p><a name="Nt_15" href="#NtA_15">[15]</a> So in the original.</p> + + <p><a name="Nt_16" href="#NtA_16">[16]</a> Baruch Spinoza, or Benedict de + Spinoza as he later called himself, the pantheistic philosopher, + excommunicated from the Jewish faith for heresy, was born at Amsterdam in + 1632 and died there in 1677.</p> + + <p><a name="Nt_17" href="#NtA_17">[17]</a> Michael Scott, or Scot, was + born about 1190, probably in Fifeshire, Scotland, and died about 1291. He + was one of the best known savants of the court of Emperor Frederick II, + and wrote upon astrology, alchemy, and the occult sciences. He was looked + upon as a great magician and is mentioned among the wizards in Dante's + <i>Inferno</i>.</p> + + <div class="poem"> + <div class="stanza"> + <p class="i12hg3">"That other, round the loins</p> + <p>So slender of his shape, was Michael Scot,</p> + <p>Practised in every slight of magic wile." <i>Inferno</i>, XX.</p> + </div> + </div> + <p>Boccaccio also speaks of him: "It is not long since there was in this + city (Florence) a great master in necromancy, who was called Michele + Scotto, because he was a Scot." <i>Decameron</i>, Dec. Giorno.</p> + + <p>Scott's mention of him in Canto Second of his <i>Lay of the Last + Minstrel</i>, is well known:</p> + + <div class="poem"> + <div class="stanza"> + <p class="hg3">"In these fair climes, it was my lot</p> + <p>To meet the wondrous Michael Scott;</p> + <p class="i2">A wizard of such dreaded fame,</p> + <p>That when, in Salamanca's cave,</p> + <p>Him listed his magic wand to wave,</p> + <p class="i2">The bells would ring in Notre Dame!"</p> + </div> + </div> + <p>Sir Walter's notes upon him are of interest.</p> + + <p><a name="Nt_18" href="#NtA_18">[18]</a> These were some of the + forgeries which Michel Chasles (1793-1880) was duped into buying. They + purported to be a correspondence between Pascal and Newton and to show + that the former had anticipated some of the discoveries of the great + English physicist and mathematician. That they were forgeries was shown + by Sir David Brewster in 1855.</p> + + <p><a name="Nt_19" href="#NtA_19">[19]</a> "Let the serpent also break + from its appointed path."</p> + + <p><a name="Nt_20" href="#NtA_20">[20]</a> Guglielmo Brutus Icilius + Timoleon Libri-Carucci della Sommaja, born at Florence in 1803; died at + Fiesole in 1869. His <i>Histoire des Sciences Mathématiques</i> appeared + at Paris in 1838, the entire first edition of volume I, save some half + dozen that he had carried home, being burned on the day that the printing + was completed. He was a great collector of early printed works on + mathematics, and was accused of having stolen large numbers of them from + other libraries. This accusation took him to London, where he bitterly + attacked his accusers. There were two auction sales of his library, and a + number of his books found their way into De Morgan's collection.</p> + + <p><a name="Nt_21" href="#NtA_21">[21]</a> Philo of Gadara lived in the + second century B.C. He was a pupil of Sporus, who worked on the problem + of the two mean proportionals.</p> + + <p><a name="Nt_22" href="#NtA_22">[22]</a> In his <i>Histoire des + Mathématiques</i>, the first edition of which appeared in 1758. Jean + Etienne Montucla was born at Lyons in 1725 and died at Versailles in + 1799. He was therefore only thirty-three years old when his great work + appeared. The second edition, with additions by D'Alembert, appeared in + 1799-1802. He also wrote a work on the quadrature of the circle, + <i>Histoire des recherches sur la Quadrature du Cercle</i>, which + appeared in 1754.</p> + + <p><a name="Nt_23" href="#NtA_23">[23]</a> Eutocius of Ascalon was born + in 480 A.D. He wrote commentaries on the first four books of the conics + of Apollonius of Perga (247-222 B.C.). He also wrote on the Sphere and + Cylinder and the Quadrature of the Circle, and on the two books on + Equilibrium of Archimedes (287-212 B.C.)</p> + + <p><a name="Nt_24" href="#NtA_24">[24]</a> Edward Cocker was born in 1631 + and died between 1671 and 1677. His famous arithmetic appeared in 1677 + and went through many editions. It was written in a style that appealed + to teachers, and was so popular that the expression "According to Cocker" + became a household phrase. Early in the nineteenth century there was a + similar saying in America, "According to Daboll," whose arithmetic had + some points of analogy to that of Cocker. Each had a well-known prototype + in the ancient saying, "He reckons like Nicomachus of Gerasa."</p> + + <p><a name="Nt_25" href="#NtA_25">[25]</a> So in the original, for + Barrême. François Barrême was to France what Cocker was to England. He + was born at Lyons in 1640, and died at Paris in 1703. He published + several arithmetics, dedicating them to his patron, Colbert. One of the + best known of his works is <i>L'arithmétique, ou le livre facile pour + apprendre l'arithmétique soi-mème</i>, 1677. The French word + <i>barême</i> or <i>barrême</i>, a ready-reckoner, is derived from his + name.</p> + + <p><a name="Nt_26" href="#NtA_26">[26]</a> Born at Rome, about 480 A.D.; + died at Pavia, 524. Gibbon speaks of him as "the last of the Romans whom + Cato or Tully could have acknowledged for their countryman." His works on + arithmetic, music, and geometry were classics in the medieval + schools.</p> + + <p><a name="Nt_27" href="#NtA_27">[27]</a> Johannes Campanus, of Novarra, + was chaplain to Pope Urban IV (1261-1264). He was one of the early + medieval translators of Euclid from the Arabic into Latin, and the first + printed edition of the <i>Elements</i> (Venice, 1482) was from his + translation. In this work he probably depended not a little upon at least + two or three earlier scholars. He also wrote <i>De computo ecclesiastico + Calendarium</i>, and <i>De quadratura circuli</i>.</p> + + <p><a name="Nt_28" href="#NtA_28">[28]</a> Archimedes gave 3-1/7, and + 3-10/71 as the limits of the ratio of the circumference to the diameter + of a circle.</p> + + <p><a name="Nt_29" href="#NtA_29">[29]</a> Friedrich W. A. Murhard was + born at Cassel in 1779 and died there in 1853. His <i>Bibliotheca + Mathematica</i>, Leipsic, 1797-1805, is ill arranged and inaccurate, but + it is still a helpful bibliography. De Morgan speaks somewhere of his + indebtedness to it.</p> + + <p><a name="Nt_30" href="#NtA_30">[30]</a> Abraham Gotthelf Kästner was + born at Leipsic in 1719, and died at Göttingen in 1800. He was professor + of mathematics and physics at Göttingen. His <i>Geschichte der + Mathematik</i> (1796-1800) was a work of considerable merit. In the text + of the <i>Budget of Paradoxes</i> the name appears throughout as Kastner + instead of Kästner.</p> + + <p><a name="Nt_31" href="#NtA_31">[31]</a> Lucas Gauricus, or Luca + Gaurico, born at Giffoni, near Naples, in 1476; died at Rome in 1558. He + was an astrologer and mathematician, and was professor of mathematics at + Ferrara in 1531. In 1545 he became bishop of Cività Ducale.</p> + + <p><a name="Nt_32" href="#NtA_32">[32]</a> John Couch Adams was born at + Lidcot, Cornwall, in 1819, and died in 1892. He and Leverrier predicted + the discovery of Neptune from the perturbations in Uranus.</p> + + <p><a name="Nt_33" href="#NtA_33">[33]</a> Urbain-Jean-Joseph Leverrier + was born at Saint-Lô, Manche, in 1811, and died at Paris in 1877. It was + his data respecting the perturbations of Uranus that were used by Adams + and himself in locating Neptune.</p> + + <p><a name="Nt_34" href="#NtA_34">[34]</a> Joseph-Juste Scaliger, the + celebrated philologist, was born at Agen in 1540, and died at Leyden in + 1609. His <i>Cyclometrica elementa</i>, to which De Morgan refers, + appeared at Leyden in 1594.</p> + + <p><a name="Nt_35" href="#NtA_35">[35]</a> The title is: <i>In hoc libra + contenta.... Introductio i geometriā.... Liber de quadratura + circuli. Liber de cubicatione sphere. Perspectiva introductio</i>. + Carolus Bovillus, or Charles Bouvelles (Boüelles, Bouilles, Bouvel), was + born at Saucourt, Picardy, about 1470, and died at Noyon about 1533. He + was canon and professor of theology at Noyon. His <i>Introductio</i> + contains considerable work on star polygons, a favorite study in the + Middle Ages and early Renaissance. His work <i>Que hoc volumine + continētur. Liber de intellectu. Liber de sensu</i>, etc., appeared + at Paris in 1509-10.</p> + + <p><a name="Nt_36" href="#NtA_36">[36]</a> Nicolaus Cusanus, Nicolaus + Chrypffs or Krebs, was born at Kues on the Mosel in 1401, and died at + Todi, Umbria, August 11, 1464. He held positions of honor in the church, + including the bishopric of Brescia. He was made a cardinal in 1448. He + wrote several works on mathematics, his <i>Opuscula varia</i> appearing + about 1490, probably at Strasburg, but published without date or place. + His <i>Opera</i> appeared at Paris in 1511 and again in 1514, and at + Basel in 1565.</p> + + <p><a name="Nt_37" href="#NtA_37">[37]</a> Henry Stephens (born at Paris + about 1528, died at Lyons in 1598) was one of the most successful + printers of his day. He was known as <i>Typographus Parisiensis</i>, and + to his press we owe some of the best works of the period.</p> + + <p><a name="Nt_38" href="#NtA_38">[38]</a> Jacobus Faber Stapulensis + (Jacques le Fèvre d'Estaples) was born at Estaples, near Amiens, in 1455, + and died at Nérac in 1536. He was a priest, vicar of the bishop of Meaux, + lecturer on philosophy at the Collège Lemoine in Paris, and tutor to + Charles, son of Francois I. He wrote on philosophy, theology, and + mathematics.</p> + + <p><a name="Nt_39" href="#NtA_39">[39]</a> Claude-François Milliet de + Challes was born at Chambéry in 1621, and died at Turin in 1678. He + edited <i>Euclidis Elementorum libri octo</i> in 1660, and published a + <i>Cursus seu mundus mathematicus</i>, which included a short history of + mathematics, in 1674. He also wrote on mathematical geography.</p> + + <p><a name="Nt_40" href="#NtA_40">[40]</a> This date should be 1503, if + he refers to the first edition. It is well known that this is the first + encyclopedia worthy the name to appear in print. It was written by + Gregorius Reisch (born at Balingen, and died at Freiburg in 1487), prior + of the cloister at Freiburg and confessor to Maximilian I. The first + edition appeared at Freiburg in 1503, and it passed through many editions + in the sixteenth and seventeenth centuries. The title of the 1504 edition + reads: <i>Aepitoma omnis phylosophiae. alias Margarita phylosophica + tractans de omni genere scibili: Cum additionibus: Quae in alijs non + habentur</i>.</p> + + <p><a name="Nt_41" href="#NtA_41">[41]</a> This is the <i>Introductio in + arithmeticam Divi S. Boetii.... Epitome rerum geometricarum ex geometrica + introductio C. Bovilli. De quadratura circuli demonstratio ex + Campano</i>, that appeared without date about 1507.</p> + + <p><a name="Nt_42" href="#NtA_42">[42]</a> Born at Liverpool in 1805, and + died there about 1872. He was a merchant, and in 1865 he published, at + Liverpool, a work entitled <i>The Quadrature of the Circle, or the True + Ratio between the Diameter and Circumference geometrically and + mathematically demonstrated</i>. In this he gives the ratio as exactly + 3⅛.</p> + + <p><a name="Nt_43" href="#NtA_43">[43]</a> "That it would be impossible + to tell him exactly, since no one had yet been able to find precisely the + ratio of the circumference to the diameter."</p> + + <p><a name="Nt_44" href="#NtA_44">[44]</a> This is the Paris edition: + "Parisiis: ex officina Ascensiana anno Christi ... MDXIIII," as appears + by the colophon of the second volume to which De Morgan refers.</p> + + <p><a name="Nt_45" href="#NtA_45">[45]</a> Regiomontanus, or Johann + Müller of Königsberg (Regiomontanus), was born at Königsberg in + Franconia, June 5, 1436, and died at Rome July 6, 1476. He studied at + Vienna under the great astronomer Peuerbach, and was his most famous + pupil. He wrote numerous works, chiefly on astronomy. He is also known by + the names Ioannes de Monte Regio, de Regiomonte, Ioannes Germanus de + Regiomonte, etc.</p> + + <p><a name="Nt_46" href="#NtA_46">[46]</a> Henry Cornelius Agrippa was + born at Cologne in 1486 and died either at Lyons in 1534 or at Grenoble + in 1535. He was professor of theology at Cologne and also at Turin. After + the publication of his <i>De Occulta Philosophia</i> he was imprisoned + for sorcery. Both works appeared at Antwerp in 1530, and each passed + through a large number of editions. A French translation appeared in + Paris in 1582, and an English one in London in 1651.</p> + + <p><a name="Nt_47" href="#NtA_47">[47]</a> Nicolaus Remegius was born in + Lorraine in 1554, and died at Nancy in 1600. He was a jurist and + historian, and held the office of procurator general to the Duke of + Lorraine.</p> + + <p><a name="Nt_48" href="#NtA_48">[48]</a> This was at the storming of + the city by the British on May 4, 1799. From his having been born in + India, all this appealed strongly to the interests of De Morgan.</p> + + <p><a name="Nt_49" href="#NtA_49">[49]</a> Orontius Finaeus, or Oronce + Finé, was born at Briançon in 1494 and died at Paris, October 6, 1555. He + was imprisoned by François I for refusing to recognize the concordat + (1517). He was made professor of mathematics in the Collège Royal (later + called the Collège de France) in 1532. He wrote extensively on astronomy + and geometry, but was by no means a great scholar. He was a pretentious + man, and his works went through several editions. His + <i>Protomathesis</i> appeared at Paris in 1530-32. The work referred to + by De Morgan is the <i>Quadratura circuli tandem inventa & clarissime + demonstrata</i> ... Lutetiae Parisiorum, 1544, fol. In the 1556 edition + of his <i>De rebus mathematicis, hactenus desideratis, Libri IIII</i>, + published at Paris, the subtitle is: <i>Quibus inter cætera, Circuli + quadratura Centum modis, & suprà, per eundem Orontium recenter + excogitatis, demonstratus</i>, so that he kept up his efforts until his + death.</p> + + <p><a name="Nt_50" href="#NtA_50">[50]</a> Johannes Buteo (Boteo, Butéon, + Bateon) was born in Dauphiné c. 1485-1489, and died in a cloister in 1560 + or 1564. Some writers give Charpey as the place and 1492 as the date of + his birth, and state that he died at Canar in 1572. He belonged to the + order of St. Anthony, and wrote chiefly on geometry, exposing the + pretenses of Finaeus. His <i>Opera geometrica</i> appeared at Lyons in + 1554, and his <i>Logistica</i> and <i>De quadratura circuli libri duo</i> + at Lyons in 1559.</p> + + <p><a name="Nt_51" href="#NtA_51">[51]</a> This is the great French + algebraist, François Viète (Vieta), who was born at Fontenay-le-Comte in + 1540, and died at Paris, December 13, 1603. His well-known <i>Isagoge in + artem analyticam</i> appeared at Tours in 1591. His <i>Opera + mathematica</i> was edited by Van Schooten in 1646.</p> + + <p><a name="Nt_52" href="#NtA_52">[52]</a> This is the <i>De Rebus + mathematicis hactenus desideratis, Libri IIII</i>, that appeared in Paris + in 1556. For the title page see Smith, D. E., <i>Rara Arithmetica</i>, + Boston, 1908, p. 280.</p> + + <p><a name="Nt_53" href="#NtA_53">[53]</a> The title is correct except + for a colon after <i>Astronomicum</i>. Nicolaus Raimarus Ursus was born + in Henstede or Hattstede, in Dithmarschen, and died at Prague in 1599 or + 1600. He was a pupil of Tycho Brahe. He also wrote <i>De astronomis + hypothesibus</i> (1597) and <i>Arithmetica analytica vulgo Cosa oder + Algebra</i> (1601).</p> + + <p><a name="Nt_54" href="#NtA_54">[54]</a> Born at Dôle, Franche-Comté, + about 1550, died in Holland about 1600. The work to which reference is + made is the <i>Quadrature du cercle, ou manière de trouver un quarré égal + au cercle donné</i>, which appeared at Delft in 1584. Duchesne had the + courage of his convictions, not only on circle-squaring but on religion + as well, for he was obliged to leave France because of his conversion to + Calvinism. De Morgan's statement that his real name is Van der Eycke is + curious, since he was French born. The Dutch may have translated his name + when he became professor at Delft, but we might equally well say, that + his real name was Quercetanus or à Quercu.</p> + + <p><a name="Nt_55" href="#NtA_55">[55]</a> This was the father of Adriaan + Metius (1571-1635). He was a mathematician and military engineer, and + suggested the ratio 355/113 for <span class="grk">π</span>, a ratio + afterwards published by his son. The ratio, then new to Europe, had long + been known and used in China, having been found by Tsu Ch'ung-chih + (428-499 A.D.).</p> + + <p><a name="Nt_56" href="#NtA_56">[56]</a> This was Jost Bürgi, or Justus + Byrgius, the Swiss mathematician of whom Kepler wrote in 1627: "Apices + logistici Justo Byrgio multis annis ante editionem Neperianam viam + præiverunt ad hos ipsissimos logarithmos." He constructed a table of + antilogarithms (<i>Arithmetische und geometrische Progress-Tabulen</i>), + but it was not published until after Napier's work appeared.</p> + + <p><a name="Nt_57" href="#NtA_57">[57]</a> Ludolphus Van Ceulen, born at + Hildesheim, and died at Leyden in 1610. It was he who first carried the + computation of <span class="grk">π</span> to 35 decimal places.</p> + + <p><a name="Nt_58" href="#NtA_58">[58]</a> Jens Jenssen Dodt, van + Flensburg, a Dutch historian, who died in 1847.</p> + + <p><a name="Nt_59" href="#NtA_59">[59]</a> I do not know this edition. + There was one "Antverpiae apud Petrum Bellerum sub scuto Burgundiae," + 4to, in 1591.</p> + + <p><a name="Nt_60" href="#NtA_60">[60]</a> Archytas of Tarentum (430-365 + B.C.) who wrote on proportions, irrationals, and the duplication of the + cube.</p> + + <p><a name="Nt_61" href="#NtA_61">[61]</a> </p> + + <div class="poem"> + <div class="stanza"> + <p class="i4"><i>The Circle Speaks.</i></p> + <p class="hg3">"At first a circle I was called,</p> + <p>And was a curve around about</p> + <p>Like lofty orbit of the sun</p> + <p>Or rainbow arch among the clouds.</p> + <p>A noble figure then was I—</p> + <p>And lacking nothing but a start,</p> + <p>And lacking nothing but an end.</p> + <p>But now unlovely do I seem</p> + <p>Polluted by some angles new.</p> + <p>This thing Archytas hath not done</p> + <p>Nor noble sire of Icarus</p> + <p>Nor son of thine, Iapetus.</p> + <p>What accident or god can then</p> + <p>Have quadrated mine area?"</p> + </div> + + <div class="stanza"> + <p class="i4"><i>The Author Replies.</i></p> + <p class="hg3">"By deepest mouth of Turia</p> + <p>And lake of limpid clearness, lies</p> + <p>A happy state not far removed</p> + <p>From old Saguntus; farther yet</p> + <p>A little way from Sucro town.</p> + <p>In this place doth a poet dwell,</p> + <p>Who oft the stars will closely scan,</p> + <p>And always for himself doth claim</p> + <p>What is denied to wiser men;—</p> + <p>An old man musing here and there</p> + <p>And oft forgetful of himself,</p> + <p>Not knowing how to rightly place</p> + <p>The compasses, nor draw a line,</p> + <p>As he doth of himself relate.</p> + <p>This craftsman fine, in sooth it is</p> + <p>Hath quadrated thine area."</p> + </div> + </div> + <p><a name="Nt_62" href="#NtA_62">[62]</a> Pietro Bongo, or Petrus + Bungus, was born at Bergamo, and died there in 1601. His work on the + Mystery of Numbers is one of the most exhaustive and erudite ones of the + mystic writers. The first edition appeared at Bergamo in 1583-84; the + second, at Bergamo in 1584-85; the third, at Venice in 1585; the fourth, + at Bergamo in 1590; and the fifth, which De Morgan calls the second, in + 1591. Other editions, before the Paris edition to which he refers, + appeared in 1599 and 1614; and the colophon of the Paris edition is dated + 1617. See the editor's <i>Rara Arithmetica</i>, pp. 380-383.</p> + + <p><a name="Nt_63" href="#NtA_63">[63]</a> William Warburton (1698-1779), + Bishop of Gloucester, whose works got him into numerous literary + quarrels, being the subject of frequent satire.</p> + + <p><a name="Nt_64" href="#NtA_64">[64]</a> Thomas Galloway (1796-1851), + who was professor of mathematics at Sandhurst for a time, and was later + the actuary of the Amicable Life Assurance Company of London. In the + latter capacity he naturally came to be associated with De Morgan.</p> + + <p><a name="Nt_65" href="#NtA_65">[65]</a> Giordano Bruno was born near + Naples about 1550. He left the Dominican order to take up Calvinism, and + among his publications was <i>L'expulsion de la bête triomphante</i>. He + taught philosophy at Paris and Wittenberg, and some of his works were + published in England in 1583-86. Whether or not he was roasted alive "for + the maintenance and defence of the holy Church," as De Morgan states, + depends upon one's religious point of view. At any rate, he was roasted + as a heretic.</p> + + <p><a name="Nt_66" href="#NtA_66">[66]</a> Referring to part of his + <i>Discours de la méthode</i>, Leyden, 1637.</p> + + <p><a name="Nt_67" href="#NtA_67">[67]</a> Bartholomew Legate, who was + born in Essex about 1575. He denied the divinity of Christ and was the + last heretic burned at Smithfield.</p> + + <p><a name="Nt_68" href="#NtA_68">[68]</a> Edward Wightman, born probably + in Staffordshire. He was anti-Trinitarian, and claimed to be the Messiah. + He was the last man burned for heresy in England.</p> + + <p><a name="Nt_69" href="#NtA_69">[69]</a> Gaspar Schopp, born at + Neumarck in 1576, died at Padua in 1649; grammarian, philologist, and + satirist.</p> + + <p><a name="Nt_70" href="#NtA_70">[70]</a> Konrad Ritterhusius, born at + Brunswick in 1560; died at Altdorf in 1613. He was a jurist of some + power.</p> + + <p><a name="Nt_71" href="#NtA_71">[71]</a> Johann Jakob Brucker, born at + Augsburg in 1696, died there in 1770. He wrote on the history of + philosophy (1731-36, and 1742-44).</p> + + <p><a name="Nt_72" href="#NtA_72">[72]</a> Daniel Georg Morhof, born at + Wismar in 1639, died at Lübeck in 1691. He was rector of the University + of Kiel, and professor of eloquence, poetry, and history.</p> + + <p><a name="Nt_73" href="#NtA_73">[73]</a> In the <i>Histoire des + Sciences Mathématiques</i>, vol. IV, note X, pp. 416-435 of the 1841 + edition.</p> + + <p><a name="Nt_74" href="#NtA_74">[74]</a> Colenso (1814-1883), + missionary bishop of Natal, was one of the leaders of his day in the + field of higher biblical criticism. De Morgan must have admired his + mathematical works, which were not without merit.</p> + + <p><a name="Nt_75" href="#NtA_75">[75]</a> Samuel Roffey Maitland, born + at London in 1792; died at Gloucester in 1866. He was an excellent + linguist and a critical student of the Bible. He became librarian at + Lambeth in 1838.</p> + + <p><a name="Nt_76" href="#NtA_76">[76]</a> Archbishop Howley (1766-1848) + was a thorough Tory. He was one of the opponents of the Roman Catholic + Relief bill, the Reform bill, and the Jewish Civil Disabilities Relief + bill.</p> + + <p><a name="Nt_77" href="#NtA_77">[77]</a> We have, in America at least, + almost forgotten the great stir made by Edward B. Pusey (1800-1882) in + the great Oxford movement in the middle of the nineteenth century. He was + professor of Hebrew at Oxford, and canon of Christ Church.</p> + + <p><a name="Nt_78" href="#NtA_78">[78]</a> That is, his <i>Magia + universalis naturae et artis sive recondita naturalium et artificialium + rerum scientia</i>, Würzburg, 1657, 4to, with editions at Bamberg in + 1671, and at Frankfort in 1677. Gaspard Schott (Königshofen 1608, + Würzburg 1666) was a physicist and mathematician, devoting most of his + attention to the curiosities of his sciences. His type of mind must have + appealed to De Morgan.</p> + + <p><a name="Nt_79" href="#NtA_79">[79]</a> <i>Salicetti Quadratura + circuli nova, perspicua, expedita, veraque tum naturalis, tum + geometrica</i>, etc., 1608.—<i>Consideratio nova in opusculum + Archimedis de circuli dimensione</i>, etc., 1609.</p> + + <p><a name="Nt_80" href="#NtA_80">[80]</a> Melchior Adam, who died at + Heidelberg in 1622, wrote a collection of biographies which was published + at Heidelberg and Frankfort from 1615 to 1620.</p> + + <p><a name="Nt_81" href="#NtA_81">[81]</a> Born at Baden in 1524; died at + Basel in 1583. The Erastians were related to the Zwinglians, and opposed + all power of excommunication and the infliction of penalties by a + church.</p> + + <p><a name="Nt_82" href="#NtA_82">[82]</a> See Acts xii. 20.</p> + + <p><a name="Nt_83" href="#NtA_83">[83]</a> Theodore de Bèse, a French + theologian; born at Vezelay, in Burgundy, in 1519; died at Geneva, in + 1605.</p> + + <p><a name="Nt_84" href="#NtA_84">[84]</a> Dr. Robert Lee (1804-1868) had + some celebrity in De Morgan's time through his attempt to introduce music + and written prayers into the service of the Scotch Presbyterian + church.</p> + + <p><a name="Nt_85" href="#NtA_85">[85]</a> Born at Veringen, + Hohenzollern, in 1512; died at Röteln in 1564.</p> + + <p><a name="Nt_86" href="#NtA_86">[86]</a> Born at Kinnairdie, + Bannfshire, in 1661; died at London in 1708. His <i>Astronomiae Physicae + et Geometriae Elementa</i>, Oxford, 1702, was an influential work.</p> + + <p><a name="Nt_87" href="#NtA_87">[87]</a> The title was carelessly + copied by De Morgan, not an unusual thing in his case. The original + reads: A Plaine Discovery, of the whole Revelation of S. Iohn: set downe + in two treatises ... set foorth by John Napier L. of Marchiston ... + whereunto are annexed, certaine Oracles of Sibylla ... London ... + 1611.</p> + + <p><a name="Nt_88" href="#NtA_88">[88]</a> I have not seen the first + edition, but it seems to have appeared in Edinburgh, in 1593, with a + second edition there in 1594. The 1611 edition was the third.</p> + + <p><a name="Nt_89" href="#NtA_89">[89]</a> It seems rather certain that + Napier felt his theological work of greater importance than that in + logarithms. He was born at Merchiston, near (now a part of) Edinburgh, in + 1550, and died there in 1617, three years after the appearance of his + <i>Mirifici logarithmorum canonis descriptio</i>.</p> + + <p><a name="Nt_90" href="#NtA_90">[90]</a> Followed, in the third + edition, from which he quotes, by a comma.</p> + + <p><a name="Nt_91" href="#NtA_91">[91]</a> There was an edition published + at Stettin in 1633. An English translation by P. F. Mottelay appeared at + London in 1893. Gilbert (1540-1603) was physician to Queen Elizabeth and + President of the College of Physicians at London. His <i>De Magnete</i> + was the first noteworthy treatise on physics printed in England. He + treated of the earth as a spherical magnet and suggested the variation + and declination of the needle as a means of finding latitude at sea.</p> + + <p><a name="Nt_92" href="#NtA_92">[92]</a> The title says "ab authoris + fratre collectum," although it was edited by J. Gruterus.</p> + + <p><a name="Nt_93" href="#NtA_93">[93]</a> Porta was born at Naples in + 1550 and died there in 1615. He studied the subject of lenses and the + theory of sight, did some work in hydraulics and agriculture, and was + well known as an astrologer. His <i>Magiae naturalis libri XX</i> was + published at Naples in 1589. The above title should read + <i>curvilineorum</i>.</p> + + <p><a name="Nt_94" href="#NtA_94">[94]</a> Cataldi was born in 1548 and + died at Bologna in 1626. He was professor of mathematics at Perugia, + Florence, and Bologna, and is known in mathematics chiefly for his work + in continued fractions. He was one of the scholarly men of his day.</p> + + <p><a name="Nt_95" href="#NtA_95">[95]</a> Georg Joachim Rheticus was + born at Feldkirch in 1514 and died at Caschau, Hungary, in 1576. He was + one of the most prominent pupils of Copernicus, his <i>Narratio de libris + revolutionum Copernici</i> (Dantzig, 1540) having done much to make the + theory of his master known.</p> + + <p><a name="Nt_96" href="#NtA_96">[96]</a> Henry Briggs, who did so much + to make logarithms known, and who used the base 10, was born at Warley + Wood, in Yorkshire, in 1560, and died at Oxford in 1630. He was Savilian + professor of mathematics at Oxford, and his grave may still be seen + there.</p> + + <p><a name="Nt_97" href="#NtA_97">[97]</a> He lived at "Reggio nella + Emilia" in the 16th and 17th centuries. His <i>Regola e modo facilissimo + di quadrare il cerchio</i> was published at Reggio in 1609.</p> + + <p><a name="Nt_98" href="#NtA_98">[98]</a> Christoph Klau (Clavius) was + born at Bamberg in 1537, and died at Rome in 1612. He was a Jesuit priest + and taught mathematics in the Jesuit College at Rome. He wrote a number + of works on mathematics, including excellent text-books on arithmetic and + algebra.</p> + + <p><a name="Nt_99" href="#NtA_99">[99]</a> Christopher Gruenberger, or + Grienberger, was born at Halle in Tyrol in 1561, and died at Rome in + 1636. He was, like Clavius, a Jesuit and a mathematician, and he wrote a + little upon the subject of projections. His <i>Prospectiva nova + coelestis</i> appeared at Rome in 1612.</p> + + <p><a name="Nt_100" href="#NtA_100">[100]</a> The name should, of course, + be Lansbergii in the genitive, and is so in the original title. Philippus + Lansbergius was born at Ghent in 1560, and died at Middelburg in 1632. He + was a Protestant theologian, and was also a physician and astronomer. He + was a well-known supporter of Galileo and Copernicus. His + <i>Commentationes in motum terrae diurnum et annuum</i> appeared at + Middelburg in 1630 and did much to help the new theory.</p> + + <p><a name="Nt_101" href="#NtA_101">[101]</a> I have never seen the work. + It is rare.</p> + + <p><a name="Nt_102" href="#NtA_102">[102]</a> The African explorer, born + in Somersetshire in 1827, died at Bath in 1864. He was the first European + to cross Central Africa from north to south. He investigated the sources + of the Nile.</p> + + <p><a name="Nt_103" href="#NtA_103">[103]</a> Prester (Presbyter, priest) + John, the legendary Christian king whose realm, in the Middle Ages, was + placed both in Asia and in Africa, is first mentioned in the chronicles + of Otto of Freisingen in the 12th century. In the 14th century his + kingdom was supposed to be Abyssinia.</p> + + <p><a name="Nt_104" href="#NtA_104">[104]</a> "It is a profane and + barbarous nation, dirty and slovenly, who eat their meat half raw and + drink mare's milk, and who use table-cloths and napkins only to wipe + their hands and mouths."</p> + + <p><a name="Nt_105" href="#NtA_105">[105]</a> "The great Prester John, + who is the fourth in rank, is emperor of Ethiopia and of the Abyssinians, + and boasts of his descent from the race of David, as having descended + from the Queen of Sheba, Queen of Ethiopia. She, having gone to Jerusalem + to see the wisdom of Solomon, about the year of the world 2952, returned + pregnant with a son whom they called Moylech, from whom they claim + descent in a direct line. And so he glories in being the most ancient + monarch in the world, saying that his empire has endured for more than + three thousand years, which no other empire is able to assert. He also + puts into his titles the following: 'We, the sovereign in my realms, + uniquely beloved of God, pillar of the faith, sprung from the race of + Judah, etc.' The boundaries of this empire touch the Red Sea and the + mountains of Azuma on the east, and on the western side it is bordered by + the River Nile which separates it from Nubia. To the north lies Egypt, + and to the south the kingdoms of Congo and Mozambique. It extends forty + degrees in length, or one thousand twenty-five leagues, from Congo or + Mozambique on the south to Egypt on the north; and in width it reaches + from the Nile on the west to the mountains of Azuma on the east, seven + hundred twenty-five leagues, or twenty-nine degrees. This empire contains + thirty large provinces, namely Medra, Gaga, Alchy, Cedalon, Mantro, + Finazam, Barnaquez, Ambiam, Fungy, Angoté, Cigremaon, Gorga, Cafatez, + Zastanla, Zeth, Barly, Belangana, Tygra, Gorgany, Barganaza, d'Ancut, + Dargaly, Ambiacatina, Caracogly, Amara, Maon (<i>sic</i>), Guegiera, + Bally, Dobora, and Macheda. All of these provinces are situated directly + under the equinoctial line between the tropics of Capricorn and Cancer; + but they are two hundred fifty leagues nearer our tropic than the other. + The name of Prester John signifies Great Lord, and is not Priest + [Presbyter] as many think. He has always been a Christian, but often + schismatic. At the present time he is a Catholic and recognizes the Pope + as sovereign pontiff. I met one of his bishops in Jerusalem, and often + conversed with him through the medium of our guide. He was of grave and + serious bearing, pleasant of speech, but wonderfully subtle in everything + he said. He took great delight in what I had to relate concerning our + beautiful ceremonies and the dignity of our prelates in their pontifical + vestments. As to other matters I will only say that the Ethiopian is + joyous and merry, not at all like the Tartar in the matter of filth, nor + like the wretched Arab. They are refined and subtle, trusting no one, + wonderfully suspicious, and very devout. They are not at all black as is + commonly supposed, by which I refer to those who do not live under the + equator or too near to it, for these are Moors as we shall see."</p> + + <p>With respect to this translation it should be said that the original + forms of the proper names have been preserved, although they are not + those found in modern works. It should also be stated that the meaning of + Prester is not the one that was generally accepted by scholars at the + time the work was written, nor is it the one accepted to-day. There seems + to be no doubt that the word is derived from Presbyter as stated in note + <a href="#Nt_103">103</a> on page <a href="#page71">71</a>, since the + above-mentioned chronicles of Otto, bishop of Freisingen about the middle + of the twelfth century, states this fact clearly. Otto received his + information from the bishop of Gabala (the Syrian Jibal) who told him the + story of John, <i>rex et sacerdos</i>, or Presbyter John as he liked to + be called. He goes on to say "Should it be asked why, with all this power + and splendor, he calls himself merely 'presbyter,' this is because of his + humility, and because it was not fitting for one whose server was a + primate and king, whose butler an archbishop and king, whose chamberlain + a bishop and king, whose master of the horse an archimandrite and king, + whose chief cook an abbot and king, to be called by such titles as + these."</p> + + <p><a name="Nt_106" href="#NtA_106">[106]</a> Thomas Fienus (Fyens) was + born at Antwerp in 1567 and died in 1631. He was professor of medicine at + Louvain. Besides the editions mentioned below, his <i>De cometis anni + 1618</i> appeared at Leipsic in 1656. He also wrote a <i>Disputatio an + coelum moveatur et terra quiescat</i>, which appeared at Antwerp in 1619, + and again at Leipsic in 1656.</p> + + <p><a name="Nt_107" href="#NtA_107">[107]</a> Libertus Fromondus (1587-c + 1653), a Belgian theologian, dean of the College Church at Harcourt, and + professor at Louvain. The name also appears as Froidmont and + Froimont.</p> + + <p><a name="Nt_108" href="#NtA_108">[108]</a> <i>L. Fromondi ... + meteorologicorum libri sex.... Cui accessit T. Fieni et L. Fromondi + dissertationes de cometa anni 1618....</i> This is from the 1670 edition. + The 1619 edition was published at Antwerp. The <i>Meteorologicorum libri + VI</i>, appeared at Antwerp in 1627. He also wrote <i>Anti-Aristarchus + sive orbis terrae immobilis liber unicus</i> (Antwerp, 1631); + <i>Labyrrinthus sive de compositione continui liber unus, Philosophis, + Mathematicis, Theologis utilis et jucundus</i> (Antwerp, 1631) and + <i>Vesta sive Anti-Aristarchi vindex adversus Jac. Lansbergium (Philippi + filium) et copernicanos</i> (Antwerp, 1634).</p> + + <p><a name="Nt_109" href="#NtA_109">[109]</a> Snell was born at Leyden in + 1591, and died there in 1626. He studied under Tycho Brahe and Kepler, + and is known for Snell's law of the refraction of light. He was the first + to determine the size of the earth by measuring the arc of a meridian + with any fair degree of accuracy. The title should read: <i>Willebrordi + Snellii R. F. Cyclometricus, de circuli dimensione secundum Logistarum + abacos, et ad Mechanicem accuratissima....</i></p> + + <p><a name="Nt_110" href="#NtA_110">[110]</a> Bacon was born at York + House, London, in 1561, and died near Highgate, London, in 1626. His + <i>Novum Organum Scientiarum or New Method of employing the reasoning + faculties in the pursuits of Truth</i> appeared at London in 1620. He had + previously published a work entitled <i>Of the Proficience and + Advancement of Learning, divine and humane</i> (London, 1605), which + again appeared in 1621. His <i>De augmentis scientiarum Libri IX</i> + appeared at Paris in 1624, and his <i>Historia naturalis et + experimentalis de ventis</i> at Leyden in 1638. He was successively + solicitor general, attorney general, lord chancellor (1619), Baron + Verulam and Viscount St. Albans. He was deprived of office and was + imprisoned in the Tower of London in 1621, but was later pardoned.</p> + + <p><a name="Nt_111" href="#NtA_111">[111]</a> The Greek form, + <i>Organon</i>, is sometimes used.</p> + + <p><a name="Nt_112" href="#NtA_112">[112]</a> James Spedding (1808-1881), + fellow of Cambridge, who devoted his life to his edition of Bacon.</p> + + <p><a name="Nt_113" href="#NtA_113">[113]</a> R. Leslie Ellis + (1817-1859), editor of the <i>Cambridge Mathematical Journal</i>. He also + wrote on Roman aqueducts, on Boole's Laws of Thought, and on the + formation of a Chinese dictionary.</p> + + <p><a name="Nt_114" href="#NtA_114">[114]</a> Douglas Derion Heath + (1811-1897), a classical and mathematical scholar.</p> + + <p><a name="Nt_115" href="#NtA_115">[115]</a> There have been numerous + editions of Bacon's complete works, including the following: Frankfort, + 1665; London, 1730, 1740, 1764, 1765, 1778, 1803, 1807, 1818, 1819, 1824, + 1825-36, 1857-74, 1877. The edition to which De Morgan refers is that of + 1857-74, 14 vols., of which five were apparently out at the time he + wrote. There were also French editions in 1800 and 1835.</p> + + <p><a name="Nt_116" href="#NtA_116">[116]</a> So in the original for + Tycho Brahe.</p> + + <p><a name="Nt_117" href="#NtA_117">[117]</a> In general these men acted + before Baron wrote, or at any rate, before he wrote the <i>Novum + Organum</i>, but the statement must not be taken too literally. The dates + are as follows: Copernicus, 1473-1543; Tycho Brahe, 1546-1601; Gilbert, + 1540-1603; Kepler, 1571-1630; Galileo, 1564-1642; Harvey, 1578-1657. For + example, Harvey's <i>Exercitatio Anatomica de Motu Cordis et + Sanguinis</i> did not appear until 1628, and his <i>Exercitationes de + Generatione</i> until 1651.</p> + + <p><a name="Nt_118" href="#NtA_118">[118]</a> Robert Hooke (1635-1703) + studied under Robert Boyle at Oxford. He was "Curator of Experiments" to + the Royal Society and its secretary, and was professor of geometry at + Gresham College, London. It is true that he was "very little of a + mathematician" although he wrote on the motion of the earth (1674), on + helioscopes and other instruments (1675), on the rotation of Jupiter + (1666), and on barometers and sails.</p> + + <p><a name="Nt_119" href="#NtA_119">[119]</a> The son of the Sir William + mentioned below. He was born in 1792 and died in 1871. He wrote a + treatise on light (1831) and one on astronomy (1836), and established an + observatory at the Cape of Good Hope where he made observations during + 1834-1838, publishing them in 1847. On his return to England he was + knighted, and in 1848 was made president of the Royal Society. The title + of the work to which reference is made is: <i>A preliminary discourse on + the Study of Natural Philosophy</i>. It appeared at London in 1831.</p> + + <p><a name="Nt_120" href="#NtA_120">[120]</a> Sir William was horn at + Hanover in 1738 and died at Slough, near Windsor in 1822. He discovered + the planet Uranus and six satellites, besides two satellites of Saturn. + He was knighted by George III.</p> + + <p><a name="Nt_121" href="#NtA_121">[121]</a> This was the work of 1836. + He also published a work entitled <i>Outlines of Astronomy</i> in + 1849.</p> + + <p><a name="Nt_122" href="#NtA_122">[122]</a> While Newton does not tell + the story, he refers in the <i>Principia</i> (1714 edition, p. 293) to + the accident caused by his cat.</p> + + <p><a name="Nt_123" href="#NtA_123">[123]</a> Marino Ghetaldi + (1566-1627), whose <i>Promotus Archimedes</i> appeared at Rome in 1603, + <i>Nonnullae propositiones de parabola</i> at Rome in 1603. and + <i>Apollonius redivivus</i> at Venice in 1607. He was a nobleman and was + ambassador from Venice to Rome.</p> + + <p><a name="Nt_124" href="#NtA_124">[124]</a> Simon Stevin (born at + Bruges, 1548; died at the Hague, 1620). He was an engineer and a soldier, + and his <i>La Disme</i> (1585) was the first separate treatise on the + decimal fraction. The contribution referred to above is probably that on + the center of gravity of three bodies (1586).</p> + + <p><a name="Nt_125" href="#NtA_125">[125]</a> Habakuk Guldin (1577-1643), + who took the name Paul on his conversion to Catholicism. He became a + Jesuit, and was professor of mathematics at Vienna and later at Gratz. In + his <i>Centrobaryca seu de centro gravitatis trium specierum quantitatis + continuae</i> (1635), of the edition of 1641, appears the Pappus rule for + the volume of a solid formed by the revolution of a plane figure about an + axis, often spoken of as Guldin's Theorem.</p> + + <p><a name="Nt_126" href="#NtA_126">[126]</a> Edward Wright was born at + Graveston, Norfolkshire, in 1560, and died at London in 1615. He was a + fellow of Caius College, Cambridge, and in his work entitled <i>The + correction of certain errors in Navigation</i> (1599) he gives the + principle of Mercator's projection. He translated the <i>Portuum + investigandorum ratio</i> of Stevin in 1599.</p> + + <p><a name="Nt_127" href="#NtA_127">[127]</a> De Morgan never wrote a + more suggestive sentence. Its message is not for his generation + alone.</p> + + <p><a name="Nt_128" href="#NtA_128">[128]</a> The eminent French + physicist, Jean Baptiste Biot (1779-1862), professor in the Collège de + France. His work <i>Sur les observatoires météorologiques</i> appeared in + 1855.</p> + + <p><a name="Nt_129" href="#NtA_129">[129]</a> George Biddell Airy + (1801-1892), professor of astronomy and physics at Cambridge, and + afterwards director of the Observatory at Greenwich.</p> + + <p><a name="Nt_130" href="#NtA_130">[130]</a> De Morgan would have + rejoiced in the rôle played by Intuition in the mathematics of to-day, + notably among the followers of Professor Klein.</p> + + <p><a name="Nt_131" href="#NtA_131">[131]</a> Colburn was the best known + of the calculating boys produced in America. He was born at Cabot, + Vermont, in 1804, and died at Norwich, Vermont, in 1840. Having shown + remarkable skill in numbers as early as 1810, he was taken to London in + 1812, whence he toured through Great Britain and to Paris. The Earl of + Bristol placed him in Westminster School (1816-1819). On his return to + America he became a preacher, and later a teacher of languages.</p> + + <p><a name="Nt_132" href="#NtA_132">[132]</a> The history of calculating + boys is interesting. Mathieu le Coc (about 1664), a boy of Lorraine, + could extract cube roots at sight at the age of eight. Tom Fuller, a + Virginian slave of the eighteenth century, although illiterate, gave the + number of seconds in 7 years 17 days 12 hours after only a minute and a + half of thought. Jedediah Buxton, an Englishman of the eighteenth + century, was studied by the Royal Society because of his remarkable + powers. Ampère, the physicist, made long calculations with pebbles at the + age of four. Gauss, one of the few infant prodigies to become an adult + prodigy, corrected his father's payroll at the age of three. One of the + most remarkable of the French calculating boys was Henri Mondeux. He was + investigated by Arago, Sturm, Cauchy, and Liouville, for the Académie des + Sciences, and a report was written by Cauchy. His specialty was the + solution of algebraic problems mentally. He seems to have calculated + squares and cubes by a binomial formula of his own invention. He died in + obscurity, but was the subject of a <i>Biographie</i> by Jacoby (1846). + George P. Bidder, the Scotch engineer (1806-1878), was exhibited as an + arithmetical prodigy at the age of ten, and did not attend school until + he was twelve. Of the recent cases two deserve special mention, Inaudi + and Diamandi. Jacques Inaudi (born in 1867) was investigated for the + Académie in 1892 by a commission including Poincaré, Charcot, and Binet. + (See the <i>Revue des Deux Mondes</i>, June 15, 1892, and the laboratory + bulletins of the Sorbonne). He has frequently exhibited his remarkable + powers in America. Périclès Diamandi was investigated by the same + commission in 1893. See Alfred Binet, <i>Psychologie des Grands + Calculateurs et Joueurs d'Echecs</i>, Paris, 1894.</p> + + <p><a name="Nt_133" href="#NtA_133">[133]</a> John Flamsteed's + (1646-1719) "old white house" was the first Greenwich observatory. He was + the Astronomer Royal and first head of this observatory.</p> + + <p><a name="Nt_134" href="#NtA_134">[134]</a> It seems a pity that De + Morgan should not have lived to lash those of our time who are demanding + only the immediately practical in mathematics. His satire would have been + worth the reading against those who seek to stifle the science they + pretend to foster.</p> + + <p><a name="Nt_135" href="#NtA_135">[135]</a> Ismael Bouillaud, or + Boulliau, was born in 1605 and died at Paris in 1694. He was well known + as an astronomer, mathematician, and jurist. He lived with De Thou at + Paris, and accompanied him to Holland. He traveled extensively, and was + versed in the astronomical work of the Persians and Arabs. It was in his + <i>Astronomia philolaica, opus novum</i> (Paris, 1645) that he attacked + Kepler's laws. His tables were shown to be erroneous by the fact that the + solar eclipse did not take place as predicted by him in 1645.</p> + + <p><a name="Nt_136" href="#NtA_136">[136]</a> As it did, until 1892, when + Airy had reached the ripe age of ninety-one.</p> + + <p><a name="Nt_137" href="#NtA_137">[137]</a> <i>Didaci a Stunica ... In + Job commentaria</i> appeared at Toledo in 1584.</p> + + <p><a name="Nt_138" href="#NtA_138">[138]</a> "The false Pythagorean + doctrine, absolutely opposed to the Holy Scriptures, concerning the + mobility of the earth and the immobility of the sun."</p> + + <p><a name="Nt_139" href="#NtA_139">[139]</a> Paolo Antonio Foscarini + (1580-1616), who taught theology and philosophy at Naples and Messina, + was one of the first to champion the theories of Copernicus. This was in + his <i>Lettera sopra l'opinione de' Pittagorici e del Copernico, della + mobilità della Terra e stabilità del Sole, e il nuovo pittagorico sistema + del mondo</i>, 4to, Naples, 1615. The condemnation of the Congregation + was published in the following spring, and in the year of Foscarini's + death at the early age of thirty-six.</p> + + <p><a name="Nt_140" href="#NtA_140">[140]</a> "To be wholly prohibited + and condemned," because "it seeks to show that the aforesaid doctrine is + consonant with truth and is not opposed to the Holy Scriptures."</p> + + <p><a name="Nt_141" href="#NtA_141">[141]</a> "As repugnant to the Holy + Scriptures and to its true and Catholic interpretation (which in a + Christian man cannot be tolerated in the least), he does not hesitate to + treat (of his subject) '<i>by hypothesis</i>', but he even adds '<i>as + most true</i>'!"</p> + + <p><a name="Nt_142" href="#NtA_142">[142]</a> "To the places in which he + discusses not by hypothesis but by making assertions concerning the + position and motion of the earth."</p> + + <p><a name="Nt_143" href="#NtA_143">[143]</a> "<i>Copernicus.</i> If by + chance there shall be vain talkers who, although ignorant of all + mathematics, yet taking it upon themselves to sit in judgment upon the + subject on account of a certain passage of Scripture badly distorted for + their purposes, shall have dared to criticize and censure this teaching + of mine, I pay no attention to them, even to the extent of despising + their judgment as rash. For it is not unknown that Lactantius, a writer + of prominence in other lines although but little versed in mathematics, + spoke very childishly about the form of the earth when he ridiculed those + who declared that it was spherical. Hence it should not seem strange to + the learned if some shall look upon us in the same way. Mathematics is + written for mathematicians, to whom these labors of ours will seem, if I + mistake not, to add something even to the republic of the Church.... + <i>Emend.</i> Here strike out everything from 'if by chance' to the words + 'these labors of ours,' and adapt it thus: 'But these labors of + ours.'"</p> + + <p><a name="Nt_144" href="#NtA_144">[144]</a> "<i>Copernicus.</i> However + if we consider the matter more carefully it will be seen that the + investigation is not yet completed, and therefore ought by no means to be + condemned. <i>Emend.</i> However, if we consider the matter more + carefully it is of no consequence whether we regard the earth as existing + in the center of the universe or outside of the center, so far as the + solution of the phenomena of celestial movements is concerned."</p> + + <p><a name="Nt_145" href="#NtA_145">[145]</a> "The whole of this chapter + may be cut out, since it avowedly treats of the earth's motion, while it + refutes the reasons of the ancients proving its immobility. Nevertheless, + since it seems to speak problematically, in order that it may satisfy the + learned and keep intact the sequence and unity of the book let it be + emended as below."</p> + + <p><a name="Nt_146" href="#NtA_146">[146]</a> "<i>Copernicus.</i> + Therefore why do we still hesitate to concede to it motion which is by + nature consistent with its form, the more so because the whole universe + is moving, whose end is not and cannot be known, and not confess that + there is in the sky an appearance of daily revolution, while on the earth + there is the truth of it? And in like manner these things are as if + Virgil's Æneas should say, 'We are borne from the harbor' ... + <i>Emend.</i> Hence I cannot concede motion to this form, the more so + because the universe would fall, whose end is not and cannot be known, + and what appears in the heavens is just as if ..."</p> + + <p><a name="Nt_147" href="#NtA_147">[147]</a> "<i>Copernicus</i>. I also + add that it would seem very absurd that motion should be ascribed to that + which contains and locates, and not rather to that which is contained and + located, that is the earth. <i>Emend.</i> I also add that it is not more + difficult to ascribe motion to the contained and located, which is the + earth, than to that which contains it."</p> + + <p><a name="Nt_148" href="#NtA_148">[148]</a> "<i>Copernicus.</i> You + see, therefore, that from all these things the motion of the earth is + more probable than its immobility, especially in the daily revolution + which is as it were a particular property of it. <i>Emend.</i> Omit from + 'You see' to the end of the chapter."</p> + + <p><a name="Nt_149" href="#NtA_149">[149]</a> "<i>Copernicus.</i> + Therefore, since there is nothing to hinder the motion of the earth, it + seems to me that we should consider whether it has several motions, to + the end that it may be looked upon as one of the moving stars. + <i>Emend.</i> Therefore, since I have assumed that the earth moves, it + seems to me that we should consider whether it has several motions."</p> + + <p><a name="Nt_150" href="#NtA_150">[150]</a> "<i>Copernicus.</i> We are + not ashamed to acknowledge ... that this is preferably verified in the + motion of the earth. <i>Emend.</i> We are not ashamed to assume ... that + this is consequently verified in the motion."</p> + + <p><a name="Nt_151" href="#NtA_151">[151]</a> "<i>Copernicus.</i> So + divine is surely this work of the Best and Greatest. <i>Emend.</i> Strike + out these last words."</p> + + <p><a name="Nt_152" href="#NtA_152">[152]</a> This should be Cap. 11, + lib. i, p. 10.</p> + + <p><a name="Nt_153" href="#NtA_153">[153]</a> "<i>Copernicus.</i> + Demonstration of the threefold motion of the earth. <i>Emend.</i> On the + hypothesis of the threefold motion of the earth and its + demonstration."</p> + + <p><a name="Nt_154" href="#NtA_154">[154]</a> This should be Cap. 20, + lib. iv, p. 122.</p> + + <p><a name="Nt_155" href="#NtA_155">[155]</a> "<i>Copernicus.</i> + Concerning the size of these three stars, the sun, the moon and the + earth. <i>Emend.</i> Strike out the words 'these three stars,' because + the earth is not a star as Copernicus would make it."</p> + + <p><a name="Nt_156" href="#NtA_156">[156]</a> He seems to speak + problematically in order to satisfy the learned.</p> + + <p><a name="Nt_157" href="#NtA_157">[157]</a> One of the Church Fathers, + born about 250 A.D., and died about 330, probably at Trèves. He wrote + <i>Divinarum Institutionum Libri VII.</i> and other controversial and + didactic works against the learning and philosophy of the Greeks.</p> + + <p><a name="Nt_158" href="#NtA_158">[158]</a> Giovanni Battista Riccioli + (1598-1671) taught philosophy and theology at Parma and Bologna, and was + later professor of astronomy. His <i>Almagestum novum</i> appeared in + 1651, and his <i>Argomento fisico-matematico contro il moto diurno della + terra</i> in 1668.</p> + + <p><a name="Nt_159" href="#NtA_159">[159]</a> He was a native of + Arlington, Sussex, and a pensioner of Christ's College, Cambridge. In + 1603 he became a master of arts at Oxford.</p> + + <p><a name="Nt_160" href="#NtA_160">[160]</a> Straying, i.e., from the + right way.</p> + + <p><a name="Nt_161" href="#NtA_161">[161]</a> "Private subjects may, in + the presence of danger, defend themselves or their families against a + monarch as against any malefactor, if the monarch assaults them like a + bandit or a ravisher, and provided they are unable to summon the usual + protection and cannot in any way escape the danger."</p> + + <p><a name="Nt_162" href="#NtA_162">[162]</a> Daniel Neal (1678-1743), an + independent minister, wrote a <i>History of the Puritans</i> that + appeared in 1732. The account may be found in the New York edition of + 1843-44, vol. I, p. 271.</p> + + <p><a name="Nt_163" href="#NtA_163">[163]</a> Anthony Wood (1632-1695), + whose <i>Historia et Antiquitates Universitatis Oxoniensis</i> (1674) and + <i>Athenae Oxoniensis</i> (1691) are among the classics on Oxford.</p> + + <p><a name="Nt_164" href="#NtA_164">[164]</a> Part of the title, not here + quoted, shows the nature of the work more clearly: "liber unicus, in quo + decretum S. Congregationis S. R. E. Cardinal. an. 1616, adversus + Pythagorico-Copernicanos editum defenditur."</p> + + <p><a name="Nt_165" href="#NtA_165">[165]</a> This was John Elliot + Drinkwater Bethune (1801-1851), the statesman who did so much for + legislative and educational reform in India. His father, John Drinkwater + Bethune, wrote a history of the siege of Gibraltar.</p> + + <p><a name="Nt_166" href="#NtA_166">[166]</a> The article referred to is + about thirty years old; since it appeared another has been given + (<i>Dubl. Rev.</i>, Sept. 1865) which is of much greater depth. In it + will also be found the Roman view of Bishop Virgil (<i>ante</i>, p. + 32).—A. De M.</p> + + <p><a name="Nt_167" href="#NtA_167">[167]</a> Jean Baptiste Morin + (1583-1656), in his younger days physician to the Bishop of Boulogne and + the Duke of Luxemburg, became in 1630 professor of mathematics at the + Collège Royale. His chief contribution to the problem of the + determination of longitude is his <i>Longitudinum terrestrium et + coelestium nova et hactenus optata scientia</i> (1634). He also wrote + against Copernicus in his <i>Famosi problematis de telluris motu vel + quiete hactenus optata solutio</i> (1631), and against Lansberg in his + <i>Responsio pro telluris quiete</i> (1634).</p> + + <p><a name="Nt_168" href="#NtA_168">[168]</a> The work appeared at Leyden + in 1626, at Amsterdam in 1634, at Copenhagen in 1640 and again at Leyden + in 1650. The title of the 1640 edition is <i>Arithmeticae Libri II et + Geometriae Libri VI</i>. The work on which it is based is the + <i>Arithmeticae et Geometriae Practica</i>, which appeared in 1611.</p> + + <p><a name="Nt_169" href="#NtA_169">[169]</a> The father's name was + Adriaan, and Lalande says that it was Montucla who first made the mistake + of calling him Peter, thinking that the initials P. M. stood for Petrus + Metius, when in reality they stood for <i>piae memoriae</i>! The ratio + 355/113 was known in China hundreds of years before his time. See note <a + href="#Nt_55">55</a>, page <a href="#page52">52</a>.</p> + + <p><a name="Nt_170" href="#NtA_170">[170]</a> Adrian Metius (1571-1635) + was professor of medicine at the University of Franeker. His work was, + however, in the domain of astronomy, and in this domain he published + several treatises.</p> + + <p><a name="Nt_171" href="#NtA_171">[171]</a> The first edition was + entitled: <i>The Discovery of a World in the Moone. Or, a Discourse + Tending to prove that 'tis probable there may be another habitable World + in that Planet</i>. 1638, 8vo. The fourth edition appeared in 1684. John + Wilkins (1614-1672) was Warden of Wadham College, Oxford; master of + Trinity, Cambridge; and, later, Bishop of Chester. He was influential in + founding the Royal Society.</p> + + <p><a name="Nt_172" href="#NtA_172">[172]</a> The first edition was + entitled: <i>C. Hugenii</i> <span title="Kosmotheôros" class="grk" + >Κοσμοθεωρος</span>, + <i>sive de Terris coelestibus, earumque ornatu, conjecturae</i>, The + Hague, 1698, 4to. There were several editions. It was also translated + into French (1718), and there was another English edition (1722). + Huyghens (1629-1695) was one of the best mathematical physicists of his + time.</p> + + <p><a name="Nt_173" href="#NtA_173">[173]</a> It is hardly necessary to + say that science has made enormous advance in the chemistry of the + universe since these words were written.</p> + + <p><a name="Nt_174" href="#NtA_174">[174]</a> William Whewell (1794-1866) + is best known through his <i>History of the Inductive Sciences</i> (1837) + and <i>Philosophy of the Inductive Sciences</i> (1840).</p> + + <p><a name="Nt_175" href="#NtA_175">[175]</a> Thomas Chalmers + (1780-1847), the celebrated Scotch preacher. These discourses were + delivered while he was minister in a large parish in the poorest part of + Glasgow, and in them he attempted to bring science into harmony with the + Bible. He was afterwards professor of moral philosophy at St. Andrew's + (1823-28), and professor of theology at Edinburgh (1828). He became the + leader of a schism from the Scotch Presbyterian Church,—the Free + Church.</p> + + <p><a name="Nt_176" href="#NtA_176">[176]</a> That is, in Robert Watt's + (1774-1819) <i>Bibliotheca Britannica</i> (posthumous, 1824). Nor is it + given in the <i>Dictionary of National Biography</i>.</p> + + <p><a name="Nt_177" href="#NtA_177">[177]</a> The late Greek satirist and + poet, c. 120-c. 200 A.D.</p> + + <p><a name="Nt_178" href="#NtA_178">[178]</a> François Rabelais (c. + 1490-1553) the humorist who created Pantagruel (1533) and Gargantua + (1532). His work as a physician and as editor of the works of Galen and + Hippocrates is less popularly known.</p> + + <p><a name="Nt_179" href="#NtA_179">[179]</a> Francis Godwin (1562-1633) + bishop of Llandaff and Hereford. Besides some valuable historical works + he wrote <i>The Man in the Moone, or a Discourse of a voyage thither by + Domingo Gonsales, the Speed Messenger of London</i>, 1638.</p> + + <p><a name="Nt_180" href="#NtA_180">[180]</a> Bernard Le Bovier de + Fontenelle (1657-1757), historian, critic, mathematician, Secretary of + the Académie des Sciences, and member of the Académie Française. His + <i>Entretien sur la pluralité des mondes</i> appeared at Paris in + 1686.</p> + + <p><a name="Nt_181" href="#NtA_181">[181]</a> Athanasius Kircher + (1602-1680), Jesuit, professor of mathematics and philosophy, and later + of Hebrew and Syriac, at Wurzburg; still later professor of mathematics + and Hebrew at Rome. He wrote several works on physics. His collection of + mathematical instruments and other antiquities became the basis of the + Kircherian Museum at Rome.</p> + + <p><a name="Nt_182" href="#NtA_182">[182]</a> "Both belief and non-belief + are dangerous. Hippolitus died because his stepmother was believed. Troy + fell because Cassandra was not believed. Therefore the truth should be + investigated long before foolish opinion can properly judge." (Prove = + probe?).</p> + + <p><a name="Nt_183" href="#NtA_183">[183]</a> Jacobus Grandamicus + (Jacques Grandami) was born at Nantes in 1588 and died at Paris in 1672. + He was professor of theology and philosophy in the Jesuit colleges at + Rennes, Tours, Rouen, and other places. He wrote several works on + astronomy.</p> + + <p><a name="Nt_184" href="#NtA_184">[184]</a> "And I, if I be lifted up + from the earth, will draw all men unto me." John xii. 32.</p> + + <p><a name="Nt_185" href="#NtA_185">[185]</a> Andrea Argoli (1568-1657) + wrote a number of works on astronomy, and computed ephemerides from 1621 + to 1700.</p> + + <p><a name="Nt_186" href="#NtA_186">[186]</a> So in the original edition + of the <i>Budget</i>. It is Johannem Pellum in the original title. John + Pell (1610 or 1611-1685) studied at Cambridge and Oxford, and was + professor of mathematics at Amsterdam (1643-46) and Breda (1646-52). He + left many manuscripts but published little. His name attaches by accident + to an interesting equation recently studied with care by Dr. E. E. + Whitford (New York, 1912).</p> + + <p><a name="Nt_187" href="#NtA_187">[187]</a> Christianus Longomontanus + (Christen Longberg or Lumborg) was born in 1569 at Longberg, Jutland, and + died in 1647 at Copenhagen. He was an assistant of Tycho Brahe and + accepted the diurnal while denying the orbital motion of the earth. His + <i>Cyclometria e lunulis reciproce demonstrata</i> appeared in 1612 under + the name of Christen Severin, the latter being his family name. He wrote + several other works on the quadrature problem, and some treatises on + astronomy.</p> + + <p><a name="Nt_188" href="#NtA_188">[188]</a> The names are really pretty + well known. Giles Persone de Roberval was born at Roberval near Beauvais + in 1602, and died at Paris in 1675. He was professor of philosophy at the + Collège Gervais at Paris, and later at the Collège Royal. He claimed to + have discovered the theory of indivisibles before Cavalieri, and his work + is set forth in his <i>Traité des indivisibles</i> which appeared + posthumously in 1693.</p> + + <p>Hobbes (1588-1679), the political and social philosopher, lived a good + part of his time (1610-41) in France where he was tutor to several young + noblemen, including the Cavendishes. His <i>Leviathan</i> (1651) is said + to have influenced Spinoza, Leibnitz, and Rousseau. His <i>Quadratura + circuli, cubatio sphaerae, duplicatio cubi ...</i> (London, 1669), + <i>Rosetum geometricum ...</i> (London, 1671), and <i>Lux Mathematica, + censura doctrinae Wallisianae contra Rosetum Hobbesii</i> (London, 1674) + are entirely forgotten to-day. (See a further note, <i>infra</i>.)</p> + + <p>Pierre de Carcavi, a native of Lyons, died at Paris in 1684. He was a + member of parliament, royal librarian, and member of the Académie des + Sciences. His attempt to prove the impossibility of the quadrature + appeared in 1645. He was a frequent correspondent of Descartes.</p> + + <p>Cavendish (1591-1654) was Sir (not Lord) Charles. He was, like De + Morgan himself, a bibliophile in the domain of mathematics. His life was + one of struggle, his term as member of parliament under Charles I being + followed by gallant service in the royal army. After the war he sought + refuge on the continent where he met most of the mathematicians of his + day. He left a number of manuscripts on mathematics, which his widow + promptly disposed of for waste paper. If De Morgan's manuscripts had been + so treated we should not have had his revision of his <i>Budget of + Paradoxes</i>.</p> + + <p>Marin Mersenne (1588-1648), a minorite, living in the cloisters at + Nevers and Paris, was one of the greatest Franciscan scholars. He edited + Euclid, Apollonius, Archimedes, Theodosius, and Menelaus (Paris, 1626), + translated the Mechanics of Galileo into French (1634), wrote + <i>Harmonicorum Libri XII</i> (1636), and <i>Cogitata + physico-mathematica</i> (1644), and taught theology and philosophy at + Nevers.</p> + + <p>Johann Adolph Tasse (Tassius) was born in 1585 and died at Hamburg in + 1654. He was professor of mathematics in the Gymnasium at Hamburg, and + wrote numerous works on astronomy, chronology, statics, and elementary + mathematics.</p> + + <p>Johann Ludwig, Baron von Wolzogen, seems to have been one of the early + unitarians, called <i>Fratres Polonorum</i> because they took refuge in + Poland. Some of his works appear in the <i>Bibliotheca Fratrum + Polonorum</i> (Amsterdam, 1656). I find no one by the name who was + contributing to mathematics at this time.</p> + + <p>Descartes is too well known to need mention in this connection.</p> + + <p>Bonaventura Cavalieri (1598-1647) was a Jesuit, a pupil of Galileo, + and professor of mathematics at Bologna. His greatest work, <i>Geometria + indivisibilibus continuorum nova quadam ratione promota</i>, in which he + makes a noteworthy step towards the calculus, appeared in 1635.</p> + + <p>Jacob (Jacques) Golius was born at the Hague in 1596 and died at + Leyden in 1667. His travels in Morocco and Asia Minor (1622-1629) gave + him such knowledge of Arabic that he became professor of that language at + Leyden. After Snell's death he became professor of mathematics there. He + translated Arabic works on mathematics and astronomy into Latin.</p> + + <p><a name="Nt_189" href="#NtA_189">[189]</a> It would be interesting to + follow up these rumors, beginning perhaps with the tomb of Archimedes. + The Ludolph van Ceulen story is very likely a myth. The one about Fagnano + may be such. The Bernoulli tomb does have the spiral, however (such as it + is), as any one may see in the cloisters at Basel to-day.</p> + + <p><a name="Nt_190" href="#NtA_190">[190]</a> Collins (1625-1683) was + secretary of the Royal Society, and was "a kind of register of all new + improvements in mathematics." His office brought him into correspondence + with all of the English scientists, and he was influential in the + publication of various important works, including Branker's translation + of the algebra by Rhonius, with notes by Pell, which was the first work + to contain the present English-American symbol of division. He also + helped in the publication of editions of Archimedes and Apollonius, of + Kersey's Algebra, and of the works of Wallis. His profession was that of + accountant and civil engineer, and he wrote three unimportant works on + mathematics (one published posthumously, and the others in 1652 and + 1658).</p> + + <p>Heinrich Christian Schumacher (1780-1850) was professor of astronomy + at Copenhagen and director of the observatory at Altona. His translation + of Carnot's <i>Géométrie de position</i> (1807) brought him into personal + relations with Gauss, and the friendship was helpful to Schumacher. He + was a member of many learned societies and had a large circle of + acquaintances. He published numerous monographs and works on + astronomy.</p> + + <p>Gassendi (1592-1655) might well have been included by De Morgan in the + group, since he knew and was a friend of most of the important + mathematicians of his day. Like Mersenne, he was a minorite, but he was a + friend of Galileo and Kepler, and wrote a work under the title + <i>Institutio astronomica, juxta hypotheses Copernici, Tychonis-Brahaei + et Ptolemaei</i> (1645). He taught philosophy at Aix, and was later + professor of mathematics at the College Royal at Paris.</p> + + <p>Burnet is the Bishop Gilbert Burnet (1643-1715) who was so strongly + anti-Romanistic that he left England during the reign of James II and + joined the ranks of the Prince of Orange. William made him bishop of + Salisbury.</p> + + <p><a name="Nt_191" href="#NtA_191">[191]</a> There is some substantial + basis for De Morgan's doubts as to the connection of that + <i>mirandula</i> of his age, Sir Kenelm Digby (1603-1665), with the + famous <i>poudre de sympathie</i>. It is true that he was just the one to + prepare such a powder. A dilletante in everything,—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: <i>Discours fait en une célèbre + assemblée par le chevalier Digby .... touchant la guérison de playes par + la poudre de sympathie</i>. The London edition referred to by De Morgan + also came out in 1658, and several editions followed it in England, + France and Germany. But Nathaniel Highmore in his <i>History of + Generation</i> (1651) referred to the concoction as "Talbot's Powder" + some years before Digby took it up. The basis seems to have been vitriol, + and it was claimed that it would heal a wound by simply being applied to + a bandage taken from it.</p> + + <p><a name="Nt_192" href="#NtA_192">[192]</a> This work by Thomas Birch + (1705-1766) came out in 1756-57. Birch was a voluminous writer on English + history. He was a friend of Dr. Johnson and of Walpole, and he wrote a + life of Robert Boyle.</p> + + <p><a name="Nt_193" href="#NtA_193">[193]</a> We know so much about John + Evelyn (1620-1706) through the diary which he began at the age of eleven, + that we forget his works on navigation and architecture.</p> + + <p><a name="Nt_194" href="#NtA_194">[194]</a> I suppose this was the + seventh Earl of Shrewsbury (1553-1616).</p> + + <p><a name="Nt_195" href="#NtA_195">[195]</a> This is interesting in view + of the modern aseptic practice of surgery and the antiseptic treatment of + wounds inaugurated by the late Lord Lister.</p> + + <p><a name="Nt_196" href="#NtA_196">[196]</a> Perhaps De Morgan had not + heard the <i>bon mot</i> of Dr. Holmes: "I firmly believe that if the + whole <i>materia medica</i> could be sunk to the bottom of the sea, it + would be all the better for mankind and all the worse for the + fishes."</p> + + <p><a name="Nt_197" href="#NtA_197">[197]</a> The full title is worth + giving, because it shows the mathematical interests of Hobbes, and the + nature of the six dialogues: <i>Examinatio et emendatio mathematicae + hodiernae qualis explicatur in libris Johannis Wallisii geometriae + professoris Saviliani in Academia Oxoniensi: distributa in sex dialogos + (1. De mathematicae origine ...; 2. De principiis traditis ab Euclide; 3. + De demonstratione operationum arithmeticarum ...; 4. De rationibus; 5. De + angula contactus, de sectionibus coni, et arithmetica infinitorum; 6. + Dimensio circuli tribus methodis demonstrata ... item cycloidis verae + descriptio et proprietates aliquot.)</i> Londini, 1660 (not 1666). For a + full discussion of the controversy over the circle, see George Croom + Robertson's biography of Hobbes in the eleventh edition of the + <i>Encyclopaedia Britannica</i>.</p> + + <p><a name="Nt_198" href="#NtA_198">[198]</a> This is his + <i>Animadversions upon Mr. Hobbes' late book De principiis et + ratiocinatione geometrarum</i>, 1666, or his <i>Hobbianae quadraturae + circuli, cubationis sphaerae et duplicationis cubi confutatio</i>, also + of 1669.</p> + + <p><a name="Nt_199" href="#NtA_199">[199]</a> This is the work of 1669 + referred to above.</p> + + <p><a name="Nt_200" href="#NtA_200">[200]</a> Gregoire de St. Vincent + (1584-1667) published his <i>Opus geometricum quadraturae circuli et + sectionum coni</i> at Antwerp in 1647.</p> + + <p><a name="Nt_201" href="#NtA_201">[201]</a> This appears in <i>J. + Scaligeri cyclometrica elementa duo</i>, Lugduni Batav., 1594.</p> + + <p><a name="Nt_202" href="#NtA_202">[202]</a> Adriaen van Roomen + (1561-1615) gave the value of <span class="grk">π</span> to sixteen + decimal places in his <i>Ideae mathematicae pars prima</i> (1593), and + wrote his <i>In Archimedis circuli dimensionem expositio & + analysis</i> in 1597.</p> + + <p><a name="Nt_203" href="#NtA_203">[203]</a> Kästner. See note <a + href="#Nt_30">30</a> on page <a href="#page43">43</a>.</p> + + <p><a name="Nt_204" href="#NtA_204">[204]</a> Bentley (1662-1742) might + have done it, for as the head of Trinity College, Cambridge, and a + follower of Newton, he knew some mathematics. Erasmus (1466-1536) lived a + little too early to attempt it, although his brilliant satire might have + been used to good advantage against those who did try.</p> + + <p><a name="Nt_205" href="#NtA_205">[205]</a> "In grammar, to give the + winds to the ships and to give the ships to the winds mean the same + thing. But in geometry it is one thing to assume the circle BCD not + greater than thirty-six segments BCDF, and another (to assume) the + thirty-six segments BCDF not greater than the circle. The one assumption + is true, the other false."</p> + + <p><a name="Nt_206" href="#NtA_206">[206]</a> The Greek scholar + (1559-1614) who edited a Greek and Latin edition of Aristotle in + 1590.</p> + + <p><a name="Nt_207" href="#NtA_207">[207]</a> Jacques Auguste de Thou + (1553-1617), the historian and statesman.</p> + + <p><a name="Nt_208" href="#NtA_208">[208]</a> "To value Scaliger higher + even when wrong, than the multitude when right."</p> + + <p><a name="Nt_209" href="#NtA_209">[209]</a> "I would rather err with + Scaliger than be right with Clavius."</p> + + <p><a name="Nt_210" href="#NtA_210">[210]</a> "The perimeter of the + dodecagon to be inscribed in a circle is greater than the perimeter of + the circle. And the more sides a polygon to be inscribed in a circle + successively has, so much the greater will the perimeter of the polygon + be than the perimeter of the circle."</p> + + <p><a name="Nt_211" href="#NtA_211">[211]</a> De Morgan took, perhaps, + the more delight in speaking thus of Sir William Hamilton (1788-1856) + because of a spirited controversy that they had in 1847 over the theory + of logic. Possibly, too, Sir William's low opinion of mathematics had its + influence.</p> + + <p><a name="Nt_212" href="#NtA_212">[212]</a> Edwards (1699-1757) wrote + <i>The canons of criticism</i> (1747) in which he gave a scathing + burlesque on Warburton's Shakespeare. It went through six editions.</p> + + <p><a name="Nt_213" href="#NtA_213">[213]</a> Antoine Teissier (born in + 1632) published his <i>Eloges des hommes savants, tirés de l'histoire de + M. de Thou</i> in 1683.</p> + + <p><a name="Nt_214" href="#NtA_214">[214]</a> "He boasted without reason + of having found the quadrature of the circle. The glory of this admirable + discovery was reserved for Joseph Scaliger, as Scévole de St. Marthe has + written."</p> + + <p><a name="Nt_215" href="#NtA_215">[215]</a> <i>Natural and political + observations mentioned in the following Index, and made upon the Bills of + Mortality.... With reference to the government, religion, trade, growth, + ayre, and diseases of the said city.</i> London, 1662, 4to. The book went + through several editions.</p> + + <p><a name="Nt_216" href="#NtA_216">[216]</a> <i>Ne sutor ultra + crepidam</i>, "Let the cobbler stick to his last," as we now say.</p> + + <p><a name="Nt_217" href="#NtA_217">[217]</a> The author (1632-1695) of + the <i>Historia et Antiquitates Universitatis Oxoniensis</i> (1674). See + note <a href="#Nt_163">163</a>, page <a href="#page98">98</a>.</p> + + <p><a name="Nt_218" href="#NtA_218">[218]</a> The mathematical guild owes + Samuel Pepys (1633-1703) for something besides his famous diary + (1659-1669). Not only was he president of the Royal Society (1684), but + he was interested in establishing Sir William Boreman's mathematical + school at Greenwich.</p> + + <p><a name="Nt_219" href="#NtA_219">[219]</a> John Graunt (1620-1674) was + a draper by trade, and was a member of the Common Council of London until + he lost office by turning Romanist. Although a shopkeeper, he was elected + to the Royal Society on the special recommendation of Charles II. Petty + edited the fifth edition of his work, adding much to its size and value, + and this may be the basis of Burnet's account of the authorship.</p> + + <p><a name="Nt_220" href="#NtA_220">[220]</a> Petty (1623-1687) was a + mathematician and economist, and a friend of Pell and Sir Charles + Cavendish. His survey of Ireland, made for Cromwell, was one of the first + to be made on a large scale in a scientific manner. He was one of the + founders of the Royal Society.</p> + + <p><a name="Nt_221" href="#NtA_221">[221]</a> The story probably arose + from Graunt's recent conversion to the Roman Catholic faith.</p> + + <p><a name="Nt_222" href="#NtA_222">[222]</a> He was born in 1627 and + died in 1704. He published a series of ephemerides, beginning in 1659. He + was imprisoned in 1679, at the time of the "Popish Plot," and again for + treason in 1690. His important astrological works are the <i>Animal + Cornatum, or the Horn'd Beast</i> (1654) and <i>The Nativity of the late + King Charls</i> (1659).</p> + + <p><a name="Nt_223" href="#NtA_223">[223]</a> Isaac D'Israeli + (1766-1848), in his <i>Curiosities of Literature</i> (1791), speaking of + Lilly, says: "I shall observe of this egregious astronomer, that there is + in this work, so much artless narrative, and at the same time so much + palpable imposture, that it is difficult to know when he is speaking what + he really believes to be the truth." He goes on to say that Lilly relates + that "those adepts whose characters he has drawn were the lowest + miscreants of the town. Most of them had taken the air in the pillory, + and others had conjured themselves up to the gallows. This seems a true + statement of facts."</p> + + <p><a name="Nt_224" href="#NtA_224">[224]</a> It is difficult to estimate + William Lilly (1602-1681) fairly. His <i>Merlini Anglici ephemeris</i>, + issued annually from 1642 to 1681, brought him a great deal of money. Sir + George Wharton (1617-1681) also published an almanac annually from 1641 + to 1666. He tried to expose John Booker (1603-1677) by a work entitled + <i>Mercurio-Coelicio-Mastix; or, an Anti-caveat to all such, as have + (heretofore) had the misfortune to be Cheated and Deluded by that Grand + and Traiterous Impostor of this Rebellious Age, John Booker</i>, 1644. + Booker was "licenser of mathematical [astrological] publications," and as + such he had quarrels with Lilly, Wharton, and others.</p> + + <p><a name="Nt_225" href="#NtA_225">[225]</a> See note <a + href="#Nt_171">171</a> on page <a href="#page100">100</a>.</p> + + <p><a name="Nt_226" href="#NtA_226">[226]</a> This is the <i>Ars + Signorum, vulgo character universalis et lingua philosophica</i>, that + appeared at London in 1661, 8vo. George Dalgarno anticipated modern + methods in the teaching of the deaf and dumb.</p> + + <p><a name="Nt_227" href="#NtA_227">[227]</a> See note <a + href="#Nt_200">200</a> on page <a href="#page110">110</a>.</p> + + <p><a name="Nt_228" href="#NtA_228">[228]</a> If the hyperbola is + referred to the asymptotes as axes, the area between two ordinates + (<i>x</i> = <i>a</i>, <i>x</i> = <i>b</i>) is the difference of the + logarithms of <i>a</i> and <i>b</i> to the base <i>e</i>. E.g., in the + case of the hyperbola <i>xy</i> = 1, the area between <i>x</i> = <i>a</i> + and <i>x</i> = 1 is log <i>a</i>.</p> + + <p><a name="Nt_229" href="#NtA_229">[229]</a> "On ne peut lui refuser la + justice de remarquer que personne avant lui ne s'est porté dans cette + recherche avec autant de génie, & même, si nous en exceptons son + objet principal, avec autant de succès." <i>Quadrature du Cercle</i>, p. + 66.</p> + + <p><a name="Nt_230" href="#NtA_230">[230]</a> The title proceeds: <i>Seu + duae mediae proportionales inter extremas datas per circulum et per + infinitas hyperbolas, vel ellipses et per quamlibet exhibitae</i>.... + René Francois, Baron de Sluse (1622-1685) was canon and chancellor of + Liège, and a member of the Royal Society. He also published a work on + tangents (1672). The word <i>mesolabium</i> is from the Greek <span + title="mesolabion" class="grk" + >μεσολάβιον</span> + or <span title="mesolabon" class="grk" + >μεσόλαβον</span>, + an instrument invented by Eratosthenes for finding two mean + proportionals.</p> + + <p><a name="Nt_231" href="#NtA_231">[231]</a> The full title has some + interest: <i>Vera circuli et hyperbolae quadratura cui accedit geometriae + pars universalis inserviens quantitatum curvarum transmutationi et + mensurae. Authore Jacobo Gregorio Abredonensi Scoto ... Patavii</i>, + 1667. That is, James Gregory (1638-1675) of Aberdeen (he was really born + near but not in the city), a good Scot, was publishing his work down in + Padua. The reason was that he had been studying in Italy, and that this + was a product of his youth. He had already (1663) published his <i>Optica + promota</i>, and it is not remarkable that his brilliancy brought him a + wide circle of friends on the continent and the offer of a pension from + Louis XIV. He became professor of mathematics at St Andrews and later at + Edinburgh, and invented the first successful reflecting telescope. The + distinctive feature of his <i>Vera quadratura</i> is his use of an + infinite converging series, a plan that Archimedes used with the + parabola.</p> + + <p><a name="Nt_232" href="#NtA_232">[232]</a> Jean de Beaulieu wrote + several works on mathematics, including <i>La lumière de + l'arithmétique</i> (n.d.), <i>La lumière des mathématiques</i> (1673), + <i>Nouvelle invention d'arithmétique</i> (1677), and some mathematical + tables.</p> + + <p><a name="Nt_233" href="#NtA_233">[233]</a> A just estimate. There were + several works published by Gérard Desargues (1593-1661), of which the + greatest was the <i>Brouillon Proiect</i> (Paris, 1639). There is an + excellent edition of the <i>Œuvres de Desargues</i> by M. Poudra, + Paris, 1864.</p> + + <p><a name="Nt_234" href="#NtA_234">[234]</a> "A certain M. de Beaugrand, + a mathematician, very badly treated by Descartes, and, as it appears, + rightly so."</p> + + <p><a name="Nt_235" href="#NtA_235">[235]</a> This is a very old + approximation for <span class="grk">π</span>. One of the latest + pretended geometric proofs resulting in this value appeared in New York + in 1910, entitled <i>Quadrimetry</i> (privately printed).</p> + + <p><a name="Nt_236" href="#NtA_236">[236]</a> "Copernicus, a German, made + himself no less illustrious by his learned writings; and we might say of + him that he stood alone and unique in the strength of his problems, if + his excessive presumption had not led him to set forth in this science a + proposition so absurd that it is contrary to faith and reason, namely + that the circumference of a circle is fixed and immovable while the + center is movable: on which geometrical principle he has declared in his + astrological treatise that the sun is fixed and the earth is in + motion."</p> + + <p><a name="Nt_237" href="#NtA_237">[237]</a> So in the original.</p> + + <p><a name="Nt_238" href="#NtA_238">[238]</a> Franciscus Maurolycus + (1494-1575) was really the best mathematician produced by Sicily for a + long period. He made Latin translations of Theodosius, Menelaus, Euclid, + Apollonius, and Archimedes, and wrote on cosmography and other + mathematical subjects.</p> + + <p><a name="Nt_239" href="#NtA_239">[239]</a> "Nicolaus Copernicus is + also tolerated who asserted that the sun is fixed and that the earth + whirls about it; and he rather deserves a whip or a lash than a + reproof."</p> + + <p><a name="Nt_240" href="#NtA_240">[240]</a> "Algebra is the curious + science of scholars, and particularly for a general of an army, or a + captain, in order quickly to draw up an army in battle array and to + number the musketeers and pikemen who compose it, without the figures of + arithmetic. This science has five special figures of this kind: P means + <i>plus</i> in commerce and <i>pikemen</i> in the army; M means + <i>minus</i>, and <i>musketeer</i> in the art of war;... R signifies + <i>root</i> in the measurement of a cube, and <i>rank</i> in <i>the + army</i>; Q means <i>square</i> (French <i>quarè</i>, as then spelled) in + both cases; C means <i>cube</i> in mensuration, and <i>cavalry</i> in + arranging batallions and squadrons. As for the operations of this + science, they are as follows: to add a <i>plus</i> and a <i>plus</i>, the + sum will be <i>plus</i>; to add <i>minus</i> with <i>plus</i>, take the + less from the greater and the remainder will be the sum required or the + number to be found. I say this only in passing, for the benefit of those + who are wholly ignorant of it."</p> + + <p><a name="Nt_241" href="#NtA_241">[241]</a> He refers to the <i>Joannis + de Beaugrand ... Geostatice, seu de vario pondere gravium secundum varia + a terrae (centro) intervalla dissertatio mathematica</i>, Paris, 1636. + Pascal relates that de Beaugrand sent all of Roberval's theorems on the + cycloid and Fermat's on maxima and minima to Galileo in 1638, pretending + that they were his own.</p> + + <p><a name="Nt_242" href="#NtA_242">[242]</a> More (1614-1687) was a + theologian, a fellow of Christ College, Cambridge, and a Christian + Platonist.</p> + + <p><a name="Nt_243" href="#NtA_243">[243]</a> Matthew Hale (1609-1676) + the famous jurist, wrote a number of tracts on scientific, moral, and + religious subjects. These were collected and published in 1805.</p> + + <p><a name="Nt_244" href="#NtA_244">[244]</a> They might have been + attributed to many a worse man than Dr. Hales (1677-1761), who was a + member of the Royal Society and of the Paris Academy, and whose scheme + for the ventilation of prisons reduced the mortality at the Savoy prison + from one hundred to only four a year. The book to which reference is made + is <i>Vegetable Staticks or an Account of some statical experiments on + the sap in Vegetables</i>, 1727.</p> + + <p><a name="Nt_245" href="#NtA_245">[245]</a> <i>Pleas of the Crown; or a + Methodical Summary of the Principal Matters relating to the subject</i>, + 1678.</p> + + <p><a name="Nt_246" href="#NtA_246">[246]</a> <i>Thomae Streete + Astronomia Carolina, a new theory of the celestial motions</i>, 1661. It + also appeared at Nuremberg in 1705, and at London in 1710 and 1716 + (Halley's editions). He wrote other works on astronomy.</p> + + <p><a name="Nt_247" href="#NtA_247">[247]</a> This was the Sir Thomas + Street (1626-1696) who passed sentence of death on a Roman Catholic + priest for saying mass. The priest was reprieved by the king, but in the + light of the present day one would think the justice more in need of + pardon. He took part in the trial of the Rye House Conspirators in + 1683.</p> + + <p><a name="Nt_248" href="#NtA_248">[248]</a> Edmund Halley (1656-1742), + who succeeded Wallis (1703) as Savilian professor of mathematics at + Oxford, and Flamsteed (1720) as head of the Greenwich observatory. It is + of interest to note that he was instrumental in getting Newton's + <i>Principia</i> printed.</p> + + <p><a name="Nt_249" href="#NtA_249">[249]</a> Shepherd (born in 1760) was + one of the most famous lawyers of his day. He was knighted in 1814 and + became Attorney General in 1817.</p> + + <p><a name="Nt_250" href="#NtA_250">[250]</a> This was William Hone + (1780-1842), a book publisher, who wrote satires against the government, + and who was tried three times because of his parodies on the catechism, + creed, and litany (illustrated by Cruikshank). He was acquitted on all of + the charges.</p> + + <p><a name="Nt_251" href="#NtA_251">[251]</a> Valentinus was a + Benedictine monk and was still living at Erfurt in 1413. His <i>Currus + triumphalis antimonii</i> appeared in 1624. Synesius was Bishop of + Ptolemaide, who died about 430. His works were printed at Paris in 1605. + Theodor Kirckring (1640-1693) was a fellow-student of Spinoza's. Besides + the commentary on Valentine he left several works on anatomy. His + commentary appeared at Amsterdam in 1671. There were several editions of + the <i>Chariot</i>.</p> + + <p><a name="Nt_252" href="#NtA_252">[252]</a> The chief difficulty with + this curious "monk-bane" etymology is its absurdity. The real origin of + the word has given etymologists a good deal of trouble.</p> + + <p><a name="Nt_253" href="#NtA_253">[253]</a> Robert Boyle (1627-1691), + son of "the Great Earl" (of Cork). Perhaps his best-known discovery is + the law concerning the volume of gases.</p> + + <p><a name="Nt_254" href="#NtA_254">[254]</a> The real name of Eirenaeus + Philalethes (born in 1622) is unknown. It may have been Childe. He + claimed to have discovered the philosopher's stone in 1645. His tract in + this work is <i>The Secret of the Immortal Liquor Alkahest or + Ignis-Aqua</i>. See note <a href="#Nt_260">260</a>, <i>infra</i>.</p> + + <p><a name="Nt_255" href="#NtA_255">[255]</a> Johann Baptist van Helmont, + Herr von Merode, Royenborg etc. (1577-1644). His chemical discoveries + appeared in his <i>Ortus medicinae</i> (1648), which went through many + editions.</p> + + <p><a name="Nt_256" href="#NtA_256">[256]</a> De Morgan should have + written up Francis Anthony (1550-1623), whose <i>Panacea aurea sive + tractatus duo de auro potabili</i> (Hamburg, 1619) described a panacea + that he gave for every ill. He was repeatedly imprisoned for practicing + medicine without a license from the Royal College of Physicians.</p> + + <p><a name="Nt_257" href="#NtA_257">[257]</a> Bernardus Trevisanus + (1406-1490), who traveled even through Barbary, Egypt, Palestine, and + Persia in search of the philosopher's stone. He wrote several works on + alchemy,—<i>De Chemica</i> (1567), <i>De Chemico Miraculo</i> + (1583), <i>Traité de la nature de l'oeuf des philosophes</i> (1659), + etc., all published long after his death.</p> + + <p><a name="Nt_258" href="#NtA_258">[258]</a> George Ripley (1415-1490) + was an Augustinian monk, later a chamberlain of Innocent VIII, and still + later a Carmelite monk. His <i>Liber de mercuris philosophico</i> and + other tracts first appeared in <i>Opuscula quaedam chymica</i> + (Frankfort, 1614).</p> + + <p><a name="Nt_259" href="#NtA_259">[259]</a> Besides the <i>Opus + majus</i>, and other of the better known works of this celebrated + Franciscan (1214-1294), there are numerous tracts on alchemy that + appeared in the <i>Thesaurus chymicus</i> (Frankfort, 1603).</p> + + <p><a name="Nt_260" href="#NtA_260">[260]</a> George Starkey (1606-1665 + or 1666) has special interest for American readers. He seems to have been + born in the Bermudas and to have obtained the bachelor's degree in + England. He then went to America and in 1646 obtained the master's degree + at Harvard, apparently under the name of Stirk. He met Eirenaeus + Philalethes (see note <a href="#Nt_254">254</a> above) in America and + learned alchemy from him. Returning to England, he sold quack medicines + there, and died in 1666 from the plague after dissecting a patient who + had died of the disease. Among his works was the <i>Liquor Alcahest, or a + Discourse of that Immortal Dissolvent of Paracelsus and Helmont</i>, + which appeared (1675) some nine years after his death.</p> + + <p><a name="Nt_261" href="#NtA_261">[261]</a> Platt (1552-1611) was the + son of a London brewer. Although he left a manuscript on alchemy, and + wrote a book entitled <i>Delights for Ladies to adorne their Persons</i> + (1607), he was knighted for some serious work on the chemistry of + agriculture, fertilizing, brewing, and the preserving of foods, published + in <i>The Jewell House of Art and Nature</i> (1594).</p> + + <p><a name="Nt_262" href="#NtA_262">[262]</a> "Those who wish to call a + man a liar and deceiver speak of him a writer of almanacs; but those who + (would call him) a scoundrel and an imposter (speak of him as) a + chemist."</p> + + <p><a name="Nt_263" href="#NtA_263">[263]</a> "Trust your barque to the + winds but not your body to a chemist; any breeze is safer than the faith + of a chemist."</p> + + <p><a name="Nt_264" href="#NtA_264">[264]</a> Probably the Jesuit, Père + Claude François Menestrier (1631-1705), a well known historian.</p> + + <p><a name="Nt_265" href="#NtA_265">[265]</a> The author was Christopher + Nesse (1621-1705), a belligerent Calvinist, who wrote many controversial + works and succeeded in getting excommunicated four times. One of his most + virulent works was <i>A Protestant Antidote against the Poison of + Popery</i>.</p> + + <p><a name="Nt_266" href="#NtA_266">[266]</a> John Case (c. 1660-1700) + was a famous astrologer and physician. He succeeded to Lilly's practice + in London. In a darkened room, wherein he kept an array of mystical + apparatus, he pretended to show the credulous the ghosts of their + departed relatives. Besides his astrological works he wrote one serious + treatise, the <i>Compendium Anatomicum nova methodo institutum</i> + (1695), in which he defends Harvey's theories of embryology.</p> + + <p><a name="Nt_267" href="#NtA_267">[267]</a> Marcelis (1636-after 1714) + was a soap maker of Amsterdam. It is to be hoped that he made better soap + than values of <span class="grk">π</span>.</p> + + <p><a name="Nt_268" href="#NtA_268">[268]</a> John Craig (died in 1731) + was a Scotchman, but most of his life was spent at Cambridge reading and + writing on mathematics. He endeavored to introduce the Leibnitz + differential calculus into England. His mathematical works include the + <i>Methodus Figurarum ... Quadraturas determinandi</i> (1685), + <i>Tractatus ... de Figurarum Curvilinearum Quadraturis et locis + Geometricis</i> (1693), and <i>De Calculo Fluentium libri duo</i> + (1718).</p> + + <p><a name="Nt_269" href="#NtA_269">[269]</a> As is well known, this + subject owes much to the Bernoullis. Craig's works on the calculus + brought him into controversy with them. He also wrote on other subjects + in which they were interested, as in his memoir <i>On the Curve of the + quickest descent</i> (1700), <i>On the Solid of least resistance</i> + (1700), and the <i>Solution of Bernoulli's problem on Curves</i> + (1704).</p> + + <p><a name="Nt_270" href="#NtA_270">[270]</a> This is Samuel Lee + (1783-1852), the young prodigy in languages. He was apprenticed to a + carpenter at twelve and learned Greek while working at the trade. Before + he was twenty-five he knew Hebrew, Chaldee, Syriac, Samaritan, Persian, + and Hindustani. He later became Regius professor of Hebrew at + Cambridge.</p> + + <p><a name="Nt_271" href="#NtA_271">[271]</a> "Where the devil, Master + Ludovico, did you pick up such a collection?"</p> + + <p><a name="Nt_272" href="#NtA_272">[272]</a> Lord William Brounker (c. + 1620-1684), the first president of the Royal Society, is best known in + mathematics for his contributions to continued fractions.</p> + + <p><a name="Nt_273" href="#NtA_273">[273]</a> Horace Walpole (1717-1797) + published his <i>Catalogue of the Royal and Noble Authors of England</i> + in 1758. Since his time a number of worthy names in the domain of science + in general and of mathematics in particular might be added from the + peerage of England.</p> + + <p><a name="Nt_274" href="#NtA_274">[274]</a> It was written by Charles + Hayes (1678-1760), a mathematician and scholar of no mean attainments. He + travelled extensively, and was deputy governor of the Royal African + Company. His <i>Treatise on Fluxions</i> (London, 1704) was the first + work in English to explain Newton's calculus. He wrote a work entitled + <i>The Moon</i> (1723) to prove that our satellite shines by its own as + well as by reflected light. His <i>Chronographia Asiatica & + Aegyptica</i> (1758) gives the results of his travels.</p> + + <p><a name="Nt_275" href="#NtA_275">[275]</a> <i>Publick</i> in the + original.</p> + + <p><a name="Nt_276" href="#NtA_276">[276]</a> Whiston (1667-1752) + succeeded Newton as Lucasian professor of mathematics at Cambridge. In + 1710 he turned Arian and was expelled from the university. His work on + <i>Primitive Christianity</i> appeared the following year. He wrote many + works on astronomy and religion.</p> + + <p><a name="Nt_277" href="#NtA_277">[277]</a> Ditton (1675-1715) was, on + Newton's recommendation, made Head of the mathematical school at Christ's + Hospital, London. He wrote a work on fluxions (1706). His idea for + finding longitude at sea was to place stations in the Atlantic to fire + off bombs at regular intervals, the time between the sound and the flash + giving the distance. He also corresponded with Huyghens concerning the + use of chronometers for the purpose.</p> + + <p><a name="Nt_278" href="#NtA_278">[278]</a> This was John Arbuthnot (c. + 1658-1735), the mathematician, physician and wit. He was intimate with + Pope and Swift, and was Royal physician to Queen Anne. Besides various + satires he published a translation of Huyghens's work on probabilities + (1692) and a well-known treatise on ancient coins, weights, and measures + (1727).</p> + + <p><a name="Nt_279" href="#NtA_279">[279]</a> Greene (1678-1730) was a + very eccentric individual and was generally ridiculed by his + contemporaries. In his will he directed that his body be dissected and + his skeleton hung in the library of King's College, Cambridge. + Unfortunately for his fame, this wish was never carried out.</p> + + <p><a name="Nt_280" href="#NtA_280">[280]</a> This was the historian, + Robert Sanderson (1660-1741), who spent most of his life at + Cambridge.</p> + + <p><a name="Nt_281" href="#NtA_281">[281]</a> I presume this was William + Jones (1675-1749) the friend of Newton and Halley, vice-president of the + Royal Society, in whose <i>Synopsis Palmariorum Matheseos</i> (1706) the + symbol <span class="grk">π</span> is first used for the circle + ratio.</p> + + <p><a name="Nt_282" href="#NtA_282">[282]</a> This was the <i>Geometrica + solidorum, sive materiae, seu de varia compositione, progressione, + rationeque velocitatum</i>, Cambridge, 1712. The work was parodied in + <i>A Taste of Philosophical Fanaticism ... by a gentleman of the + University of Gratz</i>.</p> + + <p><a name="Nt_283" href="#NtA_283">[283]</a> The antiquary and scientist + (1690-1754), president of the Royal Society, member of the Académie, + friend of Newton, and authority on numismatics.</p> + + <p><a name="Nt_284" href="#NtA_284">[284]</a> She was Catherine Barton, + Newton's step-niece. She married John Conduitt, master of the mint, who + collected materials for a life of Newton.</p> + + <p><i>A propos</i> of Mrs. Conduitt's life of her illustrious uncle, Sir + George Greenhill tells a very good story on Poincaré, the well-known + French mathematician. At an address given by the latter at the + International Congress of Mathematicians held in Rome in 1908 he spoke of + the story of Newton and the apple as a mere fable. After the address Sir + George asked him why he had done so, saying that the story was first + published by Voltaire, who had heard it from Newton's niece, Mrs. + Conduitt. Poincaré looked blank and said, "Newton, et la nièce de Newton, + et Voltaire,—non! je ne vous comprends pas!" He had thought Sir + George meant Professor Volterra of Rome, whose name in French is + Voltaire, and who could not possibly have known a niece of Newton without + bridging a century or so.</p> + + <p><a name="Nt_285" href="#NtA_285">[285]</a> This was the Edmund Turnor + (1755-1829) who wrote the <i>Collections for the Town and Soke of + Grantham, containing authentic Memoirs of Sir Isaac Newton, from Lord + Portsmouth's Manuscripts</i>, London, 1806.</p> + + <p><a name="Nt_286" href="#NtA_286">[286]</a> It may be recalled to mind + that Sir David (1781-1868) wrote a life of Newton (1855).</p> + + <p><a name="Nt_287" href="#NtA_287">[287]</a> "They are in the country. + We rejoice."</p> + + <p><a name="Nt_288" href="#NtA_288">[288]</a> "I am here, chatterbox, + suck!"</p> + + <p><a name="Nt_289" href="#NtA_289">[289]</a> "I have been graduated! I + decline!"</p> + + <p><a name="Nt_290" href="#NtA_290">[290]</a> Giovanni Castiglioni + (Castillon, Castiglione), was born at Castiglione, in Tuscany, in 1708, + and died at Berlin in 1791. He was professor of mathematics at Utrecht + and at Berlin. He wrote on De Moivre's equations (1762), Cardan's rule + (1783), and Euclid's treatment of parallels (1788-89).</p> + + <p><a name="Nt_291" href="#NtA_291">[291]</a> This was the <i>Isaaci + Newtoni, equitis aurati, opuscula mathematica, philosophica et + philologica</i>, Lausannae & Genevae, 1744.</p> + + <p><a name="Nt_292" href="#NtA_292">[292]</a> At London, 4to.</p> + + <p><a name="Nt_293" href="#NtA_293">[293]</a> "All the English attribute + it to Newton."</p> + + <p><a name="Nt_294" href="#NtA_294">[294]</a> Stephen Peter Rigaud + (1774-1839), Savilian professor of geometry at Oxford (1810-27) and later + professor of astronomy and head of the Radcliffe Observatory. He wrote + <i>An historical Essay on first publication of Sir Isaac Newton's + Principia</i>, Oxford, 1838, and a two-volume work entitled + <i>Correspondence of Scientific Men of the 17th Century</i>, 1841.</p> + + <p><a name="Nt_295" href="#NtA_295">[295]</a> It is no longer considered + by scholars as the work of Newton.</p> + + <p><a name="Nt_296" href="#NtA_296">[296]</a> J. Edleston, the author of + the <i>Correspondence of Sir Isaac Newton and Professor Cotes</i>, + London, 1850.</p> + + <p><a name="Nt_297" href="#NtA_297">[297]</a> Palmer (1601-1647) was + Master of Queen's College, Cambridge, a Puritan but not a separatist. His + work, <i>The Characters of a believing Christian, in Paradoxes and + seeming contradictions</i>, appeared in 1645.</p> + + <p><a name="Nt_298" href="#NtA_298">[298]</a> Grosart (1827-1899) was a + Presbyterian clergyman. He was a great bibliophile, and issued numerous + reprints of rare books.</p> + + <p><a name="Nt_299" href="#NtA_299">[299]</a> This was the year after + Palmer's death. The title was, <i>The Remaines of ... Francis Lord + Verulam....; being Essays and severall Letters to severall great + personages, and other pieces of various and high concernment not + heretofore published</i>, London, 1648, 4to.</p> + + <p><a name="Nt_300" href="#NtA_300">[300]</a> Shaw (1694-1763) was + physician extraordinary to George II. He wrote on chemistry and medicine, + and his edition of the <i>Philosophical Works of Francis Bacon</i> + appeared at London in 1733.</p> + + <p><a name="Nt_301" href="#NtA_301">[301]</a> John Locke (1632-1704), the + philosopher. This particular work appeared in 1695. There was an edition + in 1834 (vol. 25 of the <i>Sacred Classics</i>) and one in 1836 (vol. 2 + of the <i>Christian Library</i>).</p> + + <p><a name="Nt_302" href="#NtA_302">[302]</a> I use the word + <i>Socinian</i> because it was so much used in Locke's time: it is used + in our own day by the small fry, the unlearned clergy and their immediate + followers, as a term of reproach for <i>all</i> Unitarians. I suspect + they have a kind of liking for the <i>word</i>; it sounds like <i>so + sinful</i>. The learned clergy and the higher laity know better: they + know that the bulk of the modern Unitarians go farther than Socinus, and + are not correctly named as his followers. The Unitarians themselves + neither desire nor deserve a name which puts them one point nearer to + orthodoxy than they put themselves. That point is the doctrine that + direct prayer to Jesus Christ is lawful and desirable: this Socinus held, + and the modern Unitarians do not hold. Socinus, in treating the subject + in his own <i>Institutio</i>, an imperfect catechism which he left, lays + much more stress on John xiv. 13 than on xv. 16 and xvi. 23. He is not + disinclined to think that <i>Patrem</i> should be in the first citation, + where some put it; but he says that to ask the Father in the name of the + Son is nothing but praying to the Son in prayer to the Father. He labors + the point with obvious wish to secure a conclusive sanction. In the + Racovian Catechism, of which Faustus Socinus probably drew the first + sketch, a clearer light is arrived at. The translation says: "But wherein + consists the divine honor due to Christ? In adoration likewise and + invocation. For we ought at all times to adore Christ, and may in our + necessities address our prayers to him as often as we please; and there + are many reasons to induce us to do this freely." There are some who like + accuracy, even in aspersion—A. De M.</p> + + <p>Socinus, or Fausto Paolo Sozzini (1539-1604), was an antitrinitarian + who believed in prayer and homage to Christ. Leaving Italy after his + views became known, he repaired to Basel, but his opinions were too + extreme even for the Calvinists. He then tried Transylvania, attempting + to convert to his views the antitrinitarian Bishop Dávid. The only result + of his efforts was the imprisonment of Dávid and his own flight to + Poland, in which country he spent the rest of his life (1579-1604). His + complete works appeared first at Amsterdam in 1668, in the <i>Bibliotheca + Fratres Polonorum</i>. The <i>Racovian Catechism</i> (1605) appeared + after his death, but it seems to have been planned by him.</p> + + <p><a name="Nt_303" href="#NtA_303">[303]</a> "As much of faith as is + necessary to salvation is contained in this article, Jesus is the + Christ."</p> + + <p><a name="Nt_304" href="#NtA_304">[304]</a> Edwards (1637-1716) was a + Cambridge fellow, strongly Calvinistic. He published many theological + works, attacking the Arminians and Socinians. Locke and Whiston were + special objects of attack.</p> + + <p><a name="Nt_305" href="#NtA_305">[305]</a> <i>Sir I. Newton's views on + points of Trinitarian Doctrine; his Articles of Faith, and the General + Coincidence of his Opinions with those of J. Locke; a Selection of + Authorities, with Observations</i>, London, 1856.</p> + + <p><a name="Nt_306" href="#NtA_306">[306]</a> <i>A Confession of the + Faith</i>, Bristol, 1752, 8vo.</p> + + <p><a name="Nt_307" href="#NtA_307">[307]</a> This was really very + strange, because Laud (1573-1644), while he was Archbishop of Canterbury, + forced a good deal of High Church ritual on the Puritan clergy, and even + wished to compel the use of a prayer book in Scotland. It was this + intolerance that led to his impeachment and execution.</p> + + <p><a name="Nt_308" href="#NtA_308">[308]</a> The name is Jonchère. He + was a man of some merit, proposing (1718) an important canal in Burgundy, + and publishing a work on the <i>Découverte des longitudes estimées + généralement impossible à trouver</i>, 1734 (or 1735).</p> + + <p><a name="Nt_309" href="#NtA_309">[309]</a> Locke invented a kind of an + instrument for finding longitude, and it is described in the appendix, + but I can find nothing about the man. There was published some years + later (London, 1751) another work of his, <i>A new Problem to discover + the longitude at sea</i>.</p> + + <p><a name="Nt_310" href="#NtA_310">[310]</a> Baxter, concerning whom I + know merely that he was a schoolmaster, starts with the assumption of + this value, and deduces from it some fourteen properties relating to the + circle.</p> + + <p><a name="Nt_311" href="#NtA_311">[311]</a> John, who died in 1780, was + a well-known character in his way. He was a bookseller on Fleet Street, + and his shop was a general rendezvous for the literary men of his time. + He wrote the <i>Memoirs of the Life and Writings of Mr. William + Whiston</i> (1749, with another edition in 1753). He was one of the first + to issue regular catalogues of books with prices affixed.</p> + + <p><a name="Nt_312" href="#NtA_312">[312]</a> The name appears both as + Hulls and as Hull. He was born in Gloucestershire in 1699. In 1754 he + published <i>The Art of Measuring made Easy by the help of a new Sliding + Scale</i>.</p> + + <p><a name="Nt_313" href="#NtA_313">[313]</a> Thomas Newcomen (1663-1729) + invented the first practical steam engine about 1710. It was of about + five and a half horse power, and was used for pumping water from coal + mines. Savery had described such an engine in 1702, but Newcomen improved + upon it and made it practical.</p> + + <p><a name="Nt_314" href="#NtA_314">[314]</a> The well-known benefactor + of art (1787-1863).</p> + + <p><a name="Nt_315" href="#NtA_315">[315]</a> The tract was again + reprinted in 1860.</p> + + <p><a name="Nt_316" href="#NtA_316">[316]</a> Hulls made his experiment + on the Avon, at Evesham, in 1737, having patented his machine in 1736. He + had a Newcomen engine connected with six paddles. This was placed in the + front of a small tow boat. The experiment was a failure.</p> + + <p><a name="Nt_317" href="#NtA_317">[317]</a> William Symington + (1763-1831). In 1786 he <span class="correction" title="text reads `contructed'" + >constructed</span> a working model of a steam road carriage. The + machinery was applied to a small boat in 1788, and with such success as + to be tried on a larger boat in 1789. The machinery was clumsy, however, + and in 1801 he took out a new patent for the style of engine still used + on paddle wheel steamers. This engine was successfully used in 1802, on + the Charlotte Dundas. Fulton (1765-1815) was on board, and so impressed + Robert Livingston with the idea that the latter furnished the money to + build the Clermont (1807), the beginning of successful river + navigation.</p> + + <p><a name="Nt_318" href="#NtA_318">[318]</a> Louis Bertrand Castel + (1688-1757), most of whose life was spent in trying to perfect his + <i>Clavecin oculaire</i>, an instrument on the order of the harpsichord, + intended to produce melodies and harmonies of color. He also wrote + <i>L'Optique des couleurs</i> (1740) and <i>Sur le fond de la Musique</i> + (1754).</p> + + <p><a name="Nt_319" href="#NtA_319">[319]</a> Dr. Robinson (1680-1754) + was professor of physic at Trinity College, Dublin, and three times + president of King and Queen's College of Physicians. In his <i>Treatise + on the Animal Economy</i> (1732-3, with a third edition in 1738) he + anticipated the discoveries of Lavoisier and Priestley on the nature of + oxygen.</p> + + <p><a name="Nt_320" href="#NtA_320">[320]</a> There was another edition, + published at London in 1747, 8vo.</p> + + <p><a name="Nt_321" href="#NtA_321">[321]</a> The author seems to have + shot his only bolt in this work. I can find nothing about him.</p> + + <p><a name="Nt_322" href="#NtA_322">[322]</a> <i>Quod Deus sit, mundusque + ab ipso creatus fuerit in tempore, ejusque providentia gubernetur. + Selecta aliquot theoremata adversos atheos</i>, etc., Paris, 1635, + 4to.</p> + + <p><a name="Nt_323" href="#NtA_323">[323]</a> The British Museum + Catalogue mentions a copy of 1740, but this is possibly a misprint.</p> + + <p><a name="Nt_324" href="#NtA_324">[324]</a> This was Johann II + (1710-1790), son of Johann I, who succeeded his father as professor of + mathematics at Basel.</p> + + <p><a name="Nt_325" href="#NtA_325">[325]</a> Samuel Koenig (1712-1757), + who studied under Johann Bernoulli I. He became professor of mathematics + at Franeker (1747) and professor of philosophy at the Hague (1749).</p> + + <p><a name="Nt_326" href="#NtA_326">[326]</a> "In accordance with the + hypotheses laid down in this memoir it is so evident that <i>t</i> must = + 34, <i>y</i> = 1, and <i>z</i> = 1, that there is no need of proof or + authority for it to be recognized by every one."</p> + + <p><a name="Nt_327" href="#NtA_327">[327]</a> "I subscribe to the + judgment of Mr. Bernoulli as a result of these hypotheses."</p> + + <p><a name="Nt_328" href="#NtA_328">[328]</a> "It clearly appears from my + present analysis and demonstration that they have already recognized and + perfectly agreed to the fact that the quadrature of the circle is + mathematically demonstrated."</p> + + <p><a name="Nt_329" href="#NtA_329">[329]</a> Dr. Knight (died in 1772) + made some worthy contributions to the literature of the mariner's + compass. As De Morgan states, he was librarian of the British Museum.</p> + + <p><a name="Nt_330" href="#NtA_330">[330]</a> Sir Anthony Panizzi + (1797-1879) fled from Italy under sentence of death (1822). He became + assistant (1831) and chief (1856) librarian of the British Museum, and + was knighted in 1869. He began the catalogue of printed books of the + Museum.</p> + + <p><a name="Nt_331" href="#NtA_331">[331]</a> Wright (1711-1786) was a + physicist. He was offered the professorship of mathematics at the + Imperial Academy of St. Petersburg but declined to accept it. This work + is devoted chiefly to the theory of the Milky Way, the <i>via lactea</i> + as he calls it after the manner of the older writers.</p> + + <p><a name="Nt_332" href="#NtA_332">[332]</a> Troughton (1753-1835) was + one of the world's greatest instrument makers. He was apprenticed to his + brother John, and the two succeeded (1770) Wright and Cole in Fleet + Street. Airy called his method of graduating circles the greatest + improvement ever made in instrument making. He constructed (1800) the + first modern transit circle, and his instruments were used in many of the + chief observatories of the world.</p> + + <p><a name="Nt_333" href="#NtA_333">[333]</a> William Simms (1793-1860) + was taken into partnership by Troughton (1826) after the death of the + latter's brother. The firm manufactured some well-known instruments.</p> + + <p><a name="Nt_334" href="#NtA_334">[334]</a> This was George Horne + (1730-1792), fellow of Magdalen College, Oxford, vice-Chancellor of the + University (1776), Dean of Canterbury (1781), and Bishop of Norwich + (1790). He was a great satirist, but most of his pamphlets against men + like Adam Smith, Swedenborg, and Hume, were anonymous, as in the case of + this one against Newton. He was so liberal in his attitude towards the + Methodists that he would not have John Wesley forbidden to preach in his + diocese. He was twenty-one when this tract appeared.</p> + + <p><a name="Nt_335" href="#NtA_335">[335]</a> Martin (1704-1782) was by + no means "old Benjamin Martin" when Horne wrote this pamphlet in 1749. In + fact he was then only forty-five. He was a physicist and a well-known + writer on scientific instruments. He also wrote <i>Philosophia Britannica + or a new and comprehensive system of the Newtonian Philosophy</i> + (1759).</p> + + <p><a name="Nt_336" href="#NtA_336">[336]</a> Jean Théophile Desaguliers, + or Des Aguliers (1683-1744) was the son of a Protestant who left France + after the revocation of the Edict of Nantes. He became professor of + physics at Oxford, and afterwards gave lectures in London. Later he + became chaplain to the Prince of Wales. He published several works on + physics.</p> + + <p><a name="Nt_337" href="#NtA_337">[337]</a> Charles Hutton (1737-1823), + professor of mathematics at Woolwich (1772-1807). His <i>Mathematical + Tables</i> (1785) and <i>Mathematical and Philosophical Dictionary</i> + (1795-1796) are well known.</p> + + <p><a name="Nt_338" href="#NtA_338">[338]</a> James Epps (1773-1839) + contributed a number of memoirs on the use and corrections of + instruments. He was assistant secretary of the Astronomical Society.</p> + + <p><a name="Nt_339" href="#NtA_339">[339]</a> John Hutchinson (1674-1737) + was one of the first to try to reconcile the new science of geology with + Genesis. He denied the Newtonian hypothesis as dangerous to religion, and + because it necessitated a vacuum. He was a mystic in his interpretation + of the Scriptures, and created a sect that went under the name of + Hutchinsonians.</p> + + <p><a name="Nt_340" href="#NtA_340">[340]</a> John Rowning, a + Lincolnshire rector, died in 1771. He wrote on physics, and published a + memoir on <i>A machine for finding the roots of equations universally</i> + (1770).</p> + + <p><a name="Nt_341" href="#NtA_341">[341]</a> It is always difficult to + sanction this spelling of the name of this Jesuit father who is so often + mentioned in the analytic treatment of conics. He was born in Ragusa in + 1711, and the original spelling was Ruđer Josip + Bošković. When he went to live in Italy, as professor of + mathematics at Rome (1740) and at Pavia, the name was spelled Ruggiero + Giuseppe Boscovich, although Boscovicci would seem to a foreigner more + natural. His astronomical work was notable, and in his <i>De maculis + solaribus</i> (1736) there is the first determination of the equator of a + planet by observing the motion of spots on its surface. Boscovich came + near having some contact with America, for he was delegated to observe in + California the transit of Venus in 1755, being prevented by the + dissolution of his order just at that time. He died in 1787, at + Milan.</p> + + <p><a name="Nt_342" href="#NtA_342">[342]</a> James Granger (1723-1776) + who wrote the <i>Biographical History of England</i>, London, 1769. His + collection of prints was remarkable, numbering some fourteen + thousand.</p> + + <p><a name="Nt_343" href="#NtA_343">[343]</a> He was curator of + experiments for the Royal Society. He wrote a large number of books and + monographs on physics. He died about 1713.</p> + + <p><a name="Nt_344" href="#NtA_344">[344]</a> Lee seems to have made no + impression on biographers.</p> + + <p><a name="Nt_345" href="#NtA_345">[345]</a> This work appeared at + London in 1852.</p> + + <p><a name="Nt_346" href="#NtA_346">[346]</a> Of course this is no longer + true. The most scholarly work to-day is that of Rudio, <i>Archimedes, + Huygens, Lambert, Legendre, vier Abhandlungen über die Kreismessung ... + mit einer Uebersicht über die Geschichte des Problems von der Quadratur + des Zirkels, von den ältesten Zeiten bis auf unsere Tage</i>, Leipsic, + 1892.</p> + + <p><a name="Nt_347" href="#NtA_347">[347]</a> Joseph Jérome le François + de Lalande (1732-1807), professor of astronomy in the Collège de France + (1753) and director of the Paris Observatory (1761). His writings on + astronomy and his <i>Bibliographie astronomique, avec l'histoire de + l'astronomie depuis 1781 jusqu'en 1802</i> (Paris, 1803) are well + known.</p> + + <p><a name="Nt_348" href="#NtA_348">[348]</a> De Morgan refers to his + <i>Histoire de l'Astronomie au 18e siècle</i>, which appeared in 1827, + five years after Delambre's death. Jean Baptiste Joseph Delambre + (1749-1822) was a pupil of and a collaborator with Lalande, following his + master as professor of astronomy in the Collège de France. His work on + the measurements for the metric system is well known, and his four + histories of astronomy, <i>ancienne</i> (1817), <i>au moyen âge</i> + (1819), <i>moderne</i> (1821), and <i>au 18e siècle</i> (posthumous, + 1827) are highly esteemed.</p> + + <p><a name="Nt_349" href="#NtA_349">[349]</a> Jean-Joseph Rive + (1730-1792), a priest who left his cure under grave charges, and a + quarrelsome character. His attack on Montucla was a case of the pot + calling the kettle black; for while he was a brilliant writer he was a + careless bibliographer.</p> + + <p><a name="Nt_350" href="#NtA_350">[350]</a> Isaac Barrow (1630-1677) + was quite as well known as a theologian as he was from his Lucasian + professorship of mathematics at Cambridge.</p> + + <p><a name="Nt_351" href="#NtA_351">[351]</a> "Besides we can see by this + that Barrow was a poor philosopher; for he believed in the immortality of + the soul and in a Divinity other than universal nature."</p> + + <p><a name="Nt_352" href="#NtA_352">[352]</a> The <i>Récréations + mathématiques et physiques</i> (Paris, 1694) of Jacques Ozanam + (1640-1717) is a work that is still highly esteemed. Among various other + works he wrote a <i>Dictionnaire mathématique ou Idée générale des + mathématiques</i> (1690) that was not without merit. The + <i>Récréations</i> went through numerous editions (Paris, 1694, 1696, + 1741, 1750, 1770, 1778, and the Montucla edition of 1790; London, 1708, + the Montucla-Hutton edition of 1803 and the Riddle edition of 1840; + Dublin, 1790).</p> + + <p><a name="Nt_353" href="#NtA_353">[353]</a> Hendryk van Etten, the + <i>nom de plume</i> of Jean Leurechon (1591-1670), rector of the Jesuit + college at Bar, and professor of philosophy and mathematics. He wrote on + astronomy (1619) and horology (1616), and is known for his <i>Selecta + Propositiones in tota sparsim mathematica pulcherrime propositae in + solemni festo SS. Ignatii et Francesci Xaverii</i>, 1622. The book to + which De Morgan refers is his <i>Récréation mathématicque, composée de + plusieurs problèmes plaisants et facetieux</i>, Lyons, 1627, with an + edition at Pont-à-Mousson, 1629. There were English editions published at + London in 1633, 1653, and 1674, and Dutch editions in 1662 and 1672.</p> + + <p>I do not understand how De Morgan happened to miss owning the work by + Claude Gaspar Bachet de Meziriac (1581-1638), <i>Problèmes plaisans et + délectables</i>, which appeared at Lyons in 1612, 8vo, with a second + edition in 1624. There was a fifth edition published at Paris in + 1884.</p> + + <p><a name="Nt_354" href="#NtA_354">[354]</a> His title page closes with + "Paris, Chez Ch. Ant. Jombert.... M DCC LIV."</p> + + <p>This was Charles-Antoine Jombert (1712-1784), a printer and bookseller + with some taste for painting and architecture. He wrote several works and + edited a number of early treatises.</p> + + <p><a name="Nt_355" href="#NtA_355">[355]</a> The late Professor Newcomb + made the matter plain even to the non-mathematical mind, when he said + that "ten decimal places are sufficient to give the circumference of the + earth to the fraction of an inch, and thirty decimal places would give + the circumference of the whole visible universe to a quantity + imperceptible with the most powerful microscope."</p> + + <p><a name="Nt_356" href="#NtA_356">[356]</a> <i>Antinewtonianismi pars + prima, in qua Newtoni de coloribus systema ex propriis principiis + geometrice evertitur, et nova de coloribus theoria luculentissimis + experimentis demonstrantur</i>.... Naples, 1754; <i>pars secunda</i>, + Naples, 1756.</p> + + <p><a name="Nt_357" href="#NtA_357">[357]</a> Celestino Cominale + (1722-1785) was professor of medicine at the University of Naples.</p> + + <p><a name="Nt_358" href="#NtA_358">[358]</a> The work appeared in the + years from 1844 to 1849.</p> + + <p><a name="Nt_359" href="#NtA_359">[359]</a> There was a Vienna edition + in 1758, 4to, and another in 1759, 4to. This edition is described on the + title page as <i>Editio Veneta prima ipso auctore praesente, et + corrigente</i>.</p> + + <p><a name="Nt_360" href="#NtA_360">[360]</a> The first edition was + entitled <i>De solis ac lunae defectibus libri V. P. Rogerii Josephi + Boscovich ... cum ejusdem auctoris adnotationibus</i>, London, 1760. It + also appeared in Venice in 1761, and in French translation by the Abbé de + Baruel in 1779, and was a work of considerable influence.</p> + + <p><a name="Nt_361" href="#NtA_361">[361]</a> Paulian (1722-1802) was + professor of physics at the Jesuit college at Avignon. He wrote several + works, the most popular of which, the <i>Dictionnaire de physique</i> + (Avignon, 1761), went through nine editions by 1789.</p> + + <p><a name="Nt_362" href="#NtA_362">[362]</a> This is correct.</p> + + <p><a name="Nt_363" href="#NtA_363">[363]</a> Probably referring to the + fact that Hill (1795-1879), who had done so much for postal reform, was + secretary to the postmaster general (1846), and his name was a synonym + for the post office directory.</p> + + <p><a name="Nt_364" href="#NtA_364">[364]</a> Richard Lovett (1692-1780) + was a good deal of a charlatan. He claimed to have studied electrical + phenomena, and in 1758 advertised that he could effect marvelous cures, + especially of sore throat, by means of electricity. Before publishing the + works mentioned by De Morgan he had issued others of similar character, + including <i>The Subtile Medium proved</i> (London, 1756) and <i>The + Reviewers Reviewed</i> (London, 1760).</p> + + <p><a name="Nt_365" href="#NtA_365">[365]</a> Jean Sylvain Bailly + (1736-1793), member of the <i>Académie française</i> and of the + <i>Académie des sciences</i>, first deputy elected to represent Paris in + the <i>Etats-généraux</i> (1789), president of the first National + Assembly, and mayor of Paris (1789-1791). For his vigor as mayor in + keeping the peace, and for his manly defence of the Queen, he was + guillotined. He was an astronomer of ability, but is best known for his + histories of the science.</p> + + <p><a name="Nt_366" href="#NtA_366">[366]</a> These were the <i>Histoire + de l'Astronomie ancienne</i> (1775), <i>Histoire de l'Astronomie + moderne</i> (1778-1783), <i>Histoire de l'Astronomie indienne et + orientale</i> (1787), and <i>Lettres sur l'origine des peuples de + l'Asie</i> (1775).</p> + + <p><a name="Nt_367" href="#NtA_367">[367]</a> "The sick old man of + Ferney, V., a boy of a hundred years." Voltaire was born in 1694, and + hence was eighty-three at this time.</p> + + <p><a name="Nt_368" href="#NtA_368">[368]</a> In Palmézeaux's <i>Vie de + Bailly</i>, in Bailly's <i>Ouvrage Posthume</i> (1810), M. de Sales is + quoted as saying that the <i>Lettres sur l'Atlantide</i> were sent to + Voltaire and that the latter did not approve of the theory set forth.</p> + + <p><a name="Nt_369" href="#NtA_369">[369]</a> The British Museum + catalogue gives two editions, 1781 and 1782.</p> + + <p><a name="Nt_370" href="#NtA_370">[370]</a> A mystic and a + spiritualist. His chief work was the one mentioned here.</p> + + <p><a name="Nt_371" href="#NtA_371">[371]</a> Jacob Behmen, or Böhme + (1575-1624), known as "the German theosophist," was founder of the sect + of Boehmists, a cult allied to the Swedenborgians. He was given to the + study of alchemy, and brought the vocabulary of the science into his + mystic writings. His sect was revived in England in the eighteenth + century through the efforts of William Law. Saint-Martin translated into + French two of his Latin works under the titles <i>L'Aurore naissante, ou + la Racine de la philosophie</i> (1800), and <i>Les trois principes de + l'essence divine</i> (1802). The originals had appeared nearly two + hundred years earlier,—<i>Aurora</i> in 1612, and <i>De tribus + principiis</i> in 1619.</p> + + <p><a name="Nt_372" href="#NtA_372">[372]</a> "Unknown."</p> + + <p><a name="Nt_373" href="#NtA_373">[373]</a> "Skeptical."</p> + + <p><a name="Nt_374" href="#NtA_374">[374]</a> "Man, man, man."</p> + + <p><a name="Nt_375" href="#NtA_375">[375]</a> "Men, men, men."</p> + + <p><a name="Nt_376" href="#NtA_376">[376]</a> It is interesting to read + De Morgan's argument against Saint-Martin's authorship of this work. It + is attributed to Saint-Martin both by the <i>Biographie Universelle</i> + and by the <i>British Museum Catalogue</i>, and De Morgan says by + "various catalogues and biographies."</p> + + <p><a name="Nt_377" href="#NtA_377">[377]</a> "To explain things by man + and not man by things. <i>On Errors and Truth</i>, by a Ph.... + Inc...."</p> + + <p><a name="Nt_378" href="#NtA_378">[378]</a> "If we would preserve + ourselves from all illusions, and above all from the allurements of + pride, by which man is so often seduced, we should never take man, but + always God, for our term of comparison."</p> + + <p><a name="Nt_379" href="#NtA_379">[379]</a> "And here is found already + an explanation of the numbers four and nine which caused some perplexity + in the work cited above. Man is lost in passing from four to nine."</p> + + <p><a name="Nt_380" href="#NtA_380">[380]</a> Williams also took part in + the preparation of some tables for the government to assist in the + determination of longitude. He had published a work two years before the + one here cited, on the same subject,—<i>An entire new work and + method to discover the variation of the Earth's <span class="correction" + title="text reads `Diaameters'">Diameters</span></i>, London, 1786.</p> + + <p><a name="Nt_381" href="#NtA_381">[381]</a> This is Gabriel Mouton + (1618-1694), a vicar at Lyons, who suggested as a basis for a natural + system of measures the <i>mille</i>, a minute of a degree of the + meridian. This appeared in his <i>Observationes diametrorum solis et + lunae apparentium, meridianarumque aliquot altitudinum cum tabula + declinationum solis</i>.... Lyons, 1670.</p> + + <p><a name="Nt_382" href="#NtA_382">[382]</a> Jacques Cassini + (1677-1756), one of the celebrated Cassini family of astronomers. After + the death of his father he became director of the observatory at Paris. + The basis for a metric unit was set forth by him in his <i>Traité de la + grandeur et de la figure de la terre</i>, Paris, 1720. He was a prolific + writer on astronomy.</p> + + <p><a name="Nt_383" href="#NtA_383">[383]</a> Alexis Jean Pierre Paucton + (1732-1798). He was, for a time, professor of mathematics at Strassburg, + but later (1796) held office in Paris. His leading contribution to + metrology was his <i>Métrologie ou Traité des mesures</i>, Paris, + 1780.</p> + + <p><a name="Nt_384" href="#NtA_384">[384]</a> He was an obscure writer, + born at Deptford.</p> + + <p><a name="Nt_385" href="#NtA_385">[385]</a> He was also a writer of no + scientific merit, his chief contributions being religious tracts. One of + his productions, however, went through many editions, even being + translated into French; <i>Three dialogues between a Minister and one of + his Parishioners; on the true principles of Religion and salvation for + sinners by Jesus Christ</i>. The twentieth edition appeared at Cambridge + in 1786.</p> + + <p><a name="Nt_386" href="#NtA_386">[386]</a> This was the <i>Reflections + on the Revolution in France, and on the proceedings in certain societies + in London relative to that event</i> (London, 1790) by Edmund Burke + (1729-1797). Eleven editions of the work appeared the first year.</p> + + <p><a name="Nt_387" href="#NtA_387">[387]</a> Paine (1736-1809) was born + in Norfolkshire, of Quaker parents. He went to America at the beginning + of the Revolution and published, in January 1776, a violent pamphlet + entitled <i>Common Sense</i>. He was a private soldier under Washington, + and on his return to England after the war he published <i>The Rights of + Man</i>. He was indicted for treason and was outlawed to France. He was + elected to represent Calais at the French convention, but his plea for + moderation led him perilously near the guillotine. His <i>Age of + Reason</i> (1794) was dedicated to Washington. He returned to America in + 1802 and remained there until his death.</p> + + <p><a name="Nt_388" href="#NtA_388">[388]</a> Part I appeared in 1791 and + was so popular that eight editions appeared in that year. It was followed + in 1792 by Part II, of which nine editions appeared in that year. Both + parts were immediately republished in Paris, and there have been several + subsequent editions.</p> + + <p><a name="Nt_389" href="#NtA_389">[389]</a> Mary Wollstonecraft + (1759-1797) was only thirty-three when this work came out. She had + already published <i>An historical and moral View of the Origin and + Progress of the French Revolution</i> (1790), and <i>Original Stories + from Real Life</i> (1791). She went to Paris in 1792 and remained during + the Reign of Terror.</p> + + <p><a name="Nt_390" href="#NtA_390">[390]</a> Samuel Parr (1747-1827) was + for a time head assistant at Harrow (1767-1771), afterwards headmaster in + other schools. At the time this book was written he was vicar of Hatton, + where he took private pupils (1785-1798) to the strictly limited number + of seven. He was a violent Whig and a caustic writer.</p> + + <p><a name="Nt_391" href="#NtA_391">[391]</a> On Mary Wollstonecraft's + return from France she married (1797) William Godwin (1756-1836). He had + started as a strong Calvinistic Nonconformist minister, but had become + what would now be called an anarchist, at least by conservatives. He had + written an <i>Inquiry concerning Political Justice</i> (1793) and a novel + entitled <i>Caleb Williams, or Things as they are</i> (1794), both of + which were of a nature to attract his future wife.</p> + + <p><a name="Nt_392" href="#NtA_392">[392]</a> This child was a daughter. + She became Shelley's wife, and Godwin's influence on Shelley was very + marked.</p> + + <p><a name="Nt_393" href="#NtA_393">[393]</a> This was John Nichols + (1745-1826), the publisher and antiquary. He edited the <i>Gentleman's + Magazine</i> (1792-1826) and his works include the <i>Literary Anecdotes + of the Eighteenth Century</i> (1812-1815), to which De Morgan here + refers.</p> + + <p><a name="Nt_394" href="#NtA_394">[394]</a> William Bellenden, a Scotch + professor at the University of Paris, who died about 1633. His textbooks + are now forgotten, but Parr edited an edition of his works in 1787. The + Latin preface, <i>Praefatio ad Bellendum de Statu</i>, was addressed to + Burke, North, and Fox, and was a satire on their political opponents.</p> + + <p><a name="Nt_395" href="#NtA_395">[395]</a> As we have seen, he had + been head-master before he began taking "his handful of private + pupils."</p> + + <p><a name="Nt_396" href="#NtA_396">[396]</a> The story has evidently got + mixed up in the telling, for Tom Sheridan (1721-1788), the great actor, + was old enough to have been Dr. Parr's father. It was his son, Richard + Brinsley Sheridan (1751-1816), the dramatist and politician, who was the + pupil of Parr. He wrote <i>The Rivals</i> (1775) and <i>The School for + Scandal</i> (1777) soon after Parr left Harrow.</p> + + <p><a name="Nt_397" href="#NtA_397">[397]</a> Horner (1785-1864) was a + geologist and social reformer. He was very influential in improving the + conditions of child labor.</p> + + <p><a name="Nt_398" href="#NtA_398">[398]</a> William Cobbett + (1762-1835), the journalist, was a character not without interest to + Americans. Born in Surrey, he went to America at the age of thirty and + remained there eight years. Most of this time he was occupied as a + bookseller in Philadelphia, and while thus engaged he was fined for libel + against the celebrated Dr. Rush. On his return to England he edited the + <i>Weekly Political Register</i> (1802-1835), a popular journal among the + working classes. He was fined and imprisoned for two years because of his + attack (1810) on military flogging, and was also (1831) prosecuted for + sedition. He further showed his paradox nature by his <i>History of the + Protestant Reformation</i> (1824-1827), an attack on the prevailing + Protestant opinion. He also wrote a <i>Life of Andrew Jackson</i> (1834). + After repeated attempts he succeeded in entering parliament, a result of + the Reform Bill.</p> + + <p><a name="Nt_399" href="#NtA_399">[399]</a> Robinson (1735-1790) was a + Baptist minister who wrote several theological works and a number of + hymns. His work at Cambridge so offended the students that they at one + time broke up the services.</p> + + <p><a name="Nt_400" href="#NtA_400">[400]</a> This work had passed + through twelve editions by 1823.</p> + + <p><a name="Nt_401" href="#NtA_401">[401]</a> Dyer (1755-1841), the poet + and reformer, edited Robinson's <i>Ecclesiastical Researches</i> (1790). + He was a life-long friend of Charles Lamb, and in their boyhood they were + schoolmates at Christ's Hospital. His <i>Complaints of the Poor People of + England</i> (1793) made him a worthy companion of the paradoxers above + mentioned.</p> + + <p><a name="Nt_402" href="#NtA_402">[402]</a> These were John Thelwall + (1764-1834) whose <i>Politics for the People or Hogswash</i> (1794) took + its title from the fact that Burke called the people the "swinish + multitude." The book resulted in sending the author to the Tower for + sedition. In 1798 he gave up politics and started a school of elocution + which became very famous. Thomas Hardy (1752-1832), who kept a + bootmaker's shop in Piccadilly, was a fellow prisoner with Thelwall, + being arrested for high treason. He was founder (1792) of The London + Corresponding Society, a kind of clearing house for radical associations + throughout the country. Horne Tooke was really John Horne (1736-1812), he + having taken the name of his friend William Tooke in 1782. He was a + radical of the radicals, and organized a number of reform societies. + Among these was the Constitutional Society that voted money (1775) to + assist the American revolutionists, appointing him to give the + contribution to Franklin. For this he was imprisoned for a year. With his + fellow rebels in the Tower in 1794, however, he was acquitted. As a + philologist he is known for his early advocacy of the study of + Anglo-Saxon and Gothic, and his <i>Diversions of Purley</i> (1786) is + still known to readers.</p> + + <p><a name="Nt_403" href="#NtA_403">[403]</a> This was the admiral, Adam + Viscount Duncan (1731-1804), who defeated the Dutch off Camperdown in + 1797.</p> + + <p><a name="Nt_404" href="#NtA_404">[404]</a> He was created Duke of + Clarence and St. Andrews in 1789 and was Admiral of the Fleet escorting + Louis XVIII on his return to France in 1814. He became Lord High Admiral + in 1827, and reigned as William IV from 1830 to 1837.</p> + + <p><a name="Nt_405" href="#NtA_405">[405]</a> This was Charles Abbott + (1762-1832) first Lord Tenterden. He succeeded Lord Ellenborough as Chief + Justice (1818) and was raised to the peerage in 1827. He was a strong + Tory and opposed the Catholic Relief Bill, the Reform Bill, and the + abolition of the death penalty for forgery. </p> + + <p><a name="Nt_406" href="#NtA_406">[406]</a> Edward Law (1750-1818), + first Baron Ellenborough. He was chief counsel for Warren Hastings, and + his famous speech in defense of his client is well known. He became Chief + Justice and was raised to the peerage in 1802. He opposed all efforts to + modernize the criminal code, insisting upon the reactionary principle of + new death penalties. </p> + + <p><a name="Nt_407" href="#NtA_407">[407]</a> Edmund Law (1703-1787), + Bishop of Carlisle (1768), was a good deal more liberal than his son. His + <i>Considerations on the Propriety of requiring subscription to the + Articles of Faith</i> (1774) was published anonymously. In it he asserts + that not even the clergy should be required to subscribe to the + thirty-nine articles.</p> + + <p><a name="Nt_408" href="#NtA_408">[408]</a> Joe Miller (1684-1738), the + famous Drury Lane comedian, was so illiterate that he could not have + written the <i>Joe Miller's Jests, or the Wit's Vade-Mecum</i> that + appeared the year after his death. It was often reprinted and probably + contained more or less of Miller's own jokes.</p> + + <p><a name="Nt_409" href="#NtA_409">[409]</a> The sixth duke (1766-1839) + was much interested in parliamentary reform. He was a member of the + Society of Friends of the People. He was for fourteen years a member of + parliament (1788-1802) and was later Lord Lieutenant of Ireland + (1806-1807). He afterwards gave up politics and became interested in + agricultural matters.</p> + + <p><a name="Nt_410" href="#NtA_410">[410]</a> George Jeffreys (c. + 1648-1689), the favorite of James II, who was active in prosecuting the + Rye House conspirators. He was raised to the peerage in 1684 and held the + famous "bloody assize" in the following year, being made Lord Chancellor + as a result. He was imprisoned in the Tower by William III and died + there.</p> + + <p><a name="Nt_411" href="#NtA_411">[411]</a> <i>The Every Day Book, + forming a Complete History of the Year, Months, and Seasons, and a + perpetual Key to the Almanack</i>, 1826-1827.</p> + + <p><a name="Nt_412" href="#NtA_412">[412]</a> The first and second + editions appeared in 1820. Two others followed in 1821.</p> + + <p><a name="Nt_413" href="#NtA_413">[413]</a> <i>The three trials of W. + H., for publishing three parodies; viz the late John Wilkes' Catechism, + the Political Litany, and the Sinecurists Creed; on three ex-officio + informations, at Guildhall, London, ... Dec. 18, 19, & 20, + 1817</i>,... London, 1818.</p> + + <p><a name="Nt_414" href="#NtA_414">[414]</a> The <i>Political Litany</i> + appeared in 1817.</p> + + <p><a name="Nt_415" href="#NtA_415">[415]</a> That is, Castlereagh's.</p> + + <p><a name="Nt_416" href="#NtA_416">[416]</a> The well-known caricaturist + (1792-1878), then only twenty-nine years old.</p> + + <p><a name="Nt_417" href="#NtA_417">[417]</a> Robert Stewart (1769-1822) + was second Marquis of Londonderry and Viscount Castlereagh. As Chief + Secretary for Ireland he was largely instrumental in bringing about the + union of Ireland and Great Britain. He was at the head of the war + department during most of the Napoleonic wars, and was to a great extent + responsible for the European coalition against the Emperor. He suicided + in 1822.</p> + + <p><a name="Nt_418" href="#NtA_418">[418]</a> John Murray (1778-1843), + the well-known London publisher. He refused to finish the publication of + Don Juan, after the first five cantos, because of his Tory + principles.</p> + + <p><a name="Nt_419" href="#NtA_419">[419]</a> Only the first two cantos + appeared in 1819.</p> + + <p><a name="Nt_420" href="#NtA_420">[420]</a> Proclus (412-485), one of + the greatest of the neo-Platonists, studied at Alexandria and taught + philosophy at Athens. He left commentaries on Plato and on part of + Euclid's <i>Elements</i>.</p> + + <p><a name="Nt_421" href="#NtA_421">[421]</a> Thomas Taylor (1758-1835), + called "the Platonist," had a liking for mathematics, and was probably + led by his interest in number mysticism to a study of neo-Platonism. He + translated a number of works from the Latin and Greek, and wrote two + works on theoretical arithmetic (1816, 1823).</p> + + <p><a name="Nt_422" href="#NtA_422">[422]</a> There was an earlier + edition, 1788-89.</p> + + <p><a name="Nt_423" href="#NtA_423">[423]</a> Georgius Gemistus, or + Georgius Pletho (Plethon), lived in the fourteenth and fifteenth + centuries. He was a native of Constantinople, but spent most of his time + in Greece. He devoted much time to the propagation of the Platonic + philosophy, but also wrote on divinity, geography, and history.</p> + + <p><a name="Nt_424" href="#NtA_424">[424]</a> Hannah More (1745-1833), + was, in her younger days, a friend of Burke, Reynolds, Dr. Johnson, and + Garrick. At this time she wrote a number of poems and aspired to become a + dramatist. Her <i>Percy</i> (1777), with a prologue and epilogue by + Garrick, had a long run at Covent Garden. Somewhat later she came to + believe that the playhouse was a grave public evil, and refused to attend + the revival of her own play with Mrs. Siddons in the leading part. After + 1789 she and her sisters devoted themselves to starting schools for poor + children, teaching them religion and housework, but leaving them + illiterate.</p> + + <p><a name="Nt_425" href="#NtA_425">[425]</a> These were issued at the + rate of three each month,—a story, a ballad, and a Sunday tract. + They were collected and published in one volume in 1795. It is said that + two million copies were sold the first year. There were also editions in + 1798, 1819, 1827, and 1836-37.</p> + + <p><a name="Nt_426" href="#NtA_426">[426]</a> That is, Dr. Johnson + (1709-1784). The <i>Rambler</i> was published in 1750-1752, and was an + imitation of Addison's <i>Spectator</i>.</p> + + <p><a name="Nt_427" href="#NtA_427">[427]</a> Dr. Moore, referred to + below.</p> + + <p><a name="Nt_428" href="#NtA_428">[428]</a> Dr. John Moore (1729-1802), + physician and novelist, is now best known for his <i>Journal during a + Residence in France from the beginning of August to the middle of + December, 1792</i>, a work quoted frequently by Carlyle in his <i>French + Revolution</i>.</p> + + <p><a name="Nt_429" href="#NtA_429">[429]</a> Sir John Moore (1761-1809), + Lieutenant General in the Napoleonic wars. He was killed in the battle of + Corunna. The poem by Charles Wolfe (1791-1823), <i>The Burial of Sir John + Moore</i> (1817), is well known.</p> + + <p><a name="Nt_430" href="#NtA_430">[430]</a> Referring to the novels of + Thomas Love Peacock (1785-1866), who succeeded James Mill as chief + examiner of the East India Company, and was in turn succeeded by John + Stuart Mill.</p> + + <p><a name="Nt_431" href="#NtA_431">[431]</a> Frances Burney, Madame + d'Arblay (1752-1840), married General d'Arblay, a French officer and + companion of Lafayette, in 1793. She was only twenty-five when she + acquired fame by her <i>Evelina, or a Young Lady's Entrance into the + World</i>. Her <i>Letters and Diaries</i> appeared posthumously + (1842-45).</p> + + <p><a name="Nt_432" href="#NtA_432">[432]</a> Henry Peter, Baron Brougham + and Vaux (1778-1868), well known in politics, science, and letters. He + was one of the founders of the <i>Edinburgh Review</i>, became Lord + Chancellor in 1830, and took part with men like William Frend, De + Morgan's father-in-law, in the establishing of London University. He was + also one of the founders of the Society for the Diffusion of Useful + Knowledge. He was always friendly to De Morgan, who entered the faculty + of London University, whose work on geometry was published by the Society + mentioned, and who was offered the degree of doctor of laws by the + University of Edinburgh while Lord Brougham was Lord Rector. The + Edinburgh honor was refused by De Morgan who said he "did not feel like + an LL.D."</p> + + <p><a name="Nt_433" href="#NtA_433">[433]</a> Maria Edgeworth + (1767-1849).</p> + + <p><a name="Nt_434" href="#NtA_434">[434]</a> Sydney Owenson (c. + 1783-1859) married Sir Thomas Morgan, a well-known surgeon, in 1812. Her + Irish stories were very popular with the patriots but were attacked by + the <i>Quarterly Review</i>. <i>The Wild Irish Girl</i> (1806) went + through seven editions in two years.</p> + + <p><a name="Nt_435" href="#NtA_435">[435]</a> 1775-1817.</p> + + <p><a name="Nt_436" href="#NtA_436">[436]</a> 1771-1832.</p> + + <p><a name="Nt_437" href="#NtA_437">[437]</a> The famous preacher + (1732-1808). He was the first chairman of the Religious Tract Society. He + is also known as one of the earliest advocates of vaccination, in his + <i>Cow-pock Inoculation vindicated and recommended from matters of + fact</i>, 1806.</p> + + <p><a name="Nt_438" href="#NtA_438">[438]</a> Sir Rowland Hill + (1795-1879), the father of penny postage.</p> + + <p><a name="Nt_439" href="#NtA_439">[439]</a> Beilby Porteus (1731-1808), + Bishop of Chester (1776) and Bishop of London (1787). He encouraged the + Sunday-school movement and the dissemination of Hannah More's tracts. He + was an active opponent of slavery, but also of Catholic emancipation.</p> + + <p><a name="Nt_440" href="#NtA_440">[440]</a> Henrietta Maria Bowdler + (1754-1830), generally known as Mrs. Harriet Bowdler. She was the author + of many religious tracts and poems. Her <i>Poems and Essays</i> (1786) + were often reprinted. The story goes that on the appearance of her + <i>Sermons on the Doctrines and duties of Christianity</i> (published + anonymously), Bishop Porteus offered the author a living under the + impression that it was written by a man.</p> + + <p><a name="Nt_441" href="#NtA_441">[441]</a> William Frend (1757-1841), + whose daughter Sophia Elizabeth became De Morgan's wife (1837), was at + one time a clergyman of the Established Church, but was converted to + Unitarianism (1787). He came under De Morgan's definition of a true + paradoxer, carrying on a zealous warfare for what he thought right. As a + result of his <i>Address to the Inhabitants of Cambridge</i> (1787), and + his efforts to have abrogated the requirement that candidates for the + M.A. must subscribe to the thirty-nine articles, he was deprived of his + tutorship in 1788. A little later he was banished (see De Morgan's + statement in the text) from Cambridge because of his denunciation of the + abuses of the Church and his condemnation of the liturgy. His + eccentricity is seen in his declining to use negative quantities in the + operations of algebra. He finally became an actuary at London and was + prominent in radical associations. He was a mathematician of ability, + having been second wrangler and having nearly attained the first place, + and he was also an excellent scholar in Latin, Greek, and Hebrew.</p> + + <p><a name="Nt_442" href="#NtA_442">[442]</a> George Peacock (1791-1858), + Fellow of Trinity College, Cambridge, Lowndean professor of astronomy, + and Dean of Ely Cathedral (1839). His tomb may be seen at Ely where he + spent the latter part of his life. He was one of the group that + introduced the modern continental notation of the calculus into England, + replacing the cumbersome notation of Newton, passing from "the + <i>dot</i>age of fluxions to the <i>de</i>ism of the calculus."</p> + + <p><a name="Nt_443" href="#NtA_443">[443]</a> Robert Simson (1687-1768); + professor of mathematics at Glasgow. His restoration of Apollonius (1749) + and his translation and restoration of Euclid (1756, and + 1776—posthumous) are well known.</p> + + <p><a name="Nt_444" href="#NtA_444">[444]</a> Francis Maseres + (1731-1824), a prominent lawyer. His mathematical works had some + merit.</p> + + <p><a name="Nt_445" href="#NtA_445">[445]</a> These appeared annually + from 1804 to 1822.</p> + + <p><a name="Nt_446" href="#NtA_446">[446]</a> Henry Gunning (1768-1854) + was senior esquire bedell of Cambridge. The <i>Reminiscences</i> appeared + in two volumes in 1854.</p> + + <p><a name="Nt_447" href="#NtA_447">[447]</a> John Singleton Copley, + Baron Lyndhurst (1772-1863), the son of John Singleton Copley the + portrait painter, was born in Boston. He was educated at Trinity College, + Cambridge, and became a lawyer. He was made Lord Chancellor in 1827.</p> + + <p><a name="Nt_448" href="#NtA_448">[448]</a> Sir William Rough (c. + 1772-1838), a lawyer and poet, became Chief Justice of Ceylon in 1836. He + was knighted in 1837.</p> + + <p><a name="Nt_449" href="#NtA_449">[449]</a> Herbert Marsh, afterwards + Bishop of Peterborough, a relation of my father.—S. E. De M.</p> + + <p>He was born in 1757 and died in 1839. On the trial of Frend he + publicly protested against testifying against a personal confidant, and + was excused. He was one of the first of the English clergy to study + modern higher criticism of the Bible, and amid much opposition he wrote + numerous works on the subject. He was professor of theology at Cambridge + (1707), Bishop of Llandaff (1816), and Bishop of Peterborough.</p> + + <p><a name="Nt_450" href="#NtA_450">[450]</a> George Butler (1774-1853), + Headmaster of Harrow (1805-1829), Chancellor of Peterborough (1836), and + Dean of Peterborough (1842).</p> + + <p><a name="Nt_451" href="#NtA_451">[451]</a> James Tate (1771-1843), + Headmaster of Richmond School (1796-1833) and Canon of St. Paul's + Cathedral (1833). He left several works on the classics.</p> + + <p><a name="Nt_452" href="#NtA_452">[452]</a> Francis Place (1771-1854), + at first a journeyman breeches maker, and later a master tailor. He was a + hundred years ahead of his time as a strike leader, but was not so + successful as an agitator as he was as a tailor, since his shop in + Charing Cross made him wealthy. He was a well-known radical, and it was + largely due to his efforts that the law against the combinations of + workmen was repealed in 1824. His chief work was <i>The Principles of + Population</i> (1822).</p> + + <p><a name="Nt_453" href="#NtA_453">[453]</a> Speed (1552-1629) was a + tailor until Grevil (Greville) made him independent of his trade. He was + not only an historian of some merit, but a skilful cartographer. His maps + of the counties were collected in the <i>Theatre of the Empire of Great + Britaine</i>, 1611. About this same time he also published <i>Genealogies + recorded in Sacred Scripture</i>, a work that had passed through + thirty-two editions by 1640.</p> + + <p><a name="Nt_454" href="#NtA_454">[454]</a> <i>The history of Great + Britaine under the conquests of ye Romans, Saxons, Danes, and + Normans....</i> London, 1611, folio. The second edition appeared in 1623; + the third, to which De Morgan here refers, posthumously in 1632; and the + fourth in 1650.</p> + + <p><a name="Nt_455" href="#NtA_455">[455]</a> William Nicolson + (1655-1727) became Bishop of Carlisle in 1702, and Bishop of Derry in + 1718. His chief work was the <i>Historical Library</i> (1696-1724), in + the form of a collection of documents and chronicles. It was reprinted in + 1736 and in 1776.</p> + + <p><a name="Nt_456" href="#NtA_456">[456]</a> Sir Fulk Grevil, or Fulke + Greville (1554-1628), was a favorite of Queen Elizabeth, Chancellor of + the Exchequer under James I, a patron of literature, and a friend of Sir + Philip Sidney.</p> + + <p><a name="Nt_457" href="#NtA_457">[457]</a> See note <a + href="#Nt_443">443</a> on page <a href="#page197">197</a>.</p> + + <p><a name="Nt_458" href="#NtA_458">[458]</a> See note <a + href="#Nt_444">444</a> on page <a href="#page197">197</a>.</p> + + <p><a name="Nt_459" href="#NtA_459">[459]</a> See note <a + href="#Nt_439">439</a> on page <a href="#page193">193</a>.</p> + + <p><a name="Nt_460" href="#NtA_460">[460]</a> Edward Waring (1736-1796) + was Lucasian professor of mathematics at Cambridge. He published several + works on analysis and curves. The work referred to was the <i>Miscellanea + Analytica de aequationibus algebraicis et curvarum proprietatibus</i>, + Cambridge, 1762.</p> + + <p><a name="Nt_461" href="#NtA_461">[461]</a> <i>A Dissertation on the + use of the Negative Sign in Algebra...; to which is added, Machin's + Quadrature of the Circle</i>, London, 1758.</p> + + <p><a name="Nt_462" href="#NtA_462">[462]</a> The paper was probably one + on complex numbers, or possibly one on quaternions, in which direction as + well as absolute value is involved.</p> + + <p><a name="Nt_463" href="#NtA_463">[463]</a> De Morgan quotes from one + of the Latin editions. Descartes wrote in French, the title of his first + edition being: <i>Discours de la méthode pour bien conduire sa raison et + chercher la vérité dans les sciences, plus la dioptrique, les météores et + la géométrie qui sont des essais de cette méthode</i>, Leyden, 1637, + 4to.</p> + + <p><a name="Nt_464" href="#NtA_464">[464]</a> "I have observed that + algebra indeed, as it is usually taught, is so restricted by definite + rules and formulas of calculation, that it seems rather a confused kind + of an art, by the practice of which the mind is in a certain manner + disturbed and obscured, than a science by which it is cultivated and made + acute."</p> + + <p><a name="Nt_465" href="#NtA_465">[465]</a> It appeared in 93 volumes, + from 1758 to 1851.</p> + + <p><a name="Nt_466" href="#NtA_466">[466]</a> <i>The principles of the + doctrine of life-annuities; explained in a familiar manner ... with a + variety of new tables</i> ..., London, 1783.</p> + + <p><a name="Nt_467" href="#NtA_467">[467]</a> I suppose the one who wrote + <i>Conjectures on the physical causes of Earthquakes and Volcanoes</i>, + Dublin, 1820.</p> + + <p><a name="Nt_468" href="#NtA_468">[468]</a> <i>Scriptores Logarithmici; + or, a Collection of several curious</i> <i>tracts on the nature and + construction of Logarithms ... together with same tracts on the Binomial + Theorem</i> ..., 6 vols., London, 1791-1807.</p> + + <p><a name="Nt_469" href="#NtA_469">[469]</a> Charles Babbage + (1792-1871), whose work on the calculating machine is well known. Maseres + was, it is true, ninety-two at this time, but Babbage was thirty-one + instead of twenty-nine. He had already translated Lacroix's <i>Treatise + on the differential and integral calculus</i> (1816), in collaboration + with Herschel and Peacock. He was Lucasian professor of mathematics at + Cambridge from 1828 to 1839.</p> + + <p><a name="Nt_470" href="#NtA_470">[470]</a> <i>The great and new Art of + weighing Vanity, or a discovery of the ignorance of the great and new + artist in his pseudo-philosophical writings.</i> The "great and new + artist" was Sinclair.</p> + + <p><a name="Nt_471" href="#NtA_471">[471]</a> George Sinclair, probably a + native of East Lothian, who died in 1696. He was professor of philosophy + and mathematics at Glasgow, and was one of the first to use the barometer + in measuring altitudes. The work to which De Morgan refers is his + <i>Hydrostaticks</i> (1672). He was a firm believer in evil spirits, his + work on the subject going through four editions: <i>Satan's Invisible + World Discovered; or, a choice collection of modern relations, proving + evidently against the Saducees and Athiests of this present age, that + there are Devils, Spirits, Witches, and Apparitions</i>, Edinburgh, + 1685.</p> + + <p><a name="Nt_472" href="#NtA_472">[472]</a> This was probably William + Sanders, Regent of St. Leonard's College, whose <i>Theses + philosophicae</i> appeared in 1674, and whose <i>Elementa geometriae</i> + came out a dozen years later.</p> + + <p><a name="Nt_473" href="#NtA_473">[473]</a> <i>Ars nova et magna + gravitatis et levitatis; sive dialogorum philosophicorum libri sex de + aeris vera ac reali gravitate</i>, Rotterdam, 1669, 4to.</p> + + <p><a name="Nt_474" href="#NtA_474">[474]</a> Volume I, Nos. 1 and 2, + appeared in 1803.</p> + + <p><a name="Nt_475" href="#NtA_475">[475]</a> His daughter, Mrs. De + Morgan, says in her <i>Memoir</i> of her husband: "My father had been + second wrangler in a year in which the two highest were close together, + and was, as his son-in-law afterwards described him, an exceedingly clear + thinker. It is possible, as Mr. De Morgan said, that this mental + clearness and directness may have caused his mathematical heresy, the + rejection of the use of negative quantities in algebraical operations; + and it is probable that he thus deprived himself of an instrument of + work, the use of which might have led him to greater eminence in the + higher branches." <i>Memoir of Augustus De Morgan</i>, London, 1882, p. + 19.</p> + + <p><a name="Nt_476" href="#NtA_476">[476]</a> "If it is not true it is a + good invention." A well-known Italian proverb.</p> + + <p><a name="Nt_477" href="#NtA_477">[477]</a> See page <a + href="#page86">86</a>, note <a href="#Nt_132">132</a>.</p> + + <p><a name="Nt_478" href="#NtA_478">[478]</a> He was born at Paris in + 1713, and died there in 1765.</p> + + <p><a name="Nt_479" href="#NtA_479">[479]</a> <i>Recherches sur les + courbes à double courbure</i>, Paris, 1731. Clairaut was then only + eighteen, and was in the same year made a member of the Académie des + sciences. His <i>Elémens de géométrie</i> appeared in 1741. Meantime he + had taken part in the measurement of a degree in Lapland (1736-1737). His + <i>Traité de la figure de la terre</i> was published in 1741. The Academy + of St. Petersburg awarded him a prize for his <i>Théorie de la lune</i> + (1750). His various works on comets are well known, particularly his + <i>Théorie du mouvement des comètes</i> (1760) in which he applied the + "problem of three bodies" to Halley's comet as retarded by Jupiter and + Saturn.</p> + + <p><a name="Nt_480" href="#NtA_480">[480]</a> Joseph Privat, Abbé de + Molières (1677-1742), was a priest of the Congregation of the Oratorium. + In 1723 he became a professor in the Collège de France. He was well known + as an astronomer and a mathematician, and wrote in defense of Descartes's + theory of vortices (1728, 1729). He also contributed to the methods of + finding prime numbers (1705).</p> + + <p><a name="Nt_481" href="#NtA_481">[481]</a> "Deserves not only to be + printed, but to be admired as a marvel of imagination, of understanding, + and of ability."</p> + + <p><a name="Nt_482" href="#NtA_482">[482]</a> Blaise Pascal (1623-1662), + the well-known French philosopher and mathematician. He lived for some + time with the Port Royalists, and defended them against the Jesuits in + his <i>Provincial Letters</i>. Among his works are the following: + <i>Essai pour les coniques</i> (1640); <i>Recit de la grande expérience + de l'équilibre des liqueurs</i> (1648), describing his experiment in + finding altitudes by barometric readings; <i>Histoire de la roulette</i> + (1658); <i>Traité du triangle arithmétique</i> (1665); <i>Aleae + geometria</i> (1654).</p> + + <p><a name="Nt_483" href="#NtA_483">[483]</a> This proposition shows that + if a hexagon is inscribed in a conic (in particular a circle) and the + opposite sides are produced to meet, the three points determined by their + intersections will be in the same straight line.</p> + + <p><a name="Nt_484" href="#NtA_484">[484]</a> Jacques Curabelle, + <i>Examen des Œuvres du Sr. Desargues</i>, Paris, 1644. He also + published without date a work entitled: <i>Foiblesse pitoyable du Sr. G. + Desargues employée contre l'examen fait de ses œuvres</i>.</p> + + <p><a name="Nt_485" href="#NtA_485">[485]</a> See page <a + href="#page119">119</a>, note <a href="#Nt_233">233</a>.</p> + + <p><a name="Nt_486" href="#NtA_486">[486]</a> Until "this great + proposition called Pascal's should see the light."</p> + + <p><a name="Nt_487" href="#NtA_487">[487]</a> The story is that his + father, Etienne Pascal, did not wish him to study geometry until he was + thoroughly grounded in Latin and Greek. Having heard the nature of the + subject, however, he began at the age of twelve to construct figures by + himself, drawing them on the floor with a piece of charcoal. When his + father discovered what he was doing he was attempting to demonstrate that + the sum of the angles of a triangle equals two right angles. The story is + given by his sister, Mme. Perier.</p> + + <p><a name="Nt_488" href="#NtA_488">[488]</a> Sir John Wilson (1741-1793) + was knighted in 1786 and became Commissioner of the Great Seal in 1792. + He was a lawyer and jurist of recognized merit. He stated his theorem + without proof, the first demonstration having been given by Lagrange in + the Memoirs of the Berlin Academy for 1771,—<i>Demonstration d'un + théorème nouveau concernant les nombres premiers</i>. Euler also gave a + proof in his <i>Miscellanea Analytica</i> (1773). Fermat's works should + be consulted in connection with the early history of this theorem.</p> + + <p><a name="Nt_489" href="#NtA_489">[489]</a> He wrote, in 1760, a tract + in defense of Waring, a point of whose algebra had been assailed by a Dr. + Powell. Waring wrote another tract of the same date.—A. De M.</p> + + <p>William Samuel Powell (1717-1775) was at this time a fellow of St. + John's College, Cambridge. In 1765 he became Vice Chancellor of the + University. Waring was a Magdalene man, and while candidate for the + Lucasian professorship he circulated privately his <i>Miscellanea + Analytica</i>. Powell attacked this in his <i>Observations on the First + Chapter of a Book called Miscellanea</i> (1760). This attack was probably + in the interest of another candidate, a man of his own college (St. + John's), William Ludlam.</p> + + <p><a name="Nt_490" href="#NtA_490">[490]</a> William Paley (1743-1805) + was afterwards a tutor at Christ's College, Cambridge. He never + contributed anything to mathematics, but his <i>Evidences of + Christianity</i> (1794) was long considered somewhat of a classic. He + also wrote <i>Principles of Morality and Politics</i> (1785), and + <i>Natural Theology</i> (1802).</p> + + <p><a name="Nt_491" href="#NtA_491">[491]</a> Edward, first Baron Thurlow + (1731-1806) is known to Americans because of his strong support of the + Royal prerogative during the Revolution. He was a favorite of George III, + and became Lord Chancellor in 1778.</p> + + <p><a name="Nt_492" href="#NtA_492">[492]</a> George Wilson Meadley + (1774-1818) published his <i>Memoirs of ... Paley</i> in 1809. He also + published <i>Memoirs of Algernon Sidney</i> in 1813. He was a merchant + and banker, and had traveled extensively in Europe and the East. He was a + convert to unitarianism, to which sect Paley had a strong leaning.</p> + + <p><a name="Nt_493" href="#NtA_493">[493]</a> Watson (1737-1816) was a + strange kind of man for a bishopric. He was professor of chemistry at + Cambridge (1764) at the age of twenty-seven. It was his experiments that + led to the invention of the black-bulb thermometer. He is said to have + saved the government £100,000 a year by his advice on the manufacture of + gunpowder. Even after he became professor of divinity at Cambridge (1771) + he published four volumes of <i>Chemical Essays</i> (vol. I, 1781). He + became Bishop of Llandaff in 1782.</p> + + <p><a name="Nt_494" href="#NtA_494">[494]</a> James Adair (died in 1798) + was counsel for the defense in the trial of the publishers of the + <i>Letters of Junius</i> (1771). As King's Serjeant he assisted in + prosecuting Hardy and Horne Tooke.</p> + + <p><a name="Nt_495" href="#NtA_495">[495]</a> Morgan (1750-1833) was + actuary of the Equitable Assurance Society of London (1774-1830), and it + was to his great abilities that the success of that company was due at a + time when other corporations of similar kind were meeting with disaster. + The Royal Society awarded him a medal (1783) for a paper on + <i>Probability of Survivorship</i>. He wrote several important works on + insurance and finance.</p> + + <p><a name="Nt_496" href="#NtA_496">[496]</a> Dr. Price (1723-1791) was a + non-conformist minister and a writer on ethics, economics, politics, and + insurance. He was a defender of the American Revolution and a personal + friend of Franklin. In 1778 Congress invited him to America to assist in + the financial administration of the new republic, but he declined. His + famous sermon on the French Revolution is said to have inspired Burke's + <i>Reflections on the Revolution in France</i>.</p> + + <p><a name="Nt_497" href="#NtA_497">[497]</a> Elizabeth Gurney + (1780-1845), a Quaker, who married Joseph Fry (1800), a London merchant. + She was the prime mover in the Association for the Improvement of the + Female Prisoners in Newgate, founded in 1817. Her influence in prison + reform extended throughout Europe, and she visited the prisons of many + countries in her efforts to improve the conditions of penal servitude. + The friendship of Mrs. Fry with the De Morgans began in 1837. Her scheme + for a female benefit society proved worthless from the actuarial + standpoint, and would have been disastrous to all concerned if it had + been carried out, and it was therefore fortunate that De Morgan was + consulted in time. Mrs. De Morgan speaks of the consultation in these + words: "My husband, who was very sensitive on such points, was charmed + with Mrs. Fry's voice and manner as much as by the simple + self-forgetfulness with which she entered into this business; her own + very uncomfortable share of it not being felt as an element in the + question, as long as she could be useful in promoting good or preventing + mischief. I can see her now as she came into our room, took off her + little round Quaker cap, and laying it down, went at once into the + matter. 'I have followed thy advice, and I think nothing further can be + done in this case; but all harm is prevented.' In the following year I + had an opportunity of seeing the effect of her most musical tones. I + visited her at Stratford, taking my little baby and nurse with me, to + consult her on some articles on prison discipline, which I had written + for a periodical. The baby—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." <i>Memoirs</i>, p. 91.</p> + + <p><a name="Nt_498" href="#NtA_498">[498]</a> Mrs. Fry certainly believed + that the writer was the old actuary of the Equitable, when she first + consulted him upon the benevolent Assurance project; but we were + introduced to her by our old and dear friend Lady Noel Byron, by whom she + had been long known and venerated, and who referred her to Mr. De Morgan + for advice. An unusual degree of confidence in, and appreciation of each + other, arose on their first meeting between the two, who had so much that + was externally different, and so much that was essentially alike, in + their natures.—S. E. De M.</p> + + <p>Anne Isabella Milbanke (1792-1860) married Lord Byron in 1815, when + both took the additional name of Noel, her mother's name. They were + separated in 1816.</p> + + <p><a name="Nt_499" href="#NtA_499">[499]</a> An obscure writer not + mentioned in the ordinary biographies.</p> + + <p><a name="Nt_500" href="#NtA_500">[500]</a> Not mentioned in the + ordinary biographies, and for obvious reasons.</p> + + <p><a name="Nt_501" href="#NtA_501">[501]</a> "Before" and "after."</p> + + <p><a name="Nt_502" href="#NtA_502">[502]</a> On Bishop Wilkins see note + <a href="#Nt_171">171</a> on page <a href="#page100">100</a>.</p> + + <p><a name="Nt_503" href="#NtA_503">[503]</a> Provision for a + journey.</p> + + <p><a name="Nt_504" href="#NtA_504">[504]</a> See note <a + href="#Nt_179">179</a> on page <a href="#page103">103</a>.</p> + + <p><a name="Nt_505" href="#NtA_505">[505]</a> Thomas Bradwardine + (1290-1349), known as <i>Doctor Profundus</i>, proctor and professor of + theology at Oxford, and afterwards Chancellor of St. Paul's and confessor + to Edward III. The English ascribed their success at Crécy to his + prayers.</p> + + <p><a name="Nt_506" href="#NtA_506">[506]</a> He was consecrated + Archbishop of Canterbury by the Pope at Avignon, July 13, 1349, and died + of the plague at London in the same year.</p> + + <p><a name="Nt_507" href="#NtA_507">[507]</a> "One paltry little + year."</p> + + <p><a name="Nt_508" href="#NtA_508">[508]</a> The title is carelessly + copied, as is so frequently the case in catalogues, even of the Libri + class. It should read: <i>Arithmetica thome brauardini</i> || <i>Olivier + Senant</i> || <i>Venum exponuntur ab Oliuiario senant in vico diui Jacobi + sub signo beate Barbare sedente</i>. The colophon reads: <i>Explicit + arithmetica speculatiua thōe brauardini b<span + class="over">n</span> reuisa et correcta a Petro sanchez Ciruelo + aragonensi mathematicas legēte Parisius, īpressa per + Thomā anguelart</i>. There were Paris editions of 1495, 1496, 1498, + s. a. (c. 1500), 1502, 1504, 1505, s. a. (c. 1510), 1512, 1530, a + Valencia edition of 1503, two Wittenberg editions of 1534 and 1536, and + doubtless several others. The work is not "very rare," although of course + no works of that period are common. See the editor's <i>Rara + Arithmetica</i>, page 61.</p> + + <p><a name="Nt_509" href="#NtA_509">[509]</a> This is his <i>Tractatus de + proportionibus</i>, Paris, 1495; Venice, 1505; Vienna, 1515, with other + editions.</p> + + <p><a name="Nt_510" href="#NtA_510">[510]</a> The colophon of the 1495 + edition reads: <i>Et sic explicit Geometria Thome brauardini cū + tractatulo de quadratura circuli bene reuisa a Petro sanchez ciruelo: + operaqz Guidonis mercatoris diligētissime impresse + parisi<sup>o</sup> in cāpo gaillardi. Anno d<span + class="over">n</span>i. 1495. die. 20, maij.</i></p> + + <p>This Petro Ciruelo was born in Arragon, and died in 1560 at Salamanca. + He studied mathematics and philosophy at Paris, and took the doctor's + degree there. He taught at the University of Alcalà and became canon of + the Cathedral at Salamanca. Besides his editions of Bradwardine he wrote + several works, among them the <i>Liber arithmeticae practicae qui dicitur + algorithmus</i> (Paris, 1495) and the <i>Cursus quatuor mathematicarum + artium liberalium</i> (Alcalà, 1516).</p> + + <p><a name="Nt_511" href="#NtA_511">[511]</a> Star polygons, a subject of + considerable study in the later Middle Ages. See note <a + href="#Nt_35">35</a> on page <a href="#page44">44</a>.</p> + + <p><a name="Nt_512" href="#NtA_512">[512]</a> "A new theory that adds + lustre to the fourteenth century."</p> + + <p><a name="Nt_513" href="#NtA_513">[513]</a> There is nothing in the + edition of 1495 that leads to this conclusion.</p> + + <p><a name="Nt_514" href="#NtA_514">[514]</a> The full title is: + <i>Nouvelle théorie des parallèles, avec un appendice contenant la + manière de perfectionner la théorie des parallèles de A. M. Legendre</i>. + The author had no standing as a scientist.</p> + + <p><a name="Nt_515" href="#NtA_515">[515]</a> Adrien Marie Legendre + (1752-1833) was one of the great mathematicians of the opening of the + nineteenth century. His <i>Eléments de géométrie</i> (1794) had great + influence on the geometry of the United States. His <i>Essai sur la + théorie des nombres</i> (1798) is one of the classics upon the subject. + The work to which Kircher refers is the <i>Nouvelle théorie des + parallèles</i> (1803), in which the attempt is made to avoid using + Euclid's postulate of parallels, the result being merely the substitution + of another assumption that was even more unsatisfactory. The best + presentations of the general theory are W. B. Frankland's <i>Theories of + Parallelism</i>, Cambridge, 1910, and Engel and Stäckel's <i>Die Theorie + der Parallellinien von Euclid bis auf Gauss</i>, Leipsic, 1895. Legendre + published a second work on the theory the year of his death, + <i>Réflexions sur ... la théorie des parallèles</i> (1833). His other + works include the <i>Nouvelles méthodes pour la détermination des orbites + des comètes</i> (1805), in which he uses the method of least squares; the + <i>Traité des fonctions elliptiques et des intégrales</i> (1827-1832), + and the <i>Exercises de calcul intégral</i> (1811, 1816, 1817).</p> + + <p><a name="Nt_516" href="#NtA_516">[516]</a> Johann Joseph Ignatz von + Hoffmann (1777-1866), professor of mathematics at Aschaffenburg, + published his <i>Theorie der Parallellinien</i> in 1801. He supplemented + this by his <i>Kritik der Parallelen-Theorie</i> in 1807, and his <i>Das + eilfte Axiom der Elemente des Euclidis neu bewiesen</i> in 1859. He wrote + other works on mathematics, but none of his contributions was of any + importance.</p> + + <p><a name="Nt_517" href="#NtA_517">[517]</a> Johann Karl Friedrich Hauff + (1766-1846) was successively professor of mathematics at Marburg, + director of the polytechnic school at Augsburg, professor at the + Gymnasium at Cologne, and professor of mathematics and physics at Ghent. + The work to which Kircher refers is his memoirs on the Euclidean + <i>Theorie der Parallelen</i> in Hindenburg's <i>Archiv</i>, vol. III + (1799), an article of no merit in the general theory.</p> + + <p><a name="Nt_518" href="#NtA_518">[518]</a> Wenceslaus Johann Gustav + Karsten (1732-1787) was professor of logic at Rostock (1758) and Butzow + (1760), and later became professor of mathematics and physics at Halle. + His work on parallels is the <i>Versuch einer völlig berichtigten Theorie + der Parallellinien</i> (1779). He also wrote a work entitled + <i>Anfangsgründe der mathematischen Wissenschaften</i> (1780), but + neither of these works was more than mediocre.</p> + + <p><a name="Nt_519" href="#NtA_519">[519]</a> Johann Christoph Schwab + (not Schwal) was born in 1743 and died in 1821. He was professor at the + Karlsschule at Stuttgart. De Morgan's wish was met, for the catalogues + give "c. fig. 8," so that it evidently had eight illustrations instead of + eight volumes. He wrote several other works on the principles of + geometry, none of any importance.</p> + + <p><a name="Nt_520" href="#NtA_520">[520]</a> Gaetano Rossi of Catanzaro. + This was the libretto writer (1772-1855), and hence the imperfections of + the work can better be condoned. De Morgan should have given a little + more of the title: <i>Solusione esatta e regolare ... del ... problema + della quadratura del circolo</i>. There was a second edition, London, + 1805.</p> + + <p><a name="Nt_521" href="#NtA_521">[521]</a> This identifies Rossi, for + Joséphine Grassini (1773-1850) was a well-known contralto, <i>prima + donna</i> at Napoleon's court opera.</p> + + <p><a name="Nt_522" href="#NtA_522">[522]</a> William Spence (1783-1860) + was an entomologist and economist of some standing, a fellow of the Royal + Society, and one of the founders of the Entomological Society of London. + The work here mentioned was a popular one, the first edition appearing in + 1807, and four editions being justified in a single year. He also wrote + <i>Agriculture the Source of Britain's Wealth</i> (1808) and + <i>Objections against the Corn Bill refuted</i> (1815), besides a work in + four volumes on entomology (1815-1826) in collaboration with William + Kirby.</p> + + <p><a name="Nt_523" href="#NtA_523">[523]</a> "That used to be so, but we + have changed all that."</p> + + <p><a name="Nt_524" href="#NtA_524">[524]</a> "Meet the coming + disease."</p> + + <p><a name="Nt_525" href="#NtA_525">[525]</a> George Douglas (or + Douglass) was a Scotch writer. He got out an edition of the <i>Elements + of Euclid</i> in 1776, with an appendix on trigonometry and a set of + tables. His work on <i>Mathematical Tables</i> appeared in 1809, and his + <i>Art of Drawing in Perspective, from mathematical principles</i>, in + 1810.</p> + + <p><a name="Nt_526" href="#NtA_526">[526]</a> See note <a + href="#Nt_443">443</a>, on page <a href="#page197">197</a>.</p> + + <p><a name="Nt_527" href="#NtA_527">[527]</a> John Playfair (1748-1848) + was professor of mathematics (1785) and natural philosophy (1805) at the + University of Edinburgh. His <i>Elements of Geometry</i> went through + many editions.</p> + + <p><a name="Nt_528" href="#NtA_528">[528]</a> "Tell Apella" was an + expression current in classical Rome to indicate incredulity and to show + the contempt in which the Jew was held. Horace says: <i>Credat Judæus + Apella</i>, "Let Apella the Jew believe it." Our "Tell it to the + marines," is a similar phrase.</p> + + <p><a name="Nt_529" href="#NtA_529">[529]</a> As De Morgan says two lines + later, "No mistake is more common than the natural one of imagining that + the"—University of Virginia is at Richmond. The fact is that it is + not there, and that it did not exist in 1810. It was not chartered until + 1819, and was not opened until 1825, and then at Charlottesville. The act + establishing the Central College, from which the University of Virginia + developed, was passed in 1816. The Jean Wood to whom De Morgan refers was + one John Wood who was born about 1775 in Scotland and who emigrated to + the United States in 1800. He published a <i>History of the + Administration of J. Adams</i> (New York, 1802) that was suppressed by + Aaron Burr. This act called forth two works, a <i>Narrative of the + Suppression, by Col. Burr, of the 'History of the Administration of John + Adams'</i> (1802), in which Wood was sustained; and the <i>Antidote to + John Wood's Poison</i> (1802), in which he was attacked. The work + referred to in the "printed circular" may have been the <i>New theory of + the diurnal rotation of the earth</i> (Richmond, Va., 1809). Wood spent + the last years of his life in Richmond, Va., making county maps. He died + there in 1822. A careful search through works relating to the University + of Virginia fails to show that Wood had any connection with it.</p> + + <p><a name="Nt_530" href="#NtA_530">[530]</a> There seems to be nothing + to add to Dobson's biography beyond what De Morgan has so deliciously set + forth.</p> + + <p><a name="Nt_531" href="#NtA_531">[531]</a> "Give to each man his + due."</p> + + <p><a name="Nt_532" href="#NtA_532">[532]</a> Hester Lynch Salusbury + (1741-1821), the friend of Dr. Johnson, married Henry Thrale (1763), a + brewer, who died in 1781. She then married Gabriel Piozzi (1784), an + Italian musician. Her <i>Anecdotes of the late Samuel Johnson</i> (1786) + and <i>Letters to and from Samuel Johnson</i> (1788) are well known. She + also wrote numerous essays and poems.</p> + + <p><a name="Nt_533" href="#NtA_533">[533]</a> Samuel Pike (c. 1717-1773) + was an independent minister, with a chapel in London and a theological + school in his house. He later became a disciple of Robert Sandeman and + left the Independents for the Sandemanian church (1765). The + <i>Philosophia Sacra</i> was first published at London in 1753. De Morgan + here cites the second edition.</p> + + <p><a name="Nt_534" href="#NtA_534">[534]</a> Pike had been dead over + forty years when Kittle published this second edition. Kittle had already + published a couple of works: <i>King Solomon's portraiture of Old Age</i> + (Edinburgh, 1813), and <i>Critical and Practical Lectures on the + Apocalyptical Epistles to the Seven Churches of Asia Minor</i> (London, + 1814).</p> + + <p><a name="Nt_535" href="#NtA_535">[535]</a> See note <a + href="#Nt_334">334</a>, on page <a href="#page152">152</a>.</p> + + <p><a name="Nt_536" href="#NtA_536">[536]</a> William Stukely (1687-1765) + was a fellow of the Royal Society and of the College of Physicians and + Surgeons. He afterwards (1729) entered the Church. He was prominent as an + antiquary, especially in the study of the Roman and Druidic remains of + Great Britain. He was the author of numerous works, chiefly on + paleography.</p> + + <p><a name="Nt_537" href="#NtA_537">[537]</a> William Jones (1726-1800), + who should not be confused with his namesake who is mentioned in note <a + href="#Nt_281">281</a> on page <a href="#page135">135</a>. He was a + lifelong friend of Bishop Horne, and his vicarage at Nayland was a + meeting place of an influential group of High Churchmen. Besides the + <i>Physiological Disquisitions</i> (1781) he wrote <i>The Catholic + Doctrine of the Trinity</i> (1756) and <i>The Grand Analogy</i> + (1793).</p> + + <p><a name="Nt_538" href="#NtA_538">[538]</a> Robert Spearman (1703-1761) + was a pupil of John Hutchinson, and not only edited his works but wrote + his life. He wrote a work against the Newtonian physics, entitled <i>An + Enquiry after Philosophy and Theology</i> (Edinburgh, 1755), besides the + <i>Letters to a Friend concerning the Septuagint Translation</i> + (Edinburgh, 1759) to which De Morgan refers.</p> + + <p><a name="Nt_539" href="#NtA_539">[539]</a> A writer of no importance, + at least in the minds of British biographers.</p> + + <p><a name="Nt_540" href="#NtA_540">[540]</a> Alexander Catcott + (1725-1779), a theologian and geologist, wrote not only a work on the + creation (1756) but a <i>Treatise on the Deluge</i> (1761, with a second + edition in 1768). Sir Charles Lyell considered the latter work a valuable + contribution to geology.</p> + + <p><a name="Nt_541" href="#NtA_541">[541]</a> James Robertson + (1714-1795), professor of Hebrew at the University of Edinburgh. Probably + De Morgan refers to his <i>Grammatica Linguae Hebrææ</i> (Edinburgh, + 1758; with a second edition in 1783). He also wrote <i>Clavis + Pentateuchi</i> (1770).</p> + + <p><a name="Nt_542" href="#NtA_542">[542]</a> Benjamin Holloway (c. + 1691-1759), a geologist and theologian. He translated Woodward's + <i>Naturalis Historia Telluris</i>, and was introduced by Woodward to + Hutchinson. The work referred to by De Morgan appeared at Oxford in two + volumes in 1754.</p> + + <p><a name="Nt_543" href="#NtA_543">[543]</a> His work was <i>The + Christian plan exhibited in the interpretation of Elohim: with + observations upon a few other matters relative to the same subject</i>, + Oxford, 1752, with a second edition in 1755.</p> + + <p><a name="Nt_544" href="#NtA_544">[544]</a> Duncan Forbes (1685-1747) + studied Oriental languages and Civil law at Leyden. He was Lord President + of the Court of Sessions (1737). He wrote a number of theological + works.</p> + + <p><a name="Nt_545" href="#NtA_545">[545]</a> Should be 1756.</p> + + <p><a name="Nt_546" href="#NtA_546">[546]</a> Edward Henry Bickersteth + (1825-1906), bishop of Exeter (1885-1900); published <i>The Rock of Ages; + or scripture testimony to the one Eternal Godhead of the Father, and of + the Son, and of the Holy Ghost</i> at Hampstead in 1859. A second edition + appeared at London in 1860.</p> + + <p><a name="Nt_547" href="#NtA_547">[547]</a> Thomas Sadler (1822-1891) + took his Ph.D. at Erlangen in 1844, and became a Unitarian minister at + Hampstead, where Bickersteth's work was published. Besides writing the + <i>Gloria Patri</i> (1859), he edited Crabb Robinson's Diaries.</p> + + <p><a name="Nt_548" href="#NtA_548">[548]</a> This was his <i>Virgil's + Bucolics and the two first Satyrs of Juvenal</i>, 1634.</p> + + <p><a name="Nt_549" href="#NtA_549">[549]</a> Possibly in his <i>Twelve + Questions or Arguments drawn out of Scripture, wherein the commonly + received Opinion touching the Deity of the Holy Spirit is clearly and + fully refuted</i>, 1647. This was his first heretical work, and it was + followed by a number of others that were written during the intervals in + which the Puritan parliament allowed him out of prison. It was burned by + the hangman as blasphemous. Biddle finally died in prison, unrepentant to + the last.</p> + + <p><a name="Nt_550" href="#NtA_550">[550]</a> The first edition of the + <span class="correction" title="text reads `anonynous'">anonymous</span> + <span title="Haireseôn anastasis" class="grk" + >Ἁιρεσεων + ἀναστασις</span> (by + Vicars?) appeared in 1805.</p> + + <p><a name="Nt_551" href="#NtA_551">[551]</a> Possibly by Thomas Pearne + (c. 1753-1827), a fellow of St. Peter's College, Cambridge, and a + Unitarian minister.</p> + + <p><a name="Nt_552" href="#NtA_552">[552]</a> Thomas Wentworth, Earl of + Strafford, was borne in London in 1593, and was executed there in 1641. + He was privy councilor to Charles I, and was Lord Deputy of Ireland. On + account of his repressive measures to uphold the absolute power of the + king he was impeached by the Long Parliament and was executed for + treason. The essence of his defence is in the sentence quoted by De + Morgan, to which Pym replied that taken as a whole, the acts tended to + show an intention to change the government, and this was in itself + treason.</p> + + <p><a name="Nt_553" href="#NtA_553">[553]</a> The name assumed by a + writer who professed to give a mathematical explanation of the Trinity, + see farther on.—S. E. De M.</p> + + <p><a name="Nt_554" href="#NtA_554">[554]</a> Sabellius (fl. 230 A.D.) + was an early Christian of Libyan origin. He taught that Father, Son, and + Holy Spirit were different names for the same person.</p> + + <p><a name="Nt_555" href="#NtA_555">[555]</a> Sir Richard Phillips was + born in London in 1767 (not 1768 as stated above), and died there in + 1840. He was a bookseller and printer in Leicester, where he also edited + a radical newspaper. He went to London to live in 1795 and started the + <i>Monthly Magazine</i> there in 1796. Besides the works mentioned by De + Morgan he wrote on law and economics.</p> + + <p><a name="Nt_556" href="#NtA_556">[556]</a> It was really eighteen + months.</p> + + <p><a name="Nt_557" href="#NtA_557">[557]</a> While he was made sheriff + in 1807 he was not knighted until the following year.</p> + + <p><a name="Nt_558" href="#NtA_558">[558]</a> James Mitchell (c. + 1786-1844) was a London actuary, or rather a Scotch actuary living a good + part of his life in London. Besides the work mentioned he compiled a + <i>Dictionary of Chemistry, Mineralogy, and Geology</i> (1823), and wrote + <i>On the Plurality of Worlds</i> (1813) and <i>The Elements of + Astronomy</i> (1820).</p> + + <p><a name="Nt_559" href="#NtA_559">[559]</a> Richarda Smith, wife of Sir + George Biddell Airy (see note <a href="#Nt_129">129</a>, page <a + href="#page85">85</a>) the astronomer. In 1835 Sir Robert Peel offered a + pension of £300 a year to Airy, who requested that it be settled on his + wife.</p> + + <p><a name="Nt_560" href="#NtA_560">[560]</a> Mary Fairfax (1780-1872) + married as her second husband Dr. William Somerville. In 1826 she + presented to the Royal Society a paper on <i>The Magnetic Properties of + the Violet Rays of the Solar Spectrum</i>, which attracted much + attention. It was for her <i>Mechanism of the Heavens</i> (1831), a + popular translation of Laplace's <i>Mécanique Céleste</i>, that she was + pensioned.</p> + + <p><a name="Nt_561" href="#NtA_561">[561]</a> Dominique François Jean + Arago (1786-1853) the celebrated French astronomer and physicist.</p> + + <p><a name="Nt_562" href="#NtA_562">[562]</a> For there is a well-known + series</p> + + <div class="poem"> + <div class="stanza"> + <p>1 + 1/2<sup>2</sup> + 1/3<sup>2</sup> + ... = <span class="grk">π</span><sup>2</sup>/6.</p> + </div> + </div> + <p>If, therefore, the given series equals 1, we have</p> + + <div class="poem"> + <div class="stanza"> + <p>2 = 1/6 <span class="grk">π</span><sup>2</sup></p> + </div> + + <div class="stanza"> + <p>or <span class="grk">π</span><sup>2</sup> = 12,</p> + </div> + + <div class="stanza"> + <p>whence <span class="grk">π</span> = 2 √3.</p> + </div> + </div> + <p>But c = <span class="grk">π</span>d, and twice the diagonal of a + cube on the diameter is 2d √3.</p> + + <p><a name="Nt_563" href="#NtA_563">[563]</a> There was a second edition + in 1821.</p> + + <p><a name="Nt_564" href="#NtA_564">[564]</a> London, 1830.</p> + + <p><a name="Nt_565" href="#NtA_565">[565]</a> He was a resident of + Chatham, and seems to have published no other works.</p> + + <p><a name="Nt_566" href="#NtA_566">[566]</a> Richard Whately (1787-1863) + was, as a child, a calculating prodigy (see note <a + href="#Nt_132">132</a>, page <a href="#page86">86</a>), but lost the + power as is usually the case with well-balanced minds. He was a fellow of + Oriel College, Oxford, and in 1825 became principal of St. Alban Hall. He + was a friend of Newman, Keble, and others who were interested in the + religious questions of the day. He became archbishop of Dublin in 1831. + He was for a long time known to students through his <i>Logic</i> (1826) + and <i>Rhetoric</i> (1828).</p> + + <p><a name="Nt_567" href="#NtA_567">[567]</a> William King, D.C.L. + (1663-1712), student at Christ Church, Oxford, and celebrated as a wit + and scholar. His <i>Dialogues of the Dead</i> (1699) is a satirical + attack on Bentley.</p> + + <p><a name="Nt_568" href="#NtA_568">[568]</a> Thomas Ebrington + (1760-1835) was a fellow of Trinity College, Dublin, and taught divinity, + mathematics, and natural philosophy there. He became provost of the + college in 1811, bishop of Limerick in 1820, and bishop of Leighlin and + Ferns in 1822. His edition of Euclid was reprinted a dozen times. The + <i>Reply to John Search's Considerations on the Law of Libel</i> appeared + at Dublin in 1834.</p> + + <p><a name="Nt_569" href="#NtA_569">[569]</a> Joseph Blanco White + (1775-1841) was the son of an Irishman living in Spain. He was born at + Seville and studied for orders there, being ordained priest in 1800. He + lost his faith in the Roman Catholic Church, and gave up the ministry, + escaping to England at the time of the French invasion. At London he + edited <i>Español</i>, a patriotic journal extensively circulated in + Spain, and for this service he was pensioned after the expulsion of the + French. He then studied at Oriel College, Oxford, and became intimate + with men like Whately, Newman, and Keble. In 1835 he became a Unitarian. + Among his theological writings is his <i>Evidences against + Catholicism</i> (1825). The "rejoinder" to which De Morgan refers + consisted of two letters: <i>The law of anti-religious Libel + reconsidered</i> (Dublin, 1834) and <i>An Answer to some Friendly Remarks + on "The Law of Anti-Religious Libel Reconsidered"</i> (Dublin, 1834).</p> + + <p><a name="Nt_570" href="#NtA_570">[570]</a> The work was translated + from the French.</p> + + <p><a name="Nt_571" href="#NtA_571">[571]</a> J. Hoëné Wronski + (1778-1853) served, while yet a mere boy, as an artillery officer in + Kosciusko's army (1791-1794). He was imprisoned after the battle of + Maciejowice. He afterwards lived in Germany, and (after 1810) in Paris. + For the bibliography of his works see S. Dickstein's article in the + <i>Bibliotheca Mathematica</i>, vol. VI (2), page 48.</p> + + <p><a name="Nt_572" href="#NtA_572">[572]</a> Perhaps referring to his + <i>Introduction à la philosophie des mathématiques</i> (1811).</p> + + <p><a name="Nt_573" href="#NtA_573">[573]</a> Read "equation of the."</p> + + <p><a name="Nt_574" href="#NtA_574">[574]</a> Thomas Young (1773-1829), + physician and physicist, sometimes called the founder of physiological + optics. He seems to have initiated the theory of color blindness that was + later developed by Helmholtz. The attack referred to was because of his + connection with the Board of Longitude, he having been made (1818) + superintendent of the Nautical Almanac and secretary of the Board. He + opposed introducing into the Nautical Almanac anything not immediately + useful to navigation, and this antagonized many scientists.</p> + + <p><a name="Nt_575" href="#NtA_575">[575]</a> Isaac Milner (1750-1820) + was professor of natural philosophy at Cambridge (1783) and later became, + as De Morgan states, president of Queens' College (1788). In 1791 he + became dean of Carlisle, and in 1798 Lucasian professor of mathematics. + His chief interest was in chemistry and physics, but he contributed + nothing of importance to these sciences or to mathematics.</p> + + <p><a name="Nt_576" href="#NtA_576">[576]</a> Thomas Perronet Thompson + (1783-1869), fellow of Queens' College, Cambridge, saw service in Spain + and India, but after 1822 lived in England. He became major general in + 1854, and general in 1868. Besides some works on economics and politics + he wrote a <i>Geometry without Axioms</i> (1830) that De Morgan includes + later on in his <i>Budget</i>. In it Thompson endeavored to prove the + parallel postulate.</p> + + <p><a name="Nt_577" href="#NtA_577">[577]</a> De Morgan's father-in-law. + See note <a href="#Nt_441">441</a>, page <a href="#page196">196</a>.</p> + + <p><a name="Nt_578" href="#NtA_578">[578]</a> Johann Friedrich Herbart + (1776-1841), successor of Kant as professor of philosophy at Königsberg + (1809-1833), where he established a school of pedagogy. From 1833 until + his death he was professor of philosophy at Göttingen. The title of the + pamphlet is: <i>De Attentionis mensura causisque primariis. Psychologiae + principia statica et mechanica exemplo illustraturus.... Regiomonti,... + 1822</i>. The formulas in question are given on pages 15 and 17, and De + Morgan has omitted the preliminary steps, which are, for the first + one:</p> + + <div class="poem"> + <div class="stanza"> + <p><span class="grk">β</span> (<span class="grk">φ</span> - <i>z</i>) <span class="grk">δ</span><i>t</i> = <span class="grk">δ</span><i>z</i></p> + </div> + + <div class="stanza"> + <p>unde <span class="grk">β</span><i>t</i>= Const / (<span class="grk">φ</span> - <i>z</i>).</p> + </div> + + <div class="stanza"> + <p>Pro <i>t</i> = 0 etiam <i>z</i> = 0; hinc <span class="grk">β</span><i>t</i> = log <span class="grk">φ</span>/(<span class="grk">φ</span> - <i>z</i>).</p> + </div> + + <div class="stanza"> + <p><i>z</i> = <span class="grk">φ</span> (1 - <span class="grk">ε</span><sup>-<span class="grk">β</span><i>t</i></sup>);</p> + </div> + + <div class="stanza"> + <p>et <span class="grk">δ</span><i>z</i>/<span class="grk">δ</span><i>t</i> = <span class="grk">β</span><span class="grk">φ</span><span class="grk">ε</span><sup>-<span class="grk">β</span><i>t</i></sup></p> + </div> + </div> + <p>These are, however, quite elementary as compared with other portions + of the theory.</p> + + <p><a name="Nt_579" href="#NtA_579">[579]</a> See note <a + href="#Nt_371">371</a>, page <a href="#page168">168</a>.</p> + + <p><a name="Nt_580" href="#NtA_580">[580]</a> William Law (1686-1761) was + a clergyman, a fellow of Emanuel College, Cambridge, and in later life a + convert to Behmen's philosophy. He was so free in his charities that the + village in which he lived became so infested by beggars that he was urged + by the citizens to leave. He wrote <i>A serious call to a devout and holy + life</i> (1728).</p> + + <p><a name="Nt_581" href="#NtA_581">[581]</a> He was a curate at + Cheshunt, and wrote the <i>Spiritual voice to the Christian Church and to + the Jews</i> (London, 1760), <i>A second warning to the world by the + Spirit of Prophecy</i> (London, 1760), and <i>Signs of the Times; or a + Voice to Babylon</i> (London, 1773).</p> + + <p><a name="Nt_582" href="#NtA_582">[582]</a> His real name was Thomas + Vaughan (1622-1666). He was a fellow of Jesus College, Oxford, taking + orders, but was deprived of his living on account of drunkenness. He + became a mystic philosopher and gave attention to alchemy. His works had + a large circulation, particularly on the continent. He wrote <i>Magia + Adamica</i> (London, 1650), <i>Euphrates; or the Waters of the East</i> + (London, 1655), and <i>The Chymist's key to shut, and to open; or the + True Doctrine of Corruption and Generation</i> (London, 1657).</p> + + <p><a name="Nt_583" href="#NtA_583">[583]</a> Emanuel Swedenborg, or + Svedberg (1688-1772) the mystic. It is not commonly known to + mathematicians that he was one of their guild, but he wrote on both + mathematics and chemistry. Among his works are the <i>Regelkonst eller + algebra</i> (Upsala, 1718) and the <i>Methodus nova inveniendi + longitudines locorum, terra marique, ope lunae</i> (Amsterdam, 1721, + 1727, and 1766). After 1747 he devoted his attention to mystic + philosophy.</p> + + <p><a name="Nt_584" href="#NtA_584">[584]</a> Pierre Simon Laplace + (1749-1827), whose <i>Exposition du système du monde</i> (1796) and + <i>Traité de mécanique celeste</i> (1799) are well known.</p> + + <p><a name="Nt_585" href="#NtA_585">[585]</a> See note <a + href="#Nt_117">117</a>, page <a href="#page76">76</a>.</p> + + <p><a name="Nt_586" href="#NtA_586">[586]</a> John Dalton (1766-1844), + who taught mathematics and physics at New College, Manchester (1793-1799) + and was the first to state the law of the expansion of gases known by his + name and that of Gay-Lussac. His <i>New system of Chemical Philosophy</i> + (Vol. I, pt. i, 1808; pt. ii, 1810; vol. II, 1827) sets forth his atomic + theory.</p> + + <p><a name="Nt_587" href="#NtA_587">[587]</a> Howison was a poet and + philosopher. He lived in Edinburgh and was a friend of Sir Walter Scott. + This work appeared in 1822.</p> + + <p><a name="Nt_588" href="#NtA_588">[588]</a> He was a shoemaker, born + about 1765 at Haddiscoe, and his "astro-historical" lectures at Norwich + attracted a good deal of attention at one time. He traced all geologic + changes to differences in the inclination of the earth's axis to the + plane of its orbit. Of the works mentioned by De Morgan the first + appeared at Norwich in 1822-1823, and there was a second edition in 1824. + The second appeared in 1824-1825. The fourth was <i>Urania's Key to the + Revelation; or the analyzation of the writings of the Jews...</i>, and + was first published at Norwich in 1823, there being a second edition at + London in 1833. His books were evidently not a financial success, for + Mackey died in an almshouse at Norwich.</p> + + <p><a name="Nt_589" href="#NtA_589">[589]</a> Godfrey Higgins + (1773-1833), the archeologist, was interested in the history of religious + beliefs and in practical sociology. He wrote <i>Horae Sabbaticae</i> + (1826), <i>The Celtic Druids</i> (1827 and 1829), and <i>Anacalypsis, an + attempt to draw aside the veil of the Saitic Isis; or an Inquiry into the + Origin of Languages, Nations, and Religions</i> (posthumously published, + 1836), and other works. See also page <a href="#page274">274</a>, + <i>infra</i>.</p> + + <p><a name="Nt_590" href="#NtA_590">[590]</a> The work also appeared in + French. Wirgman wrote, or at least began, two other works: + <i>Divarication of the New Testament into Doctrine and History; part I, + The Four Gospels</i> (London, 1830), and <i>Mental Philosophy; part I, + Grammar of the five senses; being the first step to infant education</i> + (London, 1838).</p> + + <p><a name="Nt_591" href="#NtA_591">[591]</a> He was born at Shandrum, + County Limerick, and supported himself by teaching writing and + arithmetic. He died in an almshouse at Cork.</p> + + <p><a name="Nt_592" href="#NtA_592">[592]</a> George Boole (1815-1864), + professor of mathematics at Queens' College, Cork. His <i>Laws of + Thought</i> (1854) was the first work on the algebra of logic.</p> + + <p><a name="Nt_593" href="#NtA_593">[593]</a> Oratio Grassi (1582-1654), + the Jesuit who became famous for his controversy with Galileo over the + theory of comets. Galileo ridiculed him in <i>Il Saggiatore</i>, although + according to the modern view Grassi was the more nearly right. It is said + that the latter's resentment led to the persecution of Galileo.</p> + + <p><a name="Nt_594" href="#NtA_594">[594]</a> De Morgan might have found + much else for his satire in the letters of Walsh. He sought, in his + <i>Theory of Partial Functions</i>, to substitute "partial equations" for + the differential calculus. In his diary there is an entry: "Discovered + the general solution of numerical equations of the fifth degree at 114 + Evergreen Street, at the Cross of Evergreen, Cork, at nine o'clock in the + forenoon of July 7th, 1844; exactly twenty-two years after the invention + of the Geometry of Partial Equations, and the expulsion of the + differential calculus from Mathematical Science."</p> + + <p><a name="Nt_595" href="#NtA_595">[595]</a> "It has been ordered, sir, + it has been ordered."</p> + + <p><a name="Nt_596" href="#NtA_596">[596]</a> Bartholomew Prescot was a + Liverpool accountant. De Morgan gives this correct spelling on page <a + href="#page278">278</a>. He died after 1849. His <i>Inverted Scheme of + Copernicus</i> appeared in Liverpool in 1822.</p> + + <p><a name="Nt_597" href="#NtA_597">[597]</a> Robert Taylor (1784-1844) + had many more ups and downs than De Morgan mentions. He was a priest of + the Church of England, but resigned his parish in 1818 after preaching + against Christianity. He soon recanted and took another parish, but was + dismissed by the Bishop almost immediately on the ground of heresy. As + stated in the text, he was convicted of blasphemy in 1827 and was + sentenced to a year's imprisonment, and again for two years on the same + charge in 1831. He then married a woman who was rich in money and in + years, and was thereupon sued for breach of promise by another woman. To + escape paying the judgment that was rendered against him he fled to Tours + where he took up surgery.</p> + + <p><a name="Nt_598" href="#NtA_598">[598]</a> Herbert Marsh, Bishop of + Peterborough. See note <a href="#Nt_449">449</a> on page <a + href="#page199">199</a>.</p> + + <p><a name="Nt_599" href="#NtA_599">[599]</a> "Argument from the + prison."</p> + + <p><a name="Nt_600" href="#NtA_600">[600]</a> Richard Carlile + (1790-1843), one of the leading radicals of his time. He published Hone's + parodies (see note <a href="#Nt_250">250</a>, page <a + href="#page124">124</a>) after they had been suppressed, and an edition + of Thomas Paine (1818). He was repeatedly imprisoned, serving nine years + in all. His continued conflict with the authorities proved a good + advertisement for his bookshop.</p> + + <p><a name="Nt_601" href="#NtA_601">[601]</a> Wilhelm Ludwig Christmann + (1780-1835) was a protestant clergyman and teacher of mathematics. For a + while he taught under Pestalozzi. Disappointed in his ambition to be + professor of mathematics at Tubingen, he became a confirmed misanthrope + and is said never to have left his house during the last ten years of his + life. He wrote several works: <i>Ein Wort über Pestalozzi und + Pestalozzismus</i> (1812); <i>Ars cossae promota</i> (1814); + <i>Philosophia cossica</i> (1815); <i>Aetas argentea cossae</i> (1819); + <i>Ueber Tradition und Schrift, Logos und Kabbala</i> (1829), besides the + one mentioned above. The word <i>coss</i> in the above titles was a + German name for algebra, from the Italian <i>cosa</i> (thing), the name + for the unknown quantity. It appears in English in the early name for + algebra, "the cossic art."</p> + + <p><a name="Nt_602" href="#NtA_602">[602]</a> See note <a + href="#Nt_174">174</a>, page <a href="#page101">101</a>.</p> + + <p><a name="Nt_603" href="#NtA_603">[603]</a> See note <a + href="#Nt_589">589</a>, page <a href="#page257">257</a>.</p> + + <p><a name="Nt_604" href="#NtA_604">[604]</a> He seems to have written + nothing else.</p> + + <p><a name="Nt_605" href="#NtA_605">[605]</a> See note <a + href="#Nt_596">596</a> on page <a href="#page270">270</a>. The name is + here spelled correctly.</p> + + <p><a name="Nt_606" href="#NtA_606">[606]</a> Joseph Jacotot (1770-1840), + the father of this Fortuné Jacotot, was an infant prodigy. At nineteen he + was made professor of the humanities at Dijon. He served in the army, and + then became professor of mathematics at Dijon. He continued in his chair + until the restoration of the Bourbons, and then fled to Louvain. It was + here that he developed the method with which his name is usually + connected. He wrote a <i>Mathématiques</i> in 1827, which went through + four editions. The <i>Epitomé</i> is by his son, Fortuné.</p> + + <p><a name="Nt_607" href="#NtA_607">[607]</a> He wrote on educational + topics and a <i>Sacred History</i> that went through several + editions.</p> + + <p><a name="Nt_608" href="#NtA_608">[608]</a> "All is in all."</p> + + <p><a name="Nt_609" href="#NtA_609">[609]</a> "Know one thing and refer + everything else to it," as it is often translated.</p> + + <p><a name="Nt_610" href="#NtA_610">[610]</a> A writer of no + reputation.</p> + + <p><a name="Nt_611" href="#NtA_611">[611]</a> Sir John Lubbock + (1803-1865), banker, scientist, publicist, astronomer, one of the + versatile men of his time.</p> + + <p><a name="Nt_612" href="#NtA_612">[612]</a> See note <a + href="#Nt_165">165</a>, page <a href="#page99">99</a>.</p> + + <p><a name="Nt_613" href="#NtA_613">[613]</a> "Those about to die salute + you."</p> + + <p><a name="Nt_614" href="#NtA_614">[614]</a> Georges Louis Leclerc + Buffon (1707-1788), the well-known biologist. He also experimented with + burning mirrors, his results appearing in his <i>Invention des miroirs + ardens pour brûler à une grande distance</i> (1747). The reference here + may be to his <i>Resolution des problèmes qui regardent le jeu du franc + carreau</i> (1733). The prominence of his <i>Histoire naturelle</i> (36 + volumes, 1749-1788) has overshadowed the credit due to him for his + translation of Newton's work on Fluxions.</p> + + <p><a name="Nt_615" href="#NtA_615">[615]</a> See page <a + href="#page285">285</a>. This article was a supplement to No. 14 in the + <i>Athenæum</i> Budget.—A. De M.</p> + + <p><a name="Nt_616" href="#NtA_616">[616]</a> There are many similar + series and products. Among the more interesting are the following:</p> + +<table class="math"><tr><td> +<span class="grk">π</span><br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />2</td><td>=</td><td>2·2·4·4·6·6·8...<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />1·3·3·5·5·7·7...</td><td>, +</td></tr></table> + +<table class="math"><tr><td> +<span class="grk">π</span>-3<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />4</td><td>=</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />2·3·4</td><td>-</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />4·5·6</td><td>+</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />6·7·8</td><td>-..., +</td></tr></table> + +<table class="math"><tr><td> +<span class="grk">π</span><br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />6</td><td>=</td><td><img src="images/$sqrt.png" style="height:4ex; width:0.5em" alt="square root" /></td><td></td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3</td><td>·</td><td><img src="images/$lbracket.png" style="height:4ex; width:0.5em" alt="left bracket" /></td><td>1 -</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3·3</td><td>+</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3<sup>2</sup>·5</td><td>-</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3<sup>3</sup>·7</td><td>+</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3<sup>4</sup>·9</td><td>- ...</td><td><img src="images/$rbracket.png" style="height:4ex; width:0.5em" alt="right bracket" /></td><td>, +</td></tr></table> + +<table class="math"><tr><td> +<span class="grk">π</span><br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />4</td><td>= 4</td><td><img src="images/$lbracket.png" style="height:4ex; width:0.5em" alt="left bracket" /></td><td></td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />5</td><td>-</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3·5<sup>3</sup></td><td>+</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />5·5<sup>5</sup></td><td>-</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />7·5<sup>7</sup></td><td>+ ...</td><td><img src="images/$rbracket.png" style="height:4ex; width:0.5em" alt="right bracket" /></td><td> - </td><td><img src="images/$lbracket.png" style="height:4ex; width:0.5em" alt="left bracket" /></td><td></td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />239</td><td>-</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />3·239<sup>3</sup></td><td>+</td><td>1<br /><img src="images/$line.png" style="width:100%; height:1px; line-height:1px;" alt="/" /><br />5·239<sup>5</sup></td><td>- ...</td><td><img src="images/$rbracket.png" style="height:4ex; width:0.5em" alt="right bracket" /></td><td>. +</td></tr></table> + + <p><a name="Nt_617" href="#NtA_617">[617]</a> "To a privateer, a + privateer and a half."</p> + + <p><a name="Nt_618" href="#NtA_618">[618]</a> Joshua Milne (1776-1851) + was actuary of the Sun Life Assurance Society. He wrote <i>A Treatise on + the Valuation of Annuities and Assurances on Lives and Survivorships; on + the Construction of tables of mortality; and on the Probabilities and + Expectations of Life</i>, London, 1815. Upon the basis of the Carlisle + bills of mortality of Dr. Heysham he reconstructed the mortality tables + then in use and which were based upon the Northampton table of Dr. Price. + His work revolutionized the actuarial science of the time. In later years + he devoted his attention to natural history.</p> + + <p><a name="Nt_619" href="#NtA_619">[619]</a> See note <a + href="#Nt_576">576</a>, page <a href="#page252">252</a>. He also wrote + the <i>Theory of Parallels. The proof of Euclid's axiom looked for in the + properties of the equiangular spiral</i> (London, 1840), which went + through four editions, and the <i>Theory of Parallels. The proof that the + three angles of a triangle are equal to two right angles looked for in + the inflation of the sphere</i> (London, 1853), of which there were three + editions.</p> + + <p><a name="Nt_620" href="#NtA_620">[620]</a> For the latest summary, see + W. B. Frankland, <i>Theories of Parallelism, an historical critique</i>, + Cambridge, 1910.</p> + + <p><a name="Nt_621" href="#NtA_621">[621]</a> Joseph Louis Lagrange + (1736-1813), author of the <i>Mécanique analytique</i> (1788), <i>Théorie + des functions analytiques</i> (1797), <i>Traité de la résolution des + équations numériques de tous degrés</i> (1798), <i>Leçons sur le calcul + des fonctions</i> (1806), and many memoirs. Although born in Turin and + spending twenty of his best years in Germany, he is commonly looked upon + as the great leader of French mathematicians. The last twenty-seven years + of his life were spent in Paris, and his remarkable productivity + continued to the time of his death. His genius in the theory of numbers + was probably never excelled except by Fermat. He received very high + honors at the hands of Napoleon and was on the first staff of the Ecole + polytechnique (1797).</p> + + <p><a name="Nt_622" href="#NtA_622">[622]</a> "I shall have to think it + over again."</p> + + <p><a name="Nt_623" href="#NtA_623">[623]</a> Henry Goulburn (1784-1856) + held various government posts. He was under-secretary for war and the + colonies (1813), commissioner to negotiate peace with America (1814), + chief secretary to the Lord Lieutenant of Ireland (1821), and several + times Chancellor of the Exchequer. On the occasion mentioned by De Morgan + he was standing for parliament, and was successful.</p> + + <p><a name="Nt_624" href="#NtA_624">[624]</a> On Drinkwater Bethune see + note <a href="#Nt_165">165</a>, page <a href="#page99">99</a>.</p> + + <p><a name="Nt_625" href="#NtA_625">[625]</a> Charles Henry Cooper + (1808-1866) was a biographer and antiquary. He was town clerk of + Cambridge (1849-1866) and wrote the <i>Annals of Cambridge</i> + (1842-1853). His <i>Memorials of Cambridge</i> (1874) appeared after his + death. Thompson Cooper was his son, and the two collaborated in the + <i>Athenae Cantabrigiensis</i> (1858).</p> + + <p><a name="Nt_626" href="#NtA_626">[626]</a> William Yates Peel + (1789-1858) was a brother of Sir Robert Peel, he whose name degenerated + into the familiar title of the London "Bobby" or "Peeler." Yates Peel was + a member of parliament almost continuously from 1817 to 1852. He + represented Cambridge at Westminster from 1831 to 1835.</p> + + <p><a name="Nt_627" href="#NtA_627">[627]</a> Henry John Temple, third + Viscount of Palmerston (1784-1865), was member for Cambridge in 1811, + 1818, 1820, 1826 (defeating Goulburn), and 1830. He failed of reelection + in 1831 because of his advocacy of reform. This must have been the time + when Goulburn defeated him. He was Foreign Secretary (1827) and Secretary + of State for Foreign Affairs (1830-1841, and 1846-1851). It is said of + him that he "created Belgium, saved Portugal and Spain from absolutism, + rescued Turkey from Russia and the highway to India from France." He was + Prime Minister almost continuously from 1855 to 1865, a period covering + the Indian Mutiny and the American Civil War.</p> + + <p><a name="Nt_628" href="#NtA_628">[628]</a> William Cavendish, seventh + Duke of Devonshire (1808-1891). He was member for Cambridge from 1829 to + 1831, but was defeated in 1831 because he had favored parliamentary + reform. He became Earl of Burlington in 1834, and Duke of Devonshire in + 1858. He was much interested in the promotion of railroads and in the + iron and steel industries.</p> + + <p><a name="Nt_629" href="#NtA_629">[629]</a> Richard Sheepshanks + (1794-1855) was a brother of John Sheepshanks the benefactor of art. (See + note <a href="#Nt_314">314</a>, p. <a href="#page147">147</a>.) He was a + fellow of Trinity College, Cambridge, a fellow of the Royal Society and + secretary of the Astronomical Society. Babbage (See note <a + href="#Nt_469">469</a>, p. <a href="#page207">207</a>) suspected him of + advising against the government support of his calculating machine and + attacked him severely in his <i>Exposition of 1851</i>, in the chapter on + <i>The Intrigues of Science</i>. Babbage also showed that Sheepshanks got + an astronomical instrument of French make through the custom house by + having Troughton's (See note <a href="#Nt_332">332</a>, page <a + href="#page152">152</a>) name engraved on it. Sheepshanks admitted this + second charge, but wrote a <i>Letter in Reply to the Calumnies of Mr. + Babbage</i>, which was published in 1854. He had a highly controversial + nature.</p> + + <p><a name="Nt_630" href="#NtA_630">[630]</a> See note <a + href="#Nt_469">469</a>, page <a href="#page207">207</a>. The work + referred to is <i>Passages from the Life of a Philosopher</i>, London, + 1864.</p> + + <p><a name="Nt_631" href="#NtA_631">[631]</a> Drinkwater Bethune. See + note <a href="#Nt_165">165</a>, page <a href="#page99">99</a>.</p> + + <p><a name="Nt_632" href="#NtA_632">[632]</a> Siméon-Denis Poisson + (1781-1840) was professor of calculus and mechanics at the Ecole + polytechnique. He was made a baron by Napoleon, and was raised to the + peerage in 1837. His chief works are the <i>Traité de mécanìque</i> + (1811) and the <i>Traité mathématique de la chaleur</i> (1835).</p> + + <p><a name="Nt_633" href="#NtA_633">[633]</a> "As to M. Poisson, I really + wish I had a thousandth part of his mathematical knowledge that I might + prove my system to the incredulous."</p> + + <p><a name="Nt_634" href="#NtA_634">[634]</a> This list includes most of + the works of Antoine-Louis-Guénard Demonville. There was also the + <i>Nouveau système du monde ... et hypothèses conformes aux expériences + sur les vents, sur la lumière et sur le fluide électro-magnétique</i>, + Paris, 1830.</p> + + <p><a name="Nt_635" href="#NtA_635">[635]</a> Paris, 1835.</p> + + <p><a name="Nt_636" href="#NtA_636">[636]</a> Paris, 1833.</p> + + <p><a name="Nt_637" href="#NtA_637">[637]</a> The second part appeared in + 1837. There were also editions in 1850 and 1852, and one edition appeared + without date.</p> + + <p><a name="Nt_638" href="#NtA_638">[638]</a> Paris, 1842.</p> + + <p><a name="Nt_639" href="#NtA_639">[639]</a> Parsey also wrote <i>The + Art of Miniature Painting on Ivory</i> (1831), <i>Perspective + Rectified</i> (1836), and <i>The Science of Vision</i> (1840), the third + being a revision of the second.</p> + + <p><a name="Nt_640" href="#NtA_640">[640]</a> William Ritchie (1790-1837) + was a physicist who had studied at Paris under Biot and Gay-Lussac. He + contributed several papers on electricity, heat, and elasticity, and was + looked upon as a good experimenter. Besides the geometry he wrote the + <i>Principles of the Differential and Integral Calculus</i> (1836).</p> + + <p><a name="Nt_641" href="#NtA_641">[641]</a> Alfred Day (1810-1849) was + a man who was about fifty years ahead of his time in his attempt to get + at the logical foundations of geometry. It is true that he laid himself + open to criticism, but his work was by no means bad. He also wrote <i>A + Treatise on Harmony</i> (1849, second edition 1885), <i>The Rotation of + the Pendulum</i> (1851), and several works on Greek and Latin + Grammar.</p> + + <p><a name="Nt_642" href="#NtA_642">[642]</a> Walter Forman wrote a + number of controversial tracts. His first seems to have been <i>A plan + for improving the Revenue without adding to the burdens of the + people</i>, a letter to Canning in 1813. He also wrote <i>A New Theory of + the Tides</i> (1822). His <i>Letter to Lord John Russell, on Lord + Brougham's most extraordinary conduct; and another to Sir J. Herschel, on + the application of Kepler's third law</i> appeared in 1832.</p> + + <p><a name="Nt_643" href="#NtA_643">[643]</a> Lord John Russell + (1792-1878) first Earl Russell, was one of the strongest supporters of + the reform measures of the early Victorian period. He became prime + minister in 1847, and again in 1865.</p> + + <p><a name="Nt_644" href="#NtA_644">[644]</a> Lauder seems never to have + written anything else.</p> + + <p><a name="Nt_645" href="#NtA_645">[645]</a> See note <a + href="#Nt_22">22</a>, page <a href="#page40">40</a>.</p> + + <p><a name="Nt_646" href="#NtA_646">[646]</a> The names of Alphonso Cano + de Molina, Yvon, and Robert Sara have no standing in the history of the + subject beyond what would be inferred from De Morgan's remark.</p> + + <p><a name="Nt_647" href="#NtA_647">[647]</a> Claude Mydorge (1585-1647), + an intimate friend of Descartes, was a dilletante in mathematics who read + much but accomplished little. His <i>Récréations mathématiques</i> is his + chief work. Boncompagni published the "Problèmes de Mydorge" in his + <i>Bulletino</i>.</p> + + <p><a name="Nt_648" href="#NtA_648">[648]</a> Claude Hardy was born + towards the end of the 16th century and died at Paris in 1678. In 1625 he + edited the <i>Data Euclidis</i>, publishing the Greek text with a Latin + translation. He was a friend of Mydorge and Descartes, but an opponent of + Fermat.</p> + + <p><a name="Nt_649" href="#NtA_649">[649]</a> That is, in the + <i>Bibliotheca Realis</i> of Martin Lipen, or Lipenius (1630-1692), which + appeared in six folio volumes, at Frankfort, 1675-1685.</p> + + <p><a name="Nt_650" href="#NtA_650">[650]</a> See note <a + href="#Nt_29">29</a>, page <a href="#page43">43</a>.</p> + + <p><a name="Nt_651" href="#NtA_651">[651]</a> Baldassare Boncompagni + (1821-1894) was the greatest general collector of mathematical works that + ever lived, possibly excepting Libri. His magnificent library was + dispersed at his death. His <i>Bulletino</i> (1868-1887) is one of the + greatest source books on the history of mathematics that we have. He also + edited the works of Leonardo of Pisa.</p> + + <p><a name="Nt_652" href="#NtA_652">[652]</a> He seems to have attracted + no attention since De Morgan's search, for he is not mentioned in recent + bibliographies.</p> + + <p><a name="Nt_653" href="#NtA_653">[653]</a> Joseph-Louis Vincens de + Mouléon de Causans was born about the beginning of the l8th century. He + was a Knight of Malta, colonel in the infantry, prince of Conti, and + governor of the principality of Orange. His works on geometry are the + <i>Prospectus apologétique pour la quadrature du cercle</i> (1753), and + <i>La vraie géométrie transcendante</i> (1754).</p> + + <p><a name="Nt_654" href="#NtA_654">[654]</a> See note <a + href="#Nt_119">119</a>, page <a href="#page80">80</a>.</p> + + <p><a name="Nt_655" href="#NtA_655">[655]</a> See note <a + href="#Nt_120">120</a>, page <a href="#page81">81</a>.</p> + + <p><a name="Nt_656" href="#NtA_656">[656]</a> Lieut. William Samuel + Stratford (1791-1853), was in active service during the Napoleonic wars + but retired from the army in 1815. He was first secretary of the + Astronomical Society (1820) and became superintendent of the Nautical + Almanac in 1831. With Francis Baily he compiled a star catalogue, and + wrote on Halley's (1835-1836) and Encke's (1838) comets.</p> + + <p><a name="Nt_657" href="#NtA_657">[657]</a> See Sir J. Herschel's + <i>Astronomy</i>, p. 369.—A. De M.</p> + + <p><a name="Nt_658" href="#NtA_658">[658]</a> Captain Ross had just stuck + a bit of brass there.—A. De M.</p> + + <p>Sir James Clark Ross (1800-1862) was a rear admiral in the British + navy and an arctic and antarctic explorer of prominence. De Morgan's + reference is to Ross's discovery of the magnetic pole on June 1, 1831. In + 1838 he was employed by the Admiralty on a magnetic survey of the United + Kingdom. He was awarded the gold medal of the geographical societies of + London and Paris in 1842.</p> + + <p><a name="Nt_659" href="#NtA_659">[659]</a> John Partridge (1644-1715), + the well-known astrologer and almanac maker. Although bound to a + shoemaker in his early boyhood, he had acquired enough Latin at the age + of eighteen to read the works of the astrologers. He then mastered Greek + and Hebrew and studied medicine. In 1680 he began the publication of his + almanac, the <i>Merlinus Liberatus</i>, a book that acquired literary + celebrity largely through the witty comments upon it by such writers as + Swift and Steele.</p> + + <p><a name="Nt_660" href="#NtA_660">[660]</a> See note <a + href="#Nt_642">642</a> on page <a href="#page296">296</a>.</p> + + <p><a name="Nt_661" href="#NtA_661">[661]</a> William Woodley also + published several almanacs (1838, 1839, 1840) after his rejection by the + Astronomical Society in 1834.</p> + + <p><a name="Nt_662" href="#NtA_662">[662]</a> It appeared at London.</p> + + <p><a name="Nt_663" href="#NtA_663">[663]</a> The first edition appeared + in 1830, also at London.</p> + + <p><a name="Nt_664" href="#NtA_664">[664]</a> See note <a + href="#Nt_441">441</a>, page <a href="#page196">196</a>.</p> + + <p><a name="Nt_665" href="#NtA_665">[665]</a> Thomas Kerigan wrote <i>The + Young Navigator's Guide to the siderial and planetary parts of Nautical + Astronomy</i> (London, 1821, second edition 1828), a work on eclipses + (London, 1844), and the work on tides (London, 1847) to which De Morgan + refers.</p> + + <p><a name="Nt_666" href="#NtA_666">[666]</a> Jean Sylvain Bailly, who + was guillotined. See note <a href="#Nt_365">365</a>, page <a + href="#page166">166</a>.</p> + + <p><a name="Nt_667" href="#NtA_667">[667]</a> See note <a + href="#Nt_670">670</a>, page <a href="#page309">309</a>.</p> + + <p><a name="Nt_668" href="#NtA_668">[668]</a> Laurent seems to have had + faint glimpses of the modern theory of matter. He is, however, + unknown.</p> + + <p><a name="Nt_669" href="#NtA_669">[669]</a> See note <a + href="#Nt_133">133</a>, page <a href="#page87">87</a>.</p> + + <p><a name="Nt_670" href="#NtA_670">[670]</a> Francis Baily (1774-1844) + was a London stockbroker. His interest in science in general and in + astronomy in particular led to his membership in the Royal Society and to + his presidency of the Astronomical Society. He wrote on interest and + annuities (1808), but his chief works were on astronomy.</p> + + <p><a name="Nt_671" href="#NtA_671">[671]</a> If the story is correctly + told Baily must have enjoyed his statement that Gauss was "the oldest + mathematician now living." As a matter of fact he was then only 58, three + years the junior of Baily himself. Gauss was born in 1777 and died in + 1855, and Baily was quite right in saying that he was "generally thought + to be the greatest" mathematician then living.</p> + + <p><a name="Nt_672" href="#NtA_672">[672]</a> Margaret Cooke, who married + Flamsteed in 1692.</p> + + <p><a name="Nt_673" href="#NtA_673">[673]</a> John Brinkley (1763-1835), + senior wrangler, first Smith's prize-man (1788), Andrews professor of + astronomy at Dublin, first Astronomer Royal for Ireland (1792), F.R.S. + (1803), Copley medallist, president of the Royal Society and Bishop of + Cloyne. His <i>Elements of Astronomy</i> appeared in 1808.</p> + + <p><a name="Nt_674" href="#NtA_674">[674]</a> See note <a + href="#Nt_248">248</a>, page <a href="#page124">124</a>.</p> + + <p><a name="Nt_675" href="#NtA_675">[675]</a> See note <a + href="#Nt_276">276</a>, page <a href="#page133">133</a>.</p> + + <p><a name="Nt_676" href="#NtA_676">[676]</a> See note <a + href="#Nt_352">352</a>, page <a href="#page161">161</a>.</p> + + <p><a name="Nt_677" href="#NtA_677">[677]</a> "It becomes the doctors of + the Sorbonne to dispute, the Pope to decree, and the mathematician to go + to Paradise on a perpendicular line."</p> + + <p><a name="Nt_678" href="#NtA_678">[678]</a> See note <a + href="#Nt_124">124</a>, page <a href="#page83">83</a>.</p> + + <p><a name="Nt_679" href="#NtA_679">[679]</a> See note <a + href="#Nt_621">621</a>, page <a href="#page288">288</a>.</p> + + <p><a name="Nt_680" href="#NtA_680">[680]</a> Sylvain van de Weyer, who + was born at Louvain in 1802. He was a jurist and statesman, holding the + portfolio for foreign affairs (1831-1833), and being at one time + ambassador to England.</p> + + <p><a name="Nt_681" href="#NtA_681">[681]</a> Henry Crabb Robinson + (1775-1867), correspondent of the <i>Times</i> at Altona and in the + Peninsula, and later foreign editor. He was one of the founders of the + Athenæum Club and of University College, London. He seems to have known + pretty much every one of his day, and his posthumous <i>Diary</i> + attracted attention when it appeared.</p> + + <p><a name="Nt_682" href="#NtA_682">[682]</a> Was this Whewell, who was + at Trinity from 1812 to 1816 and became a fellow in 1817?</p> + + <p><a name="Nt_683" href="#NtA_683">[683]</a> Tom Cribb (1781-1848) the + champion pugilist. He had worked as a coal porter and hence received his + nickname, the Black Diamond.</p> + + <p><a name="Nt_684" href="#NtA_684">[684]</a> John Finleyson, or + Finlayson, was born in Scotland in 1770 and died in London in 1854. He + published a number of pamphlets that made a pretense to being scientific. + Among his striking phrases and sentences are the statements that the + stars were made "to amuse us in observing them"; that the earth is "not + shaped like a garden turnip as the Newtonians make it," and that the + stars are "oval-shaped immense masses of frozen water." The first edition + of the work here mentioned appeared at London in 1830.</p> + + <p><a name="Nt_685" href="#NtA_685">[685]</a> Richard Brothers + (1757-1824) was a native of Newfoundland. He went to London when he was + about 30, and a little later set forth his claim to being a descendant of + David, prince of the Hebrews, and ruler of the world. He was confined as + a criminal lunatic in 1795 but was released in 1806.</p> + + <p><a name="Nt_686" href="#NtA_686">[686]</a> Charles Grey (1764-1845), + second Earl Grey, Viscount Howick, was then Prime Minister. The Reform + Bill was introduced and defeated in 1831. The following year, with the + Royal guarantees to allow him to create peers, he finally carried the + bill in spite of "the number of the beast."</p> + + <p><a name="Nt_687" href="#NtA_687">[687]</a> The letters of obscure men, + the <i>Epistolæ obscurorum virorum ad venerabilem virum Magistrum + Ortuinum Gratium Dauentriensem</i>, by Joannes Crotus, Ulrich von Hutten, + and others appeared at Venice about 1516.</p> + + <p><a name="Nt_688" href="#NtA_688">[688]</a> The lamentations of obscure + men, the <i>Lamentationes obscurorum virorum, non prohibete per sedem + Apostolicam. Epistola D. Erasmi Roterodami: quid de obscuris sentiat</i>, + by G. Ortwinus, appeared at Cologne in 1518.</p> + + <p><a name="Nt_689" href="#NtA_689">[689]</a> The criticism was timely + when De Morgan wrote it. At present it would have but little force with + respect to the better class of algebras.</p> + + <p><a name="Nt_690" href="#NtA_690">[690]</a> Thomas Ignatius Maria + Forster (1789-1860) was more of a man than one would infer from this + satire upon his theory. He was a naturalist, astronomer, and + physiologist. In 1812 he published his <i>Researches about Atmospheric + Phenomena</i>, and seven years later (July 3, 1819) he discovered a + comet. With Sir Richard Phillips he founded a Meteorological Society, but + it was short lived. He declined a fellowship in the Royal Society because + he disapproved of certain of its rules, so that he had a recognized + standing in his day. The work mentioned by De Morgan is the second + edition, the first having appeared at Frankfort on the Main in 1835 under + the title, <i>Recueil des ouvrages et des pensées d'un physicien et + metaphysicien</i>.</p> + + <p><a name="Nt_691" href="#NtA_691">[691]</a> Zadkiel, whose real name + was Richard James Morrison (1795-1874), was in his early years an officer + in the navy. In 1831 he began the publication of the <i>Herald of + Astrology</i>, which was continued as <i>Zadkiel's Almanac</i>. His name + became familiar throughout Great Britain as a result.</p> + + <p><a name="Nt_692" href="#NtA_692">[692]</a> See note <a + href="#Nt_566">566</a>, page <a href="#page246">246</a>.</p> + + <p><a name="Nt_693" href="#NtA_693">[693]</a> Sumner (1780-1862) was an + Eton boy. He went to King's College, Cambridge, and was elected fellow in + 1801. He took many honors, and in 1807 became M.A. He was successively + Canon of Durham (1820), Bishop of Chester (1828), and Archbishop of + Canterbury (1848). Although he voted for the Catholic Relief Bill (1829) + and the Reform Bill (1832), he opposed the removal of Jewish + disabilities.</p> + + <p><a name="Nt_694" href="#NtA_694">[694]</a> Charles Richard Sumner + (1790-1874) was not only Bishop of Winchester (1827), but also Bishop of + Llandaff and Dean of St. Paul's, London (1826). He lost the king's favor + by voting for the Catholic Relief Bill.</p> + + <p><a name="Nt_695" href="#NtA_695">[695]</a> John Bird Sumner, brother + of Charles Richard.</p> + + <p><a name="Nt_696" href="#NtA_696">[696]</a> Thomas Musgrave (1788-1860) + became Fellow of Trinity in 1812, and senior proctor in 1831. He was also + Dean of Bristol.</p> + + <p><a name="Nt_697" href="#NtA_697">[697]</a> Charles Thomas Longley + (1794-1868) was educated at Westminster School and at Christ Church, + Oxford. He became M.A. in 1818 and D.D. in 1829. Besides the bishoprics + mentioned he was Bishop of Ripon (1836-1856), and before that was + headmaster of Harrow (1829-1836).</p> + + <p><a name="Nt_698" href="#NtA_698">[698]</a> Thomson (1819-1890) was + scholar and fellow of Queen's College, Oxford. He became chaplain to the + Queen in 1859.</p> + + <p><a name="Nt_699" href="#NtA_699">[699]</a> This is worthy of the + statistical psychologists of the present day.</p> + + <p><a name="Nt_700" href="#NtA_700">[700]</a> The famous Moon Hoax was + written by Richard Adams Locke, who was born in New York in 1800 and died + in Staten Island in 1871. He was at one time editor of the <i>Sun</i>, + and the Hoax appeared in that journal in 1835. It was reprinted in London + (1836) and Germany, and was accepted seriously by most readers. It was + published in book form in New York in 1852 under the title <i>The Moon + Hoax</i>. Locke also wrote another hoax, the <i>Lost Manuscript of Mungo + Park</i>, but it attracted relatively little attention.</p> + + <p><a name="Nt_701" href="#NtA_701">[701]</a> It is true that + Jean-Nicolas Nicollet (1756-1843) was at that time in the United States, + but there does not seem to be any very tangible evidence to connect him + with the story. He was secretary and librarian of the Paris observatory + (1817), member of the Bureau of Longitudes (1822), and teacher of + mathematics in the Lycée Louis-le-Grand. Having lost his money through + speculations he left France for the United States in 1831 and became + connected with the government survey of the Mississippi Valley.</p> + + <p><a name="Nt_702" href="#NtA_702">[702]</a> This was Alexis Bouvard + (1767-1843), who made most of the computations for Laplace's <i>Mécanique + céleste</i> (1793). He discovered eight new comets and calculated their + orbits. In his tables of Uranus (1821) he attributed certain + perturbations to the presence of an undiscovered planet, but unlike + Leverrier and Adams he did not follow up this clue and thus discover + Neptune.</p> + + <p><a name="Nt_703" href="#NtA_703">[703]</a> Patrick Murphy (1782-1847) + awoke to find himself famous because of his natural guess that there + would be very cold weather on January 20, although that is generally the + season of lowest temperature. It turned out that his forecasts were + partly right on 168 days and very wrong on 197 days.</p> + + <p><a name="Nt_704" href="#NtA_704">[704]</a> He seems to have written + nothing else. If one wishes to enter into the subject of the mathematics + of the Great Pyramid there is an extensive literature awaiting him. + Richard William Howard Vyse (1784-1853) published in 1840 his + <i>Operations carried on at the Pyramids of Gizeh in 1837</i>, and in + this he made a beginning of a scientific metrical study of the subject. + Charles Piazzi Smyth (1819-1900), astronomer Royal for Scotland + (1845-1888) was much carried away with the number mysticism of the Great + Pyramid, so much so that he published in 1864 a work entitled <i>Our + Inheritance in the Great Pyramid</i>, in which his vagaries were set + forth. Although he was then a Fellow of the Royal Society (1857), his + work was so ill received that when he offered a paper on the subject it + was rejected (1874) and he resigned in consequence of this action. The + latest and perhaps the most scholarly of all investigators of the subject + is William Matthew Flinders Petrie (born in 1853), Edwards professor of + Egyptology at University College, London, whose <i>Pyramids and Temples + of Gizeh</i> (1883) and subsequent works are justly esteemed as + authorities.</p> + + <p><a name="Nt_705" href="#NtA_705">[705]</a> As De Morgan subsequently + found, this name reversed becomes Oliver B...e, for Oliver Byrne, one of + the odd characters among the minor mathematical writers of the middle of + the last century. One of his most curious works is <i>The first six Books + of the Elements of Euclid; in which coloured diagrams and symbols are + used instead of letters</i> (1847). There is some merit in speaking of + the red triangle instead of the triangle ABC, but not enough to give the + method any standing. His <i>Dual Arithmetic</i> (1863-1867) was also a + curious work.</p> + + <p><a name="Nt_706" href="#NtA_706">[706]</a> Brenan also wrote on + English composition (1829), a work that went through fourteen editions by + 1865; a work entitled <i>The Foreigner's English Conjugator</i> (1831), + and a work on the national debt.</p> + + <p><a name="Nt_707" href="#NtA_707">[707]</a> See note <a + href="#Nt_211">211</a>, page <a href="#page112">112</a>.</p> + + <p><a name="Nt_708" href="#NtA_708">[708]</a> See note <a + href="#Nt_592">592</a>, page <a href="#page261">261</a>.</p> + + <p><a name="Nt_709" href="#NtA_709">[709]</a> Sir William Rowan Hamilton + (1805-1865), the discoverer of quaternions (1852), was an infant prodigy, + competing with Zerah Colburn as a child. He was a linguist of remarkable + powers, being able, at thirteen years of age, to boast that he knew as + many languages as he had lived years. When only sixteen he found an error + in Laplace's <i>Mécanique céleste</i>. When only twenty-two he was + appointed Andrews professor of astronomy, and he soon after became + Astronomer Royal of Ireland. He was knighted in 1835. His earlier work + was on optics, his <i>Theory of Systems of Rays</i> appearing in 1823. In + 1827 he published a paper on the principle of <i>Varying Action</i>. He + also wrote on dynamics.</p> + + <p><a name="Nt_710" href="#NtA_710">[710]</a> "Let him not leave the + kingdom,"—a legal phrase.</p> + + <p><a name="Nt_711" href="#NtA_711">[711]</a> Probably De Morgan is + referring to Johann Bernoulli III (1744-1807), who edited Lambert's + <i>Logische und philosophische Abhandlungen</i>, Berlin, 1782. He was + astronomer of the Academy of Sciences at Berlin.</p> + + <p><a name="Nt_712" href="#NtA_712">[712]</a> Jacob Bernoulli (1654-1705) + was one of the two brothers who founded the famous Bernoulli family of + mathematicians, the other being Johann I. His <i>Ars conjectandi</i> + (1713), published posthumously, was the first distinct treatise on + probabilities.</p> + + <p><a name="Nt_713" href="#NtA_713">[713]</a> Johann Heinrich Lambert + (1728-1777) was one of the most learned men of his time. Although + interested chiefly in mathematics, he wrote also on science, logic, and + philosophy.</p> + + <p><a name="Nt_714" href="#NtA_714">[714]</a> Joseph Diez Gergonne + (1771-1859), a soldier under Napoleon, and founder of the <i>Annales de + mathématiques</i> (1810).</p> + + <p><a name="Nt_715" href="#NtA_715">[715]</a> Gottfried Ploucquet + (1716-1790) was at first a clergyman, but afterwards became professor of + logic at Tübingen.</p> + + <p><a name="Nt_716" href="#NtA_716">[716]</a> "In the premises let the + middle term be omitted; what remains indicates the conclusion."</p> + + <p><a name="Nt_717" href="#NtA_717">[717]</a> Probably Sir William Edmond + Logan (1789-1875), who became so interested in geology as to be placed at + the head of the geological survey of Canada (1842). The University of + Montreal conferred the title LL.D. upon him, and Napoleon III gave him + the cross of the Legion of Honor.</p> + + <p><a name="Nt_718" href="#NtA_718">[718]</a> "So strike that he may + think himself to die."</p> + + <p><a name="Nt_719" href="#NtA_719">[719]</a> "Witticism or piece of + stupidity."</p> + + <p><a name="Nt_720" href="#NtA_720">[720]</a> A very truculently unjust + assertion: for Sir W. was as great a setter up of some as he was a puller + down of others. His writings are a congeries of praises and blames, both + <i>cruel smart</i>, as they say in the States. But the combined + instigation of prose, rhyme, and retort would send Aristides himself to + Tartarus, if it were not pretty certain that Minos would grant a <i>stet + processus</i> under the circumstances. The first two verses are + exaggerations standing on a basis of truth. The fourth verse is quite + true: Sir W. H. was an Edinburgh Aristotle, with the difference of + ancient and modern Athens well marked, especially the <i>perfervidum + ingenium Scotorum</i>.—A. De M.</p> + + <p><a name="Nt_721" href="#NtA_721">[721]</a> See note <a + href="#Nt_576">576</a>, p. <a href="#page252">252</a>. There was also a + <i>Theory of Parallels</i> that differed from these, London, 1853, second + edition 1856, third edition 1856.</p> + + <p><a name="Nt_722" href="#NtA_722">[722]</a> The work was written by + Robert Chambers (1802-1871), the Edinburgh publisher, a friend of Scott + and of many of his contemporaries in the literary field. He published the + <i>Vestiges of the Natural History of Creation</i> in 1844, not 1840.</p> + + <p><a name="Nt_723" href="#NtA_723">[723]</a> Everett (1784-1872) was at + that time a good Wesleyan, but was expelled from the ministry in 1849 for + having written <i>Wesleyan Takings</i> and as under suspicion for having + started the <i>Fly Sheets</i> in 1845. In 1857 he established the United + Methodist Free Church.</p> + + <p><a name="Nt_724" href="#NtA_724">[724]</a> Smith was a Primitive + Methodist preacher. He also wrote an <i>Earnest Address to the + Methodists</i> (1841) and <i>The Wealth Question</i> (1840?).</p> + + <p><a name="Nt_725" href="#NtA_725">[725]</a> He wrote the <i>Nouveau + traité de Balistique</i>, Paris, 1837.</p> + + <p><a name="Nt_726" href="#NtA_726">[726]</a> Joseph Denison, known to + fame only through De Morgan. See also page <a + href="#page353">353</a>.</p> + + <p><a name="Nt_727" href="#NtA_727">[727]</a> The radical (1784?-1858), + advocate of the founding of London university (1826), of medical reform + (1827-1834), and of the repeal of the duties on newspapers and corn, and + an ardent champion of penny postage.</p> + + <p><a name="Nt_728" href="#NtA_728">[728]</a> I. e., Roman Catholic + Priest.</p> + + <p><a name="Nt_729" href="#NtA_729">[729]</a> Murphy (1806-1843) showed + extraordinary powers in mathematics even before the age of thirteen. He + became a fellow of Caius College, Cambridge, in 1829, dean in 1831, and + examiner in mathematics in London University in 1838.</p> + + <p><a name="Nt_730" href="#NtA_730">[730]</a> See note <a + href="#Nt_442">442</a>, page <a href="#page196">196</a>.</p> + + <p><a name="Nt_731" href="#NtA_731">[731]</a> Sir John Bowring + (1792-1872), the linguist, writer, and traveler, member of many learned + societies and a writer of high reputation in his time. His works were + not, however, of genuine merit.</p> + + <p><a name="Nt_732" href="#NtA_732">[732]</a> Joseph Hume (1777-1855) + served as a surgeon with the British army in India early in the + nineteenth century. He returned to England in 1808 and entered parliament + as a radical in 1812. He was much interested in all reform movements.</p> + + <p><a name="Nt_733" href="#NtA_733">[733]</a> Sir Robert Harry Inglis + (1786-1855), a strong Tory, known for his numerous addresses in the House + of Commons rather than for any real ability.</p> + + <p><a name="Nt_734" href="#NtA_734">[734]</a> Sir Robert Peel (1788-1850) + began his parliamentary career in 1809 and was twice prime minister. He + was prominent in most of the great reforms of his time.</p> + + <p><a name="Nt_735" href="#NtA_735">[735]</a> See note <a + href="#Nt_627">627</a>, page <a href="#page290">290</a>.</p> + + <p><a name="Nt_736" href="#NtA_736">[736]</a> John Taylor (1781-1864) was + a publisher, and published several pamphlets opposed to Peel's currency + measures. De Morgan refers to his work on the Junius question. This was + done early in his career, and resulted in <i>A Discovery of the author of + the Letters of Junius</i> (1813), and <i>The Identity of Junius with a + distinguished living character established</i> (1816), this being Sir + Philip Francis.</p> + + <p><a name="Nt_737" href="#NtA_737">[737]</a> See note <a + href="#Nt_665">665</a>, page <a href="#page308">308</a>.</p> + + <p><a name="Nt_738" href="#NtA_738">[738]</a> See page <a + href="#page348">348</a>.</p> + + <p><a name="Nt_739" href="#NtA_739">[739]</a> See note <a + href="#Nt_348">348</a>, page <a href="#page160">160</a>.</p> + + <p><a name="Nt_740" href="#NtA_740">[740]</a> Sir Nicholas Harris Nicolas + (1799-1848) was a reformer in various lines,—the Record Commission, + the Society of Antiquaries, and the British Museum,—and his work + was not without good results.</p> + + <p><a name="Nt_741" href="#NtA_741">[741]</a> See note <a + href="#Nt_98">98</a>, page <a href="#page69">69</a>.</p> + + <p><a name="Nt_742" href="#NtA_742">[742]</a> In the <i>Companion to the + Almanac</i> for 1845 is a paper by Prof. De Morgan, "On the + Ecclesiastical Calendar," the statements of which, so far as concerns the + Gregorian Calendar, are taken direct from the work of Clavius, the + principal agent in the arrangement of the reformed reckoning. This was + followed, in the <i>Companion to the Almanac</i> for 1846, by a second + paper, by the same author, headed "On the Earliest Printed Almanacs," + much of which is written in direct supplement to the former + article.—S. E. De Morgan.</p> + + <p><a name="Nt_743" href="#NtA_743">[743]</a> It may be necessary to + remind some English readers that in Latin and its derived European + languages, what we call Easter is called the passover (<i>pascha</i>). + The Quartadecimans had the <i>name</i> on their side: a possession which + often is, in this world, nine points of the law.—A. De M.</p> + + <p><a name="Nt_744" href="#NtA_744">[744]</a> Socrates Scholasticus was + born at Constantinople c. 379, and died after 439. His <i>Historia + Ecclesiastica</i> (in Greek) covers the period from Constantine the Great + to about 439, and includes the Council of Nicæa. The work was printed in + Paris 1544.</p> + + <p><a name="Nt_745" href="#NtA_745">[745]</a> Theodoretus or Theodoritus + was born at Antioch and died about 457. He was one of the greatest + divines of the fifth century, a man of learning, piety, and judicial + mind, and a champion of freedom of opinion in all religious matters.</p> + + <p><a name="Nt_746" href="#NtA_746">[746]</a> He died in 417. He was a + man of great energy and of high attainments.</p> + + <p><a name="Nt_747" href="#NtA_747">[747]</a> He died in 461, having + reigned as pope for twenty-one years. It was he who induced Attila to + spare Rome in 452.</p> + + <p><a name="Nt_748" href="#NtA_748">[748]</a> He succeeded Leo as pope in + 461, and reigned for seven years.</p> + + <p><a name="Nt_749" href="#NtA_749">[749]</a> Victorinus or Victorius + Marianus seems to have been born at Limoges. He was a mathematician and + astronomer, and the cycle mentioned by De Morgan is one of 532 years, a + combination of the Metonic cycle of 19 years with the solar cycle of 28 + years. His canon was published at Antwerp in 1633 or 1634, <i>De doctrina + temporum sive commentarius in Victorii Aquitani et aliorum canones + paschales</i>.</p> + + <p><a name="Nt_750" href="#NtA_750">[750]</a> He went to Rome about 497, + and died there in 540. He wrote his <i>Liber de paschate</i> in 525, and + it was in this work that the Christian era was first used for calendar + purposes.</p> + + <p><a name="Nt_751" href="#NtA_751">[751]</a> See note <a + href="#Nt_259">259</a>, page <a href="#page126">126</a>.</p> + + <p><a name="Nt_752" href="#NtA_752">[752]</a> Johannes de Sacrobosco + (Holy wood), or John of Holywood. The name was often written, without + regard to its etymology, Sacrobusto. He was educated at Oxford and taught + in Paris until his death (1256). He did much to make the Hindu-Arabic + numerals known to European scholars.</p> + + <p><a name="Nt_753" href="#NtA_753">[753]</a> See note <a + href="#Nt_36">36</a>, page <a href="#page44">44</a>.</p> + + <p><a name="Nt_754" href="#NtA_754">[754]</a> See note <a + href="#Nt_45">45</a>, page <a href="#page48">48</a>.</p> + + <p><a name="Nt_755" href="#NtA_755">[755]</a> The Julian year is a year + of the Julian Calendar, in which there is leap year every fourth year. + Its average length is therefore 365 days and a quarter.—A. De + M.</p> + + <p><a name="Nt_756" href="#NtA_756">[756]</a> Ugo Buoncompagno + (1502-1585) was elected pope in 1572.</p> + + <p><a name="Nt_757" href="#NtA_757">[757]</a> He was a Calabrian, and as + early as 1552 was professor of medicine at Perugia. In 1576 his + manuscript on the reform of the calendar was presented to the Roman Curia + by his brother, Antonius. The manuscript was not printed and it has not + been preserved.</p> + + <p><a name="Nt_758" href="#NtA_758">[758]</a> The title of this work, + which is the authority on all points of the new Calendar, is + <i>Kalendarium Gregorianum Perpetuum. Cum Privilegio Summi Pontificis Et + Aliorum Principum. Romæ, Ex Officina Dominici Basæ. MDLXXXII. Cum + Licentia Superiorum</i> (quarto, pp. 60).—A. De M.</p> + + <p><a name="Nt_759" href="#NtA_759">[759]</a> <i>Manuels-Roret. Théorie + du Calendrier et collection de tous les Calendriers des Années passées et + futures</i>.... Par L. B. Francœur,... Paris, à la librairie + encyclopédique de Roret, rue Hautefeuille, 10 bis. 1842. (12mo.) In this + valuable manual, the 35 possible almanacs are given at length, with such + preliminary tables as will enable any one to find, by mere inspection, + which almanac he is to choose for any year, whether of old or new style. + [1866. I may now refer to my own <i>Book of Almanacs</i>, for the same + purpose].—A. De M.</p> + + <p>Louis Benjamin Francœur (1773-1849), after holding positions in + the Ecole polytechnique (1804) and the Lycée Charlemagne (1805), became + professor of higher algebra in the University of Paris (1809). His + <i>Cours complet des mathématiques pures</i> was well received, and he + also wrote on mechanics, astronomy, and geodesy.</p> + + <p><a name="Nt_760" href="#NtA_760">[760]</a> Albertus Pighius, or Albert + Pigghe, was born at Kempen c. 1490 and died at Utrecht in 1542. He was a + mathematician and a firm defender of the faith, asserting the supremacy + of the Pope and attacking both Luther and Calvin. He spent some time in + Rome. His greatest work was his <i>Hierarchiæ ecclesiasticæ assertio</i> + (1538).</p> + + <p><a name="Nt_761" href="#NtA_761">[761]</a> This was A. F. Vogel. The + work was his translation from the German edition which appeared at + Leipsic the same year, <i>Entdeckung einer numerischen General-Auflösung + aller höheren endlichen Gleichungen von jeder beliebigen algebraischen + und transcendenten Form</i>.</p> + + <p><a name="Nt_762" href="#NtA_762">[762]</a> The latest edition of + Burnside and Panton's <i>Theory of Equations</i> has this brief summary + of the present status of the problem: "Demonstrations have been given by + Abel and Wantzel (see Serret's <i>Cours d'Algèbre Supérieure</i>, Art. + 516) of the impossibility of resolving algebraically equations + unrestricted in form, of a degree higher than the fourth. A + transcendental solution, however, of the quintic has been given by M. + Hermite, in a form involving elliptic integrals."</p> + + <p><a name="Nt_763" href="#NtA_763">[763]</a> There was a second edition + of this work in 1846. The author's <i>Astronomy Simplified</i> was + published in 1838, and the <i>Thoughts on Physical Astronomy</i> in 1840, + with a second edition in 1842.</p> + + <p><a name="Nt_764" href="#NtA_764">[764]</a> This was <i>The Science of + the Weather, by several authors... edited by B.</i>, Glasgow, 1867.</p> + + <p><a name="Nt_765" href="#NtA_765">[765]</a> This was Y. Ramachandra, + son of Sundara Lāla. He was a teacher of science in Delhi College, + and the work to which De Morgan refers is <i>A Treatise on problems of + Maxima and Minima solved by Algebra</i>, which appeared at Calcutta in + 1850. De Morgan's edition was published at London nine years later.</p> + + <p><a name="Nt_766" href="#NtA_766">[766]</a> Abraham de Moivre + (1667-1754), French refugee in London, poor, studying under difficulties, + was a man with tastes in some respects like those of De Morgan. For one + thing, he was a lover of books, and he had a good deal of interest in the + theory of probabilities to which De Morgan also gave much thought. His + introduction of imaginary quantities into trigonometry was an event of + importance in the history of mathematics, and the theorem that bears his + name, (cos <span class="grk">φ</span> + <i>i</i> sin <span + class="grk">φ</span>)<sup><i>n</i></sup> = cos <i>n</i><span + class="grk">φ</span> + <i>i</i> sin <i>n</i><span + class="grk">φ</span>, is one of the most important ones in all + analysis.</p> + + <p><a name="Nt_767" href="#NtA_767">[767]</a> John Dolland (1706-1761), + the silk weaver who became the greatest maker of optical instruments in + his time.</p> + + <p><a name="Nt_768" href="#NtA_768">[768]</a> Thomas Simpson (1710-1761), + also a weaver, taking his leisure from his loom at Spitalfields to teach + mathematics. His <i>New Treatise on Fluxions</i> (1737) was written only + two years after he began working in London, and six years later he was + appointed professor of mathematics at Woolwich. He wrote many works on + mathematics and Simpson's Formulas for computing trigonometric tables are + still given in the text-books.</p> + + <p><a name="Nt_769" href="#NtA_769">[769]</a> Nicholas Saunderson + (1682-1739), the blind mathematician. He lost his eyesight through + smallpox when only a year old. At the age of 25 he began lecturing at + Cambridge on the principles of the Newtonian philosophy. His + <i>Algebra</i>, in two large volumes, was long the standard treatise on + the subject.</p> + + <p><a name="Nt_770" href="#NtA_770">[770]</a> He was not in the class + with the others mentioned.</p> + + <p><a name="Nt_771" href="#NtA_771">[771]</a> Not known in the literature + of mathematics.</p> + + <p><a name="Nt_772" href="#NtA_772">[772]</a> Probably J. Butler Williams + whose <i>Practical Geodesy</i> appeared in 1842, with a third edition in + 1855.</p> + + <p><a name="Nt_773" href="#NtA_773">[773]</a> Benjamin Gompertz + (1779-1865) was debarred as a Jew from a university education. He studied + mathematics privately and became president of the Mathematical Society. + De Morgan knew him professionally through the fact that he was prominent + in actuarial work.</p> + + <p><a name="Nt_774" href="#NtA_774">[774]</a> Referring to the + contributions of Archimedes (287-212 B.C.) to the mensuration of the + sphere.</p> + + <p><a name="Nt_775" href="#NtA_775">[775]</a> The famous Alexandrian + astronomer (c. 87-c. 165 A.D.), author of the <i>Almagest</i>, a treatise + founded on the works of Hipparchus.</p> + + <p><a name="Nt_776" href="#NtA_776">[776]</a> Dr. Whewell, when I + communicated this song to him, started the opinion, which I had before + him, that this was a very good idea, of which too little was + made.—A. De M.</p> + + <p><a name="Nt_777" href="#NtA_777">[777]</a> See note <a + href="#Nt_117">117</a>, page <a href="#page76">76</a>.</p> + + <p><a name="Nt_778" href="#NtA_778">[778]</a> The common epithet of rank: + <i>nobilis Tycho</i>, as he was a nobleman. The writer had been at + history.—A. De M.</p> + + <p>See note <a href="#Nt_117">117</a>, page <a href="#page76">76</a>.</p> + + <p><a name="Nt_779" href="#NtA_779">[779]</a> He lost it in a duel, with + Manderupius Pasbergius. A contemporary, T. B. Laurus, insinuates that + they fought to settle which was the best mathematician! This seems odd, + but it must be remembered they fought in the dark, "<i>in tenebris + densis</i>"; and it is a nice problem to shave off a nose in the dark, + without any other harm.—A. De M.</p> + + <p>Was this T. B. Laurus Joannes Baptista Laurus or Giovanni Battista + Lauro (1581-1621), the poet and writer?</p> + + <p><a name="Nt_780" href="#NtA_780">[780]</a> See note <a + href="#Nt_117">117</a>, page <a href="#page76">76</a>.</p> + + <p><a name="Nt_781" href="#NtA_781">[781]</a> Referring to Kepler's + celebrated law of planetary motion. He had previously wasted his time on + analogies between the planetary orbits and the polyhedrons.—A. De + M.</p> + + <p><a name="Nt_782" href="#NtA_782">[782]</a> See note <a + href="#Nt_117">117</a>, page <a href="#page76">76</a>.</p> + + <p><a name="Nt_783" href="#NtA_783">[783]</a> "It does move though."</p> + + <p><a name="Nt_784" href="#NtA_784">[784]</a> As great a lie as ever was + told: but in 1800 a compliment to Newton without a fling at Descartes + would have been held a lopsided structure.—A. De M.</p> + + <p><a name="Nt_785" href="#NtA_785">[785]</a> Jean-le-Rond D'Alembert + (1717-1783), the foundling who was left on the steps of Jean-le-Rond in + Paris, and who became one of the greatest mathematical physicists and + astronomers of his century.</p> + + <p><a name="Nt_786" href="#NtA_786">[786]</a> Leonhard Euler (1707-1783), + friend of the Bernoullis, the greatest of Swiss mathematicians, prominent + in the theory of numbers, and known for discoveries in all lines of + mathematics as then studied.</p> + + <p><a name="Nt_787" href="#NtA_787">[787]</a> See notes <a + href="#Nt_478">478</a>, <a href="#Nt_479">479</a>, page <a + href="#page219">219</a>.</p> + + <p><a name="Nt_788" href="#NtA_788">[788]</a> See note <a + href="#Nt_621">621</a>, page <a href="#page288">288</a>.</p> + + <p><a name="Nt_789" href="#NtA_789">[789]</a> See note <a + href="#Nt_584">584</a>, page <a href="#page255">255</a>.</p> + + <p><a name="Nt_790" href="#NtA_790">[790]</a> The <i>siderial</i> day is + about four minutes short of the solar; there are 366 sidereal days in the + year.—A. De M.</p> + + <p><a name="Nt_791" href="#NtA_791">[791]</a> The founding of the London + Mathematical Society is discussed by Mrs. De Morgan in her <i>Memoir</i> + (p. 281). The idea came from a conversation between her brilliant son, + George Campbell De Morgan, and his friend Arthur Cowper Ranyard in 1864. + The meeting of organization was held on Nov. 7, 1864, with Professor De + Morgan in the chair, and the first regular meeting on January 16, + 1865.</p> + + <p><a name="Nt_792" href="#NtA_792">[792]</a> See note <a + href="#Nt_33">33</a>, page <a href="#page43">43</a>.</p> + + <p><a name="Nt_793" href="#NtA_793">[793]</a> See note <a + href="#Nt_119">119</a>, page <a href="#page80">80</a>.</p> + + <p><a name="Nt_794" href="#NtA_794">[794]</a> John Russell Hind (b. + 1823), the astronomer. Between 1847 and 1854 he discovered ten + planetoids.</p> + + <p><a name="Nt_795" href="#NtA_795">[795]</a> Sir Roderick Impey + Murchison (1792-1871), the great geologist. He was knighted in 1846 and + devoted the latter part of his life to the work of the Royal Geographical + Society and to the geology of Scotland.</p> + + <p><a name="Nt_796" href="#NtA_796">[796]</a> Friedrich Wilhelm Bessel + (1784-1846), the astronomer and physicist. He was professor of astronomy + at Königsberg.</p> + + <p><a name="Nt_797" href="#NtA_797">[797]</a> This was the <i>Reduction + of the Observations of Planets made ... from 1750 to 1830: computed ... + under the superintendence of George Biddell Airy</i> (1848). See note <a + href="#Nt_129">129</a>, page <a href="#page85">85</a>.</p> + + <p><a name="Nt_798" href="#NtA_798">[798]</a> The expense of this + magnificent work was defrayed by Government grants, obtained, at the + instance of the British Association, in 1833—A. De M.</p> + + <p><a name="Nt_799" href="#NtA_799">[799]</a> See note <a + href="#Nt_32">32</a>, page <a href="#page43">43</a>.</p> + + <p><a name="Nt_800" href="#NtA_800">[800]</a> Franz Friedrich Ernst + Brünnow (1821-1891) was at that time or shortly before director of the + observatory at Dusseldorf. He then went to Berlin and thence (1854) to + Ann Arbor, Michigan. He then went to Dublin and finally became Royal + Astronomer of Ireland.</p> + + <p><a name="Nt_801" href="#NtA_801">[801]</a> Johann Gottfried Galle + (1812-1910), at that time connected with the Berlin observatory, and + later professor of astronomy at Breslau.</p> + + <p><a name="Nt_802" href="#NtA_802">[802]</a> George Bishop (1785-1861), + in whose observatory in Regent's Park important observations were made by + Dawes, Hind, and Marth.</p> + + <p><a name="Nt_803" href="#NtA_803">[803]</a> James Challis (1803-1882), + director of the Cambridge observatory, and successor of Airy as Plumian + professor of astronomy.</p> + + <p><a name="Nt_804" href="#NtA_804">[804]</a> On Leverrier and Arago see + note <a href="#Nt_33">33</a>, page <a href="#page43">43</a>, and note <a + href="#Nt_561">561</a>, page <a href="#page243">243</a>.</p> + + <p><a name="Nt_805" href="#NtA_805">[805]</a> Robert Grant's (1814-1892) + <i>History of Physical Astronomy from the Earliest Ages to the Middle of + the Nineteenth Century</i> appeared in 1852. He was professor of + astronomy and director of the observatory at Glasgow.</p> + + <p><a name="Nt_806" href="#NtA_806">[806]</a> John Debenham was more + interested in religion than in astronomy. He wrote <i>The Strait Gate; + or, the true scripture doctrine of salvation clearly explained</i>, + London, 1843, and <i>Tractatus de magis et Bethlehemæ stella et Christi + in deserto tentatione</i>, privately printed at London in 1845.</p> + + <p><a name="Nt_807" href="#NtA_807">[807]</a> More properly the Sydney + Smirke reading room, since it was built from his designs.</p> + + <p><a name="Nt_808" href="#NtA_808">[808]</a> The Antinomians were + followers of Johannes Agricola (1494-1566). They believed that Christians + as such were released from all obligations to the Old Testament. Some + went so far as to assert that, since all Christians were sanctified, they + could not lose this sanctity even though they disobeyed God. The sect was + prominent in England in the seventeenth century, and was transferred to + New England. Here it suffered a check in the condemnation of Mrs. Ann + Hutchinson (1636) by the Newton Synod.</p> + + <p><a name="Nt_809" href="#NtA_809">[809]</a> Aside from this work and + his publications on Reeve and Muggleton he wrote nothing. With Joseph + Frost he published <i>A list</i> <i>of Books and general index to J. + Reeve and L. Muggleton's works</i> (1846), <i>Divine Songs of the + Muggletonians</i> (1829), and the work mentioned on page <a + href="#page396">396</a>. <i>The works of J. Reeve and L. Muggleton</i> + (1832).</p> + + <p><a name="Nt_810" href="#NtA_810">[810]</a> About 1650 he and his + cousin John Reeve (1608-1658) began to have visions. As part of their + creed they taught that astronomy was opposed by the Bible. They asserted + that the sun moves about the earth, and Reeve figured out that heaven was + exactly six miles away. Both Muggleton and Reeve were imprisoned for + their unitarian views. Muggleton wrote a <i>Transcendant Spirituall + Treatise</i> (1652). I have before me <i>A true Interpretation of All the + Chief Texts ... of the whole Book of the Revelation of St. John.... By + Lodowick Muggleton, one of the two last Commissioned Witnesses & + Prophets of the onely high, immortal, glorious God, Christ Jesus</i> + (1665), in which the interpretation of the "number of the beast" occupies + four pages without arriving anywhere.</p> + + <p><a name="Nt_811" href="#NtA_811">[811]</a> In 1652 he was, in a + vision, named as the Lord's "last messenger," with Muggleton as his + "mouth," and died six years later, probably of nervous tension resulting + from his divine "illumination." He was the more spiritual of the two.</p> + + <p><a name="Nt_812" href="#NtA_812">[812]</a> William Guthrie (1708-1770) + was a historian and political writer. His <i>History of England</i> + (1744-1751) was the first attempt to base history on parliamentary + records. He also wrote a <i>General History of Scotland</i> in 10 volumes + (1767). The work to which Frost refers is the <i>Geographical, + Historical, and Commercial Grammar</i> (1770) which contained an + astronomical part by J. Ferguson. By 1827 it had passed through 24 + editions.</p> + + <p><a name="Nt_813" href="#NtA_813">[813]</a> George Fox (1624-1691), + founder of the Society of Friends; a mystic and a disciple of Boehme. He + was eight times imprisoned for heresy.</p> + + <p><a name="Nt_814" href="#NtA_814">[814]</a> If they were friends they + were literary antagonists, for Muggleton wrote against Fox <i>The Neck of + the Quakers Broken</i> (1663), and Fox replied in 1667. Muggleton also + wrote <i>A Looking Glass for George Fox</i>.</p> + + <p><a name="Nt_815" href="#NtA_815">[815]</a> John Conduitt (1688-1737), + who married (1717) Newton's half niece, Mrs. Katherine Barton. See note + <a href="#Nt_284">284</a>, page <a href="#page136">136</a>.</p> + + <p><a name="Nt_816" href="#NtA_816">[816]</a> Probably Peter Mark Roget's + (1779-1869) <i>Thesaurus of English Words</i> (1852) is not much used at + present, but it went through 28 editions in his lifetime. Few who use the + valuable work are aware that Roget was a professor of physiology at the + Royal Institution (London), that he achieved his title of F. R. S. + because of his work in perfecting the slide rule, and that he followed + Sir John Herschel as secretary of the Royal Society.</p> + + <p><a name="Nt_817" href="#NtA_817">[817]</a> See note <a + href="#Nt_703">703</a>, page <a href="#page327">327</a>. This work went + into a second edition in the year of its first publication.</p> + + <p><a name="Nt_818" href="#NtA_818">[818]</a> See note <a + href="#Nt_398">398</a>, page <a href="#page177">177</a>.</p> + + <p><a name="Nt_819" href="#NtA_819">[819]</a> See note <a + href="#Nt_528">528</a>, page <a href="#page233">233</a>.</p> + + <p><a name="Nt_820" href="#NtA_820">[820]</a> George Jacob Holyoake + (1817-1906) entered into a controversial life at an early age. In 1841 he + was imprisoned for six months for blasphemy. He founded and edited <i>The + Reasoner</i> (Vols. 1-26, 1846-1861). In his later life he did much to + promote cooperation among the working class.</p> + + <p><a name="Nt_821" href="#NtA_821">[821]</a> See note <a + href="#Nt_176">176</a>, page <a href="#page102">102</a>.</p> + + <p><a name="Nt_822" href="#NtA_822">[822]</a> William Thomas Lowndes + (1798-1843), whose <i>Bibliographer's Manual of English Literature</i>, 4 + vols., London, 1834 (also 1857-1864, and 1869) is a classic in its + line.</p> + + <p><a name="Nt_823" href="#NtA_823">[823]</a> Jacques Charles Brunet + (1780-1867), the author of the great French bibliography, the <i>Manuel + du Libraire</i> (1810).</p> + +</div> + + + + + + + +<pre> + + + + + +End of the Project Gutenberg EBook of A Budget of Paradoxes, Volume I (of II), by +Augustus De Morgan + +*** END OF THIS PROJECT GUTENBERG EBOOK A BUDGET OF PARADOXES *** + +***** This file should be named 23100-h.htm or 23100-h.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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