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diff --git a/26408.txt b/26408.txt new file mode 100644 index 0000000..c40f12e --- /dev/null +++ b/26408.txt @@ -0,0 +1,15500 @@ +The Project Gutenberg eBook, A Budget of Paradoxes, Volume II (of II), by +Augustus de Morgan, Edited by David Eugene Smith + + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + + + + +Title: A Budget of Paradoxes, Volume II (of II) + + +Author: Augustus de Morgan + +Editor: David Eugene Smith + +Release Date: August 23, 2008 [eBook #26408] + +Language: English + +Character set encoding: ISO-646-US (US-ASCII) + + +***START OF THE PROJECT GUTENBERG EBOOK A BUDGET OF PARADOXES, VOLUME II +(OF II)*** + + +E-text prepared by David Starner, Keith Edkins, and the Project Gutenberg +Online Distributed Proofreading Team (http://www.pgdp.net) + + + +Transcriber's note: + + A few typographical errors have been corrected: they are + listed at the end of the text. + + In mathematical formulae the carat (^) and underscore (_) + introduce superscripts or subscripts respectively, of one + character or a group enclosed in curly braces ({xyz}). + Elsewhere underscores delimit italics in the text, and + braces enclose the original page numbers thus {123}. + + + + + +BY AUGUSTUS DE MORGAN + +A BUDGET OF +PARADOXES + +REPRINTED WITH THE AUTHOR'S ADDITIONS FROM THE ATHENAEUM + +SECOND EDITION EDITED BY DAVID EUGENE SMITH + +WITH A NEW INTRODUCTION BY ERNEST NAGEL + +PROFESSOR OF PHILOSOPHY, COLUMBIA UNIVERSITY + +UNABRIDGED EDITION--TWO VOLUMES BOUND AS ONE + +Volume II + + + + + + + +DOVER PUBLICATIONS, INC., NEW YORK + + * * * * * + +_This new Dover Edition, published in 1954, +is an unabridged republication of the Second Edition +of 1915, with a new introduction by Professor Ernest Nagel._ + +_Copyright 1954 by Dover Publications, Inc. +Manufactured in the United States of America_ + + * * * * * + + +{1} + +A BUDGET OF PARADOXES. + +VOLUME II. + +ON SOME PHILOSOPHICAL ATHEISTS. + +With the general run of the philosophical atheists of the last century the +notion of a God was an hypothesis. There was left an admitted possibility +that the vague somewhat which went by more names than one, might be +personal, intelligent, and superintendent. In the works of Laplace,[1] who +is sometimes called an atheist from his writings, there is nothing from +which such an inference can be drawn: unless indeed a Reverend Fellow of +the Royal Society may be held to be the fool who said in his heart, etc., +etc., if his contributions to the _Philosophical Transactions_ go no higher +than _nature_. The following anecdote is well known in Paris, but has never +been printed entire. Laplace once went in form to present some edition of +his "Systeme du Monde" to the First Consul, or Emperor. Napoleon, whom some +wags had told that this book contained no mention of the name of God, and +who was fond of putting embarrassing questions, received it with--"M. +Laplace, they tell me you have written this large book on the system of the +universe, and have never even mentioned its Creator." Laplace, who, though +the most supple of politicians, was as stiff as a martyr on every point of +his philosophy or religion (e. g., even under Charles X he never concealed +his dislike of the priests), drew himself up and answered {2} bluntly, "Je +n'avais pas besoin de cette hypothese-la."[2] Napoleon, greatly amused, +told this reply to Lagrange, who exclaimed, "Ah! c'est une belle hypothese; +ca explique beaucoup de choses."[3] + +It is commonly said that the last words of Laplace were, "Ce que nous +connaissons est peu de chose; ce que nous ignorons est immense."[4] This +looks like a parody on Newton's pebbles:[5] the following is the true +account; it comes to me through one remove from Poisson.[6] After the +publication (in 1825) of the fifth volume of the _Mecanique Celeste_, +Laplace became gradually weaker, and with it musing and abstracted. He +thought much on the great problems of existence, and often muttered to +himself, _Qu'est ce que c'est que tout cela!_[7] After many alternations, +he appeared at last so permanently prostrated that his family applied to +his favorite pupil, M. Poisson, to try to get a word from him. Poisson paid +a visit, and after a few words of salutation, said, "J'ai une bonne +nouvelle a vous annoncer: on a recu au Bureau des Longitudes une lettre +d'Allemagne annoncant que M. Bessel a verifie par l'observation vos +decouvertes theoriques sur les satellites de Jupiter."[8] Laplace opened +his eyes and answered with deep {3} gravity, "_L'homme ne poursuit que des +chimeres_."[9] He never spoke again. His death took place March 5, 1827. + +The language used by the two great geometers illustrates what I have said: +a supreme and guiding intelligence--apart from a blind rule called _nature +of things_--was an _hypothesis_. The absolute denial of such a ruling power +was not in the plan of the higher philosophers: it was left for the smaller +fry. A round assertion of the non-existence of anything which stands in the +way is the refuge of a certain class of minds: but it succeeds only with +things subjective; the objective offers resistance. A philosopher of the +appropriative class tried it upon the constable who appropriated _him_: I +deny your existence, said he; Come along all the same, said the +unpsychological policeman. + +Euler[10] was a believer in God, downright and straightforward. The +following story is told by Thiebault,[11] in his _Souvenirs de vingt ans de +sejour a Berlin_,[12] published in his old age, about 1804. This volume was +fully received as trustworthy; and Marshall Mollendorff[13] told the Duc de +Bassano[14] in 1807 that it was the most veracious of books written by the +most honest of men. Thiebault says that he has no personal knowledge of the +truth of the story, but {4} that it was believed throughout the whole of +the north of Europe. Diderot[15] paid a visit to the Russian Court at the +invitation of the Empress. He conversed very freely, and gave the younger +members of the Court circle a good deal of lively atheism. The Empress was +much amused, but some of her councillors suggested that it might be +desirable to check these expositions of doctrine. The Empress did not like +to put a direct muzzle on her guest's tongue, so the following plot was +contrived. Diderot was informed that a learned mathematician was in +possession of an algebraical demonstration of the existence of God, and +would give it him before all the Court, if he desired to hear it. Diderot +gladly consented: though the name of the mathematician is not given, it was +Euler. He advanced towards Diderot, and said gravely, and in a tone of +perfect conviction: _Monsieur,_ (a + b^{n}) / n = x, _donc Dieu existe; +repondez!_[16] Diderot, to whom algebra was Hebrew, was embarrassed and +disconcerted; while peals of laughter rose on all sides. He asked +permission to return to France at once, which was granted. + + + +ROTATION OF THE MOON. + + An examination of the Astronomical doctrine of the Moon's rotation. By + J. L.[17] Edinburgh, 1847, 8vo. + +A systematic attack of the character afterwards made with less skill and +more notice by Mr. Jellinger Symons. + +July 1866, J. L. appears as Mr. James Laurie, with a new pamphlet "The +Astronomical doctrines of the Moon's rotation ..." Edinburgh. Of all the +works I have seen on the question, this is the most confident, and the +sorest. {5} A writer on astronomy said of Mr. Jellinger Symons,[18] "Of +course he convinced no one who knew anything of the subject." This +"ungenerous slur" on the speculator's memory appears to have been keenly +felt; but its truth is admitted. Those who knew anything of the subject are +"the so-called men of science," whose three P's were assailed; prestige, +pride, and prejudice: this the author tries to effect for himself with +three Q's; quibble, quirk, and quiddity. He explains that the Scribes and +Pharisees would not hear Jesus, and that the lordly bishop of Rome will not +cast his tiara and keys at the feet of the "humble presbyter" who now plays +the part of pope in Scotland. I do not know whom he means: but perhaps the +friends of the presbyter-pope may consider this an ungenerous slur. The +best proof of the astronomer is just such "as might have been expected from +the merest of blockheads"; but as the giver is of course not a blockhead, +this circumstance shows how deeply blinded by prejudice he must be. + +Of course the paradoxers do not persuade any persons who know their +subjects: and so these Scribes and Pharisees reject the Messiah. We must +suppose that the makers of this comparison are Christians: for if they +thought the Messiah an enthusiast or an impostor, they would be absurd in +comparing those who reject what they take for truth with others who once +rejected what they take for falsehood. And if Christians, they are both +irreverent and blind to all analogy. The Messiah, with His Divine mission +proved by miracles which all might see who chose to look, is degraded into +a prototype of James Laurie, ingeniously astronomizing upon ignorant +geometry and false logic, and comparing to blockheads those who expose his +nonsense. Their comparison is as foolish as--supposing {6} them +Christians--it is profane: but, like errors in general, its other end +points to truth. There were Pseudochrists and Antichrists; and a +Concordance would find the real forerunners of all the paradoxers. But they +are not so clever as the old false prophets: there are none of whom we +should be inclined to say that, if it were possible, they would deceive the +very educated. Not an Egyptian among them all can make uproar enough to +collect four thousand men that are murderers--of common sense--to lead out +into the wilderness. Nothing, says the motto of this work, is so difficult +to destroy as the errors and false facts propagated by illustrious men +whose words have authority. I deny it altogether. There are things much +more difficult to destroy: it is much more difficult to destroy the truths +and real facts supported by such men. And again, it is much more difficult +to prevent men of no authority from setting up false pretensions; and it is +much more difficult to destroy assertions of fancy speculation. Many an +error of thought and learning has fallen before a gradual growth of +thoughtful and learned opposition. But such things as the quadrature of the +circle, etc., are never put down. And why? Because thought can influence +thought, but thought cannot influence self-conceit: learning can annihilate +learning: but learning cannot annihilate ignorance. A sword may cut through +an iron bar; and the severed ends will not reunite: let it go through the +air, and the yielding substance is whole again in a moment. + + + + Miracles _versus_ Nature: being an application of certain propositions + in the theory of chances to the Christian miracles. By + Protimalethes.[19] Cambridge, 1847, 8vo. + +The theory, as may be supposed, is carried further than most students of +the subject would hold defensible. + +{7} + + + + An astronomical Lecture. By the Rev. R. Wilson.[20] Greenock, 1847, + 12mo. + +Against the moon's rotation on her axis. + + + + [Handed about in the streets in 1847: I quote the whole:] Important + discovery in astronomy, communicated to the Astronomer Royal, December + 21st, 1846. That the Sun revolve round the Planets in 25748-2/5 years, + in consequence of the combined attraction of the planets and their + satellites, and that the Earth revolve round the Moon in 18 years and + 228 days. D. T. GLAZIER [altered with a pen into GLAZION.] Price one + penny. + +1847. In the _United Service Magazine_ for September, 1847, Mrs. +Borron,[21] of Shrewsbury, published some remarks tending to impeach the +fact that Neptune, the planet found by Galle,[22] really was the planet +which Le Verrier and Adams[23] had a right to claim. This was followed +(September 14) by two pages, separately circulated, of "Further +Observations upon the Planets Neptune and Uranus, with a Theory of +Perturbations"; and (October 19, 1848) by three pages of "A Review of M. +Leverrier's Exposition." Several persons, when the remarkable discovery was +made, contended that the planet actually discovered was an intruder; and +the future histories of the discovery must contain some account of this +little afterpiece. Tim Linkinwater's theory that there is no place like +London for coincidences, would have been utterly overthrown in favor of +what they used to call the celestial spaces, if there had been a planet +which by chance was put {8} near the place assigned to Neptune at the time +when the discovery was made. + + + +EARLY IDEAS OF AVIATION. + + Aerial Navigation; containing a description of a proposed flying + machine, on a new principle. By Daedalus Britannicus. London, 1847, 8vo. + +In 1842-43 a Mr. Henson[24] had proposed what he called an aeronaut +steam-engine, and a Bill was brought in to incorporate an "Aerial Transit +Company." The present plan is altogether different, the moving power being +the explosion of mixed hydrogen and air. Nothing came of it--not even a +Bill. What the final destiny of the balloon may be no one knows: it may +reasonably be suspected that difficulties will at last be overcome. +Darwin,[25] in his "Botanic Garden" (1781), has the following prophecy: + + "Soon shall thy arm, unconquered Steam! afar + Drag the slow barge, or drive the rapid car; + Or, on wide-waving wings expanded, bear + The flying chariot through the fields of air." + +Darwin's contemporaries, no doubt, smiled pity on the poor man. It is worth +note that the two true prophecies have been fulfilled in a sense different +from that of the predictions. Darwin was thinking of the suggestion of +Jonathan Hulls,[26] when he spoke of dragging the slow barge: it is only +very recently that the steam-tug has been employed on the canals. The car +was to be driven, not drawn, and on the common roads. Perhaps, the flying +chariot will {9} be something of a character which we cannot imagine, even +with the two prophecies and their fulfilments to help us.[27] + + + +THE SECRET OF THE UNIVERSE DIVULGED. + + A book for the public. New Discovery. The causes of the circulation of + the blood; and the true nature of the planetary system. London, 1848, + 8vo. + +Light is the sustainer of motion both in the earth and in the blood. The +natural standard, the pulse of a person in health, four beats to one +respiration, gives the natural second, which is the measure of the earth's +progress in its daily revolution. The Greek fable of the Titans is an +elaborate exposition of the atomic theory: but any attempt to convince +learned classics would only meet their derision; so much does long-fostered +prejudice stand in the way of truth. The author complains bitterly that men +of science will not attend to him and others like him: he observes, that +"in the time occupied in declining, a man of science might test the +merits." This is, alas! too true; so well do applicants of this kind know +how to stick on. But every rule has its exception: I have heard of one. The +late Lord Spencer[28]--the Lord Althorp of the House of Commons--told me +that a speculator once got access to him at the Home Office, and was +proceeding to unfold his way of serving the public. "I do not understand +these things," said Lord Althorp, "but I happen to have ---- (naming an +eminent engineer) upstairs; suppose you talk to him on the subject." The +discoverer went up, and in half-an-hour returned, and said, "I am very much +obliged to your Lordship for introducing me to Mr. ----; he has convinced +me {10} that I am quite wrong." I supposed, when I heard the story--but it +would not have been seemly to say it--that Lord A. exhaled candor and +sense, which infected those who came within reach: he would have done so, +if anybody. + + + +THE TRISECTION AND QUADRATURE AGAIN. + + A method to trisect a series of angles having relation to each other; + also another to trisect any given angle. By James Sabben. 1848 (two + quarto pages). + +"The consequence of years of intense thought": very likely, and very sad. + +1848. The following was sent to me in manuscript. I give the whole of it: + +"_Quadrature of the Circle_.--A quadrant is a curvilinear angle traversing +round and at an equal distance from a given point, called a center, no two +points in the curve being at the same angle, but irreptitiously graduating +from 90 to 60. It is therefore a mean angle of 90 and 60, which is 75, +because it is more than 60, and less than 90, approximately from 60 to 90, +and from 90 to 60, with equal generation in each irreptitious +approximation, therefore meeting in 75, and which is the mean angle of the +quadrant. + +"Or suppose a line drawn from a given point at 90, and from the same point +at 60. Let each of these lines revolve on this point toward each other at +an equal ratio. They will become one line at 75, and bisect the curve, +which is one-sixth of the entire circle. The result, taking 16 as a +diameter, gives an area of 201.072400, and a circumference of 50.2681. + +"The original conception, its natural harmony, and the result, to my own +mind is a demonstrative truth, which I presume it right to make known, +though perhaps at the hazard of unpleasant if not uncourteous remarks." + +I have added punctuation: the handwriting and spelling {11} are those of an +educated person; the word _irreptitious_ is indubitable. The whole is a +natural curiosity. + + + + The quadrature and exact area of the circle demonstrated. By Wm. + Peters. 8vo. _n. d._ (circa 1848).[29] + + Suggestions as to the necessity for a revolution in philosophy; and + prospectus for the establishment of a new quarterly, to be called the + _Physical Philosopher and Heterodox Review_. By Q. E. D. 8vo. 1848. + +These works are by one author, who also published, as appears by +advertisement, + +"Newton rescued from the precipitancy of his followers through a century +and a half,"[30] and "Dangers along a coast by correcting (as it is called) +a ship's reckoning by bearings of the land at night fall, or in a fog, +nearly out of print. Subscriptions are requested for a new edition." + +The area of a circle is made four-fifths of the circumscribed square: +proved on an assumption which it is purposed to explain in a longer +essay.[31] The author, as Q. E. D., was in controversy with the _Athenaeum_ +journal, and criticised a correspondent, D., who wrote against a certain +class of discoverers. He believed the common theories of hydrostatics to be +wrong, and one of his questions was: + +"Have you ever taken into account anent gravity and gravitation the fact +that a five grain cube of cork will of itself half sink in the water, +whilst it will take 20 grains of brass, which will sink of itself, to pull +under the other half? Fit this if you can, friend D., to your notions of +gravity and specific gravity, as applied to the construction of a universal +law of gravitation." + +This the _Athenaeum_ published--but without some Italics, for which the +editor was sharply reproved, as a sufficient {12} specimen of the _quod +erat_ D. _monstrandum_: on which the author remarks--"D,--Wherefore the e +caret? is it D apostrophe? D', D'M, D'Mo, D'Monstrandum; we cannot find the +_wit_ of it." This I conjecture to contain an illusion to the name of the +supposed author; but whether De Mocritus, De Mosthenes, or De Moivre was +intended, I am not willing to decide. + + + + The Scriptural Calendar and Chronological Reformer, for the statute + year 1849. Including a review of recent publications on the Sabbath + question. London, 1849, 12mo.[32] + +This is the almanac of a sect of Christians who keep the Jewish Sabbath, +having a chapel at Mill Yard, Goodman's Fields. They wrote controversial +works, and perhaps do so still; but I never chanced to see one. + + + + Geometry _versus_ Algebra; or the trisection of an angle geometrically + solved. By W. Upton, B.A.[33] Bath (circa 1849). 8vo. + +The author published two tracts under this title, containing different +alleged proofs: but neither gives any notice of the change. Both contain +the same preface, complaining of the British Association for refusing to +examine the production. I suppose that the author, finding his first proof +wrong, invented the second, of which the Association never had the offer; +and, feeling sure that they would have equally refused to examine the +second, thought it justifiable to {13} present that second as the one which +they had refused. Mr. Upton has discovered that the common way of finding +the circumference is wrong, would set it right if he had leisure, and, in +the mean time, has solved the problem of the duplication of the cube. + +_The trisector of an angle, if he demand attention from any mathematician, +is bound to produce, from his construction, an expression for the sine or +cosine of the third part of any angle, in terms of the sine or cosine of +the angle itself, obtained by help of no higher than the square root._ The +mathematician knows that such a thing cannot be; but the trisector +virtually says it can be, and is bound to produce it, to save time. This is +the misfortune of most of the solvers of the celebrated problems, that they +have not knowledge enough to present those consequences of their results by +which they can be easily judged. Sometimes they have the knowledge and +quibble out of the use of it. In many cases a person makes an honest +beginning and presents what he is sure is a solution. By conference with +others he at last feels uneasy, fears the light, and puts self-love in the +way of it. Dishonesty sometimes follows. The speculators are, as a class, +very apt to imagine that the mathematicians are in fraudulent confederacy +against them: I ought rather to say that each one of them consents to the +mode in which the rest are treated, and fancies conspiracy against himself. +The mania of conspiracy is a very curious subject. I do not mean these +remarks to apply to the author before me. + +One of Mr. Upton's trisections, if true, would prove the truth of the +following equation: + + 3 cos ([theta] / 3) = 1 + [root](4 - sin^2[theta]) + +which is certainly false.[34] + +{14} + +In 1852 I examined a terrific construction, at the request of the late Dr. +Wallich,[35] who was anxious to persuade a poor countryman of his, that +trisection of the angle was waste of time. One of the principles was, that +"magnitude and direction determine each other." The construction was +equivalent to the assertion that, [theta] being any angle, the cosine of +its third part is + + sin 3[theta] . cos(5[theta]/2) + sin^2 [theta] sin (5[theta]/2) + +divided by the square root of + + sin^2 3[theta] . cos^2 (5[theta]/2) + sin^4 [theta] + sin 3[theta] . sin + 5[theta] . sin^2 [theta]. + +This is from my rough notes, and I believe it is correct.[36] It is so +nearly true, unless the angle be very obtuse, that common drawing, applied +to the construction, will not detect the error. There are many formulae of +this kind: and I have several times found a speculator who has discovered +the corresponding construction, has seen the approximate success of his +drawing--often as great as absolute truth could give in graphical +practice,--and has then set about his demonstration, in which he always +succeeds to his own content. + +There is a trisection of which I have lost both cutting and reference: I +think it is in the _United Service Journal_. I could not detect any error +in it, though certain there must {15} be one. At least I discovered that +two parts of the diagram were incompatible unless a certain point lay in +line with two others, by which the angle to be trisected--and which was +trisected--was bound to be either 0 deg. or 180 deg.. + +Aug. 22, 1866. Mr. Upton sticks to his subject. He has just published "The +Uptonian Trisection. Respectfully dedicated to the schoolmasters of the +United Kingdom." It seems to be a new attempt. He takes no notice of the +sentence I have put in italics: nor does he mention my notice of him, +unless he means to include me among those by whom he has been "ridiculed +and sneered at" or "branded as a brainless heretic." I did neither one nor +the other: I thought Mr. Upton a paradoxer to whom it was likely to be +worth while to propound the definite assertion now in italics; and Mr. +Upton does not find it convenient to take issue on the point. He prefers +general assertions about algebra. So long as he cannot meet algebra on the +above question, he may issue as many "respectful challenges" to the +mathematicians as he can find paper to write: he will meet with no +attention. + + + +There is one trisection which is of more importance than that of the angle. +It is easy to get half the paper on which you write for margin; or a +quarter; but very troublesome to get a third. Show us how, easily and +certainly, to fold the paper into three, and you will be a real benefactor +to society. + +Early in the century there was a Turkish trisector of the angle, Hussein +Effendi, who published two methods. He was the father of Ameen Bey, who was +well known in England thirty years ago as a most amiable and cultivated +gentleman and an excellent mathematician. He was then a student at +Cambridge; and he died, years ago, in command of the army in Syria. Hussein +Effendi was instructed in mathematics by Ingliz Selim Effendi, who +translated a work {16} of Bonnycastle[37] into Turkish.[38] This Englishman +was Richard Baily, brother of Francis Baily[39] the astronomer, who +emigrated to Turkey in his youth, and adopted the manners of the Turks, but +whether their religion also I never heard, though I should suppose he did. + +I now give the letters from the agricultural laborer and his friend, +described on page 12, Vol. I. They are curiosities; and the history of the +quadrature can never be well written without some specimens of this kind: + +"Doctor Morgan, Sir. Permit me to address you + +"Brute Creation may perhaps enjoy the faculty of beholding visible things +with a more penitrating eye than ourselves. But Spiritual objects are as +far out of their reach as though they had no being + +"Nearest therefore to the brute Creation are those men who Suppose +themselves to be so far governed by external objects as to believe nothing +but what they See and feel And Can accomedate to their Shallow +understanding and Imaginations + +"My Dear Sir Let us all Consult ourselves by the wise proverb. + +"I believe that evry man^s merit & ability aught to be appreciated and +valued In proportion to its worth & utility + +"In whatever State or Circumstances they may fortunately or unfortunately +be placed + +"And happy it is for evry man to know his worth and place + +"When a Gentleman of your Standing in Society Clad with those honors Can +not understand or Solve a problem That is explicitly explained by words and +Letters and {17} mathematically operated by figuers He had best consult the +wise proverd + +"Do that which thou Canst understand and Comprehend for thy good. + +"I would recommend that Such Gentleman Change his business + +"And appropriate his time and attention to a Sunday School to Learn what he +Could and keep the Litle Children form durting their Close + +"With Sincere feelings of Gratitude for your weakness and Inability I am + + "Sir your Superior in Mathematics ----" + +"1849 June th29." + + + +"Dor Morgin Sir + +"I wrote and Sent my work to Professor ---- of ---- State of ---- United +States + +"I am now in the possession of the facts that he highly approves of my +work. And Says he will Insure me Reward in the States + +"I write this that you may understand that I have knowledge of the unfair +way that I am treated In my own nati County + +"I am told and have reasons to believe that it is the Clergy that treat me +so unjust. + +"I am not Desirous of heaping Disonors upon my own nation. But if I have to +Leave this kingdom without my Just dues. The world Shall know how I am and +have been treated. + + "I am Sir Desirous of my + "Just dues ----" + +"1849 July 3." + + + +"July 7th, 1849. + +"Sir, I have been given to understand that a friend of mine one whom I +shall never be ashamed to acknowledge as {18} such tho' lowly his origine; +nay not only not ashamed but proud of doing so for I am one of those who +esteem and respect a man according to his ability and probity, deeming with +Dr. Watts 'that the mind is the standard of the man,'[40] has laid before +you and asked your opinion of his extraordinary performance, viz. the +quadrature of the circle, he did this with the firmest belief that you +would not only treat the matter in a straightforward manner but with the +conviction that from your known or supposed knowledge of mathematicks would +have given an upright and honorable decision upon the subject; but the +question is have you done so? Could I say yes I would with the greatest of +pleasure and have congratulated you upon your decision whatever it might +have been but I am sorry to say that I cannot your letter is a paltry +evasion, you say 'that it is a great pity that you (Mr. ----) should have +attempted this (the quadrature of the circle) for your mathematical +knowledge is not sufficient to make you know in what the problem consists,' +you don't say in what it does consist _according to your ideas_, oh! no +nothing of the sort, you enter into no disquisition upon the subject in +order to show where you think Mr. ---- is wrong and why you have not is +simply--_because you cannot_--you know that he has done it and what is if I +am not wrongly informed _you have been heard to say so_. He has done what +you nor any other mathematician as those who call themselves such have +done. And what is the reason that you will not candidly acknowledge to him +as you have to others that he has squared the circle shall I tell you? it +is because he has performed the feat to obtain the glory of which +mathematicians have battled from time immemorial that they might encircle +their brows with a wreath of laurels far more glorious than ever conqueror +won it is simply this that it is a poor man a {19} humble artisan who has +gained that victory that you don't like to acknowledge it you don't like to +be beaten and worse to acknowledge that you have miscalculated, you have in +short too small a soul to acknowledge that he is right. + +"I was asked my opinion and _I_ gave it unhesitatingly in the affirmative +and I am backed in my opinion not only by Mr. ---- a mathematician and +watchmaker residing in the boro of Southwark but by no less an authority +than the Professor of mathematics of ---- College ---- ---- United States +Mr. ---- and I presume that he at least is your equal as an authority and +Mr. ---- says that the government of the U.S. will recompense M. D. for the +discovery he has made if so what a reflection upon Old england the boasted +land of freedom the nursery of arts and sciences that her sons are obliged +to go to a foreign country to obtain that recompense to which they are +justly entitled + +"In conclusion I had to contradict an assertion you made to the effect that +'there is not nor ever was any reward offered by the government of this +country for the discovery of the quadrature of the circle.' I beg to inform +you that there _was_ but that it having been deemed an impossibility the +government has withdrawn it. I do this upon no less an authority than the +Marquis of Northampton.[41] + + "I am, sir, yours ----" + +"Dr. Morgan." + + + +THE MOON'S ROTATION. + + Notes on the Kinematic Effects of Revolution and Rotation, with + reference to the Motions of the Moon and of the earth. By Henry + Perigal, Jun. Esq. London, 1846-1849, 8vo. + + On the misuse of technical terms. Ambiguity of the terms _Rotation_ and + _Revolution_, owing to the double meaning improperly {20} attributed to + each of the words. (No date nor place, but by Mr. Perigal,[42] I have + no doubt, and containing letters of 1849 and 1850.) + + The moon controversy. Facts _v._ Definitions. By H. P., Jun. London, + 1856, 8vo. (pp. 4.) + +Mr. Henry Perigal helped me twenty years ago with the diagrams, direct from +the lathe to the wood, for the article "Trochoidal Curves," in the _Penny +Cyclopaedia_: these cuts add very greatly to the value of the article, +which, indeed, could not have been made intelligible without them. He has +had many years' experience, as an amateur turner, in combination of double +and triple circular motions, and has published valuable diagrams in +profusion. A person to whom the double circular motion is familiar in the +lathe naturally looks upon one circle moving upon another as in _simple_ +motion, if the second circle be fixed to the revolving radius, so that one +and the same point of the moving circle travels upon the fixed circle. Mr. +Perigal commenced his attack upon the moon for moving about her axis, in +the first of the tracts above, ten years before Mr. Jellinger Symons;[43] +but he did not think it necessary to make it a subject for the _Times_ +newspaper. His familiarity with combined motions enabled him to handle his +arguments much better than Mr. J. Symons could do: in fact, he is the +clearest assailant of the lot which turned out with Mr. J. Symons. But he +is as wrong as the rest. The assault is now, I suppose, abandoned, until it +becomes epidemic again. This it will do: it is one of those fallacies which +are very tempting. There was a dispute on the subject in 1748, between +James Ferguson[44] and an anonymous opponent; and I think there have been +others. + +{21} + +A poet appears in the field (July 19, 1863) who calls himself Cyclops, and +writes four octavo pages. He makes a distinction between _rotation_ and +_revolution_; and his doctrines and phrases are so like those of Mr. +Perigal that he is a follower at least. One of his arguments has so often +been used that it is worth while to cite it: + + "Would Mathematicals--forsooth-- + If true, have failed to prove its truth? + Would not they--if they could--submit + Some overwhelming proofs of it? + But still it totters _proofless_! Hence + There's strong presumptive evidence + None do--or can--such proof profound + Because _the dogma is unsound_. + For, were there means of doing so, + They would have proved it long ago." + +This is only one of the alternatives. Proof requires a person who can give +and a person who can receive. I feel inspired to add the following: + + "A blind man said, As to the Sun, + I'll take my Bible oath there's none; + For if there had been one to show + They would have shown it long ago. + How came he such a goose to be? + Did he not know he couldn't see? + Not he!" + +The absurdity of the verses is in the argument. The writer was not so +ignorant or so dishonest as to affirm that nothing had been offered by the +other side as proof; accordingly, his syllogism amounts to this: If your +proposition were true, you could have given proof satisfactory to _me_; but +this you have not done, therefore, your proposition is not true. + +The echoes of the moon-controversy reached Benares in 1857, in which year +was there published a pamphlet "Does the Moon Rotate?" in Sanskrit and +English. The {22} arguments are much the same as those of the discussion at +home. + + + +ON THE NAMES OF RELIGIOUS BODIES. + +We see that there are paradoxers in argument as well as in assertion of +fact: my plan does not bring me much into contact with these; but another +instance may be useful. Sects, whether religious or political, give +themselves names which, in meaning, are claimed also by their opponents; +loyal, liberal, conservative (of good), etc. have been severally +appropriated by parties. _Whig_ and _Tory_ are unobjectionable names: the +first--which occurs in English ballad as well as in Scotland--is sour +milk;[45] the second is a robber. In theology, the Greek Church is +_Orthodox_, the Roman is _Catholic_, the modern Puritan is _Evangelical_, +etc. + +The word _Christian_ (Vol. I, p. 248[46]) is an instance. When words begin, +they carry their meanings. The Jews, who had their Messiah to come, and the +followers of Jesus of Nazareth, who took _Him_ for their Messiah, were both +_Christians_ (which means _Messianites_): the Jews would never have +invented the term to signify _Jesuans_, nor would the disciples have +invented such an ambiguous term for themselves; had they done so, the Jews +would have disputed it, as they would have done in later times if they had +had fair play. The Jews of our day, I see by their newspapers, speak of +Jesus Christ as the _Rabbi Joshua_. But the {23} heathens, who knew little +or nothing about the Jewish hope, would naturally apply the term +_Christians_ to the only followers of a _Messiah_ of whom they had heard. +For the _Jesuans_ invaded them in a missionary way; while the Jews did not +attempt, at least openly, to make proselytes. + +All such words as Catholic, etc., are well enough as mere nomenclature; and +the world falls for the most part, into any names which parties choose to +give themselves. Silly people found inferences on this concession; and, as +usually happens, they can cite some of their betters. St. Augustine,[47] a +freakish arguer, or, to put it in the way of an old writer, _lectorem ne +multiloquii taedio fastidiat, Punicis quibusdam argutiis recreare +solet_,[48] asks, with triumph, to what chapel a stranger would be +directed, if he inquired the way to the _Catholic assembly_. But the best +exhibition of this kind in our own century is that made by the excellent +Dr. John Milner,[49] in a work (first published in 1801 or 1802) which I +suppose still circulates, "The End of Religious Controversy": a startling +title which, so far as its truth is concerned, might as well have been "The +floor of the bottomless pit." This writer, whom every one of his readers +will swear to have been a worthy soul, though many, even of his own sect, +will not admire some of his logic, speaks as follows: + +"Letter xxv. _On the true Church being Catholic._ In treating of this third +mark of the true Church, as expressed in our common creed, I feel my +spirits sink within me, and I am almost tempted to throw away my pen in +despair. For what chance is there of opening the eyes of candid Protestants +to the other marks of the Church, if they are capable of keeping them shut +to this? Every time they address the {24} God of Truth, either in solemn +worship or in private devotion [stretch of rhetoric], they are forced, each +of them, to repeat: _I believe in_ THE CATHOLIC _Church_, and yet if I ask +any of them the question: _Are you a_ CATHOLIC? he is sure to answer me, +_No, I am a_ PROTESTANT! Was there ever a more glaring instance of +inconsistency and self-condemnation among rational beings!" + + "John Milner, honest and true, + Did what honest people still may do, + If they write for the many and not for the few, + But what by and bye they must eschew." + +He _shortened his clause_; and for a reason. If he had used the whole +epithet which he knew so well, any one might have given his argument a +half-turn. Had he written, as he ought, "the _Holy_ Catholic Church" and +then argued as above, some sly Protestant would have parodied him with "and +yet if I ask any of them the question: _Are you_ HOLY? he is sure to answer +me _No, I am a_ SINNER." To take the adjective from the Church, and apply +it to the individual partisan, is recognized slipslop, but not ground of +argument. If Dr. M. had asked his Protestant whether he belonged to the +Catholic _Church_, the answer would have been Yes, but not to the Roman +branch. When he put his question as he did, he was rightly answered and in +his own division. This leaving out words is a common practice, especially +when the omitter is in authority, and cannot be exposed. A year or two ago +a bishop wrote a snubbing letter to a poor parson, who had complained that +he was obliged, in burial, to send the worst of sinners to everlasting +happiness. The bishop sternly said, "_hope_[50] is not _assurance_." {25} +Could the clergyman have dared to answer, he would have said, "No, my Lord! +but '_sure and certain_ hope' is as like assurance as a _minikin_ man is +like a dwarf." Sad to say, a theologian must be illogical: I feel sure that +if you took the clearest headed writer on logic that ever lived, and made a +bishop of him, he would be shamed by his own books in a twelvemonth. + +Milner's sophism is glaring: but why should Dr. Milner be wiser than St. +Augustine, one of his teachers? I am tempted to let out the true derivation +of the word _Catholic, as exclusively applied to the Church of Rome_. All +can find it who have access to the _Rituale_ of Bonaventura Piscator[51] +(lib. i. c. 12, _de nomine Sacrae Ecclesiae_, p. 87 of the Venice {26} folio +of 1537). I am told that there is a _Rituale_ in the Index Expurgatorius, +but I have not thought it worth while to examine whether this be the one: I +am rather inclined to think, as I have heard elsewhere, that the book was +held too dangerous for the faithful to know of it, even by a prohibition: +it would not surprise me at all if Roman Christians should deny its +existence.[52] + +It amuses me to give, at a great distance of time, a small Rowland for a +small Oliver,[53] which I received, _de par l'Eglise_,[54] so far as lay in +the Oliver-carrier more than twenty years ago. The following contribution +of mine to _Notes and Queries_ (3d Ser. vi. p. 175, Aug. 27, 1864) will +explain what I say. There had been a complaint that a contributor had used +the term _Papist_, which a very excellent dignitary of the Papal system +pronounced an offensive term: + + + +PAPIST. + +The term _papist_ should be stripped of all except its etymological +meaning, and applied to those who give the higher and final authority to +the declaration _ex cathedra_[55] of the Pope. See Dr. Wiseman's[56] +article, _Catholic Church_, in the _Penny Cyclopaedia_. + +What is one to do about these names? First, it is clear that offence +should, when possible, be avoided: secondly, no one must be required to +give a name which favors _any_ assumption made by those to whom it is +given, and not {27} granted by those who give it. Thus the subdivision +which calls itself distinctly _Evangelical_ has no right to expect others +to concede the title. Now the word _Catholic_, of course, falls under this +rule; and even _Roman Catholic_ may be refused to those who would restrict +the word _Catholic_ to themselves. _Roman Christian_ is unobjectionable, +since the Roman Church does not deny the name of Christian to those whom +she calls heretics. No one is bound in this matter by Acts of Parliament. +In many cases, no doubt, names which have offensive association are used +merely by habit, sometimes by hereditary transmission. Boswell records of +Johnson that he always used the words "dissenting teacher," refusing +_minister_ and _clergyman_ to all but the recipients of episcopal +ordination. + +This distinctive phrase has been widely adopted: it occurs in the Index of +3d S. iv. [_Notes and Queries_]. Here we find "Platts (Rev. John), +Unitarian teacher, 412;" the article indexed has "Unitarian minister." + +This, of course is habit: an intentional refusal of the word _minister_ +would never occur in an index. I remember that, when I first read about Sam +Johnson's little bit of exclusiveness, I said to myself: "Teacher? Teacher? +surely I remember One who is often called _teacher_, but never _minister_ +or _clergyman_: have not the dissenters got the best of it?" + +When I said that the Roman Church concedes the epithet Christians to +Protestants, I did not mean that all its adherents do the same. There is, +or was, a Roman newspaper, the _Tablet_, which, seven or eight years ago, +was one of the most virulent of the party journals. In it I read, referring +to some complaint of grievance about mixed marriages, that if _Christians_ +would marry _Protestants_ they must take the consequences. My memory notes +this well; because I recollected, when I saw it, that there was in the +stable a horse fit to run in the curricle with this one. About seventeen +years ago an Oxford M. A., who hated {28} mathematics like a genuine +Oxonian of the last century, was writing on education, and was compelled to +give some countenance to the nasty subject. He got out cleverly; for he +gave as his reason for the permission, that man is an arithmetical, +geometrical, and mechanical _animal_, as well as a rational _soul_. + +The _Tablet_ was founded by an old pupil of mine, Mr. Frederic Lucas,[57] +who availed himself of his knowledge of me to write some severe +articles--even abusive, I was told, but I never saw them--against me, for +contributing to the _Dublin Review_, and poking my heretic nose into +orthodox places. Dr. Wiseman, the editor, came in for his share, and ought +to have got all. Who ever blamed the pig for intruding himself into the +cabin when the door was left open? When Mr. Lucas was my pupil, he was of +the Society of Friends--in any article but this I should say _Quaker_--and +was quiet and gentlemanly, as members of that Church--in any article but +this I should, from mere habit, say _sect_--usually are. This is due to his +memory; for, by all I heard, when he changed his religion he ceased to be +Lucas couchant, and became Lucas rampant, fanged and langued gules. (I +looked into Guillim[58] to see if my terms were right: I could not find +them; but to prove I have been there, I notice that he calls a violin a +_violent_. How comes the word to take this form?) I met with several Roman +Christians, born and bred, who were very much annoyed at Mr. Lucas and his +doings; and said some severe things about new converts needing +kicking-straps. + +{29} + +The mention of Dr. Wiseman reminds me of another word, appropriated by +Christians to themselves: _fides_;[59] the Roman faith is _fides_, and +nothing else; and the adherents are _fideles_.[60] Hereby hangs a retort. +When Dr. Wiseman was first in England, he gave a course of lectures in +defence of his creed, which were thought very convincing by those who were +already convinced. They determined to give him a medal, and there was a +very serious discussion about the legend. Dr. Wiseman told me himself that +he had answered to his subscribers that he would not have the medal at all +unless--(naming some Italian authority, whom I forget) approved of the +legend. At last _pro fide vindicata_[61] was chosen: this may be read +either in a Popish or heretical sense. The feminine substantive _fides_ +means confidence, trust, (it is made to mean _belief_), but _fidis_, with +the same ablative, _fide_, and also feminine, is a _fiddle-string_.[62] If +a Latin writer had had to make a legend signifying "For the defence of the +fiddle-string," he could not have done it otherwise, in the terseness of a +legend, than by writing _pro fide vindicata_. Accordingly, when a Roman +Christian talks to you of the _faith_, as a thing which is his and not +yours, you may say _fiddle_. I have searched Bonaventura Piscator in vain +for notice of this ambiguity. But the Greeks said fiddle; according to +Suidas,[63] [Greek: skindapsos][64]--a word meaning a four stringed +instrument played with a quill--was an exclamation of contemptuous dissent. +How the wits of different races jump! + +{30} + +I am reminded of a case of _fides vindicata_, which, being in a public +letter, responding to a public invitation, was not meant to be +confidential. Some of the pupils of University College, in which all +subdivisions of religion are (1866; _were_, 1867) on a level, have of +course changed their views in after life, and become adherents of various +high churches. On the occasion of a dinner of old students of the College, +convened by circular, one of these students, whether then Roman or +Tractarian Christian I do not remember, not content with simply giving +negative answer, or none at all, concocted a jorum of theological rebuke, +and sent it to the Dinner Committee. Heyday! said one of them, this man got +out of bed backwards! How is that? said the rest. Why, read his name +backwards, and you will see. As thus read it was--_No grub_![65] + + + +THE WORD CHURCH. + +To return to _Notes and Queries_. The substitution in the (editorial) index +of "Unitarian teacher," for the contributor's "Unitarian minister," struck +me very much. I have seldom found such things unmeaning. But as the journal +had always been free from editorial sectarianisms,--and very apt to check +the contributorial,--I could not be sure in this case. True it was, that +the editor and publisher had been changed more than a year before; but this +was not of much force. Though one swallow does not make a summer, I have +generally found it show that summer is coming. However, thought I to +myself, if this be Little Shibboleth, we shall have Big Shibboleth +by-and-bye. At last it came. About a twelvemonth afterwards, (3d S. vii. p. +36) the following was the _editorial_ answer to the question when the +establishment was first called the "Church of England and Ireland": + +{31} + +"That unmeaning clause, 'The United Church of England and Ireland,' which +occurs on the title-page of _The Book of Common Prayer_, was first used at +the commencement of the present century. The authority for this phrase is +the fifth article of the Union of 1800: 'That the Churches of England and +Ireland be united into one _Protestant_ (!) episcopal Church, to be called +"The United Church of England and Ireland."' Of course, churchmen are not +responsible for the theology of Acts of Parliament, especially those passed +during the dark ages of the Georgian era." + +That is to say, the journal gives its adhesion to the party which--under +the assumed title of _the_ Church of England--claims for the endowed +corporation for the support of religion rights which Parliament cannot +control, and makes it, in fact, a power above the State. The State has +given an inch: it calls this corporation by the name of the "United +_Church_ of England and Ireland," as if neither England nor Ireland had any +other Church. The corporation, accordingly aspires to an ell. But this the +nation will only give with the aspiration prefixed. To illustrate my +allusion in a delicate way to polite ears, I will relate what happened in a +Johnian lecture-room at Cambridge, some fifty years ago, my informant being +present. A youth of undue aspirations was giving a proposition, and at last +said, "Let E F be produced to 'L':" "Not quite so far, Mr. ----," said the +lecturer, quietly, to the great amusement of the class, and the utter +astonishment of the aspirant, who knew no more than a Tractarian the +tendency of his construction. + +This word _Church_ is made to have a very mystical meaning. The following +dialogue between Ecclesiastes and Haereticus, which I cannot vouch for, has +often taken place in spirit, if not in letter: E. The word _Church_ +([Greek: ekklesia])[66] is never used in the New Testament except generally +or locally for that holy and mystical body to which the sacraments and the +ordinances of Christianity are entrusted. {32} H. Indeed! E. It is beyond a +doubt (here he quoted half a dozen texts in support). H. Do you mean that +any doctrine or ordinance which was solemnly practised by the [Greek: +ekklesia] is binding upon you and me? E. Certainly, unless we should be cut +off from the congregation of the faithful. H. Have you a couple of hours to +spare? E. What for? H. If you have, I propose we spend them in crying, +Great is Diana of the Ephesians! E. What do you mean? H. You ought to know +the solemn service of the [Greek: ekklesia] (Acts xix. 32, 41), at Ephesus; +which any one might take to be true Church, by the more part not knowing +wherefore they were come together, and which was dismissed, after one of +the most sensible sermons ever preached, by the Recorder. E. I see your +meaning: it is true, there is that one exception! H. Why, the Recorder's +sermon itself contains another, the [Greek: ennomos ekklesia],[67] +legislative assembly. E. Ah! the New Testament can only be interpreted by +the Church! H. I see! the Church interprets itself into existence out of +the New Testament, and then interprets the New Testament out of existence +into itself! + +I look upon all the Churches as fair game which declare of me that _absque +dubio in aeternum peribo_;[68] not for their presumption towards God, but +for their personal insolence towards myself. I find that their sectaries +stare when I say this. Why! they do not speak of you in _particular_! These +poor reasoners seem to think that there could be no meaning, as against me, +unless it should be propounded that "without doubt he shall perish +everlastingly, especially A. De Morgan." But I hold, with the schoolmen, +that "_Omnis_ homo est animal" in conjunction with "Sortes est homo" +amounts to "_Sortes_ est animal."[69] But they do not mean it _personally_! +Every universal proposition is {33} personal to every instance of the +subject. If this be not conceded, then I retort, in their own sense and +manner, "Whosoever would serve God, before all things he must not pronounce +God's decision upon his neighbor. Which decision, except every one leave to +God himself, without doubt he is a bigoted noodle." + +The reasoning habit of the educated community, in four cases out of five, +permits universal propositions to be stated at one time, and denied, _pro +re nata_,[70] at another. "Before we proceed to consider any question +involving physical principles, we should set out with _clear ideas_ of the +naturally possible and impossible." The eminent man who said this, when +wanting it for his views of mental education (!) never meant it for more +than what was in hand, never assumed it in the researches which will give +him to posterity! I have heard half-a-dozen defences of his having said +this, not one of which affirmed the truth of what was said. A worthy +clergyman wrote that if A. B. had said a certain thing the point in +question would have been established. It was shown to him that A. B. _had_ +said it, to which the reply was a refusal to admit the point because A. B. +said it in a second pamphlet and in answer to objections. And I might give +fifty such instances with very little search. Always assume more than you +want; because you cannot tell how much you may want: put what is over into +the didn't-mean-that basket, or the extreme case what-not. + + + +PROTESTANT AND PAPAL CHRISTENDOM. + +Something near forty years of examination of the theologies on and +off--more years very much on than quite off--have given me a good title--to +myself, I ask no one else for leave--to make the following remarks: A +conclusion has _premises_, facts or doctrines from proof or authority, and +_mode of inference_. There may be invention or {34} falsehood of premise, +with good logic; and there may be tenable premise, followed by bad logic; +and there may be both false premise _and_ bad logic. The Roman system has +such a powerful manufactory of premises, that bad logic is little wanted; +there is comparatively little of it. The doctrine-forge of the Roman Church +is one glorious compound of everything that could make Heraclitus[71] sob +and Democritus[72] snigger. But not the only one. The Protestants, in +tearing away from the Church of Rome, took with them a fair quantity of the +results of the Roman forge, which they could not bring themselves to give +up. They had more in them of Martin than of Jack. But they would have no +premises, except from the New Testament; though some eked out with a few +general Councils. The consequence is that they have been obliged to find +such a logic as would bring the conclusions they require out of the +canonical books. And a queer logic it is; nothing but the Roman forge can +be compared with the Protestant loom. The picking, the patching, the +piecing, which goes to the Protestant _termini ad quem_,[73] would be as +remarkable to the general eye, as the Roman manufacture of _termini a +quo_,[74] if it were not that the world at large seizes the character of an +asserted fact better than that of a mode of inference. A grand step towards +the deification of a lady, made by alleged revelation 1800 years after her +death, is of glaring evidence: two or three additional shiffle-shuffles +towards defence of saying the Athanasian curse in church and unsaying it +out of church, are hardly noticed. Swift has bungled his satire where he +makes Peter a party to finding out what he wants, _totidem syllabis_ and +_totidem literis_, {35} when he cannot find it _totidem verbis_[75] This is +Protestant method: the Roman plan is _viam faciam_; the Protestant plan is +_viam inveniam_.[76] The public at large begins to be conversant with the +ways of _wriggling out_, as shown in the interpretations of the damnatory +parts of the Athanasian Creed, the phrases of the Burial Service, etc. The +time will come when the same public will begin to see the ways of +_wriggling in_. But one thing at a time: neither Papal Rome nor Protestant +Rome was built--nor will be pulled down--in a day. + +The distinction above drawn between the two great antitheses of Christendom +may be illustrated as follows. Two sets of little general dealers lived +opposite to one another: all sold milk. Each vaunted its own produce: one +set said that the stuff on the other side the way was only chalk and water; +the other said that the opposites sold all sorts of filth, of which calves' +brain was the least nasty. Now the fact was that both sets sold milk, and +from the same dairy: but adulterated with different sorts of dirty water: +and both honestly believed that the mixture was what they were meant to +sell and ought to sell. The great difference between them, about which the +apprentices fought each other like Trojans, was that the calves' brain men +poured milk into the water, and the chalk men poured water into the milk. +The Greek and Roman sects on one side, the Protestant sects on the other, +must all have _churches_: the Greek and Roman sects pour the New Testament +into their churches; the Protestant sects pour their churches into the New +Testament. The Greek and Roman insist upon the New Testament being no more +than part and parcel of their churches: the Protestant insist upon their +churches being as much part and parcel of the New Testament. All dwell +vehemently upon the doctrine that there must be milk {36} somewhere; and +each says--I have it. The doctrine is true: and can be verified by any one +who can and will go to the dairy for himself. Him will the several traders +declare to have no milk at all. They will bring their own wares, and +challenge a trial: they want nothing but to name the judges. To vary the +metaphor, those who have looked at Christianity in open day, know that all +who see it through painted windows shut out much of the light of heaven and +color the rest; it matters nothing that the stains are shaped into what are +meant for saints and angels. + +But there is another side to the question. To decompose any substance, it +must be placed between the poles of the battery. Now theology is but one +pole; philosophy is the other. No one can make out the combinations of our +day unless he read the writings both of the priest and the philosopher: and +if any one should hold the first word offensive, I tell him that I mean +_both_ words to be _significant_. In reading these writings, he will need +to bring both wires together to find out what it is all about. Time was +when most priests were very explicit about the fate of philosophers, and +most philosophers were very candid about their opinion of priests. But +though some extremes of the old sorts still remain, there is now, in the +middle, such a fusion of the two pursuits that a plain man is wofully +puzzled. The theologian writes a philosophy which seems to tell us that the +New Testament is a system of psychology; and the philosopher writes a +Christianity which is utterly unintelligible as to the question whether the +Resurrection be a fact or a transcendental allegory. What between the +theologian who assents to the Athanasian denunciation in what seems the +sense of no denunciation, and the philosopher who parades a Christianity +which looks like no revelation, there is a maze which threatens to have the +only possible clue in the theory that everything is something else, and +nothing is anything at all. But this is a paradox far beyond my handling: +it is a Budget of itself. {37} + + + +RELIGION AND PHILOSOPHY. + +Religion and Philosophy, the two best gifts of Heaven, set up in opposition +to each other at the revival of letters; and never did competing tradesmen +more grossly misbehave. Bad wishes and bad names flew about like swarms of +wasps. The Athanasian curses were intended against philosophers; who, had +they been a corporation, with state powers to protect them, would have +formulized a _per contra_. But the tradesmen are beginning to combine: they +are civil to each other; too civil by half. I speak especially of Great +Britain. Old theology has run off to ritualism, much lamenting, with no +comfort except the discovery that the cloak Paul left at Troas was a +chasuble. Philosophy, which always had a little sense sewed up in its +garments--to pay for its funeral?--has expended a trifle in accommodating +itself to the new system. But the two are poles of a battery; and a +question arises. + + If Peter Piper picked a peck of pepper, + Where is the peck of pepper Peter Piper picked? + +If Religion and Philosophy be the two poles of a battery, whose is the +battery Religion and Philosophy have been made the poles of? Is the change +in the relation of the wires any presumption of a removal of the managers? +We know pretty well who handled the instrument: has he resigned or been[77] +turned out? Has he been put under {38} restriction? A fool may ask more +questions than twenty sages can answer: but there is hope; for twenty sages +cannot ask more questions than one reviewer can answer. I should like to +see the opposite sides employed upon the question, What are the _commoda_, +and what the _pericula_,[78] of the current approximation of Religion and +Philosophy? + +All this is very profane and irreverent! It has always been so held by +those whose position demands such holding. To describe the Church as it is +passes for assailing the Church as it ought to be with all who cannot do +without it. In Bedlam[79] a poor creature who fancied he was St. Paul, was +told by another patient that he was an impostor; the first maniac lodged a +complaint against the second for calling St. Paul an impostor, which, he +argued, with much appearance of sanity, ought not to be permitted in a well +regulated madhouse. Nothing could persuade him that he had missed the +question, which was whether _he_ was St. Paul. The same thing takes place +in the world _at large_. And especially must be noted the refusal to permit +to the _profane_ the millionth part of the licence assumed by the _sacred_. +I give a sound churchman the epitaph of St. John Long; the usual +pronunciation of whose name must be noted-- + + "Behold! ye quacks, the vengeance strong + On deeds like yours impinging: + For here below lies St. John Long[80] + Who now must be _long singeing_." + +How shameful to pronounce this of the poor man! What, Mr. Orthodox! may I +not do in joke to one pretender what {39} you do in earnest--unless you +quibble--to all the millions of the Greek Church, and a great many others. +Enough of you and your reasoning! Go and square the circle! + +The few years which end with 1867 have shown, not merely the intermediate +fusion of Theology and Philosophy of which I have spoken, but much +concentration of the two extremes, which looks like a gathering of forces +for some very hard fought Armageddon. Extreme theology has been aiming at a +high Church in England, which is to show a new front to all heresy: and +extreme philosophy is contriving a physical organization which is to +_think_, and to show that mind is a consequence of matter, or thought a +recreation of brain. The physical speculators begin with a possible +hypothesis, in which they aim at explanation: and so the bold aspirations +of the author of the _Vestiges_ find standing-ground in the variation of +species by "natural selection." Some relics--so supposed--of extremely +ancient men are brought to help the general cause. Only distant hints are +given that by possibility it may end in the formation of all living +organisms from a very few, if not from one. The better heads above +mentioned know that their theory, if true, does not bear upon morals. The +formation of solar systems from a nebular hypothesis, followed by +organizations gradually emerging from some curious play of particles, nay, +the very evolution of mind and thought from such an apparatus, are all as +consistent with a Personal creative power to whom homage and obedience are +due, and who has declared himself, as with a blind Nature of Things. A pure +materialist, as to all things visible, may be even a bigotted Christian: +this is not frequent, but it is possible. There is a proverb which says, A +pig may fly, but it isn't a likely bird. But when the psychological +speculator comes in, he often undertakes to draw inferences from the +physical conclusions, by joining on his tremendous apparatus of _a priori_ +knowledge. He deduces that he can _do without_ a God: he can deduce all +things {40} without any such necessity. With Occam[81] and Newton he will +have no more causes than are necessary to explain phenomena _to him_: and +if by pure head-work combined with results of physical observation he can +construct his universe, he must be a very _unphilosophical_ man who would +encumber himself with a useless Creator! There is something tangible about +my method, says he; yours is vague. He requires it to be granted that his +system is _positive_ and that yours is _impositive_. So reasoned the stage +coachman when the railroads began to depose him--"If you're upset in a +stage-coach, why, there you are! but if you're upset on the railroad, where +are you?" The answer lies in another question, Which is most positive +knowledge, God deduced from man and his history, or the postulates of the +few who think they can reason _a priori_ on the tacit assumption of +unlimited command of data? + +We are not yet come to the existence of a school of philosophers who +explicitly deny a Creator: but we are on the way, though common sense may +interpose. There are always straws which show the direction of the wind. I +have before me the printed letter of a medical man--to whose professional +ability I have good testimony--who finds the vital principle in highly +rarefied oxygen. With the usual logic of such thinkers, he dismisses the +"eternal personal identity" because "If soul, spirit, mind, which are +merely modes of sensation, be the attribute or function of nerve-tissue, it +cannot possibly have any existence apart from its material organism!" How +does he know this _impossibility_? If all the mind _we_ know be from +nerve-tissue, how does it appear that mind in other planets may not be +another thing? Nay, when we come to _possibilities_, does not his own +system give a queer one? If highly rarefied oxygen be vital power, more +highly rarefied oxygen {41} may be more vital and more powerful. Where is +this to stop? Is it _impossible_ that a finite quantity, rarefied _ad +infinitum_, may be an Omnipotent? Perhaps the true Genesis, when written, +will open with "In the beginning was an imperial quart of oxygen at 60 +deg. of Fahrenheit, and the pressure of the atmosphere; and this oxygen +was infinitely rarefied; and this oxygen became God." For myself, my +aspirations as to this system are Manichaean. The quart of oxygen is the +Ormuzd, or good principle: another quart, of hydrogen, is the Ahriman, or +evil principle! My author says that his system explains Freewill and +Immortality so obviously that it is difficult to read previous speculations +with becoming gravity. My deduction explains the conflict of good and evil +with such clearness that no one can henceforward read the New Testament +with becoming reverence. The surgeon whom I have described is an early bud +which will probably be nipped by the frost and wither on the ground: but +there is a good crop coming. Material pneuma is destined to high functions; +and man is to read by gas-light. + + + +THE SUN AN ELECTRIC SPACE. + + The solar system truly solved; demonstrating by the perfect harmony of + the planets, founded on the four universal laws, the Sun to be an + electric space; and a source of every natural production displayed + throughout the solar system. By James Hopkins.[82] London, 1849, 8vo. + +The author says: + +"I am satisfied that I have given the true _laws_ constituting the _Sun_ to +be _space_; and I call upon those disposed to maintain the contrary, to +give true _laws_ showing him to be a body: until such can be satisfactorily +established, I have an undoubted claim to the credit of my theory,--That +the Sun is an _Electric Space_, fed and governed by the {42} planets, which +have the property of attracting heat from it; and the means of supplying +the necessary _pabulum_ by their degenerated air driven off towards the +central space--the wonderful alembic in which it becomes transmuted to the +revivifying necessities of continuous action; and the central space or Sun +being perfectly electric, has the counter property of repulsing the bodies +that attract it. How wonderful a conception! How beautiful, how magnificent +an arrangement! + +"O Centre! O Space! O Electric Space!" + + + +JOSEPH ADY. + +1849. _Joseph Ady_[83] is entitled to a place in this list of discoverers: +his great fault, like that of some others, lay in pushing his method too +far. He began by detecting unclaimed dividends, and disclosing them to +their right owners, exacting his fee before he made his communication. He +then generalized into trying to get fees from all of the _name_ belonging +to a dividend; and he gave mysterious hints of danger impending. For +instance, he would write to a clergyman that a legal penalty was hanging +over him; and when the alarmed divine forwarded the sum required for +disclosure, he was favored with an extract from some old statute or canon, +never repealed, forbidding a clergyman to be a member of a corporation, and +was reminded that he had insured his life in the ---- Office, which had a +royal charter. He was facetious, was Joseph: he described himself in his +circulars as "personally known to Sir Peter Laurie[84] and all other +aldermen"; which was nearly true, {43} as he had been before most of them +on charges of false pretence; but I believe he was nearly always within the +law. Sir James Duke, when Lord Mayor, having particularly displeased him by +a decision, his circulars of 1849 contain the following: + +"Should you have cause to complain of any party, Sir J. Duke has contrived +a new law of evidence, viz., write to him, he will consider your letter +sufficient proof, and make the parties complained of pay without judge or +jury, and will frank you from every expense." + +I strongly suspect that Joseph Ady believed in himself. + +He sometimes issued a second warning, of a Sibylline character: + +"Should you find cause to complain of anybody, my voluntary referee, the +Rt. Hon. Sir Peter Laurie, Kt., perpetual Deputy Lord Mayor, will see +justice done you without any charge whatever: he and his toady, -- ---- +----. The accursed of Moses can hang any man: thus, by catching him alone +and swearing Naboth spake evil against God and the King. Therefore (!) I +admit no strangers to a personal conference without a prepayment of 20s. +each. Had you attended to my former notice you would have received twice as +much: neglect this and you will lose all." + + + +ON MODERN ASTROLOGY. + + Zadkiel's Almanac for 1849. Nineteenth number. + + Raphael's Prophetic Almanac for 1849. Twenty-ninth number. + + Reasons for belief in judicial astrology, and remarks on the dangerous + character of popish priestcraft. London, 1849, 12mo. + + Astronomy in a nutshell: or the leading problems of the solar system + solved by simple proportion only, on the theory of magnetic attraction. + By Lieut. Morrison,[85] N. N. London (_s. a._) 12mo. + +{44} + +Lieut. Morrison is Zadkiel Tao Sze, and declares himself in real earnest an +astrologer. There are a great many books on astrology, but I have not felt +interest enough to preserve many of them which have come in my way. If +anything ever had a fair trial, it was astrology. The idea itself is +natural enough. A human being, set down on this earth, without any +tradition, would probably suspect that the heavenly bodies had something to +do with the guidance of affairs. I think that any one who tries will +ascertain that the planets do not prophesy: but if he should find to the +contrary, he will of course go on asking. A great many persons class +together belief in astrology and belief in apparitions: the two things +differ in precisely the way in which a science of observation differs from +a science of experiment. Many make the mistake which M. le Marquis made +when he came too late, and hoped M. Cassini[86] would do the eclipse over +again for his ladies. The apparition chooses its own time, and comes as +seldom or as often as it pleases, be it departed spirit, nervous +derangement, or imposition. Consequently it can only be observed, and not +experimented upon. But the heavens, if astrology be true, are prophesying +away day and night all the year round, and about every body. Experiments +can be made, then, except only on rare phenomena, such as eclipses: anybody +may choose his time and his question. This is the great difference: and +experiments were made, century after century. If astrology had been true, +it must have lasted in an ever-improving state. If it be true, it is a +truth, and a useful truth, which had experience and prejudice both in its +favor, and yet lost ground as soon as astronomy, its working tool, began to +improve. + + + +1850. A letter in the handwriting of an educated man, dated from a street +in which it must be taken that educated persons live, is addressed to the +Secretary of the {45} Astronomical Society about a matter on which the +writer says "his professional pursuit will enable him to give a +satisfactory reply." In a question before a court of law it is sworn on one +side that the moon was shining at a certain hour of a certain night on a +certain spot in London; on the other side it is affirmed that she was +clouded. The Secretary is requested to decide. This is curious, as the +question is not astrological. Persons still send to Greenwich, now and +then, to have their fortunes told. In one case, not very many years ago, a +young gentleman begged to know who his wife was to be, and what fee he was +to remit. + +Sometimes the astronomer turns conjurer for fun, and his prophesies are +fulfilled. It is related of Flamsteed[87] that an old woman came to know +the whereabouts of a bundle of linen which had strayed. Flamsteed drew a +circle, put a square into it, and gravely pointed out a ditch, near her +cottage, in which he said it would be found. He meant to have given the +woman a little good advice when she came back: but she came back in great +delight, with the bundle in her hand, found in the very place. The late +Baron Zach[88] received a letter from Pons,[89] a successful finder of +comets, complaining that for a certain period he had found no comets, +though he had searched diligently. Zach, a man of much sly humor, told him +that no spots had been seen on the sun for about the same time--which was +true,--and assured him that when the spots came back, the comets would come +with them. Some time after he got a letter {46} from Pons, who informed him +with great satisfaction that he was quite right, that very large spots had +appeared on the sun, and that he had found a fine comet shortly after. I do +not vouch for the first story, but I have the second in Zach's handwriting. +It would mend the joke exceedingly if some day a real relation should be +established between comets and solar spots: of late years good reason has +been shown for advancing a connection between these spots and the earth's +magnetism.[90] If the two things had been put to Zach, he would probably +have chosen the comets. Here is a hint for a paradox: the solar spots are +the dead comets, which have parted with their light and heat to feed the +sun, as was once suggested. I should not wonder if I were too late, and the +thing had been actually maintained. My list does not contain the twentieth +part of the possible whole. + +The mention of coincidences suggests an everlasting source of explanations, +applicable to all that is extraordinary. The great paradox of coincidence +is that of Leibnitz, known as the _pre-established harmony_, or _law of +coincidences_, by which, separately and independently, the body receives +impressions, and the mind proceeds as if it had perceived them from +without. Every sensation, and the consequent state of the soul, are +independent things coincident in time by the pre-established law. The +philosopher could not otherwise _account for_ the connection of mind and +matter; and he never goes by so vulgar a rule as _Whatever is, is_; to him +that which is not clear as to how, is not at all. Philosophers in general, +who tolerate each other's theories much better than Christians do each +other's failings, seldom revive Leibnitz's fantasy: they seem to act upon +the maxim quoted by Father Eustace[91] from the {47} Decretals, _Facinora +ostendi dum puniuntur, flagitia autem abscondi debent_.[92] + +The great _ghost-paradox_, and its theory of _coincidences_, will rise to +the surface in the mind of every one. But the use of the word _coincidence_ +is here at variance with its common meaning. When A is constantly +happening, and also B, the occurrence of A and B at the same moment is the +mere coincidence which may be casualty. But the case before us is that A is +constantly happening, while B, when it does happen, almost always happens +with A, and very rarely without it. That is to say, such is the phenomenon +asserted: and all who rationally refer it to casualty, affirm that B is +happening very often as well as A, but that it is not thought worthy of +being recorded except when A is simultaneous. Of course A is here a death, +and B the spectral appearance of the person who dies. In talking of this +subject it is necessary to put out of the question all who play fast and +loose with their secret convictions: these had better give us a reason, +when they feel internal pressure for explanation, that there is no +weathercock at Kilve; this would do for all cases. But persons of real +inquiry will see that first, experience does not bear out the asserted +frequency of the spectre, without the alleged coincidence of death: and +secondly, that if the crowd of purely casual spectres were so great that it +is no wonder that, now and then the person should have died at or near the +moment, we ought to expect a much larger proportion of cases in which the +spectre should come at the moment of the death of one or another of all the +cluster who are closely connected with the original of the spectre. But +this, we know, is almost without example. It remains then, for all, who +speculate at all, to look upon the asserted phenomenon, think what they may +of it, the thing which is to be explained, as a _connection_ in time of the +death, and the {48} simultaneous appearance of the dead. Any person the +least used to the theory of probabilities will see that purely casual +coincidence, the _wrong spectre_ being comparatively so rare that it may be +said never to occur, is not within the rational field of possibility. + +The purely casual coincidence, from which there is no escape except the +actual doctrine of special providences, carried down to a very low point of +special intention, requires a junction of the things the like of each of +which is always happening. I will give three instances which have occurred +to myself within the last few years: I solemnly vouch for the literal truth +of every part of all three: + +In August 1861, M. Senarmont,[93] of the French Institute, wrote to me to +the effect that Fresnel[94] had sent to England, in or shortly after 1824, +a paper for translation and insertion in the _European Review_, which +shortly afterwards expired. The question was what had become of that paper. +I examined the _Review_ at the Museum, found no trace of the paper, and +wrote back to that effect at the Museum, adding that everything now +depended on ascertaining the name of the editor, and tracing his papers: of +this I thought there was no chance. I posted this letter on my way home, at +a Post Office in the Hampstead Road at the junction with Edward Street, on +the opposite side of which is a bookstall. Lounging for a moment over the +exposed books, _sicut meus est mos_,[95] I saw, within a few minutes of the +posting of the letter, a little catch-penny book of anecdotes of Macaulay, +which I bought, and ran over for a minute. My eye was soon caught by this +sentence: "One of the young fellows immediately wrote to the editor (Mr. +Walker) {49} of the _European Review_." I thus got the clue by which I +ascertained that there was no chance of recovering Fresnel's paper. Of the +mention of current reviews, not one in a thousand names the editor. + +In the summer of 1865 I made my first acquaintance with the tales of +Nathaniel Hawthorne, and the first I read was about the siege of Boston in +the War of Independence. I could not make it out: everybody seemed to have +got into somebody else's place. I was beginning the second tale, when a +parcel arrived: it was a lot of old pamphlets and other rubbish, as he +called it, sent by a friend who had lately sold his books, had not thought +it worth while to send these things for sale, but thought I might like to +look at them and possibly keep some. The first thing I looked at was a +sheet which, being opened, displayed "A plan of Boston and its environs, +shewing the true situation of his Majesty's army and also that of the +rebels, drawn by an engineer, at Boston Oct. 1775." Such detailed plans of +current sieges being then uncommon, it is explained that "The principal +part of this plan was surveyed by Richard Williams, Lieutenant at Boston; +and sent over by the son of a nobleman to his father in town, by whose +permission it was published." I immediately saw that my confusion arose +from my supposing that the king's troops were besieging the rebels, when it +was just the other way. + +April 1, 1853, while engaged in making some notes on a logical point, an +idea occurred which was perfectly new to me, on the mode of conciliating +the notions _omnipresence_ and _indivisibility into parts_. What it was is +no matter here: suffice it that, since it was published elsewhere (in a +paper on _Infinity_, _Camb. Phil. Trans._ vol. xi. p. 1) I have not had it +produced to me. I had just finished a paragraph on the subject, when a +parcel came in from a bookseller containing Heywood's[96] _Analysis of +Kant's Critick_, 1844. + +{50} On turning over the leaves I found (p. 109) the identical thought +which up to this day, I only know as in my own paper, or in Kant. I feel +sure I had not seen it before, for it is in Kant's first edition, which was +never translated to my knowledge; and it does not appear in the later +editions. Mr. Heywood gives some account of the first edition. + +In the broadsheet which gave account of the dying scene of Charles II, it +is said that the Roman Catholic priest was introduced by P. M. A. C. F. The +chain was this: the Duchess of Portsmouth[97] applied to the Duke of York, +who may have consulted his Cordelier confessor, Mansuete, about procuring a +priest, and the priest was smuggled into the king's room by the Duchess and +Chiffinch.[98] Now the letters are a verbal acrostic of _Pere Mansuete a +Cordelier Friar_, and a syllabic acrostic of _PortsMouth and ChifFinch_. +This is a singular coincidence. Macaulay adopted the first interpretation, +preferring it to the second, which I brought before him as the conjecture +of a near relative of my own. But Mansuete is not mentioned in his +narrative: it may well be doubted whether the writer of a broadside for +English readers would use _Pere_ instead of _Father_. And the person who +really "reminded" the Duke of "the duty he owed to his brother," was the +Duchess and not Mansuete. But my affair is only with the coincidence. + +But there are coincidences which are really connected without the +connection being known to those who find in them matter of astonishment. +Presentiments furnish marked cases: sometimes there is no mystery to those +who have the clue. In the _Gentleman's Magazine_ (vol. 80, part 2, p. 33) +we read, the subject being presentiment of death, as follows: "In 1778, to +come nearer the recollection of {51} survivors, at the taking of +Pondicherry, Captain John Fletcher, Captain De Morgan, and Lieutenant +Bosanquet, each distinctly foretold his own death on the morning of his +fate." I have no doubt of all three; and I knew it of my grandfather long +before I read the above passage. He saw that the battery he commanded was +unduly exposed: I think by the sap running through the fort when produced. +He represented this to the engineer officers, and to the +commander-in-chief; the engineers denied the truth of the statement, the +commander believed them, my grandfather quietly observed that he must make +his will, and the French fulfilled his prediction. His will bore date the +day of his death; and I always thought it more remarkable than the +fulfilment of the prophecy that a soldier should not consider any danger +short of one like the above, sufficient reason to make his will. I suppose +the other officers were similarly posted. I am told that military men very +often defer making their wills until just before an action: but to face the +ordinary risks intestate, and to wait until speedy death must be the all +but certain consequence of a stupid mistake, is carrying the principle very +far. In the matter of coincidences there are, as in other cases, two +wonderful extremes with every intermediate degree. At one end we have the +confident people who can attribute anything to casual coincidence; who +allow Zadok Imposture and Nathan Coincidence to anoint Solomon Selfconceit +king. At the other end we have those who see something _very curious_ in +any coincidence you please, and whose minds yearn for a deep reason. A +speculator of this class happened to find that Matthew viii. 28-33 and Luke +viii. 26-33 contain the same account, that of the demons entering into the +swine. Very odd! chapters tallying, and verses so nearly: is the +versification rightly managed? Examination is sure to show that there are +monstrous inconsistencies in the mode of division, which being corrected, +the verses tally as well as the chapters. And then how comes it? I cannot +go on, {52} for I have no gift at torturing a coincidence, but I would lay +twopence, if I could make a bet--which I never did in all my life--that +some one or more of my readers will try it. Some people say that the study +of chances tends to awaken a spirit of gambling: I suspect the contrary. At +any rate, I myself, the writer of a mathematical book and a comparatively +popular book, have never laid a bet nor played for a stake, however small: +not one single time. + +It is useful to record such instances as I have given, with precision and +on the solemn word of the recorder. When such a story as that of Flamsteed +is told, _a priori_ assures us that it could not have been: the story may +have been a _ben trovato_,[99] but not the bundle. It is also useful to +establish some of the good jokes which all take for inventions. My friend +Mr. J. Bellingham Inglis,[100] before 1800, saw the tobacconist's carriage +with a sample of tobacco in a shield, and the motto _Quid rides_[101] (_N._ +& _Q._, 3d S. i. 245). His father was able to tell him all about it. The +tobacconist was Jacob Brandon, well known to the elder Mr. Inglis, and the +person who started the motto, the instant he was asked for such a thing, +was Harry Calender of Lloyd's, a scholar and a wit. My friend Mr. H. Crabb +Robinson[102] remembers the King's Counsel (Samuel Marryat) who took the +motto _Causes produce effects_, when his success enabled him to start a +carriage. + +The coincidences of errata are sometimes very remarkable: it may be that +the misprint has a sting. The death of Sir W. Hamilton[103] of Edinburgh +was known in London on a Thursday, and the editor of the _Athenaeum_ wrote +to {53} me in the afternoon for a short obituary notice to appear on +Saturday. I dashed off the few lines which appeared without a moment to +think: and those of my readers who might perhaps think me capable of +contriving errata with meaning will, I am sure, allow the hurry, the +occasion, and my own peculiar relation to the departed, as sufficient +reasons for believing in my entire innocence. Of course I could not see a +proof: and two errata occurred. The words "addition to Stewart"[104] +require "_for_ addition to _read_ edition of." This represents what had +been insisted on by the Edinburgh publisher, who, frightened by the edition +of Reid,[105] had stipulated for a simple reprint without notes. Again +"principles of logic and mathematics" required "_for_ mathematics _read_ +metaphysics." No four words could be put together which would have so good +a title to be Hamilton's motto. + + + +April 1850, found in the letter-box, three loose leaves, well printed and +over punctuated, being + + Chapter VI. Brethren, lo I come, holding forth the word of life, for so + I am commanded.... Chapter VII. Hear my prayer, O generations! and walk + by the way, to drink the waters of the river.... Chapter VIII. Hearken + o earth, earth, earth, and the kings of the earth, and their armies.... + +A very large collection might be made of such apostolic writings. They go +on well enough in a misty--meant for mystical--imitation of St. Paul or the +prophets, until at last some prodigious want of keeping shows the education +of the writer. For example, after half a page which might {54} pass for +Irving's[106] preaching--though a person to whom it was presented as such +would say that most likely the head and tail would make something more like +head and tail of it--we are astounded by a declaration from the _Holy +Spirit_, speaking of himself, that he is "not ashamed of the Gospel of +Christ." It would be long before we should find in _educated_ rhapsody--of +which there are specimens enough--such a thing as a person of the Trinity +taking merit for moral courage enough to stand where St. Peter fell. The +following declaration comes next--"I will judge between cattle and cattle, +that use their tongues." + + + +THE FIGURE OF THE EARTH. + + The figure of the earth. By J. L. Murphy,[107] of Birmingham. (London + and Birmingham, 4 pages, 12mo.) (1850?) + +Mr. Murphy invites attention and objection to some assertions, as that the +earth is prolate, not oblate. "If the philosopher's conclusion be right, +then the pole is the center of a valley (!) thirteen miles deep." Hence it +would be very warm. It is answer enough to ask--Who knows that it is not? + + + + *** A paragraph in the MS. appears to have been inserted in this place + by mistake. It will be found in the Appendix at the end of this + volume.--S. E. De M. + + + +PERPETUAL MOTION. + +1851. The following letter was written by one of a class of persons whom, +after much experience of them, I {55} do _not_ pronounce insane. But in +this case the second sentence gives a suspicion of actual delusion of the +senses; the third looks like that eye for the main chance which passes for +sanity on the Stock Exchange and elsewhere: + +15th Sept. 1851. + +"Gentlemen,--I pray you take steps to make known that yesterday I completed +my invention which will give motion to every country on the Earth;--to move +Machinery!--the long sought in vain 'Perpetual Motion'!!--I was supported +at the time by the Queen and H.R.H. Prince Albert. If, Gentlemen, you can +advise me how to proceed to claim the reward, if any is offered by the +Government, or how to secure the PATENT for the machine, or in any way +assist me by advice in this great work, I shall most graciously acknowledge +your consideration. + +These are my convictions that my SEVERAL discoveries will be realized: and +this great one can be at once acted upon: although at this moment it only +exists in my mind, from my knowledge of certain fixed principles in +nature:--the Machine I have not made, as I only completed the discovery +YESTERDAY, Sunday! + + I have, etc. ---- ----" + + To the Directors of the + London University, Gower Street. + + + +ON SPIRITUALISM. + + The Divine Drama of History and Civilisation. By the Rev. James Smith, + M.A.[108] London, 1854, 8vo. + +I have several books on that great paradox of our day, _Spiritualism_, but +I shall exclude all but three. The bibliography of this subject is now very +large. The question is one both of evidence and speculation;--Are the facts +{56} true? Are they caused by spirits? These I shall not enter upon: I +shall merely recommend this work as that of a spiritualist who does not +enter on the subject, which he takes for granted, but applies his derived +views to the history of mankind with learning and thought. Mr. Smith was a +man of a very peculiar turn of thinking. He was, when alive, the editor, or +_an_ editor, of the _Family Herald_: I say when alive, to speak according +to knowledge; for, if his own views be true, he may have a hand in it +still. The answers to correspondents, in his time, were piquant and +original above any I ever saw. I think a very readable book might be made +out of them, resembling "Guesses at Truth:" the turn given to an inquiry +about morals, religion, or socials, is often of the highest degree of +_unexpectedness_; the poor querist would find himself right in a most +unpalatable way. + +Answers to correspondents, in newspapers, are very often the fag ends of +literature. I shall never forget the following. A person was invited to +name a rule without exception, if he could: he answered "A man _must_ be +present when he is shaved." A lady--what right have ladies to decide +questions about shaving?--said this was not properly a rule; and the oracle +was consulted. The editor agreed with the lady; he said that "a man _must_ +be present when he is shaved" is not a _rule_, but a _fact_. + + + +[Among my anonymous communicants is one who states that I have done +injustice to the Rev. James Smith in "referring to him as a spiritualist," +and placing his "Divine Drama" among paradoxes: "it is no paradox, nor do +_spiritualistic_ views mar or weaken the execution of the design." Quite +true: for the design is to produce and enforce "spiritualistic views"; and +leather does not mar nor weaken a shoemaker's plan. I knew Mr. Smith well, +and have often talked to him on the subject: but more testimony from me is +unnecessary; his book will speak for itself. {57} His peculiar style will +justify a little more quotation than is just necessary to prove the point. +Looking at the "battle of opinion" now in progress, we see that Mr. Smith +was a prescient: + +(P. 588.) "From the general review of parties in England, it is evident +that no country in the world is better prepared for the great Battle of +Opinion. Where else can the battle be fought but where the armies are +arrayed? And here they all are, Greek, Roman, Anglican, Scotch, Lutheran, +Calvinist, Established and Territorial, with Baronial Bishops, and +Nonestablished of every grade--churches with living prophets and apostles, +and churches with dead prophets and apostles, and apostolical churches +without apostles, and philosophies without either prophets or apostles, and +only wanting one more, 'the Christian Church,' like Aaron's rod, to swallow +up and digest them all, and then bud and flourish. As if to prepare our +minds for this desirable and inevitable consummation, different parties +have been favored with a revival of that very spirit of revelation by which +the Church itself was originally founded. There is a complete series of +spiritual revelations in England and the United States, besides mesmeric +phenomena that bear a resemblance to revelation, and thus gradually open +the mind of the philosophical and infidel classes, as well as the professed +believers of that old revelation which they never witnessed in living +action, to a better understanding of that Law of Nature (for it is a Law of +Nature) in which all revelation originates and by which its spiritual +communications are regulated." + +Mr. Smith proceeds to say that there are _only_ thirty-five incorporated +churches in England, all formed from the New Testament except five, to each +of which five he concedes a revelation of its own. The five are the +Quakers, the Swedenborgians, the Southcottians, the Irvingites, and the +Mormonites. Of Joanna Southcott he speaks as follows: {58} + +(P. 592.) "Joanna Southcott[109] is not very gallantly treated by the +gentlemen of the Press, who, we believe, without knowing anything about +her, merely pick up their idea of her character from the rabble. We once +entertained the same rabble idea of her; but having read her works--for we +really have read them--we now regard her with great respect. However, there +is a great abundance of chaff and straw to her grain; but the grain is +good, and as we do not eat either the chaff or straw if we can avoid it, +nor even the raw grain, but thrash it and winnow it, and grind it and bake +it, we find it, after undergoing this process, not only very palatable, but +a special dainty of its kind. But the husk is an insurmountable obstacle to +those learned and educated gentlemen who judge of books entirely by the +style and the grammar, or those who eat grain as it grows, like the cattle. +Such men would reject all prological revelation; for there never was and +probably never will be a revelation by voice and vision communicated in +classical manner. It would be an invasion of the rights and prerogatives of +Humanity, and as contrary to the Divine and Established order of mundane +government, as a field of quartern loaves or hot French rolls." + + + +Mr. Smith's book is spiritualism from beginning to end; and my anonymous +gainsayer, honest of course, is either ignorant of the work he thinks he +has read, or has a most remarkable development of the organ of +imperception.] + + + +A CONDENSED HISTORY OF MATHEMATICS. + +I cut the following from a Sunday paper in 1849: + +"X. Y.--The Chaldeans began the mathematics, in which the Egyptians +excelled. Then crossing the sea, by means {59} of Thales,[110] the +Milesian, they came into Greece, where they were improved very much by +Pythagoras,[111] Anaxagoras,[112] and Anopides[113] of Chios. These were +followed by Briso,[114] Antipho, [two circle-squarers; where is Euclid?] +and Hippocrates,[115] but the excellence of the algebraic art was begun by +Geber,[116] an Arabian astronomer, and was carried on by Cardanus,[117] +Tartaglia,[118] Clavius,[119], Stevinus,[120] Ghetaldus,[121] +Herig_e_nius,[122] Fran. Van Schooten [meaning Francis Van Schooten[123]], +Florida de Beau_m_e,[124] etc." + +Bryso was a mistaken man. Antipho had the disadvantage of being in advance +of his age. He had the notion of which the modern geometry has made so +much, that of {60} a circle being the polygon of an infinitely great number +of sides. He could make no use of it, but the notion itself made him a +sophist in the eyes of Aristotle, Eutocius,[125] etc. Geber, an Arab +astronomer, and a reputed conjurer in Europe, seems to have given his name +to unintelligible language in the word _gibberish_. At one time _algebra_ +was traced to him; but very absurdly, though I have heard it suggested that +_algebra_ and _gibberish_ must have had one inventor. + +Any person who meddles with the circle may find himself the crane who was +netted among the geese: as Antipho for one, and Olivier de Serres[126] for +another. This last gentleman ascertained, by weighing, that the area of the +circle is very nearly that of the square on the side of the inscribed +equilateral triangle: which it is, as near as 3.162 ... to 3.141.... He did +not pretend to more than approximation; but Montucla and others +misunderstood him, and, still worse, misunderstood their own +misunderstanding, and made him say the circle was exactly double of the +equilateral triangle. He was let out of limbo by Lacroix, in a note to his +edition of Montucla's _History of Quadrature_. + + + +ST. VITUS, PATRON OF CYCLOMETERS. + + Quadratura del cerchio, trisezione dell' angulo, et duplicazione del + cubo, problemi geometricamente risolute e dimostrate dal Reverendo + Arciprete di San Vito D. Domenico Anghera,[127] Malta, 1854, 8vo. + + {61} + + Equazioni geometriche, estratte dalla lettera del Rev. Arciprete ... al + Professore Pullicino[128] sulla quadratura del cerchio. Milan, 1855 or + 1856, 8vo. + + Il Mediterraneo gazetta di Malta, 26 Decembre 1855, No. 909: also 911, + 912, 913, 914, 936, 939. + + The Malta Times, Tuesday, 9th June 1857. + + Misura esatta del cerchio, dal Rev. D. Anghera. Malta, 1857, 12mo. + + Quadrature of the circle ... by the Rev. D. Anghera, Archpriest of St. + Vito. Malta, 1858, 12mo. + +I have looked for St. Vitus in catalogues of saints, but never found his +legend, though he figures as a day-mark in the oldest almanacs. He must be +properly accredited, since he was an archpriest. And I pronounce and +ordain, by right accruing from the trouble I have taken in this subject, +that he, St. Vitus, who leads his votaries a never-ending and unmeaning +dance, shall henceforth be held and taken to be the patron saint of the +circle-squarer. His day is the 15th of June, which is also that of St. +Modestus,[129] with whom the said circle-squarer often has nothing to do. +And he must not put himself under the first saint with a slantendicular +reference to the other, as is much to be feared was done by the Cardinal +who came to govern England with a title containing St. Pudentiana,[130] who +shares a day with _St. Dunstan_. The Archpriest of St. Vitus will have it +that the square inscribed in a semicircle is half of the semicircle, or the +circumference 3-1/5 diameters. He is active and able, with {62} nothing +wrong about him except his paradoxes. In the second tract named he has +given the testimonials of crowned heads and ministers, etc. as follows. +Louis-Napoleon gives thanks. The minister at Turin refers it to the Academy +of Sciences, and hopes so much labor will be judged _degna di pregio_.[131] +The Vice-Chancellor of Oxford--a blunt Englishman--begs to say that the +University has never proposed the problem, as some affirm. The Prince +Regent of Baden has received the work with lively interest. The Academy of +Vienna is not in a position to enter into the question. The Academy of +Turin offers the most _distinct_ thanks. The Academy della Crusca attends +only to literature, but gives thanks. The Queen of Spain has received the +work with the highest appreciation. The University of Salamanca gives +infinite thanks, and feels true satisfaction in having the book. Lord +Palmerston gives thanks, by the hand of "William San." The Viceroy of +Egypt, not being yet up in Italian, will spend his first moments of leisure +in studying the book, when it shall have been translated into French: in +the mean time he congratulates the author upon his victory over a problem +so long held insoluble. All this is seriously published as a rate in aid of +demonstration. If these royal compliments cannot make the circumference of +a circle about 2 per cent. larger than geometry will have it --which is all +that is wanted--no wonder that thrones are shaky. + +I am informed that the legend of St. Vitus is given by Ribadeneira[132] in +his lives of Saints, and that Baronius,[133] in {63} his _Martyrologium +Romanum_, refers to several authors who have written concerning him. There +is an account in Mrs. Jameson's[134] _History of Sacred and Legendary Art_ +(ed. of 1863, p. 544). But it seems that St. Vitus is the patron saint of +_all_ dances; so that I was not so far wrong in making him the protector of +the cyclometers. Why he is represented with a cock is a disputed point, +which is now made clear: next after _gallus gallinaceus_[135] himself, +there is no crower like the circle-squarer. + + + +CELEBRATED APPROXIMATIONS OF [pi]. + +The following is an extract from the _English Cyclopaedia_, Art. TABLES: + +"1853. William Shanks,[136] _Contributions to Mathematics, comprising +chiefly the Rectification of the Circle to 607 Places of Tables_, London, +1853. (QUADRATURE OF THE CIRCLE.) Here is a _table_, because it tabulates +the results of the subordinate steps of this enormous calculation as far as +527 decimals: the remainder being added as results only during the +printing. For instance, one step is the calculation of the reciprocal of +601.5^{601}; and the result is given. The number of pages required to +describe these results is 87. Mr. Shanks has also thrown off, as chips or +splinters, the values of the base of Napier's logarithms, and of its +logarithms of 2, 3, 5, 10, to 137 decimals; and the value of the modulus +.4342 ... to 136 decimals: with the 13th, 25th, 37th ... up to the 721st +powers of 2. These tremendous stretches of calculation--at least we so call +them in our day--are useful in several respects; they prove more than {64} +the capacity of this or that computer for labor and accuracy; they show +that there is in the community an increase of skill and courage. We say in +the community: we fully believe that the unequalled turnip which every now +and then appears in the newspapers is a sufficient presumption that the +average turnip is growing bigger, and the whole crop heavier. All who know +the history of the quadrature are aware that the several increases of +numbers of decimals to which [pi] has been carried have been indications of +a general increase in the power to calculate, and in courage to face the +labor. Here is a comparison of two different times. In the day of +Cocker,[137] the pupil was directed to perform a common subtraction with a +voice-accompaniment of this kind: '7 from 4 I cannot, but add 10, 7 from 14 +remains 7, set down 7 and carry 1; 8 and 1 which I carry is 9, 9 from 2 I +cannot, etc.' We have before us the announcement of the following _table_, +undated, as open to inspection at the Crystal Palace, Sydenham, in two +diagrams of 7 ft. 2 in, by 6 ft. 6 in.: 'The figure 9 involved into the +912th power, and antecedent powers or involutions, containing upwards of +73,000 figures. Also, the proofs of the above, containing upwards of +146,000 figures. By Samuel Fancourt, of Mincing Lane, London, and completed +by him in the year 1837, at the age of sixteen. N.B. The whole operation +performed by simple arithmetic.' The young operator calculated by +successive squaring the 2d, 4th, 8th, etc., powers up to the 512th, with +proof by division. But 511 multiplications by 9, in the short (or 10-1) +way, would have been much easier. The 2d, 32d, 64th, 128th, 256th, and +512th powers are given at the back of the announcement. The powers of 2 +have been calculated for many purposes. In Vol. II of his _Magia +Universalis Naturae et Artis_, Herbipoli, 1658, 4to, the Jesuit Gaspar +Schott[138] having discovered, on some grounds of theological {65} magic, +that the degrees of grace of the Virgin Mary were in number the 256th power +of 2, calculated that number. Whether or no his number correctly +represented the result he announced, he certainly calculated it rightly, as +we find by comparison with Mr. Shanks." + + + +There is a point about Mr. Shanks's 608 figures of the value of [pi] which +attracts attention, perhaps without deserving it. It might be expected +that, in so many figures, the nine digits and the cipher would occur each +about the same number of times; that is, each about 61 times. But the fact +stands thus: 3 occurs 68 times; 9 and 2 occur 67 times each; 4 occurs 64 +times; 1 and 6 occur 62 times each; 0 occurs 60 times; 8 occurs 58 times; 5 +occurs 56 times; and 7 occurs only 44 times. Now, if all the digits were +equally likely, and 608 drawings were made, it is 45 to 1 against the +number of sevens being as distant from the probable average (say 61) as 44 +on one side or 78 on the other. There must be some reason why the number 7 +is thus deprived of its fair share in the structure. Here is a field of +speculation in which two branches of inquirers might unite. There is but +one number which is treated with an unfairness which is incredible as an +accident; and that number is the mystic number _seven_! If the cyclometers +and the apocalyptics would lay their heads together until they come to a +unanimous verdict on this phenomenon, and would publish nothing until they +are of one mind, they would earn the gratitude of their race.--I was wrong: +it is the Pyramid-speculator who should have been appealed to. A +correspondent of my friend Prof. Piazzi Smyth[139] notices that 3 is the +number of most frequency, and that 3-1/7 is the nearest approximation to it +in simple digits. Professor Smyth himself, whose word on Egypt is paradox +of a very high order, backed by a great quantity of useful labor, the +results which will be made available by those who do not receive {66} the +paradoxes, is inclined to see confirmation for some of his theory in these +phenomena. + + + +CURIOUS CALCULATIONS. + +These paradoxes of calculation sometimes appear as illustrations of the +value of a new method. In 1863, Mr. G. Suffield,[140] M.A., and Mr. J. R. +Lunn,[141] M.A., of Clare College and of St. John's College, Cambridge, +published the whole quotient of 10000 ... divided by 7699, throughout the +whole of one of the recurring periods, having 7698 digits. This was done in +illustration of Mr. Suffield's method of _Synthetic division_. + +Another instance of computation carried to paradoxical length, in order to +illustrate a method, is the solution of x^3 - 2x = 5, the example given of +Newton's method, on which all improvements have been tested. In 1831, +Fourier's[142] posthumous work on equations showed 33 figures of solution, +got with enormous labor. Thinking this a good opportunity to illustrate the +superiority of the method of W. G. Horner,[143] not yet known in France, +and not much known in {67} England, I proposed to one of my classes, in +1841, to beat Fourier on this point, as a Christmas exercise. I received +several answers, agreeing with each other, to 50 places of decimals. In +1848, I repeated the proposal, requesting that 50 places might be exceeded: +I obtained answers of 75, 65, 63, 58, 57, and 52 places. But one answer, by +Mr. W. Harris Johnston,[144] of Dundalk, and of the Excise Office, went to +101 decimal places. To test the accuracy of this, I requested Mr. Johnston +to undertake another equation, connected with the former one in a way which +I did not explain. His solution verified the former one, but he was unable +to see the connection, even when his result was obtained. My reader may be +as much at a loss: the two solutions are: + + 2.0945514815423265... + 9.0544851845767340... + +The results are published in the _Mathematician_, Vol. III, p. 290. In +1851, another pupil of mine, Mr. J. Power Hicks,[145] carried the result to +152 decimal places, without knowing what Mr. Johnston had done. The result +is in the _English Cyclopaedia_, article INVOLUTION AND EVOLUTION. + +I remark that when I write the initial of a Christian name, the most usual +name of that initial is understood. I never saw the name of W. G. Horner +written at length, until I applied to a relative of his, who told me that +he was, as I supposed, Wm. _George_, but that he was named after a relative +of that _surname_. + +The square root of 2, to 110 decimal places, was given {68} me in 1852 by +my pupil, Mr. William Henry Colvill, now (1867) Civil Surgeon at Baghdad. +It was + + 1.4142135623730950488016887242096980785696 + 7187537694807317667973799073247846210703 + 885038753432764157273501384623 + +Mr. James Steel[146] of Birkenhead verified this by actual multiplication, +and produced + + 2 - 2580413 / 10^{117} + +as the square. + + + + Calcolo decidozzinale del Barone Silvio Ferrari. Turin, 1854, 4to. + +This is a serious proposal to alter our numeral system and to count by +twelves. Thus 10 would be twelve, 11 thirteen, etc., two new symbols being +invented for ten and eleven. The names of numbers must of course be +changed. There are persons who think such changes practicable. I thought +this proposal absurd when I first saw it, and I think so still:[147] but +the one I shall presently describe beats it so completely in that point, +that I have not a smile left for this one. + + + +ON COMETS. + + The successful and therefore probably true theory of Comets. London, + 1854. (4pp. duodecimo.) + +The author is the late Mr. Peter Legh,[148] of Norbury Booths Hall, +Knutsford, who published for eight or ten {69} years the _Ombrological +Almanac_, a work of asserted discovery in meteorology. The theory of comets +is that the joint attraction of the new moon and several planets in the +direction of the sun, draws off the gases from the earth, and forms these +cometic meteors. But how these meteors come to describe orbits round the +sun, and to become capable of having their returns predicted, is not +explained. + + + +A NEW PHASE OF MORMONISM. + + The Mormon, New York, Saturday, Oct. 27, 1855. + +A newspaper headed by a grand picture of starred and striped banners, +beehive, and eagle surmounting it. A scroll on each side: on the left, +"Mormon creed. Mind your own business. Brigham Young;"[149] on the right, +"Given by inspiration of God. Joseph Smith."[150] A leading article on the +discoveries of Prof. Orson Pratt[151] says, "Mormonism has long taken the +lead in religion: it will soon be in the van both in science and politics." +At the beginning of the paper is Professor Pratt's "Law of Planetary +Rotation." The cube roots of the densities of the planets are as the square +roots of their periods of rotation. The squares of the cube roots of the +masses divided by the squares of the diameters are as the periods of +rotation. Arithmetical verification attempted, and the whole very modestly +stated {70} and commented on. Dated G. S. L. City, Utah Ter., Aug. 1, 1855. +If the creed, as above, be correctly given, no wonder the Mormonites are in +such bad odor. + + + +MATHEMATICAL ILLUSTRATIONS OF DOCTRINE. + + The two estates; or both worlds mathematically considered. London, + 1855, small (pp. 16). + +The author has published mathematical works with his name. The present +tract is intended to illustrate mathematically a point which may be guessed +from the title. But the symbols do very little in the way of illustration: +thus, x being the _present value_ of the future estate (eternal happiness), +and a of all that this world can give, the author impresses it on the +mathematician that, x being infinitely greater than a, x + a = x, so that a +need not be considered. This will not act much more powerfully on a +mathematician by virtue of the symbols than if those same symbols had been +dispensed with: even though, as the author adds, "It was this method of +neglecting infinitely small quantities that Sir Isaac Newton was indebted +to for his greatest discoveries." + +There has been a moderate quantity of well-meant attempt to enforce, +sometimes motive, sometimes doctrine, by arguments drawn from mathematics, +the proponents being persons unskilled in that science for the most part. +The ground is very dangerous: for the illustration often turns the other +way with greater power, in a manner which requires only a little more +knowledge to see. I have, in my life, heard from the pulpit or read, at +least a dozen times, that all sin is infinitely great, proved as follows. +The greater the being, the greater the sin of any offence against him: +therefore the offence committed against an infinite being is infinitely +great. Now the mathematician, of which the proposers of this argument are +not aware, is perfectly familiar with quantities which increase together, +and never cease increasing, but so that one of them remains finite when +{71} the other becomes infinite. In fact, the argument is a perfect _non +sequitur_.[152] Those who propose it have in their minds, though in a +cloudy and indefinite form, the idea of the increase of guilt being +_proportionate_ to the increase of greatness in the being offended. But +this it would never do to state: for by such statement not only would the +argument lose all that it has of the picturesque, but the asserted premise +would have no strong air of exact truth. How could any one undertake to +appeal to conscience to declare that an offence against a being 4-7/10 +times as great as another is exactly, no more and no less, 4-7/10 times as +great an offence against the other? + +The infinite character of the offence against an infinite being is laid +down in Dryden's _Religio Laici_,[153] and is, no doubt, an old argument: + + "For, granting we have sinned, and that th' offence + Of man is made against Omnipotence, + Some price that bears proportion must be paid, + And infinite with infinite be weighed. + See then the Deist lost; remorse for vice + Not paid; or, paid, inadequate in price." + +Dryden, in the words "bears proportion" is in verse more accurate than most +of the recent repeaters in prose. And this is not the only case of the kind +in his argumentative poetry. + +My old friend, the late Dr. Olinthus Gregory,[154] who was a sound and +learned mathematician, adopted this dangerous kind of illustration in his +_Letters on the Christian Religion_. {72} He argued, by parallel, from what +he supposed to be the necessarily mysterious nature of the _impossible_ +quantity of algebra to the necessarily mysterious nature of certain +doctrines of his system of Christianity. But all the difficulty and mystery +of the impossible quantity is now cleared away by the advance of +algebraical thought: and yet Dr. Gregory's book continues to be sold, and +no doubt the illustration is still accepted as appropriate. + +The mode of argument used by the author of the tract above named has a +striking defect. He talks of reducing this world and the next to "present +value," as an actuary does with successive lives or next presentations. +Does value make interest? and if not, why? And if it do, then the present +value of an eternity is _not_ infinitely great. Who is ignorant that a +perpetual annuity at five per cent is worth only twenty years' purchase? +This point ought to be discussed by a person who treats heaven as a +deferred perpetual annuity. I do not ask him to do so, and would rather he +did not; but if he _will_ do it, he must either deal with the question of +discount, or be asked the reason why. + +When a very young man, I was frequently exhorted to one or another view of +religion by pastors and others who thought that a mathematical argument +would be irresistible. And I heard the following more than once, and have +since seen it in print, I forget where. Since eternal happiness belonged to +the particular views in question, a benefit infinitely great, then, even if +the probability of their arguments were small, or even infinitely small, +yet the product of the chance and benefit, according to the usual rule, +might give a result which no one ought in prudence to pass over. They did +not see that this applied to all systems as well as their own. I take this +argument to be the most perverse of all the perversions I have heard or +read on the subject: there is some high authority for it, whom I forget. + +The moral of all this is, that such things as the preceding should be kept +out of the way of those who are not {73} mathematicians, because they do +not understand the argument; and of those who are, because they do. + +[The high authority referred to above is Pascal, an early cultivator of +mathematical probability, and obviously too much enamoured of his new +pursuit. But he conceives himself bound to wager on one side or the other. +To the argument (_Pensees_, ch. 7)[155] that "le juste est de ne point +parier," he answers, "Oui: mais il faut parier: vous etes embarque; et ne +parier point que Dieu est, c'est parier qu'il n'est pas."[156] Leaving +Pascal's argument to make its way with a person who, _being a sceptic_, is +yet positive that the issue is salvation or perdition, if a God there +be,--for the case as put by Pascal requires this,--I shall merely observe +that a person who elects to believe in God, as the best chance of gain, is +not one who, according to Pascal's creed, or any other worth naming, will +really secure that gain. I wonder whether Pascal's curious imagination ever +presented to him in sleep his convert, in the future state, shaken out of a +red-hot dice-box upon a red-hot hazard-table, as perhaps he might have +been, if Dante had been the later of the two. The original idea is due to +the elder Arnobius,[157] who, as cited by Bayle,[158] speaks thus: + +"Sed et ipse [Christus] quae pollicetur, non probat. Ita est. Nulla enim, ut +dixi, futurorum potest existere comprobatio. Cum ergo haec sit conditio +futurorum, ut teneri et comprehendi nullius possint anticipationis attactu; +nonne {74} purior ratio est, ex duobus incertis, et in ambigua expectatione +pendentibus, id potius credere, quod aliquas spes ferat, quam omnino quod +nullas? In illo enim periculi nihil est, si quod dicitur imminere, cassum +fiat et vacuum: in hoc damnum est maximum, id est salutis amissio, si cum +tempus advenerit aperiatur non fuisse mendacium."[159] + +Really Arnobius seems to have got as much out of the notion, in the third +century, as if he had been fourteen centuries later, with the arithmetic of +chances to help him.] + + + +NOVUM ORGANUM MORALIUM. + + The Sentinel, vol. ix. no. 27. London, Saturday, May 26, 1855. + +This is the first London number of an Irish paper, Protestant in politics. +It opens with "Suggestions on the subject of a _Novum Organum Moralium_," +which is the application of algebra and the differential calculus to +morals, socials, and politics. There is also a leading article on the +subject, and some applications in notes to other articles. A separate +publication was afterwards made, with the addition of a long Preface; the +author being a clergyman who I presume must have been the editor of the +_Sentinel_. + + Suggestions as to the employment of a _Novum Organum Moralium_. Or, + thoughts on the nature of the Differential Calculus, and on the + application of its principles to metaphysics, with a view to the + attainment of demonstration and certainty in moral, {75} political and + ecclesiastical affairs. By Tresham Dames Gregg,[160] Chaplain of St. + Mary's, within the church of St. Nicholas intra muros, Dublin. London, + 1859, 8vo. (pp. xl + 32). + +I have a personal interest in this system, as will appear from the +following extract from the newspaper: + + "We were subsequently referred to De Morgan's _Formal Logic_ and + Boole's _Laws of Thought_[161] both very elaborate works, and greatly + in the direction taken by ourselves. That the writers amazingly surpass + us in learning we most willingly admit, but we venture to pronounce of + both their learned treatises, that they deal with the subject in a mode + that is scholastic to an excess.... That their works have been for a + considerable space of time before the world and effected nothing, would + argue that they have overlooked the vital nature of the theme.... On + the whole, the writings of De Morgan and Boole go to the full + justification of our principle without in any wise so trenching upon + our ground as to render us open to reproach in claiming our Calculus as + a great discovery.... But we renounce any paltry jealousy as to a + matter so vast. If De Morgan and Boole have had a priority in the case, + to them we cheerfully shall resign the glory and honor. If such be the + truth, they have neither done justice to the discovery, nor to + themselves [quite true]. They have, under the circumstances, acted like + 'the foolish man, who roasteth not that which he taketh {76} in + hunting.... It will be sufficient for us, however, to be the Columbus + of these great Americi, and popularize what they found, _if_ they found + it. We, as from the mountain top, will then become _their_ trumpeters, + and cry glory to De Morgan and glory to Boole, under Him who is the + source of all glory, the only good and wise, to Whom be glory for ever! + _If_ they be our predecessors in this matter, they have, under Him, + taken moral questions out of the category of probabilities, and + rendered them perfectly certain. In that case, let their books be read + by those who may doubt the principles this day laid before the world as + a great discovery, by our newspaper. Our cry shall be [Greek: + eurekasi]![162] Let us hope that they will join us, and henceforth keep + their light [_sic_] from under their bushel." + +For myself, and for my old friend Mr. Boole, who I am sure would join me, I +disclaim both priority, simultaneity, and posteriority, and request that +nothing may be trumpeted from the mountain top except our abjuration of all +community of thought or operation with this _Novum Organum_. + +To such community we can make no more claim than Americus could make to +being the forerunner of Columbus who popularized his discoveries. We do not +wish for any [Greek: eurekasi] and not even for [Greek: heurekasi]. For +self and Boole, I point out what would have convinced either of us that +this house is divided against itself. + +[Alpha] being an apostolic element, [delta] the doctrinal element, and +[Chi] the body of the faithful, the church is [Alpha] [delta] [Chi], we are +told. Also, that if [Alpha] become negative, or the Apostolicity become +Diabolicity [my words]; or if [delta] become negative, and doctrine become +heresy; or if [Chi] become negative, that is, if the faithful become +unfaithful; the church becomes negative, "the very opposite to what it +ought to be." For self and Boole, I admit this. But--which is not +noticed--if [Alpha] and [delta] should _both_ become negative, diabolical +origin {77} and heretical doctrine, then the church, [Alpha] [delta] [Chi], +is still positive, what it ought to be, unless [Chi] be also negative, or +the people unfaithful to it, in which case it is a bad church. Now, self +and Boole--though I admit I have not asked my partner--are of opinion that +a diabolical church with false doctrine does harm when the people are +faithful, and can do good only when the people are unfaithful. We may be +wrong, but this is what we _do_ think. Accordingly, we have caught nothing, +and can therefore roast nothing of our own: I content myself with roasting +a joint of Mr. Gregg's larder. + +These mathematical vagaries have uses which will justify a large amount of +quotation: and in a score of years this may perhaps be the only attainable +record. I therefore proceed. + +After observing that by this calculus juries (heaven help them! say I) can +calculate damages "almost to a nicety," and further that it is made +abundantly evident that c e x is "the general expression for an +individual," it is noted that the number of the Beast is not given in the +Revelation in words at length, but as [Greek: chxw'].[163] On this the +following remark is made: + +"Can it be possible that we have in this case a specimen given to us of the +arithmetic of heaven, and an expression revealed, which indicates by its +function of addibility, the name of the church in question, and of each +member of it; and by its function of multiplicability the doctrine, the +mission, and the members of the great Synagogue of Apostacy? We merely +propound these questions;--we do not pretend to solve them." + +After a translation in blank verse--a very pretty one--of the 18th Psalm, +the author proceeds as follows, to render it into differential calculus: + +{78} + +"And the whole tells us just this, that David did what he could. He +augmented those elements of his constitution which were (_exceptis +excipiendis_)[164] subject to himself, and the Almighty then augmented his +personal qualities, and his vocational _status_. Otherwise, to throw the +matter into the expression of our notation, the variable e was augmented, +and c x rose proportionally. The law of the variation, according to our +theory, would be thus expressed. The resultant was David the king c e x [c += r?] (who had been David the shepherd boy), and from the conditions of the +theorem we have + + du/de = ce(dx/de) + ex(dc/de)x + cx + +which, in the terms of ordinary language, just means, the increase of +David's educational excellence or qualities--his piety, his prayerfulness, +his humility, obedience, etc.--was so great, that when multiplied by his +original talent and position, it produced a product so great as to be equal +in its amount to royalty, honor, wealth, and power, etc.: in short, to all +the attributes of majesty."[165] + +The "solution of the family problem" is of high interest. It is to +determine the effect on the family in general from a change [of conduct] in +one of them. The person chosen is one of the maid-servants. + +"Let c e x be the father; c_1e_1x_1 the mother, etc. The family then +consists of the maid's master, her mistress, her young master, her young +mistress, and fellow servant. Now the master's calling (or c) is to +exercise his share of control over this servant, and mind the rest of his +business: call this remainder a, and let his calling generally, or all his +affairs, be to his maid-servant as m : y, i.e., y = (mz/c); ... {79} and +this expression will represent his relation to the servant. Consequently, + + c e x = (a + mz/c)e x; otherwise (a + mz/c)e x + +is the expression for the father when viewed as the girl's master." + +I have no objection to repeat so far; but I will not give the formula for +the maid's relation to her young master; for I am not quite sure that all +young masters are to be trusted with it. Suffice it that the son will be +affected directly as his influence over her, and inversely as his +vocational power: if then he should have some influence and no vocational +power, the effect on him would be infinite. This is dismal to think of. +Further, the formula brings out that if one servant improve, the other must +deteriorate, and _vice versa_. This is not the experience of most families: +and the author remarks as follows: + +"That is, we should venture to say, a very beautiful result, and we may say +it yielded us no little astonishment. What our calculation might lead to we +never dreamt of; that it should educe a conclusion so recondite that our +unassisted power never could have attained to, and which, if we could have +conjectured it, would have been at best the most distant probability, that +conclusion being itself, as it would appear, the quintessence of truth, +afforded us a measure of satisfaction that was not slight." + +That the writings of Mr. Boole and myself "go to the full justification of" +this "principle," is only true in the sense in which the Scotch use, or did +use, the word _justification_. + + + +A TRIBUTE TO BOOLE. + +[The last number of this Budget had stood in type for months, waiting until +there should be a little cessation of correspondence more connected with +the things of the day. {80} I had quite forgotten what it was to contain; +and little thought, when I read the proof, that my allusions to my friend +Mr. Boole, then in life and health, would not be printed till many weeks +after his death. Had I remembered what my last number contained, I should +have added my expression of regret and admiration to the numerous obituary +testimonials, which this great loss to science has called forth. + +The system of logic alluded to in the last number of this series is but one +of many proofs of genius and patience combined. I might legitimately have +entered it among my _paradoxes_, or things counter to general opinion: but +it is a paradox which, like that of Copernicus, excited admiration from its +first appearance. That the symbolic processes of algebra, invented as tools +of numerical calculation, should be competent to express every act of +thought, and to furnish the grammar and dictionary of an all-containing +system of logic, would not have been believed until it was proved. When +Hobbes,[166] in the time of the Commonwealth, published his _Computation or +Logique_, he had a remote glimpse of some of the points which are placed in +the light of day by Mr. Boole. The unity of the forms of thought in all the +applications of reason, however remotely separated, will one day be matter +of notoriety and common wonder: and Boole's name will be remembered in +connection with one of the most important steps towards the attainment of +this knowledge.] + + + +DECIMALS RUN RIOT. + + The Decimal System as a whole. By Dover Statter.[167] London and + Liverpool, 1856, 8vo. + +{81} + +The proposition is to make everything decimal. The day, now 24 hours, is to +be made 10 hours. The year is to have ten months, Unusber, Duober, etc. +Fortunately there are ten commandments, so there will be neither addition +to, nor deduction from, the moral law. But the twelve apostles! Even +rejecting Judas, there is a whole apostle of difficulty. These points the +author does not touch. + + + +ON PHONETIC SPELLING. + + The first book of Phonetic Reading. London, Fred. Pitman,[168] Phonetic + Depot, 20, Paternoster Row, 1856, 12mo. + + The Phonetic Journal. Devoted to the propagation of phonetic reading, + phonetic longhand, phonetic shorthand, and phonetic printing. No. 46. + Saturday, 15 November 1856. Vol. 15. + +I write the titles of a couple out of several tracts which I have by me. +But the number of publications issued by the promoters of this spirited +attempt is very large indeed.[169] The attempt itself has had no success +with the mass of the public. This I do not regret. Had the world found that +the change was useful, I should have gone contentedly with the stream; but +not without regretting our old language. I admit the difficulties which our +unpronounceable spelling puts in the way of learning to read: and I have no +doubt that, as affirmed, it is easier to teach children phonetically, and +afterwards to introduce them to our common system, than to proceed in the +usual way. But by the usual way I mean proceeding by letters from the very +beginning. If, which I am sure is a better plan, children be taught at the +commencement very much by _complete words_, as if they were learning +Chinese, and be gradually accustomed to {82} resolve the known words into +letters, a fraction, perhaps a considerable one, of the advantage of the +phonetic system is destroyed. It must be remembered that a phonetic system +can only be an approximation. The differences of pronunciation existing +among educated persons are so great, that, on the phonetic system, +different persons ought to spell differently. + +But the phonetic party have produced something which will immortalize their +plan: I mean their _shorthand_, which has had a fraction of the success it +deserves. All who know anything of shorthand must see that nothing but a +phonetic system can be worthy of the name: and the system promulgated is +skilfully done. Were I a young man I should apply myself to it +systematically. I believe this is the only system in which books were ever +published. I wish some one would contribute to a public journal a brief +account of the dates and circumstances of the phonetic movement, not +forgetting a list of the books published in shorthand. + +A child beginning to read by himself may owe terrible dreams and waking +images of horror to our spelling, as I did when six years old. In one of +the common poetry-books there is an admonition against confining little +birds in cages, and the child is asked what if a great giant, amazingly +strong, were to take you away, shut you up, + + And feed you with vic-tu-als you ne-ver could bear. + +The book was hyphened for the beginner's use; and I had not the least idea +that _vic-tu-als_ were _vittles_: by the sound of the word I judged they +must be of iron; and it entered into my soul. + +The worst of the phonetic shorthand book is that they nowhere, so far as I +have seen, give _all_ the symbols, in every stage of advancement, together, +in one or following pages. It is symbols and talk, more symbols and more +talk, etc. A universal view of the signs ought to begin the works. {83} + + + +A HANDFUL OF LITTLE PARADOXERS. + + Ombrological Almanac. Seventeenth year. An essay on Anemology and + Ombrology. By Peter Legh,[170] Esq. London, 1856, 12mo. + +Mr. Legh, already mentioned, was an intelligent country gentleman, and a +legitimate speculator. But the clue was not reserved for him. + + The proof that the three angles of a triangle are equal to two right + angles looked for in the inflation of the circle. By Gen. Perronet + Thompson. London, 1856, 8vo. (pp. 4.) + +Another attempt, the third, at this old difficulty, which cannot be put +into few words of explanation.[171] + + Comets considered as volcanoes, and the cause of their velocity and + other phenomena thereby explained. London (_circa_ 1856), 8vo. + +The title explains the book better than the book explains the title. + + + +1856. A stranger applied to me to know what the ideas of a friend of his +were worth upon the magnitude of the earth. The matter being one involving +points of antiquity, I mentioned various persons whose speculations he +seemed to have ignored; among others, Thales. The reply was, "I am +instructed by the author to inform you that he is perfectly acquainted with +the works of Thales, Euclid, Archimedes, ..." I had some thought of asking +whether he had used the Elzevir edition of Thales,[172] which is known to +be very incomplete, or that of Professor Niemand with the lections, +Nirgend, 1824, 2 vols. folio; just to see whether the {84} last would not +have been the very edition he had read. But I refrained, in mercy. + + + + The moon is the image of the Earth, and is not a solid body. By T^{he} + Longitude.[173] (Private Circulation.) In five parts. London, 1856, + 1857, 1857; Calcutta, 1858, 1858, 8vo. + +The earth is "brought to a focus"; it describes a "looped orbit round the +sun." The eclipse of the sun is thus explained: "At the time of eclipses, +the image is more or less so directly before or behind the earth that, in +the case of new moon, bright rays of the sun fall and bear upon the spot +where the figure of the earth is brought to a focus, that is, bear upon the +image of the earth, when a darkness beyond is produced reaching to the +earth, and the sun becomes more or less eclipsed." How the earth is +"brought to a focus" we do not find stated. Writers of this kind always +have the argument that some things which have been ridiculed at first have +been finally established. Those who put into the lottery had the same kind +of argument; but were always answered by being reminded how many blanks +there were to one prize. I am loath to pronounce against anything: but it +does force itself upon me that the author of these tracts has drawn a +blank. + + + +LUNAR MOTION AGAIN. + + _Times_, April 6 or 7, 1856. The moon has no rotary motion. + +A letter from Mr. Jellinger Symons,[174] inspector of schools, which +commenced a controversy of many letters and pamphlets. This dispute comes +on at intervals, and will continue to do so. It sometimes arises from +inability to understand the character of simple rotation, geometrically; +sometimes from not understanding the mechanical doctrine of rotation. + +{85} + + + + Lunar Motion. The whole argument stated, and illustrated by diagrams; + with letters from the Astronomer Royal. By Jellinger C. Symons. London, + 1856, 8vo. + +The Astronomer Royal endeavored to disentangle Mr. J. C. Symons, but +failed. Mr. Airy[175] can correct the error of a ship's compasses, because +he can put her head which way he pleases: but this he cannot do with a +speculator. + +Mr. Symons, in this tract, insinuated that the rotation of the moon is one +of the silver shrines of the craftsmen. To see a thing so clearly as to be +satisfied that all who say they do not see it are telling wilful falsehood, +is the nature of man. Many of all sects find much comfort in it, when they +think of the others; many unbelievers solace themselves with it against +believers; priests of old time founded the right of persecution upon it, +and of our time, in some cases, the right of slander: many of the +paradoxers make it an argument against students of science. But I must say +for men of science, for the whole body, that they are fully persuaded of +the honesty of the paradoxers. The simple truth is, that all those I have +mentioned, believers, unbelievers, priests, paradoxers, are not so sure +they are right in their points of difference that they can safely allow +themselves to be persuaded of the honesty of opponents. Those who know +demonstration are differently situated. I suspect a train might be laid for +the formation of a better habit in this way. We know that Suvaroff[176] +taught his Russians at Ismail not to fear the Turks by accustoming them to +charge bundles of faggots dressed in turbans, etc. + + At which your wise men sneered in phrases witty, + He made no answer--but he took the city! + +Would it not be a good thing to exercise boys, in pairs, in the following +dialogue:--Sir, you are quite wrong!--Sir, {86} I am sure you honestly +think so! This was suggested by what used to take place at Cambridge in my +day. By statute, every B.A. was obliged to perform a certain number of +disputations, and the _father_ of the college had to affirm that it had +been done. Some were performed in earnest: the rest were huddled over as +follows. Two candidates occupied the places of the respondent and the +opponent: _Recte statuit Newtonus_, said the respondent: _Recte non statuit +Newtonus_,[177] said the opponent. This was repeated the requisite number +of times, and counted for as many _acts_ and _opponencies_. The parties +then changed places, and each unsaid what he had said on the other side of +the house: I remember thinking that it was capital drill for the House of +Commons, if any of us should ever get there. The process was repeated with +every pair of candidates. + +The real disputations were very severe exercises. I was badgered for two +hours with arguments given and answered in Latin,--or what we called +Latin--against Newton's first section, Lagrange's[178] derived functions, +and Locke[179] on innate principles. And though I _took off_ everything, +and was pronounced by the moderator to have disputed _magno honore_,[180] I +never had such a strain of thought in my life. For the inferior opponents +were made as sharp as their betters by their tutors, who kept lists of +queer objections, drawn from all quarters. The opponents used to meet the +day before to compare their arguments, that the same might not come twice +over. But, after I left Cambridge, it became the fashion to invite the +respondent to be present, who therefore learnt all that was to be brought +against him. This made the whole thing a farce: and the disputations were +abolished. + +{87} + + + + The Doctrine of the Moon's Rotation, considered in a letter to the + Astronomical Censor of the _Athenaeum_. By Jones L. MacElshender.[181] + Edinburgh, 1856, 8vo. + +This is an appeal to those cultivated persons who will read it "to overrule +the _dicta_ of judges who would sacrifice truth and justice to professional +rule, or personal pique, pride, or prejudice"; meaning, the great mass of +those who have studied the subject. But how? Suppose the "cultivated +persons" were to side with the author, would those who have conclusions to +draw and applications to make consent to be wrong because the "general body +of intelligent men," who make no special study of the subject, are against +them? They would do no such thing: they would request the general body of +intelligent men to find their own astronomy, and welcome. But the truth is, +that this intelligent body knows better: and no persons know better that +they know better than the speculators themselves. + +But suppose the general body were to combine, in opposition to those who +have studied. Of course all my list must be admitted to their trial; and +then arises the question whether both sides are to be heard. If so, the +general body of the intelligent must hear all the established side have to +say: that is, they must become just as much of students as the inculpated +orthodox themselves. And will they not then get into _professional rule_, +pique, pride, and prejudice, as the others did? But if, which I suspect, +they are intended to judge as they are, they will be in a rare difficulty. +All the paradoxers are of like pretensions: they cannot, as a class, be +right, for each one contradicts a great many of the rest. There will be the +puzzle which silenced the crew of the cutter in Marryat's novel of the Dog +Fiend.[182] "A tog is a tog," said Jansen.--"Yes," replied another, "we all +know a dog is a dog; but the question is--Is _this_ dog {88} a dog?" And +this question would arise upon every dog of them all. + + + +ZETETIC ASTRONOMY. + + Zetetic Astronomy: Earth not a globe. 1857 (Broadsheet). + +Though only a traveling lecturer's advertisement, there are so many +arguments and quotations that it is a little pamphlet. The lecturer gained +great praise from provincial newspapers for his ingenuity in proving that +the earth is a flat, surrounded by ice. Some of the journals rather incline +to the view: but the _Leicester Advertiser_ thinks that the statements +"would seem very seriously to invalidate some of the most important +conclusions of modern astronomy," while the _Norfolk Herald_ is clear that +"there must be a great error on one side or the other." This broadsheet is +printed at Aylesbury in 1857, and the lecturer calls himself _Parallax_: +but at Trowbridge, in 1849, he was S. Goulden.[183] In this last +advertisement is the following announcement: "A paper on the above subjects +was read before the Council and Members of the Royal Astronomical Society, +Somerset House, Strand, London (Sir John F. W. Herschel,[184] President), +Friday, Dec. 8, 1848." No account of such a paper appears in the _Notice_ +for that month: I suspect that the above is Mr. S. Goulden's way of +representing the following occurrence: Dec. 8, 1848, the Secretary of the +Astronomical Society (De Morgan by name) said, at the close of the +proceedings,--"Now, gentlemen, if you will promise not to tell the Council, +I will read something for your amusement": and he then read a few of the +arguments which had been transmitted by the lecturer. The fact is worth +noting that from 1849 to 1857, arguments on the roundness or flatness of +the earth did itinerate. I have {89} no doubt they did much good: for very +few persons have any distinct idea of the evidence for the rotundity of the +earth. The _Blackburn Standard_ and _Preston Guardian_ (Dec. 12 and 16, +1849) unite in stating that the lecturer ran away from his second lecture +at Burnley, having been rather too hard pressed at the end of his first +lecture to explain why the large hull of a ship disappeared before the +sails. The persons present and waiting for the second lecture assuaged +their disappointment by concluding that the lecturer had slipped off the +icy edge of his flat disk, and that he would not be seen again till he +peeped up on the opposite side. + +But, strange as it may appear, the opposer of the earth's roundness has +more of a case--or less of a want of case--than the arithmetical squarer of +the circle. The evidence that the earth is round is but cumulative and +circumstantial: scores of phenomena ask, separately and independently, what +other explanation can be imagined except the sphericity of the earth. The +evidence for the earth's figure is tremendously powerful of its kind; but +the proof that the circumference is 3.14159265... times the diameter is of +a higher kind, being absolute mathematical demonstration. + +The Zetetic system still lives in lectures and books; as it ought to do, +for there is no way of teaching a truth comparable to opposition. The last +I heard of it was in lectures at Plymouth, in October, 1864. Since this +time a prospectus has been issued of a work entitled "The Earth not a +Globe"; but whether it has been published I do not know. The contents are +as follows: + + + +"The Earth a Plane--How circumnavigated.--How time is lost or gained.--Why +a ship's hull disappears (when outward bound) before the mast head.--Why +the Polar Star sets when we proceed Southward, etc.--Why a pendulum +vibrates with less velocity at the Equator than {90} at the Pole.--The +allowance for rotundity _supposed_ to be made by surveyors, not made in +practice.--Measurement of Arcs of the Meridian unsatisfactory.--Degrees of +Longitude North and South of the Equator considered.--Eclipses and Earth's +form considered.--The Earth no motion on axis or in orbit.--How the Sun +moves above the Earth's surface concentric with the North Pole.--Cause of +Day and Night, Winter and Summer; the long alternation of light and +darkness at the Pole.--Cause of the Sun rising and setting.--Distance of +the Sun from London, 4,028 miles--How measured.--_Challenge to +Mathematicians._--Cause of Tides.--Moon self-luminous, NOT a +reflector.--Cause of Solar and Lunar eclipses.--Stars _not worlds_; their +distance.--Earth, the _only material_ world; its true position in the +universe; its condition and ultimate destruction by fire (2 Peter iii.), +etc." + +I wish there were geoplatylogical lectures in every town; in England +(_platylogical_, in composition, need not mean _babbling_). The late Mr. +Henry Archer[185] would, if alive, be very much obliged to me for recording +his vehement denial of the roundness of the earth: he was excited if he +heard any one call it a globe. I cannot produce his proof from the +Pyramids, and from some caves in Arabia. He had other curious notions, of +course: I should no more believe that a flat earth was a man's only +paradox, than I should that Dutens,[186] the editor of Leibnitz, was +eccentric only in supplying a tooth which he had lost by one which he found +in an Italian tomb, and fully believed that it had once belonged to Scipio +Africanus, whose family vault was discovered, it is supposed, in 1780. Mr. +Archer is of note as {91} the suggester of the perforated border of the +postage-stamps, and, I think, of the way of doing it; for this he got +4000l. reward. He was a civil engineer. + +(_August 28, 1865._) The _Zetetic Astronomy_ has come into my hands. When, +in 1851, I went to see the Great Exhibition, I heard an organ played by a +performer who seemed very desirous to exhibit one particular stop. "What do +you think of that stop?" I was asked.--"That depends on the name of it," +said I.--"Oh! what can the name have to do with the sound? 'that which we +call a rose,' etc."--"The name has everything to do with it: if it be a +flute-stop, I think it very harsh; but if it be a railway-whistle-stop, I +think it very sweet." So as to this book: if it be childish, it is clever; +if it be mannish, it is unusually foolish. The flat earth, floating +tremulously on the sea; the sun moving always over the flat, giving day +when near enough, and night when too far off; the self-luminous moon, with +a semi-transparent invisible moon, created to give her an eclipse now and +then; the new law of perspective, by which the vanishing of the hull before +the masts, usually thought to prove the earth globular, really proves it +flat;--all these and other things are well fitted to form exercises for a +person who is learning the elements of astronomy. The manner in which the +sun dips into the sea, especially in tropical climates, upsets the whole. +Mungo Park,[187] I think, gives an African hypothesis which explains +phenomena better than this. The sun dips into the western ocean, and the +people there cut him in pieces, fry him in a pan, and then join him +together again, take him round the underway, and set him up in the east. I +hope this book will be read, and that many will be puzzled by it: for there +are many whose notions of astronomy deserve no better fate. There is no +subject on which there is so little {92} accurate conception as that of the +motions of the heavenly bodies. The author, though confident in the +extreme, neither impeaches the honesty of those whose opinions he assails, +nor allots them any future inconvenience: in these points he is worthy to +live on a globe, and to revolve in twenty-four hours. + + + +(_October, 1866._) A follower appears, in a work dedicated to the preceding +author: it is _Theoretical Astronomy examined and exposed by Common Sense_. +The author has 128 well-stuffed octavo pages. I hope he will not be the +last. He prints the newspaper accounts of his work: the _Church Times_ +says--not seeing how the satire might be retorted--"We never began to +despair of Scripture until we discovered that 'Common Sense' had taken up +the cudgels in its defence." This paper considers our author as the type of +a _Protestant_. The author himself, who gives a summary of his arguments in +verse, has one couplet which is worth quoting: + + "How is't that sailors, bound to sea, with _a 'globe'_ would never start, + But in its place will always take _Mercator's_[188] LEVEL _chart_!" + +To which I answer: + + Why, really Mr. Common Sense, you've never got so far + As to think Mercator's planisphere shows countries as they are; + It won't do to measure distances; it points out how to steer, + But this distortion's not for you; another is, I fear. + The earth must be a cylinder, if seaman's charts be true, + Or else the boundaries, right and left, are one as well as two; + They contradict the notion that we dwell upon a plain, + For straight away, without a turn, will bring you home again. + There are various plane projections; and each one has its use: + I wish a milder word would rhyme--but really you're a goose! + +The great wish of persons who expose themselves as above, is to be argued +with, and to be treated as reputable {93} and refutable opponents. "Common +Sense" reminds us that no amount of "blatant ridicule" will turn right into +wrong. He is perfectly correct: but then no amount of bad argument will +turn wrong into right. These two things balance; and we are just where we +were: but you should answer our arguments, for whom, I ask? Would reason +convince this kind of reasoner? The issue is a short and a clear one. If +these parties be what I contend they are, then ridicule is made for them: +if not, for what or for whom? If they be right, they are only passing +through the appointed trial of all good things. Appeal is made to the +future: and my Budget is intended to show samples of the long line of +heroes who have fallen without victory, each of whom had his day of +confidence and his prophecy of success. Let the future decide: they say +roundly that the earth is flat; I say flatly that it is round. + +The paradoxers all want reason, and not ridicule: they are all accessible, +and would yield to conviction. Well then, let them reason with one another! +They divide into squads, each with a subject, and as many different +opinions as persons in each squad. If they be really what they say they +are, the true man of each set can put down all the rest, and can come +crowned with glory and girdled with scalps, to the attack on the orthodox +misbelievers. But they know, to a man, that the rest are not fit to be +reasoned with: they pay the regulars the compliment of believing that the +only chance lies with them. They think in their hearts, each one for +himself, that ridicule is of fit appliance to the rest. + + + + Miranda. A book divided into three parts, entitled Souls, Numbers, + Stars, on the Neo-Christian Religion ... Vol. i. London, 1858, 1859, + 1860. 8vo. + +The name of the author is Filopanti.[189] He announces himself as the 49th +and last Emanuel: his immediate {94} predecessors were Emanuel Washington, +Emanuel Newton, and Emanuel Galileo. He is to collect nations into one +family. He knows the transmigrations of the whole human race. Thus +Descartes became William III of England: Roger Bacon became Boccaccio. But +Charles IX,[190] in retribution for the massacre of St. Bartholomew, was +hanged in London under the name of Barthelemy for the murder of Collard: +and many of the Protestants whom he killed as King of France were shouting +at his death before the Old Bailey. + + + +THE SABBATH--THE GREAT PYRAMID + + A Letter to the members of the Anglo-Biblical Institute, dated Sept. 7, + 1858, and signed 'Herman Heinfetter.'[191] (Broadsheet.) + +This gentleman is well known to the readers of the _Athenaeum_, in which, +for nearly twenty years, he has inserted, as advertisements, long arguments +in favor of Christians keeping the Jewish Sabbath, beginning on Friday +Evening. The present letter maintains that, by the force of the definite +article, the _days_ of creation may not be consecutive, but may have any +time--millions of years--between them. This ingenious way of reconciling +the author of Genesis and the indications of geology is worthy to be added +to the list, already pretty numerous. Mr. Heinfetter has taken such pains +to make himself a public agitator, that {95} I do not feel it to be any +invasion of private life if I state that I have heard he is a large +corn-dealer. No doubt he is a member of the congregation whose almanac has +already been described. + + + + The great Pyramid. Why was it built? And who built it? By John Taylor, + 1859,[192] 12mo. + +This work is very learned, and may be referred to for the history of +previous speculations. It professes to connect the dimensions of the +Pyramid with a system of metrology which is supposed to have left strong +traces in the systems of modern times; showing the Egyptians to have had +good approximate knowledge of the dimensions of the earth, and of the +quadrature of the circle. These are points on which coincidence is hard to +distinguish from intention. Sir John Herschel[193] noticed this work, and +gave several coincidences, in the _Athenaeum_, Nos. 1696 and 1697, April 28 +and May 5, 1860: and there are some remarks by Mr. Taylor in No. 1701, June +2, 1860. + +Mr. Taylor's most recent publication is-- + + The battle of the Standards: the ancient, of four thousand years, + against the modern, of the last fifty years--the less perfect of the + two. London, 1864, 12mo. + +This is intended as an appendix to the work on the Pyramid. Mr. Taylor +distinctly attributes the original system to revelation, of which he says +the Great Pyramid is the record. We are advancing, he remarks, towards the +end of the Christian dispensation, and he adds that it is satisfactory to +see that we retain the standards which were given by unwritten revelation +700 years before Moses. This is lighting the candle at both ends; for +myself, I shall not undertake to deny or affirm either what is said about +the dark past or what is hinted about the dark future. + +{96} + +My old friend Mr. Taylor is well known as the author of the argument which +has convinced many, even most, that Sir Philip Francis[194] was Junius: +pamphlet, 1813; supplement, 1817; second edition "The Identity of Junius +with a distinguished living character established," London, 1818, 8vo. He +told me that Sir Philip Francis, in a short conversation with him, made +only this remark, "You may depend upon it you are quite mistaken:" the +phrase appears to me remarkable; it has an air of criticism on the book, +free from all personal denial. He also mentioned that a hearer told him +that Sir Philip said, speaking of writers on the question,--"Those fellows, +for half-a-crown, would prove that Jesus Christ was Junius." + +Mr. Taylor implies, I think, that he is the first who started the +suggestion that Sir Philip Francis was Junius, which I have no means either +of confirming or refuting. If it be so [and I now know that Mr. Taylor +himself never heard of any predecessor], the circumstance is very +remarkable: it is seldom indeed that the first proposer of any solution of +a great and vexed question is the person who so nearly establishes his +point in general opinion as Mr. Taylor has done. + +As to the Junius question in general, there is a little bit of the +philosophy of horse-racing which may be usefully applied. A man who is so +confident of his horse that he places him far above any other, may +nevertheless, and does, refuse to give odds against all in the field: for +many small adverse chances united make a big chance for one or other of the +opponents. I suspect Mr. Taylor has made it at least 20 to 1 for Francis +against any one competitor who has been named: but what the odds may be +against the {97} whole field is more difficult to settle. What if the real +Junius should be some person not yet named? + +Mr. Jopling, _Leisure Hour_, May 23, 1863, relies on the porphyry coffer of +the Great Pyramid, in which he finds "the most ancient and accurate +standard of measure in existence." + +I am shocked at being obliged to place a thoughtful and learned writer, and +an old friend, before such a successor as he here meets with. But +chronological arrangement defies all other arrangement. + +(I had hoped that the preceding account would have met Mr. Taylor's eye in +print: but he died during the last summer. For a man of a very thoughtful +and quiet temperament, he had a curious turn for vexed questions. But he +reflected very long and very patiently before he published: and all his +works are valuable for their accurate learning, whichever side the reader +may take.) + + + +MRS. ELIZABETH COTTLE. + +1859. _The Cottle Church._--For more than twenty years printed papers have +been sent about in the name of Elizabeth Cottle.[195] It is not so +remarkable that such papers should be concocted as that they should +circulate for such a length of time without attracting public attention. +Eighty years ago Mrs. Cottle might have rivalled Lieut. Brothers or Joanna +Southcott.[196] Long hence, when the now current volumes of our journals +are well-ransacked works of reference, those who look into them will be +glad to see this {98} feature of our time: I therefore make a few extracts, +faithfully copied as to type. The Italic is from the New Testament; the +Roman is the requisite interpretation: + +"Robert Cottle '_was numbered_ (5196) _with the transgressors_' at the back +of the Church in Norwood Cemetery, May 12, 1858--Isa. liii. 12. The Rev. +J. G. Collinson, Minister of St. James's Church, Chapham, the then district +church, before All Saints was built, read the funeral service _over the +Sepulchre wherein never before man was laid_. + +"_Hewn on the stone_, 'at the mouth of the Sepulchre,' is his name,--Robert +Cottle, born at Bristol, June 2, 1774; died at Kirkstall Lodge, Clapham +Park, May 6, 1858. _And that day_ (May 12, 1858) _was the preparation_ (day +and year for 'the PREPARED place for you'--Cottleites---by the widowed +mother of the Father's house, at Kirkstall Lodge--John xiv. 2, 3). _And the +Sabbath_ (Christmas Day, Dec. 25, 1859) _drew on_ (for the resurrection of +the Christian body on 'the third [Protestant Sun]-day'--1 Cor. xv. 35). +_Why seek ye the living_ (God of the New Jerusalem--Heb. xii. 22; Rev. iii. +12) _among the dead_ (men): _he_ (the God of Jesus) _is not here_ (in the +grave), _but is risen_ (in the person of the Holy Ghost, from the supper of +'the dead in the second death' of Paganism). _Remember how he spake unto +you_ (in the church of the Rev. George Clayton,[197] April 14, 1839). _I +will not drink henceforth_ (at this last Cottle supper) _of the fruit of +this_ (Trinity) _vine, until that day_ (Christmas Day, 1859), _when I_ +(Elizabeth Cottle) _drink it new with you_ (Cottleites) _in my Father's +kingdom_--John xv. _If this_ (Trinitarian) _cup may not pass away from me_ +(Elizabeth Cottle, April 14, 1839), _except I drink it_ ('new with you +Cottleites, in my Father's Kingdom'), _thy will be done_--Matt. xxvi. 29, +42, 64. 'Our Father which art (God) in Heaven,' _hallowed be thy name, thy_ +(Cottle) _kingdom_ {99} _come, thy will be done in earth, as it is_ (done) +_in_ (the new) _Heaven_ (and new earth of the new name of Cottle--Rev. xxi. +1; iii. 12). + +"... Queen Elizabeth, from A.D. 1558 to 1566. _And this_ WORD _yet once +more_ (by a second Elizabeth--the WORD of his oath) _signifieth_ (at John +Scott's baptism of the Holy Ghost) _the removing of those things_ (those +Gods and those doctrines) _that are made_ (according to the Creeds and +Commandments of men) _that those things_ (in the moral law of God) _which +cannot be shaken_ (as a rule of faith and practice) _may remain, wherefore +we receiving_ (from Elizabeth) _a kingdom_ (of God,) _which cannot be +moved_ (by Satan) _let us have grace_ (in his Grace of Canterbury) _whereby +we may serve God acceptably_ (with the acceptable sacrifice of Elizabeth's +body and blood of the communion of the Holy Ghost) _with reverence_ (for +truth) _and godly fear_ (of the unpardonable sin of blasphemy against the +Holy Ghost) _for our God_ (the Holy Ghost) _is a consuming fire_ (to the +nation that will not serve him in the Cottle Church). We cannot defend +ourselves against the Almighty, and if He is our defence, no nation can +invade us. + +"In verse 4 the Church of St. Peter is _in prison between four quaternions +of soldiers_--the Holy Alliance of 1815. Rev. vii. i. Elizabeth, _the Angel +of the Lord_ Jesus _appears_ to the Jewish and Christian body with _the +vision_ of prophecy to the Rev. Geo. Clayton and his clerical brethren, +April 8th, 1839. _Rhoda_ was the name of her maid at Putney Terrace who +used _to open the door to her Peter_, the Rev. Robert Ashton,[198] the +Pastor of 'the little flock' 'of 120 names together, assembled in an upper +(school) room' at Putney Chapel, to which little flock she gave the +revelation (Acts. i. 13, 15) _of Jesus the same_ King of the Jews +_yesterday_ at the prayer meeting, Dec. 31, 1841, _and to-day_, {100} Jan. +1, 1842, _and for ever_. See book of Life, page 24. Matt. xviii. 19, xxi. +13-16. In verse 6 the Italian body of St. Peter _is sleeping_ 'in the +second death' _between the two_ Imperial _soldiers_ of France and Austria. +The Emperor of France from Jan. 1, to July 11, 1859, causes the Italian +_chains of St. Peter to fall off from his_ Imperial _hands_. + +"_I say unto thee_, Robert Ashton, _thou art Peter_, a stone, _and upon +this rock_, of truth, _will I_ Elizabeth, the angel of Jesus, _build my_ +Cottle _Church, and the gates of hell_, the doors of St. Peter, at Rome, +shall not prevail against it--Matt. xvi. 18. Rev. iii. 7-12." + +This will be enough for the purpose. When any one who pleases can circulate +new revelations of this kind, uninterrupted and unattended to, new +revelations will cease to be a good investment of excentricity. I take it +for granted that the gentlemen whose names are mentioned have nothing to do +with the circulars or their doctrines. Any lady who may happen to be +intrusted with a revelation may nominate her own pastor, or any other +clergyman, one of her apostles; and it is difficult to say to what court +the nominees can appeal to get the commission abrogated. + +_March 16, 1865._ During the last two years the circulars have continued. +It is hinted that funds are low: and two gentlemen who are represented as +gone "to Bethlehem asylum in despair" say that Mrs. Cottle "will spend all +that she hath, while Her Majesty's Ministers are flourishing on the wages +of sin." The following is perhaps one of the most remarkable passages in +the whole: + +"_Extol and magnify Him_ (Jehovah, the Everlasting God, see the Magnificat +and Luke i. 45, 46--68--73--79), _that rideth_ (by rail and steam over land +and sea, from his holy habitation at Kirkstall Lodge, Psa. lxxvii. 19, 20), +_upon the_ (Cottle) _heavens, as it were_ (Sept. 9, 1864, see pages 21, +170), _upon an_ (exercising, Psa. cxxxi. 1), _horse_-(chair, bought of Mr. +John Ward, Leicester-square)." {101} + +I have pretty good evidence that there is a clergyman who thinks Mrs. +Cottle a very sensible woman. + +[_The Cottle Church._ Had I chanced to light upon it at the time of +writing, I should certainly have given the following. A printed letter to +the _Western Times_, by Mr. Robert Cottle, was accompanied by a manuscript +letter from Mrs. Cottle, apparently a circular. The date was Nov^{r}. 1853, +and the subject was the procedure against Mr. Maurice[199] at King's +College for doubting that God would punish human sins by an existence of +torture lasting through years numbered by millions of millions of millions +of millions (repeat the word _millions_ without end,) etc. The memory of +Mr. Cottle has, I think, a right to the quotation: he seems to have been no +participator in the notions of his wife: + +"The clergy of the Established Church, taken at the round number of 20,000, +may, in their first estate, be likened to 20,000 gold blanks, destined to +become sovereigns, in succession,--they are placed between the matrix of +the Mint, when, by the pressure of the screw, they receive the impress that +fits them to become part of the current coin of the realm. In a way +somewhat analogous this great body of the clergy have each passed through +the crucibles of Oxford and Cambridge,--have been assayed by the Bishop's +chaplain, touching the health of their souls, and the validity of their +call by the Divine Spirit, and then the gentle pressure of a prelate's hand +upon their heads; and the words--'Receive the Holy Ghost,' have, in a brief +space of time, wrought a {102} change in them, much akin to the miracle of +transubstantiation--the priests are completed, and they become the current +ecclesiastical coin of our country. The whole body of clergy, here spoken +of, have undergone the preliminary induction of baptism and confirmation; +and all have been duly ordained, _professing_ to hold one faith, and to +believe in the selfsame doctrines! In short, to be as identical as the +20,000 sovereigns, if compared one with the other. But mind is not +malleable and ductile, like gold; and all the preparations of tests, +creeds, and catechisms will not insure uniformity of belief. No stamp of +orthodoxy will produce the same impress on the minds of different men. +Variety is manifest, and patent, upon everything mental and material. The +Almighty has not created, nor man fashioned, two things alike! How futile, +then, is the attempt to shape and mould man's apprehension of divine truth +by one fallible standard of man's invention! If proof of this be required, +an appeal might be made to history and the experience of eighteen hundred +years." + +This is an argument of force against the reasonableness of expecting tens +of thousands of educated readers of the New Testament to find the doctrine +above described in it. The lady's argument against the doctrine itself is +very striking. Speaking of an outcry on this matter among the Dissenters +against one of their body, who was the son of "the White Stone (Rev. ii. +17), or the Roman cement-maker," she says-- + +"If the doctrine for which they so wickedly fight were true, what would +become of the black gentlemen for whose redemption I have been sacrificed +from April 8 1839." + +There are certainly very curious points about this revelation. There have +been many surmises about the final restoration of the infernal spirits, +from the earliest ages of Christianity until our own day: a collection of +them would be worth making. On reading this in proof, I see a possibility +that by "black gentlemen" may be meant the clergy: {103} I suppose my first +interpretation must have been suggested by context: I leave the point to +the reader's sagacity.] + + + +JAMES SMITH, ARCH-PARADOXER. + + The Problem of squaring the circle solved; or, the circumference and + area of the circle discovered. By James Smith.[200] London, 1859, 8vo. + + On the relations of a square inscribed in a circle. Read at the British + Association, Sept. 1859, published in the Liverpool Courier, Oct. 8, + 1859, and reprinted in broadsheet. + + The question: Are there any commensurable relations between a circle + and other Geometrical figures? Answered by a member of the British + Association ... London, 1860, 8vo.--[This has been translated into + French by M. Armand Grange, Bordeaux, 1863, 8vo.] + + The Quadrature of the Circle. Correspondence between an eminent + mathematician and James Smith, Esq. (Member of the Mersey Docks and + Harbour Board), London, 1861, 8vo. (pp. 200). + + Letter to the ... British Association ... by James Smith, Esq. + Liverpool, 1861, 8vo. + + Letter to the ... British Association ... by James Smith, Esq. + Liverpool, 1862, 8vo.--[These letters the author promised to continue.] + + A Nut to crack for the readers of Professor De Morgan's 'Budget of + Paradoxes.' By James Smith, Esq. Liverpool, 1863, 8vo. + + Paper read at the Liverpool Literary and Philosophical Society, + reported in the Liverpool Daily Courier, Jan. 26, 1864. Reprinted as a + pamphlet. + + The Quadrature of the circle, or the true ratio between the diameter + and circumference geometrically and mathematically demonstrated. By + James Smith, Esq. Liverpool, 1865, 8vo. + + {104} + + [On the relations between the dimensions and distances of the Sun, + Moon, and Earth; a paper read before the Literary and Philosophical + Society of Liverpool, Jan. 25, 1864. By James Smith, Esq. + + The British Association in Jeopardy, and Dr. Whewell, the Master of + Trinity, in the stocks without hope of escape. Printed for the authors + (J. S. confessed, and also hidden under _Nauticus_). (No date, 1865). + + The British Association in Jeopardy, and Professor De Morgan in the + Pillory without hope of escape. London, 1866, 8vo.] + +When my work appeared in numbers, I had not anything like an adequate idea +of Mr. James Smith's superiority to the rest of the world in the points in +which he is superior. He is beyond a doubt the ablest head at unreasoning, +and the greatest hand at writing it, of all who have tried in our day to +attach their names to an error. Common cyclometers sink into puny orthodoxy +by his side. + +The behavior of this singular character induces me to pay him the +compliment which Achilles paid Hector, to drag him round the walls again +and again. He was treated with unusual notice and in the most gentle +manner. The unnamed mathematician, E. M. bestowed a volume of mild +correspondence upon him; Rowan Hamilton[201] quietly proved him wrong in a +way accessible to an ordinary schoolboy; Whewell,[202] as we shall see, +gave him the means of seeing himself wrong, even more easily than by +Hamilton's method. Nothing would do; it was small kick and silly fling at +all; and he exposed his conceit by alleging that he, James Smith, had +placed Whewell in the stocks. He will therefore be universally pronounced a +proper object of the severest literary punishment: but the opinion of all +who can put two propositions together will be that of the many strokes I +have given, the hardest and most telling are my republications of his own +attempts to reason. + +He will come out of my hands in the position he ought {105} to hold, the +Supreme Pontiff of cyclometers, the vicegerent of St. Vitus upon earth, the +Mamamouchi of burlesque on inference. I begin with a review of him which +appeared in the _Athenaeum_ of May 11, 1861. Mr. Smith says I wrote it: this +I neither affirm nor deny; to do either would be a sin against the +editorial system elsewhere described. Many persons tell me they know me by +my style; let them form a guess: I can only say that many have declared as +above while fastening on me something which I had never seen nor heard of. + + + + The Quadrature of the Circle: Correspondence between an Eminent + Mathematician and James Smith, Esq. (Edinburgh, Oliver & Boyd; London, + Simpkin, Marshall & Co.) + +"A few weeks ago we were in perpetual motion. We did not then suppose that +anything would tempt us on a circle-squaring expedition: but the +circumstances of the book above named have a peculiarity which induces us +to give it a few words. + +"Mr. James Smith, a gentleman residing near Liverpool, was some years ago +seized with the _morbus cyclometricus_.[203] The symptoms soon took a +defined form: his circumference shrank into exactly 3-1/8 times his +diameter, instead of close to 3-16/113, which the mathematician knows to be +so near to truth that the error is hardly at the rate of a foot in 2,000 +miles. This shrinking of the circumference remained until it became +absolutely necessary that it should be examined by the British Association. +This body, which as Mr. James Smith found to his sorrow, has some interest +in 'jealously guarding the mysteries of their profession,' refused at first +to entertain the question. On this Mr. Smith changed his 'tactics' and the +name of his paper, and smuggled in the subject under the form of 'The +Relations of a Circle inscribed in a Square'! The paper was thus forced +upon the Association, for Mr. Smith informs us that he {106} 'gave the +Section to understand that he was not the man that would permit even the +British Association to trifle with him.' In other words, the Association +bore with and were bored with the paper, as the shortest way out of the +matter. Mr. Smith also circulated a pamphlet. Some kind-hearted man, who +did not know the disorder as well as we do, and who appears in Mr. Smith's +handsome octavo as E. M.--the initials of 'eminent mathematician'--wrote to +him and offered to show him in a page that he was all wrong. Mr. Smith +thereupon opened a correspondence, which is the bulk of the volume. When +the correspondence was far advanced, Mr. Smith announced his intention to +publish. His benevolent instructor--we mean in intention--protested against +the publication, saying 'I do not wish to be gibbeted to the world as +having been foolish enough to enter upon what I feel now to have been a +ridiculous enterprise.' + +"For this Mr. Smith cared nothing: he persisted in the publication, and the +book is before us. Mr. Smith has had so much grace as to conceal his kind +adviser's name under E. M., that is to say, he has divided the wrong among +all who may be suspected of having attempted so hopeless a task as that of +putting a little sense into his head. He has violated the decencies of +private life. Against the will of the kind-hearted man who undertook his +case, he has published letters which were intended for no other purpose +than to clear his poor head of a hopeless delusion. He deserves the +severest castigation; and he will get it: his abuse of confidence will +stick by him all his days. Not that he has done his benefactor--in +intention, again--any harm. The patience with which E. M. put the blunders +into intelligible form, and the perseverance with which he tried to find a +cranny-hole for common reasoning to get in at, are more than respectable: +they are admirable. It is, we can assure E. M., a good thing that the +nature of the circle-squarer should be so completely exposed as in this +volume. The benefit which he intended Mr. James Smith may be {107} +conferred upon others. And we should very much like to know his name, and +if agreeable to him, to publish it. As to Mr. James Smith, we can only say +this: he is not mad. Madmen reason rightly upon wrong premises: Mr. Smith +reasons wrongly upon no premises at all. + +"E. M. very soon found out that, to all appearance, Mr. Smith got a circle +of 3-1/8 times the diameter by making it the supposition to set out with +that there was such a circle; and then finding certain consequences which, +so it happened, were not inconsistent with the supposition on which they +were made. Error is sometimes self-consistent. However, E. M., to be quite +sure of his ground, wrote a short letter, stating what he took to be Mr. +Smith's hypothesis, containing the following: 'On AC as diameter, describe +the circle D, which by hypothesis shall be equal to three and one-eighth +times the length of AC.... I beg, before proceeding further, to ask whether +I have rightly stated your argument.' To which Mr. Smith replied: 'You have +stated my argument with perfect accuracy.' Still E. M. went on, and we +could not help, after the above, taking these letters as the initials of +Everlasting Mercy. At last, however, when Mr. Smith flatly denied that the +area of the circle lies between those of the inscribed and circumscribed +polygons, E. M. was fairly beaten, and gave up the task. Mr. Smith was left +to write his preface, to talk about the certain victory of truth--which, +oddly enough, is the consolation of all hopelessly mistaken men; to compare +himself with Galileo; and to expose to the world the perverse behavior of +the Astronomer Royal, on whom he wanted to fasten a conversation, and who +replied, 'It would be a waste of time, Sir, to listen to anything you could +have to say on such a subject.' + +"Having thus disposed of Mr. James Smith, we proceed to a few remarks on +the subject: it is one which a journal would never originate, but which is +rendered necessary from time to time by the attempts of the autopseustic to +become {108} heteropseustic. To the mathematician we have nothing to say: +the question is, what kind of assurance can be given to the world at large +that the wicked mathematicians are not acting in concert to keep down their +superior, Mr. James Smith, the current Galileo of the quadrature of the +circle. + +"Let us first observe that this question does not stand alone: +independently of the millions of similar problems which exist in higher +mathematics, the finding of the diagonal of a square has just the same +difficulty, namely, the entrance of a pair of lines of which one cannot be +definitely expressed by means of the other. We will show the reader who is +up to the multiplication-table how he may go on, on, on, ever nearer, never +there, in finding the diagonal of a square from the side. + +"Write down the following rows of figures, and more, if you like, in the +way described: + + 1 2 5 12 29 70 169 408 985 + 1 3 7 17 41 99 239 577 1393 + +After the second, each number is made up of double the last increased by +the last but one: thus, 5 is 1 more than twice 2, 12 is 2 more than twice +5, 239 is 41 more than twice 99. Now, take out two adjacent numbers from +the upper line, and the one below the first from the lower: as + + 70 169 + 99. + +Multiply together 99 and 169, giving 16,731. If, then, you will say that 70 +diagonals are exactly equal to 99 sides, you are in error about the +diagonal, but an error the amount of which is not so great as the 16,731st +part of the diagonal. Similarly, to say that five diagonals make exactly +seven sides does not involve an error of the 84th part of the diagonal. + +"Now, why has not the question of _crossing the square_ been as celebrated +as that of _squaring the circle_? Merely because Euclid demonstrated the +impossibility of the first {109} question, while that of the second was not +demonstrated, completely, until the last century. + +"The mathematicians have many methods, totally different from each other, +of arriving at one and the same result, their celebrated approximation to +the circumference of the circle. An intrepid calculator has, in our own +time, carried his approximation to what they call 607 decimal places: this +has been done by Mr. Shanks,[204] of Houghton-le-Spring, and Dr. +Rutherford[205] has verified 441 of these places. But though 607 looks +large, the general public will form but a hazy notion of the extent of +accuracy acquired. We have seen, in Charles Knight's[206] _English +Cyclopaedia_, an account of the matter which may illustrate the +unimaginable, though rationally conceivable, extent of accuracy obtained. + +"Say that the blood-globule of one of our animalcules is a millionth of an +inch in diameter. Fashion in thought a globe like our own, but so much +larger that our globe is but a blood-globule in one of its animalcules: +never mind the microscope which shows the creature being rather a bulky +instrument. Call this the first globe _above_ us. Let the first globe above +us be but a blood-globule, as to size, in the animalcule of a still larger +globe, which call the second globe above us. Go on in this way to the +twentieth globe above us. Now go down just as far on the other side. Let +the blood-globule with which we started be a globe peopled with animals +like ours, but rather smaller: {110} and call this the first globe below +us. Take a blood-globule out of this globe, people it, and call it the +second globe below us: and so on to the twentieth globe below us. This is a +fine stretch of progression both ways. Now give the giant of the twentieth +globe _above_ us the 607 decimal places, and, when he has measured the +diameter of his globe with accuracy worthy of his size, let him calculate +the circumference of his equator from the 607 places. Bring the little +philosopher from the twentieth globe _below_ us with his very best +microscope, and set him to see the small error which the giant must make. +He will not succeed, unless his microscopes be much better for his size +than ours are for ours. + +"Now it must be remembered by any one who would laugh at the closeness of +the approximation, that the mathematician generally goes _nearer_; in fact +his theorems have usually no error at all. The very person who is +bewildered by the preceding description may easily forget that if there +were _no error at all_, the Lilliputian of the millionth globe below us +could not find a flaw in the Brobdingnagian of the millionth globe above. +The three angles of a triangle, of perfect accuracy of form, are +_absolutely_ equal to two right angles; no stretch of progression will +detect _any_ error. + +"Now think of Mr. Lacomme's mathematical adviser (_ante_, Vol. I, p. 46) +making a difficulty of advising a stonemason about the quantity of pavement +in a circular floor! + +"We will now, for our non-calculating reader, put the matter in another +way. We see that a circle-squarer can advance, with the utmost confidence, +the assertion that when the diameter is 1,000, the circumference is +accurately 3,125: the mathematician declaring that it is a trifle more than +3,141-1/2. If the squarer be right, the mathematician has erred by about a +200th part of the whole: or has not kept his accounts right by about 10s. +in every 100l. Of course, if he set out with such an error he will +accumulate blunder upon blunder. Now, if there be a process in which {111} +close knowledge of the circle is requisite, it is in the prediction of the +moon's place--say, as to the time of passing the meridian at Greenwich--on +a given day. We cannot give the least idea of the complication of details: +but common sense will tell us that if a mathematician cannot find his way +round the circle without a relative error four times as big as a +stockbroker's commission, he must needs be dreadfully out in his attempt to +predict the time of passage of the moon. Now, what is the fact? His error +is less than a second of time, and the moon takes 27 days odd to revolve. +That is to say, setting out with 10s. in 100l. of error in his +circumference, he gets within the fifth part of a farthing in 100l. in +predicting the moon's transit. Now we cannot think that the respect in +which mathematical science is held is great enough--though we find it not +small--to make this go down. That respect is founded upon a notion that +right ends are got by right means: it will hardly be credited that the +truth can be got to farthings out of data which are wrong by shillings. +Even the celebrated Hamilton[207] of Edinburgh, who held that in +mathematics there was no way of going wrong, was fully impressed with the +belief that this was because error was avoided from the beginning. He never +went so far as to say that a mathematician who begins wrong must end right +somehow. + +"There is always a difficulty about the mode in which the thinking man of +common life is to deal with subjects he has not studied to a professional +extent. He must form opinions on matters theological, political, legal, +medical, and social. If he can make up his mind to choose a guide, there +is, of course, no perplexity: but on all the subjects mentioned the +direction-posts point different ways. Now why should he not form his +opinion upon an abstract mathematical question? Why not conclude that, as +to the circle, it is possible Mr. James Smith may be the man, just {112} as +Adam Smith[208] was the man of things then to come, or Luther, or Galileo? +It is true that there is an unanimity among mathematicians which prevails +in no other class: but this makes the chance of their all being wrong only +different in degree. And more than this, is it not generally thought among +us that priests and physicians were never so much wrong as when there was +most appearance of unanimity among them? To the preceding questions we see +no answer except this, that the individual inquirer may as rationally +decide a mathematical question for himself as a theological or a medical +question, so soon as he can put himself into a position in mathematics, +level with that in which he stands in theology or medicine. The every-day +thought and reading of common life have a certain resemblance to the +thought and reading demanded by the learned faculties. The research, the +balance of evidence, the estimation of probabilities, which are used in a +question of medicine, are closely akin in character, however different the +matter of application, to those which serve a merchant to draw his +conclusions about the markets. But the mathematicians have methods of their +own, to which nothing in common life bears close analogy, as to the nature +of the results or the character of the conclusions. The logic of +mathematics is certainly that of common life: but the data are of a +different species; they do not admit of doubt. An expert arithmetician, +such as is Mr. J. Smith, may fancy that calculation, merely as such, is +mathematics: but the value of his book, and in this point of view it is not +small, is the full manner in which it shows that a practised arithmetician, +venturing into the field of mathematical demonstration, may show himself +utterly destitute of all that distinguishes the reasoning geometrical +investigator from the calculator. + +{113} + +"And further, it should be remembered that in mathematics the power of +verifying results far exceeds that which is found in anything else: and +also the variety of distinct methods by which they can be attained. It +follows from all this that a person who desires to be as near the truth as +he can will not judge the results of mathematical demonstration to be open +to his criticism, in the same degree as results of other kinds. Should he +feel compelled to decide, there is no harm done: his circle may be 3-1/8 +times its diameter, if it please him. But we must warn him that, in order +to get this circle, he must, as Mr. James Smith has done, _make it at +home_: the laws of space and thought beg leave respectfully to decline the +order." + + + +I will insert now at length, from the _Athenaeum_ of June 8, 1861, the easy +refutation given by my deceased friend, with the remarks which precede. + +"Mr. James Smith, of whose performance in the way of squaring the circle we +spoke some weeks ago in terms short of entire acquiescence, has advertised +himself in our columns, as our readers will have seen. He has also +forwarded his letter to the Liverpool _Albion_, with an additional +statement, which he did not make in _our_ journal. He denies that he has +violated the decencies of private life, since his correspondent revised the +proofs of his own letters, and his 'protest had respect only to making his +name public.' This statement Mr. James Smith precedes by saying that we +have treated as true what we well knew to be false: and he follows by +saying that we have not read his work, or we should have known the above +facts to be true. Mr. Smith's pretext is as follows. His correspondent +E. M. says, 'My letters were not intended for publication, and I protest +against their being published,' and he subjoins 'Therefore I must desire +that my name may not be used.' The obvious meaning is that E. M. protested +against the publication altogether, but, judging that Mr. Smith was {114} +determined to publish, desired that his name should not be used. That he +afterwards corrected the proofs merely means that he thought it wiser to +let them pass under his own eyes than to leave them entirely to Mr. Smith. + +"We have received from Sir W. Rowan Hamilton[209] a proof that the +circumference is more than 3-1/8 diameters, requiring nothing but a +knowledge of four books of Euclid. We give it in brief as an exercise for +our juvenile readers to fill up. It reminds us of the old days when real +geometers used to think it worth while seriously to demolish pretenders. +Mr. Smith's fame is now assured: Sir W. R. Hamilton's brief and easy +exposure will procure him notice in connection with this celebrated +problem. + +"It is to be shown that the perimeter of a regular polygon of 20 sides is +greater than 3-1/8 diameters of the circle, and still more, of course, is +the circumference of the circle greater than 3-1/8 diameters. + +"1. It follows from the 4th Book of Euclid, that the rectangle under the +side of a regular decagon inscribed in a circle, and that side increased by +the radius, is equal to the square of the radius. But the product 791 (791 ++ 1280) is less than 1280 x 1280; if then the radius be 1280 the side of +the decagon is greater than 791. + +"2. When a diameter bisects a chord, the square of the chord is equal to +the rectangle under the doubles of the segments of the diameter. But the +product 125 (4 x 1280 - 125) is less than 791 x 791. If then the bisected +chord be a side of the decagon, and if the radius be still 1280, the double +of the lesser segment exceeds 125. + +"3. The rectangle under this doubled segment and the radius is equal to the +square of the side of an inscribed regular polygon of 20 sides. But the +product 125 x 1280 is equal to 400 x 400; therefore, the side of the +last-mentioned polygon is greater than 400, if the radius be still 1280. In +other words, if the radius be represented by the new {115} member 16, and +therefore the diameter by 32, this side is greater than 5, and the +perimeter exceeds 100. So that, finally, if the diameter be 8, the +perimeter of the inscribed regular polygon of 20 sides, and still more the +circumference of the circle, is greater than 25: that is, the circumference +is more than 3-1/8 diameters." + +The last work in the list was thus noticed in the _Athenaeum_, May 27, 1865. + +"Mr. James Smith appears to be tired of waiting for his place in the Budget +of Paradoxes, and accordingly publishes a long letter to Professor De +Morgan, with various prefaces and postscripts. The letter opens by a hint +that the Budget appears at very long intervals, and 'apparently without any +sufficient reason for it.' As Mr. Smith hints that he should like to see +Mr. De Morgan, whom he calls an 'elephant of mathematics,' 'pumping his +brains' 'behind the scenes'--an odd thing for an elephant to do, and an odd +place to do it in--to get an answer, we think he may mean to hint that the +Budget is delayed until the pump has worked successfully. Mr. Smith is +informed that we have had the whole manuscript of the Budget, excepting +only a final summing-up, in our hands since October, 1863. [This does not +refer to the Supplement.] There has been no delay: we knew from the +beginning that a series of historical articles would be frequently +interrupted by the things of the day. Mr. James Smith lets out that he has +never been able to get a private line from Mr. De Morgan in answer to his +communications: we should have guessed it. He says, 'The Professor is an +old bird and not to be easily caught, and by no efforts of mine have I been +able, up to the present moment, either to induce or twit him into a +discussion....' Mr. Smith curtails the proverb: old birds are not to be +caught with _chaff_, nor with _twit_, which seems to be Mr. Smith's word +for his own chaff, and, so long as the first letter is sounded, a very +proper word. Why does he not try a little grain of sense? Mr. Smith +evidently {116} thinks that, in his character as an elephant, the Professor +has not pumped up brain enough to furnish forth a bird. In serious earnest, +Mr. Smith needs no answer. In one thing he excites our curiosity: what is +meant by demonstrating 'geometrically _and_ mathematically?'" + +I now proceed to my original treatment of the case. + + + +Mr. James Smith will, I have no doubt, be the most uneclipsed +circle-squarer of our day. He will not owe this distinction to his being an +influential and respected member of the commercial world of Liverpool, even +though the power of publishing which his means give him should induce him +to issue a whole library upon one paradox. Neither will he owe it to the +pains taken with him by a mathematician who corresponded with him until the +joint letters filled an octavo volume. Neither will he owe it to the notice +taken of him by Sir William Hamilton, of Dublin, who refuted him in a +manner intelligible to an ordinary student of Euclid, which refutation he +calls a remarkable paradox easily explainable, but without explaining it. +What he will owe it to I proceed to show. + +Until the publication of the _Nut to Crack_ Mr. James Smith stood among +circle-squarers in general. I might have treated him with ridicule, as I +have done others: and he says that he does not doubt he shall come in for +his share at the tail end of my Budget. But I can make a better job of him +than so, as Locke would have phrased it: he is such a very striking example +of something I have said on the use of logic that I prefer to make an +example of his writings. On one point indeed he well deserves the +_scutica_,[210] if not the _horribile flagellum_.[211] He tells me that he +will bring his solution to me in such a form as shall compel me to admit it +as _un fait accompli_ [_une faute accomplie?_][212] {117} or leave myself +open to the humiliating charge of mathematical ignorance and folly. He has +also honored me with some private letters. In the first of these he gives +me a "piece of information," after which he cannot imagine that I, "as an +honest mathematician," can possibly have the slightest hesitation in +admitting his solution. There is a tolerable reservoir of modest assurance +in a man who writes to a perfect stranger with what he takes for an +argument, and gives an oblique threat of imputation of dishonesty in case +the argument be not admitted without hesitation; not to speak of the minor +charges of ignorance and folly. All this is blind self-confidence, without +mixture of malicious meaning; and I rather like it: it makes me understand +how Sam Johnson came to say of his old friend Mrs. Cobb,[213]--"I love Moll +Cobb for her impudence." I have now done with my friend's _suaviter in +modo_,[214] and proceed to his _fortiter in re_[215]: I shall show that he +_has_ convicted himself of ignorance and folly, with an honesty and candor +worthy of a better value of [pi]. + +Mr. Smith's method of proving that every circle is 3-1/8 diameters is to +assume that it is so,--"if you dislike the term datum, then, by hypothesis, +let 8 circumferences be exactly equal to 25 diameters,"--and then to show +that every other supposition is thereby made absurd. The right to this +assumption is enforced in the "Nut" by the following analogy: + +"I think you (!) will not dare (!) to dispute my right to this hypothesis, +when I can prove by means of it that every other value of [pi] will lead to +the grossest absurdities; unless indeed, you are prepared to dispute the +right of Euclid to adopt a false line hypothetically for the purpose {118} +of a '_reductio ad absurdum_'[216] demonstration, in pure geometry." + + + +Euclid assumes what he wants to _disprove_, and shows that his _assumption_ +leads to absurdity, and so _upsets itself_. Mr. Smith assumes what he wants +to _prove_, and shows that _his_ assumption makes _other propositions_ lead +to absurdity. This is enough for all who can reason. Mr. James Smith cannot +be argued with; he has the whip-hand of all the thinkers in the world. +Montucla would have said of Mr. Smith what he said of the gentleman who +squared his circle by giving 50 and 49 the same square root, _Il a perdu le +droit d'etre frappe de l'evidence_.[217] + +It is Mr. Smith's habit, when he finds a conclusion agreeing with its own +assumption, to regard that agreement as proof of the assumption. The +following is the "piece of information" which will settle me, if I be +honest. Assuming [pi] to be 3-1/8, he finds out by working instance after +instance that the mean proportional between one-fifth of the area and +one-fifth of eight is the radius. That is, + + if [pi] = 25/8, sqrt(([pi]r^2)/5 . 8/5) = r. + +This "remarkable general principle" may fail to establish Mr. Smith's +quadrature, even in an honest mind, if that mind should happen to know +that, a and b being any two numbers whatever, we need only assume-- + + [pi] = a^2/b, to get at sqrt(([pi]r^2)/a . b/a) = r. + +We naturally ask what sort of glimmer can Mr. Smith have of the subject +which he professes to treat? On this point he has given satisfactory +information. I had mentioned the old problem of finding two mean +proportionals, {119} as a preliminary to the duplication of the cube. On +this mention Mr. Smith writes as follows. I put a few words in capitals; +and I write rq[218] for the sign of the square root, which embarrasses +small type: + +"This establishes the following _infallible_ rule, for finding two mean +proportionals OF EQUAL VALUE, and is more than a preliminary, to the famous +old problem of 'Squaring the circle.' Let any finite number, say 20, and +its fourth part = (1/4)(20) = 5, be given numbers. Then rq(20 x 5) = rq 100 = +10, is their mean proportional. Let this be a given mean proportional TO +FIND ANOTHER MEAN PROPORTIONAL OF EQUAL VALUE. Then + + 20 x [pi]/4 = 20 x 3.125/4 = 20 x .78125 = 15.625 + +will be the first number; as + + 25 : 16 :: rq 20 : rq 8.192: and (rq 8.192)^2 x [pi]/4 = 8.192 x .78125 = + 6.4 + +will be the second number; therefore rq(15.625 x 6.4) = rq 100 = 10, is the +required mean proportional.... Now, my good Sir, however competent you may +be to prove every man a fool [not _every_ man, Mr. Smith! only _some_; pray +learn logical quantification] who now thinks, or in times gone by has +thought, the 'Squaring of the Circle' _a possibility_; I doubt, and, on the +evidence afforded by your Budget, I cannot help doubting, whether you were +ever before competent to find two mean proportionals _by my unique +method_."--(_Nut_, pp. 47, 48.) [That I never was, I solemnly declare!] + +All readers can be made to see the following exposure. When 5 and 20 are +given, x is a mean proportional when in 5, x, 20, 5 is to x as x to 20. And +x must be 10. But x and y are two mean proportionals when in 5, x, y, 20, x +{120} is a mean proportional between 5 and y, and y is a mean proportional +between x and 20. And these means are x = 5 [cuberoot]4, y = 5 +[cuberoot]16. But Mr. Smith finds _one_ mean, finds it _again_ in a +roundabout way, and produces 10 and 10 as the two (equal!) means, in +solution of the "famous old problem." This is enough: if more were wanted, +there is more where this came from. Let it not be forgotten that Mr. Smith +has found a translator abroad, two, perhaps three, followers at home, +and--most surprising of all--a real mathematician to try to set him right. +And this mathematician did not discover the character of the subsoil of the +land he was trying to cultivate until a goodly octavo volume of letters had +passed and repassed. I have noticed, in more quarters than one, an apparent +want of perception of the _full_ amount of Mr. Smith's ignorance: persons +who have not been in contact with the non-geometrical circle-squarers have +a kind of doubt as to whether anybody can carry things so far. But I am an +"old bird" as Mr. Smith himself calls me; a Simorg, an "all-knowing Bird of +Ages" in matters of cyclometry. + +The curious phenomena of thought here exhibited illustrate, as above said, +a remark I have long ago made on the effect of proper study of logic. Most +persons reason well enough on matter to which they are accustomed, and in +terms with which they are familiar. But in unaccustomed matter, and with +use of strange terms, few except those who are practised in the +abstractions of pure logic can be tolerably sure to keep their feet. And +one of the reasons is easily stated: terms which are not quite familiar +partake of the vagueness of the X and Y on which the student of logic +learns to see the formal force of a proposition independently of its +material elements. + +I make the following quotation from my fourth paper on logic in the +_Cambridge Transactions_: + +"The uncultivated reason proceeds by a process almost entirely material. +Though the necessary law of thought {121} must determine the conclusion of +the ploughboy as much as that of Aristotle himself, the ploughboy's +conclusion will only be tolerably sure when the matter of it is such as +comes within his usual cognizance. He knows that geese being all birds does +not make all birds geese, but mainly because there are ducks, chickens, +partridges, etc. A beginner in geometry, when asked what follows from +'Every A is B,' answers 'Every B is A.' That is, the necessary laws of +thought, except in minds which have examined their tools, are not very sure +to work correct conclusions except upon familiar matter.... As the +cultivation of the individual increases, the laws of thought which are of +most usual application are applied to familiar matter with tolerable +safety. But difficulty and risk of error make a new appearance with a new +subject; and this, in most cases, until new subjects are familiar things, +unusual matter common, untried nomenclature habitual; that is, until it is +a habit to be occupied upon a novelty. It is observed that many persons +reason well in some things and badly in others; and this is attributed to +the consequence of employing the mind too much upon one or another subject. +But those who know the truth of the preceding remarks will not have far to +seek for what is often, perhaps most often, the true reason.... I maintain +that logic tends to make the power of reason over the unusual and +unfamiliar more nearly equal to the power over the usual and familiar than +it would otherwise be. The second is increased; but the first is almost +created." + +Mr. James Smith, by bringing ignorance, folly, dishonesty into contact with +my name, in the way of conditional insinuation, has done me a good turn: he +has given me right to a freedom of personal remark which I might have +declined to take in the case of a person who is useful and respected in +matters which he understands. + +Tit for tat is logic all the world over. By the way, what has become of the +rest of the maxim: we never hear it {122} now. When I was a boy, in some +parts of the country at least, it ran thus: + + "Tit for tat; + Butter for fat: + If you kill my dog, + I'll kill your cat." + +He is a glaring instance of the truth of the observations quoted above. I +will answer for it that, at the Mersey Dock Board, he never dreams of +proving that the balance at the banker's is larger than that in the book by +assuming that the larger sum is there, and then proving that the other +supposition--the smaller balance--is upon that assumption, an absurdity. He +never says to another director, How can you dare to refuse me a right to +assume the larger balance, when you yourself, the other day, +said,--Suppose, for argument's sake, we had 80,000l. at the banker's, +though you knew the book only showed 30,000l.? This is the way in which he +has supported his geometrical paradox by Euclid's example: and this is not +the way he reasons at the board; I know it by the character of him as a man +of business which has reached my ears from several quarters. But in +geometry and rational arithmetic he is a smatterer, though expert at +computation; at the board he is a trained man of business. The language of +geometry is so new to him that he does not know what is meant by "two mean +proportionals:" but all the phrases of commerce are rooted in his mind. He +is most unerasably booked in the history of the squaring of the circle, as +the speculator who took a right to assume a proposition for the destruction +of other propositions, on the express ground that Euclid assumes a +proposition to show that it destroys itself: which is as if the curate +should demand permission to throttle the squire because St. Patrick drove +the vermin to suicide to save themselves from slaughter. He is conspicuous +as a speculator who, more visibly than almost any other known to history, +reasoned in a circle by way of reasoning on a circle. But {123} what I have +chiefly to do with is the force of instance which he has lent to my +assertion that men who have not had real training in pure logic are unsafe +reasoners in matter which is not familiar. It is hard to get first-rate +examples of this, because there are few who find the way to the printer +until practice and reflection have given security against the grossest +slips. I cannot but think that his case will lead many to take what I have +said into consideration, among those who are competent to think of the +great mental disciplines. To this end I should desire him to continue his +efforts, to amplify and develop his great principle, that of proving a +proposition by assuming it and taking as confirmation every consequence +that does not contradict the assumption. + +Since my Budget commenced, Mr. Smith has written me notes: the portion +which I have preserved--I suppose several have been mislaid--makes a +hundred and seven pages of note-paper, closely written. To all this I have +not answered one word: but I think I cannot have read fewer than forty +pages. In the last letter the writer informs me that he will not write at +greater length until I have given him an answer, according to the "rules of +good society." Did I not know that for every inch I wrote back he would +return an ell? Surely in vain the net is spread in the eyes of anything +that hath a wing. There were several good excuses for not writing to Mr. J. +Smith: I will mention five. First, I distinctly announced at the beginning +of this Budget that I would not communicate with squarers of the circle. +Secondly, any answer I might choose to give might with perfect propriety be +reserved for this article; had the imputation of incivility been made after +the first note, I should immediately have replied to this effect: but I +presumed it was quite understood. Thirdly, Mr. Smith, by his publication of +E. M.'s letters against the wish of the writer, had put himself out of the +pale of correspondence. Fourthly, he had also gone beyond the rules of good +society in sending {124} letter after letter to a person who had shown by +his silence an intention to avoid correspondence. Fifthly, these same rules +of good society are contrived to be flexible or frangible in extreme cases: +otherwise there would be no living under them; and good society would be +bad. Father Aldrovand has laid down the necessary distinction--"I tell +thee, thou foolish Fleming, the text speaketh but of promises made unto +Christians, and there is in the rubric a special exemption of such as are +made to Welchmen." There is also a rubric to the rules of good society; and +squarers of the circle are among those whom there is special permission not +to answer: they are the wild Welchmen of geometry, who are always +assailing, but never taking, the Garde Douloureuse[219] of the circle. "At +this commentary," proceeds the story, "the Fleming grinned so broadly as to +show his whole case of broad strong white teeth." I know not whether the +Welchman would have done the like, but I hope Mr. James Smith will: and I +hope he has as good a case to show as Wilkin Flammock. For I wish him long +life and long health, and should be very glad to see so much energy +employed in a productive way. I hope he wishes me the same: if not, I will +give him what all his judicious friends will think a good reason for doing +so. His pamphlets and letters are all tied up together, and will form a +curious lot when death or cessation of power to forage among book-shelves +shall bring my little library to the hammer. And this time may not be far +off: for I was X years old in A.D. X^2; not 4 in A.D. 16, nor 5 in A.D. 25, +but still in one case under that law. And now I have made my own age a +problem of quadrature, and Mr. J. Smith may solve it. But I protest against +his method of assuming a result, and making itself prove itself: he might +in this way, as sure as eggs is eggs (a corruption of X is X), make me +1,864 years old, which is a great deal too much. + +{125} + +_April 5, 1864._--Mr. Smith continues to write me long letters, to which he +hints that I am to answer. In his last, of 31 closely written sides of +note-paper, he informs me, with reference to my obstinate silence, that +though I think myself and am thought by others to be a mathematical +Goliath, I have resolved to play the mathematical snail, and keep within my +shell. A mathematical _snail_! This cannot be the thing so called which +regulates the striking of a clock; for it would mean that I am to make Mr. +Smith sound the true time of day, which I would by no means undertake upon +a clock that gains 19 seconds odd in every hour by false quadrature. But he +ventures to tell me that pebbles from the sling of simple truth and common +sense will ultimately crack my shell, and put me _hors de combat_.[220] The +confusion of images is amusing: Goliath turning himself into a snail to +avoid [pi] = 3-1/8, and James Smith, Esq., of the Mersey Dock Board: and +put _hors de combat_--which should have been _cache_[221]--by pebbles from +a sling. If Goliath had crept into a snail-shell, David would have cracked +the Philistine with his foot. There is something like modesty in the +implication that the crack-shell pebble has not yet taken effect; it might +have been thought that the slinger would by this time have been singing-- + + "And thrice [and one-eighth] I routed all my foes, + And thrice [and one-eighth] I slew the slain." + +But he promises to give the public his nut-cracker if I do not, before the +Budget is concluded, "unravel" the paradox, which is the +mathematico-geometrical nut he has given me to crack. Mr. Smith is a crack +man: he will crack his own nut; he will crack my shell; in the mean time he +cracks himself up. Heaven send he do not crack himself into lateral +contiguity with himself. + +On June 27 I received a letter, in the handwriting of Mr. James Smith, +signed Nauticus. I have ascertained {126} that one of the letters to the +_Athenaeum_ signed Nauticus is in the same handwriting. I make a few +extracts: + +"... The important question at issue has been treated by a brace of +mathematical birds with too much levity. It may be said, however, that +sarcasm and ridicule sometimes succeed, where reason fails.... Such a +course is not well suited to a discussion.... For this reason I shall for +the future [this implies there has been a past, so that Nauticus is not +before me for the first time] endeavor to confine myself to dry reasoning +from incontrovertible premises. + +... It appears to me that so far as his theory is concerned he comes off +unscathed. You might have found "a hole in Smith's circle" (have you seen a +pamphlet bearing this title? [I never heard of it until now]), but after +all it is quite possible the hole may have been left by design, for the +purpose of entrapping the unwary." + +[On the publication of the above, the author of the pamphlet obligingly +forwarded a copy to me of _A Hole in Smith's Circle_--by a Cantab: Longman +and Co., 1859, (pp. 15). "It is pity to lose any fun we can get out of the +affair," says my almamaternal brother: to which I add that in such a case +warning without joke is worse than none at all, as giving a false idea of +the nature of the danger. The Cantab takes some absurdities on which I have +not dwelt: but there are enough to afford a Cantab from every college his +own separate hunting ground.] + +Does this hint that his mode of proof, namely, assuming the thing to be +proved, was a design to entrap the unwary? if so, it bangs Banagher. Was +his confounding two mean proportionals with one mean proportional found +twice over a trick of the same intent? if so, it beats cockfighting. That +Nauticus is Mr. Smith appears from other internal evidence. In 1819, Mr. +J. C. Hobhouse[222] was sent to Newgate for a {127} libel on the House of +Commons which was only intended for a libel on Lord Erskine.[223] The +ex-Chancellor had taken Mr. Hobhouse to be thinking of him in a certain +sentence; this Mr. Hobhouse denied, adding, "There is but one man in the +country who is always thinking of Lord Erskine." I say that there is but +one man of our day who would couple me and Mr. James Smith as a "brace of +mathematical birds." + +Mr. Smith's "theory" is unscathed by me. Not a doubt about it: but how does +he himself come off? I should never think of refuting a theory proved by +assumption of itself. I left Mr. Smith's [pi] untouched: or, if I put in my +thumb and pulled out a plum, it was to give a notion of the cook, not of +the dish. The "important question at issue" was not the circle: it was, +wholly and solely, whether the abbreviation of _James_ might be spelled +_Jimm_.[224] This is personal to the verge of scurrility: but in literary +controversy the challenger names the weapons, and Mr. Smith begins with +charge of ignorance, folly, and dishonesty, by conditional implication. So +that the question is, not the personality of a word, but its applicability +to the person designated: it is enough if, as the Latin grammar has it, +_Verbum personale concordat cum nominativo_.[225] + +I may plead precedent for taking a liberty with the orthography of _Jem_. +An instructor of youth was scandalized at the abrupt and irregular--but +very effective--opening of Wordsworth's little piece: + +{128} + + "A simple child + That lightly draws its breath, + And feels its life in every limb, + What should it know of death?" + +So he mended the matter by instructing his pupils to read the first line +thus: + + "A simple child, dear brother ----." + +The brother, we infer from sound, was to be James, and the blank must +therefore be filled up with _Jimb_. + +I will notice one point of the letter, to make a little more distinction +between the two birds. Nauticus lays down--quite correctly--that the sine +of an angle is less than its circular measure. He then takes 3.1416 for +180 deg., and finds that 36' is .010472. But this is exactly what he finds +for the sine of 36' in tables: he concludes that either 3.1416 or the +tables must be wrong. He does not know that sines, as well as [pi], are +interminable decimals, of which the tables, to save printing, only take in +a finite number. He is a six-figure man: let us go thrice again to make up +nine, and we have as follows: + + Circular measure of 36' .010471975... + Sine of 36' .010471784... + Excess of measure over sine .000000191... + +Mr. Smith invites me to say which is wrong, the quadrature, or the tables: +I leave him to guess. He says his assertions "arise naturally and +necessarily out of the arguments of a circle-squarer:" he might just as +well lay down that all the pigs went to market because it is recorded that +"_This_ pig went to market." I must say for circle-squarers that very few +bring their pigs to so poor a market. I answer the above argument because +it is, of all which Mr. James Smith has produced, the only one which rises +to the level of a schoolboy: to meet him halfway I descend to that level. + +Mr. Smith asks me to solve a problem in the _Athenaeum_: {129} and I will do +it, because the question will illustrate what is _below_ schoolboy level. + +"Let x represent the circular measure of an angle of 15 deg., and y half +the sine of an angle of 30 deg. = area of the square on the radius of a +circle of diameter unity = .25. If x - y = xy, firstly, what is the +arithmetical value of xy? secondly, what is the angle of which xy +represents the circular measure?" + +If x represent 15 deg. and y be 1/4, xy represents 3 deg. 45', whether +x - y be xy or no. But, y being 1/4, x - y is _not_ xy unless x be 1/3, +that is, unless 12x or [pi] be 4, which Mr. Smith would not admit. How +could a person who had just received such a lesson as I had given +immediately pray for further exposure, furnishing the stuff so liberally +as this? Is it possible that Mr. Smith, because he signs himself +Nauticus, means to deny his own very regular, legible, and peculiar +hand? It is enough to make the other members of the Liverpool Dock Board +cry, Mersey on the man! + +Mr. Smith says that for the future he will give up what he calls sarcasm, +and confine himself, "as far as possible," to what he calls dry reasoning +from incontrovertible premises. If I have fairly taught him that _his_ +sarcasm will not succeed, I hope he will find that his wit's end is his +logic's beginning. + +I now reply to a question I have been asked again and again since my last +Budget appeared: Why do you take so much trouble to expose such a reasoner +as Mr. Smith? I answer as a deceased friend of mine used to answer on like +occasions--A man's capacity is no measure of his power to do mischief. Mr. +Smith has untiring energy, which does something; self-evident honesty of +conviction, which does more; and a long purse, which does most of all. He +has made at least ten publications, full of figures which few readers can +criticize. A great many people are staggered to this extent, that they +imagine there must be {130} the indefinite _something_ in the mysterious +_all this_. They are brought to the point of suspicion that the +mathematicians ought not to treat "all this" with such undisguised +contempt, at least. Now I have no fear for [pi]: but I do think it possible +that general opinion might in time demand that the crowd of +circle-squarers, etc. should be admitted to the honors of opposition; and +this would be a time-tax of five per cent., one man with another, upon +those who are better employed. Mr. James Smith may be made useful, in hands +which understand how to do it, towards preventing such opinion from +growing. A speculator who expressly assumes what he wants to prove, and +argues that all which contradicts it is absurd, _because_ it cannot stand +side by side with his assumption, is a case which can be exposed to all. +And the best person to expose it is one who has lived in the past as well +as the present, who takes misthinking from points of view which none but a +student of history can occupy, and who has something of a turn for the +business. + +Whether I have any motive but public good must be referred to those who can +decide whether a missionary chooses his pursuit solely to convert the +heathen. I shall certainly be thought to have a little of the spirit of +Col. Quagg, who delighted in strapping the Grace-walking Brethren. I must +quote this myself: if I do not, some one else will, and then where am I? +The Colonel's principle is described as follows: + +"I licks ye because I kin, and because I like, and because ye'se critters +that licks is good for. Skins ye have on, and skins I'll have off; hard or +soft, wet or dry, spring or fall. Walk in grace if ye like till pumpkins is +peaches; but licked ye must be till your toe-nails drop off and your noses +bleed blue ink. And--licked--they--were--accordingly." + +I am reminded of this by the excessive confidence with which Mr. James +Smith predicted that he would treat me as Zephaniah Stockdolloger (Sam +Slick calls it _slockdollager_) treated Goliah Quagg. He has announced his +{131} intention of bringing me, with a contrite heart, and clean +shaved,--4159265... razored down to 25,--to a camp-meeting of +circle-squarers. But there is this difference: Zephaniah only wanted to +pass the Colonel's smithy in peace; Mr. James Smith sought a fight with me. +As soon as this Budget began to appear, he oiled his own strap, and +attempted to treat me as the terrible Colonel would have treated the +inoffensive brother. + +He is at liberty to try again. + + + +THE MOON HOAX. + + The Moon-hoax; or the discovery that the moon has a vast population of + human beings. By Richard Adams Locke.[226] New York, 1859, 8vo. + +This is a reprint of the hoax already mentioned. I suppose R. A. Locke is +the name assumed by M. Nicollet.[227] The publisher informs us that when +the hoax first appeared day by day in a morning paper, the circulation +increased fivefold, and the paper obtained a permanent footing. Besides +this, an edition of 60,000 was sold off in less than one month. + +The discovery was also published under the name of A. R. Grant.[228] +Sohncke's[229] _Bibliotheca Mathematica_ confounds this Grant with Prof. R. +Grant[230] of Glasgow, the author of the _History of Physical Astronomy_, +who is accordingly made to guarantee the discoveries in the moon. I hope +Adams Locke will not merge in J. C. Adams,[231] the co-discoverer of +Neptune. Sohncke gives the titles of {132} three French translations of the +Moon hoax at Paris, of one at Bordeaux, and of Italian translations at +Parma, Palermo, and Milan. + +A Correspondent, who is evidently fully master of details, which he has +given at length, informs me that the Moon hoax appeared first in the _New +York Sun_, of which R. A. Locke was editor. It so much resembled a story +then recently published by Edgar A. Poe, in a Southern paper, "Adventures +of Hans Pfaal," that some New York journals published the two side by side. +Mr. Locke, when he left the _New York Sun_, started another paper, and +discovered the manuscript of Mungo Park;[232] but this did not deceive. The +_Sun_, however, continued its career, and had a great success in an account +of a balloon voyage from England to America, in seventy-five hours, by Mr. +Monck Mason,[233] Mr. Harrison Ainsworth,[234] and others. I have no doubt +that M. Nicollet was the author of the Moon hoax,[235] written in a way +which marks the practised observatory astronomer beyond all doubt, and by +evidence seen in the most minute details. Nicollet had an eye to Europe. I +suspect that he took Poe's story, and made it a basis for his own. Mr. +Locke, it would seem, when he attempted a fabrication for himself, did not +succeed. + + + + The Earth we inhabit, its past, present, and future. By Capt. + Drayson.[236] London, 1859, 8vo. + +The earth is growing; absolutely growing larger: its diameter increases +three-quarters of an inch per mile every year. The foundations of our +buildings will give way in {133} time: the telegraph cables break, and no +cause ever assigned except ships' anchors, and such things. The book is for +those whose common sense is unwarped, who can judge evidence as well as the +ablest philosopher. The prospect is not a bad one, for population increases +so fast that a larger earth will be wanted in time, unless emigration to +the Moon can be managed, a proposal of which it much surprises me that +Bishop Wilkins has a monopoly. + + + +IMPALEMENT BY REQUEST. + +_Athenaeum_, August, 19, 1865. _Notice to Correspondents._ + +"R. W.--If you will consult the opening chapter of the Budget of Paradoxes, +you will see that the author presents only works in his own library at a +given date; and this for a purpose explained. For ourselves we have +carefully avoided allowing any writers to present themselves in our columns +on the ground that the Budget has passed them over. We gather that Mr. De +Morgan contemplates additions at a future time, perhaps in a separate and +augmented work; if so, those who complain that others of no greater claims +than themselves have been ridiculed may find themselves where they wish to +be. We have done what we can for you by forwarding your letter to Mr. De +Morgan." + +The author of "An Essay on the Constitution of the Earth," published in +1844, demanded of the _Athenaeum_, as an _act of fairness_, that a letter +from him should be published, proving that he had as much right to be +"impaled" as Capt. Drayson. He holds, on speculative grounds, what the +other claims to have proved by measurement, namely, that the earth is +growing; and he believes that in time--a good long time, not _our_ +time--the earth and other planets may grow into suns, with systems of their +own. + +This gentleman sent me a copy of his work, after the commencement of my +Budget; but I have no recollection of having received it, and I cannot find +it on the (nursery? {134} quarantine?) shelves on which I keep my +unestablished discoveries. Had I known of this work in time, (see the +Introduction) I should of course, have impaled it (heraldically) with the +other work; but the two are very different. Capt. Drayson professes to +prove his point by results of observation; and I think he does not succeed. +The author before me only speculates; and a speculator can get any +conclusion into his premises, if he will only build or hire them of shape +and size to suit. It reminds me of a statement I heard years ago, that a +score of persons, or near it, were to dine inside the skull of one of the +aboriginal animals, dear little creatures! Whereat I wondered vastly, +nothing doubting; facts being stubborn and not easy drove, as Mrs. Gamp +said. But I soon learned that the skull was not a real one, but +artificially constructed by the methods--methods which have had striking +verifications, too--which enable zoologists to go the whole hog by help of +a toe or a bit of tail. This took off the edge of the wonder: a hundred +people can dine inside an inference, if you draw it large enough. The +method might happen to fail for once: for instance, the toe-bone might have +been abnormalized by therian or saurian malady; and the possibility of such +failure, even when of small probability, is of great alleviation. The +author before me is, apparently, the sole fabricator of his own premises. +With vital force in the earth and continual creation on the part of the +original Creator, he expands our bit of a residence as desired. But, as the +Newtoness of Cookery observed, First catch your hare. When this is done, +when you _have_ a growing earth, you shall dress it with all manner of +proximate causes, and serve it up with a growing Moon for sauce, a growing +Sun, if it please you, at the other end, and growing planets for +side-dishes. Hoping this amount of impalement will be satisfactory, I go on +to something else. {135} + + + +THE HAILESEAN SYSTEM OF ASTRONOMY. + + _The Hailesean System of Astronomy._ By John Davey Hailes[237] (two + pages duodecimo, 1860). + +He offers to _take_ 100,000l. to 1,000l. that he shows the sun to be less +than seven millions of miles from the earth. The earth in the center, +revolving eastward, the sun revolving westward, so that they "meet at half +the circle distance in the 24 hours." The diameter of the circle being +9839458303, the circumference is 30911569920. + +The following written challenge was forwarded to the Council of the +Astronomical Society: it will show the "general reader"--and help him +towards earning his name--what sort of things come every now and then to +our scientific bodies. I have added punctuation: + + _Challenge._ + 1,000 to 30,000. + "Leverrier's[238] name stand placed first. Do the worthy Frenchman + justice. + By awarding him the medal in a trice. + Give Adams[239] an extra--of which neck and neck the race. + Now I challenge to meet them and the F.R.S.'s all, + For good will and _one_ thousand pounds to their _thirty_ thousand + withall, + That I produce a system, which shall measure the time, + When the Sun was vertical to Gibeon, afterward to Syene. + To meet any time in London--name your own period, + To be decided by a majority of twelve persons--a President, _odd_. + That mean, if the twelve equally divide, the President decide, + I should prefer the Bishop of London, over the meeting to preside. + JOHN DAVY HAILES." + Feb. 17, 1847." + +Mr. Hailes still issues his flying sheets. The last I have met with +(October 7, 1863) informs us that the latitude of {136} England is slowly +increasing, which is the true cause of the alteration in the variation of +the magnet. + +[Mr. Hailes continues his researches. Witness his new Hailesean system of +Astronomy, displaying Joshua's miracle-time, origin of time from science, +with Bible and Egyptian history. Rewards offered for astronomical problems. +With magnetism, etc. etc. Astronomical challenge to all the world. +Published at Cambridge, in 1865. The author agrees with Newton in one +marked point. _Errores quam minimi non sunt contemnendi_,[240] says Isaac: +meaning in figures, not in orthography. Mr. Hailes enters into the spirit, +both positive and negative, of this dictum, by giving the distance of +_Sidius_ from the center of the earth at 163,162,008 miles 10 feet 8 inches +17-28ths of an inch. Of course, he is aware that the center of _figure_ of +the earth is 17.1998 inches from the center of _gravity_. Which of the two +is he speaking of?] + + + + The Divine Mystery of Life. London [1861], 18mo. (pp.32). + +The author has added one class to zoology, which is printed in capitals, as +derived from _zoe_, life, not from _zoon_, animal. That class is of +_Incorporealia_, order I., _Infinitum_, of one genus without plurality, +_Deus_: order II., _Finita_, angels good and evil. The rest is all about a +triune system, with a diagram. The author is not aware that [Greek: zoon] +is not _animal_, but _living being_. Aristotle had classed gods under +[Greek: zoa], and has been called to account for it by moderns who have +taken the word to mean _animal_. + + + +A CHANCE FOR INVENTORS. + + Explication du Zodiaque de Denderah, des Pyramides, et de Genese. Par + le Capitaine au longcours Justin Roblin.[241] Caen, 1861. 8vo. + +{137} + +Capt. Roblin, having discovered the sites of gold and diamond mines by help +of the zodiac of Denderah, offered half to the shareholders of a company +which he proposed to form. One of our journals, by help of the zodiac of +Esne, offered, at five francs a head, to tell the shareholders the exact +amount of gold and diamonds which each would get, and to make up the amount +predicted to those who got less. There are moods of the market in England +in which this company could have been formed: so we must not laugh at our +neighbors. + + + +JOHANNES VON GUMPACH. + + A million's worth of property, and five hundred lives annually lost at + sea by the Theory of Gravitation. A letter on the true figure of the + earth, addressed to the Astronomer Royal, by Johannes von Gumpach.[242] + London, 1861, 8vo. (pp. 54). + + The true figure and dimensions of the earth, in a letter addressed to + the Astronomer Royal. By Joh. von Gumpach. 2nd ed. entirely recast. + London, 1862, 8vo. (pp. 266). + + Two issues of a letter published with two different title-pages, one + addressed to the Secretary of the Royal Society, the other to the + Secretary of the Royal Astronomical Society. It would seem that the + same letter is also issued with two other titles, addressed to the + British Association and the Royal Geographical Society. By Joh. von + Gumpach. London, 1862, 8vo. + + Baby-Worlds. An essay on the nascent members of our solar household. By + Joh. von Gumpach. London, 1863, 8vo. + +The earth, it appears, instead of being flattened, is elongated at the +poles: by ignorance of which the loss above mentioned occurs yearly. There +is, or is to be, a substitute for attraction and an "application hitherto +neglected, of a {138} recognized law of optics to the astronomical theory, +showing the true orbits of the heavenly bodies to be perfectly circular, +and their orbital motions to be perfectly uniform." all irregularities +being, I suppose, optical delusions. Mr. Von Gumpach is a learned man; what +else, time must show. + + + +SLANDER PARADOXES. + + Perpetuum Mobile: or Search for self-motive Power. By Henry + Dircks.[243] London, 1861, 8vo. + +A useful collection on the history of the attempts at perpetual motion, +that is, at obtaining the consequences of power without any power to +produce them. September 7, 1863, a correspondent of the _Times_ gave an +anecdote of George Stephenson,[244] which he obtained from Robert +Stephenson.[245] A perpetual motionist wanted to explain his method; to +which George replied--"Sir! I shall believe it when I see you take yourself +up by the waistband, and carry yourself about the room." Never was the +problem better stated. + +There is a paradox of which I ought to give a specimen, I mean the +_slander-paradox_; the case of a person who takes it into his head, upon +evidence furnished entirely by the workings of his own thoughts, that some +other person has committed a foul act of which the world at large would no +more suppose him guilty than they would suppose that the earth is a flat +bordered by ice. If I were to determine on giving cases in which the +self-deluded person imagines {139} a conspiracy against _himself_, there +would be no end of choices. Many of the grosser cases are found at last to +be accompanied by mental disorder, and it is difficult to avoid referring +the whole class to something different from simple misuse of the reasoning +power. The first instance is one which puts in a strong light the state of +things in which we live, brought about by our glorious freedom of thought, +speech, and writing. The Government treated it with neglect, the press with +silent contempt, and I will answer for it many of my readers now hear of it +for the first time, when it comes to be enrolled among circle-squarers and +earth-stoppers, where, as the old philosopher said, it will not gravitate, +being _in proprio loco_.[246] + +1862. On new year's day, 1862, when the nation was in the full tide of +sympathy with the Queen, and regret for its own loss, a paper called the +_Free Press_ published a number devoted to the consideration of the causes +of the death of the Prince Consort. It is so rambling and inconsecutive +that it takes more than one reading to understand it. It is against the +_Times_ newspaper. First, the following insinuation: + +"To the legal mind, the part of [the part taken by] the _Times_ will +present a _prima facie_ case of the gravest nature, in the evident +fore-knowledge of the event, and the preparation to turn it to account when +it should have occurred. The article printed on Saturday must have been +written on Friday. That article could not have appeared had the Prince been +intended to live." + +Next, it is affirmed that the _Times_ intended to convey the idea that the +Prince had been poisoned. + +"Up to this point we are merely dealing with words which the _Times_ +publishes, and these can leave not a shadow of doubt that there is an +intention to promulgate the idea that Prince Albert had been poisoned." + +The article then goes on with a strange olio of {140} insinuations to the +effect that the Prince was the obstacle to Russian intrigue, and that if he +should have been poisoned,--which the writer strongly hints may have been +the case,--some Minister under the influence of Russia must have done it. +Enough for this record. _Un sot trouve toujours un plus sot qui +l'admire_:[247] who can he be in this case? + + + +THE NEPTUNE CONTROVERSY. + +1846. At the end of this year arose the celebrated controversy relative to +the discovery of Neptune. Those who know it are well aware that Mr. +Adams's[248] now undoubted right to rank with Le Verrier[249] was made sure +at the very outset by the manner in which Mr. Airy,[250] the Astronomer +Royal, came forward to state what had taken place between himself and Mr. +Adams. Those who know all the story about Mr. Airy being arrested in his +progress by the neglect of Mr. Adams to answer a letter, with all the +imputations which might have been thrown upon himself for laxity in the +matter, know also that Mr. Airy's conduct exhibited moral courage, honest +feeling, and willingness to sacrifice himself, if need were, to the +attainment of the ends of private justice, and the establishment of a +national claim. A writer in a magazine, in a long and elaborate article, +argued the supposition--put in every way except downright assertion, after +the fashion of such things--that Mr. Airy had communicated Mr. Adams's +results to M. Le Verrier, with intention that they should be used. His +presumption as to motive is that, had Mr. Adams been recognized, "then the +discovery must have been indisputably an _Englishman's_, and that +Englishman not the Astronomer Royal." Mr. Adams's conclusions were +"retouched in France, and sent {141} over the year after." The proof given +is that it cannot be "imagined" otherwise. + +"Can it then be imagined that the Astronomer Royal received such results +from Mr. Adams, supported as they were by Professor Challis's[251] valuable +testimony as to their probable accuracy, and did not bring the French +astronomer acquainted with them, especially as he was aware that his friend +was engaged in matters bearing directly upon these results?" + +The whole argument the author styles "evidence which I consider it +difficult to refute." He ends by calling upon certain persons, of whom I am +one, to "see ample justice done." This is the duty of every one, according +to his opportunities. So when the reputed author--the article being +anonymous--was, in 1849, proposed as a Fellow of the Astronomical Society, +I joined--if I remember right, I originated--an opposition to his election, +until either the authorship should be denied, or a proper retraction made. +The friends of the author neither denied the first, nor produced the +second: and they judged it prudent to withdraw the proposal. Had I heard of +any subsequent repentance, I would have taken some other instance, instead +of this: should I yet hear of such a thing, I will take care to notice it +in the continuation of this list, which I confidently expect, life and +health permitting, to be able to make in a few years. This much may be +said, that the author, in a lecture on the subject, given in 1849, and +published with his name, did _not_ repeat the charge. + +[The libel was published in the _Mechanics' Magazine_,[252] (vol. for 1846, +pp. 604-615): and the editor supported it as follows, (vol. for 1847, p. +476). In answer to Mr. Sheepshanks's charitable hope that he had been +hoaxed, {142} he says: "Mr. Sheepshanks cannot certainly have read the +article referred to.... Severe and inculpatory it is--unjust some may deem +it (though we ourselves are out of the number.)... A 'hoax' forsooth! May +we be often the dupes of such hoaxes!" He then goes on to describe the +article as directed against the Astronomer Royal's alleged neglect to give +Mr. Adams that "encouragement and protection" which was his due, and _does +not hint one word_ about the article containing the charge of having +secretly and fraudulently transmitted news of Mr. Adams's researches to +France, that an Englishman might not have the honor of the discovery. Mr. +Sheepshanks having called this a "deliberate calumny," without a particle +of proof or probability to support it, the editor says "what the reverend +gentleman means by this, we are at a loss to understand." He then proceeds +_not_ to remember. I repeat here, what I have said elsewhere, that the +management of the journal has changed hands; but from 1846 to 1856, it had +the collar of S.S. (scientific slander). The prayer for more such things +was answered (See p. 349).] + + + +JAMES IVORY.[253] + +I have said that those who are possessed with the idea of conspiracy +against themselves are apt to imagine both conspirators and their bad +motives and actions. A person who should take up the idea of combination +against himself without feeling ill-will and originating accusations would +be indeed a paradox. But such a paradox has existed. It is very well known, +both in and beyond the scientific world, that the late James Ivory was +subject to the {143} impression of which I am speaking; and the diaries and +other sources of anecdote of our day will certainly, sooner or later, make +it a part of his biography. The consequence will be that to his memory will +be attached the unfavorable impression which the usual conduct of such +persons creates; unless it should happen that some one who knows the real +state of the case puts the two sides of it properly together. Ivory was of +that note in the scientific world which may be guessed from Laplace's +description of him as the first geometer in Britain and one of the first in +Europe. Being in possession of accurate knowledge of his peculiarity in +more cases than one; and in one case under his own hand: and having been +able to make full inquiry about him, especially from my friend the late +Thomas Galloway[254]--who came after him at Sandhurst--one of the few +persons with whom he was intimate:--I have decided, after full +deliberation, to forestall the future biographies. + +That Ivory was haunted by the fear of which I have spoken, to the fullest +extent, came to my own public and official knowledge, as Secretary of the +Astronomical Society. It was the duty of Mr. Epps,[255] the Assistant +Secretary, at the time when Francis Baily[256] first announced his +discovery of the Flamsteed Papers, to report to me that Mr. Ivory had +called at the Society's apartments to inquire into the contents of those +papers, and to express his hope that Mr. Baily was not attacking living +persons under the names of Newton and Flamsteed.[257] Mr. Galloway, to whom +I communicated this, immediately went to Mr. Ivory, and succeeded, after +some explanation, in setting him right. This is but one of many instances +in which a man of thoroughly sound judgment in every other respect seemed +to be under a complete chain of delusions about the conduct of {144} others +to himself. But the paradox is this:--I never could learn that Ivory, +passing his life under the impression that secret and unprovoked enemies +were at work upon his character, ever originated a charge, imputed a bad +motive, or allowed himself an uncourteous expression. Some letters of his, +now in my possession, referring to a private matter, are, except in the +main impression on which they proceed, unobjectionable in every point: they +might have been written by a cautious friend, whose object was, if +possible, to prevent a difference from becoming a duel without compromising +his principal's rights or character. Knowing that in some quarters the +knowledge of Ivory's peculiarity is more or less connected with a notion +that the usual consequences followed, I think the preceding statement due +to his memory. + + + +THREE CLASSES OF JOURNALS. + +In such a record as the present, which mixes up the grossest speculative +absurdities with every degree of what is better, an instance of another +kind may find an appropriate place. The faults of journalism, when merely +exposed by other journalism pass by and are no more regarded. A distinct +account of an undeniable meanness, recorded in a work of amusement and +reference both, may have its use: such a thing may act as a warning. An +editor who is going to indulge his private grudge may be prevented from +counting upon oblivion as a matter of certainty. + +There are three kinds of journals, with reference to the mode of entrance +of contributors. First, as a thing which has been, but which now hardly +exists, there is the journal in which the editor receives a fixed sum to +_find the matter_. In such a journal, every article which the editor can +get a friend to give him is so much in his own pocket, which has a great +tendency to lower the character of the articles; but I am not concerned +with this point. Secondly, there is the journal which is supported by +voluntary contributions of {145} matter, the editor selecting. Thirdly, +there is the journal in which the contributor is paid by the proprietors in +a manner with which the literary editor has nothing to do. + +The third class is the safe class, as its editors know: and, as a usual +rule, they refuse unpaid contributions of the editorial cast. It is said +that when Canning[258] declined a cheque forwarded for an article in the +_Quarterly_, John Murray[259] sent it back with a blunt threat that if he +did not take his money he could never be admitted again. The great +publisher told him that if men like himself in position worked for nothing, +all the men like himself in talent who could not afford it would not work +for the _Quarterly_. If the above did not happen between Canning and +Murray, it _must have happened_ between some other two. Now journals of the +second class--and of the first, if such there be--have a fault to which +they alone are very liable, to say nothing of the editorial function (see +the paper at the beginning, p. 11 et seq.), being very much cramped, a sort +of gratitude towards effective contributors leads the journal to help their +personal likes and dislikes, and to sympathize with them. Moreover, this +sort of journal is more accessible than others to articles conveying +personal imputation: and when these provoke discussion, the journal is apt +to take the part of the assailant to whom it lent itself in the first +instance. + + + +THE MECHANICS' MAGAZINE. + +Among the journals which went all lengths with contributors whom they +valued, was the _Mechanics' Magazine_[260] in the period 1846-56. I cannot +say that matters have not mended in the last ten years: and I draw some +{146} presumption that they have mended from my not having heard, since +1856, of anything resembling former proceedings. And on actual inquiry, +made since the last sentence was written, I find that the property has +changed hands, the editor is no longer the same, and the management is of a +different stamp. This journal is chiefly supported by voluntary articles: +and it is the journal in which, as above noted, the ridiculous charge +against the Astronomer Royal was made in 1849. The following instance of +attempt at revenge is so amusing that I select it as the instance of the +defect which I intend to illustrate; for its puerility brings out in better +relief the points which are not so easily seen in more adult attempts. + +The _Mechanics' Magazine_, which by its connection with engineering, etc., +had always taken somewhat of a mathematical character, began, a little +before 1846, to have more to do with abstract science. Observing this, I +began to send short communications, which were always thankfully received, +inserted, and well spoken of. Any one who looks for my name in that journal +in 1846-49, will see nothing but the most respectful and even laudatory +mention. In May 1849 occurred the affair at the Astronomical Society, and +my share in forcing the withdrawal of the name of the alleged contributor +to the journal. In February 1850 occurred the opportunity of payment. The +_Companion to the Almanac_[261] had to be noticed, in which, as then usual, +was an article signed with my name. I shall give the review of this article +entire, as a sample of a certain style, as well as an illustration of my +point. The reader will observe that my name is not mentioned. This would +not have done; the readers of the Magazine would have stared to see a name +of not infrequent occurrence in previous years all of a sudden fallen from +the heaven of respect into the pit of contempt, like Lucifer, son of the +morning. But before {147} giving the review, I shall observe that Mr. +Adams, in whose _favor_ the attack on the Astronomer Royal was made, did +not appreciate the favor; and of course did not come forward to shield his +champion. This gave deadly offence, as appear from the following passage, +(February 16, 1850): + +"It was our intention to enter into a comparison of the contents of our +Nautical Almanack with those of its rival, the _Connaissance des Temps_; +but we shall defer it for the present. The Nautical Almanack for 1851 will +contain Mr. Adams's paper 'On the Perturbation of Uranus'; and when it +comes, in due course, before the public, we are quite sure that that +gentleman will expect that we shall again enter upon the subject with +peculiar delight. Whilst we have a thorough loathing for mean, cowardly, +crawlers--we have an especial pleasure in maintaining the claims of men who +are truly grateful as well as highly talented: Mr. Adams, therefore, will +find that he cannot be disappointed--and the occasion will afford us an +opportunity for making the comparison to which we have adverted." + +This passage illustrates what I have said on the editorial function (Vol. +I, p. 15). What precedes and follows has some criticism on the Government, +the Astronomer Royal, etc., but reserved in allusion, oblique in sarcasm, +and not fiercely uncourteous. The coarseness of the passage I have quoted +shows editorial insertion, which is also shown by its blunder. The inserter +is waiting for the Almanac of 1851 that he may review Mr. Adams's paper, +which is to be contained in it. His own contributor, only two sentences +before the insertion, had said, "The Nautical Almanac, we believe, is +published three or four years in advance." In fact, the Almanac for +1851--with Mr. Adams's paper at the end--was published at the end of 1847 +or very beginning of 1848; it had therefore been more than two years before +the public when the passage quoted was written. And probably every person +in the country who was fit to review Mr. Adams's {148} paper--and most of +those who were fit to read it--knew that it had been widely circulated, in +revise, at the end of 1846: my copy has written on it, "2d revise, December +27, 1846, at noon," in the handwriting of the Superintendent of the +Almanac; and I know that there was an extensive issue of these revises, +brought out by the Le-Verrier-and-Adams discussion. I now give the review +of myself, (February 23, 1850): + +"_The British Almanack and Companion._ + +"The Companion to this Almanack, for some years after its first +publication, annually contained scientific articles by Sir J. Lubbock[262] +and others of a high order and great interest; we have now, however, closed +the publication as a scientific one in remembrance of what it was, and not +in consequence of what it is. Its list of contributors on science, has +grown 'small by degrees and beautifully less,' until it has dwindled down +to one--'a last rose of summer left withering alone.' The one contributor +has contributed one paper 'On Ancient and Modern Usage in Reckoning.' + +"The learned critic's _chef d'oeuvre_, is considered, by competent judges, +to be an Essay on _Old Almanacks_ printed a few years ago in this annual, +and supposed to be written with the view of surpassing a profound memoir on +the same subject by James O. Halliwell,[263] Esq., F.R. and A.S.S., but the +tremendous effort which the learned writer then made to excel many titled +competitors for honors in the antique line appears to have had a sad effect +upon his mental powers--at any rate, his efforts have since yearly become +duller and duller; happily, at last, we should suppose, 'the ancient {149} +and modern usage in reckoning' indicates the lowest point to which the _vis +inertia_ of the learned writer's peculiar genius can force him. + +"We will give a few extracts from the article. + +"The learned author says, 'Those who are accustomed to settle the meaning +of ancient phrases by self-examination will find some _strange_ conclusions +arrived at by us.' The writer never wrote a more correct sentence--it +admits of no kind of dispute. + +"'Language and counting,' says the learned author, 'both came before the +logical discussion of either. It is not allowable to argue that something +is or was, because it ought to be or ought to have been. That two negatives +make an affirmative, ought to be; if _no_ man have done _nothing_, the man +who has done nothing does not exist, and _every_ man has done _something_. +But in Greek, and in uneducated English, it is unquestionable that 'no man +has done nothing' is only an emphatic way of saying that no man has done +_anything_; and it would be absurd to reason that it could not have been +so, because it should not.'--p. 5. + +"'But there _is_ another difference between old and new times, yet more +remarkable, for we have _nothing_ of it now: whereas in things indivisible +we count with our fathers, and should say in buying an acre of land, that +the result has no parts, and that the purchaser, till he owns all the +ground, owns none, the change of possession being instantaneous. This +second difference lies in the habit of considering nothing, nought, zero, +cipher, or whatever it may be called, to be at the beginning of the scale +of numbers. Count four days from Monday: we should now say Tuesday, +Wednesday, Thursday, Friday; formerly, it would have been Monday, Tuesday, +Wednesday, Thursday. Had we asked, what at that rate is the first day from +Monday, all would have stared at a phrase they had never heard. Those who +were capable of extending language would have said, Why it must be Monday +itself: the rest would have said, there can {150} be no first day from +Monday, for the day after is Tuesday, which must be the second day: Monday, +one; Tuesday, two,'--p. 10. + +"We assure our readers that the whole article is equally lucid, and its +logic alike formal. + +"There are some exceedingly valuable footnotes; we give one of the most +interesting, taken from the learned Mr. Halliwell's profound book on +Nursery Rhymes[264]--a celebrated production, for which it is supposed the +author was made F.R.S. + + "'_One's nine_, + Two's some, + Three's a many, + Four's a penny, + Five's a little hundred.' + +'The last line refers to five score, the so-called hundred being more +usually six score. The first line, looked at etymologically, is _one is not +one_, and the change of thought by which _nine_, the decimal of _one_, aims +to be associated with the decimal of _plurality_ is curious:'--Very. + +"This valuable and profound essay will very probably be transferred to the +next edition of the learned Mr. Halliwell's rare work, of kindred worth, +entitled 'RARA MATHEMATICA,' it will then be deservedly handed down to +posterity as a covering for cheap trunks--a most appropriate archive for +such a treasure." + + + +In December, 1846, the _Mechanics' Magazine_ published a libel on Airy in +the matter of the discovery of Neptune. In May, 1849, one * * * was to have +been brought forward for election at the Astronomical Society, and was +opposed by me and others, on the ground that he was the probable author of +this libel, and that he would not, perhaps could {151} not, deny it. [N.B. +I no more doubt that he was the author then I doubt that I am the author of +this sentence.][265] + +Accordingly, * * * was withdrawn, and a discussion took place, for which +see the _Athenaeum_, No. 1126, May 26, 1849, p. 544. The _Mechanics' +Magazine_ was very sore, but up to this day has never ventured beyond an +attack on Airy, private whisperings against Adams--(see _ante_, p. +147),--and the above against myself. In due time, I doubt not my name will +appear as one of the _ames damnees_[266] of the _Mechanics' Magazine_.[267] + + + +T. S. DAVIES ON EUCLID. + +First, as to Mr. Halliwell. The late Thomas Stephens Davies,[268] excellent +in geometry, and most learned in its history, was also a good hand at +enmity, though not implacable. He and Mr. Halliwell, who had long before +been very much one, were, at this date, very much two. I do not think T. S. +Davies wrote this article; and I think that by giving my reasons I shall do +service to his memory. It must have been written at the beginning of +February; and within three days of that time T. S. Davies was making over +to me, by his own free act, to be kept until claimed by the relatives, what +all who knew even his writings knew that he considered as the most precious +deposit he had ever had in his keeping--Horner's[269] papers. His letter +announcing the transmission is dated February 2, 1850. This is a strong +point; but there is another quite as strong. Euclid and {152} his writings +were matters on which T. S. Davies knew neither fear nor favor: he could +not have written lightly about a man who stood high with him as a judge of +Euclid. Now in this very letter of Feb. 2, there is a sentence which I +highly value, because, as aforesaid, it is on a point on which he would +never have yielded anything, to which he had paid life-long attention, and +on which he had the bias of having long stood alone. In fact, knowing--and +what I shall quote confirms me,--that in the matter of Euclid his hand was +against every man, I expected, when I sent him a copy of my 22-column +article, "Eucleides" in Smith's _Dictionary_,[270] to have received back a +criticism, that would have blown me out of the water: and I thought it not +unlikely that a man so well up in the subject might have made me feel +demolished on some points. Instead of this, I got the following: "Although +on one or two minor points I do not quite accord with your views, yet as a +whole and without regard to any minor points, I think you are the first who +has succeeded in a delineation of Euclid as a geometer." All this duly +considered, it is utterly incredible that T. S. Davies should have written +the review in question. And yet Mr. Halliwell is treated just as T. S. +Davies would have treated him, as to tone and spirit. The inference in my +mind is that we have here a marked instance of the joining of hatreds which +takes place in journals supported by voluntary contributions of matter. +Should anything ever have revived this article--and no one ever knows what +might have been fished up from the forgotten mass of journals--the +treatment of Mr. Halliwell would certainly have thrown a suspicion on T. S. +Davies, a large and regular contributor to the Magazine. It is good service +to his memory to point out what makes it incredible that he should have +written so unworthy an article. + +The fault is this. There are four extracts: the first {153} three are +perfectly well printed. The printing of the _Mechanics' Magazine_ was very +good. I was always exceedingly satisfied with the manner in which my +articles appeared, without my seeing proof. Most likely these extracts were +printed from my printed paper; if not the extractor was a good copier. I +know this by a test which has often served me. I use the subjunctive--"if +no man _have_ done nothing," an ordinary transcriber, narrating a quotation +almost always lets his own habit write _has_. The fourth extract has three +alterations, all tending to make me ridiculous. _None_ is altered, in two +places, into _nine_, _denial_ into _decimal_, and _comes_ into _aims_; so +that "none, the denial of one, comes to be associated with the denial of +plurality," reads as "nine, the decimal of one, aims to be associated with +the decimal of plurality." This is intentional; had it been a compositor's +reading of bad handwriting, these would not have been the only mistakes; to +say nothing of the corrector of the press. And both the compositor and +reader would have guessed, from the first line being translated into "one +is not one," that it must have been "one's none," not "one's nine." But it +was not intended that the gem should be recovered from the unfathomed cave, +and set in a Budget of Paradoxes. + +We have had plenty of slander-paradox. I now give a halfpennyworth of bread +to all this sack, an instance of the paradox of benevolence, in which an +individual runs counter to all the ideas of his time, and sees his way into +the next century. At Amiens, at the end of the last century, an institution +was endowed by a M. de Morgan, to whom I hope I am of kin, but I cannot +trace it; the name is common at Amiens. It was the first of the kind I ever +heard of. It is a Salle d'Asyle for children, who are taught and washed and +taken care of during the hours in which their parents must be at work. The +founder was a large wholesale grocer and colonial importer, who was made a +Baron by Napoleon I for his commercial success and his charities. {154} + + + +JAS. SMITH AGAIN. + +1862. Mr. Smith replies to me, still signing himself Nauticus: I give an +extract: + +"By hypothesis [what, again!] let 14 deg. 24' be the chord of an arc of +15 deg. [but I wont, says 14 deg. 24'], and consequently equal to a side +of a regular polygon of 24 sides inscribed in the circle. Then 4 times +14 deg. 24' = 57 deg. 36' = the radius of the circle ..." + +That is, four times the chord of an arc is the chord of four times the arc: +and the sum of four sides of a certain pentagon is equal to the fifth. This +is the capital of the column, the crown of the arch, the apex of the +pyramid, the watershed of the elevation. Oh! J. S.! J. S.! groans +Geometry--_Summum J. S. summa injuria_![271] The other J. S., Joseph +Scaliger,[272] as already mentioned, had his own way of denying that a +straight line is always the shortest distance between two points. A +parallel might be instituted, but not in half a column. And J. S. the +_second_ has been so tightly handled that he may now be dismissed, with an +inscription for his circular shield, obtained by changing _Lexica contexat_ +into _Circus quadrandus_ in an epigram of J. S. the _first_: + + "Si quem dura manet sententia judicis, olim + Damnatum aerumnis suppliciisque caput, + Hunc neque fabrili lassent ergastula massa, + Nec rigidas vexent fossa metalla manus. + Circus quadrandus: nam--caetera quid moror?--omnes + Poenarum facies hic labor unus habet."[273] + +{155} + +I had written as far as _damnatum_ when in came the letter of Nauticus as a +printed slip, with a request that I would consider the slip as a 'revised +copy.' Not a word of alteration in the part I have quoted! And in the +evening came a letter desiring that I would alter a gross error; but not +the one above: this is revising without revision! If there were cyclometers +enough of this stamp, they would, as cultivation progresses--and really, +with John Stuart Mill in for Westminster, it seems on the move, even +though, as I learn while correcting the proof, Gladstone be out from +Oxford; for Oxford is no worse than in 1829, while Westminster is far above +what she ever has been: election time excuses even such a parenthesis as +this--be engaged to amuse those who can afford it with paralogism at their +meals, after the manner of the other jokers who wore the caps and bells. +The rich would then order their dinners with _panem et Circenses_,--up with +the victuals and the circle-games--as the poor did in the days of old. + +Mr. Smith is determined that half a column shall not do. Not a day without +something from him: letter, printed proof, pamphlet. In what is the last at +this moment of writing he tells me that part of the title of a work of his +will be "Professor De Morgan in the pillory without hope of escape." And +where will he be himself? This I detected by an effort of reasoning which I +never could have made except by following in his steps. In all matters +connected with [pi] the letters l and g are closely related: this appears +in the well-known formula for the time of oscillation [pi] [sqrt](l : g). +Hence g may be written for l, but only once: do it twice, and you require +the time to be [pi] [sqrt](l^2 : g^2). This may be reinforced by observing +that if as a datum, or if you dislike that word, by hypothesis, the first l +be a g, it is absurd that it should be an l. Write g for the first l, and +we have _un fait accompli_. I shall be in pillory; and overhead, in a +cloud, will sit Mr. James Smith on one stick laid across two others, under +a nimbus of 3-1/8 diameters to {156} the circumference--in [pi]-glory. Oh +for a drawing of this scene! Mr. De Morgan presents his compliments to Mr. +James Smith, and requests the honor of an exchange of photographs. + +_July 26._--Another printed letter.--Mr. James Smith begs for a distinct +answer to the following plain question: "Have I not in this communication +brought under your notice _truths_ that were never before dreamed of in +your geometrical and mathematical philosophy?" To which, he having taken +the precaution to print the word _truths_ in italics, I can conscientiously +answer, Yes, you have. And now I shall take no more notice of these +_truths_, until I receive something which surpasses all that has yet been +done. + + + +A FEW SMALL PARADOXERS. + + The Circle secerned from the Square; and its area gauged in terms of a + triangle common to both. By Wm. Houlston,[274] Esq. London and Jersey, + 1862, 4to. + +Mr. Houlston squares at about four poetical quotations in a page, and +brings out [pi] = 3.14213.... His frontispiece is a variegated diagram, +having parts designated Inigo and Outigo. All which relieves the subject, +but does not remove the error. + + + + Considerations respecting the figure of the Earth.... By C. F. + Bakewell.[275] London, 1862, 8vo. + +Newton and others think that in a revolving sphere the {157} loose surface +matter will tend to the equator: Mr. Bakewell thinks it will tend to the +poles. + + + + On eccentric and centric force: a new theory of projection. By H. F. A. + Pratt, M.D.[276] London, 1862, 8vo. + +Dr. Pratt not only upsets Newton, but cuts away the very ground he stands +on: for he destroys the first law of motion, and will not have the natural +tendency of matter in motion to be rectilinear. This, as we have seen, was +John Walsh's[277] notion. In a more recent work "On Orbital Motion," +London, 1863, 8vo., Dr. Pratt insists on another of Walsh's notions, +namely, that the precession of the equinoxes is caused by the motion of the +solar system round a distant central sun. In this last work the author +refers to a few notes, which completely destroy the theory of gravitation +in terms "perfectly intelligible as well to the unlearned as to the +learned": to me they are quite unintelligible, which rather tends to +confirm a notion I have long had, that I am neither one thing nor the +other. There is an ambiguity of phrase which delights a writer on logic, +always on the look-out for specimens of _homonymia_ or _aequivocatio_. The +author, as a physician, is accustomed to "appeal from mere formulae": +accordingly, he sets at nought the whole of the mathematics, which he does +not understand. This equivocation between the formula of the physician and +that of the mathematician is as good, though not so perceptible to the +world at large, as that made by Mr. Briggs's friend in _Punch's_ picture, +which I cut out to paste into my Logic. Mr. Briggs wrote for a couple of +_bruisers_, meaning to prepare oats for his horses: his friend sent him the +Whitechapel Chicken and the Bayswater Slasher, with the gloves, all ready. + +{158} + + + + On matter and ether, and the secret laws of physical change. By T. R. + Birks, M.A.[278] Cambridge, 1862, 8vo. + +Bold efforts are made at molecular theories, and the one before me is ably +aimed. When the Newton of this subject shall be seated in his place, books +like the present will be sharply looked into, to see what amount of +anticipation they have made. + + + +DR. THORN AND MR. BIDEN. + + The history of the 'thorn tree and bush' from the earliest to the + present time: in which is clearly and plainly shown the descent of her + most gracious Majesty and her Anglo-Saxon people from the half tribe of + Ephraim, and possibly from the half tribe of Manasseh; and consequently + her right and title to possess, at the present moment, for herself and + for them, a share or shares of the desolate cities and places in the + land of their forefathers! By Theta, M.D.[279] (Private circulation.) + London, 1862, 8vo. + +This is much about _Thorn_, and its connected words, Thor, Thoth, Theta, +etc. It is a very mysterious vagary. The author of it is the person whom I +have described elsewhere as having for his device the round man in the +three-cornered hole, the writer of the little heap of satirical anonymous +letters about the Beast and 666. By accident I discovered the writer: so +that if there be any more thorns to crackle under the pot, they need not be +anonymous. + +Nor will they be anonymous. Since I wrote the above, I have received +_onymous_ letters, as _ominous_ as the rest. The writer, William Thorn, +M.D., is obliged to reveal {159} himself, since it is his object to prove +that he himself is one 666. By using W for double Vau (or 12) he cooks the +number out of his own name. But he says it is the number not of a beast but +of a man, and adds, "Thereby hangs a tale!" which sounds like +contradiction. He informs me that he will talk the matter over with me: but +I shall certainly have nothing to say to a gentleman of his number; it is +best to keep on the safe side. + +In one letter I am informed that not a line should I have had, but for my +"sneer at 666," which, therefore, I am well pleased to have given. I am +also told that my name means the "'garden of death,' that place in which +the tree of knowledge was plucked, and so you are like your name 'dead' to +the fact that you are an Israelite, like those in Ezekiel 37 ch." Some +hints are given that I shall not fare well in the next world, which any one +who reads the chapter in Ezekiel will see is quite against his comparison. +The reader must not imagine that my prognosticator means _Morgan_ to be a +corruption of _Mortjardin_; he proves his point by Hebrew: but any +philologist would tell him the true derivation of the name, and how +_Glamorgan_ came to get it. It will be of much comfort to those young men +who have not got through to know that the tree of knowledge itself was once +in the same case. And so good bye to 666 for the present, and the +assumption that the enigma is to be solved by the united numeral forces of +the letters of a word. + +It is worthy of note that, as soon as my Budget commenced, two guardian +spirits started up, fellow men as to the flesh, both totally unknown to me: +they have stuck to me from first to last. James Smith, Esq., finally +Nauticus, watches over my character in this world, and would fain preserve +me from ignorance, folly, and dishonesty, by inclosing me in a magic circle +of 3-1/8 diameters in circumference. The round man in the three-cornered +hole, finally William Thorn, M.D., takes charge of my future destiny, {160} +and tries to bring me to the truth by unfolding a score of meanings--all +right--of 666. He hints that I, and my wife, are servants of Satan: at +least he desires us both to remember that we cannot serve God and Satan; +and he can hardly mean that we are serving the first, and that he would +have us serve the second. As becomes an interpreter of the Apocalypse, he +uses seven different seals; but not more than one to one letter. If his +seals be all signet-rings, he must be what Aristophanes calls a +sphragidonychargocometical fellow. But--and many thanks to him for the +same--though an M.D., he has not sent me a single vial. And so much for my +tree of secular knowledge and my tree of spiritual life: I dismiss them +with thanks from myself and thanks from my reader. The dual of the +Pythagorean system was Isis and Diana; of the Jewish law, Moses and Aaron; +and of the City of London, Gog and Magog; of the Paradoxiad, James Smith, +Esq., and William Thorn, M.D. + +_September, 1866._ Mr. James Biden[280] has favored me with some of his +publications. He is a rival of Dr. Thorn; a prophet by name-right and +crest-right. He is of royal descent through the De Biduns. He is the +_watchman_ of Ezekiel: God has told him so. He is the author of _The True +Church_, a phrase which seems to have a book-meaning and a mission-meaning. +He shall speak for himself: + +"A crest of the Bidens has significance. It is a lion rampant between +wings--wings in Scripture denote the flight of time. Thus the beasts or +living creatures of the Revelations have each six wings, intimating a +condition of mankind up to and towards the close of six thousand years of +Bible teaching. The two wings of the crest would thus intimate power +towards the expiration of 2000 years, as time is marked in the history of +Great Britain. + +{161} + +"In a recent publication, _The Pestilence, Why Inflicted_, are given many +reasons why the writer thinks himself to be the appointed watchman foretold +by Ezekiel, chapters iii. and xxxiii. Among the reasons are many prophecies +fulfilled in him. Of these it is now needful to note two as bearing +especially on the subject of the reign of Darius. + +"1.--In Daniel it is said, 'Darius the Median took the kingdom, being about +threescore and two years old.'--Daniel v. 31. + +"When 'Belshazzar' the king of the Chaldeans is found wanting, Darius takes +the kingdom. It is not given him by the popular voice; he asserts his +right, and this is not denied. He takes it when about sixty-two years of +age. The language of Daniel is prophetic, and Darius has in another an +antitype. The writer was born July 18th, 1803; and the claim was asserted +at the close of 1865, when he was about sixty-two years of age. + +"The claims which have been asserted demand a settled faith, and which +could only be reached through a long course of divine teaching." + +When I was a little boy at school, one of my school-fellows took it into +his head to set up a lottery of marbles: the thing took, and he made a +stony profit. Soon, one after another, every boy had his lottery, and it +was, "I won't put into yours unless you put into mine." This knocked up the +scheme. It will be the same with the prophets. Dr. Thorn, Mr. Biden, Mrs. +Cottle,[281] etc. will grow imitators, until we are all pointed out in the +Bible: but A will not admit B's claim unless B admits his. For myself, as +elsewhere shown, I am the first Beast in the Revelations. + +Every contraband prophet gets a few followers: it is a great point to make +these sequacious people into Buridan's asses, which they will become when +prophets are so numerous that there is no choosing. + +{162} + + + +SIR G. C. LEWIS. + + An historical survey of the Astronomy of the Ancients. By the Rt. Hon. + Sir G. C. Lewis.[282] 8vo. 1862. + +There are few men of our day whom I admire more than the late Sir G. Lewis: +he was honest, earnest, sagacious, learned, and industrious. He probably +sacrificed his life to his conjunction of literature and politics: and he +stood high as a minister of state in addition to his character as a man of +letters. The work above named is of great value, and will be read for its +intrinsic merit, consulted for its crowd of valuable references, quoted for +its aid to one side of many a discussion, and opposed for its force against +the other. Its author was also a wit and a satirist. I know of three +classical satires of our day which are inimitable imitations: Mr. +Malden's[283] _Pragmatized Legends_, Mr. Mansel's[284] _Phrontisterion_, +and Sir G. Cornewall Lewis's _Inscriptio Antiqua_. In this last, +HEYDIDDLEDIDDLETHECATANDTHEFIDDLE etc. is treated as an Oscan inscription, +and rendered into Latin by approved methods. As few readers have seen it, I +give the result: + + "Hejus dedit libenter, dedit libenter. Deus propitius [est], deus + [donatori] libenter favet. Deus in viarum {163} junctura ovorum dape + [colitur], deus mundi. Deus in litatione voluit, benigno animo, haedum, + taurum intra fines [loci sacri] portandos. Deus, bis lustratus, beat + fossam sacrae libationis."[285] + +How then comes the history of astronomy among the paradoxes? Simply because +the author, so admirably when writing about what he knew, did not know what +he did not know, and blundered like a circle-squarer. And why should the +faults of so good a writer be recorded in such a list as the present? For +three reasons: First, and foremost, because if the exposure be not made by +some one, the errors will gradually ooze out, and the work will get the +character of inaccurate. Nothing hurts a book of which few can fathom the +depths so much as a plain blunder or two on the surface. Secondly, because +the reviews either passed over these errors or treated them too gently, +rather implying their existence than exposing them. Thirdly, because they +strongly illustrate the melancholy truth, that no one knows enough to write +about what he does not know. The distinctness of the errors is a merit; it +proceeds from the clear-headedness of the author. The suppression in the +journals may be due partly to admiration of the talent and energy which +lived two difficult lives at once, partly to respect for high position in +public affairs, partly to some of the critics being themselves men of +learning only, unable to detect the errors. But we know that action and +reaction are equal and contrary. If our generation take no notice of +defects, and allow them to go down undetected among merits, the next +generation will discover them, will perhaps believe us incapable of +detecting them, at least will pronounce our judgment good for nothing, and +will form an {164} opinion in which the merits will be underrated: so it +has been, is, and will be. The best thing that can be done for the memory +of the author is to remove the unsound part that the remainder may thrive. +The errors do not affect the work; they occur in passages which might very +well have been omitted: and I consider that, in making them conspicuous, I +am but cutting away a deleterious fungus from a noble tree. + +(P. 154). The periodic times of the five planets were stated by +Eudoxus,[286] as we learn from Simplicius;[287] the following is his +statement, to which the true times are subjoined, for the sake of +comparison: + + STATEMENT OF EUDOXUS TRUE TIME + Mercury 1 year -- 87d. 23h. + Venus 1 " -- 224d. 16h. + Mars 2 " 1y. 321d. 23h. + Jupiter 12 " 11y. 315d. 14h. + Saturn 30 " 29y. 174d. 1h. + +Upon this determination two remarks may be made. First, the error with +respect to Mercury and Venus is considerable; with respect to Mercury, it +is, in round numbers, 365 instead of 88 days, more than four times too +much. Aristotle remarks that Eudoxus distinguishes Mercury and Venus from +the other three planets by giving them one sphere each, with the poles in +common. The proximity of Mercury to the sun would render its course +difficult to observe and to measure, but the cause of the large error with +respect to Venus (130 days) is not apparent. + +{165} + +Sir G. Lewis takes Eudoxus as making the planets move round the sun; he has +accordingly compared the _geocentric_ periods of Eudoxus with our +_heliocentric_ periods. What greater blunder can be made by a writer on +ancient astronomy than giving Eudoxus the Copernican system? If Mercury +were a black spot in the middle of the sun it would of course move round +the earth in a year, or appear to do so: let it swing a little on one side +and the other of the sun, and the average period is still a year, with +slight departures both ways. The same for Venus, with larger departures. +Say that a person not much accustomed to the distinction might for once +write down the mistake; how are we to explain its remaining in the mind in +a permanent form, and being made a ground for such speculation as that of +the difficulty of observing Mercury leading to a period four times what it +ought to be, corrected in proof and published by an industrious and +thoughtful person? Only in one way: the writer was quite out of his depth. +This one case is conclusive; be it said with all respect for the real +staple of the work and of the author. He knew well the difference of the +systems, but not the effect of the difference: he is another instance of +what I have had to illustrate by help of a very different person, that it +is difficult to reason well upon matter which is not familiar. + + + +(P. 254). Copernicus, in fact, supposed the axis of the earth to be always +turned towards the Sun.^{(169)} [(169). See Delambre, _Hist. Astr. Mod._, +Vol. I, p. 96]. It was reserved to Kepler to propound the hypothesis of the +constant parallelism of the earth's axis to itself. + + + +If there be one thing more prominent than another in the work of Copernicus +himself, in the popular explanations of it, and in the page of +Delambre[288] cited, it is that the _parallelism of the earth's axis_ is a +glaring part of the {166} theory of Copernicus. What Kepler[289] did was to +throw away, as unnecessary, the method by which Copernicus, _per fas et +nefas_,[290] secured it. Copernicus, thinking of the earth's orbital +revolution as those would think who were accustomed to the _solid +orbs_--and much as the stoppers of the moon's rotation do now: why do they +not strengthen themselves with Copernicus?--thought that the earth's axis +would always incline the same end towards the sun, unless measures were +taken to prevent it. He _did_ take measures: he invented a _compensating_ +conical motion of the axis to preserve the parallelism; and, which is one +of the most remarkable points of his system, he obtained the precession of +the equinoxes by giving the necessary trifle more than compensation. What +stares us in the face at the beginning of the paragraph to which the author +refers? + +"C'est donc pour arriver a ce parallelisme, ou pour le conserver, que +Copernic a cru devoir recourir a ce mouvement egal et oppose qui detruit +l'effet qu'il attribue si gratuitement au premier, de deranger le +parallelisme."[291] + +Parallelism at any price, is the motto of Copernicus: you need not pay so +dear, is the remark of Kepler. + +The opinions given by Sir G. Lewis about the effects of modern astronomy, +which he does not understand and singularly undervalues, will now be seen +to be of no authority. He fancies that--to give an instance--for the +determination of a ship's place, the invention of chronometers has been far +more important than any improvement in astronomical theory (p. 254). Not to +speak of latitude,--though the omission is not without importance,--he +ought to have known that longitude is found by the difference between what +o'clock it is at Greenwich and at the ship's place, at {167} one absolute +moment of time. Now if a chronometer were quite perfect--which no +chronometer is, be it said--and would truly tell Greenwich mean time all +over the world, it ought to have been clear that just as good a watch is +wanted for the time at _the place of observation_, before the longitude of +that place with respect to Greenwich can be found. There is no such watch, +except the starry heaven itself: and that watch can only be read by +astronomical observation, aided by the best knowledge of the heavenly +motions. + +I think I have done Sir G. Lewis's very excellent book more good than all +the reviewers put together. + +I will give an old instance in which literature got into confusion about +astronomy. Theophrastus,[292] who is either the culprit or his historian, +attributes to Meton,[293] the contriver of the lunar calendar of nineteen +years, which lasts to this day, that his solstices were determined for him +by a certain Phaeinus of Elis on Mount Lycabettus. Nobody else mentions +this astronomer: though it is pretty certain that Meton himself made more +than one appointment with him for the purpose of observing solstices; and +we may be sure that if either were behind his time, it was Meton. For +_Phaeinus Helius_ is the shining sun himself; and in the astronomical poet +Aratus[294] we read about the nineteen years of the shining sun: + + [Greek: Enneakaideka kukla phaeinou eelioio].[295] + +Some man of letters must have turned Apollo into Phaeinus of Elis; and +there he is in the histories of astronomy to {168} this day. Salmasius[296] +will have Aratus to have meant him, and proposes to read [Greek: eleioio]: +he did not observe that Phaeinus is a very common adjective of Aratus, and +that, if his conjecture were right, this Phaeinus would be the only +non-mythical man in the poems of Aratus. + +[When I read Sir George Lewis's book, the points which I have criticized +struck me as not to be wondered at, but I did not remember why at the time. +A Chancellor of the Exchequer and a writer on ancient astronomy are birds +of such different trees that the second did not recall the first. In 1855 I +was one of a deputation of about twenty persons who waited on Sir G. Lewis, +as Chancellor of the Exchequer, on the subject of a decimal coinage. The +deputation was one of much force: Mr. Airy, with myself and others, +represented mathematics; William Brown,[297] whose dealings with the United +States were reckoned by yearly millions, counted duodecimally in England +and decimally in America, was the best, but not the only, representative of +commerce. There were bullionists, accountants, retailers, etc. Sir G. L. +walked into the room, took his seat, and without waiting one moment, began +to read the deputation a smart lecture on the evils of a decimal coinage; +it would require alteration of all the tables, it would impede calculation, +etc. etc. Of those arguments against it which weighed with many of better +knowledge than his, he obviously knew nothing. The members of the +deputation began to make their statements, and met with curious denials. He +interrupted me with "Surely there is no doubt that the calculations of our +books of arithmetic are easier {169} than those in the French books." He +was not aware that the _universally admitted_ superiority of decimal +_calculation_ made many of those who prefer our system for the market and +the counter cast a longing and lingering look towards decimals. My answer +and the smiles which he saw around, made him give a queer puzzled look, +which seemed to say, "I may be out of my depth here!" His manner changed, +and he listened. I saw both the slap-dash mode in which he dealt with +subjects on which he had not thought, and the temperament which admitted +suspicion when the means of knowledge came in his way. Having seen his two +phases, I wonder neither at his more than usual exhibition of shallowness +when shallow, nor at the intensity of the contrast when he had greater +depth.] + + + +DECIMAL COINAGE. + +Among the paradoxers are the political paradoxers who care not how far they +go in debate, their only object being to carry the House with them for the +current evening. What I have said of editors I repeat of them. The +preservation of a very marked instance, the association of political +recklessness with cyclometrical and Apocalyptic absurdity, may have a +tendency to warn, not indeed any hardened public-man and sinner, but some +young minds which have yearnings towards politics, and are in formation of +habits. + +In the debate on decimal coinage of July 12, 1855, Mr. Lowe,[298] then +member for Kidderminster, an effective speaker and a smart man, exhibited +himself in a speech on which I wrote a comment for the Decimal Association. +I have seldom seen a more wretched attempt to distort the points of a +public question than the whole of this speech. Looking at the intelligence +shown by the speaker on other occasions, {170} it is clear that if charity, +instead of believing all things, believed only all things but one, he might +tremble for his political character; for the honesty of his intention on +this occasion might be the incredible exception. I give a few paragraphs +with comments: + +"In commenting on the humorous, but still argumentative speech of Mr. Lowe, +the member for Kidderminster, we may observe, in general, that it consists +of points which have been several times set forth, and several times +answered. Mr. Lowe has seen these answers, but does not allude to them, far +less attempt to meet them. There are, no doubt, individuals, who show in +their public speaking the outward and visible signs of a greater degree of +acuteness than they can summon to guide their private thinking. If Mr. Lowe +be not one of these, if the power of his mind in the closet be at all +comparable to the power of his tongue in the House, it may be suspected +that his reserve with respect to what has been put forward by the very +parties against whom he was contending, arises from one or both of two +things--a high opinion of the arguments which he ignored--a low opinion of +the generality of the persons whom he addressed. [Both, I doubt not]. + +"Did they calculate in florins In the name of common sense, +?" how can it be objected to a + system that people do not use + it before it is introduced? + Let the decimal system be + completed, and calculation + shall be made in florins; that + is, florins shall take their + proper place. If florins were + introduced _now_, there must + be a column for the odd + shilling. +"He was glad that some hon. If the hon. gentleman make +gentleman had derived benefit this assertion of himself, it +from the issue of florins. His is not for us to gainsay it. +only experience of their It only proves that he is one +convenience was, that when he of that class of {171} men who +ought to have received are described in the old song, +half-a-crown, he had generally of which one couplet runs +received a florin, and when he thus: +ought to have paid a florin, +he had generally paid I sold my cow to buy me a +half-a-crown." (Hear, hear, calf; +and laughter.) I never make a bargain but I + lose half, + With a etc. etc. etc. + +But he cannot mean that Englishmen in general are so easily managed. And as +to Jonathan, who is but John lengthened out a little, he would see creation +whittled into chips before he would even split what may henceforth be +called the Kidderminster difference. The House, not unmoved--for it +laughed--with sly humor decided that the introduction of the florin had +been "eminently successful and satisfactory." + +The truth is that Mr. Lowe here attacks nothing except the coexistence of +the florin and half-crown. We are endeavoring to abolish the half-crown. +Let Mr. Lowe join us; and he will, if we succeed, be relieved from the +pressure on his pocket which must arise from having the turn of the market +always against him. + +"From a florin they get to 2 Note the sophism of expressing +2-5ths of a penny, but who our coin in terms of the +ever bought anything, who ever penny, which we abandon, +reckoned or wished to reckon instead of the florin, which +in such a coin as that?" we retain. Remember that this +(Hear, hear.) 2 2-5ths is the hundredth part + of the pound, which is called, + as yet, a _cent_. Nobody buys + anything at a cent, because + the cent is not yet + introduced. Nobody reckons in + cents for the same reason. + Everybody wishes to reckon in + cents, who wishes to combine + the advantage of decimal + reckoning with the + preservation of the pound as + {172} the highest unit of + account; amongst others, a + majority of the House of + Commons, the Bank of England, + the majority of London + bankers, the Chambers of + Commerce in various places, + etc. etc. etc. +"Such a coin could never come Does 2-1/2d. never pass from +into general circulation hand to hand? And is 2-1/2d. +because it represents nothing so precisely the modulus of +which corresponds with any of popular wants, that an +the wants of the people." alteration of 4 per cent. + would make it useless? Of all + the values which 2-1/2d. + measures, from three pounds of + potatoes down to certain + arguments used in the House of + Commons, there is not one for + which a cent would not do just + as well. Mr. Lowe has fallen + into the misconception of the + person who admired the + dispensation of Providence by + which large rivers are made to + run through cities so great + and towns so many. If the cent + were to be introduced + to-morrow, straightway the + buns and cakes, the soda-water + bottles, the short omnibus + fares, the bunches of + radishes, etc. etc. etc., + would adapt themselves to the + coin. +"If the proposed system were The confusion of ideas here +adopted, they would all be exhibited is most instructive. +compelled to live in decimals The speaker is under the +for ever; if a man dined at a impression that _we_ are +public house he would have to introducing fractions: the +pay for his dinner in decimal truth is, that we only want to +fractions. (Hear, hear.) He abandon the _more difficult_ +objected to that, for he fractions which we _have got_, +thought that a man ought to be and to introduce _easier +able to pay for his dinner in fractions_. Does he deny this? +integers." (Hear, hear, and a Let us trace his denial to its +laugh.) legitimate consequences. A man + ought to pay for his dinner in + integers. + +{173} + +Now, if Mr. Lowe insists on it that our integer is the pound, he is bound +to admit that the present integer is the pound, of which a shilling, etc., +are fractions. The next time he has a chop and a pint of stout in the city, +the waiter should say--"A pound, sir, to you," and should add, "Please to +remember the waiter in integers." Mr. Lowe fancies that when he pays one +and sixpence, he pays in integers, and so he does, if his integer be a +penny or a sixpence. Let him bring his mind to contemplate a mil as the +integer, the lowest integer, and the seven cents five mils which he would +pay under the new system would be payment in integers also. But, as it +happens with some others, he looks _up_ the present system, with +Cocker,[299] and Walkingame,[300] and always looks _down_ the proposed +system. The word _decimal_ is obstinately associated with _fractions_, for +which there is no need. Hence it becomes so much of a bugbear, that, to +parody the lines of Pope, which probably suggested one of Mr. Lowe's +phrases-- + + "Dinner he finds too painful an endeavor, + Condemned to pay in decimals for ever." + +"The present system, however, A pleasant sum even for an +had not yet been changed into accomplished mathematician. +decimal system. That change What does divided by the +might appear very easy to decimal of a pound mean? +accomplished mathematicians Perhaps it means _reduced_ to +and men of science, but it was the decimal of a pound! Mr. +one which it would be very Lowe supposes, as many others +difficult to carry out. (Hear, do, that, after the change, +hear). What would have to be all calculations will be +done? Every sum would have to _proposed in old money_, and +be reduced into a vulgar then _converted into new_. He +fraction of a pound, and then cannot hit the {174} idea that +divided by the decimal of a the new coins will take the +pound--a pleasant sum for an place of the old. This lack of +old applewoman to work out!" apprehension will presently +(Hear, hear, and laughter.) appear further. +"It would not be an agreeable Let the members be assured +task, even for some members of that nine half-pence will be, +that House, to reduce 4-1/2d., for every practical purpose, +or nine half-pence, to mils." 18 mils. But now to the fact +(Hear, hear.) asserted. Davies Gilbert[301] + used to maintain that during + the long period he sat in the + House, he never knew more than + three men in it, at one time, + who had a tolerable notion of + fractions. [I heard him give + the names of three at the time + when he spoke: they were + Warburton,[302] Pollock,[303] + and Hume.[304] He himself was + then out of Parliament.] + Joseph Hume affirmed that he + had never met with more than + ten members who were + arithmeticians. But both these + gentlemen had a high standard. + Mr. Lowe has given a much more + damaging opinion. He evidently + means that the general run of + members could not do his + question. It is done as + follows: Since farthings gain + on mils, at the rate of a + whole mil in 24 farthings (24 + farthings being 25 mils), it + is clear that 18 farthings + being three-quarters of 24 + farthings, will gain + three-quarters of a mil; that + is, 18 farthings are eighteen + {175} mils and three-quarters + of a mil. Any number of + farthings is as many mils and + as many twenty-fourths of a + mil. To a certain extent, we + feel able to protest against + the manner in which + Kidderminster has treated the + other constituencies. We do + not hold it impossible to give + the Members of the House in + general a sufficient knowledge + of the meaning and + consequences of the _decimal_ + succession of units, tens, + hundreds, thousands, etc.; and + we believe that there are in + the House itself competent + men, in number enough to teach + all the rest. All that is + wanted is the power of + starting from the known to + arrive at the unknown. Now + there is one kind of decimals + with which every member is + acquainted--the _Chiltern + Hundreds_. If public opinion + would enable the competent + minority to start from this in + their teaching, not as a + basis, but as an alternative, + in three weeks the + fundamentals would be + acquired, and members in + general would be as fit to + turn 4-1/2d. into mils, as any + boys on the lower forms of a + commercial school. + + For a long period of years, + allusion to the general + ignorance of arithmetic, has + been a standing mode of + argument, and has always been + well received: whenever one + member describes others as + _knownothings_, those others + cry _Hear_ to the country in a + transport of delight. In the + meanwhile the country is + gradually arriving at the + conclusion that a true joke is + no joke. +"The main objection was, if Fine words, wrongly used. The +they went below 6d., that the new coins are commensurable +new scale of coins would not with, and in a finite ratio +be commensurate in any finite to, the old ones. The farthing +ratio with anything in this is to the mil as 25 to 24. The +new currency of mils." speaker has something here in + the bud, which we shall + presently meet with in the + flower; and fallacies are more + easily nipped in flower than + in bud. {176} +"No less than five of our This dreadful change of value +present coins must be called consists in sixpence farthing +in, or else--which would be going to the half-shilling +worse--new values must be instead of sixpence. Whether +given to them." the new farthings be called + mils or not is of no + consequence. +"If a poor man put a penny in Mr. Lowe, who cannot pass a +his pocket, it would come out half-crown for more than a +a coin of different value, florin, or get in a florin at +which he would not understand. less than half-a-crown, has +Suppose he owed another man a such a high faith in the +penny, how was he to pay him ? sterner stuff of his fellow +Was he to pay him in mils? countrymen, that he believes +Four mils would be too little, any two of them would go to +and five mils would be too fisty cuffs for the 25th part +much. The hon. gentlemen said of a farthing. He reasons +there would be only a mil thus: He has often heard in +between them. That was exactly the streets, "I'd fight you +it. He believed there would be for the fiftieth part of a +a 'mill' between them." (Much farden:" and having (that is, +laughter.) for a Member) a notion both of + fractions and logic, he infers + that those who would fight for + the 50th of a farthing would, + _a fortiori_, fight for a + 25th. His mistake arises from + his not knowing that when a + person offers to fight another + for 1/200d., he really means + to fight for love; and that + the stake is merely a matter + of form, a feigned issue, a + _pro forma_ report of + progress. Do the Members of + the House think they have all + the forms to themselves? +"What would be the present We should hardly believe all +expression for four-pence? this to be uttered in earnest, +Why, 0.166 (a laugh); for if we had not known {177} that +threepence? .0125; for a several persons who have not +penny? .004166, and so on _ad Mr. Lowe's humor, nevertheless +infinitum_ (a laugh); for a have his impressions on this +half-penny? .002083 _ad point. It must therefore be +infinitum_. (A laugh). What answered; but how is this to +would be the present be done seriously? +expression for a farthing? +Why, .0010416 _ad infinitum_. _Dialogue between a member of +(A laugh). And this was the Parliament and an orange-boy, +system which was to cause such three days after the +a saving in figures, and these introduction of the complete +were the quantities into which decimal system. The member, +the poor would have to reduce going down to the House, wants +the current coin of the realm. oranges to sustain his voice +(Cheers). With every respect in a two hours' speech on +for decimal fractions, of moving that 100000l. be placed +which he boasted no profound at the disposal of Her +knowledge, he doubted whether Majesty, to supply the poor +the poor were equal to mental with ready-reckoners._ +arithmetic of this kind, +(hear, hear) and he hoped the _Boy._ Fine oranges! two a +adoption of the system would penny! two a penny! {178} +be deferred until there were +some proof that they would be _Member._ Here boy, two! Now, +able to understand it; for, how am I to pay you? +after all, this was the +question of the poor, and the _Boy._ Give you change, your +whole weight of the change honor. +would fall upon them. Let the +rich by all means have _Member._ Ah! but how? Where's +permission to perplex your ready-reckoner? +themselves by any division of +a pound they pleased; but do _Boy._ I sells a better sort +not let them, by any nor them. Mine's real Cheyny. +experiment like this, impose +difficulties upon the poor and _Member._ But you see a +compel men to carry farthing is now .0014166666 +ready-reckoners in their _ad infinitum_, and if we +pocket to give them all these multiply this by 4---- +fractional quantities." (Hear, +hear.) _Boy._ Hold hard, Guv'ner; I + sees what you're arter. Now + what'll you stand if I puts + you up to it? which Bill Smith + he put me up in two minutes, + cause he goes to the Ragged + School. + + _Member._ You don't mean that + you do without a book! + + _Boy._ Book be blowed. Come + now, old un, here's summut for + both on us. I got a florin, + you gives me a half-a-crown + for it, and I larns you the + new money, gives you your + oranges, and calls you a brick + into the bargain. + + _Member_ (_to himself_). Never + had such a chance of getting + off half-a-crown for value + since that ---- fellow Bowring + carried his crochet. + (_Aloud._) Well, boy, it's a + bargain. Now! + + _Boy._ Why, look 'e here, my + trump, its a farden more to + the tizzy--that's what it is. + + _Member_. What's that? + + _Boy._ Why, you knows a + sixpence when you sees it. + (_Aside_). Blest if I think he + does! Well, its six browns and + a farden now. A lady buys two + oranges, and forks {179} out a + sixpence; well in coorse, I + hands over fippence farden + astead of fippence. I always + gives a farden more change, + and takes according. + + _Member_ (_in utter surprise, + lets his oranges tumble into + the gutter_). Never mind! They + won't be wanted now. (_Walks + off one way. Boy makes a pass + of naso-digital mesmerism, and + walks off the other way_). + +To the poor, who keep no books, the whole secret is "Sixpence farthing to +the half shilling, twelve pence halfpenny to the shilling." The _new +twopence halfpenny_, or cent, will be at once five to the shilling. + +In conclusion, we remark that three very common misconceptions run through +the hon. Member's argument; and, combined in different proportions, give +variety to his patterns. + +First, he will have it that we design to bring the uneducated into contact +with _decimal fractions_. If it be so, it will only be as M. Jourdain was +brought into contact with prose. In fact, _Quoi! quand je dis, Nicole, +apportez-moi mes pantoufles, c'est de la prose?_[305] may be rendered: +"What! do you mean that _ten to the florin is a cent a piece_ must be +called decimal reckoning?" If we had to comfort a poor man, horror-struck +by the threat of _decimals_, we should tell him what manner of fractions +had been inflicted upon him hitherto; nothing less awful than +_quarto-duodecimo-vicesimals_, we should assure him. + +Secondly, he assumes that the penny, such as it now is, will remain, as a +coin of estimation, after it has ceased to be a coin of exchange; and that +the mass of the people will continue to think of prices in old pence, and +to calculate them in new ones, or else in new mils. No answer is required +to this, beyond the mere statement of the nature of the assumption and +denial. + +{180} + +Thirdly, he attributes to the uneducated community a want of perception and +of operative power which really does not belong to them. The evidence +offered to the Committee of the House shows that no fear is entertained on +this point by those who come most in contact with farthing purchasers. And +this would seem to be a rule,--that is, fear of the intelligence of the +lower orders in the minds of those who are not in daily communication with +them, no fear at all in the minds of those who are. + +A remarkable instance of this distinction happened five-and-twenty years +ago. The Admiralty requested the Astronomical Society to report on the +alterations which should be made in the _Nautical Almanac_, the seaman's +guide-book over the ocean. The greatest alteration proposed was the +description of celestial phenomena in _mean_ (or clock time), instead of +_apparent_ (or sundial) time, till then always employed. This change would +require that in a great many operations the seaman should let alone what he +formerly altered by addition or subtraction, and alter by addition or +subtraction what he formerly let alone; provided always that what he +formerly altered by addition he should, when he altered at all, alter by +subtraction, and _vice versa_. This was a tolerably difficult change for +uneducated skippers, working by rules they had only learned by rote. The +Astronomical Society appointed a Committee of forty, of whom nine were +naval officers or merchant seamen [I was on this Committee]. Some men of +science were much afraid of the change. They could not trust an ignorant +skipper or mate to make those alterations in their routine, on the +correctness of which the ship might depend. Had the Committee consisted of +men of science only, the change might never have been ventured on. But the +naval men laughed, and said there was nothing to fear; and on their +authority the alteration was made. The upshot was, that, after the new +almanacs appeared, not a word of complaint was ever heard on the matter. +Had the House of Commons had to {181} decide this question, with Mr. Lowe +to quote the description given by Basil Hall[306] (who, by the way, was one +of the Committee) of an observation on which the safety of the ship +depended, worked out by the light of a lantern in a gale of wind off a lee +shore, this simple and useful change might at this moment have been in the +hands of its tenth Government Commission. + + + +[_Aug. 14, 1866._ The Committee was appointed in the spring of 1830: it +consisted of forty members. Death, of course, has been busy; there are now +left Lord Shaftesbury,[307] Mr. Babbage,[308] Sir John Herschel,[309] Sir +Thomas Maclear[310] (Astronomer Royal at the Cape of Good Hope), Dr. +Robinson[311] (of Armagh), Sir James South,[312] Lord Wrottesley,[313] and +myself]. + +{182} + + + +THE TONAL SYSTEM. + + Project of a new system of arithmetic, weight, measure, and coins, + proposed to be called the tonal system, with sixteen to the base. By + J. W. Mystrom.[314] Philadelphia, 1862, 8vo. + +That is to say, sixteen is to take the place of ten, and to be written 10. +The whole language is to be changed; every man of us is to be +sixteen-stringed Jack and every woman sixteen-stringed Jill. Our old _one_, +_two_, _three_, up to sixteen, are to be (_Noll_ going for nothing, which +will please those who dislike the memory of _Old Noll_) replaced by An, De, +Ti, Go, Su, By, Ra, Me, Ni, Ko, Hu, Vy, La, Po, Fy, Ton; and then Ton-an, +Ton-de, etc. for 17, 18, etc. The number which in the system has the symbol + + 28(13)5(11)7(14)0(15) + +(using our present compounds instead of new types) is to be pronounced + + Detam-memill-lasan-suton-hubong-ramill-posanfy. + +The year is to have sixteen months, and here they are: + + Anuary, Debrian, Timander, Gostus, + Suvenary, Bylian, Ratamber, Mesudius, + Nictoary, Kolumbian, Husamber, Vyctorius, + Lamboary, Polian, Fylander, Tonborius. + +Surely An-month, De-month, etc. would do as well. Probably the wants of +poetry were considered. But what are we to do with our old poets? For +example-- + + "It was a night of lovely June, + High rose in cloudless blue the moon." + +Let us translate-- + + "It was a night of lovely Nictoary, + High rose in cloudless blue the (what, in the name of all that is + absurd?)." + +And again, _Fylander_ thrown into our December! What is {183} to become of +those lines of Praed, which I remember coming out when I was at +Cambridge,-- + + "Oh! now's the time of all the year for flowers and fun, the Maydays; + To trim your whiskers, curl your hair, and sinivate the ladies." + +If I were asked which I preferred, this system or that of Baron +Ferrari[315] already mentioned, proceeding by _twelves_, I should reply, +with Candide, when he had the option given of running the gauntlet or being +shot: Les volontes sont libres, et je ne veux ni l'un ni l'autre.[316] We +can imagine a speculator providing such a system for Utopia as it would be +in the mind of a Laputan: but to explain how an engineer who has surveyed +mankind from Philadelphia to Rostof on the Don should for a moment +entertain the idea of such a system being actually adopted, would beat a +jury of solar-system-makers, though they were shut up from the beginning of +Anuary to the end of Tonborius. When I see such a scheme as this imagined +to be practicable, I admire the wisdom of Providence in providing the +quadrature of the circle, etc., to open a harmless sphere of action to the +possessors of the kind of ingenuity which it displays. Those who cultivate +mathematics have a right to speak strongly on such efforts of arithmetic as +this: for, to my knowledge, persons who have no knowledge are frequently +disposed to imagine that their makers are true brothers of the craft, a +little more intelligible than the rest. + + + +SOME SMALL PARADOXERS. + + Vis inertiae victa,[317] or Fallacies affecting science. By James + Reddie.[318] London, 1862, 8vo. + +{184} + +An attack on the Newtonian mechanics; revolution by gravitation +demonstrably impossible; much to be said for the earth being the immovable +center. A good analysis of contents at the beginning, a thing seldom found. +The author has followed up his attack in a paper submitted to the British +Association, but which it appears the Association declined to consider. It +is entitled-- + + + + _Victoria Toto Coelo_; or, Modern Astronomy recast. London, 1863, 8vo. + +At the end is a criticism of Sir G. Lewis's _History of Ancient Astronomy_. + + + + On the definition and nature of the Science of Political Economy. By H. + Dunning Macleod,[319] Esq. Cambridge, 1862, 8vo. + +A paper read--but, according to the report, not understood--at the British +Association. There is a notion that political economy is entirely +mathematical; and its negative quantity is strongly recommended for study: +it contains "the whole of the Funds, Credit, 32 parts out of 33 of the +value of Land...." The mathematics are described as consisting of--first, +number, or Arithmetic; secondly, the theory of dependent quantities, +subdivided into dependence by cause and effect, and dependence by +simultaneous variations; thirdly, "independent quantities or unconnected +events, which is the theory of probabilities." I am not ashamed, having the +British Association as a co-non-intelligent, to say I do not understand +this: there is a paradox in it, and the author should give further +explanation, especially of his negative quantity. Mr. Macleod has gained +{185} praise from great names for his political economy; but this, I +suspect, must have been for other parts of his system. + + + + On the principles and practice of just Intonation, with a view to the + abolition of temperament.... By General Perronet Thompson.[320] Sixth + Edition. London, 1862, 8vo. + +Here is General Thompson again, with another paradox: but always master of +the subject, always well up in what his predecessors have done, and always +aiming at a useful end. He desires to abolish temperament by additional +keys, and has constructed an enharmonic organ with forty sounds in the +octave. If this can be introduced, I, for one, shall delight to hear it: +but there are very great difficulties in the way, greater than stood even +in the way of the repeal of the bread-tax. + +In a paper on the beats of organ-pipes and on temperament published some +years ago, I said that equal temperament appeared to me insipid, and not so +agreeable as the effect of the instrument when in progress towards being +what is called out of tune, before it becomes offensively wrong. There is +throughout that period unequal temperament, determined by accident. General +Thompson, taking me one way, says I have launched a declaration which is +likely to make an epoch in musical practice; a public musical critic, +taking me another way, quizzes me for preferring music _out of tune_. I do +not think I deserve either one remark or the other. My opponent critic, I +suspect, takes _equally tempered_ and _in tune_ to be phrases of one +meaning. But by equal temperament is meant equal distribution among all the +keys of the error which an instrument _must_ have, which, with twelve +sounds only in the octave, professes to be fit for all the keys. I am +reminded of the equal temperament which was once applied to the postmen's +jackets. The coats were all made for the average man: the {186} consequence +was that all the tall men had their tails too short; all the short men had +them too long. Some one innocently asked why the tall men did not change +coats with the short ones. + + + + A diagram illustrating a discovery in the relation of circles to + right-lined geometrical figures. London, 1863, 12mo. + +The circle is divided into equal sectors, which are joined head and tail: +but a property is supposed which is not true. + + + + An attempt to assign the square roots of negative powers; or what is + [sqrt] -1? By F.H. Laing.[321] London, 1863, 8vo. + +If I understand the author, -a and +a are the square roots of -a^2, as +proved by multiplying them together. The author seems quite unaware of what +has been done in the last fifty years. + + + +BYRNE'S DUAL ARITHMETIC. + + Dual Arithmetic. A new art. By Oliver Byrne.[322] London, 1863, 8vo. + +The plan is to throw numbers into the form a(1.1)^{b} (1.01)^{c} +(1.001)^{d}... and to operate with this form. This is an ingenious and +elaborate speculation; and I have no doubt the author has practised his +method until he could surprise any one else by his use of it. But I doubt +if he will persuade others to use it. As asked of Wilkins's universal +language, Where is the second man to come from? + +An effective predecessor in the same line of invention {187} was the late +Mr. Thomas Weddle,[323] in his "New, simple, and general method of solving +numeric equations of all orders," 4to, 1842. The Royal Society, to which +this paper was offered, declined to print it: they ought to have printed an +organized method, which, without subsidiary tables, showed them, in six +quarto pages, the solution (x=8.367975431) of the equation + + 1379.664 x^{622} + 2686034 x 10^{432} x^{152} - 17290224 x 10^{518} + x^{60} + 2524156 x 10^{574} = 0. + +The method proceeds by successive factors of the form, a being the first +approximation, a x 1.b x 1.0c x 1.00d.... In my copy I find a few +corrections made by me at the time in Mr. Weddle's announcement. "It was +read before that learned body [the R. S.] and they were pleased [but] to +transmit their thanks to the author. The en[dis]couragement which he +received induces [obliges] him to lay the result of his enquiries in this +important branch of mathematics before the public [, at his own expense; he +being an usher in a school at Newcastle]." Which is most satirical, Mr. +Weddle or myself? The Society, in the account which it gave of this paper, +described it as a "new and remarkably simple method" possessing "several +important advantages." Mr. Rutherford's[324] extended value of [pi] was +read at the very next meeting, and was printed in the _Transactions_; and +very properly: Mr. Weddle's paper was excluded, and very very improperly. + + + +HORNER'S METHOD. + +I think it may be admited that the indisposition to look at and encourage +improvements of calculation which once {188} marked the Royal Society is no +longer in existence. But not without severe lessons. They had the luck to +accept Horner's[325] now celebrated paper, containing the method which is +far on the way to become universal: but they refused the paper in which +Horner developed his views of this and other subjects: it was printed by +T. S. Davies[326] after Horner's death. I make myself responsible for the +statement that the Society could not reject this paper, yet felt unwilling +to print it, and suggested that it should be withdrawn; which was done. + +But the severest lesson was the loss of _Barrett's Method_,[327] now the +universal instrument of the actuary in his highest calculations. It was +presented to the Royal Society, and refused admission into the +_Transactions_: Francis Baily[328] printed it. The Society is now better +informed: "_live and learn_," meaning "_must live, so better learn_," ought +to be the especial motto of a corporation, and is generally acted on, more +or less. + +Horner's method begins to be introduced at Cambridge: it was published in +1820. I remember that when I first went to Cambridge (in 1823) I heard my +tutor say, in conversation, there is no doubt that the true method of +solving equations is the one which was published a few years ago in the +_Philosophical Transactions_. I wondered it was not taught, but presumed +that it belonged to the higher mathematics. This Horner himself had in his +head: and in a sense it is true; for all lower branches belong to the +higher: but he would have stared to have been told that he, Horner, {189} +was without a European predecessor, and in the distinctive part of his +discovery was heir-at-law to the nameless +Brahmin--Tartar--Antenoachian--what you please--who concocted the +extraction of the square root. + +It was somewhat more than twenty years after I had thus heard a Cambridge +tutor show sense of the true place of Horner's method, that a pupil of mine +who had passed on to Cambridge was desired by his college tutor to solve a +certain cubic equation--one of an integer root of two figures. In a minute +the work and answer were presented, by Horner's method. "How!" said the +tutor, "this can't be, you know." "There is the answer, Sir!" said my +pupil, greatly amused, for my pupils learnt, not only Horner's method, but +the estimation it held at Cambridge. "Yes!" said the tutor, "there is the +answer certainly; but it _stands to reason_ that a cubic equation cannot be +solved in this space." He then sat down, went through a process about ten +times as long, and then said with triumph: "There! that is the way to solve +a cubic equation!" + +I think the tutor in this case was never matched, except by the country +organist. A master of the instrument went into the organ-loft during +service, and asked the organist to let him _play the congregation out_; +consent was given. The stranger, when the time came, began a voluntary +which made the people open their ears, and wonder who had got into the +loft: they kept their places to enjoy the treat. When the organist saw +this, he pushed the interloper off the stool, with "You'll never play 'em +out this side Christmas." He then began his own drone, and the congregation +began to move quietly away. "There," said he, "that's the way to play 'em +out!" + +I have not scrupled to bear hard on my own university, on the Royal +Society, and on other respectable existences: being very much the friend of +all. I will now clear the Royal Society from a very small and obscure +slander, simply because I know how. This dissertation began with {190} the +work of Mr. Oliver Byrne, the dual arithmetician, etc. This writer +published, in 1849, a method of calculating logarithms.[329] First, a long +list of instances in which, as he alleges, foreign discoverers have been +pillaged by Englishmen, or turned into Englishmen: for example, +O'Neill,[330] so called by Mr. Byrne, the rectifier of the semi-cubical +parabola claimed by the Saxons under the name of _Neal_: the grandfather of +this mathematician was conspicuous enough as _Neal_; he was archbishop of +York. This list, says the writer, might be continued without end; but he +has mercy, and finishes with his own case, as follows:--"About twenty years +ago, I discovered this method of directly calculating logarithms. I could +generally find the logarithm of any number in a minute or two without the +use of books or tables. The importance of the discovery subjected me to all +sorts of prying. Some asserted that I committed a table of logarithms to +memory; others attributed it to a peculiar mental property; and when +Societies and individuals failed to extract my secret, they never failed to +traduce the inventor and the invention. Among the learned Societies, the +Royal Society of London played a very base part. When I have more space and +time at my disposal, I will revert to this subject again." + +Such a trumpery story as this remains unnoticed at the time; but when all +are gone, a stray copy from a stall falls into hands which, not knowing +what to make of it, make history of it. It is a very curious distortion. +The reader may take it on my authority, that the Royal Society played no +part, good or bad, nor had the option of playing a part. {191} But I myself +_pars magna fui_:[331] and when the author has "space and time" at his +disposal, he must not take all of them; I shall want a little of both. + + + +ARE ATOMS WORLDS? + + The mystery of being; or are ultimate atoms inhabited worlds? By + Nicholas Odgers.[332] Redruth and London, 1863, 8vo. + +This book, as a paradox, beats quadrature, duplication, trisection, +philosopher's stone, perpetual motion, magic, astrology, mesmerism, +clairvoyance, spiritualism, homoeopathy, hydropathy, kinesipathy, Essays +and Reviews, and Bishop Colenso,[333] all put together. Of all the +suppositions I have given as actually argued, this is the one which is +hardest to deny, and hardest to admit. Reserving the question--as beyond +human discussion--whether our particles of carbon, etc. are _clusters_ of +worlds, the author produces his reasons for thinking that they are at least +single worlds. Of course--though not mentioned--the possibility is to be +added of the same thing being true of the particles which make up our +particles, and so down, for ever: and, on the other hand, of our planets +and stars as being particles in some larger universe, and so up, for ever. + + "Great fleas have little fleas upon their backs to bite 'em, + And little fleas have lesser fleas, and so _ad infinitum._ + And the great fleas themselves, in turn, have greater fleas to go on; + While these again have greater still, and greater still, and so on."[334] + +I have often had the notion that all the nebulae we see, including our own, +which we call the Milky Way, may be particles of snuff in the box of a +giant of a proportionately {192} larger universe. Of course the minim of +time--a million of years or whatever the geologists make it[335]--which our +little affair has lasted, is but a very small fraction of a second to the +great creature in whose nose we shall all be in a few tens of thousands of +millions of millions of millions of years. + +All this is quite possible, and the probabilities for and against are quite +out of reach. Perhaps also all the worlds, both above and below us, are +fac-similes of our own. If so, away goes free will for good and all; +unless, indeed, we underpin our system with the hypothesis that all the +fac-simile bodies of different sizes are actuated by a common soul. These +acute supplementary notions of mine go far to get rid of the difficulty +which some have found in the common theory that the soul inhabits the body: +it has been stated that there is, somewhere or another, a world of souls +which communicate with their bodies by wondrous filaments of a nature +neither mental nor material, but of a _tertium quid_ fit to be a +go-between; as it were a corporispiritual copper encased in a +spiritucorporeal gutta-percha. My theory is that every soul is everywhere +_in posse_, as the schoolmen said, but not anywhere _in actu_, except where +it finds one of its bodies. These _a priori_ difficulties being thus +removed, the system of particle-worlds is reduced to a dry question of +fact, and remitted to the decision of the microscope. And a grand field may +thus be opened, as optical science progresses! For the worlds are not +fac-similes of ours in time: there is not a moment of _our_ past, and not a +moment of _our_ future, but is the _present_ of one or more of the +particles. A will write the death of Caesar, and B the building of the +Pyramids, by actual observation of the processes with a power of a thousand +millions; C will discover the commencement of the Millennium, and D the +{193} termination of Ersch and Gruber's Lexicon,[336] as mere physical +phenomena. Against this glorious future there is a sad omen: the initials +of the forerunner of this discovery are--NO! + + + +THE SUPERNATURAL. + + The History of the Supernatural in all ages and nations, and in all + Churches, Christian and Pagan: demonstrating a universal faith. By Wm. + Howitt.[337] London, 2 vols. 8vo. 1863. + +Mr. Howitt is a preacher of spiritualism. He cements an enormous collection +of alleged facts with a vivid outpouring of exhortation, and an unsparing +flow of sarcasm against the scorners of all classes. He and the Rev. J. +Smith[338] (_ante_, 1854) are the most thoroughgoing universalists of all +the writers I know on spiritualism. If either can insert the small end of +the wedge, he will not let you off one fraction of the conclusion that all +countries, in all ages, have been the theaters of one vast spiritual +display. And I suspect that this consequence cannot be avoided, if any part +of the system be of truly spiritual origin. Mr. Howitt treats the +philosophers either as ignorant babies, or as conscious spirit-fearers: and +seems much inclined to accuse the world at large of dreading, lest by the +actual presence of the other world their Christianity should imbibe a +spiritual element which would unfit it for the purposes of their lives. + +{194} + + + +FROM MATTER TO SPIRIT. + + From Matter to Spirit. By C. D. With a preface by A. B.[339] London, + 1863, 8vo. + +This is a work on Spiritual Manifestations. The author upholds the facts +for spiritual phenomena: the prefator suspends his opinion as to the cause, +though he upholds the facts. The work begins systematically with the lower +class of phenomena, proceeds to the higher class, and offers a theory, +suggested by the facts, of the connection of the present and future life. I +agree in the main with A. B.; but can, of course, make none but horrescent +reference to his treatment of the smaller philosophers. This is always the +way with your paradoxers: they behave towards orthodoxy as the thresher +fish behaves towards the whale. But if true, as is said, that the drubbing +clears the great fish of parasites which he could not otherwise get rid of, +he ought to bear no malice. This preface retorts a little of that contempt +which the "philosophical world" has bestowed with heaped measure upon those +who have believed their senses, and have drawn natural, even if hasty, +inferences. There is philosophercraft as well as priestcraft, both from one +source, both of one spirit. In English cities and towns, the minister of +religion has been tamed: so many weapons are bared against him when he +obtrudes his office in a dictatory manner, that, as a rule, there is no +more quiet and modest member of society than the urban clergyman. +Domination over religious belief is reserved for the exclusive use of those +who admit the right: the rare exception to this mode of behavior is laughed +at as a bigot, or shunned as a nuisance. But the overbearing minister of +nature, who snaps you with _unphilosophical_ as the clergyman once +frightened you with _infidel_, is still a recognized member of society, +wants taming, and will get it. He wears the priest's cast-off {195} +clothes, dyed to escape detection: the better sort of philosophers would +gladly set him to square the circle. + +The book just named appeared about the same time as this Budget began in +the _Athenaeum_. It was commonly attributed, the book to my wife, the +preface to myself. Some time after, our names were actually announced by +the publisher, who ought to know. It will be held to confirm this statement +that I announce our having in our possession some twenty reviews of +different lengths, and of all characters: who ever collects a number of +reviews of a book, except the author? + +A great many of these reviews settle the matter _a priori_. If there had +been spirits in the matter, they would have done this, and they would not +have done that. Jean Meslier[340] said there could be no God over all, for, +_if_ there had been one, He would have established a universal religion. If +J. M. _knew_ that, J. M. was right: but if J. M. did not know that, then +J. M. was on the "high priori road," and may be left to his course. The +same to all who know what spirits would do and would not do. + +A. B. very distinctly said that he knew some of the asserted facts, +believed others on testimony, but did not pretend to know whether they were +caused by spirits, or had some unknown and unimagined origin. This he said +as clearly as I could have said it myself. But a great many persons cannot +understand such a frame of mind: their own apparatus is a kind of +spirit-level, and their conclusion on any subject is the little bubble, +which is always at one end or the other. Many of the reviewers declare that +A. B. is a secret believer in the spirit-hypothesis: and one of them wishes +that he had "endorsed his opinion more boldly." According to this reviewer, +any one who writes "I boldly {196} say I am unable to choose," contradicts +himself. In truth, a person who does say it has a good deal of courage, for +each side believes that he secretly favors the other; and both look upon +him as a coward. In spite of all this, A. B. boldly repeats that he feels +assured of many of the facts of _spiritualism_, and that he cannot pretend +to affirm or deny anything about their cause. + +The great bulk of the illogical part of the educated community--whether +majority or minority I know not; perhaps six of one and half-a-dozen of the +other--have not power to make a distinction, cannot be made to take a +distinction, and of course, never attempt to shake a distinction. With them +all such things are evasions, subterfuges, come-offs, loopholes, etc. They +would hang a man for horse-stealing under a statute against sheep-stealing; +and would laugh at you if you quibbled about the distinction between a +horse and a sheep. I divide the illogical--I mean people who have not that +amount of natural use of sound inference which is really not uncommon--into +three classes:--First class, three varieties: the Niddy, the Noddy, and the +Noodle. Second class, three varieties: the Niddy-Noddy, the Niddy-Noodle, +and the Noddy-Noodle. Third class, undivided: the Niddy-Noddy-Noodle. No +person has a right to be angry with me for more than one of these +subdivisions. + +The want of distinction was illustrated to me, when a boy, about 1820, by +the report of a trial which I shall never forget: boys read newspapers more +keenly than men. Every now and then a bench of country magistrates rather +astonishes the town populations, accustomed to rub their brains[341] +against one another. Such a story as the following would, {197} in our day, +bring down grave remarks from above: but I write of the olden (or +Eldon[342]) time, when nothing but conviction in a court of record would +displace a magistrate. In that day the third-class amalgamator of distinct +things was often on the bench of quarter-sessions. + +An attorney was charged with having been out at night poaching. A clear +_alibi_ was established; and perjury had certainly been committed. The +whole gave reason to suspect that some ill-willers thought the bench +disliked the attorney so much that any conviction was certain on any +evidence. The bench did dislike the attorney: but not to the extent of +thinking he could snare any partridges in the fields while he was asleep in +bed, except the dream-partridges which are not always protected by the +dream-laws. So the chairman said, "Mr. ----, you are discharged; but you +should consider this one of the most fortunate days of your life." The +attorney indignantly remonstrated, but the magistrate was right; for he +said, "Mr. ----, you have frequently been employed to defend poachers: have +you been careful to impress upon them the enormity of their practices?" It +appeared in a wrangling conversation that the magistrates saw little moral +difference between poaching and being a poacher's professional defender +without lecturing him on his wickedness: but they admitted with reluctance, +that there was a legal distinction; and the brain of N^3 could no further +go. This is nearly fifty years ago; and Westernism was not quite extinct. +If the present lords of the hills and the valleys want to shine, let them +publish a true history of their own order. I am just old enough to remember +some of the last of the squires and parsons who protested against teaching +the poor to read and write. They now write books for the working classes, +give them lectures, and the like. There is now no class, as a class, more +highly educated, broadly educated, and deeply educated, {198} than those +who were, in old times, best described as partridge-popping squireens. I +have myself, when a boy, heard Old Booby speaking with pride of Young Booby +as having too high a spirit to be confined to books: and I suspected that +his dislike to teaching the poor arose in fact from a feeling that they +would, if taught a little, pass his heir. + +A. B. recommended the spirit-theory as an hypothesis on which to ground +inquiry; that is, as the means of suggestion for the direction of inquiry. +Every person who knows anything of the progress of physics understands what +is meant; but not the reviewers I speak of. Many of them consider A. B. as +_adopting_ the spirit-hypothesis. The whole book was written, as both the +authors point out, to suggest inquiry to those who are curious; C. D. +firmly believing, A. B. as above. Neither C. D. nor A. B. make any other +pretence. Both dwell upon the absence of authentications and the +suppression of names as utterly preventive of anything like proof. And +A. B. says that his reader "will give him credit, if not himself a goose, +for seeing that the tender of an anonymous cheque would be of equal effect, +whether drawn on the Bank of England or on Aldgate Pump." By this test a +number of the reviewers are found to be geese: for they take the authors as +offering proof, and insist, against the authors, on the very point on which +the authors had themselves insisted beforehand. + +Leaving aside imperceptions of this kind, I proceed to notice a clerical +and medical review. I have lived much in the middle ages, especially since +the invention of printing; and from thence I have brought away a high +respect for and grateful recollection of--the priest in everything but +theology, and the physician in everything but medicine. The professional +harness was unfavorable to all progress, except on a beaten road; the +professional blinkers prevented all but the beaten road from being seen: +the professional reins were pulled at the slightest attempt to quicken +pace, even on the permitted path; and the {199} professional whip was +heavily laid on at the slightest attempt to diverge. But when the +intelligent man of either class turned his attention out of his ordinary +work, he had, in most cases, the freshness and vigor of a boy at play, and +like the boy, he felt his freedom all the more from the contrast of +school-restraint. + +In the case of medicine, and physics generally, the learned were, in some +essential points, more rational than many of their present impugners. They +pass for having put _a priori_ obstacles in the way of progress: they might +rather be reproved for too much belief in progress obtained by _a priori_ +means. They would have shouted with laughter at a dunce who--in a review I +read, but without making a note--declared that he would not believe his +senses except when what they showed him was capable of explanation upon +some known principle. I have seen such stuff as this attributed to the +schoolmen; but only by those who knew nothing about them. The following, +which I wrote some years ago, will give a notion of a distinction worth +remembering. It is addressed to the authorities of the College of +Physicians. + +"The ignominy of the word _empiric_ dates from the ages in which scholastic +philosophy deduced physical consequences _a priori_;--the ages in which, +because a lion is strong, rubbing with lion's fat would have been held an +infallible tonic. In those happy days, if a physician had given decoction +of a certain bark, only because in numberless instances that decoction had +been found to strengthen the patient, he would have been a miserable +empiric. Not that the colleges would have passed over his returns because +they were empirical: they knew better. They were as skilful in finding +causes for facts, as facts for causes. The president and the elects of that +day would have walked out into the forest with a rope, and would have +pulled heartily at the tree which yielded the bark: nor would they ever +have left it until they had pulled out a legitimate {200} reason. If the +tree had resisted all their efforts, they would have said, 'Ah! no wonder +now; the bark of a strong tree makes a strong man.' But if they had managed +to serve the tree as you would like to serve homoeopathy, then it would +have been 'We might have guessed it; all the _virtus roborativa_ has +settled in the bark.' They admitted, as we know from Moliere, the _virtus +dormitiva_[343] of opium, for no other reason than that opium _facit +dormire_.[344] Had the medicine not been previously _known_, they would, +strange as it may seem to modern pharmacopoeists, have accorded a _virtus +dormitiva_ to the new _facit dormire_. On this point they have been +misapprehended. They were prone to infer _facit_ from a _virtus_ imagined +_a priori_; and they were ready in supplying _facit_ in favor of an +orthodox _virtus_. They might have gone so far, for example, under +pre-notional impressions, as the alliterative allopath, who, when +maintenance of truth was busy opposing the progress of science called +_vaccination_, declared that some of its patients coughed like cows, and +bellowed like bulls; but they never refused to find _virtus_ when _facit_ +came upon them, no matter whence. They would rather have accepted Tenterden +steeple than have rejected the Goodwin Sands. They would have laughed their +modern imitators to scorn: but as they are not here, we do it for them. + +"The man of our day--the _a priori_ philosopher--tries the question whether +opium can cause sleep by finding out in the recesses of his own noddle +whether the drug can have a dormitive power: Well! but did not the +schoolman do the same? He did; but mark the distinction. The schoolman had +recourse to first principles, when there was no opium to try it by: our man +settles the point in the same way _with a lump of opium before him_. The +schoolman shifted his principles with his facts: the man of our +drawing-rooms will fight facts with his principles, just as an old {201} +physician would have done in actual practice, with the rod of his _Church_ +at his back. + +"The story about Galileo--which seems to have been either a joke made +against him, or by him--illustrates this. _Nature abhors a vacuum_ was the +explanation of the water rising in a pump: but they found that the water +would not rise more than 32 feet. They asked for explanation: what does the +satirist make the schoolmen say? That the stoppage is _not_ a fact, because +nature abhors a vacuum? No! but that the principle should be that nature +abhors a vacuum as far as 32 feet. And this is what would have been done. + +"There are still among us both priests and physicians who would have +belonged, had they lived three or four centuries ago, to the glorious band +of whom I have spoken, the majority of the intelligent, working well for +mankind out of the professional pursuit. But we have a great many who have +helped to abase their classes. Go where we may, we find specimens of the +lower orders of the ministry of religion and the ministry of health showing +themselves smaller than the small of other pursuits. And how is this? +First, because each profession is entered upon a mere working smack of its +knowledge, without any depth of education, general or professional. Not +that this is the whole explanation, nor in itself objectionable: the great +mass of the world must be tended, soul and body, by those who are neither +Hookers[345] nor Harveys[346]: let such persons not venture _ultra +crepidam_, and they are useful and respectable. But, secondly, there is a +vast upheaving of thought from the depths of commonplace learning. I am a +clergyman! Sir! I am a medical man! Sir! and forthwith the nature of things +is picked to pieces, and there is a race, with the last the winner, between +Philosophy mounted on Folly's donkey, and Folly mounted on Philosophy's +donkey. How fortunate {202} it is for Law that her battles are fought by +politicians in the Houses of Parliament. Not that it is better done: but +then _politics_ bears the blame." + +I now come to the medical review. After a quantity of remark which has been +already disposed of, the writer shows Greek learning, a field in which the +old physician would have had a little knowledge. A. B., for the joke's +sake, had left untranslated, as being too deep, a remarkably easy sentence +of Aristotle, to the effect that what has happened was possible, for if +impossible it would not have happened. The reviewer, in "simple +astonishment,"--it was simple--at the pretended incapacity--I was told by +A. B. that the joke was intended to draw out a reviewer--translates:--He +says that this sentence is A. B.'s summing up of the evidence of +Spiritualism. Now, being a sort of _alter ego_[347] of A. B., I do declare +that he is not such a fool as to rest the evidence of Spiritualism--the +_spirit explanation_--upon the occurrence of certain facts proving the +possibility of those very facts. In truth, A. B. refuses to receive +spiritualism, while he receives the facts: this is the gist of his whole +preface, which simply admits spiritualism among the qualified candidates, +and does not know what others there may be. + +The reviewer speaks of Aristotle as "that clear thinker and concise +writer." I strongly suspect that his knowledge of Aristotle was limited to +the single sentence which he had translated or got translated. Aristotle is +concise in _phrase_, not in book, and is powerful and profound in thought: +but no one who knows that his writing, all we have of him, is the very +opposite of clear, will pretend to decide that he thought clearly. As his +writing, so probably was his thought; and his books are, if not anything +but clear, at least anything good but clear. Nobody thinks them clear +except a person who always clears difficulties: which I have no doubt was +the reviewer's habit; that is, if he ever took the field {203} at all. The +gentleman who read Euclid, all except the As and Bs and the pictures of +scratches and scrawls, is the type of a numerous class. + +The reviewer finds that the word _amosgepotically_, used by A. B., is +utterly mysterious and incomprehensible. He hopes his translation of the +bit of Greek will shield him from imputation of ignorance: and thinks the +word may be referred to the "obscure dialect" out of which sprung +_aneroid_, _kalos geusis sauce_, and _Anaxyridian trousers_. To lump the +first two phrases with the third smacks of ignorance in a Greek critic; for +[Greek: anaxuridia], _breeches_, would have turned up in the lexicon; and +_kalos geusis_, though absurd, is not obscure. And [Greek: amosgepos], +_somehow or other_, is as easily found as [Greek: anaxuridia]. The word +_aneroid_, I admit, has puzzled better scholars than the critic: but never +one who knows the unscholarlike way in which words ending in [Greek: eides] +have been rendered. The _aneroid barometer_ does _not_ use a column of air +in the same way as the old instrument. Now [Greek: aeroeides]--properly +_like_ the atmosphere--is by scientific non-scholarship rendered having to +do with the atmosphere; and [Greek: anaeroeides]--say _anaeroid_--denies +having to do with the atmosphere; a nice thing to say of an instrument +which is to measure the weight of the atmosphere. One more absurdity, and +we have _aneroid_, and there you are. The critic ends with a declaration +that nothing in the book shakes his faith in a _Quarterly_ reviewer who +said that suspension of opinion, until further evidence arrives, is +justifiable: a strange summing up for an article which insists upon utter +rejection being unavoidable.[348] The expressed aim of both A. B. and C. D. +was to excite inquiry, and get further evidence: until this is done, +neither asks for a verdict. + +Oh where! and oh where! is old Medicine's learning gone! There _was_ some +in the days of yore, when Popery {204} was on! And it's oh! for some Greek, +just to find a word upon! The reviewer who, lexicon in hand, can neither +make out _anaxyridical_, _amosgepotical_, _kalos geusis_, nor distinguish +them from _aneroid_, cannot be trusted when he says he has translated a +sentence of Aristotle. He may have done it; but, as he says of +spiritualism, we must suspend our opinion until further evidence shall +arrive. + +We now come to the theological review. I have before alluded to the faults +of logic which are Protestant necessities: but I never said that Protestant +argument had _nothing but_ paralogism. The writer before me attains this +completeness: from beginning to end he is of that confusion and perversion +which, as applied to interpretation of the New Testament, is so common as +to pass unnoticed by sermon-hearers; but which, when applied out of church, +is exposed with laughter in all subjects except theology. I shall take one +instance, putting some words in italics. + +_A. B._ _Theological Critic._ + +My state of mind, which refers ... he proceeds to argue that +the whole _either_ to unseen he himself is outside its +intelligence, _or something sacred pale because he refers +which man has never had any all these strange phenomena to +conception of_, proves me to _unseen spiritual +be out of the pale of the intelligence_. +Royal Society. + +The possibility of a _yet unimagined_ cause is insisted on in several +places. On this ground it is argued by A. B. that spiritualists are +"incautious" for giving in at once to the spirit doctrine. But, it is said, +they may be justified by the philosophers, who make the flint _axes_, as +they call them, to be the works of men, because no one can see _what else +they can be_. This kind of adoption, _condemned_ as a conclusion, is +_approved_ as a provisional theory, suggestive of direction of inquiry: +experience having shown that {205} inquiry directed by a _wrong_ theory has +led to more good than inquiry without any theory at all. All this A. B. has +fully set forth, in several pages. On it the reviewer remarks that "with +infinite satisfaction he tries to justify his view of the case by urging +that there is no other way of accounting for it; after the fashion of the +philosophers of our own day, who conclude that certain flints found in the +drift are the work of men, because the geologist does not see what else +they can be." After this twist of meaning, the reviewer proceeds to say, +and A. B. would certainly join him, "There is no need to combat any such +mode of reasoning as this, because it would apply with equal force and +justice to any theory whatever, however fantastic, profane, or silly." And +so, having shown how the reviewer has hung himself, I leave him +funipendulous. + +One instance more, and I have done. A reviewer, not theological, speaking +of the common argument that things which are derided are not _therefore_ to +be rejected, writes as follows:--"It might as well be said that they who +laughed at Jenner[349] and vaccination were, in a certain but very +unsatisfactory way, witnesses to the possible excellence of the system of +St. John Long."[350] Of course it _might_: and of course it _is_ said by +all people of common sense. In introducing the word "possible," the +reviewer has hit the point: I suspect that this word was introduced during +revision, to put the sentence into fighting order; hurry preventing it +being seen that the sentence was thus made to fight on the wrong side. +Jenner, who was laughed at, was right; therefore, it is not +impossible--that is, it is _possible_--that a derided system may be right. +Mark the three gradations: _in medio tutissimus ibis_.[351] + +{206} + +_Reviewer._--If a system be derided, it is no ground of suspense that +derided systems have turned out true: if it were, you would suspend your +opinion about St. John Long on account of Jenner.--_Ans._ You ought to do +so, as to _possibility_; and _before examination_; not with the notion that +J. proves St. J. _probable_; only _possible_. + +_Common Sense._--The past emergence of truths out of derided systems proves +that there is a practical certainty of like occurrence to come. But, +inasmuch as a hundred speculative fooleries are started for one truth, the +mind is permitted to approach the examination of any one given novelty with +a bias against it of a hundred to one: and this permission is given because +so it will be, leave or no leave. Every one has licence not to jump over +the moon. + +_Paradoxer._--Great men have been derided, and I am derided: which proves +that my system ought to be adopted. This is a summary of all the degrees in +which paradoxers contend for the former derision of truths now established, +giving their systems _probability_. I annex a paragraph which D [e &c.] +inserted in the _Athenaeum_ of October 23, 1847. + +"_Discoverers and Discoveries._ + +"Aristotle once sent his servant to the cellar to fetch wine:--and the +fellow brought him back small beer. The Stagirite (who knew the difference) +called him a blockhead. 'Sir,' said the man, 'all I can say is, that I +found it in the cellar.' The philosopher muttered to himself that an +affirmative conclusion could not be proved in the second figure,--and Mrs. +Aristotle, who was by, was not less effective in her remark, that small +beer was not wine because it was in the same cellar. Both were right +enough: and our philosophers might take a lesson from either--for they +insinuate an affirmative conclusion in the second figure. Great discoverers +have been little valued by established {207} schools,--and they are little +valued. The results of true science are strange at first,--and so are +their's. Many great men have opposed existing notions,--and so do they. All +great men were obscure at first,--and they are obscure. Thinking men +doubt,--and they doubt. Their small beer, I grant, has come out of the same +cellar as the wine; but this is not enough. If they had let it stand awhile +in the old wine-casks, it might have imbibed a little of the flavor." + + + +There are better reviews than I have noticed; which, though entirely +dissenting, are unassailable on their own principles. What I have given +represents five-sixths of the whole. But it must be confessed that the +fraction of fairness and moderation and suspended opinion which the +doctrine of _Spirit Manifestations_ has met with--even in the lower +reviews--is strikingly large compared to what would have been the case +fifty years ago. It is to be hoped that our popular and periodical +literatures are giving us one thinker created for twenty geese +double-feathered: if this hope be realized, we shall do! Seeing all that I +see, I am not prepared to go the length of a friend of mine who, after +reading a good specimen of the lower reviewing, exclaimed--Oh! if all the +fools in the world could be rolled up into one fool, what a reviewer he +would make! + + + + Calendrier Universel et Perpetuel; par le Commandeur P. J. Arson.[352] + Publie par ses Enfans (Oeuvre posthume). Nice, 1863, 4to. + +I shall not give any account of this curious calendar, with all its changes +and symbols. But there is one proposal, which, could we alter the general +notions of time--a thing of very dubious possibility--would be convenient. +The week is made to wax and wane, culminating on the Sunday, {208} which +comes in the middle. Thursday, Friday, Saturday, are ascending or waxing +days; Monday, Tuesday, Wednesday, are descending or waning days. Our six +days, lumped together after the great distinguishing day, Sunday, are too +many to be distinctly thought of together: a division of three preceding +and three following the day of most note would be much more easily used. +But all this comes too late. It may be, nevertheless, that some individuals +may be able to adjust their affairs with advantage by referring Thursday, +Friday, Saturday, to the following Sunday, and Monday, Tuesday, Wednesday, +to the preceding Sunday. But M. Arson's proposal to alter the names of the +days is no more necessary than it is practicable. + + + +CYCLOMETRY. + +I am not to enter anything I do not possess. The reader therefore will not +learn from me the feats of many a man-at-arms in these subjects. He must be +content, unless he will bestir himself for himself, not to know how Mr. +Patrick Cody trisects the angle at Mullinavat, or Professor Recalcati +squares the circle at Milan. But this last is to be done by subscription, +at five francs a head: a banker is named who guarantees restitution if the +solution be not perfectly rigorous; the banker himself, I suppose, is the +judge. I have heard of a man of business who settled the circle in this +way: if it can be reduced to a debtor and creditor account, it can +certainly be done; if not, it is not worth doing. Montucla will give the +accounts of the lawsuits which wagers on the problem have produced in +France. + +Neither will I enter at length upon the success of the new squarer who +advertises (Nov. 1863) in a country paper that, having read that the +circular ratio was undetermined, "I thought it very strange that so many +great scholars in all ages should have failed in finding the true ratio, +and have been determined to try myself.... I am about to secure the {209} +benefit of the discovery, so until then the public cannot know my new and +true ratio." I have been informed that this trial makes the diameter to the +circumference as 64 to 201, giving [pi] = 3.140625 exactly. The result was +obtained by the discoverer in three weeks after he first heard of the +existence of the difficulty. This quadrator has since published a little +slip, and entered it at Stationers' Hall. He says he has done it by actual +measurement; and I hear from a private source that he uses a disk of 12 +inches diameter, which he rolls upon a straight rail. Mr. James Smith did +the same at one time; as did also his partisan at Bordeaux. We have, then, +both 3.125 and 3.140625, by actual measurement. The second result is more +than the first by about one part in 200. The second rolling is a very +creditable one; it is about as much below the mark as Archimedes was above +it. Its performer is a joiner, who evidently knows well what he is about +when he measures; he is not wrong by 1 in 3,000. + +The reader will smile at the quiet self-sufficiency with which "I have been +determined to try myself" follows the information that "so many great +scholars in all ages" have failed. It is an admirable spirit, when +accompanied by common sense and uncommon self-knowledge. When I was an +undergraduate there was a little attendant in the library who gave me the +following,--"As to cleaning this library, Sir, if I have spoken to the +Master once about it, I have spoken fifty times: but it is of no use; he +will not employ _littery_ men; and so I am obliged to look after it +myself." + +I do not think I have mentioned the bright form of quadrature in which a +square is made equal to a circle by making each side equal to a quarter of +the circumference. The last squarer of this kind whom I have seen figures +in the last number of the _Athenaeum_ for 1855: he says the thing is no +longer a _problem_, but an _axiom_. He does not know that the area of the +circle is greater than that of any other figure of the same circuit. This +any one might see without {210} mathematics. How is it possible that the +figure of greatest area should have any one length in its circuit unlike in +form to any other part of the same length? + +The feeling which tempts persons to this problem is that which, in romance, +made it impossible for a knight to pass a castle which belonged to a giant +or an enchanter. I once gave a lecture on the subject: a gentleman who was +introduced to it by what I said remarked, loud enough to be heard by all +around, "Only prove to me that it is impossible, and I will set about it +this very evening." + +This rinderpest of geometry cannot be cured, when once it has seated itself +in the system: all that can be done is to apply what the learned call +prophylactics to those who are yet sound. When once the virus gets into the +brain, the victim goes round the flame like a moth; first one way and then +the other, beginning where he ended, and ending where he begun: thus +verifying the old line + + "In girum imus nocte, ecce! et consumimur igni."[353] + +Every mathematician knows that scores of methods, differing altogether from +each other in process, all end in this mysterious 3.14159..., which insists +on calling itself the circumference to a unit of diameter. A reader who is +competent to follow processes of arithmetic may be easily satisfied that +such methods do actually exist. I will give a sketch, carried out to a few +figures, of three: the first two I never met with in my reading; the third +is the old method of Vieta.[354] [I find that both the first and second +methods are contained in a theorem of Euler.] + +What Mr. James Smith says of these methods is worth noting. He says I have +given three "_fancy_ proofs" of the value of [pi]: he evidently takes me to +be offering demonstration. He proceeds thus:-- + +"His first proof is traceable to the diameter of a circle {211} of radius +1. His second, to the side of any inscribed equilateral triangle to a +circle of radius 1. His third, to a radius of a circle of diameter 1. Now, +it may be frankly admitted that we can arrive at the same result by many +other modes of arithmetical calculation, all of which may be shown to have +some sort of relation to a circle; but, after all, these results are mere +exhibitions of the properties of numbers, and have no more to do with the +ratio of diameter to circumference in a circle than the price of sugar with +the mean height of spring tides. (_Corr._ Oct. 21, 1865)." + +I quote this because it is one of the few cases--other than absolute +assumption of the conclusion--in which Mr. Smith's conclusions would be +true if his premise were true. Had I given what follows as _proof_, it +would have been properly remarked, that I had only exhibited properties of +numbers. But I took care to tell my reader that I was only going to show +him _methods_ which end in 3.14159.... The proofs that these methods +establish the value of [pi] are for those who will read and can understand. + + 200000000 31415 3799 + 66666667 2817 + 26666667 1363 + 11428571 661 + 5079365 321 + 2308802 156 + 1065601 76 + 497281 37 + 234014 18 + 110849 9 + 52785 5 + 25245 2 + 12118 1 + 5834 + -------- -------- ------- + 314153799 31415 9265 + +{212} + +1. Take any diameter, double it, take 1-3d of that double, 2-5ths of the +last, 3-7ths of the last, 4-9ths of the last, 5-11ths of the last, and so +on. The sum of all is the circumference of that diameter. The preceding is +the process when the diameter is a hundred millions: the errors arising +from rejection of fractions being lessened by proceeding on a thousand +millions, and striking off one figure. Here 200 etc. is double of the +diameter; 666 etc. is 1-3rd of 200 etc.; 266 etc. is 2-5ths of 666 etc.; +114 etc. is 3-7ths of 266 etc.; 507 etc. is 4-9ths of 114 etc.; and so on. + +2. To the square root of 3 add its half. Take _half_ the third part of +this; half 2-5ths of the last; half 3-7ths of the last; and so on. The sum +is the circumference to a unit of diameter. + + Square root of 3.... 1.73205081 + .86602540 + ------------ + 2.59807621 + .43301270 + .08660254 + 1855768 + 412393 + 93726 + 21629 + 5047 + 1188 + 281 + 67 + 16 + 4 + 1 + ------------ + 3.14159265 + +3. Take the square root of 1/2; the square root of half of one more than +this; the square root of half of one more {213} than the last; and so on, +until we come as near to unity as the number of figures chosen will permit. +Multiply all the results together, and divide 2 by the product: the +quotient is an approximation to the circumference when the diameter is +unity. Taking aim at four figures, that is, working to five figures to +secure accuracy in the fourth, we have .70712 for the square root of 1/2; +.92390 for the square root of half one more than .70712; and so on, through +.98080, .99520, .99880, .99970, .99992, .99998. The product of the eight +results is .63667; divide 2 by this, and the quotient is 3.1413..., of +which four figures are correct. Had the product been .636363... instead of +.63667..., the famous result of Archimedes, 22-7ths, would have been +accurately true. It is singular that no cyclometer maintains that +Archimedes hit it exactly. + +A literary journal could hardly admit as much as the preceding, if it stood +alone. But in my present undertaking it passes as the halfpennyworth of +bread to many gallons of sack. Many more methods might be given, all ending +in the same result, let that result mean what it may. + +Now since dozens of methods, to which dozens more might be added at +pleasure, concur in giving one and the same result; and since these methods +are declared by all who have shown knowledge of mathematics to be +_demonstrated_: it is not asking too much of a person who has just a little +knowledge of the first elements that he should learn more, and put his hand +upon the error, before he intrudes his assertion of the existence of error +upon those who have given more time and attention to it than himself, and +who are in possession, over and above many demonstrations, of many +consequences verifying each other, of which he can know nothing. This is +all that is required. Let any one square the circle, and persuade his +friends, if he and they please: let him print, and let all read who choose. +But let him abstain from intruding himself upon those who have been +satisfied by existing demonstration, until he is prepared {214} to lay his +finger on the point in which existing demonstration is wrong. Let him also +say what this mysterious 3.14159... really is, which comes in at every door +and window, and down every chimney, calling itself the circumference to a +unit of diameter. This most impudent and successful impostor holds false +title-deeds in his hands, and invites examination: surely those who can +find out the rightful owner are equally able to detect the forgery. All the +quadrators are agreed that, be the right what it may, 3.14159... is wrong. +It would be well if they would put their heads together, and say what this +wrong result really means. The mathematicians of all ages have tried all +manner of processes, with one object in view, and by methods which are +admitted to yield demonstration in countless cases. They have all arrived +at one result. A large number of opponents unite in declaring this result +wrong, and all agree in two points: first, in differing among themselves; +secondly, in declining to point out what that curious result really is +which the mathematical methods all agree in giving. + +Most of the quadrators are not aware that it has been fully demonstrated +that no two numbers whatsoever can represent the ratio of the diameter to +the circumference with perfect accuracy. When therefore we are told that +either 8 to 25 or 64 to 201 is the true ratio, we know that it is no such +thing, without the necessity of examination. The point that is left open, +as not fully demonstrated to be impossible, is the _geometrical_ +quadrature, the determination of the circumference by the straight line and +circle, used as in Euclid. The general run of circle-squarers, hearing that +the quadrature is not pronounced to be _demonstratively_ impossible, +imagine that the _arithmetical_ quadrature is open to their ingenuity. +Before attempting the arithmetical problem, they ought to acquire knowledge +enough to read Lambert's[355] demonstration (last given in Brewster's[356] +translation {215} of Legendre's[357] Geometry) and, if they can, to refute +it. [It will be given in an Appendix.] Probably some have begun this way, +and have caught a Tartar who has refused to let them go: I have never heard +of any one who, in producing his own demonstration, has laid his finger on +the faulty part of Lambert's investigation. This is the answer to those who +think that the mathematicians treat the arithmetical squarers too lightly, +and that as some person may succeed at last, all attempts should be +examined. Those who have so thought, not knowing that there is +demonstration on the point, will probably admit that a person who +contradicts a theorem of which the demonstration has been acknowledged for +a century by all who have alluded to it as read by themselves, may +reasonably be required to point out the error before he demands attention +to his own result. + +_Apopempsis of the Tutelaries._--Again and again I am told that I spend too +much time and trouble upon my two tutelaries: but when I come to my +summing-up I shall make it appear that I have a purpose. Some say I am too +hard upon them: but this is quite a mistake. Both of them beat little +Oliver himself in the art and science of asking for more; but without +Oliver's excuse, for I had given good allowance. Both began with me, not I +with them: and both knew what they had to expect when they applied for a +second helping. + +On July 31, the Monday after the publication of my remarks on my 666 +correspondent, I found _three_ notes in separate envelopes, addressed to me +at "7A, University College." When I saw the three new digits I was taken +rhythmopoetic, as follows-- + + Here's the Doctor again with his figs, and by Heavens! + He was always at sixes, and now he's at sevens. + +To understand this fully the reader must know that the greater part of +Apocalyptic interpretation has long been condensed, in my mind, into the +Turkish street-cry--In the {216} name of the Prophet! figs! I make a few +extracts. The reader will observe that Dr. Thorn grumbles at his _private_ +letters being _publicly_ ridiculed. A man was summoned for a glutolactic +assault; he complained of the publication of his proceeding: I kicked etc. +_in confidence_, he said. + +"After reading your last, which tries in every way to hold me up to public +ridicule for daring to write you privately ['that you would be d----d,' +omitted by accident] one would say, Why have anything to do with such a +testy person? [Wrong word; no testy person can manage cool and consecutive +ridicule. Quaere, what is this word? Is it anything but a corruption of the +obsolete word _tetchy_ of the same meaning? Some think _touchy_ is our +modern form of _tetchy_, which I greatly doubt]. My answer is, the poor man +is lamentably ignorant; he is not only so, but 'out of the way' [quite +true; my readers know me by this time for an out-of-the-way person. What +other could tackle my squad of paradoxers? What other would undertake the +job?] Can he be brought back and form one of those who in Ezekiel 37 ch. +have the Spirit breathed into them and live.... Have I any other feeling +towards you except that of peace and goodwill? [Not to your distinct +knowledge; but in all those who send people to 'the other place' for +contempt of their interpretations, there is a lurking wish which is father +to the thought; 'you _will_ be d----d' and 'you _be_ d--d' are Siamese +twins]. Of course your sneer at 666 brought plain words; but when men +meddle with what they do not understand (not having the double _Vahu_) they +must be dealt with faithfully by those who do.... [They must; which +justifies the Budget of Paradoxes: but no occasion to send them anywhere; +no preachee and floggee too, as the negro said]. Many will find the text +Prov. i. 26 fully realized. [All this contains distinct assumption of a +right 'of course' to declare accursed those who do not respect the writer's +vagary].... If I could but get the [Hebrew: A], the Ox-head, which in Old +Hebrew was just the Latin Digamma, F, out {217} of your name, and could +then Thau you with the Thau of Ezekiel ix, 4, the [chi], then you would +bear the number of a man! But this is too hard for me, although not so for +the Lord! Jer. xxxii. 17.... And now a word: is ridicule the right thing in +so solemn a matter as the discussion of Holy Writ? [Is food for ridicule +the right thing? Did I discuss Holy Writ? I did not: I concussed profane +scribble. Even the Doctor did not _discuss_; he only enunciated and +denunciated out of the mass of inferences which a mystical head has found +premises for in the Bible]." + + M 40 + O 70 + R 100 + G 6 + N 50 + ---- + 266 + [Hebrew: t]=[chi] 400 + +[That ill opinions are near relations of ill wishes, will be detected by +those who are on the look out. The following was taken down in a Scotch +Church by Mr. Cobden,[358] who handed it to a Roman friend of mine, for his +delectation (in 1855): "Lord, we thank thee that thou hast brought the Pope +into trouble; and we pray that thou wouldst be mercifully pleased to +increase the same."] + +Here is a martyr who quarrels with his crown; a missionary who reviles his +persecutor: send him to New Zealand, and he would disagree with the Maoris +who ate him. Man of unilateral reciprocity! have you, who write to a +stranger with hints that that stranger and his wife are children of +perdition, the bad taste to complain of a facer in return? As James +Smith[359]--the Attorney-wit, not the Dock-cyclometer--said, or nearly +said, + + "A pretty thing, forsooth! + Is he to burn, all scalding hot, + Me and my wife, and am I not + To job him out a tooth?" + +{218} + +Those who think parody vulgar will be pleased to substitute for the above a +quotation from Butler[360]:-- + + "There's nothing so absurd or vain + Or barbarous or inhumane, + But if it lay the least pretence + To piety and godliness, + Or tender-hearted conscience, + And zeal for gospel truths profess,-- + Does sacred instantly commence, + And all that dare but question it are straight + Pronounced th' uncircumcised and reprobate, + As malefactors that escape and fly + Into a sanctuary for defence, + Must not be brought to justice thence, + Although their crimes be ne'er so great and high. + And he that dares presume to do't + Is sentenced and delivered up + To Satan that engaged him to't." + + + +THE NUMBER OF THE BEAST. + +Of all the drolleries of controversy none is more amusing than the manner +in which those who provoke a combat expect to lay down the laws of +retaliation. You must not strike this way! you must not parry that way! If +you don't take care, we shall never meddle with you again! We were not +_prepared_ for such as this! Why did we have anything to do with such a +testy person? M. Jourdain must needs show Nicole, his servant-maid, how +good a thing it was to be sure of fighting without being killed, by care +and tierce.[361] "Et cela n'est il pas beau d'etre assure de son fait quand +on se bat contre quelqu'un? La, pousse moi un peu, pour voir. NICOLE. Eh +bien! quoi? M. JOURDAIN. Tout beau. Hola! {219} Ho! doucement. Diantre soit +la coquine! NICOLE. Vous me dites de pousser. M. JOURDAIN. Oui; mais tu me +pousses en tierce, avant que de pousser en quarte, et tu n'as pas la +patience que je pare." + +His colleague, my secular tutelary, who also made an anachronistic onset, +with his repartees and his retorts, before there was anything to fire at, +takes what I give by way of subsequent provocation with a good humor which +would make a convert of me if he could afford .01659265 ... of a grain of +logic. He instantly sent me his photograph for the asking, and another +letter in proof. The Thor-hammerer does nothing but grumble, except when he +tells a good story, which he says he had from Dr. Abernethy.[362] A Mr. +James Dunlop was popping at the Papists with a 666-rifled gun, when Dr. +Chalmers[363] quietly said, "Why, Dunlop, you bear it yourself," and handed +him a paper on which the numerals in + + I A C O B V S D V N L O P V S + 1 100 5 500 5 50 5 + +were added up. This is almost as good as the _Filii Dei Vicarius_, the +numerical letters of which also make 666. No more of these crazy--I first +wrote _puerile_, but why should young cricketers be libelled?--attempts to +extract religious use from numerical vagaries, and to make God over all a +proposer of _salvation conundrums_: and no more of the trumpery hints about +future destiny which is too great a compliment to call blasphemous. If the +Doctor will cipher upon the letter in [Greek: en hoi metroi metreite +metrethesetai humin][364] with _double Vahu_ cubic measure, he will perhaps +learn to leave off trying to frighten me into gathering grapes from thorns. + +Mystical hermeneutics may be put to good use by out-of-the-way people. They +may be made to call the attention {220} of the many to a distinction well +known among the learned. The books of the New Testament have been for 1,500 +years divided into two classes: the _acknowledged_ ([Greek: +homologoumena]), which it has always been paradox not to receive; and the +_controverted_ ([Greek: antilegomena]), about which there has always been +that difference of opinion which no scholar overlooks, however he may +decide for himself after balance of evidence. Eusebius,[365] who first (l. +3, c. 25) recorded the distinction--which was much insisted on by the early +Protestants--states the books which are questioned as doubtful, but which +yet are approved and acknowledged by _many_--or _the many_, it is not easy +to say which he means--to be the Epistles of James and Jude, the second of +Peter and the second and third of John. In other places he speaks +doubtingly of the Epistle to the Hebrews. The Apocalypse he does not even +admit into this class, for he proceeds as follows--I use the second edition +of the English folio translation (1709), to avert suspicion of bias from +myself:-- + +"Among the _spurious_ [[Greek: nothoi]] let there be ranked both the work +entitled the _Acts of Paul_, and the book called _Pastor_, and the +_Revelation of Peter_: and moreover, that which is called the _Epistle of +Barnabas_, and that named the _Doctrines of the Apostles_: and moreover, as +I said, the _Revelation of John_ (if you think good), which some, as I have +said, do reject, but others allow of, and admit among those books which are +received as unquestionable and undoubted." + +Eusebius, though he will not admit the Apocalypse even into the +_controverted_ list, but gives permission to call it _spurious_, yet +qualifies his permission in a manner which almost annihilates the +distinctive force of [Greek: nothos], and gives the book a claim to rank +(if you think good, again) in the controverted list. And this is the +impression received by {221} the mind of Lardner, who gives Eusebius fully +and fairly, but when he sums up, considers his author as admitting the +Apocalypse into the second list. A stick may easily be found to beat the +father of ecclesiastical history. There are whole faggots in writers as +opposite as Baronius and Gibbon, who are perhaps his two most celebrated +sons. But we can hardly imagine him totally misrepresenting the state of +opinion of those for whom and among whom he wrote. The usual plan, that of +making an author take the views of his readers, is more easy in his case +than in that of any other writer: for, as the riddle says, he is +You-see-by-us; and to this reading of his name he has often been subjected. +Dr. Nathaniel Lardner,[366] who, though heterodox in doctrine, tries hard +to be orthodox as to the Canon, is "sometimes apt to think" that the list +should be collected and divided as in Eusebius. He would have no one of the +controverted books to be allowed, by itself, to establish any doctrine. +Even without going so far, a due use of early opinion and long continued +discussion would perhaps prevent rational people from being induced by +those who have the _double Vahu_ to place the Apocalypse _above_ the +Gospels, which all the Bivahuites do in effect, and some are said to have +done in express words. But my especial purpose is to point out that an easy +way of getting rid of 665 out of 666 of the mystics is to require them to +establish the Apocalypse before they begin. See if they even know so much +as that there is a crowd of testimonies for and against, running through +the first four centuries, which makes this book the most difficult of the +whole Canon. Try this method, and you will escape beautiful, as the French +say. Dean Alford,[367] in Vol. IV, p. 8, of his New Testament, gives an +elaborate handling of this question. He concludes by saying that he cannot +{222} venture to refuse his consent to the tradition that the Apostle is +the author. This modified adherence, or non-nonadherence, pretty well +represents the feeling of orthodox Protestants, when learning and common +sense come together. + +I have often, in former days, had the attempt made to place the Apocalypse +on my neck as containing prophecies yet unfulfilled. The preceding method +prevents success; and so does the following. It may almost be taken for +granted that theological system-fighters do not read the New Testament: +they hunt it for detached texts; they listen to it in church in that state +of quiescent nonentity which is called reverent attention: but they never +read it. When it is brought forward, you must pretend to find it necessary +to turn to the book itself: you must read "The revelation ... to show unto +his servants _things which must shortly come to pass_.... Blessed is he +that readeth ... _for the time is at hand_." You must then ask your mystic +whether things deferred for 1800 years were shortly to come to pass, etc.? +You must tell him that the Greek [Greek: en tachei], rendered "shortly," is +as strong a phrase as the language has to signify _soon_. The interpreter +will probably look as if he had never read this opening: the chances are +that he takes up the book to see whether you have been committing a fraud. +He will then give you some exquisite evasion: I have heard it pleaded that +the above was a _mere preamble_. This word _mere_ is all-sufficient: it +turns anything into nothing. Perhaps he will say that the argument is that +of the Papists: if so, tell him that there is no Christian sect but bears +true witness against some one or more absurdities in other sects. + +An anonyme suggests that [Greek: en tachei] may not be "soon," it may be +"quickly, without reference to time when:" he continues thus, "May not time +be 'at hand' when it is ready to come, no matter how long delayed?" I now +understand what *** and *** meant when they borrowed my books and promised +to return them quickly, it was "without {223} reference to time when." As +to time at _hand_--provided you make a long _arm_--I admire the quirk, but +cannot receive it: the word is [Greek: engus], which is a word of +_closeness_ in time, in place, in reckoning, in kindred, etc. + +Another gentleman is not surprised that Apocalyptic reading leads to a +doubt of the "canonicity" of the book: it ought not to rest on church +testimony, but on visible miracle. He offers me, or any reader of the +_Athenaeum_, the "sight of a miracle to that effect, and within forty-eight +hours' journey (fare paid)." I seldom travel, and my first thought was +whether my carpet-bag would be found without a regular hunt: but, on +reading further, I found that it was only a concordance that would be +wanted. Forty hours' collection and numerical calculation of Greek nouns +would make it--should I happen to agree with the writer--many hundred +millions to one that Revelation xiii is superhuman. There is but one verse +(the fifth) which the writer does not see verified. I looked at this verse, +and was much startled. The Budget began in October 1863: should it last +until March 1867--it is now August 1866--it is clear that I am the first +Beast, and my paradoxers are the saints whom I persecute. + +[The Budget _did_ terminate in March 1867: I hope the gentleman will be +satisfied with the resulting interpretation.] + +The same opponent is surprised that I should suppose a thing which "comes +to pass" must be completed, and cannot contain what is to happen 1800 years +after. All who have any knowledge of English idiom know that a thing +_comes_ to pass when it happens, and _came_ to pass afterwards. But as the +original is Greek, we must look at the Greek: it is [Greek: dei genesthai] +for "must come to pass," and we know that [Greek: egeneto] is what is +usually translated "came to pass." No word of more finished completion +exists in Greek. + +And now for a last round of biter-bit with the Thor-hammerer, of whom, as +in the other case, I shall take no {224} more notice until he can contrive +to surpass himself, which I doubt his being able to do. He informs me that +by changing A into [Hebrew: t] in my name he can make a 666 of _me_; +adding, "This is too hard for me, although not so for the Lord!" Sheer +nonsense! He could just as easily have directed to "Prof. De Morg[Hebrew: +t]n" as have assigned me apartment 7A in University College. It would have +been seen for whom it was intended: and if not, it would still have reached +me, for my colleagues have for many a year handed all out-of-the-way things +over to me. There is no 7A: but 7 is the Museum of Materia Medica. I took +the only hint which the address gave: I inquired for hellebore, but they +told me it was not now recognized, that the old notion of its value was +quite obsolete, and that they had nothing which was considered a specific +in senary or septenary cases. The great platitude is the reference of such +a difficulty as writing [Hebrew: t] for A to the Almighty! Not childish, +but fatuous: real childishness is delightful. I knew an infant to whom, +before he could speak plain, his parents had attempted to give notions of +the Divine attributes: a wise plan, many think. His father had dandled him +up-side-down, ending with, There now! Papa could not dance on his head! The +mannikin made a solemn face, and said, _But Dod tood_! I think the Doctor +has rather mistaken the way of becoming as a little child, intended in +Matt. xviii. 3: let us hope the will may be taken for the deed. + +Two poets have given images of transition from infancy to manhood: +Dryden,--for the Hind is Dryden himself on all fours! and Wordsworth, in +his own character of broad-nailed, featherless biped: + + "The priest continues what the nurse began, + And thus the child imposes on the man." + "The child's the father of the man, + And I could wish my days to be + Bound each to each by natural piety." + +{225} + +In Wordsworth's aspiration it is meant that sense and piety should grow +together: in Dryden's description a combination of Mysticism And Bigotry +(can this be the _double Vahu_?), personified as "the priest,"--who always +catches it on this score, though the same spirit is found in all +associations,--succeeds the boguey-teaching of the nurse. Never was the +contrast of smile and scowl, of light and darkness, better seen than in the +two pictures. But an acrostic distinction may be drawn. When mysticism +predominates over bigotry, we have the grotesque picturesque, and the +natural order of words gives us _Mab_, an appropriate suggestion. But when +bigotry has the upper hand, we see _Bam_, which is just as appropriate; for +bigotry nearly always deals with facts and logic so as to require the +application of at least one of the minor words by which dishonesty is +signified. I think that M is the Doctor's initial, and that Queen Mab +tickles him in his sleep with the sharp end of a 6. + +(_Monday, August 21._) Three weeks having elapsed without notice from me of +the Doctor, I receive a reminder of his existence, in which I find that as +I am the Daniel who judges the Magi of Babylon, it is to be pointed out +that Daniel "bore a certain number, that of a man (beloved), Daniel, ch. +10. v. 11, and which you certainly do not." Then, "by Greek power," +Belteshazzar is made = 666. Here is another awkward imitation of the way of +a baby child. When you have sported with the tiny creature until it runs +away offended, by the time you have got into conversation again you will +find the game is to be renewed: a little head peeps out from a hiding-place +with "I don't love you." The proper rejoinder is, "Very well! then I'll +have pussy." But in the case before me there is a rule of three sums to do; +as baby : Pussy Dr. :: 666 : the answer required. I will work it out, if I +can. + +The squaring of the circle and the discovery of the Beast are the two +goals--and goals also--of many unbalanced intellects, and of a few +instances of the better kind. {226} I might have said more of 666, but I am +not deep in its bibliography. A work has come into my hands which contains +a large number of noted cases: to some of my readers it will be a treat to +see the collection; and the sight will perhaps be of some use to those who +have read controversy on the few celebrated cases which are of general +notoriety. It is written by a learned decipherer, a man who really knew the +history of the subject, the Rev. David Thom,[368] of Bold Street Chapel, +Liverpool, who died, I am told, a few years ago. + +Anybody who reads his book will be inclined to parody a criticism which was +once made on Paley's[369] Evidences--"Well! if there be anything in +Christianity, this man is no fool." And, if he should chance to remember +it, he will be strongly reminded of a sentence in my opening chapter,--"The +manner in which a paradoxer will show himself, as to sense or nonsense, +will not depend upon what he maintains, but upon whether he has or has not +made a sufficient knowledge of what has been done by others, _especially as +to the mode of doing it_, a preliminary to inventing knowledge for +himself." And this is reinforced by the fact that Mr. Thom, though a +scholar, was not conspicuous for learning, except in this his great +pursuit. He was a paradoxer on other points. He reconciled Calvinism and +eternal reprobation with Universalism and final salvation; showing these +two doctrines to be all one. + +This gentleman must not be confounded with the Rev. John Hamilton Thom[370] +(no relation), at or near the same {227} time and until recently, of +Renshaw Street Chapel, Liverpool who was one of the minority in the +Liverpool controversy when, nearly thirty years ago, _three_ heretical +Unitarian schooners exchanged shotted sermons with _thirteen_ Orthodox +ships of the line, and put up their challengers' dander--an American +corruption of _d--d anger_--to such an extent, by quiet and respectful +argument, that those opponents actually addressed a printed intercession to +the Almighty for the Unitarian triad, as for "Jews, Turks, Infidels, and +Heretics." So much for the distinction, which both gentlemen would thank me +for making very clear: I take it quite for granted that a guesser at 666 +would feel horrified at being taken for a Unitarian, and that a Unitarian +would feel queerified at being taken for a guesser at 666. Mr. David Thom's +book is _The Number and Names of the Apocalyptic Beasts_, Part I, 1848, +8vo.: I think the second part was never published. I give the Greek and +Latin solutions, omitting the Hebrew: as usual, all the Greek letters are +numeral, but only M D C L X V I of the Latin. I do not give either the +decipherers or their reasons: I have not room for this; nor would I, if I +could, bias my reader for one rather than another. + +D. F. Julianus Caesar Atheus (or Aug.[371]); Diocles Augustus; Ludovicus; +Silvester Secundus; Linus Secundus; {228} Vicarius Filii Dei; Doctor et Rex +Latinus; Paulo V. Vice-Deo; Vicarius Generalis Dei in Terris; Ipse +Catholicae Ecclesiae Visibile Caput; Dux Cleri; Una, Vera, Catholica, +Infallibilis Ecclesia; Auctoritas politica ecclesiasticaque Papalis (Latina +will also do); Lutherus Ductor Gregis; Calvinus tristis fidei interpres; +Dic Lux ; Ludvvic; Will. Laud; [Greek: Lateinos];[372] [Greek: he latine +basileia]; [Greek: ekklesia italika]; [Greek: euanthas]; [Greek: teitan]; +[Greek: arnoume]; [Greek: lampetis]; [Greek: ho niketes]; [Greek: kakos +hodegos]; [Greek: alethes blaberos]; [Greek: palai baskanos]; [Greek: amnos +adikos]; [Greek: antemos]; [Greek: genserikos]; [Greek: euinas]; [Greek: +Benediktos]; [Greek: Bonibazios g. papa x. e. e. e. a.], meaning Boniface +III. Pope 68th, bishop of bishops the first! [Greek: oulpios]; [Greek: dios +eimi he heras]; [Greek: he missa he papike]; [Greek: loutherana]; [Greek: +saxoneios]; [Greek: Bezza antitheos] (Beza); [Greek: he alazoneia biou]; +[Greek: Maometis]; [Greek: Maometes b.]; [Greek: theos eimi epi gaies]; +[Greek: iapetos]; [Greek: papeiskos]; [Greek: dioklasianos]; [Greek: +cheina]; [Greek: braski]; [Greek: Ion Paune]; [Greek: koupoks]; (cowpox, +[Greek: s] being the _vau_; certainly the {229} vaccinated have the mark of +the Beast); [Greek: Bonneparte]; [Greek: N. Boneparte]; [Greek: euporia]; +[Greek: paradosis]; [Greek: to megatherion]. + +All sects fasten this number on their opponents. It is found in _Martin +Lauter_, affirmed to be the true way of writing the name, by carrying +numbers through the Roman Alphabet. Some Jews, according to Mr. Thorn, +found it in [Hebrew: JSHW NTSRJ] _Jesus of Nazareth_. I find on inquiry +that this satire was actually put forth by some medieval rabbis, but that +it is not idiomatic: it represents quite fairly "Jesus Nazarene," but the +Hebrew wants an article quite as much as the English wants "the." + +Mr. David Thom's own solution hits hard at all sides: he finds a 666 for +both beasts; [Greek: he phren] (the mind) for the first, and [Greek: +ekklesiai sarkikai] (fleshly churches) for the second. A solution which +embodies all mental philosophy in one beast and all dogmatic theology in +the other, is very tempting: for in these are the two great supports of +Antichrist. It will not, however, mislead me, who have known the true +explanation a long time. The three sixes indicate that any two of the three +subdivisions, Roman, Greek, and Protestant, are, in corruption of +Christianity, six of one and half a dozen of the other: the distinctions of +units, tens, hundreds, are nothing but the old way (1 Samuel xviii. 7, and +Concordance at _ten_, _hundred_, _thousand_) of symbolizing differences of +number in the subdivisions. + +It may be good to know that, even in speculations on 666, there are +different degrees of unreason. All the diviners, when they get a colleague +or an opponent, at once proceed to reckon him up: but some do it in play +and some in earnest. Mr. David Thom found a young gentleman of the name St. +Claire busy at the Beast number: he forthwith added the letters in [Greek: +st klaire] and found 666: this was good fun. But my spiritual tutelary, +when he found that he could not make a beast of me, except by changing +[Hebrew: A] into [Hebrew: T], solemnly referred the difficulty to the +Almighty: this was poor earnest. {230} + +I am glad I did not notice, in time to insert it in the _Athenaeum_, a very +remarkable paradoxer brought forward by Mr. Thom, his friend Mr. +Wapshare[373]: it is a little too strong for the general public. In the +_Athenaeum_ they would have seen and read it: but this book will be avoided +by the weaker brethren. It is as follows: + +"God, the Elohim, was six days in creating all things, and having made MAN +he entered into his rest. He is no more seen as a Creator, as Elohim, but +as Jehovah, the _Lord_ of the Sabbath, and the Spirit of life in MAN, which +Spirit worketh _sin in the flesh_; for the Spirit of Love, in all flesh, is +Lust, or the spirit of a beast, So Rom. vii. And which Spirit is +_crucified_ in the flesh. He then, as Jehovah--as the power of the Law, +_in_ and _over_ all flesh, John viii. 44--increases that which he has made +as the Elohim, and his power shall last for 6 days, or 6 periods of time, +computed at a millennium of years; and at the end of which six days, he who +is the Spirit of all flesh shall manifest himself as the Holy Spirit of +Almighty Love, and of all truth; and so shall the Church have her Sabbath +of Rest--all contention being at an end. This is, as well as I may now +express it, my solution of the mystery in Hebrew, and in Greek, and also in +Latin, IHS. For he that was lifted up _is_ King of the Jews, and is the +Lord of all Life, working in us, both to will and to do; as is manifest in +the Jews--they slaying him that his blood might be _good_ for the healing +of the nations, of all people and tongues. As the Father of all _natural_ +flesh, he is the Spirit of Lust, as in all _beasts_; as the Father, or King +of the Jews, he is the Devil, as he himself witnesseth in John viii., +already referred to. As lifted up, he is transformed into the Spirit of +Love, a light to the Gentiles, and the glory of his people Israel.... For +there is but ONE God, ONE Lord, ONE Spirit, ONE body, etc. and he who was +Satan, the Spirit of life in that body, is, in {231} Christ crucified, seen +in the Spirit that is in all, and through all and over all, God blessed for +ever." + +All this seems well meant, and Mr. Thom prints it as convinced of its +piety, and "pronounces no opinion." Mystics of all sorts! see what you may +come to, or what may come to you! I have inserted the above for your good. + +There is nothing in this world so steady as some of the paradoxers. They +are like the spiders who go on spinning after they have web enough to catch +all the flies in the neighborhood, if the flies would but come. They are +like the wild bees who go on making honey which they never can eat, proving +_sic vos non vobis_ to be a physical necessity of their own contriving. But +nobody robs their hives: no, unlike the bees, they go about offering their +ware to any who will take it as a gift. I had just written the last +sentence (Oct. 30, 1866, 8.45 A.M.) when in comes the second note received +this morning from Dr. Thorn: at 1.30 P.M. came in a third. These arise out +of the above account of the Rev. D. Thom, published Oct. 27: three notes +had arrived before. + +For curiosity I give one day's allowance, supposing these to be all: more +may arrive before night. + +29th Oct. 1866. + +"Dear Sir,-- + +In re [swastika].[374] + +"So that 'Zaphnath Paaneah' may be after all the revealer of the 'Northern +Tau' [Greek: Phaneroo]--To make manifest, shew, or explain; and this may +satisfy the House of Joseph in Amos 5^c. While Belteshazzar = 666 may be +also satisfactory to the House of David, and so we may have Zech. 10^c. +6^v. in operation when Ezekiel 37^c. 16^v. has been realised;--but there, +what is the use of writing, it is all Coptic {232} to a man who has not +[swastika], The Thau of the North, the double Vahu [Hebrew: W\qamats\W]. +Look at Jeremiah 3^c. 8^v. and then to Psalm 83 for 'hidden ones' [Hebrew: +TS\sheva\PW\dagesh\N\segol\Y Y\sheva\HW\qamats\H]--The Zephoni Jehovah, and +say whether they have any connection with the Zephon _Thau_. The Hammer of +Thor of Jeremiah 23^c. 29^v. as I gave you in No. 3 of my present edition. + +Yours truly + +LE CHEVALIER AU CIN." + +_By Greek Power._ + + C = 20 + H = 8 + E = 5 + V = 6 + A = 1 + L = 30 + I = 10 + E = 5 + R = 100 + + A = 1 + U = 400 + + C = 20 + I = 10 + N = 50 + ---- + 666 + +There will be thousands of Morgans who will be among the wise and prudent +of Hosea 14^c. 9^v. when the Seventh Angel sounds, let me number _that One_ +by Greek, Rev. 17^c. 1^v: {233} + + S = 200 + E = 5 + x V = 6 + E = 5 + N = 50 + T = 300 + H = 8 + + A = 1 + N = 50 + x G = 6 + E = 5 + L = 30 + ---- + 666 + + V and G = 12 ought to be equal to one Gammadion or ^3[swastika]3 x 4 = + 12, what say you? + +London, October 29, 1866. + +"Dear Sir,-- + +In re [swastika] versus [maltese cross]. + +However pretentious the X or [maltese cross] may be, and it is peculiarly +so just now in this land; after all it is only made of two Roman V's--and +so is only = [ one inverted](10)--and therefore is not the perfect number +12 of Revel^n, but is the mark of the goddess _Decima_! + +Yours truly + +WM. THORN." + +Had the _one_ who sent forth a pastoral (Romish) the other day, remained +amongst the faithful expectants, see how he would have numbered, whereas he +sold himself for the privilege of signing + +[maltese cross] HENRY E. MANNING.[375] + +{234} + +_By English Key._ + + H = 8 + E = 5 + N = 40 + R = 80 + Y = 140 + + E = 5 + D = 4 + W = 120 + A = 1 + R = 80 + D = 4 + + M = 30 + A = 1 + N = 40 + N = 40 + I = 9 + N = 40 + G = 7 + [swastika] = 12 + ---- + 666 + + Can you now understand the difference between [swastika] and [maltese + cross] or X? Look to my challenge. + +Cutting from newspaper:-- + +ITALY. + +Rome (_via_ Marseilles), October + +Mr. Gladstone has paid a visit to the Pope. + +_By Greek Power._ + + G = 6 + L = 30 + A = 1 + D = 4 + S = 200 + T = 300 + O = 70 + N = 50 + E = 5 + ---- + 666 + +And what then [swastika]? + +{235} + +In other letters _John Stuart Mill_ is 666 if the _a_ be left out; +_Chasuble_ is perfect. _John Brighte_[376] is a _fait accompli_; and I am +asked whether intellect can account for the final e. Very easily: this +Beast is not the M. P., but another person who spells his name differently. +But if John Sturt Mill and John Brighte choose so to write themselves, they +may. + +A curious collection; a mystical phantasmagoria! There are those who will +try to find meaning: there are those who will try to find purpose. + + "And some they said--What are you at? + And some--What are you arter?" + +My account of Mr. Thom and his 666 appeared on October 27: and on the 29th +I received from the editor a copy of Mr. Thom's sermons published in 1863 +(he died Feb. 27, 1862) with best wishes for my health and happiness. The +editor does not name himself in the book; but he signed his name in my +copy: and may my circumference never be more than 3-1/8 of my diameter if +the signature, name and writing both, were not that of my [circle square] +ing friend Mr. James Smith! And so I have come in contact with him on 666 +as well as on [pi]! I should have nothing left to live for, had I not +happened to hear that he has a perpetual motion on hand. I returned thanks +and kind regards: and Miss Miggs's words--"Here's forgivenesses of +injuries! here's amicablenesses!"--rang in my ears. But I was made slightly +uncomfortable: how could the war go on after this armistice? Could I ever +make it understood that the truce only extended to the double Vahu and +things thereunto relating? It was once held by seafaring men that there was +no peace with Spaniards beyond the line: I was determined that there must +be no concord with J. S. inside the circle; that this must be a special +exception, like Father Huddleston {236} and old Grouse in the gun-room. I +was not long in anxiety; twenty-four hours after the book of sermons there +came a copy of the threatened exposure--_The British Association in +Jeopardy, and Professor De Morgan in the Pillory without hope of escape_. +By James Smith, Esq. London and Liverpool, 8vo., 1866 (pp. 94). This +exposure consists of reprints from the _Athenaeum_ and _Correspondent_: of +things new there is but one. In a short preface Mr. J. S. particularly +recommends to "_read to the end_." At the end is an appendix of two pages, +in type as large as the work; a very prominent peroration. It is an article +from the _Athenaeum_, left out of its place. In the last sentence Mr. J. +Smith, who had asked whether his character as an honest Geometer and +Mathematician was not at stake, is warned against the _fallacia plurium +interrogationum_.[377] He is told that there is not a more honest +what's-his-name in the world: but that as to the counter which he calls his +character as a mathematician, he is assured that it has been staked years +ago, and lost. And thus truth has the last word. There is no occasion to +say much about reprints. One of them is a letter [that given above] of +August 25, 1865, written by Mr. J. S. to the _Correspondent_. It is one of +his quadratures; and the joke is that I am made to be the writer: it +appears as what Mr. J. S. hopes I shall have the sense to write in the +_Athenaeum_ and forestall him. When I saw myself thus quoted--yes! quoted! +double commas, first person--I felt as I suppose did Wm. Wilberforce[378] +when he set eyes on the affectionate benediction of the potato which +waggish comrades had imposed on a raw Irish reporter as part of his speech. +I felt as Martin[379] of {237} Galway--kind friend of the poor dumb +creatures!--when he was told that the newspapers had put him in Italics. "I +appeal to you, Mr. Speaker! I appeal to the House! Did I speak in Italics? +Do I ever speak in Italics?" I appeal to editor and readers, whether I ever +squared the circle until a week or two ago, when I gave my charitable mode +of reconciling the discrepant cyclometers. + +The absurdity of the imitation of symbolic reasoning is so lusciously rich, +that I shall insert it when I make up my final book. Somebody mastered +Spanish merely to read Don Quixote: it would be worth while to learn a +little algebra merely to enjoy this a b-istical attack on the windmills. +The principle is, Prove something in as roundabout a way as possible, +mention the circle once or twice irrelevantly in the course of your proof, +and then make an act of Q. E. D. in words at length. The following is +hardly caricature:-- + +To prove that 2 and 2 make 5. Let a = 2, b = 5: let c = 658, the number of +the House: let d = 666, the number of the Beast. Then of necessity d = a + +b + c + 1; so that 1 is a harmonious and logical quantification of the +number of which we are to take care. Now, b, the middle of our digital +system, is, by mathematical and geometrical combination, a mean between 5 + +1 and 2 + 2. Let 1 be removed to be taken care of, a thing no real +mathematician can refuse without serious injury to his mathematical and +geometrical reputation. It follows of necessity that 2 + 2 = 5, _quod erat +demonstrumhorrendum_. If Simpkin & Marshall have not, after my notice, to +account for a gross of copies more than would have gone off without me, the +world is not worthy of its James Smith! + +The only fault of the above is, that there is more {238} connection than in +the process of Faber Cyclometricus: so much, in fact, that the blunders are +visible. The utter irrelevance of premises to conclusion cannot be +exhibited with the requisite obscurity by any one who is able to follow +reasoning: it is high art displayed in a certain toning down of the _aegri +somnia_, which brings them to a certain look of reproach to reasoning which +I can only burlesque. Mr. J. S. produces something which resembles argument +much as a chimpanzee in dolor, because balked of his dinner, resembles a +thinking man at his studies. My humble attempt at imitation of him is more +like a monkey hanging by his tail from a tree and trying to crack a +cocoa-nut by his chatter. + +I could forgive Mr. J. S. anything, properly headed. I would allow him to +prove--_for himself_--that the Quadrature of the Circle is the child of a +private marriage between the Bull Unigenitus and the Pragmatic Sanction, +claiming tithe of onions for repeal of the Mortmain Act, before the Bishops +in Committee under the kitchen table: his mode of imitating reason would do +this with ease. But when he puts his imitation into my mouth, to make me +what _he_ calls a "real mathematician," my soul rises in epigram against +him. I say with the doll's dressmaker--such a job makes me feel like a +puppet's tailor myself--"He ought to have a little pepper? just a few +grains? I think the young man's tricks and manners make a claim upon his +friends for a little pepper?" De Faure[380] and Joseph Scaliger[381] come +into my head: my reader may look back for them. + + "Three circlesquarers to the manner born, + Switzerland, France, and England did adorn, + De Faure in equations did surpass, + Joseph at contradictions was an ass. + Groaned Folly, I'm used up! What shall I do + To make James Smith? Grinned Momus, _Join the two_!" + +{239} + +As to my _locus poenitentiae_,[382] the reader who is fit to enjoy the +letter I have already alluded to will see that I have a soft and easy +position; that the thing is really a _pillowry_; and that I am, like +Perrette's pot of milk, + + "Bien pose sur un coussinet."[383] + +Joanna Southcott[384] never had a follower who believed in her with more +humble piety than Mr. James Smith believes in himself. After all that has +happened to him, he asks me with high confidence to "favor the writer with +a proof" that I still continue of opinion that "the best of the argument is +in my jokes, and the best of the joke is in his arguments." I will not so +favor him. At the very outset I told him in plain English that he has the +whiphand of all the reasoners in the world, and in plain French that _il a +perdu le droit d'etre frappe de l'evidence_[385]; I might have said +_pendu_.[386] To which I now add, in plain Latin, _Sapienti pauca, indocto +nihil_.[387] The law of Chancery says that he who will have equity must do +equity: the law of reasoning says that he who will have proof must see +proof. + +The introduction of things quite irrelevant, by way of reproach, is an +argument in universal request: and it often happens that the argument so +produced really tells against the producer. So common is it that we forget +how boyish it is; but we are strikingly reminded when it actually comes +from a boy. In a certain police court, certain small boys were arraigned +for conspiring to hoot an obnoxious individual on his way from one of their +school exhibitions. This proceeding was necessary, because there seemed to +be a permanent conspiracy to annoy the gentleman; and the {240} masters did +not feel able to interfere in what took place outside the school. So the +boys were arraigned; and their friends, as silly in their way as +themselves, allowed one of them to make the defence, instead of employing +counsel; and did not even give them any useful hints. The defence was as +follows; and any one who does not see how richly it sets off the defences +of bigger boys in bigger matters has much to learn. The innocent conviction +that there was answer in the latter part is delightful. Of course fine and +recognizance followed. + +A---- said the boys had received great provocation from B----. He was +constantly threatening them with a horsewhip which he carried in his hand +[the boy did not say what had passed to induce him to take such a weapon], +and he had repeatedly insulted the master, which the boys could not stand. +B---- had in his own drawing-room told him (A----) that he had drawn his +sword against the master and thrown away the scabbard. B---- knew well that +if he came to the college he would catch it, and then he went off through a +side door--which was no sign of pluck; and then he brought Mrs. B---- with +him, thinking that her presence would protect him. + +My readers may expect a word on Mr. Thom's sermons, after my account of his +queer doings about 666. He is evidently an honest and devout man, much +wanting in discrimination. He has a sermon about private _judgment_, in +which he halts between the logical and legal meanings of the word. He +loathes those who apply their private judgment to the word of God: here he +means those who decide what it _ought to be_. He seems in other places +aware that the theological phrase means taking right to determine what it +_is_. He uses his own private judgment very freely, and is strong in the +conclusion that others ought not to use theirs except as he tells them how; +he leaves all the rest of mankind free to think with him. In this he is not +original: his fame must rest on his senary tripod. {241} + + + +JAMES SMITH ONCE MORE. + +Mr. James Smith's procedures are not caricature of reasoning; they are +caricature of blundering. The old way of proving that 2 = 1 is solemn +earnest compared with his demonstrations. As follows:[388] + + Let x = 1 + Then x^2 = x + And x^2 - 1 = x - 1 + Divide both sides by x - 1; then x + 1 = 1; but x = 1, whence 2 = 1. + +When a man is regularly snubbed, bullied, blown up, walked into, and put +down, there is usually some reaction in his favor, a kind of deostracism, +which cannot bear to hear him always called the blunderer. I hope it will +be so in this case. There is nothing I more desire than to see _sects_ of +paradoxers. There are fully five thousand adults in England who ought to be +the followers of some one false quadrature. And I have most hope of 3-1/8, +because I think Mr. James Smith better fitted to be the leader of an +organized infatuation than any one I know of. He wants no pity, and will +get none. He has energy, means, good humor, strong conviction, character, +and popularity in his own circle. And, most indispensable point of all, he +sticks at nothing; + + "In coelum jusseris, ibit."[389] + +When my instructor found I did not print an acceptance of what I have +quoted, he addressed me as follows (_Corr._, Sept 23):-- + +"In this life, however, we must do our duty, and, when {242} necessary, use +the rod, not in a spirit of revenge, but for the benefit of the culprit and +the good of society. Now, Sir, the opportunity has been thrown in your way +of slipping out of the pillory without risk of serious injury; but, like an +obstinate urchin, you have chosen to quarrel with your opportunity and +remain there, and thus you compel me to deal with you as schoolmasters used +to do with stupid boys in bygone days--that is to say, you force me to the +use of the critic's rod, compel me to put you where little Jack Horner sat, +and, as a warning to other naughty boys, to ornament you with a dunce's +cap. The task I set you was a very simple one, as I shall make manifest at +the proper time." + +In one or more places, as well as this, Mr. Smith shows that he does not +know the legend of little Jack Horner, whom he imagines to be put in the +corner as a bad boy. This is curious; for there had been many allusions to +the story in the journal he was writing in, and the Christmas pie had +become altered into the Seaforth [pi]. + +Mr. Smith is satisfied at last that--what between argument and punishment +he has convinced me. He says (_Corr._, Jan. 27, 1866): "I tell him without +hesitation that he knows the true ratio of diameter to circumference as +well as I do, and if he be wise he will admit it." I should hope I do, and +better; but there is no occasion to admit what everybody knows. + +I have often wished that we could have a slight glimpse of the reception +which was given to some of the old cyclometers: but we have nothing, except +the grave disapprobation of historians. I am resolved to give the New +Zealander a chance of knowing a little more than this about one of them at +least; and, by the fortunate entrance into life of the _Correspondent_, I +am able to do it. I omit sober mathematical answers, of which there were +several. The following letter is grave earnest: + +"Sir,--I have watched Mr. James Smith's writings on this subject from the +first, and I did hope that, as the more {243} he departs from truth the +more easy it must be to refute him, [this by no means always true] some of +your correspondents would by this time have done so. I own that I am unable +to detect the fallacy of his argument; and I am quite certain that '[Pi]' +is wrong, in No. 23, where he declares that Mr. Smith is 'ignorant of the +very elements of mathematical truth.' I have observed an immense amount of +geometrical reasoning on his part, and I cannot see that it is either fair +or honest to deny this, which may be regarded as the 'elements' of +mathematical truth. Would it not be better for '[Pi]' to answer Mr. Smith, +to refute his arguments, to point out their fallacies, and to save learners +from error, than to plunge into gross insult and unmanly abuse? Would it +not be well, also, that Professor De Morgan should favour us with a little +reasoning? + +"I have hitherto seen no attempt to overthrow Mr. Smith's arguments; I +trust that this will not continue, since the subject is one of immense +importance to science in general, especially to nautical science, and all +that thereto belongs. + +Yours, etc., + +A CAPTAIN, R.N." + +On looking at this homoeopathic treatment of the 3-1/8 +quadrature--remember, homoeopathic, _similia similibus_,[390] not +infinitesimal--and at the imputation thrown upon it, I asked myself, what +_is_ vulgarity? No two agree, except in this, that every one sees vulgarity +in what is directed against himself. Mark the world, and see if anything be +so common as the description of the other side's remarks as "vulgar attempt +at wit." "I suppose you think that very witty:" the answer is "No my +friend! your remark shows that you feel it as wit, so that the purpose is +answered; I keep my razor for something else than cutting blocks;" I am +inclined to think that "out of place" is a necessary attribute of true +vulgarity. And further, it is to be noticed that nothing is {244} +unproducible--_salvo pudore_[391]--which has classical authority, modern or +ancient, in its favor. "He is a vulgar fellow; I asked him what he was +upon, and what do you think he answered, My legs!"--"Well, and has he not +justification? what do you find in Terence? _Quid agitur? Statur._"[392] I +do not even blench from my principle where I find that it brings what is +called "taking a sight" within permissible forms of expression: Rabelais +not only establishes its antiquity, but makes it English. Our old +translation[393] has it thus (book 2. ch. 19): + +"Then made the Englishman this sign. His left hand, all open, he lifted up +into the air, then instantly shut into his fist the four fingers thereof; +and his thumb extended at length he placed upon the tip of his nose. +Presently after he lifted up his right hand all open and abased and bent it +downwards, putting the thumb thereof in the very place where the little +finger of the left hand did close in the fist, and the four right hand +fingers he softly moved in the air. Then contrarily he did with the right +hand what he had done with the left, and with the left what he had done +with the right." + +An impressive sight! The making of a fist of the left hand is a great +addition of power, and should be followed in modern practice. The gentle +sullation of the front fingers, with the clenched fist behind them, says as +plainly as possible, Put _suaviter in modo_ in the van, but don't forget to +have _fortiter in re_[394] in the rear. + +{245} + +My Budget was announced (March 23, 1867) for completion on the 30th. Mr. +James Smith wrote five letters, one before the completion, four after it; +the five contained 68 pages of quarto letter paper. Mr. J. S. had picked up +a clerical correspondent, with whom he was in the heat of battle. + +"_March 27._--Dear Sir. Very truly yours. Duty; for my own sake; just time +left to retrieve my errors; sends copy of letter to clergyman; new proof +never before thought of; merest tyro would laugh if I were to stifle it, +whether by rhodomontade or silent contempt; keep your temper. I shall be +convinced; and if world be right in supposing me incapable of a foul act, I +shall proclaim glorious discovery in the _Athenaeum_. + +"_April 15._--Sir,... My dear Sir, Your sincere tutelary. Copy of another +letter to clergyman; discovery tested by logarithms; reasons such as none +but a knave or a sinner can resist. Let me advise you to take counsel +before it is too late! Keep your temper. Let not your _pride_ get the +better of your discretion! Screw up your courage, my good friend, and +_resolve_ to show the world that you are an _honest_ man.... + +"_April 20._--Sir ... Your very sincere and favorite tutelary. I have long +played the _cur_, snapping and snarling...; suddenly lost my power, and +became _half-starved_ dog without _spirit_ to bark; try if air cannot +restore me; calls himself the _thistle_ in allusion to my other tutelary, +the _thorn_; Would I prefer his next work to be, 'A whip for the +Mathematical Cur, Prof. De M.' In some previous letter which I have +mislaid, he told me his next would be 'a muzzle for the Mathematical Bull +dog, Prof. De M.' + +"_April 23._--Sir. Very sincerely yours. More letters to clergyman; you may +as well knock your head against a stone wall to improve your intellect as +attempt to controvert my proofs. [I thought so too; and tried neither]. +{246} + +"_May 6._--My dear Sir. Very sincerely yours. All to myself, and nothing to +note. + +"_July 2._--No more in this interval. All that precedes is a desperate +attempt to induce me to continue my descriptions: notoriety at any price." + +I dare say the matter is finished: the record of so marked an instance of +self-delusion will be useful. + +I append to the foregoing a letter from Dr. Whewell[395] to Mr. James +Smith. The Master of Trinity was conspicuous as a rough customer, an +intellectual bully, an overbearing disputant: the character was as well +established as that of Sam Johnson. But there was a marked difference. It +was said of Johnson that if his pistol missed fire, he would knock you down +with the butt end of it: but Whewell, in like case, always acknowledged the +miss, and loaded again or not, as the case might be. He reminded me of +Dennis Brulgruddery, who says to Dan, Pacify me with a good reason, and +you'll find me a dutiful master. I knew him from the time when he was my +teacher at Cambridge, more than forty years. As a teacher, he was anything +but dictatorial, and he was perfectly accessible to proposal of objections. +He came in contact with me in his slashing way twice in our after joint +lives, and on both occasions he acknowledged himself overcome, by that +change of manner, and apologetic mode of continuance, which I had seen him +employ towards others under like circumstances. + +I had expressed my wish to have a _thermometer of probability_, with +impossibility at one end, as 2 and 2 make 5, and necessity at the other, as +2 and 2 make 4, and a graduated rise of examples between them. Down came a +blow: "What! put necessary and contingent propositions together! It's +absurd!" I pointed out that the two kinds of necessity are but such +extremes of probability as 0 and [infinity] are of number, and illustrated +by an urn with 1 white and _n_ black {247} balls, _n_ increasing without +limit. It was frankly seen, and the point yielded; a large company was +present. + +Again, in a large party, after dinner, and politics being the subject, I +was proceeding, in discussion with Mr. Whewell, with "I think"...--"Ugh! +_you_ think!" was the answer. I repeated my phrase, and gave as a reason +the words which Lord Grey[396] had used in the House of Lords the night +before (the celebrated advice to the Bishops to set their houses in order). +He had not heard of this, and his manner changed in an instant: he was the +rational discutient all the rest of the evening, having previously been +nothing but a disputant with all the distinctions strongly marked. + +I have said that Whewell was gentle with his pupils; it was the same with +all who wanted teaching: it was only on an armed enemy that he drew his +weapon. The letter which he wrote to Mr. J. Smith is an instance: and as it +applies with perfect fidelity to the efforts of unreasoning above +described, I give it here. Mr. James Smith is skilfully exposed, and felt +it; as is proved by "putting the writer in the stocks." + +"The Lodge, Cambridge, September 14th, 1862. + +"Sir,--I have received your explanation of your proposition that the +circumference of the circle is to its diameter as 25 to 8. I am afraid I +shall disappoint you by saying that I see no force in your proof: and I +should hope that you will see that there is no force in it if you consider +this: In the whole course of the proof, though the word cycle occurs, there +is no property of the circle employed. You may do this: you may put the +word _hexagon_ or _dodecagon_, or any other word describing a polygon in +the place of _Circle_ in your proof, and the proof would be just as good as +before. Does not this satisfy you that you cannot have proved a property of +that special figure--a circle? {248} + +"Or you may do this: calculate the side of a polygon of 24 sides inscribed +in a circle. I think you are a Mathematician enough to do this. You will +find that if the radius of the circle be one, the side of this polygon is +.264 etc. Now, the arc which this side subtends is according to your +proposition 3.125/12 = .2604, and therefore the chord is greater than its +arc, which you will allow is impossible. + +"I shall be glad if these arguments satisfy you, and + +"I am, Sir, your obedient Servant, + +"W. WHEWELL." + + + +AN M.P.'S ARITHMETIC. + +In the debate of May, 1866, on Electoral Qualifications, a question arose +about arithmetical capability. Mr. Gladstone asked how many members of the +House could divide 1330l. 7s. 6d. by 2l. 13s. 8d. Six hundred and +fifty-eight, answered one member; the thing cannot be done, answered +another. There is an old paradox to which this relates: it arises out of +the ignorance of the distinction between abstract and concrete arithmetic. +_Magnitude_ may be divided by _magnitude_; and the answer is number: how +often does 12d. contain 4d.; answer three times. _Magnitude_ may be divided +by _number_, and the answer is _magnitude_: 12d. is divided in four equal +parts, what is each part? Answer three _pence_. The honorable objector, +whose name I suppress, trusting that he has mended his ways, gave the +following utterance: + +"With regard to the division sum, it was quite possible to divide by a sum, +but not by money. How could any one divide money by 2l. 16s. 8d.? +(Laughter.) The question might be asked, 'How many times 2s. will go into +1l.?' but that was not dividing by money; it was simply dividing 20 by 2. +He might be asked, 'How many times will 6s. 8d. go into a pound?' but it +was only required to divide 240 by 80. If the right hon. gentleman were to +ask the hon. {249} member for Brighton (Professor Fawcett),[397] or any +other authority, he would receive the same answer--viz., that it was +possible to divide by a sum, but not by money. (Hear.)" + +I shall leave all comment for the second edition, if I publish one.[398] I +shall be sure to have something to laugh at. Anything said from a +respectable quarter, or supposed to be said, is sure to find defenders. Sam +Johnson, a sound arithmetician, comparing himself, and what he alone had +done in three years, with forty French Academicians and their forty years, +said it proved that an Englishman is to a Frenchman as 40 x 40 to 3, or as +1600 to 3. Boswell, who was no great hand at arithmetic, made him say that +an Englishman is to a Frenchman as 3 to 1600. When I pointed this out, the +supposed Johnson was defended through thick and thin in _Notes and +Queries_. + +I am now curious to see whether the following will find a palliator. It is +from "Tristram Shandy," book V. chapter 3. There are two curious idioms, +"for for" and "half in half"; but these have nothing to do with my point: + +"A blessing which tied up my father's tongue, and a misfortune which set it +loose with a good grace, were pretty equal: sometimes, indeed, the +misfortune was the better of the two; for, for instance, where the pleasure +of harangue was as _ten_, and the pain of the misfortune but as _five_, my +father gained half in half; and consequently was as well again off as if it +had never befallen him." + +This is a jolly confusion of ideas; and wants nothing but a defender to +make it perfect. A person who invests five {250} with a return of ten, and +one who loses five with one hand and gains ten with the other, both leave +off five richer than they began, no doubt. The first gains "half in half," +more properly "half _on_ half," that is, of the return, 10, the second 5 is +gain upon the first 5 invested. "Half _in_ half" is a queer way of saying +cent. per cent. If the 5l. invested be all the man had in the world, he +comes out, after the gain, twice as well off as he began, with reference to +his whole fortune. But it is very odd to say that balance of 5l. gain is +_twice_ as good as if nothing had befallen, either loss or gain. A +mathematician thinks 5 an infinite number of times as great as 0. The whole +confusion is not so apparent when money is in question: for money is money +whether gained or lost. But though pleasure and pain stand to one another +in the same algebraical relation as money gained and lost, yet there is +more than algebra can take account of in the difference. + +Next, Ri. Milward[399] (Richard, no doubt, but it cannot be proved) who +published Selden's[400] Table Talk, which he had collected while serving as +amanuensis, makes Selden say, "A subsidy was counted the fifth part of a +man's estate; and so fifty subsidies is five and forty times more than a +man is worth." For _times_ read _subsidies_, which seems part of the +confusion, and there remains the making all the subsidies equal to the +first, though the whole of which they are to be the fifths is perpetually +diminished. + +Thirdly, there is the confusion of the great misomath {251} of our own day, +who discovered two quantities which he avers to be identically the same, +but the greater the one the less the other. He had a truth in his mind, +which his notions of quantity were inadequate to clothe in language. This +erroneous phraseology has not found a defender; and I am almost inclined to +say, with Falstaff, The poor abuses of the time want countenance. + + + +ERRONEOUS ARITHMETICAL NOTIONS. + +"Shallow numerists," as Cocker[401] is made to call them, have long been at +work upon the question how to _multiply_ money by money. It is, I have +observed, a very common way of amusing the tedium of a sea voyage: I have +had more than one bet referred to me. Because an oblong of five inches by +four inches contains 5 x 4 or 20 _square_ inches, people say that five +inches multiplied by four inches _is_ twenty _square_ inches: and, thinking +that they have multiplied length by length, they stare when they are told +that money cannot be multiplied by money. One of my betters made it an +argument for the thing being impossible, that there is no _square money_: +what could I do but suggest that postage-stamps should be made legal +tender. Multiplication must be _repetition_: the repeating process must be +indicated by _number_ of times. I once had difficulty in persuading another +of my betters that if you repeat five shillings as often as there are hairs +in a horse's tail, you do not _multiply five shillings by a +horsetail_.[402] + +I am very sorry to say that these wrong notions have found support--I think +they do so no longer--in the University of Cambridge. In 1856 or 1857, an +examiner was displaced by a vote of the Senate. The pretext was that he was +too severe an examiner: but it was well known that {252} great +dissatisfaction had been expressed, far and wide through the Colleges, at +an absurd question which he had given. He actually proposed such a fraction +as + + 6s. 3d. + --------. + 17s. 4d. + +As common sense gained a hearing very soon, there is no occasion to say +more. In 1858, it was proposed at a college examination, to divide 22557 +days, 20 hours, 20 minutes, 48 seconds, by 57 minutes, 12 seconds, and also +to explain the fraction + + 32l. 18s. 8d. + -------------. + 62l. 12s. 9d. + +All paradoxy, in matters of demonstration, arises out of muddle about first +principles. Who can say how much of it is to be laid at the door of the +University of Cambridge, for not taking care of the elements of +arithmetical thought? + + + +ON LITERARY BARGAINS. + +The phenomena of the two ends of society, when brought together, give +interesting comparisons: I mean the early beginnings of thought and +literature, and our own high and finished state, as we think it. There is +one very remarkable point. In the early day, the letter was matter of the +closest adherence, and implied meanings were not admitted. + +The blessing of Isaac meant for Esau, went to false Jacob, in spite of the +imposition; and the writer of Genesis seems to intend to give the notion +that Isaac had no power to pronounce it null and void. And "Jacob's policy, +whereby he became rich"--as the chapter-heading puts it--in speckled and +spotted stock, is not considered as a violation of the agreement, which +contemplated natural proportions. In {253} the story of Lycurgus the +lawgiver is held to have behaved fairly when he bound the Spartans to obey +his laws until he returned--intimating a short absence--he intending never +to return. And Vishnoo, when he asked the usurper for three steps of +territory as a dwarf, and then enlarged himself until he could bring heaven +and earth under the bargain, was thought clever, certainly, but quite fair. + +There is nothing of this kind recognized in our day: so far good. But there +is a bad contrary: the age is apt, in interpretation, to upset the letter +in favor of the view--very often the after thought--of one side only. The +case of John Palmer,[403] the improver of the mail coach system, is +smothered. He was to have an office and a salary, and 2-1/2 per cent for +life on the increased _revenue_ of the Post-Office. His rights turned out +so large, that Government would not pay them. For misconduct, real or +pretended, they turned him out of his _office_: but his bargain as to the +percentage had nothing to do with his future conduct; it was payment for +his _plan_. I know nothing, except from the debates of 1808 in the two +Houses: if any one can redeem the credit of the nation, the field is open. +When I was young, the old stagers spoke of this transaction sparingly, and +dismissed it speedily. + +The government did not choose to remember what private persons must +remember, and are made to remember, if needful. When Dr. Lardner[404] made +his bargain with the {254} publishers for the _Cabinet Cyclopaedia_ he +proposed that he, as editor, should have a certain sum for every hundred +sold above a certain number: the publishers, who did not think there was +any chance of reaching the turning sale of this stipulation, readily +consented. But it turned out that Dr. Lardner saw further than they: the +returns under this stipulation gave him a very handsome addition to his +other receipts. The publishers stared; but they paid. They had no idea of +standing out that the amount was too much for an editor; they knew that, +though the editor had a percentage, they had all the rest; and they would +not have felt aggrieved if he had received ten times as much. But +governments, which cannot be brought to book before a sworn jury, are ruled +only by public opinion. John Palmer's day was also the day of Thomas Fyshe +Palmer,[405] and the governments, in their prosecutions for sedition, knew +that these would have a reflex action upon the minds of all who wrote about +public affairs. + + + +DECLARATION OF BELIEF + +1864-65.--It often happens that persons combine to maintain and enforce an +opinion; but it is, in our state of society, a paradox to unite for the +sole purpose of blaming the opposite side. To invite educated men to do +this, and above all, men of learning or science, is the next paradoxical +thing of all. But this was done by a small combination in 1864. They got +together and drew up a _declaration_, to be signed by "students of the +natural sciences," who were to express their "sincere regret that +researches into {255} scientific truth are perverted by some in our own +times into occasion for casting doubt upon the truth and authenticity of +the Holy Scriptures." In words of ambiguous sophistry, they proceeded to +request, in effect, that people would be pleased to adopt the views of +churches as to the _complete_ inspiration of all the canonical books. The +great question whether the Word of God is _in_ the Bible, or whether the +Word of God is _all_ the Bible, was quietly taken for granted in favor of +the second view; to the end that men of science might be induced to blame +those who took the first view. The first public attention was drawn to the +subject by Sir John Herschel,[406] who in refusing to sign the writ sent to +him, administered a rebuke in the _Athenaeum_, which would have opened most +eyes to see that the case was hopeless. The words of a man whose _suaviter +in modo_ makes his _fortiter in re_[407] cut blocks with a razor are worth +preserving: + +"I consider the act of calling upon me publicly to avow or disavow, to +approve or disapprove, in writing, any religious doctrine or statement, +however carefully or cautiously drawn up (in other words, to append my name +to a religious manifesto) to be an infringement of that social forbearance +which guards the freedom of religious opinion in this country with especial +sanctity.... I consider this movement simply mischievous, having a direct +tendency (by putting forward a new Shibboleth, a new verbal test of +religious partisanship) to add a fresh element of discord to the already +too discordant relations of the Christian world.... But no nicety of +wording, no artifice of human language, will suffice to discriminate the +hundredth part of the shades of meaning in which the most world-wide +differences of thought on such subjects may be involved; or prevent the +most gentle worded and apparently justifiable expression of regret, so +embodied, from grating on the {256} feelings of thousands of estimable and +well-intentioned men with all the harshness of controversial hostility." + +Other doses were administered by Sir J. Bowring,[408] Sir W. Rowan +Hamilton,[409] and myself. The signed declaration was promised for +Christmas, 1864: but nothing presentable was then ready; and it was near +Midsummer, 1865, before it was published. Persons often incautiously put +their names without seeing the _character_ of a document, because they +coincide in its _opinions_. In this way, probably, fifteen respectable +names were procured before printing; and these, when committed, were hawked +as part of an application to "solicit the favor" of other signatures. It is +likely enough no one of the fifteen saw that the declaration was, not +_maintenance_ of their own opinion, but _regret_ (a civil word for _blame_) +that others should _think differently_. + +When the list appeared, there were no fewer than 716 names! But analysis +showed that this roll was not a specimen of the mature science of the +country. The collection was very miscellaneous: 38 were designated as +"students of the College of Chemistry," meaning young men who attended +lectures in that college. But as all the Royal Society had been applied to, +a test results as follows. Of Fellows of the Royal Society, 600 in number, +62 gave their signatures; of writers in the _Philosophical Transactions_, +166 in number, 19 gave their signatures. Roughly speaking, then, only one +out of ten could be got to express disapprobation of the free comparison of +the results of science with the statements of the canonical books. And I am +satisfied that many of these thought they were signing only a declaration +of difference of opinion, not of blame for that difference. The number of +persons is not small who, when it comes to signing printed documents, would +put their names to a declaration that the coffee-pot ought to be taken +down-stairs, meaning that the teapot ought to be brought {257} up-stairs. +And many of them would defend it. Some would say that the two things are +not contradictory; which, with a snort or two of contempt, would be very +effective. Others would, in the candid and quiet tone, point out that it is +all one, because coffee is usually taken before tea, and it keeps the table +clear to send away the coffee-pot before the teapot is brought up. + +The original signatures were decently interred in the Bodleian Library: and +the advocates of scattering indefinite blame for indefinite sins of opinion +among indefinite persons are, I understand, divided in opinion about the +time at which the next attempt shall be made upon men of scientific +studies: some are for the Greek Calends, and others for the Roman +Olympiads. But, with their usual love of indefiniteness, they have +determined that the choice shall be argued upon the basis that which comes +first cannot be settled, and is of no consequence. + +I give the declaration entire, as a curiosity: and parallel with it I give +a substitute which was proposed in the _Athenaeum_, as worthy to be signed +both by students of theology, and by students of science, especially in +past time. When a new attempt is made, it will be worth while to look at +both: + +_Declaration._ _Proposed Substitute._ + +We, the undersigned Students We, the undersigned Students +of the Natural Sciences, of Theology and of Nature, +desire to express our sincere desire to express our sincere +regret, that researches into regret, that common notions of +scientific truth are perverted religious truth are perverted +by some in our own times into by some in our own times into +occasion for casting doubt occasion for casting reproach +upon the Truth and upon the advocates of +Authenticity of the Holy demonstrated or highly +Scriptures. probable scientific theories. + + {258} +We conceive that it is We conceive that it is +impossible for the Word of impossible for the Word of +God, as written in the book of God, as correctly read in the +nature, and God's Word written Book of Nature, and the Word +in Holy Scripture, to of God, as truly interpreted +contradict one another, out of the Holy Scripture, to +however much they may appear contradict one another, +to differ. however much they may appear + to differ. +We are not forgetful that We are not forgetful that +Physical Science is not neither theological +complete, but is only in a interpretation nor physical +condition of progress, and knowledge is yet complete, but +that at present our finite that both are in a condition +reason enables us only to see of progress; and that at +as through a glass darkly, present our finite reason + enables us only to see both + one and the other as through a + glass darkly [the writers of + the original declaration have + distinctively applied to + physical science the phrase by + which St. Paul denotes the + imperfections of theological + vision, which they tacitly + assume to be quite perfect], +and we confidently believe, and we confidently believe, +that a time will come when the that a time will come when the +two records will be seen to two records will be seen to +agree in every particular. We agree in every particular. We +cannot but deplore that cannot but deplore that +Natural Science should be Religion should be looked upon +looked upon with suspicion by with suspicion by some and +many who do not make a study Science by others, of the +of it, merely on account of students of either who do not +the unadvised manner in which make a study of the {259} +some are placing it in other, merely on account of +opposition to Holy Writ. the unadvised manner in which + some are placing Religion in + opposition to Science, and + some are placing Science in + opposition to Religion. +We believe that it is the duty We believe that it is the duty +of every Scientific Student to of every theological student +investigate nature simply for to investigate the Scripture, +the purpose of elucidating and of every scientific +truth, student to investigate Nature, + simply for the purpose of + elucidating truth. +and that if he finds that some And if either should find that +of his results appear to be in some of his results appear to +contradiction to the Written be in contradiction, whether +Word, or rather to his own to Scripture or to Nature, or +_interpretations_ of it, which rather to his own +may be erroneous, he should _interpretation_ of one or the +not presumptuously affirm that other, which may be erroneous, +his own conclusions must be he should not affirm as with +right, and the statements of certainty that his own +Scripture wrong; conclusion must be right, and + the other interpretation + wrong: +rather, leave the two side by but should leave the two side +side till it shall please God by side for further inquiry +to allow us to see the manner into both, until it shall +in which they may be please God to allow us to +reconciled; arrive at the manner in which + they may be reconciled. +and, instead of insisting upon In the mean while, instead of +the seeming differences insisting, and least of all +between Science and the with acrimony or injurious +Scriptures, it would be as {260} statements about others, +well to rest in faith upon the upon the seeming differences +points in which they agree. between Science and the + Scriptures, it would be a + thousand times better to rest + in faith as to our future + state, in hope as to our + coming knowledge, and in + charity as to our present + differences. + +The distinctness of the fallacies is creditable to the composers, and shows +that scientific habits tend to clearness, even to sophistry. Nowhere does +it so plainly stand out that the _Written Word_ means the sense in which +the accuser takes it, while the sense of the other side is _their +interpretation_. The infallible church on one side, arrayed against +heretical pravity on the other, is seen in all subjects in which men +differ. At school there were various games in which one or another +advantage was the right of those who first called for it. In adult argument +the same thing is often attempted: we often hear--I cried _Church_ first! + +I end with the answer which I myself gave to the application: its revival +may possibly save me from a repetition of the like. If there be anything I +hate more than another it is the proposal to place any persons, especially +those who allow freedom to me, under any abridgment of their liberty to +think, to infer, and to publish. If they break the law, take the law; but +do not make the law: [Greek: agoraioi agontai enkaleitosan allelois.][410] +I would rather be asked to take shares in an argyrosteretic company (with +limited liability) for breaking into houses by night on fork and spoon +errands. I should put aside this proposal with _nothing but laughter_. It +was a joke against Sam Rogers[411] that his appearance was very like that +of a corpse. The _John Bull_ {261} newspaper--suppose we now say Theodore +Hook[412]--averred that when he hailed a coach one night in St. Paul's +Churchyard, the jarvey said, "Ho! ho! my man; I'm not going to be taken in +that way: go back to your grave!" This is the answer I shall make for the +future to any relics of a former time who shall want to call me off the +stand for their own purposes. What obligation have I to admit that they +belong to our world? + + + +"SCRIPTURE AND SCIENCE. + +"_The Writ De Haeretico Commiserando._[413] + +Nov. 14, 1864. + +"This document was sent to me four days ago. It 'solicits the favor'--I +thought at first it was a grocer's supplication for tea and sugar +patronage--of my signature to expression of 'sincere regret' that some +persons unnamed--general warrants are illegal--differ from what I am +supposed--by persons whom it does not concern--to hold about Scripture and +Science in their real or alleged discrepancies. + +"No such favor from me: for three reasons. First, I agree with Sir. J. +Herschel that the solicitation is an intrusion to be publicly repelled. +Secondly, I do _not_ regret that others should differ from me, think what I +may: those others are as good as I, and as well able to think, and as much +entitled to their conclusions. Thirdly, even if I did regret, I should be +ashamed to put my name to bad chemistry made to do duty for good reasoning. +The declaration is an awkward attempt to saturate sophism with truism; but +the sophism is left largely in excess. + +{262} + +"I owe the inquisitors a grudge for taking down my conceit of myself. For +two months I have crowed in my own mind over my friend Sir J. Herschel, +fancying that the promoters instinctively knew better than to bring their +fallacies before a writer on logic. Ah! my dear Sir John! thought I, if you +had shown yourself to be well up in _Barbara Celarent_,[414] and had ever +and anon astonished the natives with the distinction between _simpliciter_ +and _secundum quid_, no autograph-hunters would have baited a trap with +_non sequitur_[415] to catch your signature. What can I say now? I hide my +diminished head, diminished by the horns which I have been compelled to +draw in. + +"Those who make personal solicitation for support to an opinion about +religion are bound to know their men. The king had a right to Brother +Neale's money, because Brother Neale offered it. Had he put his hand into +purse after purse by way of finding out all who were of Brother Neale's +mind, he would have been justly met by a rap on the knuckles whenever he +missed his mark. + +"The kind of test before me is the utmost our time will allow of that +inquisition into opinion which has been the curse of Christianity ever +since the State took Providence under its protection. The writ _de haeretico +commiserando_ is little more than the smell of the empty cask: and those +who issue it may represent the old woman with her + + "O suavis anima, quale in te dicam bonum + Antehac fuisse; tales cum sint reliquiae."[416] + +It is no excuse that the illegitimate bantling is a very little one. Its +parents may think themselves hardly treated when they are called lineal +successors of Tony Fire-the-faggot: {263} but, degenerate though they be, +such is their ancestry. Let every allowance be made for them: but their +unholy fire must be trodden out; so long as a spark is left, nothing but +fuel is wanted to make a blaze. If this cannot be done, let the flame be +confined to theology, though even there it burns with diminished vigor: and +let charity, candor, sense, and ridicule, be ready to play upon it whenever +there is any chance of its extending to literature and science. + +"What would be the consequence if this test-signing absurdity were to grow? +Deep would call unto deep; counter-declaration would answer declaration, +each stronger than the one before. The moves would go on like the dispute +of two German students, of whom each is bound to a sharper retort on a +graduated scale, until at last comes _dummer Junge_![417]--and then they +must fight. There is a gentleman in the upper fifteen of the signers of the +writ--the hawking of whose names appears to me very bad taste--whom I met +in cordial cooperation for many a year at a scientific board. All I knew +about his religion was that he, as a clergyman, must in some sense or other +receive the 39 Articles:--all that he could know about mine was that I was +some kind of heretic, or so reputed. If we had come to signing opposite +manifestoes, turn-about, we might have found ourselves in the lowest depths +of party discussion at our very council-table. I trust the list of +subscribers to the declaration, when it comes to be published, will show +that the bulk of those who have really added to our knowledge have seen the +thing in its true light. + +"The promoters--I say nothing about the subscribers--of the movement will, +I trust, not feel aggrieved at the course I have taken or the remarks I +have made. Walter Scott says that before we judge Napoleon by the +temptation to which he yielded, we ought to remember how much he may have +resisted: I invite them to apply this rule to myself; they can have no idea +of the feeling with which I {264} contemplate all attempts to repress +freedom of inquiry, nor of the loathing with which I recoil from the +proposal to be art and part. They have asked me to give a public opinion +upon a certain point. It is true that they have had the kindness to tender +both the opinion they wish me to form, and the shape in which they would +have it appear: I will let them draw me out, but I will not let them take +me in. If they will put an asterisk to my name, and this letter to the +asterisk, they are welcome to my signature. As I do not expect them to +relish this proposal, I will not solicit the favor of its adoption. But +they have given a right to think, for they have asked me to think; to +publish, for they have asked me to allow them to publish; to blame them, +for they have asked me to blame their betters. Should they venture to find +fault because my direction of disapproval, publicly given, is half a +revolution different from theirs, they will be known as having presented a +loaded document at the head of a traveler in the highway of discussion, +with--Your signature or your silence!" + + + +THE FLY-LEAF PARADOX. + +The paradox being the proposition of something which runs counter to what +would generally be thought likely, may present itself in many ways. There +is a _fly-leaf paradox_, which puzzled me for many years, until I found a +probable solution. I frequently saw, in the blank leaves of old books, +learned books, Bibles of a time when a Bible was very costly, etc., the +name of an owner who, by the handwriting and spelling, must have been an +illiterate person or a child, followed by the date of the book itself. +Accordingly, this uneducated person or young child seemed to be the first +owner, which in many cases was not credible. Looking one day at a +Barker's[418] Bible of 1599, I saw an {265} inscription in a child's +writing, which certainly belonged to a much later date. It was "Martha +Taylor, her book, giuen me by Granny Scott to keep for her sake." With this +the usual verses, followed by 1599, the date of the book. But it so chanced +that the blank page opposite the title, on which the above was written, was +a verso of the last leaf of a prayer book, which had been bound before the +Bible; and on the recto of this leaf was a colophon, with the date 1632. It +struck me immediately that uneducated persons and children, having seen +dates written under names, and not being quite up in chronology, did +frequently finish off with the date of the book, which stared them in the +face. + +Always write in your books. You may be a silly person--for though your +reading my book is rather a contrary presumption, yet it is not +conclusive--and your observations may be silly or irrelevant, but you +cannot tell what use they may be of long after you are gone where +Budgeteers cease from troubling. + +I picked up the following book, printed by J. Franklin[419] at Boston, +during the period in which his younger brother Benjamin was his apprentice. +And as Benjamin was apprenticed very early, and is recorded as having +learned the mechanical art very rapidly, there is some presumption that +part of it may be his work, though he was but thirteen at the time. As this +set of editions of Hodder[420] (by {266} Mose[421]) is not mentioned, to my +knowledge, I give the title in full: + + "Hodder's Arithmetick: or that necessary art made most easy: Being + explained in a way familiar to the capacity of any that desire to learn + it in a little time. By James Hodder, Writing-master. The Five and + twentieth edition, revised, augmented, and above a thousand faults + amended, by Henry Mose, late servant and successor to the author. + Boston: printed by J. Franklin, for S. Phillips, N. Buttolph, B. + Elliot, D. Henchman, G. Phillips, J. Elliot, and E. Negus, booksellers + in Boston, and sold at their shops. 1719." + +The book is a very small octavo, the type and execution are creditable, the +woodcut at the beginning is clumsy. It is a perfect copy, page for page, of +the English editions of Mose's Hodder, of which the one called seventeenth +is of London, 1690. There is not a syllable to show that the edition above +described might not be of Boston in England. Presumptions, but not very +strong ones, might be derived from the name of _Franklin_, and from the +large number of booksellers who combined in the undertaking. It chanced, +however, that a former owner had made the following note in my copy: + + "Wednessday, July y^e 14, 1796, att ten in y^e forenoon we sail^d from + Boston, came too twice, once in King Rode, and once in y^e Narrows. + Sail^d by y^e lighthouse in y^e even^g." + +{267} + +No ordinary map would decide these points: so I had to apply to my friend +Sir Francis Beaufort,[422] and the charts at the Admiralty decided +immediately for Massachusetts. + + + +PARADOXES OF ORTHOGRAPHY AND COMPUTATION. + +The French are able paradoxers in their spelling of foreign names. The Abbe +Sabatier de Castres,[423] in 1772, gives an account of an imaginary +dialogue between Swif, Adisson, Otwai, and Bolingbrocke. I had hoped that +this was a thing of former days, like the literal roasting of heretics; but +the charity which hopeth all things must hope for disappointments. Looking +at a recent work on the history of the popes, I found referred to, in the +matter of Urban VIII[424] and Galileo, references to the works of two +Englishmen, the Rev. Win Worewel and the Rev. Raden Powen. [Wm. Whewell and +Baden Powell].[425] + +I must not forget the "moderate computation" paradox. This is the way by +which large figures are usually obtained. Anything surprisingly great is +got by the "lowest computation," anything as surprisingly small by the +"utmost computation"; and these are the two great subdivisions of "moderate +computation." In this way we learn that 70,000 persons were executed in one +reign, and 150,000 persons {268} burned for witchcraft in one century. +Sometimes this computation is very close. By a card before me it appears +that all the Christians, including those dispersed in heathen countries, +those of Great Britain and Ireland excepted, are 198,728,000 people, and +pay their clergy 8,852,000l. But 6,400,000 people pay the clergy of the +Anglo-Irish Establishment 8,896,000l.; and 14,600,000 of other +denominations pay 1,024,000l. When I read moderate computations, I always +think of Voltaire and the "memoires du fameux eveque de Chiapa, par +lesquels il parait qu'il avait egorge, ou brule, ou noye dix millions +d'infideles en Amerique pour les convertir. Je crus que cet eveque +exaggerait; mais quand on reduisait ces sacrifices a cinq millions de +victimes, cela serait encore admirable."[426] + + + +CENTRIFUGAL FORCE. + +My Budget has been arranged by authors. This is the only plan, for much of +the remark is personal: the peculiarities of the paradoxer are a large part +of the interest of the paradox. As to subject-matter, there are points +which stand strongly out; the quadrature of the circle, for instance. But +there are others which cannot be drawn out so as to be conspicuous in a +review of writers: as one instance, I may take the _centrifugal force_. + +When I was about nine years old I was taken to hear a course of lectures, +given by an itinerant lecturer in a country town, to get as much as I could +of the second half of a good, sound, philosophical omniscience. The first +half (and sometimes more) comes by nature. To this end I smelt chemicals, +learned that they were different kinds of _gin_, saw young wags try to kiss +the girls under the excuse of what was called _laughing gas_--which I was +sure {269} was not to blame for more than five per cent of the requisite +assurance--and so forth. This was all well so far as it went; but there was +also the excessive notion of creative power exhibited in the millions of +miles of the solar system, of which power I wondered they did not give a +still grander idea by expressing the distances in inches. But even this was +nothing to the ingenious contrivance of the centrifugal force. "You have +heard what I have said of the wonderful centripetal force, by which Divine +Wisdom has retained the planets in their orbits round the Sun. But, ladies +and gentlemen, it must be clear to you that if there were no other force in +action, this centripetal force would draw our earth and the other planets +into the Sun, and universal ruin would ensue. To prevent such a +catastrophe, the same wisdom has implanted a centrifugal force of the same +amount, and directly opposite," etc. I had never heard of Alfonso X of +Castile,[427] but I ventured to think that if Divine Wisdom had just let +the planets alone it would come to the same thing, with equal and opposite +troubles saved. The paradoxers deal largely in speculation conducted upon +the above explanation. They provide external agents for what they call the +centrifugal force. Some make the sun's rays keep the planets off, without a +thought about what would become of our poor eyes if the _push_ of the light +which falls on the earth were a counterpoise to all its gravitation. The +true explanation cannot be given here, for want of room. + + + +CAMBRIDGE POETS. + +Sometimes a person who has a point to carry will assert a singular fact or +prediction for the sake of his point; and {270} this paradox has almost +obtained the sole use of the name. Persons who have reputation to care for +should beware how they adopt this plan, which now and then eventuates a +spanker, as the American editor said. Lord Byron, in "English Bards, etc." +(1809), ridiculing Cambridge poetry, wrote as follows: + + "But where fair Isis rolls her purer wave, + The partial muse delighted loves to lave; + On her green banks a greener wreath she wove, + To crown the bards that haunt her classic grove; + Where Richards[428] wakes a genuine poet's fires, + And modern Britons glory in their sires."[429] + +There is some account of the Rev. Geo. Richards, Fellow of Oriel and Vicar +of Bampton, (M.A. in 1791) in the _Living Authors_ by Watkins[430] and +Shoberl[431] (1816). In Rivers's _Living Authors_, of 1798, which is best +fitted for citation, as being published before Lord Byron wrote, he is +spoken of in high terms. The _Aboriginal Britons_ was an Oxford (special) +prize poem, of 1791. Charles Lamb mentions Richards as his school-fellow at +Christ's Hospital, "author of the _Aboriginal Britons_, the most spirited +of the Oxford Prize Poems: a pale, studious Grecian." + +As I never heard of Richards as a poet,[432] I conclude that his fame is +defunct, except in what may prove to be a very ambiguous kind of +immortality, conferred by Lord Byron. The awkwardness of a case which time +has broken down {271} is increased by the eulogist himself adding so +powerful a name to the list of Cambridge poets, that his college has placed +his statue in the library, more conspicuously than that of Newton in the +chapel; and this although the greatness of poetic fame had some serious +drawbacks in the moral character of some of his writings. And it will be +found on inquiry that Byron, to get his instance against Cambridge, had to +go back eighteen years, passing over seven intermediate productions, of +which he had either never heard, or which he would not cite as waking a +genuine poet's fires. + +The conclusion seems to be that the _Aboriginal Britons_ is a remarkable +youthful production, not equalled by subsequent efforts. + +To enhance the position in which the satirist placed himself, two things +should be remembered. First, the glowing and justifiable terms in which +Byron had spoken,--a hundred and odd lines before he found it convenient to +say no Cambridge poet could compare with Richards,--of a Cambridge poet who +died only three years before Byron wrote, and produced greatly admired +works while actually studying in the University. The fame of Kirke +White[433] still lives; and future literary critics may perhaps compare his +writings and those of Richards, simply by reason of the curious relation in +which they are here placed alongside of each other. And it is much to +Byron's credit that, in speaking of the deceased Cambridge poet, he forgot +his own argument and its exigencies, and proved himself only a paradoxer +_pro re nata_. + +Secondly, Byron was very unfortunate in another passage of the same poem: + +{272} + + "What varied wonders tempt us as they pass! + The cow-pox, tractors, galvanism, and gas. + In turns appear, to make the vulgar stare, + Till the swoln bubble bursts--and all is air!" + +Three of the bubbles have burst to mighty ends. The metallic tractors are +disused; but the force which, if anything, they put in action, is at this +day, under the name of mesmerism, used, prohibited, respected, scorned, +assailed, defended, asserted, denied, declared utterly obscure, and +universally known. It was hard lines to select for candidates for oblivion +not one of whom got in. I shall myself, I am assured, be some day cited for +laughing at the great discovery of ----: the blank is left for my reader to +fill up in his own way; but I think I shall not be so unlucky in four +different ways. + + + +FALSIFIED PREDICTION. + +The narration before the fact, as prophecy has been called, sometimes quite +as true as the narration after the fact, is very ridiculous when it is +wrong. Why, the pre-narrator could not know; the post-narrator might have +known. A good collection of unlucky predictions might be made: I hardly +know one so fit to go with Byron's as that of the Rev. Daniel Rivers, +already quoted, about Johnson's biographers. Peter Pindar[434] may be +excused, as personal satire was his object, for addressing Boswell and Mrs. +Piozzi[435] as follows: + + "Instead of adding splendor to his name, + Your books are downright gibbets to his fame; + You never with posterity can thrive, + 'Tis by the Rambler's death alone you live." + +But Rivers, in prose narrative, was not so excusable. He says: + +{273} + +"As admirers of the learning and moral excellence of their hero, we glow at +almost every page with indignation that his weaknesses and his failings +should be disclosed to public view.... Johnson, after the luster he had +reflected on the name of Thrale ... was to have his memory tortured and +abused by her detested itch for scribbling. More injury, we will venture to +affirm, has been done to the fame of Johnson by this Lady and her late +biographical helpmate, than his most avowed enemies have been able to +effect: and if his character becomes unpopular with some of his successors, +it is to those gossiping friends he is indebted for the favor." + +Poor dear old Sam! the best known dead man alive! clever, good-hearted, +logical, ugly bear! Where would he have been if it had not been for Boswell +and Thrale, and their imitators? What would biography have been if Boswell +had not shown how to write a life? + +Rivers is to be commended for not throwing a single Stone at Mrs. Thrale's +second marriage. This poor lady begins to receive a little justice. The +literary world seems to have found out that a blue-stocking dame who keeps +open house for a set among them has a right, if it so please her, to marry +again without taking measures to carry on the cake-shop. I was before my +age in this respect: as a boy-reader of Boswell, and a few other things +that fell in my way, I came to a clearness that the conduct of society +towards Mrs. Piozzi was _blackguard_. She wanted nothing but what was in +that day a woman's only efficient protection, a male relation with a brace +of pistols, and a competent notion of using them. + + + +BYRON AND WORDSWORTH. + +Byron's mistake about Hallam in the Pindar story may be worth placing among +absurdities. For elucidation, suppose that some poet were now to speak-- +{274} + + "Of man's first disobedience, and the fruit + Eve gave to Adam in his birthday suit--" + +and some critic were to call it nonsense, would that critic be laughing at +Milton? Payne Knight,[436] in his _Taste_, translated part of Gray's _Bard_ +into Greek. Some of his lines are + + [Greek: therma d' ho tengon dakrua stonachais] + [Greek: oulon melos phoberai] + [Greek: eeide phonai.] + +Literally thus: + + "Wetting warm tears with groans, + Continuous chant with fearful + Voice he sang." + +On which Hallam remarks: "The twelfth line [our first] is nonsense." And so +it is, a poet can no more wet his tears with his groans than wet his ale +with his whistle. Now this first line is from Pindar, but is only part of +the sense; in full it is: + + [Greek: therma de tengon dakrua stonachais] + [Greek: horthion phonase.] + +Pindar's [Greek: tengon] must be Englished by _shedding_, and he stands +alone in this use. He says, "shedding warm tears, he cried out loud, with +groans." Byron speaks of + + "Classic Hallam, much renowned for Greek:" + +and represents him as criticising _the Greek_ of all Payne's lines, and not +discovering that "the lines" were Pindar's {275} until after publication. +Byron was too much of a scholar to make this blunder himself: he either +accepted the facts from report, or else took satirical licence. And why +not? If you want to laugh at a person, and he will not give occasion, whose +fault is it that you are obliged to make it? Hallam did criticise some of +Payne Knight's Greek; but with the caution of his character, he remarked +that possibly some of these queer phrases might be "critic-traps" justified +by some one use of some one author. I remember well having a Latin essay to +write at Cambridge, in which I took care to insert a few monstrous and +unusual idioms from Cicero: a person with a Nizolius,[437] and without +scruples may get scores of them. So when my tutor raised his voice against +these oddities, I was up to him, for I came down upon him with Cicero, +chapter and verse, and got round him. And so my own solecisms, many of +them, passed unchallenged. + +Byron had more good in his nature than he was fond of letting out: whether +he was a soured misanthrope, or whether his _vein_ lay that way in poetry, +and he felt it necessary to fit his demeanor to it, are matters far beyond +me. Mr. Crabb Robinson[438] told me the following story more than once. He +was at Charles Lamb's chambers in the Temple when Wordsworth came in, with +the new _Edinburgh Review_ in his hand, and fume on his countenance. "These +reviewers," said he, "put me out of patience! Here is a young man--they say +he is a lord--who has written a volume of poetry; and these fellows, just +because he is a lord, set upon him, laugh at him, and sneer at his writing. +The young man will do something, if he goes on as he has begun. But these +reviewers seem to think {276} that nobody may write poetry, unless he lives +in a garret." Crabb Robinson told this long after to Lady Byron, who said, +"Ah! if Byron had known that, he would never have attacked Wordsworth. He +went one day to meet Wordsworth at dinner; when he came home I said, 'Well, +how did the young poet get on with the old one?' 'Why, to tell you the +truth,' said he, 'I had but one feeling from the beginning of the visit to +the end, and that was--_reverence_!'" Lady Byron told my wife that her +husband had a very great respect for Wordsworth. I suppose he would have +said--as the Archangel said to his Satan--"Our difference is po[li = +e]tical." + +I suspect that Fielding would, if all were known, be ranked among the +unlucky railers at supposed paradox. In his _Miscellanies_ (1742, 8vo) he +wrote a satire on the Chrysippus or Guinea, an animal which multiplies +itself by division, like the polypus. This he supposes to have been drawn +up by Petrus Gualterus, meaning the famous usurer, Peter Walter. He calls +it a paper "proper to be read before the R----l Society": and next year, +1743, a quarto reprint was made to resemble a paper in the _Philosophical +Transactions_. So far as I can make out, one object is ridicule of what the +zoologists said about the polypus: a reprint in the form of the +_Transactions_ was certainly satire on the Society, not on Peter Walter and +his knack of multiplying guineas. + +Old poets have recognized the quadrature of the circle as a well-known +difficulty. Dante compares himself, when bewildered, to a geometer who +cannot find the principle on which the circle is to be measured: + + "Quale e 'l geometra che tutto s' affige + Per misurar lo cerchio, e non ritruova, + Pensando qual principio ond' egli indige."[439] + +{277} And Quarles[440] speaks as follows of the _summum bonum_: + + "Or is't a tart idea, to procure + An edge, and keep the practic soul in ure, + Like that dear chymic dust, or puzzling quadrature?" + +The poetic notion of the quadrature must not be forgotten. Aristophanes, in +the _Birds_, introduces a geometer who announces his intention to _make a +square circle_. Pope, in the _Dunciad_, delivers himself as follows, with a +Greek pronunciation rather strange in a translator of Homer. Probably Pope +recognized, as a general rule, the very common practice of throwing back +the accent in defiance of quantity, seen in o'rator, au'ditor, se'nator, +ca'tenary, etc. + + "Mad _Mathesis_ alone was unconfined, + Too mad for mere material chains to bind,-- + Now to pure space lifts her ecstatic stare, + Now, running round the circle, finds it square." + +The author's note explains that this "regards the wild and fruitless +attempts of squaring the circle." The poetic idea seems to be that the +geometers try to make a square circle. Disraeli quotes it as "finds _its_ +square," but the originals do not support this reading. + + + +DE BECOURT. + +I have come in the way of a work, entitled _The Grave of Human +Philosophies_ (1827), translated from the French of R. de Becourt[441] by +A. Dalmas. It supports, but I suspect not very accurately, the views of the +old Hindu books. {278} That the sun is only 450 miles from us, and only 40 +miles in diameter, may be passed over; my affair is with the state of mind +into which persons of M. Becourt's temperament are brought by a fancy. He +fully grants, as certain, four millions of years as the duration of the +Hindu race, and 1956 as that of the universe. It must be admitted he is not +wholly wrong in saying that our errors about the universe proceed from our +ignorance of its origin, antiquity, organization, laws, and final +destination. Living in an age of light, he "avails himself of that +opportunity" to remove this veil of darkness, etc. The system of the +Brahmins is the only true one: he adds that it has never before been +attempted, as it could not be obtained except by him. The author requests +us first, to lay aside prejudice; next, to read all he says in the order in +which he says it: we may then pronounce judgment upon a work which begins +by taking the Brahmins for granted. All the paradoxers make the same +requests. They do not see that compliance would bring thousands of systems +before the world every year: we have scores as it is. How is a poor candid +inquirer to choose. Fortunately, the mind has its grand jury as well as its +little one: and it will not put a book upon its trial without a _prima +facie_ case in its favor. And with most of those who really search for +themselves, that case is never made out without evidence of knowledge, +standing out clear and strong, in the book to be examined. + + + +BEQUEST OF A QUADRATURE. + +There is much private history which will never come to light, _caret quia +vate sacro_,[442] because no Budgeteer comes across it. Many years ago a +man of business, whose life was passed in banking, amused his leisure with +quadrature, was successful of course, and bequeathed the result in a sealed +book, which the legatee was enjoined not to sell {279} under a thousand +pounds. The true ratio was 3.1416: I have the anecdote from the legatee's +executor, who opened the book. That a banker should square the circle is +very credible: but how could a City man come by the notion that a thousand +pounds could be got for it? A friend of mine, one of the twins of my +zodiac, will spend a thousand pounds, if he have not done it already, in +black and white cyclometry: but I will answer for it that he, a man of +sound business notions, never entertained the idea of [pi] recouping him, +as they now say. I speak of individual success: of course if a company were +formed, especially if it were of unlimited lie-ability, the shares would be +taken. No offence; there is nothing but what a pun will either sanctify, +justify, or nullify: + + "It comes o'er the soul like the sweet South + That breathes upon a bank of _vile hits_." + +The shares would be at a premium of 3-1/8 on the day after issue. If they +presented me with the number of shares I deserve, for suggestion and +advertisement, I should stand up for the Archpriest of St. Vitus[443] and +3-1/5, with a view to a little more gold on the bridge. + +I now insert a couple of reviews, one about Cyclopaedias, one about +epistolary collections. Should any reader wish for explanation of this +insertion, I ask him to reflect a moment, and imagine me set to justify all +the additions now before him! In truth these reviews are the repositories +of many odds and ends: they were not made to the books; the materials were +in my notes, and the books came as to a ready-made clothes shop, and found +what would fit them. Many remember Curll's[444] bequest of some very good +titles {280} which only wanted treatises written to them. Well! here were +some tolerable reviews--as times go--which only wanted books fitted to +them. Accordingly, some tags were made to join on the books; and then as +the reader sees. + +I should find it hard to explain why the insertion is made in this place +rather than another. But again, suppose I were put to make such an +explanation throughout the volume. The improver who laid out grounds and +always studied what he called _unexpectedness_, was asked what name he gave +it for those who walked over his grounds a second time. He was silenced; +but I have an answer: It is that which is given by the very procedure of +taking up my book a second time. + + + +REVIEW OF CYCLOPAEDIAS. + + October 19, 1861. _The English Cyclopaedia._ Conducted by Charles + Knight.[445] 22 vols.: viz., _Geography_, 4 vols.; _Biography_, 6 + vols.; _Natural History_, 4 vols.; _Arts and Sciences_, 8 vols. + (Bradbury & Evans.) + + _The Encyclopaedia Britannica: a Dictionary of Arts, Sciences, and + General Literature._ Eighth Edition. 21 vols. and Index. (Black.) + +The two editions above described are completed at the same time: and they +stand at the head of the two great branches into which pantological +undertakings are divided, as at once the largest and the best of their +classes. + +When the works are brought together, the first thing that strikes the eye +is the syllable of difference in the names. The word _Cyclopaedia_ is a bit +of modern purism. Though [Greek: enkuklopaideia][446] is not absolutely +Greek of Greece, we learn from both Pliny[447] and Quintilian[448] that the +circle {281} of the sciences was so called by the Greeks, and +Vitruvius[449] has thence naturalized _encyclium_ in Latin. Nevertheless we +admit that the initial _en_ would have euphonized but badly with the word +_Penny_: and the _English Cyclopaedia_ is the augmented, revised, and +distributed edition of the _Penny Cyclopaedia_. It has indeed been said that +Cyclopaedia should mean the education _of_ a circle, just as Cyropaedia is +the education _of_ Cyrus. But this is easily upset by Aristotle's word +[Greek: kuklophoria],[450] motion _in_ a circle, and by many other cases, +for which see the lexicon. + +The earliest printed Encyclopaedia of this kind was perhaps the famous +"myrrour of the worlde," which Caxton[451] translated from the French and +printed in 1480. The original Latin is of the thirteenth century, or +earlier. This is a collection of very short treatises. In or shortly after +1496 appeared the _Margarita Philosophica_ of Gregory Reisch,[452] the same +we must suppose, who was confessor to the Emperor Maximilian.[453] This is +again a collection of treatises, of much more pretension: and the +estimation formed of it is proved by the number of editions it went +through. In 1531 appeared the little collection of _works_ of +Ringelberg,[454] which is truly called an Encyclopaedia by {282} Morhof, +though the thumbs and fingers of the two hands will meet over the length of +its one volume. There are more small collections; but we pass on to the +first work to which the name of _Encyclopaedia_ is given. This is a +ponderous _Scientiarum Omnium Encyclopaedia_ of Alsted,[455] in four folio +volumes, commonly bound in two: published in 1629 and again in 1649; the +true parent of all the Encyclopaedias, or collections of treatises, or works +in which that character predominates. The first great _dictionary_ may +perhaps be taken to be Hofman's _Lexicon Universale_[456] (1677); but +Chambers's[457] (so called) _Dictionary_ (1728) has a better claim. And we +support our proposed nomenclature by observing that Alsted accidentally +called his work _En_cyclopaedia, and Chambers simply Cyclopaedia. + +We shall make one little extract from the _myrrour_, and one from +Ringelberg. Caxton's author makes a singular remark for his time; and one +well worthy of attention. The grammar rules of a language, he says, must +have been invented by foreigners: "And whan any suche tonge was perfytely +had and usyd amonge any people, than other people not used to the same +tonge caused rulys to be made wherby they myght lerne the same tonge ... +and suche rulys be called the gramer of that tonge." Ringelberg says that +if the right nostril bleed, the little finger of the right hand should be +crooked, and squeezed with great force; and the same for the left. + +{283} + +We pass on to _the_ Encyclopedie,[458] commenced in 1751; the work which +has, in many minds, connected the word _encyclopaedist_ with that of +_infidel_. Readers of our day are surprised when they look into this work, +and wonder what has become of all the irreligion. The truth is, that the +work--though denounced _ab ovo_[459] on account of the character of its +supporters--was neither adapted, nor intended, to excite any particular +remark on the subject: no work of which D'Alembert[460] was co-editor would +have been started on any such plan. For, first, he was a real _sceptic_: +that is, doubtful, with a mind not made up. Next, he valued his quiet more +than anything; and would as soon have gone to sleep over an hornet's nest +as have contemplated a systematic attack upon either religion or +government. As to Diderot[461]--of whose varied career of thought it is +difficult to fix the character of any one moment, but who is very +frequently taken among us for a pure atheist--we will quote one sentence +from the article "_Encyclopedie_," which he wrote himself:--"Dans le moral, +il n'y a que Dieu qui doit servir de modele a 1'homme; dans les art, que la +nature."[462] + +A great many readers in our country have but a very hazy idea of the +difference between the political Encyclopaedia, as we may call it, and the +_Encyclopedie Methodique_,[463] which we always take to be meant--whether +rightly or not we cannot tell--when we hear of the "great French +Encyclopaedia." This work, which takes much from its {284} predecessor, +professing to correct it, was begun in 1792, and finished in 1832. There +are 166 volumes of text, and 6439 plates, which are sometimes incorporated +with the text, sometimes make about 40 more volumes. This is still the +monster production of the kind; though probably the German Cyclopaedia of +Ersch and Gruber,[464] which was begun in 1818, and is still in progress, +will beat it in size. The great French work is a collection of +dictionaries; it consists of Cyclopaedias of all the separate branches of +knowledge. It is not a work, but a collection of works, one or another +department is to be bought from time to time; but we never heard of a +complete set for sale in one lot. As ships grow longer and longer, the +question arises what limit there is to the length. One answer is, that it +will never do to try such a length that the stern will be rotten before the +prow is finished. This wholesome rule has not been attended to in the +matter before us; the earlier parts of the great French work were +antiquated before the whole were completed: something of the kind will +happen to that of Ersch and Gruber. + +The production of a great dictionary of either of the kinds is far from an +easy task. There is one way of managing the _En_cyclopaedia which has been +largely resorted to; indeed, we may say that no such work has been free +from it. This plan is to throw all the attention upon the great treatises, +and to resort to paste and scissors, or some process of equally easy +character, for the smaller articles. However it may be done, it has been +the rule that the Encyclopaedia of treatises should have its supplemental +Dictionary of a very incomplete character. It is true that the treatises +are intended to do a good deal; and that the Index, if it be good, knits +the treatises and the dictionary into one whole of reference. Still there +are two stools, and between them a great deal will fall to the ground. The +dictionary portion of the _Britannica_ is not to be compared with its {285} +treatises; the part called Miscellaneous and Lexicographical in the +_Metropolitana_[465] is a great failure. The defect is incompleteness. The +biographical portion, for example, of the Britannica is very defective: of +many names of note in literature and science, which become known to the +reader from the treatises, there is no account whatever in the dictionary. +So that the reader who has learnt the results of a life in astronomy, for +example, must go to some other work to know when that life began and ended. +This defect has run through all the editions; it is in the casting of the +work. The reader must learn to take the results at their true value, which +is not small. He must accustom himself to regard the Britannica as a +splendid body of treatises on all that can be called heads of knowledge, +both greater and smaller; with help from the accompanying dictionary, but +not of the most complete character. Practically, we believe, this defect +cannot be avoided: two plans of essentially different structure cannot be +associated on the condition of each or either being allowed to abbreviate +the other. + +The defect of all others which it is most difficult to avoid is inequality +of performance. Take any dictionary you please, of any kind which requires +the association of a number of contributors, and this defect must result. +We do not merely mean that some will do their work better than others; this +of course: we mean that there will be structural differences of execution, +affecting the relative extent of the different parts of the whole, as well +as every other point by which a work can be judged. A wise editor will not +attempt any strong measures of correction: he will remember that if some +portions be below the rest, which is a disadvantage, it follows that some +portions must be above the rest, which is an advantage. The only practical +level, if {286} level there must be, is that of mediocrity, if not of +absolute worthlessness: any attempt to secure equality of strength will +result in equality of weakness. Efficient development may be cut down into +meager brevity, and in this way only can apparent equality of plan be +secured throughout. It is far preferable to count upon differences of +execution, and to proceed upon the acknowledged expectation that the +prominent merits of the work will be settled by the accidental character of +the contributors; it being held impossible that any editorial efforts can +secure a uniform standard of goodness. Wherever the greatest power is +found, it should be suffered to produce its natural effect. There are, +indeed, critics who think that the merit of a book, like the strength of a +chain, is that of its weakest part: but there are others who know that the +parallel does not hold, and who will remember that the union of many +writers must show exaggeration of the inequalities which almost always +exist in the production of one person. The true plan is to foster all the +good that can be got, and to give development in the directions in which +most resources are found: a Cyclopaedia, like a plant, should grow towards +the light. + +The _Penny Cyclopaedia_ had its share of this kind of defect or excellence, +according to the way in which the measure is taken. The circumstance is not +so much noticed as might be expected, and this because many a person is in +the habit of using such a dictionary chiefly with relation to one subject, +his own; and more still want it for the pure dictionary purpose, which does +not go much beyond the meaning of the word. But the person of full and +varied reference feels the differences; and criticism makes capital of +them. The Useful Knowledge Society was always odious to the organs of +religious bigotry; and one of them, adverting to the fact that geography +was treated with great ability, and most unusual fullness, in the _Penny +Cyclopaedia_, announced it by making it the sole merit of {287} the work +that, with sufficient addition, it would make a tolerably good gazetteer. + +Some of our readers may still have hanging about them the feelings derived +from this old repugnance of a class to all that did not associate direct +doctrinal teaching of religion with every attempt to communicate knowledge. +I will take one more instance, by way of pointing out the extent to which +stupidity can go. If there be an astronomical fact of the telescopic +character which, next after Saturn's ring and Jupiter's satellites, was +known to all the world, it was the existence of multitudes of double stars, +treble stars, etc. A respectable quarterly of the theological cast, which +in mercy we refrain from naming, was ignorant of this common +knowledge,--imagined that the mention of such systems was a blunder of one +of the writers in the _Penny Cyclopaedia_, and lashed the presumed ignorance +of the statement in the following words, delivered in April, 1837: + + "We have forgotten the name of that Sidrophel who lately discovered + that the fixed stars were not single stars, but appear in the heavens + like soles at Billingsgate, in pairs; while a second astronomer, under + the influence of that competition in trade which the political + economists tell us is so advantageous to the public, professes to show + us, through his superior telescope, that the apparently single stars + are really three. Before such wondrous mandarins of science, how + continually must _homunculi_ like ourselves keep in the background, + lest we come between the wind and their nobility." + +Certainly these little men ought to have kept in the background; but they +did not: and the growing reputation of the work which they assailed has +chronicled them in literary history; grubs in amber. + +This important matter of inequality, which has led us so far, is one to +which the _Encyclopaedia_ is as subject as the _Cyclopaedia_; but it is not +so easily recognized as a fault. {288} We receive the first book as mainly +a collection of treatises: we know their authors, and we treat them as +individuals. We see, for instance, the names of two leading writers on +Optics, Brewster[466] and Herschel.[467] It would not at all surprise us if +either of these writers should be found criticising the other by name, even +though the very view opposed should be contained in the same _Encyclopaedia_ +with the criticism. And in like manner, we should hold it no wonder if we +found some third writer not comparable to either of those we have named. It +is not so in the _Cyclopaedia_: here we do not know the author, except by +inference from a list of which we never think while consulting the work. We +do not dissent from this or that author: we blame the book. + +The _Encyclopaedia Britannica_ is an old friend. Though it holds a proud +place in our present literature, yet the time was when it stood by itself, +more complete and more clear than anything which was to be found elsewhere. +There must be studious men alive in plenty who remember when they were +studious boys, what a literary luxury it was to pass a few days in the +house of a friend who had a copy of this work. The present edition is a +worthy successor of those which went before. The last three editions, +terminating in 1824, 1842, and 1861, seem to show that a lunar cycle cannot +pass without an amended and augmented edition. Detailed criticism is out of +the question; but we may notice the effective continuance of the plan of +giving general historical dissertations on the progress of knowledge. Of +some of these dissertations we have had to take separate notice; and all +will be referred to in our ordinary treatment of current literature.[468] + +The literary excellence of these two extensive undertakings is of the same +high character. To many this will {289} need justification: they will not +easily concede to the cheap and recent work a right to stand on the same +shelf with the old and tried magazine, newly replenished with the best of +everything. Those who are cognizant by use of the kind of material which +fills the _Penny Cyclopaedia_ will need no further evidence: to others we +shall quote a very remarkable and certainly very complete testimony. The +_Cyclopaedia of the Physical Sciences_, published by Dr. Nichol[469] in 1857 +(noticed by us, April 4), is one of the most original of our special +dictionaries. The following is an extract from the editor's preface: + + "When I assented to Mr. Griffin's proposal that I should edit such a + Cyclopaedia, I had it in my mind that I might make the _scissors_ + eminently effective. Alas! on narrowly examining our best Cyclopaedias, + I found that the scissors had become blunted through too frequent and + vigorous use. One great exception exists: viz., the _Penny Cyclopaedia_ + of Charles Knight.[470] The cheapest and the least pretending, it is + really the most philosophical of our _scientific_ dictionaries. It is + not made up of a series of treatises, some good and many indifferent, + but is a thorough _Dictionary_, well proportioned and generally written + by the best men of the time. The more closely it is examined, the more + deeply will our obligation be felt to the intelligence and + conscientiousness of its projector and editor." + +After Dr. Nichol's candid and amusing announcement of his scissorial +purpose, it is but fair to state that nothing of the kind was ultimately +carried into effect, even upon the work in which he found so much to +praise. I quote this testimony because it is of a peculiar kind. + +{290} + +The success of the _Penny Magazine_ led Mr. Charles Knight in 1832 to +propose to the Useful Knowledge Society a Cyclopaedia in weekly penny +numbers. These two works stamp the name of the projector on the literature +of our day in very legible characters. Eight volumes of 480 pages each were +contemplated; and Mr. Long[471] and Mr. Knight were to take the joint +management. The plan embraced a popular account of Art and Science, with +very brief biographical and geographical information. The early numbers of +the work had some of the _Penny Magazine_ character: no one can look at the +pictures of the Abbot and Abbess in their robes without seeing this. By the +time the second volume was completed, it was clearly seen that the plan was +working out its own extension: a great development of design was submitted +to, and Mr. Long became sole editor. Contributors could not be found to +make articles of the requisite power in the assigned space. One of them +told us that when he heard of the eight volumes, happening to want a shelf +to be near at hand for containing the work as it went on, he ordered it to +be made to hold twenty-five volumes easily. But the inexorable logic of +facts beat him after all: for the complete work contained twenty-six +volumes and two thick volumes of Supplement. + +The penny issue was brought to an end by the state of the law, which +required, in 1833, that the first and last page of everything sold +separately should contain the name and address of the printer. The penny +numbers contained this imprint on the fold of the outer leaf: and _qui +tam_[472] informations were laid against the agents in various towns. {291} +It became necessary to call in the stock; and the penny issue was +abandoned. Monthly parts were substituted, which varied in bulk, as the +demands of the plan became more urgent, and in price from one sixpence to +three. The second volume of Supplement appeared in 1846, and during the +fourteen years of issue no one monthly part was ever behind its time. This +result is mainly due to the peculiar qualities of Mr. Long, who unites the +talents of the scholar and the editor in a degree which is altogether +unusual. If any one should imagine that a mixed mass of contributors is a +punctual piece of machinery, let him take to editing upon that hypothesis, +and he shall see what he shall see and learn what he shall learn. + +The _English_ contains about ten per cent more matter than the _Penny +Cyclopaedia_ and its supplements; including the third supplementary volume +of 1848, which we now mention for the first time. The literary work of the +two editions cost within 500l. and 50,000l.: that of the two editions of +the _Britannica_ cost 41,000l. But then it is to be remembered that the +_Britannica_ had matter to begin upon, which had been paid for in the +former editions. Roughly speaking, it is probable that the authorship of a +page of the same size would have cost nearly the same in one as in the +other. + +The longest articles in the _Penny Cyclopaedia_ were "Rome" in 98 columns +and "Yorkshire" in 86 columns. The only article which can be called a +treatise is the Astronomer Royal's "Gravitation," founded on the method of +Newton in the eleventh section, but carried to a much greater extent. In +the _English Cyclopaedia_, the longest article of geography is "Asia," in 45 +columns. In natural history the antelopes demand 36 columns. In biography, +"Wellington" uses up 42 columns, and his great military opponent 41 +columns. In the division of Arts and Sciences, which includes much of a +social and commercial character, the length of articles often depends upon +the state of the {292} times with regard to the subject. Our readers would +not hit the longest article of this department in twenty guesses: it is +"Deaf and Dumb" in 60 columns. As other specimens, we may cite Astronomy, +19; Banking, 36; Blind, 24; British Museum, 35; Cotton, 27; Drama, 26; +Gravitation, 50; Libraries, 50; Painting, 34; Railways, 18; Sculpture, 36; +Steam, etc., 37; Table, 40; Telegraph, 30; Welsh language and literature, +39; Wool, 21. These are the long articles of special subdivisions: the +words under which the _En_cyclopaedia gives treatises are not so prominent. +As in Algebra, 10; Chemistry, 12; Geometry, 8; Logic, 14; Mathematics, 5; +Music, 9. But the difference between the collection of treatises and the +dictionary may be illustrated thus: though "Mathematics" have only five +columns, "Mathematics, recent terminology of," has eight: and this article +we believe to be by Mr. Cayley,[473] who certainly ought to know his +subject, being himself a large manufacturer of the new terms which he +explains. Again, though "Music" _in genere_, as the schoolmen said, has +only nine columns, "Temperament and Tuning," has eight, and "Chord" alone +has two. And so on. + +In a dictionary of this kind it is difficult to make a total clearance of +_personality_: by which we mean that exhibition of peculiar opinion which +is offensive to taste when it is shifted from the individual on the +corporate book. The treatise of the known author may, as we have said, +carry that author's controversies on its own shoulders: and even his +crotchets, if we may use such a word. But {293} the dictionary should not +put itself into antagonism with general feeling, nor even with the feelings +of classes. We refer particularly to the ordinary and editorial teaching of +the article. If, indeed, the writer, being at issue with mankind, should +confess the difference, and give abstract of his full grounds, the case is +altered: the editor then, as it were, admits a correspondent to a statement +of his own individual views. The dictionary portion of the Britannica is +quite clear of any lapses on this point, so far as we know: the treatises +and dissertations rest upon their authors. The Penny Cyclopaedia was all but +clear: and great need was there that it should have been so. The Useful +Knowledge Society, starting on the principle of perfect neutrality in +politics and religion, was obliged to keep strict watch against the +entrance of all attempt even to look over the hedge. There were two--we +believe only two--instances of what we have called personality. The first +was in the article "Bunyan." It is worth while to extract all that is +said--in an article of thirty lines--about a writer who is all but +universally held to be the greatest master of allegory that ever wrote: + + "His works were collected in two volumes, folio, 1736-7: among them + 'The Pilgrim's Progress' has attained the greatest notoriety. If a + judgment is to be formed of the merits of a book by the number of times + it has been reprinted, and the many languages into which it has been + translated, no production in English literature is superior to this + coarse allegory. On a composition which has been extolled by Dr. + Johnson, and which in our own times has received a very high critical + opinion in its favor [probably Southey], it is hazardous to venture a + disapproval, and we, perhaps, speak the opinion of a small minority + when we confess that to us it appears to be mean, jejune and + wearisome." + +--If the unfortunate critic who thus individualized himself had been a +sedulous reader of Bunyan, his power over {294} English would not have been +so _jejune_ as to have needed that fearful word. This little bit of +criticism excited much amusement at the time of its publication: but it was +so thoroughly exceptional and individual that it was seldom or never +charged on the book. The second instance occurred in the article +"Socinians." It had been arranged that the head-words of Christian sects +should be intrusted to members of the sects themselves, on the +understanding that the articles should simply set forth the accounts which +the sects themselves give of their own doctrines. Thus the article on the +Roman Church was written by Dr. Wiseman.[474] But the Unitarians were not +allowed to come within the rule: as in other quarters, they were treated as +the gypsies of Christianity. Under the head "Socinians"--a name repudiated +by themselves--an opponent was allowed not merely to state their alleged +doctrines in his own way, but to apply strong terms, such as "audacious +unfairness," to some of their doings. The protests which were made against +this invasion of the understanding produced, in due time, the article +"Unitarians," written by one of that persuasion. We need not say that these +errors have been amended in the English Cyclopaedia: and our chief purpose +in mentioning them is to remark, that this is all we can find on the points +in question against twenty-eight large volumes produced by an editor whose +task was monthly, and whose issue was never delayed a single hour. How much +was arrested before publication none but himself can say. We have not +alluded to one or two remonstrances on questions of absolute fact, which +are beside the present purpose. + +Both kinds of encyclopaedic works have been fashioned upon predecessors, +from the very earliest which had a predecessor to be founded upon; and the +undertakings before us will be themselves the ancestors of a line of +successors. Those who write in such collections should be {295} careful +what they say, for no one can tell how long a mis-statement may live. On +this point we will give the history of a pair of epithets. When the +historian De Thou[475] died, and left the splendid library which was +catalogued by Bouillaud[476] and the brothers Dupuis[477] (Bullialdus and +Puteanus), there was a manuscript of De Thou's friend Vieta,[478] the +_Harmonicon Coeleste_, of which it is on record, under Bouillaud's hand, +that he himself lent it to Cosmo de' Medici,[479] to which must be added +that M. Libri[480] found it in the Magliabecchi Library at Florence in our +own day. Bouillaud, it seems, entirely forgot what he had done. Something, +probably, that Peter Dupuis said to Bouillaud, while they were at work on +the catalogue, remained on his memory, and was published by him in 1645, +long after; to the effect that Dupuis lent the manuscript to Mersenne,[481] +from whom it was procured by some intending plagiarist, who would not give +it back. This was repeated by Sherburne,[482] in 1675, who speaks of the +work, which "being communicated to Mersennus was, by some perfidious +acquaintance of that honest-minded person, surreptitiously taken from him, +and irrecoverably lost or suppressed, to the unspeakable detriment of the +lettered world." Now let the {296} reader look through the dictionaries of +the last century and the present, scientific or general, at the article, +"Vieta," and he will be amused with the constant recurrence of +"honest-minded" Mersenne, and his "surreptitious" acquaintance. We cannot +have seen less than thirty copies of these epithets. + + + +REVIEW OF MACCLESFIELD LETTERS. + + October 18, 1862. _Correspondence of Scientific Men of the Seventeenth + Century, in the Collection of the Earl of Macclesfield._[483] 2 vols. + (Oxford, University Press.) + +Though the title-page of this collection bears the date 1841, it is only +just completed by the publication of its Table of Contents and Index. +Without these, a work of the kind is useless for consultation, and cannot +make its way. The reason of the delay will appear: its effect is well known +to us. We have found inquirers into the history of science singularly +ignorant of things which this collection might have taught them. + +In the same year, 1841, the Historical Society of Science, which had but a +brief existence, published a collection of letters, eighty-three in number, +edited by Mr. Halliwell,[484] of English men of science, which dovetails +with the one before us, and is for the most part of a prior date. The two +should be bound up together. The smaller collection runs from 1562 to 1682; +the larger, from 1606 to past 1700. We shall speak of the two as the Museum +collection and the Macclesfield collection. And near them should be placed, +in every scientific library, the valuable collection published, by Mr. +Edleston,[485] for Trinity College, in 1850. + +{297} + +The history of these letters runs back to famous John Collins, the +attorney-general of the mathematics, as he has been called, who wrote to +everybody, heard from everybody, and sent copies of everybody's letter to +everybody else. He was in England what Mersenne[486] was in France: as +early as 1671, E. Bernard[487] addresses him as "the very Mersennus and +intelligence of this age." John Collins[488] was never more than accountant +to the Excise Office, to which he was promoted from teaching writing and +ciphering, at the Restoration: he died in 1682. We have had a man of the +same office in our own day, the late Prof. Schumacher,[489] who made the +little Danish Observatory of Altona the junction of all the lines by which +astronomical information was conveyed from one country to another. When the +collision took place between Denmark and the Duchies, the English +Government, moved by the Astronomical Society, instructed its diplomatic +agents to represent strongly to the Danish Government, when occasion should +arise, the great importance of the Observatory of Altona to the +astronomical communications of the whole world. But Schumacher had his own +celebrated journal, the _Astronomische Nachrichten_, by which to work out +part of his plan; private correspondence was his supplementary assistant. +Collins had only correspondence to rely on. Nothing is better known than +that it was Collins's collection which furnished the materials put forward +by the Committee of the Royal Society in 1712, as a defence of Newton +against the partisans of Leibnitz. The noted _Commercium Epistolicum_ is +but the abbreviation of a title which runs on with "D. Johannis Collins et +aliorum ..." + +The whole of this collection passed into the hands of {298} William +Jones,[490] the father of the Indian Judge of the same name, who died in +1749. Jones was originally a teacher, but was presented with a valuable +sinecure by the interest of George, second Earl of Macclesfield, the mover +of the bill for the change of style in Britain, who died President of the +Royal Society. This change of style may perhaps be traced to the union of +energies which were brought into concert by the accident of a common +teacher: Lord Macclesfield and Lord Chesterfield,[491] the mover and the +seconder, and Daval,[492] who drew the bill, were pupils of De Moivre.[493] +Jones, who was a respectable mathematician though not an inventor, +collected the largest mathematical library of his day, and became possessor +of the papers of Collins, which contained those of Oughtred[494] and +others. Some of these papers passed into the custody of the Royal Society: +but the bulk was either bequeathed to, or purchased by, Lord Macclesfield; +and thus they found their way to Shirburn Castle, where they still remain. + +A little before 1836, this collection attracted the attention of a +searching inquirer into points of mathematical history, the late Professor +Rigaud,[495] who died in 1839. He examined the whole collection of letters, +obtained Lord Macclesfield's consent to their publication, and induced the +Oxford Press to bear the expense. It must be particularly remembered that +there still remains at Shirburn Castle a {299} valuable mass of +non-epistolary manuscripts. So far as we can see, the best chance of a +further examination and publication lies in public encouragement of the +collection now before us: the Oxford Press might be induced to extend its +operations if it were found that the results were really of interest to the +literary and scientific world. Rigaud died before the work was completed, +and the publication was actually made by one of his sons, S. Jordan +Rigaud,[496] who died Bishop of Antigua. But this publication was little +noticed, for the reasons given. The completion now published consists of a +sufficient table of contents, of the briefest kind, by Professor De Morgan, +and an excellent index by the Rev. John Rigaud.[497] The work is now fairly +started on its career. + +If we were charged to write a volume with the title "Small things in their +connection with great," we could not do better than choose the small part +of this collection of letters as our basis. The names, as well as the +contents, are both great and small: the great names, those which are known +to every mathematician who has any infusion of the history of his pursuit, +are Briggs,[498] Oughtred, Charles Cavendish,[499] Gascoigne,[500] Seth +Ward,[501] Wallis,[502] {300} Hu[y]gens,[503] Collins,[504] William +Petty,[505] Hooke,[506] Boyle,[507] Pell,[508] Oldenburg,[509] +Brancker,[510] Slusius,[511] Bertit,[512] Bernard,[513] Borelli,[514] +Mouton,[515] Pardies,[516] Fermat,[517] Towneley,[518] Auzout,[519] {301} +D. Gregory,[520] Halley,[521] Machin,[522] Montmort,[523] Cotes,[524] +Jones,[525] Saunderson,[526] Reyneau,[527] Brook Taylor,[528] +Maupertuis,[529] Bouguer,[530] La Condamine,[531] Folkes,[532] +Macclesfield,[533] {302} Baker,[534] Barrow,[535] Flamsteed,[536] Lord +Brounker,[537] J. Gregory,[538] Newton[539] and Keill.[540] To these the +Museum collection adds the names of Thomas Digges,[541] Dee,[542] Tycho +Brahe,[543] Harriot,[544] Lydyat,[545] Briggs,[546] Warner,[547] Tarporley, +Pell,[548] Lilly,[549] Oldenburg,[550] Collins,[551] Morland.[552] + +{303} + +The first who appears on the scene is the celebrated Oughtred, who is +related to have died of joy at the Restoration: but it should be added, by +way of excuse, that he was eighty-six years old. He is an animal of extinct +race, an Eton mathematician. Few Eton men, even of the minority which knows +what a sliding rule is, are aware that the inventor was of their own school +and college: but they may be excused, for Dr. Hutton,[553] so far as his +Dictionary bears witness, seems not to have known it any more than they. A +glance at one of his letters reminds us of a letter from the Astronomer +Royal on the discovery of Neptune, which we printed March 20, 1847. Mr. +Airy[554] there contends, and proves it both by Leverrier[555] and by +Adams,[556] that the limited publication of a private letter is more +efficient than the more general publication of a printed memoir. The same +may be true of a dead letter, as opposed to a dead book. Our eye was caught +by a letter of Oughtred (1629), containing systematic use of contractions +for the words _sine_, _cosine_, etc., prefixed to the symbol of the angle. +This is so very important a step, simple as it is, that Euler[557] is +justly held to have greatly advanced trigonometry by its introduction. +Nobody that we know of has noticed that Oughtred was master of the +improvement, and willing to have taught it, if people would have learnt. +After looking at his dead letter, we naturally turned to his dead book on +trigonometry, and there we found the abbreviations _s_, _sco_, _t_, _tco_, +_se_, _seco_, regularly established as part of the system of the work. But +not one of those who have investigated the contending claims of Euler and +Thomas {304} Simpson[558] has chanced to know of Oughtred's +"Trigonometrie": and the present revival is due to his letter, not to his +book. + +A casual reader, turning over the pages, would imagine that almost all the +letters had been printed, either in the General Dictionary, or in +Birch,[559] etc.: so often does the supplementary remark begin with "this +letter has been printed in ----." For ourselves we thought, until we +counted, that a large majority of the letters had been given, either in +whole or in part. But the positive strikes the mind more forcibly than the +negative: we find that all of which any portion has been in type makes up +very little more than a quarter; the cases in which the whole letter is +given being a minority of this quarter. The person who has been best +ransacked is Flamsteed: of 36 letters from him, 34 had been previously +given in whole or in part. Of 59 letters to and from Newton, only 17 have +been culled. + +The letters have been modernized in spelling, and, to some extent, in +algebraical notation; it also seems that conjectural methods of introducing +interpolations into the text have been necessary. For all this we are +sorry: the scientific value of the collection is little altered, but its +literary value is somewhat lowered. But it could not be helped: the +printers could not work from the originals, and Professor Rigaud had to +copy everything himself. A fac-simile must have been the work of more time +than he had to give: had he attempted it, his death would have cut short +the whole undertaking, instead of allowing him to prepare everything but a +preface, and to superintend the printing of one of the volumes. We may also +add, that we believe we have notices of _all_ the letters in the +Macclesfield collection. We judge this because several which are too +trivial to print are numbered and described; and those would certainly not +have been noticed if _any_ omissions had {305} been made. And we know that +every letter was removed from Shirburn Castle to Oxford. + +Two persons emerge from oblivion in this series of letters. The first is +Michael Dary,[560] an obscure mathematician, who was in correspondence with +Newton and other stars. He was a gauger at Bristol, by the interest of +Collins; afterwards a candidate for the mathematical school at Christ's +Hospital, with a certificate from Newton: he was then a gunner in the +Tower, and is lastly described by Wallis as "Mr. Dary, the tobacco-cutter, +a knowing man in algebra." In 1674, Dary writes to Newton at Cambridge, as +follows:--"Although I sent you three papers yesterday, I cannot refrain +from sending you this. I have had fresh thoughts this morning." Two months +afterwards poor Newton writes to Collins, "Mr. Dary is very solicitous +about mathematics": but in spite of the persecution, he subscribes himself +to Dary "your loving friend." Dary's _problem_ is that of finding the rate +of interest of an annuity of which the value and term are given. Dary's +_theorem_, which he seems to have invented specially for the solution of +his problem, though it is of wide range, can be exhibited to mathematical +readers even in our columns. In modern language, it is that the limit of +[phi]^{_n_}_x_, when _n_ increases without limit, is a solution of [phi]_x_ += _x_. We have mentioned the I. Newton to whom Dary looked up; we add a +word about the one on whom he looked down. Dr. John Newton,[561] a sedulous +publisher of logarithms, tables of interest, etc., who began his career +before Isaac Newton, sometimes puzzles those who do not know him, when +described as I. Newton. The scientific world was of opinion that all that +was valuable in one of his works was taken from Dary's private +communications. + +{306} + +The second character above alluded to is one who carried mathematical +researches a far greater length than Newton himself: the assistance which +he rendered in this respect, even to Newton, has never been acknowledged in +modern times: though the work before us shows that his contemporaries were +fully aware of it, and never thought of concealing it. In his theory of +gravitation, in which, so far as he went, we have every reason to believe +he was prior to Newton, he did not extend his calculations to the distance +of the moon; his views in this matter were purely terrestrial, and led him +to charge according to weight. He was John Stiles, the London and Cambridge +carrier: his name is a household word in the Macclesfield Letters, and is +even enshrined in the depths of Birch's quartos. Dary informs Newton--let +us do his memory this justice--that he had paid John Stiles for the +carriage. At the time when the railroad to Cambridge was opened, a +correspondent recommended the directors, in our columns, to call an engine +by the name of John Stiles, and never to let that name go off the road. We +do not know whether the advice was followed: if not, we repeat it. + +Little points of life and manners come out occasionally. Baker, the author +of a work on algebra much esteemed at the time, wrote to Collins that their +circumstances are alike, "having a just and equal number of chargeable +olive-branches, and being in the same predicament and blessed condemnation +with you, not more preaching than unpaid, and preaching the art of +contentment to others, am forced to practise it." But the last sentence of +his letter runs as follows: "I have sent by the bearer ... twenty +shillings, as a token to you; desiring you to accept of it, as a small +taste from Yours, Thos. Baker." In our day, men of a station to pay parish +taxes do not offer their friends hard money to buy liquor. But +Flamsteed[562] writes to Collins as follows: "Last week he sent us down the +counterpart, which {307} my father has scaled, and I return up to you by +the carrier, with 5l. to be paid to Mr. Leneve for the writing, I have +added 2s. 6d. over, which will pay the expenses and serve to drink, with +him." This would seem as odd to us as it would have seemed thirty years ago +that half-a-crown should pay carriage for a deed from Derby to London, and +leave margin for a bottle of wine: in our day, the Post-office and the +French treaty would just manage it between them. But Flamsteed does not +limit his friend to one bottle; he adds, "If you expend more than the +half-crown, I will make it good after Whitsuntide." Collins does not +remember exactly where he had met James Gregory, and mentions two equally +likely places thus: "Sir, it was once my good hap to meet with you in an +alehouse or in Sion College." There is a little proof how universally the +dinner-hour was twelve o'clock. Astronomers well know the method of finding +time by equal altitudes of the sun before and after noon: Huyghens calls it +"le moyen de deux egales hauteurs du soleil devant et apres _diner_."[563] + +There is one mention of "Mr. Cocker,[564] our famous English graver and +writer, now a schoolmaster at Northampton." This is the true Cocker: his +genuine works are specimens of writing, such as engraved copy-books, +including some on arithmetic, with copper-plate questions and space for the +working; also a book of forms for law-stationers, with specimens of legal +handwriting. It is recorded somewhere that Cocker and another, whose name +we forget, competed with the Italians in the beauty of their flourishes. +This was his real fame: and in these matters he was great. The eighth +edition of his book of law forms (1675), published shortly after Cocker's +death, has a preface signed "J. H." This was John Hawkins, who became +possessed of Cocker's papers--at least he said so--and {308} subsequently +forged the famous Arithmetic,[565] a second work on Decimal Arithmetic, and +an English dictionary, all attributed to Cocker. The proofs of this are set +out in De Morgan's _Arithmetical Books_. Among many other corroborative +circumstances, the clumsy forger, after declaring that Cocker to his dying +day resisted strong solicitation to publish his Arithmetic, makes him write +in the preface _Ille ego qui quondam_[566] of this kind: "I have been +instrumental to the benefit of many, by virtue of those useful arts, +writing and engraving; and do _now_, with the same _wonted alacrity_, cast +this my arithmetical mite into the public treasury." The book itself is not +comparable in merit to at least half-a-dozen others. How then comes Cocker +to be the impersonation of Arithmetic? Unless some one can show proof, +which we have never found, that he was so before 1756, the matter is to be +accounted for thus. + +Arthur Murphy,[567] the dramatist, was by taste a man of letters, and ended +by being the translator of Tacitus; though many do not know that the two +are one. His friends had tried to make him a man of business; and no doubt +he had been well plied with commercial arithmetic. His first dramatic +performance, the farce of "The Apprentice," produced in 1756, is about an +idle young man who must needs turn actor. Two of the best known books of +the day in arithmetic were those of Cocker and Wingate.[568] Murphy chooses +_Wingate_ to be the name of an old merchant who {309} delights in vulgar +fractions, and _Cocker_ to be his arithmetical catchword--"You read +Shakespeare! get Cocker's Arithmetic! you may buy it for a shilling on any +stall; best book that ever was wrote!" and so on. The farce became very +popular, and, as we believe, was the means of elevating Cocker to his +present pedestal, where Wingate would have been, if his name had had the +droller sound of the two to English ears. + +A notoriety of an older day turns up, Major-General Lambert.[569] The +common story is that he was banished to Guernsey, where he passed thirty +years in confinement, rearing and painting flowers. But Baker, in 1678, +represents him as a prisoner at Plymouth, sending equations for solution as +a challenge: probably his place of confinement was varied, and his +occupation also. + +[General Lambert was removed to Plymouth, probably about 1668. His daughter +captured the son of the Governor of Guernsey, who therefore probably was +reckoned an unsafe custodier thenceforward; though he assured the king that +he had turned the young couple out of doors, and had never given them a +penny. Great importance was attached to Lambert's safe detention: probably +the remaining republicans looked upon him as to be their next Cromwell, if +such a thing were to be. There were standing orders to shoot him at once on +the first appearance of any enemy before the island. See _Notes and +Queries_, 3d S. iv. 89.] + +Collins informs James Gregory that "some of the Royal Academy wrote over to +Mr. Oldenburg, who was desired to impart the same to the Council of the +Royal Society, that the French King was willing to allow pensions to one or +two learned Englishmen, but they never made any answer {310} to such a +proposal." This was written in 1671, and the thing probably happened +several years before. Mr. De Morgan communicated the account of the +proposal to Lord Macaulay, who replied that he did not think that any +Englishman _received_ a literary pension from Louis; but that there is a +curious letter, about 1664, from the French Ambassador, in which he says +that he has, by his master's orders, been making inquiries as to the state +of learning in England, and that he is sorry to find that the best writer +is _the infamous Miltonus_. On two such independent testimonies it may be +held proved that the French King had attempted to buy a little adherence +from English literature and science; and the silent contempt of the Royal +Society is an honorable fact in their history. + +Another little bit of politics is as follows. Oughtred is informed that +"Mr. Foster,[570] our Lecturer on Astronomy at Gresham College, is put out +because he will not kneel down at the communion-table. A Scotsman [Mungo +Murray], one that is _verbi bis minister_,[571] is now lecturer in Mr. +Foster's place." Ward in his work on the Gresham Professors,[572] +suppresses the reason, and the suppression lowers the character of his +book. Foster was expelled in 1636, and re-elected on a vacancy in 1641, +when Puritanism had gained strength. + +The correspondence of Newton would require deeper sifting than could be +given in such an article as the present. The first of the letters (1669) is +curious, as presenting the {311} appearance of forms belonging to the great +calculus which, in this paragraph, we ought to call that of fluxions. We +find, of the date February 18, 1669-70, what we believe is the earliest +manifestation of that morbid part of Newton's temperament which has been so +variously represented. He had solved a problem--being that which we have +called Dary's--on which he writes as follows: "The solution of the annuity +problem, if it will be of any use, you have my leave to insert into the +_Philosophical Transactions_, so it be without my name to it. For I see not +what there is desirable in public esteem, were I able to acquire and +maintain it. It would perhaps increase my acquaintance, the thing which I +chiefly study to decline." + +Three letters touch upon "the experiment of glass rubbed to cause various +motions in bits of paper underneath": they are supplements to the account +given by Newton to the Royal Society, and printed by Birch. It was Newton, +so far as appears, who added _glass_ to the substances known to be +electric. Soon afterwards we come to a little bit of the history of the +appointment to the Mint. It has appeared from the researches of late years +that Newton was long an aspirant for public employment: the only coolness +which is known to have taken place between him and Charles Montague[573] +[Halifax] arose out of his imagining that his friend was not in earnest +about getting him into the public service. March 14, 1696, Newton writes +thus to Halley: "And if the rumour of preferment for me in the Mint should +hereafter, upon the death of Mr. Hoar [the comptroller], or any other +occasion, be revived, I pray that you would {312} endeavour to obviate it +by acquainting your friends that I neither _put in_ for _any_ place in the +Mint, nor would meddle with _Mr. Hoar's place_, were it offered to me." +This means that Mr. Hoar's place had been suggested, which Newton seems to +have declined. Five days afterwards, Montague writes to Newton that he is +to have the _Wardenship_. It is fair to Newton to say that in all +probability this was not--or only in a smaller degree--a question of +personal dignity, or of salary. It must by this time have been clear to him +that the minister, though long bound to make him an object of patronage, +was actually seeking him for the Mint, because he wanted both Newton's name +and his talents for business--which he knew to be great--in the weighty and +dangerous operation of restoring the coinage. It may have been, and +probably was, the case that Newton had a tolerably accurate notion of what +he would have to do, and of what degree of power would be necessary to +enable him to do it in his own way. + +We have said that the non-epistolary manuscripts are still unexamined. +There is a chance that one of them may answer a question of two centuries' +standing, which is worth answering, because it has been so often asked. +About 1640, Warner,[574] afterwards assisted by Pell,[575] commenced a +table of _antilogarithms_, of the kind which Dodson[576] afterwards +constructed anew and published. In the Museum collection there is inquiry +after inquiry from Charles Cavendish,[577] first, as to when the +_Analogics_, as he called them, would be finished; next, when they would be +printed. Pell answers, in 1644, that Warner left his papers to a kinsman, +who had become bankrupt, and proceeds thus: + +"I am not a little afraid that all Mr. Warner's papers, {313} and no small +share of my labours therein, are seazed upon, and most unmathematically +divided between the sequestrators and creditors, who (not being able to +ballance the account where there appeare so many numbers, and much troubled +at the sight of so many crosses and circles in the superstitious Algebra +and that black art of Geometry) will, no doubt, determine once in their +lives to become figure-casters, and so vote them all to be throwen into the +fire, if some good body doe not reprieve them for pye-bottoms, for which +purposes you know analogicall numbers are incomparably apt, if they be +accurately calculated." + +Pell afterwards told Wallis[578] that the papers had fallen into the hands +of Dr. Busby,[579] and Collins[580] writes that they were left in the hands +of Dr. Thorndike,[581] a prebendary of Westminster; whence Rigaud[582] +seems to say that Thorndike had left them to Dr. Busby. Birch[583] says +that he procured for the Royal Society four boxes from Busby's trustees, +containing papers of Warner and Pell: but there is no other tradition of +such things in the Society. But in the Birch manuscripts at the British +Museum, there turns up, as printed in what we call the Museum collection, a +list of Warner's papers, with _Collins's_ receipt to Dr. Thorndike at the +bottom, and engagement to restore them on demand. The date is December 14, +1667; Wallis's statement being in 1693. It is possible that Busby may be a +mistake altogether: he was very unlikely to have had charge of any +mathematical papers: there may have been a confusion between the Prebendary +of Westminster and the Head Master of Westminster School. If so, in all +probability Thorndike handed {314} the cumbrous lot over to the notorious +collector of mathematical papers, blessing himself that he got rid of them +in a manner which would insure their return if he were called upon by the +owners to restore them. It is much against this hypothesis that Dodson, who +certainly recalculated, can say nothing more about Warner than a repetition +of Wallis's story: though, had Collins kept the papers, they would probably +have been in Jones's possession at the very time when Dodson, who was a +friend of Jones and a user of his library, was engaged on his own +computations. But even books, and still more manuscripts, are often +singularly overlooked; and it remains not very improbable that Warner's +table is now at Shirburn Castle, among the unexamined manuscripts. + + + +CYCLOMETRY AND STEEL PENS. + +_Redit labor actus in orbem._[584] Among the matters which have come to me +since the Budget opened, there is a pamphlet of quadrature of two pages and +a half from Professor Recalcati,[585] already mentioned. It ends with +"Quelque objection qu'on fasse touchant les raisonnements ci-dessus on +tombera toujours dans l'absurde."[586] A civil engineer--so he says--has +made the quadrature "no longer a problem, but an axiom." As follows: "Take +the quadrant of a circle whose circumference is given, square the quadrant +which gives the true square of the circle. Because 30 / 4 = 7.5 x 7.5 = +56.25 = the positive square of a circle whose circumference is 30." +Brevity, the soul of wit, is the "wings of mighty-winds" to quadrature, and +sends it "flying all abroad." A _surbodhicary_--something like M.A. or +LL.D., I understand--at Calcutta, published in 1863 the division of an +{315} angle into any odd number of parts, demonstration and all in--when +the diagram is omitted--one page, good-sized, well-leaded type, small +duodecimo. But in the Preface he acknowledges "sheer inability" to execute +his task. Mr. William Dean, of Todmorden, in 1863, announced 3-9/64 as +proved both practically and geometrically: he has been already mentioned +anonymously. Next I have the tract of Don Juan Larriva, published at Leiria +in 1856, and dedicated to Queen Victoria. Mr. W. Peters,[587] already +mentioned, who has for some months been circulating diagrams on a card, +publishes (August, 1865) _The Circle Squared_. He agrees with the +Archpriest of St. Vitus. He hints that a larger publication will depend +partly on the support he receives, and partly on the castigation, for which +last, of course, he looks to me. Cyclometers have their several styles of +wit; so have anticyclometers too, for that matter. Mr. Peters will not +allow me any extra-journal being: I am essentially a quotation from the +_Athenaeum_; "A. De Morgan" _et praeterea nihil_.[588] If he had to pay for +keeping me set up, he would find out his mistake, and would be glad to +compound handsomely for a stereotype. Next comes a magnificent sheet of +pasteboard, printed on both sides. Having glanced at it and detected +quadrature, I began methodically at the beginning--"By Royal Command," with +the lion and unicorn, and all that comes between. Mercy on us! thought I to +myself: has Her Majesty referred the question to the Judicial Committee of +the Privy Council, where all the great difficulties go now-a-days, and is +this proclamation the result? On reading further I was relieved by finding +that the first side is entirely an advertisement of Joseph Gillott's[589] +steel pens, with engraving of his {316} premises, and notice of novel +application of his unrivalled machinery. The second side begins with "the +circle rectified" by W. E. Walker,[590] who finds [pi] = +3.141594789624155.... This is an off-shoot from an accurate geometrical +rectification, on which is to be presumed Mr. Gillott's new machinery is +founded. I have no doubt that Mr. Walker's error, which is only in the +sixth place of decimals, will not hurt the pens, unless it be by the +slightest possible increase of the tendency to open at the points. This +arises from Mr. Walker having rectified above proof by .000002136034362.... + +Lastly, I, even I myself, who have long felt that I was a quadrature below +par, have solved the problem by means which, in the present state of the +law of libel, I dare not divulge. But the result is permitted; and it goes +far to explain all the discordances. The ratio of the circumference to the +diameter is not always the same! Not that it varies with the radius; the +geometers are right enough on that point: but it varies with the time, in a +manner depending upon the difference of the true longitudes of the Sun and +Moon. A friend of mine--at least until he misbehaved--insisted on the mean +right ascensions: but I served him as Abraham served his guest in +Franklin's parable. The true formula is, A and a being the Sun's and Moon's +longitudes, + + [pi] = 3-13/80 + 3/80 cos(A - a). + +Mr. James Smith obtained his quadrature at full moon; the Archpriest of St. +Vitus and some others at new moon. Until I can venture to publish the +demonstration, I recommend the reader to do as I do, which is to adopt +3.14159..., and to think of the matter only at the two points of the lunar +month at which it is correct. The _Nautical Almanac_ will no doubt give +these points in a short time: I am in correspondence with the Admiralty, +with nothing {317} to get over except what I must call a perverse notion on +the part of the Superintendent of the _Almanac_, who suspects one +correction depending on the Moon's latitude; and the Astronomer Royal leans +towards another depending on the date of the Queen's accession. I have no +patience with these men: what can the Moon's node of the Queen's reign +possibly have to do with the ratio in question? But this is the way with +all the regular men of science; Newton is to them etc. etc. etc. etc. + +The following method of finding the circumference of a circle (taken from a +paper by Mr. S. Drach[591] in the _Phil. Mag._, Jan. 1863, Suppl.) is as +accurate as the use of 3.14159265. From three diameters deduct +8-thousandths and 7-millionths of a diameter; to the result add five per +cent. We have then not quite enough; but the shortcoming is at the rate of +about an inch and a sixtieth of an inch in 14,000 miles. + + + +JACOB BEHMEN. + +Though I have met with nothing but a little tract from the school of Jacob +Behmen[592] (or Boehme; I keep to the old English version of his name), yet +there has been more, and of a more recent date. I am told of an +"Introduction to Theosophy [_Theo_ private, I suppose, as in theological]; +or, the Science of the Mystery of Christ," published in 1854, mostly from +the writings of William Law[593]: and also of a volume of 688 pages, of the +same year, printed for private circulation, containing notes for a +biography of William Law. The editor of the first work wishes to grow "a +{318} generation of perfect Christians" by founding a Theosophic College, +for which he requests the public to raise a hundred thousand pounds. There +is a good account of Jacob Behmen in the _Penny Cyclopaedia_. The author +mentions inaccurate accounts, one of which he quotes, as follows: "He +derived all his mystical and rapturous doctrine from Wood's[594] _Athenae +Oxonienses_, Vol. I, p. 610, and _Hist. et Antiq. Acad. Oxon._, Vol. II, p. +308." On which the author remarks that Wood was born after Behmen's death. +There must have been a few words which slipped out: what is meant is that +Behmen "derived his doctrine from _Robert Fludd_,[595] _for whom see_ +Wood's etc. etc." Even this is absurd enough: for Behmen began to publish +in 1610, and Fludd in 1616. Fludd was a Rosicrucian, and a mystic of a +different type from Behmen. I have some of his works, and could produce out +of them paradoxes enough, according to our ways of thinking, to fit out a +host. But the Rosicrucian system was a recognized school of its day, and +Fludd, a man of great learning, had abettors enough in all which he +advanced, and predecessors in most of it. + +[A Correspondent has recently sent a short summary of the claims of Jacob +Behmen to rank higher than I have placed him. I shall gladly insert this +summary in the book I contemplate, as a statement of what is said of Behmen +far less liable to suspicion of exaggeration than anything I could write. I +shall add a few extracts from Behmen himself, in support of his right to be +in my list.] + +"_Jacob Behmen._--That Prof. De Morgan classes Jacob Behmen among +paradoxers can only be attributed to the fact of his being avowedly +unacquainted with the writings {319} of that author. Perhaps you may think +a few words from one who knows them well of sufficient interest to the +learned Professor, and your readers in general, to be worthy of space in +your columns. The metaphysical system of Behmen--the most perfect and only +true one--still awaits a qualified commentator. Behmen's countryman, +Dionysius Andreas Freher,[596] who spent the greater part of his life in +this country, and whose exposition of Behmen exists only in MS., filling +many volumes, written in English, with the exception of two, written in +German, with numerous beautiful, highly ingenious, and elaborate +illustrations,--copies of some of which are in the British Museum, but all +the originals of which are in the possession of the gentleman who is the +editor of the two works alluded to by Professor De Morgan,--this Freher was +the first to philosophically expound Behmen's system, which was afterwards, +with the help of these MSS., as it were, popularized by William Law; but +both Freher and Law confined themselves chiefly to its theological aspect. +In Behmen, however, is to be found, not only the true ground of all +theology, but also that of all physical science. He demonstrated with a +fullness, accuracy, completeness and certainty that leave nothing to be +desired, the innermost ground of Deity and Nature; and, confining myself to +the latter, I can from my own knowledge assert, that in Behmen's writings +is to be found the true and clear demonstration of every physical fact that +has been discovered since his day. Thus, the science of electricity, which +was not yet in existence when he wrote, is there anticipated; and not only +does Behmen describe all the now known phenomena of that force, but he even +gives us the origin, generation and birth of electricity itself. Again, +positive evidence can be adduced that Newton derived all his knowledge of +gravitation and its {320} laws from Behmen, with whom gravitation or +attraction is, and very properly so, as he shows us, the first of the seven +properties of Nature. The theory defended by Mr. Grove,[597] at the +Nottingham meeting of last year, that all the apparently distinct causes of +moral and physical phenomena are but so many manifestations of one central +force, and that Continuity is the law of nature, is clearly laid down, and +its truth demonstrated, by Behmen, as well as the distinction between +spirit and matter, and that the moral and material world is pervaded by a +sublime unity. And though all this was not admitted in Behmen's days, +because science was not then sufficiently advanced to understand the deep +sense of our author, many of his passages, then unintelligible, or +apparently absurd, read by the light of the present age, are found to +contain the positive enunciation of principles at whose discovery and +establishment science has only just arrived by wearisome and painful +investigations. Every new scientific discovery goes to prove his profound +and intuitive insight into the most secret workings of nature; and if +scientific men, instead of sharing the prejudice arising from ignorance of +Behmen's system, would place themselves on the vantage ground it affords, +they would at once find themselves on an eminence whence they could behold +all the arcana of nature. Behmen's system, in fact, shows us the _inside_ +of things, while modern physical science is content with looking at the +_outside_. Behmen traces back every outward manifestation or development to +its one central root,--to that one central energy which, as yet, is only +suspected; every link in the chain of his demonstration is perfect, and +there is not one link wanting. He carries us from the out-births of the +circumference, along the radius to the center, {321} or point, and beyond +that even to the zero, demonstrating the constitution of the zero, or +nothing, with mathematical precision. C. W. H." + +And so Behmen is no subject for the Budget! I waited until I should chance +to light on one of his volumes, knowing that any volume would do, and +almost any page. My first hap was on the second volume of the edition of +1664 (4to, published by M. Richardson) and opening near the beginning, a +turn or two brought me to page 13, where I saw about _sulphur_ and +_mercurius_ as follows: + + + +"Thus SUL is the soul, in an herb it is the oil, and in man also, according +to the spirit of _this_ world in the third principle, which is continually +generated out of the anguish of the will in the mind, and the +Brimstone-worm is the Spirit, which hath the fire and _burneth_: PHUR is +the sour wheel in itself which causeth that. + +"_Mercurius_ comprehendeth all the four forms, even as the life springeth +up, and yet hath not its dark beginning in the Center as the PHUR hath, but +after the flash of fire, when the sour dark form is terrified, where the +hardness is turned into pliant sharpness, and where the second will (_viz._ +the will of nature, which is called the Anguish) ariseth, there Mercurius +hath its original. For MER is the shivering wheel, very horrible, sharp, +venomous, and hostile; which assimulateth it thus in the sourness in the +flash of fire, where the sour wrathful life _ariseth_. The syllable CU is +the pressing out, of the _Anxious_ will of the mind, from Nature: which is +climbing up, and _willeth_ to be out aloft. RI is the comprehension of the +flash of fire, which in MER giveth a clear sound and tune. For the flash +maketh the tune, and it is the Salt-Spirit which _soundeth_, and its form +(or quality) is gritty like sand, and herein arise noises, sounds and +voices, and thus CU comprehendeth the flash, and so the pressure is as a +_wind_ which thrusteth, and giveth a spirit to the flash, so that it liveth +and burneth. Thus the {322} syllable US is called the burning fire, which +with the spirit continually driveth itself forth: and the syllable CU +presseth continually upon the flash." + + + +Shades of Tauler[598] and Paracelsus,[599] how strangely you do mix! Well +may Hallam call Germany the native soil of Mysticism. Had Behmen been the +least of a scholar, he would not have divided _sulph-ur_ and _merc-ur-i-us_ +as he has done: and the inflexion _us_, that boy of all work, would have +been rejected. I think it will be held that a writer from whom hundreds of +pages like the above could be brought together, is fit for the Budget. If +Sampson Arnold Mackay[600] had tied his etymologies to a mystical +Christology, instead of a mystical infidelity, he might have had a school +of followers. The nonsense about Newton borrowing gravitation from Behmen +passes only with those who know neither what Newton did, nor what was done +before him. + +The above reminds me of a class of paradoxers whom I wonder that I forgot; +they are without exception the greatest bores of all, because they can put +the small end of their paradox into any literary conversation whatever. I +mean the people who have heard the local pronunciation of celebrated names, +and attempt not only to imitate it, but to impose on others their broken +German or Arabic, or what not. They also learn the vernacular names of +those who are generally spoken of in their Latin forms; at least, they +learn a few cases, and hawk them as evidences of erudition. They are +miserably mistaken: scholarship, as a rule, {323} always accepts the +vernacular form of a name which has vernacular celebrity. Hallam writes +Behmen: his index-maker, rather superfluously, gives "_Behmen_ or Boehm." +And he retains Melanchthon,[601] the name given by Reuchlin[602] to his +little kinsman Schwartzerd, because the world has adopted it: but he will +none of Capnio, the name which Reuchlin fitted on to himself, because the +world has not adopted it. He calls the old forms pedantry: but he sees that +the rejection of well-established results of pedantry would be greater +pedantry still. The paradoxers assume the question that it is more +_correct_ to sound a man by lame imitation of his own countrymen than as +usual in the country in which the sound is to be made. Against them are, +first, the world at large; next, an overpowering majority of those who know +something about surnames and their history. Some thirty years ago--a +fact--there appeared at the police-office a complainant who found his own +law. In the course of his argument, he asked, "What does Kitty +say?"--"Who's Kitty?" said the magistrate, "your wife, or your +nurse?"--"Sir! I mean Kitty, the celebrated lawyer."--"Oh!" said the +magistrate, "I suspect you mean Mr. Chitty,[603] the author of the great +work on pleading."--"I do sir! But Chitty is an Italian name, and ought to +be pronounced _Kitty_." This man was a full-blown flower: but there is many +a modest bud; and all ought either to blush when seen or to waste their +pronunciation on the desert air. + +{324} + + + +A PLEA FOR KING CUSTOM. + +I stand up for King Custom, or _Usus_, as Horace called him, with whom is +_arbitrium_ the decision, and _jus_ the right, and _norma_ the way of +deciding, simply because he has _potestas_ the power. He may admit one and +another principle to advise: but Custom is not a constitutional king; he +may listen to his cabinet, but he decides for himself: and if the ministry +should resign, he blesses his stars and does without them. We have a +glorious liberty in England of owning neither dictionary, grammar, nor +spelling-book: as many as choose write by either of the three, and decide +all disputed points their own way, those following them who please. + +Throughout this book I have called people by the names which denote them in +their books, or by our vernacular names. This is the intelligible way of +proceeding. I might, for instance (Vol. I, p. 44), have spoken of Charles +de Bovelles,[604] of Lefevre d'Etaples,[605] of Pelerin,[606] and of +Etienne.[607] But I prefer the old plan. Those who like another plan +better, are welcome to substitute with a pen, when they know what to write; +when they do not, it is clear that they would not have understood me if I +had given modern names. + +The principal advisers of King Custom are as follows. First, there is +Etymology, the _chiffonnier_, or general rag-merchant, who has made such a +fortune of late years in his own business that he begins to be considered +highly respectable. He gives advice which is more thought of than followed, +partly on account of the fearful extremes into which he runs. He lately +asked some boys of sixteen, at a matriculation examination in _English_, to +what branch of {325} the Indo-Germanic family they felt inclined to refer +the Pushto language, and what changes in the force of the letters took +place in passing from Greek into Moeso-Gothic. Because all syllables were +once words, he is a little inclined to insist that they shall be so still. +He would gladly rule English with a Saxon rod, which might be permitted +with a certain discretion which he has never attained: and when opposed, he +defends himself with analogies of the Aryan family until those who hear him +long for the discovery of an Athanasyus. He will transport a word beyond +seas--he is recorder of Rhematopolis--on circumstantial evidence which +looks like mystery gone mad; but, strange to say, something very often +comes to light after sentence is passed which proves the soundness of the +conviction. + +The next adviser is Logic, a swearing old justice of peace, quorum, and +rotulorum, whose excesses brought on such a fit of the gout that for many +years he was unable to move. He is now mending, and his friends say he has +sown his wild oats. He has some influence with the educated subjects of +Custom, and will have more, if he can learn the line at which interference +ought to stop: with them he has succeeded in making an affirmative of two +negatives; but the vulgar won't never have nothing to say to him. He has +always railed at Milton for writing that Eve was the fairest of her +daughters; but has never satisfactorily shown what Milton ought to have +said instead. + +The third adviser has more influence with the mass of the subjects of King +Custom than the other two put together; his name is Fiddlefaddle, the +toy-shop keeper; and the other two put him forward to do their worst work. +In return, he often uses their names without authority. He took Etymology +to witness that _means_ to an end must be plural: and he would have any one +method to be a _mean_. But Etymology proved him wrong, King Custom referred +him to his Catechism, in which is "a means whereby we receive the same," +and Analogy--a subordinate of {326} Etymology--asked whether he thought it +a great _new_ to hear that he was wrong. It was either this Fiddlefaddle, +or Lindley Murray[608] his traveler, who persuaded the Miss Slipslops, of +the Ladies Seminary, to put "The Misses Slipslop" over the gate. Sixty +years ago, this bagman called at all the girls' schools, and got many of +the teachers to insist on the pupils saying "Is it not" and "Can I not" for +"Isn't it" and "Can't I": of which it came that the poor girls were +dreadfully laughed at by their irreverent brothers when they went home for +the holidays. Had this bad adviser not been severely checked, he might by +this time have proposed our saying "The Queen's of England son," declaring, +in the name of Logic, that the prince was the Queen's son, not England's. + +Lastly, there is Typography the metallurgist, an executive officer who is +always at work in secret, and whose lawless mode of advising is often done +by carrying his notions into effect without leave given. He it is who never +ceases suggesting that the same word is not to occur in a second place +within sight of the first. When the Authorized Version was first printed, +he began this trick at the passage, "Let there be light, and there was +light;" he drew a line on the proof under the second _light_, and wrote +"_luminosity?_" opposite. He is strongest in the punctuations and other +signs; he has a pepper-box full of commas always by his side. He puts +everything under marks of quotation which he has ever heard before. An +earnest preacher, in a very moving sermon, used the phrase Alas! and alack +a day! Typography stuck up the inverted commas because he had read the old +Anglo-Indian toast, "A lass and a lac a day!" If any one should have the +sense to leave out of his Greek {327} the unmeaning scratches which they +call accents, he goes to a lexicon and puts them in. He is powerful in +routine; but when two routines interlace or overlap, he frequently takes +the wrong one. + +Subject to bad advice, and sometimes misled for a season, King Custom goes +on his quiet way and is sure to be right at last. + + "Treason does never prosper: what's the reason? + Why, when it prospers, none dare call it treason." + +Language is in constant fermentation, and all that is thrown in, so far as +it is not fit to assimilate, is thrown off; and this without any obvious +struggle. In the meanwhile every one who has read good authors, from +Shakspeare downward, knows what is and what is not English; and knows, +also, that our language is not one and indivisible. Two very different +turns of phrase may both be equally good, and as good as can be: we may be +relieved of the consequences of contempt of one court by _habeas corpus_ +issuing out of another. + + + +TEST OF LANGUAGE. + +Hallam remarks that the Authorized Version of the Bible is not in the +language of the time of James the First: that it is not the English of +Raleigh or of Bacon. Here arises the question whether Raleigh and Bacon are +the true expositors of the language of their time; and whether they were +not rather the incipient promoters of a change which was successfully +resisted by--among other things--the Authorized Version of the Testaments. +I am not prepared to concede that I should have given to the English which +would have been fashioned upon that of Bacon by imitators, such as they +usually are, the admiration which is forced from me by Bacon's English from +Bacon's pen. On this point we have a notable parallel. Samuel Johnson {328} +commands our admiration, at least in his matured style: but we nauseate his +followers. It is an opinion of mine that the works of the leading writers +of an age are seldom the proper specimens of the language of their day, +when that language is in its state of progression. I judge of a language by +the colloquial idiom of educated men: that is, I take this to be the best +medium between the extreme cases of one who is ignorant of grammar and one +who is perched upon a style. Dialogue is what I want to judge by, and plain +dialogue: so I choose Robert Recorde[609] and his pupil in the _Castle of +Knowledge_, written before 1556. When Dr. Robert gets into his altitudes of +instruction, he differs from his own common phraseology as much as probably +did Bacon when he wrote morals and philosophy. But every now and then I +come to a little plain talk about a common thing, of which I propose to +show a specimen. Anything can be made to look old by such changes as +_makes_ into _maketh_, with a little old spelling. I shall invert these +changes, using the newer form of inflexion, and the modern spelling: with +no other variation whatever. + +"_Scholar._ Yet the reason of that is easy enough to be conceived, for when +the day is at the longest the Sun must needs shine the more time, and so +must it needs shine the less time when the day is at the shortest: this +reason I have heard many men declare. + +_Master._ That may be called a crabbed reason, for it {329} goes backward +like a crab. The day makes not the Sun to shine, but the Sun shining makes +the day. And so the length of the day makes not the Sun to shine long, +neither the shortness of the day causes not [_sic_] the Sun to shine the +lesser time, but contrariwise the long shining of the Sun makes the long +day, and the short shining of the Sun makes the lesser day: else answer me +what makes the days long or short? + +_Scholar._ I have heard wise men say that Summer makes the long days, and +Winter makes the long nights. + +_Master._ They might have said more wisely, that long days make summer and +short days make winter. + +_Scholar._ Why, all that seems one thing to me. + +_Master._ Is it all one to say, God made the earth, and the earth made God? +Covetousness overcomes all men, and all men overcome covetousness? + +_Scholar._ No, not so; for here the effect is turned to be the cause, and +the agent is made the patient. + +_Master._ So is it to say Summer makes long days, when you should say: Long +days make summer. + +_Scholar._ I perceive it now: but I was so blinded with the vulgar error, +that if you had demanded of me further what did make the summer, I had been +like to have answered that green leaves do make summer; and the sooner by +remembrance of an old saying that a year should come in which the summer +should not be known but by the green leaves. + +_Master._ Yet this saying does not import that green leaves do make summer, +but that they betoken summer; so are they the sign and not the cause of +summer." + +I have taken a whole page of our author, without omission, that the reader +may see that I do not pick out sentences convenient for my purpose. I have +done nothing but alter the third person of the verb and the spelling: but +great is the effect thereof. We say "the Sun shining makes the day"; +Recorde, "the Sonne shynynge maketh the daye." {330} These points apart, we +see a resemblance between our English and that of three hundred years ago, +in the common talk of educated persons, which will allow us to affirm that +the language of the authorized Bible must have been very close to that of +its time. For I cannot admit that much change can have taken place in fifty +years: and the language of the version represents both our common English +and that of Recorde with very close approximation. Take sentences from +Bacon and Raleigh, and it will be apparent that these writers will be held +to differ from all three, Recorde, the version, and ourselves, by +differences of the same character. But we speak of Recorde's conversation, +and of our own. We conclude that it is the plain and almost colloquial +character of the Authorized Version which distinguishes it from the English +of Bacon and Raleigh, by approximating it to the common idiom of the time. +If any one will cast an eye upon the letters of instruction written by +Cecil[610] and the Bishop of London to the translators themselves, or to +the general directions sent to them in the King's name, he will find that +these plain business compositions differ from the English of Bacon and +Raleigh by the same sort of differences which distinguish the version +itself. + + + +PRONUNCIATION. + +The foreign word, or the word of a district, or class of people, passes +into the general vernacular; but it is long before the specially learned +will acknowledge the right of those with whom they come in contact to +follow general usage. The rule is simple: so long as a word is technical or +local, those who know its technical or local pronunciation may reasonably +employ it. But when the word has become general, the specialist is not very +wise if he refuse to follow {331} the mass, and perfectly foolish if he +insist on others following him. There have been a few who demanded that +Euler should be pronounced in the German fashion:[611] Euler has long been +the property of the world at large; what does it matter how his own +countrymen pronounce the letters? Shall we insist on the French pronouncing +_Newton_ without that final _tong_ which they never fail to give him? They +would be wise enough to laugh at us if we did. We remember that a pedant +who was insisting on all the pronunciations being retained, was met by a +maxim in contradiction, invented at the moment, and fathered upon +Kaen-foo-tzee,[612] an authority which he was challenged to dispute. Whom +did you speak of? said the bewildered man of accuracy. Learn your own +system, was the answer, before you impose it on others; Confucius says that +too.[613] + +The old English has _fote_, _fode_, _loke_, _coke_, _roke_, etc., for +_foot_, etc. And _above_ rhymes in Chaucer to _remove_. Suspecting that the +broader sounds are the older, we may surmise that _remove_ and _food_ have +retained their old sounds, and that _cook_, once _coke_, would have rhymed +to our _Luke_, the vowel being brought a little nearer, perhaps, to the _o_ +in our present _coke_, the fuel, probably so called as used by cooks. If +this be so, the Chief Justice _Cook_[614] of our lawyers, and the _Coke_ +(pronounced like the fuel) of the greater part of the world, are equally +wrong. The lawyer has no right whatever to fasten his pronunciation upon +us: even leaving aside the general custom, he cannot prove himself right, +and is probably wrong. Those who {332} know the village of Rokeby +(pronounced Rookby) despise the world for not knowing how to name Walter +Scott's poem: that same world never asked a question about the matter, and +the reception of the parody of _Jokeby_, which soon appeared, was a +sufficient indication of their notion. Those who would fasten the hodiernal +sound upon us may be reminded that the question is, not what they call it +now, but what it was called in Cromwell's time. Throw away general usage as +a lawgiver, and this is the point which emerges. Probably _R[=u]ke-by_ +would be right, with a little turning of the Italian [=u] towards [=o] of +modern English. + +[Some of the above is from an old review. I do not always notice such +insertions: I take nothing but my own writings. A friend once said to me, +"Ah! you got that out of the _Athenaeum_!" "Excuse me," said I. "the +_Athenaeum_ got that out of me!"] + + + +APOLOGIES TO CLUVIER. + +It is part of my function to do justice to any cyclometers whose methods +have been wrongly described by any orthodox sneerers (myself included). In +this character I must notice _Dethlevus Cluverius_,[615] as the Leipzig +Acts call him (probably Dethleu Cluvier), grandson of the celebrated +geographer, Philip Cluvier. The grandson was a Fellow of the Royal Society, +elected on the same day as Halley,[616] November 30, 1678: I suppose he +lived in England. This {333} man is quizzed in the Leipzig Acts for 1686; +and, if Montucla insinuate rightly, by Leibnitz, who is further suspected +of wanting to embroil Cluvier with his own opponent Nieuwentiit,[617] on +the matter of infinitesimals. So far good: I have nothing against Leibnitz, +who though he was ironical, told us what he laughed at. But Montucla has +behaved very unfairly: he represents Cluvier as placing the essence of his +method in the solution of the problem _construere mundum divinae menti +analogum_, to construct a world corresponding to the divine mind. Nothing +to begin with: no way of proceeding. Now, it ought to have been _ex data +linea construere_,[618] etc.: there is a given line, which is something to +go on. Further, there is a way of proceeding: it is to find the product of +1, 2, 3, 4, etc. for ever. Moreover, Montucla charges Cluvier with +_unsquaring_ the parabola, which Archimedes had squared as tight as a +glove. But he never mentions how very nearly Cluvier agrees with the Greek: +they only differ by 1 divided by 3n^2, where n is the infinite number of +parts of which a parabola is composed. This must have been the conceit that +tickled Leibnitz, and made him wish that Cluvier and Nieuwentiit should +fight it out. Cluvier, was admitted, on terms of irony, into the Leipzig +Acts: he appeared on a more serious footing in London. It is very rare for +one cyclometer to refute another: _les corsaires ne se battent pas_.[619] +The only instance I recall is that of M. Cluvier, who (_Phil. Trans._, +1686, No. 185) refuted M. Mallemont de Messange,[620] who {334} published +at Paris in 1686. He does it in a very serious style, and shows himself a +mathematician. And yet in the year in which, in the _Phil. Trans._, he was +a geometer, and one who rebukes his squarer for quoting Matthew xi. 25, in +that very year he was the visionary who, in the Leipzig Acts, professed to +build a world resembling the divine mind by multiplying together 1, 2, 3, +4, etc. up to infinity. + + + +THE RAINBOW PARADOX. + +There is a very pretty opening for a paradox which has never found its +paradoxer in print. The philosophers teach that the rainbow is not +material: it comes from rain-drops, but those rain-drops do not _take_ +color. They only _give_ it, as lenses and mirrors; and each one drop gives +_all_ the colors, but throws them in different directions. Accordingly, the +same drop which furnishes red light to one spectator will furnish violet to +another, properly placed. Enter the paradoxer whom I have to invent. The +philosopher has gulled you nicely. Look into the water, and you will see +the reflected rainbow: take a looking-glass held sideways, and you see +another reflection. How could this be, if there were nothing colored to +reflect? The paradoxer's facts are true: and what are called the reflected +rainbows are _other_ rainbows, caused by those _other_ drops which are +placed so as to give the colors to the eye after reflection, at the water +or the looking-glass. A few years ago an artist exhibited a picture with a +rainbow and its apparent reflection: he simply copied what he had seen. +When his picture was examined, some started the idea that there could be no +reflection of a rainbow; they were right: they inferred that the artist had +made a mistake; they were wrong. When it was explained, some agreed and +some dissented. Wanted, {335} immediately, an able paradoxer: testimonials +to be forwarded to either end of the rainbow, No. 1. No circle-squarer need +apply, His Variegatedness having been pleased to adopt 3.14159... from Noah +downwards. + + + +TYCHO BRAHE REVIVED. + +The system of Tycho Brahe,[621] with some alteration and addition, has been +revived and contended for in our own day by a Dane, W. Zytphen,[622] who +has published _The Motion of the Sun in the Universe_, (second edition) +Copenhagen, 1865, 8vo, and _Le Mouvement Sideral_, 1865, 8vo. I make an +extract. + +"How can one explain Copernically that the velocity of the Moon must be +added to the velocity of the Earth on the one place in the Earth's orbit, +to learn how far the Moon has advanced from one fixed star to another; but +in another place in the orbit these velocities must be subtracted (the +movements taking place in opposite directions) to attain the same result? +In the Copernican and other systems, it is well known that the Moon, +abstracting from the insignificant excentricity of the orbit, always in +twenty-four hours performs an equally long distance. Why has Copernicus +never been denominated Fundamentus or Fundator? Because he has never +convinced anybody so thoroughly that this otherwise so natural epithet has +occurred to the mind." + +Really the second question is more effective against Newton than against +Copernicus; for it upsets gravity: the first is of great depth. + +{336} + + + +JAMES SMITH WILL NOT DOWN. + +The _Correspondent_ journal makes a little episode in the history of my +Budget (born May, 1865, died April, 1866). It consisted entirely of letters +written by correspondents. In August, a correspondent who signed "Fair +Play"--and who I was afterwards told was a lady--thought it would be a good +joke to bring in the Cyclometers. Accordingly a letter was written, +complaining that though Mr. Sylvester's[623] demonstration of Newton's +theorem--then attracting public attention--was duly lauded, the possibly +greater discovery of the quadrature seemed to be blushing unseen, and +wasting etc. It went on as follows: + +"Prof. De Morgan, who, from his position in the scientific world, might +fairly afford to look favourably on less practised efforts than his own, +seems to delight in ridiculing the discoverer. Science is, of course, a +very respectable person when he comes out and makes himself useful in the +world [it must have been a lady; each sex gives science to the other]: but +when, like a monk of the Middle Ages, he shuts himself up [it must have +been a lady; they always snub the bachelors] in his cloistered cell, +repeating his mumpsimus from day to day, and despising the labourers on the +outside, we begin to think of Galileo,[624] Jenner,[625] Harvey,[626] and +other glorious trios, who have been contemned ..." + +The writer then called upon Mr. James Smith[627] to come {337} forward. The +irony was not seen; and that day fortnight appeared the first of more than +thirty letters from his pen. Mr. Smith was followed by Mr. Reddie,[628] +Zadkiel,[629] and others, on their several subjects. To some of the letters +I have referred; to others I shall come. The _Correspondent_ was to become +a first-class scientific journal; the time had arrived at which truth had +an organ: and I received formal notice that I could not stifle it by +silence, nor convert it into falsehood by ridicule. When my reader sees my +extracts, he will readily believe my declaration that I should have been +the last to stifle a publication which was every week what James Mill[630] +would call a dose of capital for my Budget. A few anti-paradoxers brought +in common sense: but to the mass of the readers of the journal it all +seemed to be the difference between Tweedledum and Tweedledee. Some said +that the influx of scientific paradoxes killed the journal: but my belief +is that they made it last longer than it otherwise would have done. Twenty +years ago I recommended the paradoxers to combine and publish their views +in a common journal: with a catholic editor, who had no pet theory, but a +stern determination not to exclude anything merely for absurdity. I suspect +it would answer very well. A strong title, or motto, would be wanted: not +so coarse as was roared out in a Cambridge mob when I was an +undergraduate--"No King! No Church! No House of Lords! No nothing, blast +me!"--but something on that _principle_. + +At the end of 1867 I addressed the following letter to the _Athenaeum_: + +PSEUDOMATH, PHILOMATH, AND GRAPHOMATH. + +_December 31, 1867_ + +Many thanks for the present of Mr. James Smith's letters {338} of Sept. 28 +and of Oct. 10 and 12. He asks where you will be if you read and digest his +letters: you probably will be somewhere first. He afterwards asks what the +WE of the _Athenaeum_ will be if, finding it impossible to controvert, it +should refuse to print. I answer for you, that We-We of the _Athenaeum_, not +being Wa-Wa the wild goose, so conspicuous in "Hiawatha," will leave what +controverts itself to print itself, if it please. + +_Philomath_ is a good old word, easier to write and speak than +_mathematician_. It wants the words between which I have placed it. They +are not well formed: _pseudomathete_ and _graphomathete_ would be better: +but they will do. I give an instance of each. + +The _pseudomath_ is a person who handles mathematics as the monkey handled +the razor. The creature tried to shave himself as he had seen his master +do; but, not having any notion of the angle at which the razor was to be +held, he cut his own throat. He never tried a second time, poor animal! but +the pseudomath keeps on at his work, proclaims himself clean-shaved, and +all the rest of the world hairy. So great is the difference between moral +and physical phenomena! Mr. James Smith is, beyond doubt, the great +pseudomath of our time. His 3-1/8 is the least of a wonderful chain of +discoveries. His books, like Whitbread's barrels, will one day reach from +Simpkin & Marshall's to Kew, placed upright, or to Windsor laid +length-ways. The Queen will run away on their near approach, as Bishop +Hatto did from the rats: but Mr. James Smith will follow her were it to +John o' Groats. + +The _philomath_, for my present purpose, must be exhibited as giving a +lesson to presumption. The following anecdote is found in Thiebault's[631] +_Souvenirs de vingt ans de sejours a Berlin_, published in 1804. The book +itself got a high character for truth. In 1807 Marshal Mollendorff[632] +{339} answered an inquiry of the Duc de Bassano,[633] by saying that it was +the most veracious of books, written by the most honest of men. Thiebault +does not claim personal knowledge of the anecdote, but he vouches for its +being received as true all over the north of Europe.[634] + +Diderot[635] paid a visit to Russia at the invitation of Catherine the +Second. At that time he was an atheist, or at least talked atheism: it +would be easy to prove him either one thing or the other from his writings. +His lively sallies on this subject much amused the Empress, and all the +younger part of her Court. But some of the older courtiers suggested that +it was hardly prudent to allow such unreserved exhibitions. The Empress +thought so too, but did not like to muzzle her guest by an express +prohibition: so a plot was contrived. The scorner was informed that an +eminent mathematician had an algebraical proof of the existence of God, +which he would communicate before the whole Court, if agreeable. Diderot +gladly consented. The mathematician, who is not named, was Euler.[636] He +came to Diderot with the gravest air, and in a tone of perfect conviction +said, "_Monsieur!_ + + (a + b^n)/n = x + +_donc Dieu existe; repondez!_"[637] Diderot, to whom algebra was Hebrew, +though this is expressed in a very roundabout way by Thiebault--and whom we +may suppose to have expected some verbal argument of alleged algebraical +closeness, was disconcerted; while peals of laughter sounded on all sides. +Next day he asked permission to return to France, which was granted. An +algebraist would have {340} turned the tables completely, by saying, +"Monsieur! vous savez bien que votre raisonnement demande le developpement +de x suivant les puissances entieres de n".[638] Goldsmith could not have +seen the anecdote, or he might have been supposed to have drawn from it a +hint as to the way in which the Squire demolished poor Moses. + +The _graphomath_ is a person who, having no mathematics, attempts to +describe a mathematician. Novelists perform in this way: even Walter Scott +now and then burns his fingers. His dreaming calculator, Davy Ramsay, +swears "by the bones of the immortal Napier." Scott thought that the the +philomaths worshiped relics: so they do, in one sense. Look into +Hutton's[639] Dictionary for _Napier's Bones_, and you shall learn all +about the little knick-knacks by which he did multiplication and division. +But never a bone of his own did he contribute; he preferred elephants' +tusks. The author of _Headlong Hall_[640] makes a grand error, which is +quite high science: he says that Laplace proved the precession of the +equinoxes to be a periodical inequality. He should have said the variation +of the obliquity. But the finest instance is the following: Mr. +Warren,[641] in his well-wrought tale of the martyr-philosopher, was +incautious enough to invent the symbols by which his _savant_ satisfied +himself Laplace[642] was right on a doubtful point. And this is what he put +together-- + + [sqrt]-3a^2, [rectangle]y^2 / z^2 + 9 - n = 9, n x log e. + +Now, to Diderot and the mass of mankind this might be Laplace all over: +and, in a forged note of Pascal, would {341} prove him quite up to +gravitation. But I know of nothing like it, except in the lately received +story of the American orator, who was called on for some Latin, and +perorated thus: "Committing the destiny of the country to your hands, +Gentlemen, I may without fear declare, in the language of the noble Roman +poet, + + E pluribus unum, + Multum in parvo, + Ultima Thule, + Sine qua non."[643] + +But the American got nearer to Horace than the martyr-philosopher to +Laplace. For all the words are in Horace, except _Thule_, which might have +been there. But [rectangle] is not a symbol wanted by Laplace; nor can we +see how it could have been; in fact, it is not recognized in algebra. As to +the junctions, etc., Laplace and Horace are about equally well imitated. + +Further thanks for Mr. Smith's letters to you of Oct. 15, 18, 19, 28, and +Nov. 4, 15. The last of these letters has two curious discoveries. First, +Mr. Smith declares that he has _seen_ the editor of the _Athenaeum_: in +several previous letters he mentions a name. If he knew a little of +journalism he would be aware that editors are a peculiar race, obtained by +natural selection. They are never seen, even by their officials; only heard +down a pipe. Secondly, "an ellipse or oval" is composed of four arcs of +circles. Mr. Smith has got hold of the construction I was taught, when a +boy, for a pretty four-arc oval. But my teachers knew better than to call +it an ellipse: Mr. Smith does not; but he produces from it such +confirmation of 3-1/8 as would convince any _honest_ editor. + +Surely the cyclometer is a Darwinite development of a spider, who is always +at circles, and always begins again when his web is brushed away. He +informs you that he {342} has been privileged to discover truths unknown to +the scientific world. This we know; but he proceeds to show that he is +equally fortunate in art. He goes on to say that he will make use of you to +bring those truths to light, "just as an artist makes use of a dummy for +the purpose of arranging his drapery." The painter's lay-figure is for +flowing robes; the hairdresser's dummy is for curly locks. Mr. James Smith +should read Sam Weller's pathetic story of the "four wax dummies." As to +_his_ use of a dummy, it is quite correct. When I was at University +College, I walked one day into a room in which my Latin colleague was +examining. One of the questions was, "Give the lives and fates of Sp. +Maelius,[644] and Sp. Cassius."[645] Umph! said I, surely all know that +Spurius Maelius was whipped for adulterating flour, and that Spurius Cassius +was hanged for passing bad money. Now, a robe arranged on a dummy would +look just like the toga of Cassius on the gallows. Accordingly, Mr. Smith +is right in the drapery-hanger which he has chosen: he has been detected in +the attempt to pass bad circles. He complains bitterly that his geometry, +instead of being read and understood by you, is handed over to me to be +treated after my scurrilous fashion. It is clear enough that he would +rather be handled in this way than not handled at all, or why does he go on +writing? He must know by this time that it is a part of the institution +that his "untruthful and absurd trash" shall be distilled into mine at the +rate of about 3-1/8 pages of the first to one column of the second. Your +readers will never know how much they gain by the process, until Mr. James +Smith publishes it all in a big book, or until they get hold of what he has +already published. I have six pounds avoirdupois of pamphlets and letters; +and there is more than half a pound of letters {343} written to you in the +last two months. Your compositor must feel aggrieved by the rejection of +these clearly written documents, without erasures, and on one side only. +Your correspondent has all the makings of a good contributor, except the +knowledge of his subject and the sense to get it. He is, in fact, only a +mask: of whom the fox + + "O quanta species, inquit, cerebrum non habet."[646] + +I do not despair of Mr. Smith on any question which does not involve that +unfortunate two-stick wicket at which he persists in bowling. He has +published many papers; he has forwarded them to mathematicians: and he +cannot get answers; perhaps not even readers. Does he think that he would +get more notice if you were to print him in your journal? Who would study +his columns? Not the mathematician, we know; and he knows. Would others? +His balls are aimed too wide to be blocked by any one who is near the +wicket. He has long ceased to be worth the answer which a new invader may +get. Rowan Hamilton,[647] years ago, completely knocked him over; and he +has never attempted to point out any error in the short and easy method by +which that powerful investigator condescended to show that, be right who +may, he must be wrong. There are some persons who feel inclined to think +that Mr. Smith should be argued with: let those persons understand that he +has been argued with, refuted, and has never attempted to stick a pen into +the refutation. He stated that it was a remarkable paradox, easily +explicable; and that is all. After this evasion, Mr. James Smith is below +the necessity of being told that he is unworthy of answer. His friends +complain that I do nothing but _chaff_ him. Absurd! I winnow him; and if +nothing but chaff results, whose fault is that? I am usefully employed: for +he is the type of a class which ought to be known, and which I have done +much to make known. + +{344} + +Nothing came of this until July 1869, when I received a reprint of the +above letter, with a comment, described as Appendix D of a work in course +of publication on the geometry of the circle. The _Athenaeum_ journal +received the same: but the Editor, in his private capacity, received the +whole work, being _The Geometry of the Circle and Mathematics as applied to +Geometry by Mathematicians, shown to be a mockery, delusion, and a snare_, +Liverpool, 8vo, 1869. Mr. J. S. here appears in deep fight with Professor +Whitworth,[648] and Mr. Wilson,[649] the author of the alleged amendment of +Euclid. How these accomplished mathematicians could be inveigled into +continued discussion is inexplicable. Mr. Whitworth began by complaining of +Mr. Smith's attacks upon mathematicians, continued to correspond after he +was convinced that J. S. proved an arc and its chord to be equal, and only +retreated when J. S. charged him with believing in 3-1/8, and refusing +acknowledgment. Mr. Wilson was introduced to J. S. by a volunteer defense +of his geometry from the assaults of the _Athenaeum_. This the editor would +not publish; so J. S. sent a copy to Mr. Wilson himself. Some +correspondence ensued, but Mr. Wilson soon found out his man, and withdrew. + +There is a little derision of the _Athenaeum_ and a merited punishment for +"that unscrupulous critic and contemptible mathematical twaddler, De +Morgan." + + + +MR. REDDIE'S ASTRONOMY. + +At p. 183 I mentioned Mr. Reddie,[650] the author of _Vis Inertiae Victa_ +and of _Victoria toto coelo_,[651] which last is not {345} an address to +the whole heaven, either from a Roman Goddess or a British Queen, whatever +a scholar may suppose. Between these Mr. Reddie has published _The +Mechanics of the Heavens_, 8vo, 1862: this I never saw until he sent it to +me, with an invitation to notice it, he very well knowing that it would +catch. His speculations do battle with common notions of mathematics and of +mechanics, which, to use a feminine idiom, he blasphemes so you can't +think! and I suspect that if you do not blaspheme them too, _you_ can't +think. He appeals to the "truly scientific," and would be glad to have +readers who have read what he controverts, i.e., Newton's _Principia_: I +wish he may get them; I mean I hope he may obtain them. To none but these +would an account of his speculations be intelligible: I accordingly +disposed of him in a very short paragraph of description. Now many +paradoxers desire notice, even though it be disparaging. I have letters +from more than one--besides what have been sent to the Editor of the +_Athenaeum_--complaining that they are not laughed at; although they deserve +it, they tell me, as much as some whom I have inserted. Mr. Reddie informs +me that I have not said a single word against his books, though I have +given nearly a column to sixteen-string arithmetic, and as much to +animalcule universes. What need to say anything to readers of Newton +against a book from which I quoted that revolution by gravitation is +_demonstrably_ impossible? It would be as useless as evidence against a man +who has pleaded guilty. Mr. Reddie derisively thanks me for "small +mercies"; he wrote me private letters; he published them, and more, in the +_Correspondent_. He gave me, _pro viribus suis_,[652] such a dressing you +can't think, both for my Budget non-notice, and for reviews which he +assumed me to have written. He outlawed himself by declaring +(_Correspondent_, Nov. 11, 1856) that I--in a review--had made a quotation +which was "garbled, evidently on purpose {346} to make it appear that" he +"was advocating solely a geocentric hypothesis, which is not true." In +fact, he did his best to get larger "mercy." And he shall have it; and at a +length which shall content him, unless his mecometer be an insatiable +apparatus. But I fear that in other respects I shall no more satisfy him +than the Irish drummer satisfied the poor culprit when, after several times +changing the direction of the stroke at earnest entreaty, he was at last +provoked to call out, "Bad cess to ye, ye spalpeen! strike where one will, +there's no _plasing_ ye!" + +Mr. Reddie attaches much force to Berkeley's[653] old arguments against the +doctrine of fluxions, and advances objections to Newton's second section, +which he takes to be new. To me they appear "such as have been often made," +to copy a description given in a review: though I have no doubt Mr. Reddie +got them out of himself. But the whole matter comes to this: Mr. Reddie +challenged answer, especially from the British Association, and got none. +He presumes that this is because he is right, and cannot be answered: the +Association is willing to risk itself upon the counter-notion that he is +wrong, and need not be answered; because so wrong that none who could +understand an answer would be likely to want one. + +Mr. Reddie demands my attention to a point which had already particularly +struck me, as giving the means of showing to _all_ readers the kind of +confusion into which paradoxers are apt to fall, in spite of the clearest +instruction. It is a very honest blunder, and requires notice: it may +otherwise mislead some, who may suppose that no one able to read could be +mistaken about so simple a matter, {347} let him be ever so wrong about +Newton. According to his own mis-statement, in less than five months he +made the Astronomer Royal abandon the theory of the solar motion in space. +The announcement is made in August, 1865, as follows: the italics are not +mine: + + "The third (_Victoria ..._), although only published in September, + 1863, has already had its triumph. _It is the book that forced the + Astronomer Royal of England, after publicly teaching the contrary for + years, to come to the conclusion, "strange as it may appear," that "the + whole question of solar motion in space is at the present time in doubt + and abeyance."_ This admission is made in the Annual Report of the + Council of the Royal Astronomical Society, published in the Society's + _Monthly Notices_ for February, 1864." + +It is added that solar motion is "full of self-contradiction, which "the +astronomers" simply overlooked, but which they dare not now deny after +being once pointed out." + +The following is another of his accounts of the matter, given in the +_Correspondent_, No. 18, 1865: + + "... You ought, when you came to put me in the 'Budget,' to have been + aware of the Report of the Council of the Royal Astronomical Society, + where it appears that Professor Airy,[654] with a better appreciation + of my demonstrations, had admitted--'strange,' say the Council, 'as it + may appear,'--that 'the whole question of solar motion in space [and + here Mr. Reddie omits some words] is now in _doubt and abeyance_.' You + were culpable as a public teacher of no little pretensions, if you were + 'unaware' of this. If aware of it, you ought not to have suppressed + such an important testimony to my really having been 'very successful' + in drawing the teeth of the pegtops, though you thought them so firmly + fixed. And if you still suppress {348} it, in your Appendix, or when + you reprint your 'Budget,' you will then be guilty of a _suppressio + veri_, also of further injury to me, who have never injured you...." + +Mr. Reddie must have been very well satisfied in his own mind before he +ventured such a challenge, with an answer from me looming in the distance. +The following is the passage of the Report of the Council, etc., from which +he quotes: + + "And yet, strange to say, notwithstanding the near coincidence of all + the results of the before-mentioned independent methods of + investigation, the inevitable logical inference deduced by Mr. Airy is, + that the whole question of solar motion in space, _so far at least as + accounting for the proper motion of the stars is concerned_, [I have + put in italics the words omitted by Mr. Reddie] appears to remain at + this moment in doubt and abeyance." + +Mr. Reddie has forked me, as he thinks, on a dilemma: if unaware, culpable +ignorance; if aware, suppressive intention. But the thing is a _trilemma_, +and the third horn, on which I elect to be placed, is surmounted by a +doubly-stuffed seat. First, Mr. Airy has not changed his opinion about the +_fact_ of solar motion in space, but only suspends it as to the sufficiency +of present means to give the amount and direction of the motion. Secondly, +all that is alluded to in the Astronomical Report was said and printed +before the Victoria proclamation appeared. So that the author, instead of +drawing the tooth of the Astronomer Royal's pegtop, has burnt his own +doll's nose. + +William Herschel,[655] and after him about six other astronomers, had aimed +at determining, by the proper motions of the stars, the point of the +heavens towards which the solar system is moving: their results were +tolerably accordant. Mr. Airy, in 1859, proposed an improved method, and, +applying it to stars of large proper motion, produced {349} much the same +result as Herschel. Mr. E. Dunkin,[656] one of Mr. Airy's staff at +Greenwich, applied Mr. Airy's method to a very large number of stars, and +produced, again, nearly the same result as before. This paper was read to +the Astronomical Society in _March_, 1863, was printed in abstract in the +_Notice_ of that month, was printed in full in the volume then current, and +was referred to in the Annual Report of the Council in _February_, 1864, +under the name of "the Astronomer Royal's elaborate investigation, as +exhibited by Mr. Dunkin." Both Mr. Airy and Mr. Dunkin express grave doubts +as to the sufficiency of the data: and, regarding the coincidence of all +the results as highly curious, feel it necessary to wait for calculations +made on better data. The report of the Council states these doubts. Mr. +Reddie, who only published in _September_, 1863, happened to see the Report +of February, 1864, assumes that the doubts were then first expressed, and +declares that his book of September had the triumph of forcing the +Astronomer Royal to abandon the _fact_ of motion of the solar system by the +February following. Had Mr. Reddie, when he saw that the Council were +avowedly describing a memoir presented some time before, taken the +precaution to find out _when_ that memoir was presented, he would perhaps +have seen that doubts of the results obtained, expressed by one astronomer +in March, 1863, and by another in 1859, could not have been due to his +publication of September, 1863. And any one else would have learnt that +neither astronomer doubts the _solar motion_, though both doubt the +sufficiency of present means to determine its _amount_ and _direction_. +This is implied in the omitted words, which Mr. Reddie--whose omission +would have been dishonest if he had seen their meaning--no doubt took for +pleonasm, superfluity, overmuchness. The rashness which pushed him headlong +{350} into the quillet that _his_ thunderbolt had stopped the chariot of +the Sun and knocked the Greenwich Phaeton off the box, is the same which +betrayed him into yet grander error--which deserves the full word, +_quidlibet_--about the _Principia_ of Newton. There has been no change of +opinion at all. When a person undertakes a long investigation, his opinion +is that, at a certain date, there is _prima facie_ ground for thinking a +sound result may be obtained. Should it happen that the investigation ends +in doubt upon the sufficiency of the grounds, the investigator is not put +in the wrong. He knew beforehand that there was an alternative: and he +takes the horn of the alternative indicated by his calculations. The two +sides of this case present an instructive contrast. Eight astronomers +produce nearly the same result, and yet the last two doubt the sufficiency +of their means: compare them with the what's-his-name who rushes in where +thing-em-bobs fear to tread. + +I was not aware, until I had written what precedes, that Mr. Airy had given +a sufficient answer on the point. Mr. Reddie says (_Correspondent_, Jan. +20, 1866): + + "I claim to have forced Professor Airy to give up the notion of 'solar + motion in space' altogether, for he admits it to be 'at present in + doubt and abeyance.' I first made that claim in a letter addressed to + the Astronomer Royal himself in June, 1864, and in replying, very + courteously, to other portions of my letter, he did not gainsay that + part of it." + +Mr. Reddie is not ready at reading satire, or he never would have so missed +the meaning of the courteous reply on one point, and the total silence upon +another. Mr. Airy must be one of those peculiar persons who, when they do +not think an assertion worth notice, let it alone, without noticing it by a +notification of non-notice. He would never commit the bull of "Sir! I will +not say a word on that subject." He would put it thus, "Sir! I will only +say ten words on that subject,"--and, having thus said them, would {351} +proceed to something else. He assumed, as a matter of form, that Mr. Reddie +would draw the proper inference from his silence: and this because he did +not care whether or no the assumption was correct. + +The _Mechanics of the Heavens_, which Mr. Reddie sends to be noticed, shall +be noticed, so far as an extract goes: + + + +"My connection with this subject is, indeed, very simply explained. In +endeavoring to understand the laws of physical astronomy as generally +taught, I happened to entertain some doubt whether gravitating bodies could +revolve, and having afterwards imbibed some vague idea that the laws of the +universe were chemical and physical rather than mechanical, and somehow +connected with electricity and magnetism as opposing correlative +forces--most probably suggested to my mind, as to many others, by the +transcendent discoveries made in electro-magnetism by Professor +Faraday[657]--my former doubts about gravitation were revived, and I was +led very naturally to try and discover whether a gravitating body really +could revolve; and I became convinced it could not, before I had ever +presumed to look into the demonstrations of the _Principia_." + + + +This is enough against the book, without a word from me: I insert it only +to show those who know the subject what manner of writer Mr. Reddie is. It +is clear that "presumed" is a slip of the pen; it should have been +_condescended_. + +Mr. Reddie represents me as dreaming over paltry paradoxes. He is right; +many of my paradoxes are paltry: he is wrong; I am wide awake to them. A +single moth, beetle, or butterfly, may be a paltry thing; but when a +cabinet is arranged by genus and species, we then begin to admire the {352} +infinite variety of a system constructed on a wonderful sameness of leading +characteristics. And why should paradoxes be denied that collective +importance, paltry as many of them may individually be, which is accorded +to moths, beetles, or butterflies? Mr. Reddie himself sees that "there is a +method in" my "mode of dealing with paradoxes." I hope I have atoned for +the scantiness of my former article, and put the demonstrated impossibility +of gravitation on that level with Hubongramillposanfy arithmetic and +inhabited atoms which the demonstrator--not quite without reason--claims +for it. + +In the Introduction to a collected edition of the three works, Mr. Reddie +describes his _Mechanism of the Heavens_, from which I have just quoted, +as-- + + + +"a public challenge offered to the British Association and the +mathematicians at Cambridge, in August, 1862, calling upon them to point to +a single demonstration in the _Principia_ or elsewhere, which even attempts +to prove that Universal Gravitation is possible, or to show that a +gravitating body could possibly revolve about a center of attraction. The +challenge was not accepted, and never will be. No such demonstration +exists. And the public must judge for themselves as to the character of a +so-called "certain science," which thus shrinks from rigid examination, and +dares not defend itself when publicly attacked: also of the character of +its teachers, who can be content to remain dumb under such circumstances." + + + +ON PARADOXERS IN GENERAL. + +The above is the commonplace talk of the class, of which I proceed to speak +without more application to this paradoxer than to that. It reminds one of +the funny young rascals who used, in times not yet quite forgotten, to +abuse the passengers, as long as they could keep up with the {353} stage +coach; dropping off at last with "Why don't you get down and thrash us? +You're afraid, you're afraid!" They will allow the public to judge for +themselves, but with somewhat of the feeling of the worthy uncle in _Tom +Jones_, who, though he would let young people choose for themselves, would +_have them_ choose wisely. They try to be so awfully moral and so ghastly +satirical that they must be answered: and they are best answered in their +own division. We have all heard of the way in which sailors cat's-pawed the +monkeys: they taunted the dwellers in the trees with stones, and the +monkeys taunted them with cocoa-nuts in return. But these were silly +dendrobats: had they belonged to the British Association they would have +said--No! No! dear friends; it is not in the itinerary: if you want nuts, +you must climb, as we do. The public has referred the question to Time: the +procedure of this great king I venture to describe, from precedents, by an +adaptation of some smart anapaestic tetrameters--your anapaest is the foot +for satire to halt on, both in Greek and English--which I read about twenty +years ago, and with the point of which I was much tickled. Poetasters were +laughed at; but Mr. Slum, whom I employed--Mr. Charles Dickens obliged me +with his address--converted the idea into that of a hit at +mathematicasters, as easily as he turned the Warren acrostic into Jarley. +As he observed, when I settled his little account, it is cheaper than any +prose, though the broom was not stolen quite ready made: + + _Forty stripes save one for the smaller Paradoxers._ + + Hark to the wisdom the sages preach + Who never have learnt what they try to teach. + We are the lights of the age, they say! + We are the men, and the thinkers we! + So we build up guess-work the livelong day, + In a topsy-turvy sort of way, + Some with and some wanting _a_ plus b. + Let the British Association fuss; + What are theirs to the feats to be wrought by us? + {354} + Shall the earth stand still? Will the round come square? + Must Isaac's book be the nest of a mare? + Ought the moon to be taught by the laws of space + To turn half round without right-about-face? + Our whimsey crotchets will manage it all; + Deep! Deep! posterity will them call! + Though the world, for the present, lets them fall + Down! Down! to the twopenny box of the stall! + + Thus they--But the marplot Time stands by, + With a knowing wink in his funny old eye. + He grasps by the top an immense fool's cap, + Which he calls a philosophaster-trap: + And rightly enough, for while these little men + Croak loud as a concert of frogs in a fen, + He first singles out one, and then another, + Down goes the cap--lo! a moment's pother, + A spirit like that which a rushlight utters + As just at the last it kicks and gutters: + When the cruel smotherer is raised again + Only snuff, and but little of that, will remain. + + But though _uno avulso_ thus comes every day + _Non deficit alter_ is also in play: + For the vacant parts are, one and all, + Soon taken by puppets just as small; + Who chirp, chirp, chirp, with a grasshopper's glee, + We're the lamps of the Universe, We! We! We! + But Time, whose speech is never long,-- + He hasn't time for it--stops the song + And says--Lilliput lamps! leave the twopenny boxes, + And shine in the Budget of Paradoxes! + +When a paradoxer parades capital letters and diagrams which are as good as +Newton's to all who know nothing about it, some persons wonder why science +does not rise and triturate the whole thing. This is why: all who are fit +to read the refutation are satisfied already, and can, if they please, +detect the paradoxer for themselves. Those who are not fit to do this would +not know the difference between the true answer and the new capitals and +diagrams on which the delighted paradoxer would declare {355} that he had +crumbled the philosophers, and not they him. Trust him for having the last +word: and what matters it whether he crow the unanswerable sooner or later? +There are but two courses to take. One is to wait until he has committed +himself in something which all can understand, as Mr. Reddie has done in +his fancy about the Astronomer Royal's change of opinion: he can then be +put in his true place. The other is to construct a Budget of Paradoxes, +that the world may see how the thing is always going on, and that the +picture I have concocted by cribbing and spoiling a bit of poetry is drawn +from life. He who wonders at there being no answer has seen one or two: he +does not know that there are always fifty with equal claims, each of whom +regards his being ranked with the rest as forty-nine distinct and several +slanders upon himself, the great Mully Ully Gue. And the fifty would soon +be five hundred if any notice were taken of them. They call mankind to +witness that science _will not_ defend itself, though publicly attacked in +terms which might sting a pickpocket into standing up for his character: +science, in return, allows mankind to witness or not, at pleasure, that it +_does not_ defend itself, and yet receives no injury from centuries of +assault. Demonstrative reason never raises the cry of _Church in Danger_! +and it cannot have any Dictionary of Heresies except a Budget of Paradoxes. +Mistaken claimants are left to Time and his extinguisher, with the +approbation of all thinking non-claimants: there is no need of a succession +of exposures. Time gets through the job in his own workmanlike manner as +already described. + +On looking back more than twenty years, I find among my cuttings the +following passage, relating to a person who had signalized himself by an +effort to teach comets to the conductor of the _Nautical Almanac_: + + + +"Our brethren of the literary class have not the least idea of the small +amount of appearance of knowledge {356} which sets up the scientific +charlatan. Their world is large, and there are many who have that moderate +knowledge, and perception of what is knowledge, before which extreme +ignorance is detected in its first prank. There is a public of moderate +cultivation, for the most part sound in its judgment, always ready in its +decisions. Accordingly, all their successful pretenders have _some +pretension_. It is not so in science. Those who have a right to judge are +fewer and farther between. The consequence is, that many scientific +pretenders have _nothing but pretension_." + + + +This is nearly as applicable now as then. It is impossible to make those +who have not studied for themselves fully aware of the truth of what I have +quoted. The best chance is collection of cases; in fact, a Budget of +Paradoxes. Those who have no knowledge of the subject can thus argue from +the seen to the unseen. All can feel the impracticability of the +Hubongramillposanfy numeration, and the absurdity of the equality of +contour of a regular pentagon and hexagon in one and the same circle. Many +may accordingly be satisfied, on the assurance of those who have studied, +that there is as much of impracticability, or as much of absurdity, in +things which are hidden under + + "Sines, tangents, secants, radius, cosines + Subtangents, segments and all those signs; + Enough to prove that he who read 'em + Was just as mad as he who made 'em." + +Not that I mean to be disrespectful to mathematical terms: they are short +and easily explained, and compete favorably with those of most other +subjects: for instance, with + + "Horse-pleas, traverses, demurrers, + Jeofails, imparlances, and errors, + Averments, bars, and protestandos, + And puis d'arreign continuandos." + +{357} + +From which it appears that, taking the selections made by satirists for our +samples, there are, one with another, four letters more in a law term than +in one of mathematics. But pleading has been simplified of late years. + +All paradoxers can publish; and any one who likes may read. But this is not +enough; they find that they cannot publish, or those who can find they are +_not_ read, and they lay their plans athwart the noses of those who, they +think, ought to read. To recommend them to be content with publication, +like other authors, is an affront: of this I will give the reader an +amusing instance. My good nature, of which I keep a stock, though I do not +use it all up in this Budget, prompts me to conceal the name. + +I received the following letter, accompanied by a prospectus of a work on +metaphysics, physics, astronomy, etc. The author is evidently one whom I +should delight to honor: + +"Sir,--A friend of mine has mentioned your name in terms of panigeric +[_sic_], as being of high standing in mathematics, and of greatly original +thought. I send you the enclosed without comment; and, assuming that the +bent of your mind is in free inquiry, shall feel a pleasure in showing you +my portfolio, which, as a mathematician, you will acknowledge to be deeply +interesting, even in an educational point of view. The work is complete, +and the system so far perfected as to place it above criticism; and, so far +as regards astronomy, as will Ptolemy beyond rivalry [_sic_: no doubt some +words omitted]. Believe me to be, Sir, with the profoundest respect, etc. +The work is the result of thirty-five years' travel and observation, labor, +expense, and self-abnegation." + +I replied to the effect that my time was fully occupied, and that I was +obliged to decline discussion with many persons who have views of their +own; that the proper way is to publish, so that those who choose may read +when they can find leisure. I added that I should advise a precursor in the +shape of a small pamphlet, as two octavo volumes {358} would be too much +for most persons. This was sound advice; but it is not the first, second, +or third time that it has proved very unpalatable. I received the following +answer, to which I take the liberty of prefixing a bit of leonine wisdom: + + "Si doceas stultum, laetum non dat tibi vultum; + Odit te multum; vellet te scire sepultum.[658]" + +"Sir,--I pray you pardon the error I unintentionally have fallen into; +deceived by the F.R.S. [I am not F.R.S.] I took you to be a man of science +[_omnis homo est animal, Sortes est homo, ergo Sortes est animal_][659] +instead of the mere mathematician, or human calculating-machine. Believe +me, Sir, you also have mistaken your mission, as I have mine. I wrote to +you as I would to any other man well up in mathematics, with the intent to +call your attention to a singular fact of omission by Euclid, and other +great mathematicians: and, in selecting you, I did you an honor which, from +what I have just now heard, was entirely out of place. I think, considering +the nature of the work set forth in the prospectus, you are guilty of both +folly and presumption, in assuming the character of a patron; for your own +sense ought to have assured you that was such my object I should not have +sought him in a De Morgan, who exists only by patronage of others. On the +other hand, I deem it to be an unpardonable piece of presumption in +offering your advice upon a subject the magnitude, importance, and real +utility of which you know nothing about: by doing so you have offered me a +direct insult. The system is a manual of Philosophy, a one inseparable +whole of metaphysics and physic; embracing points the most interesting, +laws the most important, {359} doctrines the most essential to advance man +in accordance with the spirit of the times. I may not live to see it in +print; for, at ----, life at best is uncertain: but, live or die, be +assured Sir, it is not my intention to debase the work by seeking +patronage, or pandering to the public taste. Your advice was the less +needed, seeing I am an old-established ----. I remain, etc.--P.S. You will +oblige me by returning the prospectus of my work." + + + +My reader will, I am sure, not take this transition from the "profoundest +respect" to the loftiest insolence for an _apocraphical_ correspondence, to +use a word I find in the Prospectus: on my honor it is genuine. He will be +better employed in discovering whether I exist by patronizing others, or by +being patronized by them. I make any one who can find it out a fair offer: +I will give him my patronage if I turn out to be Bufo, on condition he +gives me his, if I turn out to be Bavius.[660] I need hardly say that I +considered the last letter to be one of those to which no answer is so good +as no answer. + +These letters remind me in one respect of the correspondents of the +newspapers. My other party wrote because a friend had pointed me out: but +he would not have written if he had known what another friend told him just +in time for the second letter. The man who sends his complaint to the +newspaper very often says, in effect, "Don't imagine, Sir, that I read your +columns; but a friend who sometimes does has told me ..." It is worded +thus: "My attention {360} has been directed to an article in your paper of +..." Many thanks to my friend's friends for not mentioning the Budget: had +my friend's attention been directed to it I might have lost a striking +example of the paradoxer in search of a patron. That my Friend was on this +scent in the first letter is revealed in the second. Language was given to +man to conceal his thoughts; but it is not every one who can do it. + +Among the most valuable information which my readers will get from me is +comparison of the reactions of paradoxers, when not admitted to argument, +or when laughed at. Of course, they are misrepresented; and at this they +are angry, or which is the same thing, take great pains to assure the +reader that they are not. So far natural, and so far good; anything short +of concession of a case which must be seriously met by counter-reasons is +sure to be misrepresentation. My friend Mr. James Smith and my friend Mr. +Reddie are both terribly misrepresented: they resent it by some +insinuations in which it is not easy to detect whether I am a conscious +smotherer of truth, or only muddle-headed and ignorant. [This was written +before I received my last communication from Mr. James Smith. He tells me +that I am wrong in saying that his work in which I stand in the pillory is +all reprint: I have no doubt I confounded some of it with some of the +manuscript or slips which I had received from my much not-agreed-with +correspondent. He adds that my mistake was intentional, and that my reason +is obvious to the reader. This _is_ information, as the sea-serpent said +when he read in the newspaper that he had a mane and tusks.] + + + +THE DOUBLE VAHU PROCESS. + +My friend Dr. Thorn[661] sees deeper into my mystery. By the way, he still +sends an occasional touch at the old {361} subject; and he wants me +particularly to tell my readers that the Latin numeral letters, if M be +left out, give 666. And so they do: witness DCLXVI. A person who thinks of +the origin of symbols will soon see that 666 is our number because we have +five fingers on each hand: had we had but four, our mystic number would +have been expressed by 555, and would have stood for our present 365. Had n +been the number on each hand, the great number would have been + + (n + 1) (4n^2 + 2n + 1) + +With no finger on each hand, the number would have been 1: with one finger +less than none at all on each hand, it would have been 0. But what does +this mean? Here is a question for an algebraical paradoxer! So soon as we +have found out how many fingers the inhabitants of any one planet have on +each hand, we have the means of knowing their number of the Beast, and +thence all about them. Very much struck with this hint of discovery, I +turned my attention to the means of developing it. The first point was to +clear my vision of all the old cataracts. I propose the following +experiment, subject of course to the consent of parties. Let Dr. Thorn +Double-Vahu Mr. James Smith, and Thau Mr. Reddie: if either be deparadoxed +by the treatment, I will consent to undergo it myself. Provided always that +the temperature required be not so high as the Doctor hints at: if the +Turkish Baths will do for this world, I am content. + +The three paradoxers last named and myself have a pentasyllable convention, +under which, though we go far beyond civility, we keep within civilization. +Though Mr. James Smith pronounced that I must be dishonest if I did not see +his argument, which he knew I should not do [to say nothing of recent +accusation]; though Dr. Thorn declared me a competitor for fire and +brimstone--and my wife, too, which doubles the joke: though Mr. Reddie +{362} was certain I had garbled him, evidently on purpose to make falsehood +appear truth; yet all three profess respect for me as to everything but +power to see truth, or candor to admit it. And on the other hand, though +these were the modes of opening communication with me, and though I have no +doubt that all three are proper persons of whom to inquire whether I should +go up-stairs or down-stairs, etc., yet I am satisfied they are thoroughly +respectable men, as to everything but reasoning. And I dare say our several +professions are far more true in extent than in many which are made under +more parliamentary form. We find excuses for each other: they make +allowances for my being hoodwinked by Aristotle, by Newton, by the Devil; +and I permit them to feel, for I know they cannot get on without it, that +their reasons are such as none but a knave or a sinner can resist. But +_they_ are content with cutting a slice each out of my character: neither +of them is more than an uncle, a Bone-a-part; I now come to a dreadful +nephew, Bone-the-whole. + +I will not give the name of the poor fellow who has fallen so far below +both the _honestum_ and the _utile_, to say nothing of the _decorum_ or the +_dulce_.[662] He is the fourth who has taken elaborate notice of me; and my +advice to him would be, _Nec quarta loqui persona laboret_.[663] According +to him, I scorn humanity, scandalize learning, and disgrace the press; it +admits of no manner of doubt that my object is to mislead the public and +silence truth, at the expense of the interests of science, the wealth of +the nation, and the lives of my fellow men. The only thing left to be +settled is, whether this is due to ignorance, natural distaste for truth, +personal malice, a wish to curry favor with the Astronomer Royal, or mere +toadyism. The only accusation which has truth in it is, that I have made +myself a "public scavenger of science": the assertion, which is the {363} +most false of all is, that the results of my broom and spade are "shot +right in between the columns of" the _Athenaeum_. I declare I never in my +life inserted a word between the columns of the _Athenaeum_: I feel huffed +and miffed at the very supposition. I _have_ made myself a public +scavenger; and why not? Is the mud never to be collected into a heap? I +look down upon the other scavengers, of whom there have been a few--mere +historical drudges; Montucla, Hutton, etc.--as not fit to compete with me. +I say of them what one crossing-sweeper said of the rest: "They are well +enough for the common thing; but put them to a bit of fancy-work, such as +sweeping round a post, and see what a mess they make of it!" Who can touch +me at sweeping round a paradoxer? If I complete my design of publishing a +separate work, an old copy will be fished up from a stall two hundred years +hence by the coming man, and will be described in an article which will end +by his comparing our century with his own, and sighing out in the best New +Zealand pronunciation-- + + "Dans ces tems-la + C'etait deja comme ca!"[664] + + + +ORTHODOX PARADOXERS. + +And pray, Sir! I have been asked by more than one--do your orthodox never +fall into mistake, nor rise into absurdity? They not only do both, but they +admit it of each other very freely; individually, they are convinced of +sin, but not of any particular sin. There is not a syndoxer among them all +but draws his line in such a way as to include among paradoxers a great +many whom I should exclude altogether from this work. My worst specimens +are but exaggerations of what may be found, occasionally, in the thoughts +of sagacious investigators. At the end of the {364} glorious dream, we +learn that there is a way to Hell from the gates of Heaven, as well as from +the City of Destruction: and that this is true of other things besides +Christian pilgrimage is affirmed at the end of the Budget of Paradoxes. If +D'Alembert[665] had produced _enough_ of a quality to match his celebrated +mistake on the chance of throwing head in two throws, he would have been in +my list. If Newton had produced _enough_ to match his reception of the +story that Nausicaa, Homer's Phaeacian princess, invented the celestial +sphere, followed by his serious surmise that she got it from the +Argonauts,--then Newton himself would have had an appearance entered for +him, in spite of the _Principia_. In illustration, I may cite a few words +from _Tristram Shandy_: + + + +"'A soldier,' cried my uncle Toby, interrupting the Corporal, 'is no more +exempt from saying a foolish thing, Trim, than a man of letters.'--'But not +so often, an' please your honor,' replied the Corporal. My uncle Toby gave +a nod." + + + +I now proceed to die out. Some prefatory remarks will follow in time.[666] +I shall have occasion to insist that all is not barren: I think I shall +find, on casting up, that two out of five of my paradoxers are not to be +utterly condemned. Among the better lot will be found all gradations of +merit; at the same time, as was remarked on quite a different subject, +there may be little to choose between the last of the saved and the first +of the lost. The higher and better class is worthy of blame; the lower and +worse class is worthy of praise. The higher men are to be reproved for not +taking up things in which they could do some good: the lower men are to be +commended for taking up things in which they can do no great harm. The +circle problem is like Peter Peebles's lawsuit: + +{365} + + + +"'But, Sir, I should really spoil any cause thrust on me so hastily.'--'Ye +cannot spoil it, Alan,' said my father, 'that is the very cream of the +business, man,--... the case is come to that pass that Stair or Arniston +could not mend it, and I don't think even you, Alan, can do it much harm.'" + + + +I am strongly reminded of the monks in the darker part of the Middle Ages. +To a certain proportion of them, perhaps two out of five, we are indebted +for the preservation of literature, and their contemporaries for good +teaching and mitigation of socials evils. But the remaining three were the +fleas and flies and thistles and briars with whom the satirist lumps them, +about a century before the Reformation: + + "Flen, flyys, and freris, populum domini male caedunt; + Thystlis and breris crescentia gramina laedunt. + Christe nolens guerras qui cuncta pace tueris, + Destrue per terras breris, flen, flyys, and freris. + Flen, flyys, and freris, foul falle hem thys fyften yeris, + For non that her is lovit flen, flyys ne freris."[667] + +I should not be quite so savage with my second class. Taken together, they +may be made to give useful warning to those who are engaged in learning +under better auspices: aye, even useful hints; for bad things are very +often only good things spoiled or misused. My plan is that of a predecessor +in the time of Edward the Second: + + "Meum est propositum genti imperitae + Artes frugi reddere melioris vitae."[668] + +To this end I have spoken with freedom of books as books, of opinions as +opinions, of ignorance as ignorance, of {366} presumption as presumption; +and of writers as I judge may be fairly inferred from what they have +written. Some--to whom I am therefore under great obligation--have +permitted me to enlarge my plan by assaults to which I have alluded; +assaults which allow a privilege of retort, of which I have often availed +myself; assaults which give my readers a right of partnership in the +amusement which I myself have received. + +For the present I cut and run: a Catiline, pursued by a chorus of Ciceros, +with _Quousque tandem? Quamdiu nos? Nihil ne te?_[669] ending with, _In te +conferri pestem istam jam pridem oportebat, quam tu in nos omnes jamdiu +machinaris!_ I carry with me the reflection that I have furnished to those +who need it such a magazine of warnings as they will not find elsewhere; _a +signatis cavetote_:[670] and I throw back at my pursuers--_Valete, doctores +sine doctrina; facite ut proxima congressu vos salvos corporibus et sanos +mentibus videamus._[671] Here ends the Budget of Paradoxes. + +{367} + + * * * * * + + +APPENDIX. + +I think it right to give the proof that the ratio of the circumference to +the diameter is incommensurable. This method of proof was given by +Lambert,[672] in the _Berlin Memoirs_ for 1761, and has been also given in +the notes to Legendre's[673] Geometry, and to the English translation of +the same. Though not elementary algebra, it is within the reach of a +student of ordinary books.[674] + +Let a continued fraction, such as + + a + ----- + b + c + ----- + d + e + - + f + etc., + +be abbreviated into a/b+ c/d+ e/f+ etc.: each fraction being understood as +falling down to the side of the preceding sign +. In every such fraction we +may suppose b, d, f, etc. {368} positive; a, c, e, &c. being as required: +and all are supposed integers. If this succession be continued ad +infinitum, and if a/b, c/d, e/f, etc. all lie between -1 and +1, exclusive, +the limit of the fraction must be incommensurable with unity; that is, +cannot be A/B, where A and B are integers. + +First, whatever this limit may be, it lies between -1 and +1. This is +obviously the case with any fraction p/(q + [omega]), where [omega] is +between +-1: for, p/q, being < 1, and p and q integer, cannot be brought up +to 1, by the value of [omega]. Hence, if we take any of the fractions + + a/b, a/b+ c/d, a/b+ c/d+ e/f, etc. + +say a/b+ c/d+ e/f+ g/h we have, g/h being between +-1, so is e/f+ g/h, so +therefore is c/d+ e/f+ g/h; and so therefore is a/b+ c/d+ e/f+ g/h. + +Now, if possible, let a/b+ c/d+ etc. be A/B at the limit; A and B being +integers. Let + + P = A c/d+ e/f+ etc., Q = P e/f+ g/h+ etc., R = Q g/h + i/k + etc. + +P, Q, R, etc. being integer or fractional, as may be. It is easily shown +that all must be integer: for + +{369} + + A/B = a/b+ P/A, or, P = aB - bA + + P/A = c/d+ Q/P, or, Q = cA - dP + + Q/P = e/f+ R/Q, or, R = eP - fQ + +etc., etc. Now, since a, B, b, A, are integers, so also is P; and thence Q; +and thence R, etc. But since A/B, P/A, Q/P, R/Q, etc. are all between -1 +and +1, it follows that the unlimited succession of integers P, Q, R, are +each less in numerical value than the preceding. Now there can be no such +_unlimited_ succession of _descending_ integers: consequently, it is +impossible that a/b+ c/d+, etc. can have a commensurable limit. + +It easily follows that the continued fraction is incommensurable if a/b, +c/d, etc., being at first greater than unity, become and continue less than +unity after some one point. Say that i/k, l/m,... are all less than unity. +Then the fraction i/k+ l/m+ ... is incommensurable, as proved: let it be +[kappa]. Then g/(h + [kappa]) is incommensurable, say [lambda]; e/(f + +[lambda]) is the same, say [mu]; also c/(d + [mu]), say [nu], and a/(b + +[nu]), say [rho]. But [rho] is the fraction a/b+ c/d+ ... itself; which is +therefore incommensurable. + +Let [phi]z represent + + a a^2 a^3 + 1 + - + ------- + -------------- + .... + z 2z(z+1) 2.3.z(z+1)(z+2) + +{370} Let z be positive: this series is convergent for all values of a, and +approaches without limit to unity as z increases without limit. Change z +into z + 1, and form [phi]z - [phi](z+1): the following equation will +result-- + + a + [phi]z-[phi](z+1) = ------([phi](z+2)) + z(z+1) + + a [phi](z+1) a [phi](z+1) a [phi](z+2) + or a = - ---------- . z + - ---------- . --- ---------- + z [phi]z z [phi]z z+1 [phi](z+1) + + a = [psi]z(z+[psi](z+1)) + +[psi]z being (a/z)([phi](z+1)/[phi]z); of which observe that it diminishes +without limit as z increases without limit. Accordingly, we have + + [psi]z = a/z+ [psi](z+1) = a/z+ a/(z+1)+ [psi](z+2) + = a/z+ a/(z+1)+ a/(z+2)+ [psi](z+3), etc. + +And, [psi](z + n) diminishing without limit, we have + + a/z . [phi](z+1)/[phi]z = (a/z+) (a/(z+1)+) (a/(z+2)+) (a/((z+3)+ ...)) + +Let z = 1/2; and let 4a = -x^2. Then (a/z)[phi](z+1) is -(x^2/2) ( 1 - +x^2/(2.3) + x^4/(2.3.4.5...)) or -(x/2) sin x. Again [phi]z is 1 - x^2/2 + +x^4/(2.3.4) or cos x: and the continued fraction is + + (1/4)x^2/(1/2)+ (1/4)x^2/(3/2)+ (1/4)x^2/(5/2)+ ... + or -x/2 x/1+ -x^2/3+ -x^2/5+ + ... + +{371} whence tan x = x/1+ -x^2/3+ -x^2/5+ -x^2/7+ ... + +Or, as written in the usual way, + + tan x = x + ------- + 1 - x^2 + ------- + 3 - x^2 + ------- + 5 - x^2 + ------- + 7 - ... + +This result may be proved in various ways: it may also be verified by +calculation. To do this, remember that if + + a_1/b_1+ a_2/b_2+ a_3/b_3+ ... a_n/b_n = P_n/Q_n; then + + P_1=a_1, P_2=b_2 P_1, P_3=b_3 P_2+a_3 P_1, P_4=b_4 P_3+a_4 P_2, etc. + Q_1=b_1, Q_2=b_2 Q_1+a_2, Q_3=b_3 Q_2+a_3 Q_1, Q_4=b_4 Q_3+a_4 Q_2, etc. + +in the case before us we have + + a_1=x, a_2=-x^2, a_3=-x^2, a_4=-x^2, a_5=-x^2, etc. + b_1=1, b_2=3, b_3=5, b_4=7, b_5=9, etc. + + P_1=x Q_1=1 + P_2=3x Q_2=3-x^2 + P_3=15x-x^3 Q_3=15-6x^2 + P_4=105x-10x^3 Q_4=105-45x^2+x^4 + P_5=945x-105x^3+x^5 Q_5=945-420x^2+15x^4 + P_6=10395x-1260x^3+21x^5 Q_6=10395-4725x^2+210x^4-x^6 + +We can use this algebraically, or arithmetically. If we divide P_n by Q_n, +we shall find a series agreeing with the known series for tan x, _as far +as_ n _terms_. That series is + + x + x^3/3 + 2x^5/15 + 17x^7/315 + 62x^9/2835 + ... + +{372} Take P_5, and divide it by Q_5 in the common way, and the first five +terms will be as here written. Now take _x_ = .1, which means that the +angle is to be one tenth of the actual unit, or, in degrees 5 deg..729578. +We find that when x = .1, P_6 = 1038.24021, Q_6 = 10347.770999; whence P_6 +divided by Q_6 gives .1003346711. Now 5 deg..729578 is 5 deg.43'46-1/2"; +and from the old tables of Rheticus[675]--no modern tables carry the +tangents so far--the tangent of this angle is .1003347670. + +Now let x = (1/4)[pi]; in which case tan x = 1. If (1/4)[pi] be +commensurable with the unit, let it be (m/n), m and n being integers: +we know that (1/4)[pi] < 1. We have then + + 1=(m/n)/1- (m^2/n^2)/3- (m^2/n^2)/5- ... = m/n- m^2/3n- m^2/5n- m^2/7n- + ... + +Now it is clear that m^2/3n, m^2/5n, m^2/7n, etc. must at last become and +continue severally less than unity. The continued fraction is therefore +incommensurable, and cannot be unity. Consequently [pi]^2 cannot be +commensurable: that is, [pi] is an incommensurable quantity, and so also +is [pi]^2. + + + +I thought I should end with a grave bit of appendix, deeply mathematical: +but paradox follows me wherever I go. The foregoing is--in my own +language--from Dr. (now Sir David) Brewster's[676] English edition of +Legendre's Geometry, (Edinburgh, 1824, 8vo.) translated by some one who is +not named. I picked up a notion, which others had at Cambridge in 1825, +that the translator was the late Mr. Galbraith,[677] then known at +Edinburgh as a writer and teacher. + +{373} But it turns out that it was by a very different person, and one +destined to shine in quite another walk; it was a young man named Thomas +Carlyle.[678] He prefixed, from his own pen, a thoughtful and ingenious +essay on Proportion, as good a substitute for the fifth Book of Euclid as +could have been given in the space; and quite enough to show that he would +have been a distinguished teacher and thinker on first principles. But he +left the field immediately. + + * * * * * + +(The following is the passage referred to at Vol. II, page 54.) + +Michael Stifelius[679] edited, in 1554, a second edition of the Algebra +(_Die Coss._), of Christopher Rudolff.[680] This is one of the earliest +works in which + and - are used. + +Stifelius was a queer man. He has introduced into this very work of Rudolff +his own interpretation of the number of the Beast. He determined to fix the +character of Pope Leo: so he picked the numeral letters from LEODECIMVS, +and by taking in X from LEO X. and striking out M as standing for +_mysterium_, he hit the number exactly. This discovery completed his +conversion to Luther, and his determination to throw off his monastic vows. +Luther dealt with him as straight-forwardly as with Melanchthon about his +astrology: he accepted the conclusions, but told him to clear his mind of +all the premises about the Beast. Stifelius {374} did not take the advice, +and proceeded to settle the end of the world out of the prophet Daniel: he +fixed on October, 1533. The parishioners of some cure which he held, having +full faith, began to spend their savings in all kinds of good eating and +drinking; we may charitably hope this was not the way of preparing for the +event which their pastor pointed out. They succeeded in making themselves +as fit for Heaven as Lazarus, so far as beggary went: but when the time +came, and the world lasted on, they wanted to kill their deceiver, and +would have done so but for the interference of Luther. {375} + + * * * * * + + +INDEX. + +Pages denoted by numerals of this kind (_287_) refer to biographical notes, +chiefly by the editor. Numerals like 426 refer to books discussed by De +Morgan, or to leading topics in the text. Numerals like 126 indicate minor +references. + + Abbott, Justice, I, _181_. + Abernethy, J., II, _219_. + Aboriginal Britons, a poem, II, 270. + Academy of Sciences, French, I, 163. + Adair, J., I, _223_. + Adam, M., I, _65_. + Adams, J. C., I, _43_, 82, 385, 388; II, 131, 135, 140, 303. + Ady, Joseph, II, 42, _42_. + Agnew, H. C., I, 328. + Agricola, J., I, 394. + Agricultural Laborer's letter, II, 16. + Agrippa, H. C., I, _48_, 48. + Ainsworth, W. H., II, _132_. + Airy, I, _85_, 88, 152, 242; II, 85, 140, 150, 303, 347. + Alchemy, I, 125. + Alfonso X (El Sabio), II, _269_. + Alford, H., II, _221_. + Alfred, King, Ballad of, II, 22. + Algebra, I, 121. + Algebraic symbols, I, 121. + Almanac, I, 300; II, 147, 148, 207. + (_See Easter._) + Aloysius Lilius, I, 362. + Alsted, J. H., II, _282_. + Ameen Bey, II, 15. + Amicable Society, I, 347. + Ampere, I, 86. + Amphisbaena serpent, I, 31. + Anagrams, De Morgan, I, 138. + Anaxagoras, II, _59_. + Anghera, II, 60, _60_, 61, 279. + Annuities, Fallacies of, I, 157. + Antichrist, I, 130. + Antimony, I, 125. + Antinewtonism, I, 162. + Antinomians, I, 394. + Antiphon, II, _59_. + Antonie, F., I, _126_, 126. + Apollonius, I, 41, 107. + Apparitions, II, 47. + Arago, I, _243_, 390. + Aratus, II, _167_. + Arbuthnot, I, _133_, 134. + Archer, H., II, 90. + Archimedes, I, 5, 11, 42, 83, 107. + Archytas, I, _53_. + Argoli, I, _104_. + Aristocrat, as a scientist, I, 131. + Aristotle, I, 5, 331. + Arnobius, II, _73_. + Arson, P. J., II, _207_. + Ashton, R., II, _99_. + Astrology, I, 118, 127, 128, 350; II, 43. + Astronomer's Drinking Song, I, 380. + Astronomical Aphorisms, I, 398. + Paradox, I, 394. + Police Report, I, 390. + Society. (_See Royal Astronomical Society._) + Astronomy, Bailly's exaggerated view of, I, 166. + Astunica, Didacas, I, 90. + Athanasian Creed, I, 371. + Atheists, Philosophical, I, 1. + Atoms, II, 191. + {376} + Attraction, I, 136, 151, 155. + Augustine, St., II, _23_. + Aurora borealis, I, 134. + Austen, Jane, I, 191. + Auzout, A., II, _300_. + Aviation, Early ideas of, II, 8. + + Babbage, C., I, _207_, 290, 291; II, 181. + Bachet, de Meziriac, I, _161_. + Bacon, F., I, 5, _75_, 75, 76, 79, 89, 145, 331. + Bacon, R., I, 5, _126_, 126, 360; II, 94. + Baconian controversy, I, 141. + Baden Powell, II, _267_. + Bailly, J. S., I, 166, _166_, 308. + Baily, F., I, 308, _309_; II, 16, 143, 188. + Baily, R., II, 16. + Baker, T., II, _302_. + Bakewell, F. C., II, 156, _156_. + Banks, J., I, 28. + Barberini, M., II, _267_. + Barker, C., II, _262_. + Baronius, I, 33, 35; II, _62_. + Barreme, I, _42_. + Barrett, G., II, _188_. + Barrow, I., I, _160_; II, 302. + Baruel, de, I, 165. + Bassano, Duc de, II, 3, 339. + Baxter, T., I, 146. + Bayle, P., II, _73_. + Beaufort, F., II, _267_. + Beaugrand, I, 119, _121_. + Beaulieu, I, _119_, 119, 121. + Beaune, de, II, _59_. + Becourt, R., II, 277. + Bedford, Duke of, (6th), I, _182_. + Behmen, I, _168_, 254; II, 317. + Bellenden, W., I, _175_. + Bentley, I, _110_. + Berkeley, G., II, 346. + Bernard, E., II, _297_, 300. + Bernardus Trevisanus, I, _126_, 126. + Bernoullis, I, 130, _150_, _335_, 336. + Bertius, P., II, _300_. + Bese, I, _66_. + Bessel, I, _384_; II, 2. + Bethune, I, _99_, 279, 291. + Bettesworth, I, 19. + Beza. (_See Bese._) + Bickersteth, E. H., I, _238_. + Bidder, I, _86_. + Biden, J., II, 158, _160_. + Bidle, (Biddle), I, 239. + Biot, I, _85_. + Birch, T., I, _108_; II, 304, 313. + Birks, T. R., II, 158, _158_. + Bishop, G., I, _386_. + Bishops as Paradoxers, I, 226. + Boccaccio, I, 38. + Boethius, I, _42_, 45. + Boehme. (_See Behmen._) + Boncompagni, I, _298_. + Boniface, St., I, 32. + Bonnycastle, J., II, _16_. + Booker, I, 115. + Boole, G., I, _261_, 332; II, 75, 79. + --A tribute to, II, 79. + Borelli, G. A., II, _300_. + Borello, I, _69_. + Boreman, I, 113. + Borron, Mrs., II, 7. + Boscovich, I, _156_, 164. + Bouguer, II, _301_. + Bouillaud, I, _87_; II, 295. + Bouvard, A., I, _327_. + Bovillus, I, _44_; II, 324. + --Epitome of, I, 44. + Bowdler, H. M., I, _194_. + Bowring, J., I, _352_; II, 256. + Boyle, R., I, 24, _125_; II, 300. + Bradley, I, 24. + Bradwardine, I, _227_, 228, 229. + Brahe. (_See Tycho B._) + Brancker, I, 107; II, _300_. + Brenan, J., I, 330, _330_. + Brewster, D., I, 39, _137_, 140; II, 214, 288, 372. + Briggs, I, _69_; II, 299, 302. + Bright, J., II, _235_. + Brinkley, J., I, _311_. + Britannicus, D., II, 8. + British Museum library, I, 151. + Brothers, R., I, _315_; II, 97. + Brougham, Henry, Lord, I, _191_. + Brouncker (Brounker), I, _132_; II, 302. + Brown, W., II, _168_. + Browne, T., I, 31. + Brucker, I, _61_. + Brunet, I, _402_. + Bruennow, I, _386_. + Bruno, I, _59_, 59. + Bryson, II, _59_. + Buergi, I, 52. + Buffon, I, _282_. + Bulstrode, II, 84. + Bungus, I, _55_, 55, 57. + Buoncompagno, U., I, _362_. + {377} + Burgon, J. W., II, _30_. + Buridan, I, _37_. + --Questiones morales, I, 37. + Buridan's Ass, I, 37. + Burke, E., I, _173_. + Burlesque, Frend's, I, 208. + Burnet, G., I, _107_. + Burney, Frances, I, _190_. + Burton, Frances B., I, 374. + Busby, R., II, _313_. + Buteo, I, _51_. + Butler, G., I, _199_. + Butler, S., II, _218_. + Buxton, J., I, _86_. + Byrgius. (_See Buergi._) + Byrne, O., I, _329_; II, 186, 190. + Byron, I, 186; II, 270, 273. + + Cabbala, I, 272. + Calculating Boys, I, 86. + Calculus, I, 129. + Calendar. (_See Easter._) + Cambridge Poets, II, 269. + Campanus, I, 42, _43_. + Canning, Geo., II, _145_. + Carcavi, I, _106_. + Cardanus, II, _59_. + Carlile, R., I, _271_. + Carlyle, T., II, _373_. + Carnot, I, 107. + Caroline tables, I, 124. + Casaubon, I, _111_. + Case, J., I, _128_, 128. + Cassini, J., I, _172_. + Castel, I, _148_, 148. + Castiglioni, I, _139_. + Castlereagh, I, 185, _186_. + Cataldi, I, _69_, 69. + Catcott, A., I, _237_. + Causans, de, I, _298_. + Cavalieri, I, _106_. + Cavendish, C., I, _106_; II, 299, 312. + Cavendish, W., I, _290_. + Caxton, W., II, _281_. + Cayley, A., II, _292_. + Cecil, R. (1st Earl of Salisbury), II, _330_. + Centrifugal force, II, 268. + Ceulen. (_See Van Ceulen._) + Challis, J., I, _390_; II, 141. + Chalmers, I, _102_; II, 219. + Chambers, E., II, _282_. + Chambers, R., I, _344_, 344. + Charles IX, II, 94. + Charles X, II, 1. + Chasles, I, _39_, 229. + Chesterfield, Earl of (4th), II, _298_. + Chiffinch, W., II, _50_. + Ch'in Chiu-shang, II, 66. + Chitty, J., II, _323_. + Chiu-chang, Suan-shu, II, 67. + Christian Evidence Society, I, 270. + Christie, I, 27. + Christmann, I, 272, _272_. + Church question, I, 62. + Church, The word, II, 30. + Circle squarers. (_See Squaring the Circle._) + Circulating media of mathematics, I, 107. + Ciruelo. (_See Sanchez._) + Clairaut, I, _219_, 382. + Clarence, Duke of, I, 179. + Clarke, R., I, _255_. + Clavius, I, 11, _69_, 111, 112, 335, 362, 363, 372; II, + 59. + Clayton., Geo., II, _98_. + Cluvier, D., II, 332, _332_. + Cobb, Mary, II, 117. + Cobbett, W., I, _177_, 200, 399. + Cobden, R., II, 217. + Cocker, I, _42_; II, 64, 173, 251, 307. + Cody, P., II, 208. + Coke, E., II, _331_. + Colburn, Z., I, _86_. + Colenso, I, _63_, 247; II, 191. + Collins, J., I, _107_; II, 297, 300, 302, 313. + Colvill, W. H., II, 68. + Cometic astrology, I, 128. + Comets, I, 128; II, 68, 83. + Cominale, C., I, _162_, 162. + Compton, S. J. A., II, _19_. + Computation, Paradoxes of, II, 251, 267. + Condamine, C. M. de la, II, _301_. + Conduitt, John, I, _397_. + Conduitt, Mrs., I, _136_. + Congregation of the Index, I, 90. + Converse propositions, I, 295. + Convocation at Oxford, I, 96. + Cooke, Margaret, I, _310_. + Cooper, A. A. (Shaftsbury), II, _181_. + Copernicus, I, 5, 6, _76_, 90, 121, 172, 380; II, 165, 335. + Copley, J. S., I, _198_. + Cormouls, I, 225. + Cosmology, I, 172. + {378} + Cotes, R., II, _301_. + Cottle, Mrs., II, 97, _97_, 161. + Craig, J., I, _129_, 129. + Creed, Mathematics of a, I, 329. + Cribb, T., I, _314_. + Crotus, J., I, 318. + Cruickshank, G., I, _186_. + Cube, Duplication of, I, 349. + Cumyns, Eliza, I, 299. + Cunningham, I, 172, _172_. + Curabelle, I, _221_. + Curious Calculations, II, 66. + Curll, E., II, _279_. + Cusa, I, _44_, 47, 360. + Custom, II, 324. + Cyclometry, II, 208. (_See Squaring of the Circle._) + Cyclopaedias, Review of, II, 280. + + D'Alembert, I, _382_; II, 283, 364. + Dalgarno, I, 116, _117_. + Dalton, J., I, _255_. + D'Arblay, Mme., I, _190_. + Darwin, E., II, _8_. + Darwinism, Primitive, I, 344. + Dary, M., II, _305_. + Daval, P., II, _298_. + Davies, T. S., II, 151, _151_, 188. + Day, A., I, 295, _295_. + De Baruel, I, 165. + De Beaune. (_See Beaune._) + De Becourt, II, 277, _277_. + Debenham, J., I, _393_. + De Causans. (_See Causans._) + Dechales. (_See de Challes._) + De Challes, I, _45_. + Decimal coinage, II, 80, 168, 169. + Decimals run riot, II, 80. + Dee, J., II, _302_. + De Faure, I, 149. + De la Leu, I, _297_. + Delambre, I, _160_, 167, 354; II, 165. + Democritus, II, _34_. + De Moivre, I, 24, _376_; II, 298. + De Molieres, I, _220_. + De Molina, I, _297_. + Demonville, I, 291, 293. + De Morgan, A., I, 191, 383; II, 194. + --Refusal of LL. D., I, 191. + De Morgan, G. C., I, 383. + De Morgan, Mrs., I, _196_; II, 194. + Denison, J., I, 348, 353. + Desaguliers, I, _153_, 156, 157. + Desargues, I, _119_, 221. + Descartes, I, 5, 59, 105, 132, 165, 204, 220; II, 94. + De Serres, II, _60_. + De Sluse. (_See Sluse._) + De Thou, I, 51, _111_, 113; II, 295. + De Vausenville, I, 12. + Devonshire, Duke of (7th), I, _290_. + Diamandi, I, 86. + Didacus Astunica, I, 90. + Diderot, II, _4_, 283, 339. + Digby, K., I, _108_. + Digges, T., and L., II, _302_. + Dionysius Exiguus, I, _360_. + Dircks, H., II, 138, _138_. + Discoverers and discoveries, II, 206. + Discovery, Basis of, I, 85. + D'Israeli, I., I, _115_, 118, 136, 188, 227. + Ditton, I, _133_, 133. + Division, Nature of, II, 248. + Dobson, J., I, _234_, 234. + Dodson, J., II, _312_. + Dodt, I, _52_. + Doggerel verse, I, 341. + Dolland, I, _377_. + Double Vahu Process, II, 360. + Douglas, G., I, _232_. + Drach, S. M., II, _317_. + Drayson, G. A. W., II, _132_, 132. + Dryden, II, _71_. + Dual arithmetic, II, 186. + Duchesne, I, _52_. + Dumortier, I, 313. + Duncan, A., I, _179_. + Dunkin, E., II, _349_. + Duodecimal scale, II, 68. + Duplication Problem, I, 349. + Dupuy, J. and P., II, _295_. + Dutens, L., II, _90_. + Dyer, G., I, _178_. + + Earth, Figure of, II, 54. + Easter, I, 359. + Easter Day Paradoxes, I, 353. + Ebrington, Thos., I, _247_. + Edgeworth, Maria, I, _191_. + Editorial System, I, 15. + Edleston, I, _140_; II, 296. + Edwards, J., I, _144_. + Edwards, T., I, _112_. + Eirenaeus Philalethes, I, _125_, 125, 126. + Eldon, Lord (1st), II, _197_. + Elephant story, I, 58. + Elizabeth, Queen, I, 128. + Ellenborough, Baron, I, _181_. + {379} + Ellicot, I, 24. + Ellis, I, _76_, 82. + Engel, I, 230. + English language, Origin of, I, 215. + Enriques, F., II, _367_. + Epps, J., I, _153_; II, 143. + Equation of fifth degree, I, 250, 373. + Erasmus, I, 110. + Erastus, I, _65_. + Erichsen, I, 163. + Ersch, II, _193_, 282. + Erskine, T., II, _127_. + Esperanto, Forerunner of, I, 116. + Euclid, I, 5, 43; II, 118, 151. + --Without Axioms, I, 287. + Eudoxus, II, _164_. + Euler, I, 221, _382_; II, 3, 4, 303, 331, 339. + Eusebius, II, _220_. + Eustace, J. C., II, _46_. + Eutocius, I, _41_; II, 60. + Evelyn, J., I, _108_. + Everett, J., I, _346_. + Evidence, I, 57, 58. + + Faber. (_See Stapulensis._) + Fairfax, Mary, I, _242_. + Falco, I, 53. + Faraday, M., II, _351_. + Faure, de, I, 149; II, 238. + Fawcett, H., II, _249_. + Ferguson, J., II, _20_. + Fermat, I, 122, 221; II, _300_. + Ferrari, S., II, 68. + Fiction, New era in, I, 189. + Fienus, I, _74_, 74. + Filopanti, Q. B., II, _93_. + Finaeus, I, _50_, 50, 113. + Finleyson, J., I, 314, _314_. + Flamsteed, I, _87_, 309; II, 45, 143, 302, 306. + Fletcher, I, 378. + Fludd, II, _318_. + Fly-leaf Paradox, II, 264. + Folkes, M., I, _136_; II, 301. + Fontenelle, I, _103_. + Forbes, D., I, _237_. + Forman, W., I, 296, _296_, 306. + Forster, T. I. M., I, 320, _320_. + Foscarini, I, _90_. + Foster, S., II, _310_. + Fourier, II, _66_. + Fox, G., I, _397_. + Francis, P., II, _96_. + Francoeur, I, _365_. + Frankland, W. B., I, 230, 287. + Franklin, J., II, _265_. + Freedom of opinion, Growth of, I, 265. + Freher, A., II, 319. + French academy on circle squaring, I, 163. + Frend, W., I, _196_, 196, 206, 208, 252. + Fresnel, II, _48_. + Fromondus, I, _74_, 74, 99. + Frost, I. and J., I, 394. + Fry, Elizabeth, I, 224. + Fuller, T., I, _86_. + Fulton, R., I, _148_. + + Gadbury, J., I, _115_, 115. + Galbraith, J. A., II, 372. + Galileo, I, 5, 6, 32, _76_, 82, 83, 96, 122, 381. + Galle, J. G., I, _386_; II, 7. + Galloway, I, _56_, 57; II, 143. + Gamblers, I, 280. + Garrick, I, 21. + Gascoigne, W., II, _299_. + Gassendi, I, _107_. + Gauss, I, 86, 107, 310. + Gemistus, G., I, _188_. + Gentleman's Monthly, Miscellany, I, 208. + Gephryander. (_See Salicetus._) + Gergonne, I, _336_. + Ghetaldi, I, _83_; II, 59. + Ghost paradox, II, 47. + Giddy (Gilbert), II, _174_. + Gilbert, Davies, II, 66, _174_. + Gilbert, William, I, 6, _68_, 68, 76. + Gillot, II, _315_. + Glazier (Glazion), II, 7. + Godwin, F., I, _103_. + Godwin, W., I, _174_. + Golius, I, _106_. + Gompertz, B., I, _378_. + Goulburn, I, _288_. + Goulden, S., II, 88. + Graham, I, 24. + Grandamicus, I, _104_, 104. + Granger, J., I, _156_. + Grant, A. R., II, 131. + Grant, R., I, _392_; II, 131. + Grassi, O., I, _262_. + Grassini, I, _231_. + Graunt, J., I, 113, _114_, 154. + Gravity, I, 151, 244, 348, 353. + {380} + --Newton's apple, I, 136. + Greek numerals, II, _77_. + Greene, R., I, _135_, 135. + Greenhill, Sir G., I, 136. + Greenwich observatory, I, 87. + Gregg, T. D., II, 75, _75_. + Gregorian Calendar, I, 363. + Gregory, D., I, _66_; II, 301. + Gregory, J., I, _118_, 118, 207; II, 302. + Gregory O., II, _71_. + Gregory, Pope, I, 362. + Grevil, I, _202_. + Grey, C., (2d Earl), I, _315_; II, 247. + Grosart, I, _141_, 141, 145. + Grove, W. R., II, _320_. + Gruber, II, _193_, 282. + Gruenberger, I, _70_. + Grynaeus, I, _66_. + Guaricus, I, _43_. + Guillim, J., II, _28_. + Guldin, I, _83_. + Gumpach, Von, II, 137, _137_. + Gunning, H., I, _198_. + Gurney. (_See Fry, E._) + Guthrie, W., I, _395_. + + Hailes, J. D., II, 135, _135_. + Hailesean system of astronomy, II, 135. + Hale, M., I, _123_, 123. + Hales, S., I, _123_. + Hall, B., II, _181_. + Hallam, I, 159. + Halley, I, 24, _124_, 311; II, 301, 332. + Halliwell-Phillips, II, _148_, 296. + Hamilton, W., I, _112_, 117, 331, 335, 339, 341, 342; II, + 52, 53, 111. + Hamilton, W. Rowan, I, _332_; II, 104, 256, 343. + Hanover, King of, I, 201. + Hardy, C., I, _298_. + Hardy, T., I, _178_. + Harriot, T., II, _302_. + Harvey, I, _76_, 78; II, 201. + Hauff, I, _230_. + Haughton, S., II, 372. + Hauksbee, F., I, _156_. + Hayes, C., I, _132_, 132. + Heath, D. D., I, _76_. + Heinfetter, H., II, 94, _94_. + Helmont, J. B. van, I, _125_. + Henson, II, 8. + Heraclitus, II, _34_. + Herbart, J. F., I, 253, _253_; II, 78. + Herigone, II, _59_. + Herschel, J., I, _80_, 299, 326, 383, 386; II, 88, 95, 181, + 255, 261, 262. + Herschel, W., I, _81_, 151, 192, 225, 233, 299; II, 288, 348. + Heywood, F., II, _49_. + Hicks, J. P., II, _67_. + Higgins, G., I, _257_, 274. + Hilarius, Pope, I, _359_. + Hill, J., I, 21, 22, 23, 24. + Hill, Rev. R., I, _192_. + Hill, Sir R., I, _165_, 232. + Hind, J. R., I, _384_. + Hippocrates, II, _59_. + Hoax, An interesting, I, 163. + --Lunar Caustic, I, 288. + --Moon (Herschel), I, 326; II, 131. + Hobbes, I, _105_, 109, 143, 144; II, 80. + Hobhouse, J. C., II, _126_. + Hodder, J., II, _265_. + Hodge, C. B., I, 114. + Hodges, W., I, 237. + Hoffmann, J. J., II, _282_. + Hoffmann, J. J. I. von, I, _230_. + Holloway, B., I, _237_. + Holmes, O. W., I, 109. + Holyoake, G. J., I, _399_, 399. + Hone, W., I, 124, 180, 184, 185. + Hook, T. E., II, _261_. + Hooke, I, _77_; II, 300. + Hooker, R., II, _201_. + Hopkins, J., II, 41. + Horace, I, 40. + Horne, G., I, _152_, 152, 154, 155, 236. + Horne, J., I, _178_. + Horner, L., I, _176_. + Horner, W. G., II, _66_, 151, 187. + Houlston, W., II, 156, _156_. + Howard, E., I, 131. + Howison, W., I, 256, _256_. + Howitt, W., II, 193, _193_. + Howley, I, 63. + Hulls, I, _147_, 147; II, 8. + Hume, J., I, _352_; II, 174. + Husain Rifki, II, 16. + Hussein Effendi, II, 15. + Hutchinson, J., I, 154, _154_. + Hutton, C., I, _153_, 161; II, 303, 340. + Huyghens, I, _100_, 133; II, 300. + + Imaginary numbers, II, 186. + Impalement by request, II, 133. + Inaudi, I, 86. + Index Expurgatorius, I, 90. + {381} + Infant prodigies, I, 86. + Inglis, J. B., II, _52_. + Inglis, R. H., I, _352_. + Ingliz Selim Effendi, II, 15. + Innocent I., I, _359_. + Irving, E., II, _54_. + Ivory, J., II, 142, _142_. + + Jabir ben Aflah, II, _59_. + Jack, R., I, 149. + Jacotot, J., I, 278, _278_. + Jameson, Mrs., II, _63_. + Jeffreys, G., I, _183_. + Jenner, E., II, _205_. + Jesuit contributions, I, 164. + Johnson, H. C., I, 350. + Johnson, S., I, 20, _190_, 259; II, 117. + Johnston, W. H., II, 67. + Jombert, I, _161_. + Jonchere, I, _146_, 146. + Jones, W., I, _135_; II, 298, 301. + Jones, Rev. W., I, _237_. + Jonson, B., I, 13. + Journals, Three classes of, II, 144. + + Kantesian Jeweler, I, 258. + Karsten, I, _230_. + Kaestner, I, _43_, 110, 112. + Kater, I, 11. + Keckermann, I, 3. + Keill, J., II, _302_. + Kepler, I, 52, _76_, 82, 381; II, 166. + Kerigan, T., I, _308_, 353. + Keroualle, De, II, 50. + Kersey, I, 107. + King, Wm., I, _246_. + Kircher, Adolphe, I, 229. + Kircher, Athanasius, I, _103_. + Kirkringius, T., I, 125, _125_. + Kittle, I, 236. + Klein, F., II, 367. + Knight, C., II, _109_, 280, 289. + Knight, G., I, 151, _151_. + Knight, R. P., II, _274_. + Knight, Wm., I, _97_. + Koenig, S., I, _150_. + + Lacomme, I, 46. + La Condamine, II, _301_. + Lacroix, I, 41, 159, 207. + Lactantius, I, 33, _96_. + Lagrange, I, 221, _288_, 313, 382; II, 86. + Laing, F. H., II, _186_, 186. + Lalande, I, _159_. + Lamb, C., I, 178; II, 270. + Lambert, J. H., I, _336_; II, 214, 367. + Lambert, John, II, _309_. + Language, Test of, II, 327. + Lansbergius, I, _70_, 70. + Laplace, I, 24, _255_, 382; II, 1, 340. + Lardner, D., II, _253_. + Lardner, N., I, 14; II, _221_. + Laud, I, _145_. + Lauder, W., I, 297. + Laurent, P., I, _309_, 309. + Laurie, J., II, 4. + Laurie, P., II, _42_. + Laurus, I, 381. + Law, Edmund, I, _181_. + Law, Edward, I, _181_. + Law, W., I, 168, _254_; II, 317. + Le Coq, I, _86_. + Lee, R., I, _66_. + Lee, S., I, _131_. + Lee, W., I, 157. + Legate, I, _59_. + Legendre, I, _229_; II, 215, 367. + Legh, P., II, _68_, 83. + Leibnitz, I, 5, 7; II, 46. + Leo, St., I, _359_. + Leverrier, I, _43_, 82, 383, 386, 388, 390; II, 7, 135, 140, + 303. + Lewis, G. C., II, 162, _162_. + Libri, I, _40_, 62; II, 295. + Lilius, Aloysius, I, 362. + Lilly, I, _115_; II, 302. + Lipen, M., I, _298_. + Little, J., I, 206. + Livingston, R., I, _148_. + Locke, J., I, _142_, 142, 144; + --and Socinianism, I, 142. + Locke, R., I, 146. + Locke, R. A., I, _326_; II, 86, 131. + Logan, W. E., I, _337_. + Logic, Formal, I, 158; II, 75. + --Has no paradoxes, I, 330. + London Mathematical Society, I, 383. + London, University of, I, 259; II, 71. + Long, G., II, _290_. + Long, J. St. J., II. _38_, 205. + Longitude problems, I, 132, 146, 249. + Longley, C. T., I, _325_. + Longomontanus, I, _105_, 105. + Lottery, I. 281. + Lovett, R., I, 165, _166_. + Lowe, R., II, _169_. + Lowndes, W. T., I. _402_. + Lubbock, J., I, _279_; II, 148. + {382} + Lucas, F., II, _28_. + Lucian, I, _102_. + Lunar Caustic Joke, I, 288. + Lunn, J. R., II, _66_. + Lydiat, T., II, _302_. + Lyndhurst, I, _198_. + + Macclesfield, Earls of, I, 7; II, _296_, 301. + Macclesfield, Letters, II, 296. + MacElshender, II, 87. + Machin, J., II, _301_. + Mackey, John, I, 349. + Mackey, S. A., I, _256_. + Maclear, T., II, _181_. + Macleod, H. D., II, 184, _184_. + Magic, I, 118. + Magna Charta, I, 25. + Magnus, I, 42. + Maitland, S., I, _63_, 163. + Malacarne, I, 119. + Malden, H., II, _162_. + Malius, II, _342_. + Mallemens, II, _333_. + Mankind gullible, I, 115. + Manning, H. E., (Card.), II, _233_. + Mansel, H. L., II, _162_. + Marcelis, J., I, _129_, 129. + Maret, II, _3_. + Margarita Philosophica. (_See Reisch._) + Marryat, Capt., II, _87_. + Marsh, H., I, _199_, 271. + Martin, B., I, _152_, 153. + Martin, R., II, _236_. + Maseres, F., I, _197_, 203. + Mason, M., II, _132_. + Mathematical Illustrations of Doctrine, II, 70; + --Psychology, I, 253; + --Society, I, 374, 376, 382; + --Theology, I, 149. + Mathematics, Condensed history of, II, 58. + Matter to Spirit, II, 194. + Maty, I, 23. + Maupertuis, II, _301_. + Maurice, F. D., II, _101_. + Maurolycus, I, _121_. + Maxwell, A., I, _102_. + Meadley, G. W., I, _223_. + Mechanics Magazine, II, 141, 145. + Medici, Cosmo de, II, _295_. + Medicine, Status of, I, 266. + Melanchthon, II, _323_. + Menestrier, I, _127_, 127. + Mercator, G., II, _92_. + Mercator's projection, I, 84. + Mersenne, I, _106_, 107; II, 295, 297. + Meslier, J., II, _195_. + Meteorologist, An early, I, 320. + Meteorology, I, 327. + Metius, A. and P., I, _52_, _99_, 99. + Meton, II, 167. + Metric System, Forerunner of, I, 171. + Meziriac, I, 161. + Milbanke, A. I., I, 225. + Mill, Jas., I, 260. + Miller, Joe, I, _182_. + Miller, S., I, 167. + Mills, Elizabeth, W., II, 7. + Milne, J., I, _286_. + Milner, I., I, _251_, 251. + Milner, J., II, _23_. + Milner's lamp, I, 252. + Milward, II, _250_. + Miracles _vs_. Nature, II, 6. + Mitchell, J., I, _242_. + Moliere, I, _232_. + Molina, A. C. de, I, _297_. + Mollendorff, von, II, _3_, 338. + Mondeux, I, 86. + Montague, C., II, _311_. + Montmort, P. R. de, II, _301_. + Montucla, I, 40, 45, 54, 65, 117, 120, 159, 163; II, 60. + Moon Hoax, I, 326; II, 131. + Moon, Nature of, II, 84; + --Rotation of, II, 4, 19, 84, 87. + More, Hannah, I, _189_, 192. + More, Henry, I, 123. + Moore, Dr. John, I, _190_. + Moore, Sir John, I, _190_. + Morgan, S., I, 6. + Morgan, T., I, 191. + Morgan, W., I, _223_, 224. + Morhof, I, _61_. + Morin, I, _99_, 99. + Morinus, J. B., I, 149. + Morland, S., II, _302_. + Mormonism, II, 69. + Morrison, R. J., I, _321_; II, 43. + Mose, H., II, _266_. + Mottelay, I, 68. + Motti, II, 60. + Mouton, I, _172_; II, 300. + Muggleton, I, 394, _395_. + Multiplication, Nature of, II, 251. + Murchison, R. I., I, _384_. + Murhard, I, _43_, 298. + {383} + Murphy, A., II, _308_. + Murphy, J. L., II, 54, _54_. + Murphy, P., I, _327_, 398. + Murphy, R., I, 349, _349_. + Murray, J., I, _186_; II, 145. + Murray, L., II, _326_. + Murray, Mungo, II, 310. + Musgrave, T., I, _324_. + Mydorge, I, _298_. + Mystrom, J. W., II, 182. + Mythological paradoxes, I, 256. + + Names of Religious Bodies, II, 22. + Napier, J., I, 5, 66, _67_, 82. + Napoleon, Doubts as to, I, 246. + Nautical Almanac, I, 300; II, 147. + Neal, I, _98_. + Negative numbers, I, 196, 203. + Neile, W., II, _190_. + Neptune, Discovery of, I, 387; II, 140. (_See Adams, Leverrier._) + Nesse, C, I, _128_, 128. + Newcomb, S., I, 162. + Newcomen, T., I, _147_. + Newton, Sir Isaac, I, 5, 6, 8, 24, 39, 84, 88, 130, + 136, 139, 144, 145, 148, 152, 154, 155, 162, 165, + 167, 197, 225, 237, 242, 257, 282, 296, 297, 309, + 311, 382, 394, 395, 396, 397; II, 2, 70, 184, 297, _302_, + 305. + Newton, John, II, _305_. + Nicene Creed, I, 371. + Nichol, J. P., II, _289_. + Nicholas. (_See Cusa._) + Nichols, J., I, _175_. + Nicolas, N. H., I, _354_. + Nicollet, I, _326_; II, 131. + Nicolson, W., I, _201_. + Nieuwentijt, II, _333_. + Nizzoli, M., II, 275. + Non-Euclidean geometry, II, 83. + Northampton, Marquis of (2d), II, _19_. + Novum Organum Moralium, II, 74. + Number, Mystery of, I, 55, 56, 169. + Number of the Beast (666), I, 55, 130, 272, 298, 352; II, 77, + 159, 217, 218, 361, 373. + Numeral system, II, 68. + Nursery rhymes, II, 150. + + Occam, Wm. of, II, _40_. + Odgers, N., II, 191, _191_. + Oinopides of Chios, II, _59_. + Oldenburgh, H., II, _300_, 302. + Orthodox Paradoxes, II, 363. + Orthography, Paradoxes of, II, 267. + Ortwinus, I, 319. + Oughtred, W., II, _298_, 303. + Owenson, I, _191_. + Ozanam, I, _161_, 312. + + Pagi, I, 32. + Paine, T., I, 173, _173_, 271. + Paley, W., I, _222_; II, 226. + Palmer, C., I, 225. + Palmer, H., I, _141_, 141, 145. + Palmer, J., II, _253_. + Palmer, T. F., II, _254_. + Palmer, W., II, _37_. + Palmerston, Viscount (3d), I, _290_, 352. + Palmezeaux, I, 167. + Panizzi, A., I, _151_. + Papist, II, 26. + Paracelsus, II, 322. + Paradox defined, I, 2, 31. + Paradox, religious, I, 236. + Paradoxers in general, II, 352. + Parallels, Theory of, I, 229, 344. + Pardies, I. G., II, _300_. + Park, Mungo, II, _91_, 132. + Parker, F., II, _94_. + Parker, G. (Earl of Macclesfield), II, _296_. + Parr, S., I, 173, _173_, 175, 176, 184. + Parsey, I, 293, _293_. + Partridge, J., I, _305_. + Pasbergius, I, 381. + Pascal, I, 39, 119, 122, _220_, _221_; II, 73. + Pascal's Hexagram, I, 221. + Passot, I, 279, _279_. + Passover, I, 358, 372. + Patriotic paradox, I, 231. + Paucton, I, _172_. + Paulian, I, 165, _165_. + Peacock, Geo., I, _196_, 350. + Peacock, T. L., I, _190_, 340. + Pearce, A. J., II, 43. + Pearne, T., I, _239_. + Peel, Sir R., I, 290, _352_. + Peel, W. Y., I, _290_. + Pelerin, J., II, _324_. + Pell, J., I, _105_, 105, 107; II, 300, 302, 312. + Pepys, I, _113_, 114. + Perigal, H., II, 19, _20_. + {384} + Perpetual motion, I, 118, 348; II, 55, 138. + Perspective, New theory of, I, 293. + Peters, W., II, 11, 315. + Petitioning Comet, I, 127. + Petrie, W. M. F., I, _328_. + Petty, I, _114_; II, 300. + Philalethes, Eirenaeus, I, _125_, 125, 126. + Philalethes, Eugenius, I, _255_. + Phillips, R., I, 242, _242_, 245. + Philo of Gadara, I, 40, _40_. + Philosopher's stone, I, 118, 125. + Philosophical atheists, II, 1. + Philosophy and Religion, II, 37. + Phonetic spelling, II, 81. + [pi], values of, I, 11, 43, 45, 46, 52, 69, 100, 110, + 129, 135, 146, 245, 283, 284, 294, 347, 348, 349, + 350; II, 60, 63, 105, 110, 118, 135, 156, 209, 279, 315, 316. + Pighius, I, _372_. + Pike, S., I, 236, _236_. + Pindar, P., II, _272_. + Piozzi, Mrs., I, _235_; II, 272. + Piscator, B., II, 25. + Pitman, F., II, 81, _81_. + Place, F., I, _199_. + Planets inhabitable, I, 100, 102. + Plato, I, 5. + Platt, H., I, _126_, 126. + Playfair, J., I, _233_. + Pletho, G., I, _188_. + Pliny, II, 280. + Ploucquet, I, _336_, 337. + Poe, E. A., II, 132. + Poincare, I, 136. + Poisson, I, _292_; II, 2. + Pollock, J. F., II, _174_. + Pons, II, _45_. + Pope, Wm., I, 277, _277_. + Porta, I, _68_, 68, 83. + Porteus, B., I, _193_, 203. + Porteus, H. F. A., II, 157, _157_. + Porus, I, 44. + Powell, Baden, II, _267_. + Powell, W. S., I, _222_. + Pratt, H. F. A., II, 157, _157_. + Pratt, O., II, _69_. + Predaval, Count de, I, _348_. + Prescot, B., I, 270, _270_, 278. + Prester John, I, 70, _71_, 152. + Price, R., I, _223_. + Probability, Discourse on, I, 279. + Proclus, I, 188, _188_. + Prodigies, Youthful, I, 219, 332. + Pronunciation, II, 330. + Protestant and Papal Christendom, II, 33. + Protimalethes, II, 6. + Ptolemy, I, 5, 33, _380_. + Pullicino, II, 61, _61_. + Pusey, I, _64_. + Pyramids, The, I, 328; II, 95, 136. + Pythagoras, II, _59_. + + Quadrature problem. (_See Squaring the circle._) + Quarles, F., II, _277_. + Quintilian, II, 280. + Quotem, C., I, 399. + + Rabelais, I, _102_. + Rainbow Paradox, II, 334. + Ramachandra, Y., I, _374_. + Ramchundra, I, 374. + Ramus, I, 5. + Recalcati, II, 208, 314. + Recorde, R., II, _328_. + Reddie, Jas., II, 183, _183_, 344, 360. + Reeve, J., I, _395_. + Regiomontanus, I, _48_, 360. + Reisch, I, _45_; II, 281. + Religion and Philosophy, II, 37. + Religious bodies, Names of, II, 22; + --customs, Attacks on, I, 177; + --Insurance, I, 345; + --Paradox, I, 236; + --Tract society, I, 192. + Remigius, I, _50_. + Reuchlin, J., II, _323_. + Revelations, Napier on, I, 66. + Revilo, (O. Byrne), I, 241, 329, _329_. + Reyneau, C. R., II, _301_. + Rheticus, I, _69_; II, 372. + Rhonius, II, 300. + Ribadeneira, P. de, II, _62_. + Riccioli, I, _96_. + Richards, G., II, _270_. + Rigaud, J., II, _299_. + Rigaud, S. J., II, _299_. + Rigaud, S. P., I, _140_; II, 298, 313. + Ringelbergh, J. S., II, _281_. + Ripley, G., I, _126_, 126. + Ritchie, W., I, 295, _295_. + Ritterhusius, I, _60_. + Rive, J.-J., I, _160_. + Robertson, Jas., I, _237_. + Roberval, I, _105_, 122. + {385} + Robinson, B., I, _148_, 148. + Robinson, H. C., I, _314_; II, 52, 275. + Robinson, R., I, _177_. + Robinson, T. R., II, _181_. + Roblin, J., II, 136. + Rogers, S., II, _260_. + Roget, P. M., I, _398_. + Roomen, A. van, I, _110_. + Ross, J. C., I, _303_. + Rosse, I, 26. + Rossi, G., I, 231, _231_. + Rotation of the Moon, II, 4, 19. + Rough, W., I, 198. + Rowning, J., I, _155_. + Royal Astronomical Society, I, 27; + --Forerunner of, I, 374. + Royal Society, I, 21, 22, 24-30, 56, 57, 136, 153, 163, + 164, 165. + Rudio, I, 159; II, 367. + Rudolff, C., II, 373. + Russell, Earl (1st), I, _296_. + Rutherford, W., II, _109_. + + Sabatier, A., II, _267_. + Sabellius, I, _241_. + Sacrobosco, I, _360_. + Sadler, T., I, _238_, 241. + Saint-Martin, I, 167, _168_, 206. + St.-Mesmin, M. de., I, 280. + St. Vincent, G. de., I, _110_, 117. + St. Vitus, Patron of Cyclometers, II, 60. + Sales, de, I, 167. + Salicetus, I, 64. + Salisbury, Earl of (1st), II, _330_. + Salmasius, Claudius, II, _168_. + Salusbury, Hester, I, _235_. + Sanchez, Petro, I, 229, _229_. + Sanders, W., I, 207. + Sanderson, R., I, _135_. + Sara, R., I, _297_. + Saunderson, N., I, _377_; II, 301. + Scaliger, I, _44_, 110, 111, 112, 113; II, 238. + Scevole de St. Marthe, I, 113. + Schooten, Van, II, _59_. + Schopp, I, _60_. + Schott, I, _64_; II, 64. + Schumacher, H. C., I, _107_; II, 297. + Schwab, I, _230_. + Scientific paradoxes, I, 232. + Scott, Michael, I, _38_. + Scott's Devils, I, 38. + Scott, W., I, 20, 27, 38, 39, 155, _191_. + Scripture and Science, II, 261. + Search, John, I, 247. + Selden, J., II, _250_. + Senarmont, II, _48_. + Serres, De, II, _60_. + Shaftesbury, Earl of, II, _181_. + Shakespeare, I, 13. + Shanks, II, _63_, 65, 109. + Shaw, P., I, _142_. + Sheepshanks, J., I, _147_. + Sheepshanks, R., I, _290_. + Shelley, I, 174. + Shepherd, S., I, _124_. + Sherburne, E., II, _295_. + Sheridan, R. B., I, _175_. + Sheridan, T., I, _175_. + Shoberl, F., II, _270_. + Shrewsbury, I, _108_. + Siddons, Mrs., I, 189. + Simms, W., I, _152_. + Simplicius, II, _164_. + Simpson, T., I, 377; II, 304. + Simson, R., I, _197_, 202, 233. + Sinclair, G., I, _207_. + Slander Paradoxes, II, 138. + Sloane, I, 24. + Sluse, R. de, I, _118_, 118; II, 300. + Smith, Adam, II, _112_. + Smith, Jas., I, _46_; II, 103, _103_, 154, 236, 237, 238, 241, 336, + 360. + Smith, Jas., II, _217_. + Smith, Jas. (Shepherd), II, _55_, 193. + Smith, Joseph, II, _69_. + Smith, Richarda, I, _242_. + Smith, Thomas, I, 346, _346_. + Smith, Wm., II, _152_. + Smyth, C. P., I, _328_; II, 65. + Snell, I, _75_, 75. + Socinianism, I, 142, 143. + Socinus, I, 3, _143_. + Socrates Scholasticus, I, _358_. + Sohncke, L. A., II, _131_. + Somerville, Mrs., I, _242_. + South, J., II, _181_. + Southcott, Joanna, II, _58_, 97, 239. + Spearman, R., I, _237_. + Speculative thought in England, I, 374. + Spedding, I, _76_, 82, 142. + Speed, J., I, _201_. + Speke, I, _70_. + Spelling, phonetic, II, 81. + Spence, W., I, _231_, 231. + Spencer, Earl (3d), II, _9_. + {386} + Spinoza, I, 3, _37_. + Spiritualism, II, 47, 55, 207. + Spurius Cassius Viscellinus, II, _342_. + Spurius Maelius, II, _342_. + Squaring the circle, I, 8, 42, 44, 46, 47, 50, 52, 53, + 69, 70, 75, 109, 117, 119, 129, 135, 146, 149, + 159, 163, 164, 347, 348, 374; II, 10, 11, 60, 105, 154, + 156, 208, 278, 314. + Staeckel, I, 230. + Stanhope, P. D., (Earl of Chesterfield), II, _298_. + Stapulensis, I, _44_; II, 324. + Star polygons, I, 229. + Starkie, G., I, _126_, 126. + Statter, D., II, 80. + Steamship suggested, I, 147. + Steel, Jas., II, 68. + Stenography, II, 81. + Stephens, I, _44_; II, 324. + Stephenson, G., II, _138_. + Stephenson, R., II, _138_. + Stevin, I, _83_, 313; II, 59. + Stewart, D., II, _53_. + Stewart, R., I, _186_. + Stifel, M., II, _373_. + Strafford, Earl of, I, _240_. + Stratford, W. S., I, _300_. + Street, T., I, _124_. + Stukely, W., I, _236_. + Suffield, G., II, _66_. + Suidas, II, _29_. + Sumner, C. R., I, _324_. + Sumner, J. B., I, _324_. + Sun as an electric space, II, 41. + Supernatural, The, II, 193. + Suvaroff, II, _85_. + Swastika, II, 231. + Swedenborg, E., I, _255_. + Swift, I, 19, 133. + Sylvester, J. J., II, _336_. + Symington, W., I, _148_. + Symons, II, 4, 5, 20, 84, 85. + Sympathetic powder, I, 108. + Synesius, I, 125. + + Talbot, G., I, _22_, _108_. + Talbot's powder, I, 108. + Tartaglia, II, 59. + Tasse, I, _106_. + Tate, J., I, _199_. + Tauler, J., II, _322_. + Taylor, Brook, II, _301_. + Taylor, John, I, _352_; II, 95. + Taylor, Robt., I, _270_. + Taylor, T., I, 188, _188_. + Teissier, I, _113_. + Temple, H. J., I, 290. + Tenterden, Chief Justice, I, _181_. + Thales, II, _59_, 83. + Theism independent of Revelation, I, 399. + Thelwall, J., I, _178_. + Theodoretus, I, _358_. + Theological Paradoxes, I, 316. + Theology, Mathematical, I, 129, 149. + Theophrastus, II, _167_. + Thiebault, II, _3_, 338. + Thom, D., II, _226_, 240. + Thom, J. H., II, _226_. + Thompson, P., I, _7_. + Thompson, T. P., I, _252_, 287, 344; II, 83, 185. + Thomson, Dr., I, 21. + Thomson, W., I, _325_. + Thorn, W., II, 158, _158_, 360. + Thorndike, H., II, _313_. + Thrale, Mrs., I, _235_. + Thurlow, Baron, I, _222_. + Thyraeus, I, 50. + Tides, New theory of, I, 393. + Tombstones of mathematicians, I, 106. + Tonal System, II, 182. + Tooke, H., I, _178_. + Torriano, E., I, 250. + Towneley, II, 300. + Townley, C., II, _300_. + Trisection problem, I, 118; II, 10, 12, 13, 15. + Troughton, I, _152_. + Turnor, E., I, _137_. + Tycho Brahe, I, 5, _76_, 381; II, 302, 335. + + Upton, W., II, 12, _12_, 15. + Ursus, I, _52_. + + Valentine, B., I, _125_, 125. + Van Ceulen, I, 52, 70, 100. + Van de Weyer, I, _313_. + Van Etten, I, _161_. + Van Helmont, I, _125_, 125. + Van Roomen, I, _110_. + Van Schooten, II, _59_. + Vaughan, T., I, _255_. + Victorinus, I, _359_. + Viete, I, _51_; II, 210, 295. + Virgil, St., I, 32, _33_, 34, 99. + {387} + Virginia, University of, I, 233. + Viscellinus, II, _342_. + Vitruvius, II, _281_. + Vivian, T., I, 172, _172_. + Vogel, A. F., I, 373. + Voltaire, I, 103, 165, 166, 167, 168, 248; II, 268. + Von Gumpach, II, 137, _137_. + Von Hutten, I, 318. + Von Wolzogen. (_See Wolzogen._) + Vyse, R. W. H., I, _328_. + + Walker, W. E., II, _316_. + Walkingame, F., II, _173_. + Wallich, N., II, _14_. + Wallis, J., I, 107, 109, 110; II, 299, 313. + Walpole, I, _23_, 131. + Walsh, John, I, 260, _260_; II, 157. + Wapshare, J., II, _230_. + Warburton, H., I, _349_. + Warburton, Wm., I, _55_, 112; II, 174. + Ward, S., II, _299_. + Waring, E., I, _203_, 222. + Warner, W., II, _302_, 312. + Warren, S., II, _340_. + Watkins, J., II, _270_. + Watson, Bp., I, _223_. + Watt, R., I, _102_, 402. + Watts, I., II, 18. + Weddle, T., II, _187_. + Wentworth, Thos., I, _240_. + Wharton, I, 115. + Whately, R., I, 246, _246_, 324. + Whately's Paradox, I, 246. + Whewell, I, _101_, 101, 273, 314, 380; II, 104, 246, 247. + Whigs, II, 22. + Whiston, J., I, _147_. + Whiston, W., I, 133, _133_, 146, 156, 311. + White, H. K., II, _271_. + White, J. B., I, 248. + White, R., I, 11. + Whitford, I, 105. + Whitworth, W. A., II, _344_. + Whizgig, On the, I, 254. + Wightman, I, 59. + Wilberforce, W., II, _236_. + Wilkins, J., I, 96, _100_, 116, 226. + Williams, J. B., I, _378_. + Williams, T., I, 171, _171_. + Wilson, Sir J., I, _221_. + Wilson, J. M., II, _344_. + Wilson, R., II, 7, _7_. + Wilson's Theorem, I, _222_. + Wingate, E., II, _308_. + Winter, I, 46. + Wirgman, T., I, 258, _258_. + Wiseman, N. P. S., II, _26_, 61, 294. + Wolcot, J. (Peter Pindar), II, _272_. + Wollstonecraft, I, 173, _173_. + Wolzogen, I, _106_. + Wood, A., I, _98_. + Wood, John, I, _233_. + Wood, Wm., I, 246, _246_. + Woodley, W., I, 307, _307_. + Wordsworth, II, 273. + Wright, E., I, 84. + Wright, T., I, 151, _151_, 152, 153. + Wright, W., II, 9. + Wronski, I, 249, _250_. + Wrottesley, J. (Baron), II, _181_. + + Young, B., II, _69_. + Young, J. W. A., II, 367. + Young, T., I, 24, 30, _250_. + Youthful Prodigies, I, 219. + Yvon, I, _297_. + + Zach, von, II, _45_, 196. + Zachary, Pope, I, 32, 34. + Zadkiel, I, _321_; II, 43. + Zetetic Astronomy, II, 88. + Zodiac, II, 136. + Zytphen, II, _335_. + + * * * * * + + +Notes + +Transcriber's note: References to Notes in Volume I are shown as in the +printed book, with the resequenced footnote numbers in the Project +Gutenberg Edition (EText-No. 23100) added thus {123}. + +[1] See Vol. I, page 255, note 6 {584}. + +[2] "I have no need for this hypothesis." + +[3] "Ah, it is a beautiful hypothesis; it explains many things." + +[4] "What we know is very slight; what we don't know is immense." + +[5] Brewster relates (_Life of Sir Isaac Newton_, Vol. II, p. 407) that, a +short time before his death, Newton remarked: "I do not know what I may +appear to the world, but to myself I seem to have been only like a boy +playing on the seashore, and diverting myself in now and then finding a +smoother pebble or a prettier shell than ordinary, whilst the great ocean +of truth lay all undiscovered before me." + +[6] See Vol. I, p. 292, note 1 {632}. + +[7] "What is all that!" + +[8] "I have some good news to tell you: at the Bureau of Longitudes they +have just received a letter from Germany announcing that M. Bessel has +verified by observation your theoretical discoveries on the satellites of +Jupiter." + +[9] "Man follows only phantoms." + +[10] See Vol. I, page 382, note 13 {786}. + +[11] Dieudonne Thiebault (1733-1807) was a Jesuit in his early life, but he +left the order and took up the study of law. In 1765 he went to Prussia and +became a favorite of Frederick the Great. He returned to France in 1785 and +became head of the Lycee at Versailles. + +[12] _Memories of Twenty Years of Residence in Berlin._ There was a second +French and an English edition in 1805. + +[13] Richard Joachim Heinrich von Mollendorff (1724-1816) began his career +as a page of Frederick the Great (1740) and became field marshal (1793) and +commander of the Prussian army on the Rhine (1794). + +[14] Hugues Bernard Maret (1763-1839) was not Duc de Bassano in 1807, this +title not being conferred upon him until 1809. He was ambassador to England +in 1792 and to Naples in 1793. Napoleon made him head of the cabinet and +his special confidant. The Bourbons exiled him in 1816. + +[15] Denis Diderot (1713-1784), whose _Lettre sur les aveugles_ (1749) +introduced him to the world as a philosopher, and whose work on the +_Encyclopedie_ is so well known. + +[16] "Sir, (a + b^{n}) / n = x, whence God exists; answer!" + +[17] This was one James Laurie of Musselburgh. + +[18] Jelinger Cookson Symons (1809-1860) was an office-holder with a +decided leaning towards the improvement of education and social conditions. +He wrote _A Plea for Schools_ (1847), _The Industrial Capacities of South +Wales_ (1855), and _Lunar Motion_ (1856), to which last work the critic +probably refers. + +[19] "Protimalethes" followed this by another work along the same line the +following year, _The Independence of the Testimony of St. Matthew and St. +John tested and vindicated by the theory of chances_. + +[20] Wilson had already taken up the lance against science in his +_Strictures on Geology and Astronomy, in reference to a supposed want of +harmony between these sciences and some parts of Divine Revelation_, +Glasgow, 1843. He had also ventured upon poetry in his _Pleasures of +Piety_, Glasgow, 1837. + +[21] Mrs. Borron was Elizabeth Willesford Mills before her marriage. She +made an attempt at literature in her _Sibyl's Leaves_, London (printed at +Devonport), 1826. + +[22] See Vol. I, page 386, note 10 {801}. + +[23] See Vol. I, page 43, notes 7 {32} and 8 {33}. + +[24] His flying machine, designed in 1843, was one of the earliest attempts +at aviation on any extensive scale. + +[25] Erasmus Darwin (1731-1802) was the grandfather of Charles Darwin. The +work here mentioned had great influence, being translated into French, +Portuguese, and Italian. Canning parodied it in his _Loves of the +Triangles_. + +[26] See Vol. I, page 147, note 1 {312}. + +[27] The notes on this page were written on the day of the funeral of +Wilbur Wright, June 1, 1912, the man who realized all of these prophecies, +and then died a victim of municipal crime,--of typhoid fever. + +[28] John Charles, third Earl Spencer (1782-1845), to whose efforts the +Reform Bill was greatly indebted for its final success. + +[29] This was published in London in 1851 instead of 1848. + +[30] This appeared in 1846. + +[31] This was done in _The Circle Squared_, published at Brighton in 1865. + +[32] It first appeared in 1847, under the title, _The Scriptural Calendar +and Chronological Reformer, 1848. Including a review of tracts by Dr. +Wardlaw and others on the Sabbath question. By W. H. Black._ The one above +mentioned, for 1849, was printed in 1848, and was also by Black +(1808-1872). He was pastor of the Seventh Day Baptists and was interested +in archeology and in books. He catalogued the manuscripts of the Ashmolean +Museum at Oxford. + +[33] William Upton, a Trinity College man, Dublin. He also wrote _Upton's +Physioglyphics_, London, 1844; _Pars prima. Geometria vindicata; +antiquorumque Problematum, ad hoc tempus desperatorum, Trisectionis Anguli, +Circulique Quadraturae, Solutio, per Eucliden effecta, London_ (printed at +Southampton), 1847; _The Uptonian Trisection_, London, 1866; and _The +Circle Squared_, London, 1872. + +[34] For example, if [theta] = 90 deg. we should have 3 cos 30 deg. = 1 ++ [root](4 - sin^2 90 deg.), or 3. 1/2 [root]3 = 1 + [root]3, or +1/2 [root]3 = 1. + +[35] Nathaniel Wallich (1786-1854) was surgeon at the Danish settlement at +Serampore when the East India Company took over the control in 1807. He +entered the British medical service and was invalided to England in 1828. +His _Plantae Asiaticae Rariores_ (3 vols., London, 1830-1832) was +recognized as a standard. He became vice-president of the Linnean Society, +F. R. S., and fellow of the Royal Asiatic Society. + +[36] But if [theta] = 90 deg. this asserts that + + cos 30 deg. = (sin 270 deg. . cos 225 deg. + sin^2 90 deg. + . sin 225 deg.) / [root](sin^2 + 270 deg. . cos^2 225 deg. + sin^{4} 90 deg. + sin 270 deg. + . sin 450 deg. . sin^2 90 deg.), + +or that + + 1/2 [root]3 = (-1 . (-1 /[root]2) + 1 . (-1/[root]2) / [root]1 + . 1/2 + 1 - 1 . 1 . 1) = 0 / [root](1/2), + +so that De Morgan must have made some error in copying. + +[37] John Bonnycastle (died in 1821) was professor of mathematics at +Woolwich. His edition of Bossut's _History of Mathematics_ (1803), and his +works on elementary mathematics were well known. + +[38] The bibliographies give Husain Rifki as the translator, a practical +geometry as the work, and 1802 as the date. + +[39] See Vol. I, page 309, note 2 {670}. + +[40] Probably in _The Improvement of the Mind_ which Isaac Watts +(1674-1748) published in 1741. His _Horae Lyricae_ appeared in 1706, and +the _Hymns_, by which he is still well known, in 1707. + +[41] Spencer Joshua Alwyne Compton, second Marquis of Northampton +(1790-1851), was a poet, a scientist, and a statesman. He was president of +the Royal Society from 1838 to 1849. + +[42] Besides the writings here mentioned Perigal published a work on +_Geometric Maps_ (London, 1853), and _Graphic Demonstrations of Geometric +Problems_ (1891). + +[43] See Vol. II, page 5, note 18. + +[44] James Ferguson (1710-1776) was a portrait painter, an astronomer, and +a popular writer and lecturer on various subjects. + +[45] In the old ballad of King Alfred and the Shepherd, when the latter is +tempting the disguised king into his service, he says: + + "Of whig and whey we have good store, + And keep good pease-straw fire." + +_Whig_ is then a preparation of milk. But another commonly cited derivation +may be suspected from the word _whiggamor_ being used before _whig_, as +applied to the political party; _whig_ may be a contraction. Perhaps both +derivations conspired: the word _whiggamor_, said to be a word of command +to the horses, might contract into _whig_, and the contraction might be +welcomed for its own native meaning.--A. De M. + +[46] This was p. 147 in the first edition. + +[47] St. Augustine (354-430) was bishop of Hippo. His _Confessiones_, in +13 books, was written in 397, and his _De Civitate Dei_ in 426. + +[48] "He was wont to indulge in certain Punic subtleties lest he should +weary the reader by much speaking." + +[49] John Milner (1751-1826), bishop of Castabala, a well-known +antiquarian. + +[50] It will be said that when the final happiness is spoken of in "sure +and certain hope," it is _the_ Resurrection, generally; but when afterwards +application is made to the individual, simple "hope" is all that is +predicated which merely means "wish?" I know it: but just before the +general declaration, it is declared that it _has_ pleased God of his great +mercy to _take unto Himself_, the soul of our dear brother: and between the +"hopes" hearty thanks are given that it _has_ pleased God to deliver our +dear brother out of the miseries of this wicked world, with an additional +prayer that the number of the elect may shortly be accomplished. All which +means, that our dear brother is declared to be taken to God, to be in a +place not so miserable as this world--a description which excludes the +"wicked place"--and to be of the elect. Yes, but it will be said again! do +you not know that when this Liturgy was framed, all who were not in the +road to Heaven were excommunicated burial service read over them. Supposing +the fact to have been true in old time, which is a very spicy supposition, +how does that excuse the present practice? Have you a right _always_ to say +what you believe _cannot always_ be true, because you think it was once +_always_ true? Yes, but, choose whom you please, you cannot be _certain_ He +is _not_ gone to Heaven. True, and choose which Bishop you please, you +cannot be demonstratively _certain_, he is _not_ a concealed unbeliever: +may I therefore say of the whole bench, _singulatim et seriatim_, that they +_are_ unbelievers? No! No! The voice of common sense, of which common logic +is a part, is slowly opening the eyes of the multitude to the unprincipled +reasoning of theologians. Remember 1819. What chance had Parliamentary +Reform when the House of Commons thanked the Manchester sabre-men? If you +do not reform your Liturgy, it will be reformed for you, and sooner than +you think! The dishonest interpretations, by defence of which even the +minds of children are corrupted, and which throw their shoots into +literature and commerce, will be sent to the place whence they came: and +over the door of the established organization for teaching religion will be +posted the following notice: + + "Shift and Subterfuge, Shuffle and Dodge, + No longer here allowed to lodge!" + +All this ought to be written by some one who belongs to the Establishment: +in him, it would be quite prudent and proper; in me, it is kind and +charitable.--A. De M. + +[51] But few do have access to it, for the work is not at all common, and +this Piscator is rarely mentioned. + +[52] This derivation has been omitted.--S. E. De M. + +[53] A blow for a blow. Roland and Oliver were two of the paladins of +Charlemagne whose exploits were so alike that each was constantly receiving +credit for what the other did. Finally they met and fought for five days on +an island in the Rhine, but even at the end of that period it was merely a +drawn battle. + +[54] "In the name of the church." + +[55] "From the chair," officially. + +[56] Nicholas Patrick Stephen Wiseman (1802-1865), whose elevation to the +archbishopric of Westminster and the cardinalate (1850) led to the act +prohibiting Roman Catholics from assuming episcopal titles in England, a +law that was never enforced. + +[57] He was born in 1812 and was converted to Catholicism in 1839. He +founded the _Tablet_ in London in 1840, removing its office to Dublin in +1849. He became M. P. in 1852, and at the time of his death (1855) he was +preparing a memorial to the Pope asking him to annul the proclamation of an +Irish bishop prohibiting his priests from taking part in politics. + +[58] John Guillim (1565-1621) was the first to systematize and illustrate +the whole science of heraldry. He published _A display of Heraldrie: +manifesting a more easie accesse to the knowledge thereof_ in 1610. + +[59] "Faith." + +[60] "Faithful." + +[61] "For the faith vindicated." + +[62] The words are of the same root, and hence our word _fiddle_. Some +suppose this root means a _rope_, which, as that to which you trust, +becomes, in one divergence, confidence itself--just as a _rock_, and other +words, come to mean reliance--and in another, a little string.--A. De M. + +[63] The Greek lexicographer, a Christian, living after 1000 A. D. His +lexicon was first printed at Milan in 1499. + +[64] _Skindapsos._ + +[65] This was John William Burgon (1813-1888), Gresham professor of +theology (1867) and dean of Chichester. He was an ultra-conservative, +opposing the revised version of the New Testament, and saying of the +admission of women to the university examinations that it was "a thing +inexpedient and immodest." + +[66] _Ekklesia_, or _ecclesia_. + +[67] _Ennomos ekklesia._ + +[68] "Without doubt I shall perish forever." + +[69] "Every man is an animal." "Sortes is a man." "Sortes is an animal." + +[70] "For a special purpose." + +[71] Heraclitus of Ephesus, the weeping philosopher, 6th century B. C. + +[72] Democritus, the laughing philosopher, founder of the atomistic theory, +5th century B. C. + +[73] "Ends to which." + +[74] "Ends from which." + +[75] "In just as many syllables," "With just as many letters," "In just as +many words." + +[76] "I shall make a way," "I shall find a way." + +[77] The notion that the Evil Spirit is a functionary liable to be +dismissed for not attending to his duty, is, so far as my reading goes, +utterly unknown in theology. My first wrinkle on the subject was the remark +of the Somersetshire farmer upon Palmer the poisoner-- "Well! if the Devil +don't take he, he didn't ought to be allowed to be devil no longer."--A. De +M. + +William Palmer (1824-1856) was a member of the Royal College of Surgeons +and practised medicine at London. He was hanged in 1856 for having poisoned +a friend and was also suspected of having poisoned his wife and brother for +their insurance money, besides being guilty of numerous other murders. His +trial was very much in the public attention at the time. + +[78] Advantages and dangers. + +[79] The old priory of St. Mary of Bethlehem in London, was used as an +asylum for the insane. The name was corrupted to Bedlam. + +[80] Referring to the common English pronunciation of St. John, almost +Sinjin. John St. John Long (1798-1834), an Irishman by birth, practised +medicine in London. He claimed to have found a specific for rheumatism and +tuberculosis, but upon the death of one of his patients in 1830 he was +tried for manslaughter. He died of tuberculosis four years later, refusing +to take his own treatment. + +[81] William of Occam (d. 1349), so called from his birthplace, Ockham, in +Surrey. He was a Franciscan, and lectured on philosophy in the Sorbonne. + +[82] He signs himself "James Hopkins, schoolmaster," and this seems to have +been his only published effort. + +[83] Joseph Ady (1770-1852) was a famous swindler. One of his best-known +schemes was to send out letters informing the recipients that they would +learn something to their advantage on payment of a certain sum. He spent +some time in prison. + +[84] Sir Peter Laurie (c. 1779-1861) was worth referring to, for he was +prominent as a magistrate and was honored because of his interest in all +social reforms. He made a fortune as a contractor, became sheriff of London +in 1823, and was knighted in the following year. He became Lord Mayor of +London in 1832. + +[85] See Vol. I, page 321, note 2 {691}. The _Astronomy in a nutshell_ +appeared in 1860. _The Herald of Astrology_ was first published in London +in 1831, "by Zadkiel the Seer." It was continued as _The Astrological +Almanac_ (London, 1834), as _Zadkiel's Almanac and Herald of Astrology_ +(_ibid._, 1835, edited by R. J. Morrison, and subsequently by A. J. +Pearce), and as _Raphael's Prophetic Almanac_ (1840-1855). + +[86] See Vol. I, page 172, note 3 {382}. + +[87] See Vol. I, page 87, note 4 {133}. + +[88] Franz Xaver, Freiherr von Zach (1754-1832) was director of the +observatory at Seeberge near Gotha. He wrote the _Tabulae speciales +aberrationis et mutationis_ (1806-7), _Novae et correctae tabulae solis_ +(1792), and _L'attraction des montagnes et ses effets sur le fil a plomb_ +(1814). + +[89] Jean Louis Pons (1761-1831) was connected with the observatory at +Marseilles for thirty years (1789-1819). He later became director of the +observatory at Marlia, near Lucca, and subsequently filled the same office +at Florence. He was an indefatigable searcher for comets, discovering 37 +between 1801 and 1827, among them being the one that bears Encke's name. + +[90] This hypothesis has now become an established fact. + +[91] John Chetwode Eustace (c. 1762-1815) was born in Ireland. Although a +Roman Catholic priest he lived for a time at Cambridge where he did some +tutoring. His _Classical Tour_ appeared in 1813 and went through several +editions. + +[92] "Crimes should be exposed when they are punished, but disgraceful acts +should be hidden." + +[93] Henri Hureau de Senarmont (1808-1862) was professor of mineralogy at +the _Ecole des mines_ and examiner at the _Ecole polytechnique_ at Paris. + +[94] Augustin Jean Fresnel (1788-1827), "Ingenieur des ponts et chaussees," +gave the first experimental proofs of the wave theory of light. He studied +the questions of interference and polarization, and determined the +approximate velocity of light. + +[95] "As is my custom." + +[96] Francis Heywood (1796-1858) made the first English translation of +Kant's _Critick of Pure Reason_ (1838, reprinted in 1848). The _Analysis_ +came out, as here stated, in 1844. + +[97] Louise Renee de Keroualle, Duchess of Portsmouth and Aubigny +(1649-1734), was a favorite of Charles II. She used her influence to keep +him under the control of Louis XIV. + +[98] William Chiffinch (c. 1602-1688) was page of the king's bed-chamber +and keeper of the private closet to Charles II. He was one of the king's +intimates and was an unscrupulous henchman. + +[99] "Well devised." + +[100] "John Bellingham Inglis. His _Philobiblion_ "translated from the +first edition (of Ricardus d'Aungervile, Bishop of Durham), 1473," appeared +at London in 1832. It was republished in America (Albany, N. Y.) in 1864. + +[101] "What are you laughing at?" + +[102] See Vol. I, page 314, note 4 {681}. + +[103] See Vol. I, page 112, note 7 {211}. + +[104] Referring to Hamilton's edition of the _Collected Works of Dugald +Stewart_, 10 volumes, Edinburgh, 1854-58. It is not commonly remembered +that Stewart (1753-1828) taught mathematics at the University of Edinburgh +before he took up philosophy. + +[105] This was Hamilton's edition of the _Works of Thomas Reid_ (2 vols., +Edinburgh, 1846-1863). Reid (1710-1796) included mathematics in his work in +philosophy at Aberdeen. In 1764 he succeeded Adam Smith at Glasgow. + +[106] Edward Irving (1792-1834), the famous preacher. At first he assisted +Dr. Chalmers at Glasgow, but in 1822 he went to London where he met with +great success. A few years later he became mentally unbalanced and was +finally expelled from his church (1832) for heresy. He was a great friend +of Carlyle. + +[107] He also wrote a number of other paradoxes, including _An Essay +towards a Science of Consciousness_ (1838), _Instinctive Natural Religion_ +(1858), _Popular Treatise on the structure, diseases, and treatment of the +human teeth_ (1837), and _On Headache_ (1859). + +[108] James Smith (1801-1857), known as Shepherd Smith, was a socialist and +a mystic, with a philosophy that was wittily described as "Oriental +pantheism translated into Scotch." He was editor of several journals. + +[109] Joanna Southcott (1750-1814) was known for her rhyming prophecies in +which she announced herself as the woman spoken of in Revelations xii. She +had at one time as many as 100,000 disciples, and she established a sect +that long survived her. + +[110] Thales, c. 640-548 B. C. + +[111] Pythagoras, 580-501 B. C. + +[112] Anaxagoras, 499-428 B. C., the last of the Ionian school, teacher of +Euripides and Pericles. Plutarch speaks of him as having squared the +circle. + +[113] Oinopides of Chios, contemporary of Anaxagoras. Proclus tells us that +Oinopides was the first to show how to let fall a perpendicular to a line +from an external point. + +[114] Bryson and Antiphon, contemporaries of Socrates, invented the +so-called method of exhaustions, one of the forerunners of the calculus. + +[115] He wrote, c. 440 B. C., the first elementary textbook on mathematics +in the Greek language. The "lunes of Hippocrates" are well known in +geometry. + +[116] Jabir ben Aflah. He lived c. 1085, at Seville, and wrote on astronomy +and spherical trigonometry. The _Gebri filii Affla Hispalensis de +astronomia libri_ IX was published at Nuremberg in 1533. + +[117] Hieronymus Cardanus, or Girolamo Cardano (1501-1576), the great +algebraist. His _Artis magnae sive de regulis Algebrae_ was published at +Nuremberg in 1545. + +[118] Nicolo Tartaglia (c. 1500-1557), the great rival of Cardan. + +[119] See note 5 {98}, Vol. I, page 69. + +[120] See note 10 {124}, Vol. I., page 83. + +[121] See note 9 {123}, Vol. I, page 83. + +[122] Pierre Herigone lived in Paris the first half of the 17th century. +His _Cours mathematique_ (6 vols., 1634-1644) had some standing but was not +at all original. + +[123] Franciscus van Schooten (died in 1661) was professor of mathematics +at Leyden. He edited Descartes's _La Geometrie_. + +[124] Florimond de Beaune (1601-1652) was the first Frenchman to write a +commentary on Descartes's _La Geometrie_. He did some noteworthy work in +the theory of curves. + +[125] See note 3 {23}, Vol. I, page 41. + +[126] Olivier de Serres (b. in 1539) was a writer on agriculture. Montucla +speaks of him in his _Quadrature du cercle_ (page 227) as having asserted +that the circle is twice the inscribed equilateral triangle, although, as +De Morgan points out, this did not fairly interpret his position. + +[127] Anghera wrote not only the three works here mentioned, but also the +_Problemi del piu alto interesse scientifico, geometricamente risoluti e +dimostrati_, Naples, 1861. His quadrature was defended by Giovanni Motti in +a work entitled _Matematica Vera. Falsita del sistema ciclometrico +d'Archimede, quadratura del cerchio d'Anghera, ricerca algebraica dei lati +di qualunque poligono regolare inscritto in un circolo_, Voghera, 1877. The +_Problemi_ of 1861 contains Anghera's portrait, and states that he lived at +Malta from 1849 to 1861. It further states that the Malta publications are +in part reproduced in this work. + +[128] This was his friend Paolo Pullicino whose _Elogio_ was pronounced by +L. Farrugia at Malta in 1890. He wrote a work _La Santa Effegie della Blata +Vergine Maria_, published at Valetta in 1868. + +[129] St. Vitus, St. Modestus, and St. Crescentia were all martyred the +same day, being torn limb from limb after lions and molten lead had proved +of no avail. At least so the story runs. + +[130] The reference is to Cardinal Wiseman. See Vol. II, page 26, note 56. + +[131] "Worthy of esteem." + +[132] Pedro de Ribadeneira (Ribadeneyra, Rivadeneira), was born at Toledo +in 1526 and died in 1611. He held high position in the Jesuit order. The +work referred to is the _Flos Sanctorum o libro de las vidas de los +santos_, of which there was an edition at Barcelona in 1643. His life of +Loyola (1572) and _Historia ecclesiastica del Cisma del reino de +Inglaterra_ were well known. + +[133] Caesar Baronius (1538-1607) was made a cardinal in 1595 and became +librarian at the Vatican in 1597. The work referred to appeared at Rome in +1589. + +[134] Mrs. Jameson's (1794-1860) works were very popular half a century +ago, and still have some circulation among art lovers. The first edition of +the work mentioned appeared in 1848. + +[135] The barnyard cock. + +[136] Shanks did nothing but computing. The title should, of course, read +"to 607 Places of _Decimals_." He later carried the computation to 707 +decimal places. (_Proc. Roy. Society_, XXI, p. 319.) He also prepared a +table of prime numbers up to 60,000. (_Proc. Roy. Society_, XXII, p. 200.) + +[137] See Vol. I, page 42, note 4 {24}. + +[138] See Vol. I, page 64, note 1 {78}. + +[139] See Vol. I, page 328, note 1 {704}. + +[140] George Suffield published _Synthetic Division in Arithmetic_, to +which reference is made, in 1863. + +[141] John Robert Lunn wrote chiefly on Church matters, although he +published a work on motion in 1859. + +[142] Jean Baptiste Joseph, Baron Fourier (1768-1830), sometime professor +in the Military School at Paris, and later at the _Ecole polytechnique_. He +is best known by his _Theorie analytique de la chaleur_ (Paris, 1822), in +which the Fourier series is used. The work here referred to is the _Analyse +des equations determinees_ (Paris, 1831). + +[143] William George Horner (1786-1837) acquired a name for himself in +mathematics in a curious manner. He was not a university man nor was he a +mathematician of any standing. He taught school near Bristol and at Bath, +and seems to have stumbled upon his ingenious method for finding the +approximate roots of numerical higher equations, including as a special +case the extracting of the various roots of numbers. Davies Gilbert +presented the method to the Royal Society in 1819, and it was reprinted in +the _Ladies' Diary_ for 1838, and in the _Mathematician_ in 1843. The +method was original as far as Horner was concerned, but it is practically +identical with the one used by the Chinese algebraist Ch'in Chiu-shang, in +his _Su-shu Chiu-chang_ of 1247. But even Ch'in Chiu-shang can hardly be +called the discoverer of the method since it is merely the extension of a +process for root extracting that appeared in the _Chiu-chang Suan-shu_ of +the second century B. C. + +[144] He afterwards edited Loftus's _Inland Revenue Officers' Manual_ +(London, 1865). The two equations mentioned were x^3 - 2x = 5 and y^3 - +90y^2 + 2500y - 16,000 = 0, in which y = 30 - 10x. Hence each place of y is +the complement of the following place of x with respect to 9. + +[145] Probably the John Power Hicks who wrote a memoir on T. H. Key, +London, 1893. + +[146] Possibly the one who wrote on the quadrature of the circle in 1881. + +[147] As it is. But what a pity that we have not 12 fingers, with +duodecimal fractions instead of decimals! We should then have 0.6 for 1/2, +0.4 for 1/3, 0.8 for 2/3, 0.3 for 1/4, 0.9 for 3/4, and 0.16 for 1/8, +instead of 0.5, 0.333+, 0.666+, 0.25, 0.75, and 0.125 as we now have +with our decimal system. In other words, the most frequently used +fractions in business would be much more easily represented on the +duodecimal scale than on the decimal scale that we now use. + +[148] He wrote Hints for an _Essay on Anemology and Ombrology_ (London, +1839-40) and _The Music of the Eye_ (London, 1831). + +[149] Brigham Young (1801-1877) was born at Whitingham, Vermont, and +entered the Mormon church in 1832. In 1840 he was sent as a missionary to +England. After the death of Joseph Smith he became president of the Mormons +(1847), leading the church to Salt Lake City (1848). + +[150] Joseph Smith (1805-1844) was also born in Vermont, and was four years +the junior of Brigham Young. The _Book of Mormon_ appeared in 1827, and the +church was founded in 1830. He was murdered in 1844. + +[151] Orson Pratt (1811-1881) was one of the twelve apostles of the Mormon +Church (1835), and made several missionary journeys to England. He was +professor of mathematics in the University of Deseret (the Mormon name for +Utah). Besides the paper mentioned Pratt wrote the _Divine Authenticity of +the Book of Mormon_ (1849), _Cubic and Biquadratic Equations_ (1866), and a +_Key to the Universe_ (1866). + +[152] "It does not follow." + +[153] Dryden (1631-1700) published his _Religio Laici_ in 1682. The use of +the word "proportion" in the sense of ratio was common before his time, but +he uses it in the sense of having four terms; that is, that price is to +price as offence is to offence. + +[154] Olinthus Gilbert Gregory (1774-1841) succeeded Hutton as professor of +mathematics at Woolwich. He was, with De Morgan, much interested in +founding the University of London. He wrote on astronomy (1793), mechanics +(1806), practical mathematics (1825), and Christian evidences (1811). + +[155] See Vol. I, page 220, note 6 {482}. The _Pensees_ appeared +posthumously in 1670. + +[156] "The right thing to do is not to wager at all." "Yes, but you ought +to wager; you have started out; and not to wager at all that God exists is +to wager that he does not exist." + +[157] He lived about 300 A.D., in Africa, and wrote _Libri septem adversus +Gentes_. This was printed at Rome in 1542-3. + +[158] Pierre Bayle (1647-1706) was professor of philosophy at the +Prostestant University at Sedan from 1675 until its dissolution in 1681. He +then became professor at Rotterdam (1681-1693). In 1684 he began the +publication of his journal of literary criticism _Nouvelles de la +Republique des Lettres_. He is best known for his erudite _Dictionnaire +historique et critique_ (1697). + +[159] "But Christ himself does not prove what he promises. It is true. For, +as I have said, there cannot be any absolute proof of future events. +Therefore since it is a condition of future events that they cannot be +grasped or comprehended by any efforts of anticipation, is it not more +reasonable, out of two alternatives that are uncertain and that are hanging +in doubtful expectation, to give credence to the one that gives some hope +rather than to the one that offers none at all? For in the former case +there is no danger if, as is said to threaten, it becomes empty and void; +while in the latter case the danger is greatest, that is, the loss of +salvation, if when the time comes it is found that it was not a falsehood." + +[160] Gregg wrote several other paradoxes, including the following: _The +Authentic Report of the extraordinary case of Tresham Dames Gregg ... his +committal to Bridewell for refusing to give his recognizance_ (Dublin, +1841), _An Appeal to Public Opinion upon a Case of Injury and Wrong ... in +the case of a question of prerogative that arose between_ [R. Whately] _... +Archbishop of Dublin and the author_ (London, 1861), _The Cosmology of Sir +Isaac Newton proved to be in accordance with the Bible_ (London, 1871), +_The Steam Locomotive as revealed in the Bible_ (London 1863) and _On the +Sacred Law of 1866, conferring perpetual life with immunity from decay and +disease. A cento of decisive scriptural oracles strangely discovered_ +(London and Dublin, 1875). These titles will help the reader to understand +the man whom De Morgan so pleasantly satirizes. + +[161] See Vol. I, page 261, note 2 {592}. + +[162] "They have found it." + +[163] The late Greeks used the letters of their alphabet as numerals, +adding three early alphabetic characters. The letter [chi] represented 600, +[xi] represented 60, and [digamma] stood for 6. This gives 666, the number +of the Beast given in the Revelation. + +[164] "Allowing for necessary exceptions." + +[165] Mr. Gregg is not alone in his efforts to use the calculus in original +lines, as any one who has read Herbart's application of the subject to +psychology will recall. + +[166] See Vol. I, page 105, note 4 {188}; page 109, note 1 {197}. + +[167] The full title shows the plan,--_The Decimal System as a whole, in +its relation to time, measure, weight, capacity, and money, in unison with +each other._ But why is this so much worse than the French plan of which we +have only the metric system and the decimal division of the angle left? + +[168] One of the brothers of Sir Isaac Pitman (1813-1897), the inventor of +modern stenography. Of these brothers, Benjamin taught the art in America, +Jacob in Australia, and Joseph, Henry, and Frederick in England. + +[169] For example, _The Phonographic Lecturer_ (London, 1871 etc.), _The +Phonographic Student_ (1867, etc.), and _The Shorthand Magazine_ (1866, +etc.). + +[170] See Vol. II, page 68, note 148. + +[171] It involves the theory of non-Euclidean geometry, Euclid's postulate +of parallels being used in proving this theorem. + +[172] Referring to the fact that none of the works of Thales is extant. + +[173] The author was one B. Bulstrode. Parts 4 and 5 were printed at +Calcutta. + +[174] See Vol. II, page 5, note 18. + +[175] See Vol. I, page 85, note 2 {129}. + +[176] Alexander Vasilievich Suvaroff (1729-1800), a Russian general who +fought against the Turks, in the Polish wars, and in the early Napoleonic +campaigns. When he took Ismail in 1790 he sent this couplet to Empress +Catherine. + +[177] "Newton hath determined rightly," "Newton hath not determined +rightly." + +[178] See Vol. I, page 288, note 3 {621}. + +[179] See Vol. I, page 326, note 1 {700}. + +[180] "With great honor." + +[181] Apparently unknown to biographers. He seems to have written nothing +else. + +[182] Captain Marryat (1792-1848) published _Snarley-yow, or the Dog Fiend_ +in 1837. + +[183] He is not known to biographers, and published nothing else under this +name. + +[184] See Vol. I, page 80, note 5 {119}. + +[185] He published a _Family and Commercial Illustrated Almanack and Year +Book ... for 1861_ (Bath, 1860). + +[186] Louis Dutens (1730-1812) was born at Tours, but went to England as a +young man. He made the first collection of the works of Leibnitz, against +the advice of Voltaire, who wrote to him: "Les ecrits de Leibnitz sont +epars comme les feuilles de la Sybille, et aussi obscurs que les ecrits de +cette vieille." The work appeared at Geneva, in six volumes, in 1769. + +[187] Mungo Park (1771-1806), the first European to explore the Niger +(1795-6). His _Travels in the Interior of Africa_ appeared in 1799. He died +in Africa. + +[188] Gerhard Mercator (1512-1594) the well-known map maker of Louvain. The +"Mercator's Projection" was probably made as early as 1550, but the +principle of its construction was first set forth by Edward Wright (London, +1599). + +[189] Quirico Barilli Filopanti wrote a number of works and monographs. He +succeeded in getting his _Cesare al Rubicone_ and _Degli_ _usi idraulici +della Tela_ in the _Memoria letta ... all' Accademia delle Scienze in +Bologna_ (1847, 1866). He also wrote _Dio esiste_ (1881), _Dio Liberale_ +(1880), and _Sunto della memoria sulle geuranie ossia di alcune singolari +relazioni cosmiche della terra e del cielo_ (1862). + +[190] The periods of disembodiment may be interesting. They will be seen +from the following dates: Descartes (1596-1650), William III (1650-1702); +Roger Bacon (1214 to c. 1294), Boccaccio (1313-1375). Charles IX was born +in 1550 and died in 1574. + +[191] His real name was Frederick Parker, and he wrote several works on the +Greek language and on religion. Among these were a translation of the New +Testament from the Vatican MS. (1864), _The Revealed History of Man_ +(1854), _An Enquiry respecting the Punctuation of Ancient Greek_ (1841), +and _Rules for Ascertaining the sense conveyed in Ancient Greek +Manuscripts_ (1848, the seventh edition appearing in 1862). + +[192] See Vol. I, page 352, second note 1 {736}. + +The literature on the subject of the Great Pyramid, considered from the +standpoint of metrology, is extensive. + +[193] See Vol. I, page 80, note 5 {119}. + +[194] Sir Philip Francis (1740-1818) was a Whig politician. The evidence +that he was the author of the _Letters of Junius_ (1769-1772) is purely +circumstantial. He was clerk in the war office at the time of their +publication. In 1774 he was made a member of the Supreme Council of Bengal, +and was a vigorous opponent of Warren Hastings, the two fighting a duel in +1780. He entered parliament in 1784 and was among the leaders in the +agitation for parliamentary reform. + +[195] Mrs. Cottle published a number of letters that attracted attention at +the time. Among these were letters to the emperor of France and king of +Sardinia (1859) relating to the prophecies of the war between France and +Austria; to G. C. Lavis and Her Majesty's Ministers (1859) relating to her +claims as a prophetess; and to the "Crowned Heads" at St. James, the King +of Prussia, and others (1860), relating to certain passages of Scripture. +She also wrote _The Lamb's Book of Life for the New Jerusalem Church and +Kingdom, interpreted for all nations_ (1861). + +[196] See Vol. I, page 315, note 2 {685}, and Vol. II, page 58, note 109. + +[197] A Congregational minister, who published a number of sermons, chiefly +obituaries, between 1804 and 1851. His _Frailty of Human Life_, two sermons +delivered on the occasion of the death of Princess Charlotte, went through +at least three editions. + +[198] He was secretary of the Congregational Board and editor of the +_Congregational Year Book_ (from 1846) and the _Congregational Manual_. + +[199] Frederick Denison Maurice (1805-1872) began his preaching as a +Unitarian but entered the Established Church in 1831, being ordained in +1834. He was professor of English and History at King's College, London, +from 1840 to 1853. He was one of the founders of Queen's College for women, +and was the first principal of the Working Men's College, London. The +subject referred to by De Morgan is his expression of opinion in his +_Theological Essays_ (1853) that future punishment is not eternal. As a +result of this expression he lost his professorship at King's College. In +1866 he was made Knightbridge Professor of Casuistry, Moral Theology, and +Moral Philosophy at Cambridge. + +[200] See Vol. I, page 46, note 1 {42}. Besides the books mentioned in +this list he wrote _The Ratio between Diameter and Circumference +demonstrated by angles, and Euclid's Theorem, Proposition 32, Book I, +proved to be fallacious_ (Liverpool, 1870). This is the theorem which +asserts that the exterior angle of a triangle is equal to the sum of the +two opposite interior angles, and that the sum of the interior angles +equals two right angles. He also published his _Curiosities of Mathematics_ +in 1870, a work containing an extensive correspondence with every one who +would pay any attention to him. De Morgan was then too feeble to show any +interest in the final effort of the subject of some of his keenest satire. + +[201] See Vol. I, page 332, note 4 {709}. + +[202] See Vol. I, page 101, note 4 {174}. + +[203] "The circle-squaring disease"; literally, "the circle-measuring +disease." + +[204] See Vol. II, page 63, note 136. + +[205] William Rutherford (c. 1798-1871), teacher of mathematics at +Woolwich, secretary of the Royal Astronomical Society, editor of _The +Mathematician_, and author of various textbooks. _The Extension of [pi] to +440 places_, appeared in the _Proceedings_ of the Royal Society in 1853 (p. +274). + +[206] Charles Knight (1791-1873) was associated with De Morgan for many +years. After 1828 he superintended the publications of the Society for the +Diffusion of Useful Knowledge, to which De Morgan contributed, and he +edited the _Penny Cyclopedia_ (1833-1844) for which De Morgan wrote the +articles on mathematics. + +[207] Sir William Hamilton. See Vol. I, page 112, note 7 {211}. + +[208] Adam Smith (1723-1790) was not only known for his _Wealth of Nations_ +(1776), but for his _Theory of Moral Sentiments_ (1759), published while he +was professor of moral philosophy at Glasgow (1752-1764). He was Lord +Rector of the university in 1787. + +[209] See Vol. I, page 332, note 4 {709}. + +[210] "Whip." + +[211] "Terrible lash." + +[212] "An accomplished fact [an accomplished fault]." + +[213] See _Extracts from the Diary and Letters of Mrs. Mary Cobb_, London, +1805. + +[214] "Gentle in manner." + +[215] "Brave in action." The motto of Earl Newborough was "Suaviter in +modo, fortiter in re." + +[216] "Reduction to an absurdity," a method of proof occasionally used in +geometry and in logic. + +[217] "He has lost the right of being moved (struck) by evidence." + +[218] For _radix quadratus_. The usual root sign is supposed to be derived +from _r_ (for radix), and at one time _q_ was commonly used for square, as +in Viete's style of writing Aq for A^2. + +[219] The Garde Douloureuse was a castle in the marches of Wales and +received its name because of its exposure to attacks by the Welsh. + +[220] "Out of the fight." + +[221] "Hidden." + +[222] John Cam Hobhouse (1786-1869), Baron Broughton, was committed to +Newgate for two months in 1819 for his anonymous pamphlet, _A Trifling +Mistake_. This was a great advertisement for him, and upon his release he +was at once elected to parliament for Westminster. He was a strong +supporter of all reform measures, and was Secretary for War in 1832. He was +created Baron Broughton de Gyfford in 1851. + +[223] Thomas Erskine (1750-1823), the famous orator. He became Lord +Chancellor in 1806, but sat in the House of Commons most of his life. + +[224] The above is explained in the MS. by a paragraph referring to some +anagrams, in one of which, by help of the orthography suggested, a +designation for this cyclometer was obtained from the letters of his +name.--S. E. De M. + +[225] "A personal verb agrees with its subject." + +[226] See Vol. I, page 326, note 1 {700}. + +[227] See Vol. I, page 326, note 2 {701}. + +[228] Apparently unknown to biographers. + +[229] The _Bibliotheca Mathematica_ of Ludwig Adolph Sohncke (1807-1853), +professor of mathematics at Koenigsberg and Halle, covered the period from +1830 to 1854, being completed by W. Engelmann. It appeared in 1854. + +[230] See Vol. I, page 392, note 2 {805}. + +[231] See Vol. I, page 43, note 7 {32}. + +[232] See Vol. II, page 91, note 187. + +[233] Mason made a notable balloon trip from London to Weilburg, in the +Duchy of Nassau, in November, 1836, covering 500 miles in 18 hours. He +published an account of this trip in 1837, and a work entitled +_Aeronautica_ in 1838. + +[234] William Harrison Ainsworth (1805-1885) the novelist. + +[235] On this question see Vol. I, page 326, note 2 {701}. + +[236] Major General Alfred Wilks Drayson, author of various works on +geology, astronomy, military surveying, and adventure. + +[237] Hailes also wrote several other paradoxes on astronomy and circle +squaring during the period 1843-1872. + +[238] See Vol. I, page 43, note 8 {33}. + +[239] See Vol. I, page 43, note 7 {32}. + +[240] "Very small errors are not to be condemned." + +[241] He seems to have written nothing else. + +[242] Besides the paradoxes here mentioned by De Morgan he wrote several +other works, including the following: _Abriss der Babylonisch-Assyrischen +Geschichte_ (Mannheim, 1854), _A Popular Inquiry into the Moon's rotation +on her axis_ (London, 1856), _Practical Tables for the reduction of the +Mahometan dates to the Christian kalendar_ (London, 1856), _Grundzuege einer +neuen Weltlehre_ (Munich, 1860), and _On the historical Antiquity of the +People of Egypt_ (London, 1863). + +[243] Dircks (1806-1873) was a civil engineer of prominence, and a member +of the British Association and the Royal Society of Edinburgh. He wrote +(1863) on "Pepper's Ghost," an ingenious optical illusion invented by him. +There was a second edition of the _Perpetuum Mobile_ in 1870. + +[244] George Stephenson (1781-1848), the inventor of the first successful +steam locomotive. His first engine was tried in 1814. + +[245] Robert Stephenson (1803-1859), the only son of George. Most of the +early improvements in locomotive manufacture were due to him. He was also +well known for his construction of great bridges. + +[246] "In its proper place." + +[247] "A fool always finds a bigger fool to admire him." + +[248] See Vol. I, page 43, note 7 {32}. + +[249] See Vol. I, page 43, note 8 {33}. + +[250] See Vol. I, page 85, note 2 {129}. + +[251] See Vol. I, page 390, note 1 {390}. + +[252] From 1823 to 1852 it was edited by I. C. Robertson; from 1852 to 1857 +by R. A. Brooman; and from 1857 to 1863 by Brooman and E. J. Reed. + +[253] Sir James Ivory (1765-1842) was, as a young man, manager of a flax +mill in Scotland. In 1804 he was made professor of mathematics at the Royal +Military College, then at Marlow and later at Sandhurst. He was deeply +interested in mathematical physics, and there is a theorem on the +attraction of ellipsoids that bears his name. He was awarded three medals +of the Royal Society, and was knighted together with Herschel and Brewster, +in 1831. + +[254] See Vol. I, page 56, note 1 {64}. + +[255] See Vol. I, page 153, note 5 {338}. + +[256] See Vol. I, page 309, note 2 {670}. + +[257] See Vol. I, page 87, note 4 {133}. + +[258] George Canning (1770-1857), the Tory statesman and friend of Scott, +was much interested in founding the _Quarterly Review_ (1808) and was a +contributor to its pages. + +[259] See Vol. I, page 186, note 14 {418}. + +[260] See Vol. II, page 141, note 252. + +[261] De Morgan had a number of excellent articles in this publication. + +[262] See Vol. I, page 279, note 1 {611}. + +[263] James Orchard Halliwell (1820-1889), afterwards Halliwell-Phillips, +came into prominence as a writer at an early age. When he was seventeen he +wrote a series of lives of mathematicians for the _Parthenon_. His _Rara +Mathematica_ appeared when he was but nineteen. He was a great bibliophile +and an enthusiastic student of Shakespeare. + +[264] This was written at the age of twenty-two. + +[265] The subject of this criticism is of long past date, and as it has +only been introduced by the author as an instance of faulty editorship, I +have omitted the name of the writer of the libel, and a few lines of +further detail.--S. E. De M. + +[266] "Condemned souls." + +[267] The editor of the _Mechanics' Magazine_ died soon after the above was +written.--S. E. De M. + +[268] Thomas Stephens Davies (1795-1851) was mathematical master at +Woolwich and F. R. S. He contributed a series of "Geometrical Notes" to the +_Mechanics' Magazine_ and edited the _Mathematician_. He also published a +number of text-books. + +[269] See Vol. II, page 66, note 143. + +[270] The _Dictionary of Greek and Roman Biography_ (1849), edited by Sir +William Smith (1813-1893), whose other dictionaries on classical and +biblical matters are well known. + +[271] "O J. S.! This is the worst! the greatest possible injury!" + +[272] See Vol. I, page 44, note 9 {34} and page 110, note 5 {201}. + +[273] + + "If there's a man whom the judge's pitiless sentence awaiteth, + His head condemned to penalties and tribulations, + Let neither penitentiaries tire him with laborer's burdens + Nor let his stiffened hands be harrassed by work in the mines. + He must square the circle! For what else do I care?--all + Known punishments this one task hath surely included." + +[274] Houlston was in the customs service. He also published _Inklings of +Areal Autometry_, London, 1874. + +[275] This is Frederick C. Bakewell. He had already published _Natural +Evidence of a Future Life_ (London, 1835), _Philosophical Conversations_ +(London, 1833, with other editions), and _Electric Science_ (London, 1853, +with other editions). + +[276] Henry F. A. Pratt had already published _A Dissertation on the power +of the intercepted pressure of the Atmosphere_ (London, 1844) and _The +Genealogy of Creation_ (1861). Later he published a work _On Orbital +Motion_ (1863), and _Astronomical Investigations_ (1865). + +[277] See Vol. I, page 260, note 1 {591}. + +[278] Thomas Rawson Birks (1810-1883), a theologian and controversialist, +fellow of Trinity College, Cambridge, and (1872) professor of moral +philosophy in that university. He wrote _Modern Rationalism_ (1853), _The +Bible and Modern Thought_ (1861), _The First Principles of Moral Science_ +(1873), and _Modern Physical Fatalism and the Doctrine of Evolution_ +(1876), the last being an attack on Herbert Spencer's _First Principles_. + +[279] Pseudonym for William Thorn. In the following year (1863) he +published a second work, _The Thorn-Tree: being a History of Thorn +Worship_, a reply to Bishop Colenso's work entitled _The Pentateuch and the +Book of Joshua critically examined_. + +[280] Besides _The Pestilence_ (1866) he published _The True Church_ +(1851), _The Church and her destinies_ (1855), _Religious reformation +imperatively demanded_ (1864), and _The Bible plan unfolded_ (second +edition, 1872). + +[281] See Vol. II, page 97, note 195. + +[282] Sir George Cornewall Lewis (1806-1863) also wrote an _Essay on the +Origin and Formation of the Romance Languages_ (1835), an _Essay on the +Government of Dependencies_ (1841), and an _Essay on Foreign Jurisdiction +and the Extradition of Criminals_ (1859). He was Chancellor of the +Exchequer in 1855 and Home Secretary in 1859. + +[283] Henry Malden (1800-1876), a classical scholar, fellow of Trinity +College, Cambridge, and professor of Greek at University College +(1831-1876), then (1831) the University of London. He wrote a _History of +Rome to 390 B. C._ (1830), and _On the Origin of Universities and +Academical Degrees_ (1835). + +[284] Henry Longueville Mansel (1820-1871), theologian and metaphysician, +reader in theology at Magdalen College, Oxford (1855), and professor of +ecclesiastical history and Dean of St. Paul's (1866). He wrote on +metaphysics, and his Bampton Lectures (1858) were reprinted several times. + +[285] "Hejus gave freely, gave freely. God is propitious, God is favorable +to him who gives freely. God is honored with a banquet of eggs at the cross +roads, the god of the world. God, with benignant spirit, desired in +sacrifice a goat, a bull to be carried within the precincts of the holy +place. God, twice propitiated, blesses the pit of the sacred libation." + +[286] Eudoxus of Cnidus (408-355 B. C.) had much to do with the early +scientific astronomy of the Greeks. The fifth book of Euclid is generally +attributed to him. His astronomical works are known chiefly through the +poetical version of Aratus mentioned in note 13, page 167. + +[287] Simplicius, a native of Cilicia, lived in the 6th century of our era. +He was driven from Athens by Justinian and went to Persia (531), but he +returned later and had some fame as a teacher. + +[288] See Vol. I, page 160, note 3 {348}. + +[289] See Vol. I, page 76, note 3 {112}. + +[290] "Through right and wrong." + +[291] "It is therefore to arrive at this parallelism, or to preserve it, +that Copernicus feared to be obliged to have recourse to this equal and +opposite movement which destroys the effect which he attributed so freely +to the first, of deranging the parallelism." + +[292] A contemporary of Plato and a disciple of Aristotle. + +[293] Meton's solstice, the beginning of the Metonic cycles, has been +placed at 432 B. C. Ptolemy states that he made the length of the year +365-1/4 + 1/72 days. + +[294] Aratus lived about 270 B. C., at the court of Antigonus of Macedonia, +and probably practiced medicine there. He was the author of two +astronomical poems, the [Greek: Phainomena], apparently based on the lost +work of Eudoxus, and the [Greek: Dioseeia] based on Aristotle's +_Meteorologica_ and _De Signis Ventorum_ of Theophrastus. + +[295] "The nineteen (-year) cycle of the shining sun." + +[296] Claudius Salmasius (1588-1653), or Claude Saumaise, was a +distinguished classicist, and professor at the University of Leyden. The +word [Greek: eleioio] means Elian, thus making the phrase refer to the +brilliant one of Elis. + +[297] Sir William Brown (1784-1864). In 1800 the family moved to Baltimore, +and there the father, Alexander Brown, became prominent in the linen trade. +William went to Liverpool where he acquired great wealth as a merchant and +banker. He was made a baronet in 1863. + +[298] Robert Lowe (1811-1892), viscount Sherbrooke, was a fellow of +Magdalen College, Oxford (1835). He went to Australia in 1842 and was very +successful at the bar. He returned to England in 1850 and became leader +writer on the _Times_. He was many years in parliament, and in 1880 was +raised to the peerage. + +[299] See Vol. I, page 42, note 4 {24}. + +[300] Francis Walkingame (fl. about 1751-1785), whose _Tutor's Assistant_ +went through many editions from 1751-1854. + +[301] Davies Gilbert (1767-1839). His family name was Giddy, but he assumed +his wife's name. He sat in parliament from 1806 to 1832. In 1819 he secured +the establishment of the Cape of Good Hope observatory. He was Treasurer +(1820-1827) and President (1827-1830) of the Royal Society. + +[302] See Vol. I, page 55, note 2 {63}. + +[303] Sir Jonathan Frederick Pollock (1783-1870) entered parliament in 1831 +and was knighted in 1834. + +[304] Joseph Hume (1777-1855) entered parliament in 1812 and for thirty +years was leader of the Radical party. + +[305] "What! when I say, 'Nicole, bring me my slippers,' is that prose?" + +[306] Captain Basil Hall (1788-1844), a naval officer, carried on a series +of pendulum observations in 1820-1822, while on a cruise of the west coast +of North America. The results were published in 1823 in the _Philosophical +Transactions_. He also wrote two popular works on travel that went through +numerous editions. + +[307] Anthony Ashley Cooper (1801-1885), Earl of Shaftesbury. His name is +connected with philanthropic work and factory legislation. + +[308] See Vol. I, page 207, note 12 {469}. + +[309] See Vol. I, page 80, note 5 {119}. + +[310] Sir Thomas Maclear (1794-1879), an Irishman by birth, became +Astronomer Royal at the Cape of Good Hope in 1833. He was an indefatigable +observer. He was knighted in 1860. + +[311] Thomas Romney Robinson (1792-1882), another Irish astronomer of +prominence. He was a deputy professor at Trinity College, Dublin, but took +charge of the Armagh observatory in 1823 and remained there until his +death. + +[312] Sir James South (1785-1867) was in early life a surgeon, but gave up +his practice in 1816 and fitted up a private observatory. He contributed to +the science of astronomy, particularly with respect to the study of double +stars. + +[313] Sir John Wrottesley (1798-1867), second Baron Wrottesley. Like Sir +James South, he took up the study of astronomy after a professional +career,--in his case in law. He built a private observatory in 1829 and +made a long series of observations, publishing three star catalogues. He +was president of the Astronomical Society from 1841 to 1843, and of the +Royal Society from 1854 to 1857. + +[314] He seems to have written nothing else. + +[315] See Vol. II, page 68, note 147. + +[316] "The wills are free, and I wish neither the one nor the other." + +[317] "The force of inertia conquered." + +[318] Reddie also wrote _The Mechanics of the Heavens_, referred to later +in this work. He must not be confused with Judge James Reddie (1773-1852), +of Glasgow, who wrote on international law, although this is done in the +printed edition of the British Museum catalogue, for he is mentioned by De +Morgan somewhat later as alive in 1862. + +[319] Henry Dunning Macleod (1821-1902), a lawyer and writer on political +economy, was a Scotchman by birth. He wrote on economical questions, and +lectured on banking at Cambridge (1877) and at King's College, London +(1878). He was a free lance in his field, and was not considered orthodox +by the majority of economists of his time. He was an unsuccessful candidate +for the chairs of political economy at Cambridge (1863), Edinburgh (1871), +and Oxford (1888). + +[320] See Vol. I, page 252, note 2 {576}. + +[321] Francis Henry Laing (1816-1889) was a graduate of Queen's College, +Cambridge, and a clergyman in the Church of England until 1846, when he +entered the Church of Rome. He taught in various Jesuit colleges until +1862, when his eccentricity was too marked to warrant the Church in +allowing him to continue. He published various controversial writings +during his later years. Of course if he had known the works of Wessel, +Gaus, Buee, Argand, and others, he would not have made such a sorry +exhibition of his ignorance of mathematics. + +[322] See Vol. I, page 329, note 1 {705}. The book went into a second +edition in 1864. + +[323] Thomas Weddle (1817-1853) was, at the time of publishing this paper, +a teacher in a private school. In 1851 he became professor of mathematics +at Sandhurst. He contributed several papers to the _Cambridge and Dublin +Mathematical Journal_, chiefly on geometry. + +[324] See Vol. II, page 109, note 205. + +[325] See Vol. II, page 66, note 143. + +[326] See Vol. II, page 151, note 268. + +[327] George Barrett (1752-1821) worked from 1786 to 1811 on a set of life +insurance and annuity tables. He invented a plan known as the "columnar +method" for the construction of such tables, and as De Morgan states, this +was published by Francis Baily, appearing in the appendix to his work on +annuities, in the edition of 1813. Some of his tables were used in +Babbage's _Comparative View of the various Institutions for the Assurance +of Lives_ (1826). + +[328] See Vol. I, page 309, note 2 {670}. + +[329] This was his _Practical short and direct Method of Calculating the +Logarithm of any given Number, and the Number corresponding to any given +Logarithm_ (1849). + +[330] This is William Neile (1637-1670), grandson of Richard Neile (not +Neal), Archbishop of York. At the age of 19, in 1657, he gave the first +rectification of the semicubical parabola. Although he communicated it to +Brouncker, Wren, and others, it was not published until 1639, when it +appeared in John Wallis's _De Cycloide_. + +[331] I myself "was a considerable part." + +[332] He also wrote _A Glance at the Universe_ ("2d thousand" in 1862), and +_The Resurrection Body_ (1869). + +[333] See Vol. I, page 63, note 1 {74}. + +[334] As Swift gave it in his _Poetry. A Rhapsody_, it is as follows: + + "So, naturalists observe, a flea + Has smaller fleas that on him prey; + And these have smaller still to bite 'em. + And so proceed _ad infinitum_." + +[335] Perhaps 1,600,000,000 years, if Boltwood's recent computations based +on radium disintegration stand the test. This would mean, according to +MacCurdy's estimate, 60,000,000 years since life first appeared on the +earth. + +[336] De Morgan wrote better than he knew, for this work, the _Allgemeine +Encyclopaedie der Wissenschaften und Kuenste_, begun at Leipsic in 1818, is +still (1913) unfinished. Section I, A-G, consists of 99 parts in 56 +volumes; Section II, H-N, consists of 43 volumes and is not yet completed; +and Section III, O-Z, consists of 25 volumes thus far, with most of the +work still to be done. Johann Samuel Ersch (1766-1828), the founder, was +head librarian at Halle. Johann Gottfried Gruber (1774-1851), his +associate, was professor of philosophy at the same university. + +[337] William Howitt (1792-1879) was a poet, a spiritualist, and a +miscellaneous writer. He and his wife became spiritualists about 1850. He +wrote numerous popular works on travel, nature and history. + +[338] See Vol. II, page 55, note 108. + +[339] As will be inferred from the text, C. D. was Mrs. De Morgan, and +A. B. was De Morgan. + +[340] Jean Meslier (1678-1733), cure of Estrepigny, in Champagne, was a +skeptic, but preached only strict orthodoxy to his people. It was only in +his manuscript, _Mon Testament_, that was published after his death, and +that caused a great sensation in France, that his antagonism to +Christianity became known. + +[341] Baron Zach relates that a friend of his, in a writing intended for +publication, said _Un esprit doit se frotter contre un autre_. The censors +struck it out. The Austrian police have a keen eye for consequences.--A. De +M. + +"One mind must rub against another." On Baron Zach, see Vol. II, page 45, +note 4. + +[342] Referring to the first Lord Eldon (1751-1838), who was Lord +Chancellor from 1799 to 1827, with the exception of one year. + +[343] "Sleeping power." + +[344] "Causes sleep." + +[345] Richard Hooker (c. 1554-1600), a theologian, "the ablest living +advocate of the Church of England as by law established." + +[346] See Vol. I, page 76, note 3 {112}. + +[347] "Other I,"--other self. + +[348] This "utter rejection" has been repeated (1872) by the same +writer.--S. E. De M. + +[349] Edward Jenner (1749-1823) was a physician and biologist. His first +experiments in vaccination were made in 1796, and his discovery was +published in 1798. + +[350] See Vol. II, page 38, note 80. + +[351] "You will go most safely in the middle (way)." + +[352] Pierre Joseph Arson was known early in the 19th century for his +controversy with Hoene Wronski the mathematician, whom he attacked in his +_Document pour l'histoire des grands fourbes qui ont figure sur la terre_ +(1817-1818). + +[353] "We enter the course by night and are consumed by fire." + +[354] See Vol. I, page 51, note 3 {51}. + +[355] See Vol. I, page 336, note 8 {713}. + +[356] See Vol. I, page 137, note 8 {286}. + +[357] See Vol. I, page 229, note 2 {515}. + +[358] Richard Cobden (1804-1865), the cotton manufacturer and statesman who +was prominent in his advocacy of the repeal of the Corn Laws. + +[359] James Smith (1775-1839), solicitor to the Board of Ordnance. With his +brother Horatio he wrote numerous satires. His _Horace in London_ (1813) +imitated the Roman poet. His works were collected and published in 1840. + +[360] Samuel Butler (1612-1680), the poet and satirist, author of +_Hudibras_ (1663-1678). + +[361] "Is it not fine to be sure of one's action when entering in a combat +with another? There, push me a little in order to see. NICOLE. Well! what's +the matter? M. JOURDAIN. Slowly. Ho there! Ho! gently. Deuce take the +rascal! NICOLE. You told me to push. M. JOURDAIN. Yes, but you pushed me +_en tierce_, before you pushed _en quarte_, and you did not give me time to +parry." + +[362] John Abernethy (1764-1831), the famous physician and surgeon. + +[363] See Vol. I, page 102, note 5 {175}. + +[364] "With what measure ye mete, it shall be measured to you again." + +[365] Eusebius of Caesarea (c. 260-340), leader of the moderate party at the +Council of Nicaea, and author of a _History of the Christian Church_ in ten +books (c. 324 A. D.). + +[366] Nathaniel Lardner (1684-1768), a non-conformist minister and one of +the first to advocate the scientific study of early Christian literature. + +[367] Henry Alford (1810-1871) Dean of Canterbury (1857-1871) and editor of +the Greek Testament (1849-1861). + +[368] The work was _The Number and Names of the Apocalyptic Beasts: with an +explanation and application. Part I._ London, 1848, as mentioned below. +Thom also wrote _The Assurance of Faith, or Calvinism identified with +Universalism_ (London, 1833), and various other religious works. + +[369] See Vol. I, page 222, note 14 {490}. + +[370] John Hamilton Thom (1808-1894) was converted to Unitarianism and was +long a minister in that church, preaching in the Renshaw Street Chapel from +1831 to 1866. De Morgan refers to the Liverpool Unitarian controversy +conducted by James Martineau and Henry Giles in response to a challenge by +thirteen Anglican Clergy. In 1839 Thom contributed four lectures and a +letter to this controversy. Among his religious works were a _Life of +Blanco White_ (1845) and _Hymns, Chants, and Anthems_ (1854). + +[371] The spelling of these names is occasionally changed to meet the +condition that the numerical value of the letters shall be 666, "the number +of the beast" of Revelations. The names include Julius Caesar; Valerius +Jovius Diocletianus (249-313), emperor from 287 to 305, persecutor of the +Christians; Louis, presumably Louis XIV; Gerbert (940-1003), who reigned as +Pope Sylvester II from 999 to 1003, known to mathematicians for his abacus +and his interest in geometry, and accused by his opponents as being in +league with the devil; Linus, the second Bishop of Rome, the successor of +Peter; Camillo Borghese (1552-1621), who reigned as Pope Paul V from 1605 +to 1621, and who excommunicated all Venice in 1606 for its claim to try +ecclesiastics before lay tribunals, thus taking a position which he was +forced to abandon; Luther, Calvin; Laud (see Vol. I, page 145, note 7 +{307}); Genseric (c. 406-477), king of the Vandals, who sacked Rome in 455 +and persecuted the orthodox Christians in Africa; Boniface III, who was +pope for nine months in 606; Beza (see Vol. I, page 66, note 6 {83}); +Mohammed; [Greek: braski], who was Giovanni Angelo Braschi (1717-1799), and +who reigned as Pope Pius VI from 1775 to 1799, dying in captivity because +he declined to resign his temporal power to Napoleon; Bonaparte; and, under +[Greek: Ion Paune], possibly Pope John XIV, who reigned in 983 and 984 +during the absence of Boniface VII in Constantinople. + +[372] The Greek words and names are also occasionally misspelled so as to +fit them to the number 666. They are [Greek: Lateinos] (Latin), [Greek: he +latine basileia] (the Latin kingdom), [Greek: ekklesia italika] (the +Italian Church), [Greek: euanthas] (blooming), [Greek: teitan] (Titan), +[Greek: arnoume] (renounce), [Greek: lampetis] (the lustrous), [Greek: ho +niketes] (conqueror), [Greek: kakos hodegos] (bad guide), [Greek: alethes +blaberos] (truthful harmful one), [Greek: palai baskanos] (a slanderer of +old), [Greek: amnos adikos] (unmanageable lamb), [Greek: antemos] +(Antemos), [Greek: genserikos] (Genseric), [Greek: euinas] (with stout +fibers), [Greek: Benediktos] (Benedict), [Greek: Bonibazios g. papa x. e. +e. e. a.] (Boniface III, pope 68, bishop of bishops I), [Greek: oulpios] +(baneful), [Greek: dios eimi he heras] (I, a god, am the), [Greek: he missa +he papike] (the papal brief), [Greek: loutherana] (Lutheran), [Greek: +saxoneios] (Saxon), [Greek: Bezza antitheos] (Beza antigod), [Greek: he +alazoneia biou] (the illusion of life), [Greek: Maometis] (Mahomet); +[Greek: Maometes b.] (Mahomet II), [Greek: theos eimi epi gaies] (I am lord +over the earth), [Greek: iapetos] (Iapetos, father of Atlas), [Greek: +papeiskos] (Papeiskos), [Greek: dioklasianos] (Diocletian), [Greek: cheina] +(Cheina = Cain? China?), [Greek: braski] (Braschi, as explained in note +10), [Greek: Ion Paune] (Paunian violet, but see note 10), [Greek: koupoks] +(cowpox), [Greek: Bonneparte] (Bonneparte), [Greek: N. Boneparte] (N. +Boneparte), [Greek: euporia] (facility), [Greek: paradosis] (surrender), +[Greek: to megatherion] (the megathereum, the beast). + +[373] James Wapshare, whose _Harmony of the Word of God in Spirit and in +Truth_ appeared in 1849. + +[374] The literature relating to the _Swastika_ is too extended to permit +of any adequate summary in these notes. + +[375] Henry Edward Manning (1808-1892), at first an Anglican clergyman, he +became a Roman Catholic priest in 1851, and became Cardinal in 1875. He +succeeded Cardinal Wiseman as Archbishop of Westminster in 1865. He wrote a +number of religious works. + +[376] John Bright (1811-1889), Quaker, cotton manufacturer, and statesman. +He worked with Cobden for free trade, peace, and reform of the electorate. + +[377] "The fallacy of many questions." + +[378] William Wilberforce (1759-1833), best known for his long fight for +the abolition of the slave trade. + +[379] Richard Martin (1754-1834), high sheriff of County Galway and owner +of a large estate in Connemara. Curiously enough, he was known both for his +readiness in duelling and for his love for animals. He was known as +"Humanity Martin," and in 1822 secured the passage of an act "to prevent +the cruel and improper treatment of cattle." He was one of the founders +(1824) of the Royal Society for the Prevention of Cruelty to Animals. He is +usually considered the original of Godfrey O'Malley in Lever's novel, +_Charles O'Malley_. + +[380] See Vol. I, page 149, note 1 {323}, also text on same page. + +[381] See Vol. I, page 44, note 9 {34}, also text, Vol. I, page 110. + +[382] "Penitential seat." + +[383] "Well placed upon the cushion." + +[384] See Vol. II, page 58, note 109. + +[385] "He has lost the right of being influenced by evidence." + +[386] "Hung up." + +[387] "A few things to the wise, nothing to the unlettered." + +[388] The fallacy results from dividing both members of an equation by 0, x +- 1 being the same as 1 - 1, and calling the quotients finite. + +[389] "If you order him to the sky he will go." + +[390] _Similia similibus curanter_, "Like cures like," the homeopathic +motto. + +[391] "Without harm to the proprieties." + +[392] "What are you doing? I am standing here." + +[393] Lors feist l'Anglois tel signe. La main gausche toute ouverte il leva +hault en l'aer, puis ferma au poing les quatres doigtz d'icelle et le +poulce estendu assit sus la pinne du nez. Soubdain apres leva la dextre +toute ouverte, et toute ouverte la baissa, joignant la poulce au lieu que +fermait le petit doigt de la gausche, et les quatre doigtz d'icelle mouvoit +lentement en l'aer. Puis au rebours feit de la dextre ce qu'il avoit faict +de la gausche, et de la gausche ce que avoit faict de la dextre.--A. De M. + +[394] _Suaviter in modo, fortiter in re_, "Gentle in manners, firm in +action." + +[395] See Vol. I, page 101, note 4 {174}. + +[396] See Vol. I, page 315, note 3 {686}. + +[397] Henry Fawcett (1833-1884) became totally blind in 1858, but in spite +of this handicap he became professor of political economy at Cambridge and +sat in parliament for a number of years. He championed the cause of reform +and in particular he was prominent in the protection of the native +interests of India. The establishing of the parcels post (1882) took place +while he was postmaster general (1880-1884). + +[398] Of course the whole thing depends upon what definition of division is +taken. We can multiply 2 ft. by 3 ft. if we define multiplication so as to +allow it, or 2 ft. by 3 lb, getting foot-pounds, as is done in physics. + +[399] Richard Milward (1609-1680), for so the name is usually given, was +rector of Great Braxted (Essex) and canon of Windsor. He was long the +amanuensis of John Selden, and the _Table Talk_ was published nine years +after Milward's death, from notes that he left. Some doubt has been cast +upon the authenticity of the work owing to many of the opinions that it +ascribes to Selden. + +[400] John Selden (1584-1654) was a jurist, legal antiquary, and Oriental +scholar. He sat in the Long Parliament, and while an advocate of reform he +was not an extremist. He was sent to the Tower for his support of the +resolution against "tonnage and poundage," in 1629. His _History of Tythes_ +(1618) was suppressed at the demand of the bishops. His _De Diis Syriis_ +(1617) is still esteemed a classic on Semitic mythology. + +[401] See Vol. I, page 42, note 4 {24}. + +[402] See Vol. II, page 249, note 398. + +[403] John Palmer (1742-1818) was a theatrical manager. In 1782 he set +forth a plan for forwarding the mails by stage coaches instead of by +postmen. Pitt adopted the plan in 1784. Palmer was made comptroller-general +of the post office in 1786 and was dismissed six years later for +arbitrarily suspending a deputy. He had been verbally promised 2-1/2% on +the increased revenue, but Pitt gave him only a pension of L3000. In 1813 +he was awarded L50,000 in addition to his pension. + +[404] Dionysius Lardner (1793-1859), professor of natural philosophy in +London University (now University College). His _Cabinet Cyclopaedia_ +(1829-1849) contained 133 volumes. De Morgan wrote on probabilities, and +Lardner on various branches of mathematics, and there were many other +well-known contributors. Lardner is said to have made $200,000 on a lecture +tour in America. + +[405] Thomas Fysche Palmer (1747-1802) joined the Unitarians in 1783, and +in 1785 took a charge in Dundee. He was arrested for sedition because of an +address that it was falsely alleged that he gave before a society known as +the "Friends of Liberty." As a matter of fact the address was given by an +uneducated weaver, and Palmer was merely asked to revise it, declining to +do even this. Nevertheless he was sentenced to Botany Bay (1794) for seven +years. The trial aroused great indignation. + +[406] See Vol. I, page 80, note 5 {119}. + +[407] See Vol. II, page 244, note 394. + +[408] See Vol. I, page 352, note 1 {731}. + +[409] See Vol. I, page 332, note 4 {709}. + +[410] "The lawyers are brought into court; let them accuse each other." + +[411] Samuel Rogers (1763-1855), the poet and art connoisseur. He declined +the laureateship on the death of Wordsworth (1850). Byron, his pretended +friend, wrote a lampoon (1818) ridiculing his cadaverous appearance. + +[412] Theodore Edward Hook (1788-1841), the well-known wit. He is satirized +as Mr. Wagg in _Vanity Fair_. The _John Bull_ was founded in 1820 and Hook +was made editor. + +[413] "On pitying the heretic." + +[414] A term of medieval logic. Barbara: All M is P, all S is M, hence all +S is P. Celarent: No M is P, all S is M, hence no S is P. + +[415] "Simply," "According to which," "It does not follow." + +[416] + + "O sweet soul, what good shall I declare + That heretofore was thine, since such are thy remains!" + +[417] "Stupid fellow!" + +[418] Christopher Barker (c. 1529-1599), also called Barkar, was the +Queen's printer. He began to publish books in 1569, but did no actual +printing until 1576. In 1575 the Geneva Bible was first printed in England, +the work being done for Barker. He published 38 partial or complete +editions of the Bible from 1575 to 1588, and 34 were published by his +deputies (1588-1599). + +[419] James Franklin (1697-1735) was born in Boston, Mass., and was sent to +London to learn the printer's trade. He returned in 1717 and started a +printing house. Benjamin, his brother, was apprenticed to him but ran away +(1723). James published the _New England Courant_ (1721-1727), and Benjamin +is said to have begun his literary career by writing for it. + +[420] James Hodder was a writing master in Tokenhouse Yard, Lothbury, in +1661, and later kept a boarding school in Bromley-by-Bow. His famous +arithmetic appeared at London in 1661 and went through many editions. It +was the basis of Cocker's work. (See Vol. I, page 42, note 4 {24}.) It was +long thought to have been the first arithmetic published in America, and it +was the first English one. There was, however, an arithmetic published much +earlier than this, in Mexico, the _Sumario compendioso ... con algunas +reglas tocantes al Aritmetica_, by "Juan Diaz Freyle," in 1556. + +[421] Henry Mose, Hodder's successor, kept a school in Sherborne Lane, +London. + +[422] Rear Admiral Sir Francis Beaufort (1774-1857), F.R.S., was +hydrographer to the Navy from 1829 to 1855. He prepared an atlas that was +printed by the Society for the Diffusion of Useful Knowledge. + +[423] Antoine Sabatier (1742-1817), born at Castres, was known as the Abbe +but was really nothing more than a "clerc tonsure." He lived at Court and +was pensioned to write against the philosophers of the Voltaire group. He +posed as the defender of morality, a commodity of which he seems to have +possessed not the slightest trace. + +[424] Maffeo Barberini was pope, as Urban VIII, from 1623 to 1644. It was +during his ambitious reign that Galileo was summoned to Rome to make his +recantation (1633), the exact nature of which is still a matter of dispute. + +[425] This Baden Powell (1796-1860) was the Savilian professor of geometry +(1827-1860) at Oxford. + +[426] "Memoirs of the famous bishop of Chiapa, by which it appears that he +had butchered or burned or drowned ten million infidels in America in order +to convert them. I believe that this bishop exaggerated; but if we should +reduce these sacrifices to five million victims, this would still be +admirable." + +[427] Alfonso X (1221-1284), known as El Sabio (the Wise), was interested +in astronomy and caused the Alphonsine Tables to be prepared. These table +were used by astronomers for a long time. It is said that when the +Ptolemaic system of the universe was explained to him he remarked that if +he had been present at the Creation he could have shown how to arrange +things in a much simpler fashion. + +[428] George Richards (c. 1767-1837), fellow of Oriel (1790-1796), Bampton +lecturer (1800), Vicar of St. Martin's-in-the-Fields, Westminster (1824), +and a poet of no mean ability. + +[429] The "Aboriginal Britons," an excellent poem, by Richards. (Note by +Byron.)--A. De M. + +[430] John Watkins (d. after 1831), a teacher and miscellaneous writer. + +[431] Frederic Shoberl (1775-1853), a miscellaneous writer. + +[432] He wrote, besides the _Aboriginal Britons_, _Songs of the Aboriginal +Bards_ (1792), _Modern France: a Poem_ (1793), _Odin, a drama_ (1804), +_Emma, a drama on the model of the Greek theatre_ (1804), _Poems_ (2 +volumes, 1804), and a _Monody on the Death of Lord Nelson_ (1806). + +[433] Henry Kirke White (1785-1806), published his first volume of poems at +the age of 18. Southey and William Wilberforce became interested in him and +procured for him a sizarship at St. John's College, Cambridge. He at once +showed great brilliancy, but he died of tuberculosis at the age of 21. + +[434] John Wolcot, known as Peter Pindar (1738-1819), was a London +physician. He wrote numerous satirical poems. His _Bozzy and Piozzi, or the +British Biographers_, appeared in 1786, and reached the 9th edition in +1788. + +[435] See Vol. I, page 235, note 8 {532}. + +[436] Richard Payne Knight (1750-1824) was a collector of bronzes, gems, +and coins, many of his pieces being now in the British Museum. He sat in +parliament for twenty-six years (1780-1806), but took no active part in +legislation. He opposed the acquisition of the Elgin Marbles, holding them +to be of little importance. His _Analytical Inquiry into the Principles of +Taste_ appeared in 1808. + +[437] Mario Nizzoli (1498-1566), a well-known student of Cicero, was for a +time professor at the University of Parma. His _Observationes in M. Tullium +Ciceronem_ appeared at Pratalboino in 1535. It was revised by his nephew +under the title _Thesaurus Ciceronianus_ (Venice, 1570). + +[438] See Vol. I, page 314, note 4 {681}. + +[439] + + "Like the geometer, who bends all his powers + To measure the circle, and does not succeed, + Thinking what principle he needs." + +[440] Francis Quarles (1592-1644), a religious poet. He wrote paraphrases +of the Bible and numerous elegies. In the early days of the revolutionary +struggle he sided with the Royalists. One of his most popular works was the +_Emblems_ (1635), with illustrations by William Marshall. + +[441] Regnault de Becourt wrote _La Creation du monde, ou Systeme +d'organisation primitive suivi de l'interpretation des principaux +phenomenes et accidents que se sont operes dans la nature depuis l'origine +de univers jusqu'a nos jours_ (1816). This may be the work translated by +Dalmas. + +[442] "Because it lacks a holy prophet." + +[443] Anghera. See Vol. II, page 60, note 127. + +[444] Edmund Curll (1675-1747), a well-known bookseller, publisher, and +pamphleteer. He was for a time at "The Peacock without Temple Bar," and +later at "The Dial and Bible against St. Dunstan's Church." He was fined +repeatedly for publishing immoral works, and once stood in the pillory for +it. He is ridiculed in the _Dunciad_ for having been tossed in a blanket by +the boys of Westminster School because of an oration that displeased them. + +[445] See Vol. II, page 109, note 206. + +[446] Encyclopaedia. + +[447] Author of the _Historia Naturalis_ (77 A.D.) + +[448] Author of the _De Institutione Oratorio Libri_ XII (c. 91 A.D.) + +[449] His _De Architectures Libri_ X was not merely a work on architecture +and building, but on the education of the architect. + +[450] Cyclophoria. + +[451] William Caxton (c. 1422-c.1492), sometime Governor of the Company of +Merchant Adventurers in Bruges (between 1449 and 1470). He learned the art +of printing either at Bruges or Cologne, and between 1471 and 1477 set up a +press at Westminster. Tradition says that the first book printed in England +was his _Game and Playe of Chesse_ (1474). The _Myrrour of the Worlde and +th'ymage of the same_ appeared in 1480. It contains a brief statement on +arithmetic, the first mathematics to appear in print in England. + +[452] See Vol. I, page 45, note 6 {40}. De Morgan is wrong as to the date +of the _Margarita Philosophica_. The first edition appeared at Freiburg in +1503. + +[453] Reisch was confessor to Maximilian I (1459-1519), King of the Romans +(1486) and Emperor (1493-1519). + +[454] Joachim Sterck Ringelbergh (c. 1499-c. 1536), teacher of philosophy +and mathematics in various cities of France and Germany. His _Institutionum +astronomicarum libri III_ appeared at Basel in 1528, his _Cosmographia_ at +Paris in 1529, and his _Opera_ at Leyden in 1531. + +[455] Johannes Heinrich Alsted (1588-1638) was professor of philosophy and +theology at his birthplace, Herborn, in Nassau, and later at Weissenberg. +He published several works, including the _Elementale mathematicum_ (1611), +_Systema physicae harmonicae_ (1612), _Methodus admirandorum +mathematicorum_ (1613), _Encyclopaedia septem tomis distincta_ (1630), and +the work mentioned above. + +[456] Johann Jakob Hoffmann (1635-1706), professor of Greek and history at +his birthplace, Basel. He also wrote the _Epitome metrica historiae +universalis civilis et sacrae ab orbe condito_ (1686). + +[457] Ephraim Chambers (c. 1680-1740), a crotchety, penurious, but +kind-hearted freethinker. His _Cyclopaedia, or an Universal Dictionary_ was +translated into French and is said to have suggested the great +_Encyclopedie_. + +[458] _Encyclopedie, ou Dictionnaire raisonne des sciences, des arts et des +metiers, par un societe de gens de lettres. Mis en ordre et publie par M. +Diderot, et quant a la partie mathematique, par M. d'Alembert._ Paris, +1751-1780, 35 volumes. + +[459] "From the egg" (state). + +[460] See Vol. I, page 382, note 12 {785}. + +[461] See Vol. II, page 4, note 15. + +[462] "In morals nothing should serve man as a model but God; in the arts, +nothing but nature." + +[463] _Encyclopedie Methodique, ou par ordre de matieres._ Paris, +1782-1832, 166-1/2 volumes. + +[464] See Vol. II, page 193, note 336. + +[465] _Encyclopaedia Metropolitana; or, Universal Dictionary of Knowledge._ +London, 1845, 29 volumes. A second edition came out in 1848-1858 in 40 +volumes. + +[466] See Vol. I, page 137, note 8 {286}. + +[467] See Vol. I, page 80, note 5 {119}. + +[468] De Morgan should be alive to satirize some of the statements on the +history of mathematics in the eleventh edition. + +[469] John Pringle Nichol (1804-1859), Regius professor of astronomy at +Glasgow and a popular lecturer on the subject. He lectured in the United +States in 1848-1849. His _Views of the Architecture of the Heavens_ (1838) +was a very popular work, and his _Planetary System_ (1848, 1850) contains +the first suggestion for the study of sun spots by the aid of photography. + +[470] See Vol. II, page 109, note 206. + +[471] George Long (1800-1879), a native of Poulton, in Lancashire, was +called to the University of Virginia when he was only twenty-four years old +as professor of ancient languages. He returned to England in 1828 to become +professor of Greek at London University. From 1833 to 1849 he edited the +twenty-nine volumes of the _Penny Cyclopaedia_. He was an authority on Roman +law. + +[472] A legal phrase, "Qui tam pro domina regina, quam pro se ipso +sequitur,"--"Who sues as much on the Queen's account as on his own." + +[473] Arthur Cayley (1821-1895) was a fellow of Trinity College, Cambridge +(1842-1846) and was afterwards a lawyer (1849-1863). During his fourteen +years at the bar he published some two hundred mathematical papers. In 1863 +he became professor of mathematics at Cambridge, and so remained until his +death. His collected papers, nine hundred in number, were published by the +Cambridge Press in 13 volumes (1889-1898). He contributed extensively to +the theory of invariants and covariants. De Morgan's reference to his +coining of new names is justified, although his contemporary, Professor +Sylvester, so far surpassed him in this respect as to have been dubbed "the +mathematical Adam." + +[474] See Vol. II, page 26, note 56. + +[475] See Vol. I, page 111, note 3 {207}. + +[476] See Vol. I, page 87, note 6 {135}. + +[477] Pierre Dupuy (1582-1651) was a friend and relative of De Thou. With +the collaboration of his brother and Nicolas Rigault he published the 1620 +and 1626 editions of De Thou's History. He also wrote on law and history. +His younger brother, Jacques (died in 1656), edited his works. The two had +a valuable collection of books and manuscripts which they bequeathed to the +Royal Library at Paris. + +[478] See Vol. I, page 51, note 3 {51}. + +[479] It was Cosmo de' Medici (1590-1621) who was the patron of Galileo. + +[480] See Vol. I, page 40, note 4 {20}. + +[481] See Vol. I, page 106, note 4 {188}. + +[482] Sir Edward Sherburne (1618-1702), a scholar of considerable +reputation. The reference by De Morgan is to _The Sphere of Marcus +Manilius_, in the appendix to which is a _Catalogue of Astronomers, ancient +and modern_. + +[483] George Parker, second Earl of Macclesfield (1697-1764). He erected an +observatory at Shirburn Castle, Oxfordshire, in 1739, and fitted it out +with the best equipment then available. He was President of the Royal +Society in 1752. + +[484] See Vol. II, page 148, note 263. + +[485] See Vol. I, page 140, note 7 {296}. + +[486] See Vol. I, page 106, note 4 {188}. + +[487] Edward Bernard (1638-1696), although Savilian professor of astronomy +at Oxford, was chiefly interested in archeology. + +[488] See Vol. I, page 107, note 1 {190}. + +[489] See Vol. I, page 107, note 1 {190}. + +[490] See Vol. I, page 135, note 3 {281}. + +[491] Philip Dormer Stanhope, fourth Earl of Chesterfield (1694-1773), well +known for the letters written to his son which were published posthumously +(1774). + +[492] Peter Daval (died in 1763), Vice-President of the Royal Society, and +an astronomer of some ability. + +[493] See Vol. I, page 376, note 1 {766}. + +[494] William Oughtred (c. 1573-1660), a fellow of King's College, +Cambridge, and afterwards vicar of Aldbury, Surrey, wrote the best-known +arithmetic and trigonometry of his time. His _Arithmeticae in Numero & +Speciebus Institutio ... quasi Clavis Mathematicae est_ (1631) went through +many editions and appeared in English as _The Key to the Mathematicks new +forged and filed_ in 1647. + +[495] See Vol. I, page 140, note 5 {294}. + +[496] Stephen Jordan Rigaud (1816-1859) was senior assistant master of +Westminster School (1846) and head master of Queen Elizabeth's School at +Ipswich (1850). He was made Bishop of Antigua in 1858 and died of yellow +fever the following year. + +[497] He also wrote a memoir of his father, privately printed at Oxford in +1883. + +[498] See Vol. I, page 69, note 3 {96}. + +[499] See Vol. I, page 106, note 4 {188}. + +[500] William Gascoigne was born at Middleton before 1612 and was killed in +the battle of Marston Moor in 1644. He was an astronomer and invented the +micrometer with movable threads (before 1639). + +[501] Seth Ward (1617-1689) was deprived of his fellowship at Cambridge for +refusing to sign the covenant. He became professor of astronomy at Oxford +(1649), Bishop of Exeter (1662), Bishop of Salisbury (1667), and Chancellor +of the Garter (1671). He is best known for his solution of Kepler's problem +to approximate a planet's orbit, which appeared in his _Astronomia +geometrica_ in 1656. + +[502] See Vol. I, page 110, note 2 {198}. + +[503] See Vol. I, page 100, note 2 {172}. + +[504] See Vol. I, page 107, note 1 {190}. + +[505] See Vol. I page 114, note 6 {220}. + +[506] See Vol. I, page 77, note 4 {118}. + +[507] See Vol. I, page 125, note 3 {253}. + +[508] See Vol. I, page 105, note 2 {186}. + +[509] Heinrich Oldenburgh (1626-1678) was consul in England for the City +of Bremen, his birthplace, and afterwards became a private teacher in +London. He became secretary of the Royal Society and contributed on +physics and astronomy to the _Philosophical Transactions_. + +[510] Thomas Brancker, or Branker (1636-1676) wrote the _Doctrinae +sphaericae adumbratio et usus globorum artificialium_ (1662) and +translated the algebra of Rhonius with the help of Pell. The latter work +appeared under the title of _An Introduction to Algebra_ (1668), and +is noteworthy as having brought before English mathematicians the +symbol / for division. The symbol never had any standing on the +Continent for this purpose, but thereafter became so popular in England +that it is still used in all the English-speaking world. + +[511] See Vol. I, page 118, note 1 {230}. + +[512] Pierre Bertius (1565-1629) was a native of Flanders and was educated +at London and Leyden. He became a professor at Leyden, and later held the +chair of mathematics at the College de France. He wrote chiefly on +geography. + +[513] See Vol. II, page 297, note 487. + +[514] Giovanni Alphonso Borelli (1608-1679) was professor of mathematics at +Messina (1646-1656) and at Pisa (1656-1657), after which he taught in Rome +at the Convent of St. Panteleon. He wrote several works on geometry, +astronomy, and physics. + +[515] See Vol. I, page 172, note 2 {381}. + +[516] Ignace Gaston Pardies (c. 1636-1673), a Jesuit, professor of ancient +languages and later of mathematics and physics at the College of Pau, and +afterwards professor of rhetoric at the College Louis-le-Grand at Paris. He +wrote on geometry, astronomy and physics. + +[517] Pierre Fermat was born in 1608 (or possibly in 1595) near Toulouse, +and died in 1665. Although connected with the parliament of Toulouse, his +significant work was in mathematics. He was one of the world's geniuses in +the theory of numbers, and was one of the founders of the theory of +probabilities and of analytic geometry. After his death his son published +his edition of Diophantus (1670) and his _Varia opera mathematica_ (1679). + +[518] This may be Christopher Townley (1603-1674) the antiquary, or his +nephew, Richard, who improved the micrometer already invented by Gascoigne. + +[519] Adrien Auzout a native of Rouen, who died at Rome in 1691. He +invented a screw micrometer with movable threads (1666) and made many +improvements in astronomical instruments. + +[520] See Vol. I, page 66, note 9 {86}. + +[521] See Vol. I, page 124, note 7 {248}. + +[522] John Machin (d. 1751) was professor of astronomy at Gresham College +(1713-1751) and secretary of the Royal Society. He translated Newton's +_Principia_ into English. His computation of [pi] to 100 places is given in +William Jones's _Synopsis palmariorum matheseos_ (1706). + +[523] Pierre Remond de Montmort (1678-1719) was canon of Notre Dame until +his marriage. He was a gentleman of leisure and devoted himself to the +study of mathematics, especially of probabilities. + +[524] Roger Cotes (1682-1716), first Plumian professor of astronomy and +physics at Cambridge, and editor of the second edition of Newton's +_Principia_. His posthumous _Harmonia Mensurarum_ (1722) contains "Cotes's +Theorem" on the binomial equation. Newton said of him, "If Mr. Cotes had +lived we had known something." + +[525] See Vol. I, page 135, note 3 {281}. + +[526] See Vol. I, page 377, note 4 {769}. + +[527] Charles Rene Reyneau (1656-1728) was professor of mathematics at +Angers. His _Analyse demontree, ou Maniere de resoudre les problemes de +mathematiques_ (1708) was a successful attempt to popularize the theories +of men like Descartes, Newton, Leibnitz, and the Bernoullis. + +[528] Brook Taylor (1685-1731), secretary of the Royal Society, and student +of mathematics and physics. His _Methodus incrementorum directa et inversa_ +(1715) was the first treatise on the calculus of finite differences. It +contained the well-known theorem that bears his name. + +[529] Pierre Louis Moreau de Maupertuis (1698-1759) was sent with Clairaut +(1735) to measure an arc of a meridian in Lapland. He was head of the +physics department in the Berlin Academy from 1745 until 1753. He wrote +_Sur la figure de la terre_ (1738) and on geography and astronomy. + +[530] Pierre Bouguer (1698-1758) was professor of hydrography at Paris, and +was one of those sent by the Academy of Sciences to measure an arc of a +meridian in Peru (1735). The object of this and the work of Maupertuis was +to determine the shape of the earth and see if Newton's theory was +supported. + +[531] Charles Marie de la Condamine (1701-1774) was a member of the Paris +Academy of Sciences and was sent with Bouguer to Peru, for the purpose +mentioned in the preceding note. He wrote on the figure of the earth, but +was not a scientist of high rank. + +[532] See Vol. I, page 136, note 5 {283}. + +[533] See Vol. II, page 296, note 483. + +[534] Thomas Baker (c. 1625-1689) gave a geometric solution of the +biquadratic in his _Geometrical Key, or Gate of Equations unlocked_ (1684). + +[535] See Vol. I, page 160, note 5 {350}. + +[536] See Vol. I, page 87, note 4 {133}. + +[537] See Vol. I, page 132, note 2 {272}. + +[538] See Vol. I, page 118, second note 1 {231}. + +[539] The name of Newton is so well known that no note seems necessary. He +was born at Woolsthorpe, Lincolnshire, in 1642, and died at Kensington in +1727. + +[540] John Keill (1671-1721), professor of astronomy at Oxford from 1710, +is said to have been the first to teach the Newtonian physics by direct +experiment, the apparatus being invented by him for the purpose. He wrote +on astronomy and physics. His _Epistola de legibus virium centripetarum_, +in the Philosophical Transactions for 1708, accused Leibnitz of having +obtained his ideas of the calculus from Newton, thus starting the priority +controversy. + +[541] Thomas Digges (d. in 1595) wrote _An Arithmeticall Militare Treatise, +named Stratioticos_ (1579), and completed _A geometrical practise, named +Pantometria_ (1571) that had been begun by his father, Leonard Digges. + +[542] John Dee (1527-1608), the most famous astrologer of his day, and +something of a mathematician, wrote a preface to Billingsley's translation +of Euclid into English (1570). + +[543] See Vol. I, page 76, note 3 {112}. + +[544] Thomas Harriot (1560-1621) was tutor in mathematics to Sir Walter +Raleigh, who sent him to survey Virginia (1585). He was one of the best +English algebraists of his time, but his _Artis Analyticae Praxis ad +Aequationes Algebraicas resolvendas_ (1631) did not appear until ten years +after his death. + +[545] Thomas Lydiat (1572-1626), rector of Alkerton, devoted his life +chiefly to the study of chronology, writing upon the subject and taking +issue with Scaliger (1601). + +[546] See Vol. I, page 69, note 3 {96}. + +[547] Walter Warner edited Harriot's _Artis Analyticae Praxis_ (1631). +Tarporley is not known in mathematics. + +[548] See Vol. I, page 105, note 2 {186}. + +[549] See Vol. I, page 115, note 3 {224}. + +[550] See Vol. II, page 300, note 509. + +[551] See Vol. I, page 107, note 1 {190}. + +[552] Sir Samuel Morland (1625-1695) was a diplomat and inventor. For some +years he was assistant to John Pell, then ambassador to Switzerland. He +wrote on arithmetical instruments invented by him (1673), on hydrostatics +(1697) and on church history (1658). + +[553] See Vol. I, page 153, note 4 {337}. + +[554] See Vol. I, page 85, note 2 {129}. + +[555] See Vol. I, page 43, note 8 {33}. + +[556] See Vol. I, page 43, note 7 {32}. + +[557] See Vol. I, page 382, note 13 {786}. The history of the subject may +be followed in Braunmuehl's _Geschichte der Trigonometrie_. + +[558] See Vol. I, page 377, note 3 {768}. + +[559] See Vol. I, page 108, note 2 {192}. + +[560] Michael Dary wrote _Dary's Miscellanies_ (1669), _Gauging epitomised_ +(1669), and _The general Doctrine of Equation_ (1664). + +[561] John Newton (1622-1678), canon of Hereford (1673), educational +reformer, and writer on elementary mathematics and astronomy. + +[562] See Vol. I, page 87, note 4 {133}. + +[563] "The average of the two equal altitudes of the sun before and after +dinner." + +[564] See Vol. I, page 42, note 4 {24}. + +[565] London, 1678. It went though many editions. + +[566] "This I who once ..." + +[567] Arthur Murphy (1727-1805) worked in a banking house until 1754. He +then went on the stage and met with some success at Covent Garden. His +first comedy, _The Apprentice_ (1756) was so successful that he left the +stage and took to play writing. His translation of Tacitus appeared in +1793, in four volumes. + +[568] Edmund Wingate (1596-1656) went to Paris in 1624 as tutor to Princess +Henrietta Maria and remained there several years. He wrote _L'usage de la +regle de proportion_ (Paris, 1624, with an English translation in 1626), +_Arithmetique Logarithmetique_ (Paris, 1626, with an English translation in +1635), and _Of Natural and Artificial Arithmetick_ (London, 1630, revised +in 1650-1652), part I of which was one of the most popular textbooks ever +produced in England. + +[569] John Lambert (1619-1694) was Major-General during the Revolution and +helped to draw up the request for Cromwell to assume the protectorate. He +was imprisoned in the Tower by the Rump Parliament. He was confined in +Guernsey until the clandestine marriage of his daughter Mary to Charles +Hatton, son of the governor, after which he was removed (1667) to St. +Nicholas in Plymouth Sound. + +[570] Samuel Foster (d. in 1652) was made professor of astronomy at Gresham +College in March, 1636, but resigned in November of that year, being +succeeded by Mungo Murray. Murray vacated his chair by marriage in 1641 and +Foster succeeded him. He wrote on dialling and made a number of +improvements in geometric instruments. + +[571] "Twice of the word a minister," that is, twice a minister of the +Gospel. + +[572] This is _The Lives of the Professors of Gresham College to which is +prefixed the Life of the Founder, Sir Thomas Gresham_, London, 1740. It was +written by John Ward (c. 1679-1758), professor of rhetoric (1720) at +Gresham College and vice-president (1752) of the Royal Society. + +[573] Charles Montagu (1661-1715), first Earl of Halifax, was Lord of the +Treasury in 1692, and was created Baron Halifax in 1700 and Viscount +Sunbury and Earl of Halifax in 1714. He introduced the bill establishing +the Bank of England, the bill becoming a law in 1694. He had troubles of +his own, without considering Newton, for he was impeached in 1701, and was +the subject of a damaging resolution of censure as auditor of the exchequer +in 1703. Although nothing came of either of these attacks, he was out of +office during much of Queen Anne's reign. + +[574] See Vol. II, page 302, note 547. + +[575] See Vol. I, page 105, note 2 {186}. + +[576] James Dodson (d. 1757) was master of the Royal Mathematical School, +Christ's Hospital. He was De Morgan's great-grandfather. The +_Anti-Logarithmic Canon_ was published in 1742. + +[577] See Vol. I, page 106, note 4 {188}. + +[578] See Vol. I, page 110, note 2 {198}. + +[579] Richard Busby, (1606-1695), master of Westminster School (1640) had +among his pupils Dryden and Locke. + +[580] See Vol. I, page 107, note 1 {190}. + +[581] Herbert Thorndike (1598-1672), fellow of Trinity College, Cambridge +(1620-1646), and Prebend of Westminster (1661), was a well-known +theological writer of the time. + +[582] See Vol. I, page 140, note 5 {294}. + +[583] See Vol. I, page 108, note 2 {192}. + +[584] "Labor performed returns in a circle." + +[585] See Vol. II, page 208. + +[586] "Whatever objections one may make to the above arguments, one always +falls into an absurdity." + +[587] See Vol. II. page 11, note 29. _The Circle Squared; and the solution +of the problem adapted to explain the difference between square and +superficial measurement_ appeared at Brighton in 1865. + +[588] "And beyond that nothing." + +[589] Gillott (1759-1873) was the pioneer maker of steel pens by machinery, +reducing the price from 1s. each to 4d. a gross. He was a great collector +of paintings and old violins. + +[590] William Edward Walker wrote five works on circle squaring (1853, +1854, 1857, 1862, 1864), mostly and perhaps all published at Birmingham. + +[591] Solomon M. Drach wrote _An easy Rule for formulizing all Epicyclical +Curves_ (London, 1849), _On the Circle area and Heptagon-chord_ (London, +1864), _An easy general Rule for filling up all Magic Squares_ (London, +1873), and _Hebrew Almanack-Signs_ (London, 1877), besides numerous +articles in journals. + +[592] See Vol. I, page 168, note 3 {371}. + +[593] See Vol. I, page 254, note 2 {580}. + +[594] See Vol. I, page 98, note 6 {163}. + +[595] Robert Fludd or Flud (1574-1637) was a physician with a large London +practice. He denied the diurnal rotation of the earth, and was attacked by +Kepler and Mersenne, and accused of magic by Gassendi. His _Apologia +Compendiania, Fraternitatem de Rosea Cruce suspicionis ... maculis +aspersam, veritatis quasi Fluctibus abluens_ (Leyden, 1616) is one of a +large number of works of the mystic type. + +[596] Consult _To the Christianity of the Age. Notes ... comprising an +elucidation of the scope and contents of the writings ... of Dionysius +Andreas Freher_ (1854). + +[597] Sir William Robert Grove (1811-1896), although called to the bar +(1835) and to the bench (1853), is best known for his work as a physicist. +He was professor of experimental philosophy (1840-1847) at the London +Institution, and invented a battery (1839) known by his name. His +_Correlation of Physical Forces_ (1846) went through six editions and was +translated into French. + +[598] Johann Tauler (c. 1300-1361), a Dominican monk of Strassburg, a +mystic, closely in touch with the Gottesfreunde of Basel. His _Sermons_ +first appeared in print at Leipsic in 1498. + +[599] Paracelsus (c. 1490-1541). His real name was Theophrastes Bombast von +Hohenheim, and he took the name by which he is generally known because he +held himself superior to Celsus. He was a famous physician and pharmacist, +but was also a mystic and neo-Platonist. He lectured in German on medicine +at Basel, but lost his position through the opposition of the orthodox +physicians and apothecaries. + +[600] See Vol. I, page 256, note 2 {588}. + +[601] Philip Schwarzerd (1497-1560) was professor of Greek at Wittenberg. +He helped Luther with his translation of the Bible. + +[602] Johann Reuchlin (1455-1522), the first great German humanist, was +very influential in establishing the study of Greek and Hebrew in Germany. +His lectures were mostly delivered privately in Heidelberg and Stuttgart. +Unlike Melanchthon, he remained in the Catholic Church. + +[603] Joseph Chitty (1776-1841) published his _Precedents of Pleading_ in +1808 and his _Reports of Cases on Practice and Pleading_ in 1820-23 (2 +volumes). + +[604] See Vol. I, page 44, note 1 {35}. + +[605] See Vol. I, page 44, note 4 {38}. + +[606] Jean Pelerin, also known as Viator, who wrote on perspective. His +work appeared in 1505, with editions in 1509 and 1521. + +[607] Henry Stephens. See Vol. I, page 44, note 3 {37}. + +[608] The well-known grammarian (1745-1826). He was born at Swatara, in +Pennsylvania, and practised law in New York until 1784, after which he +resided in England. His grammar (1795) went through 50 editions, and the +abridgment (1818) through 120 editions. Murray's friend Dalton, the +chemist, said that "of all the contrivances invented by human ingenuity for +puzzling the brains of the young, Lindley Murray's grammar was the worst." + +[609] Robert Recorde (c. 1510-1558) read and probably taught mathematics +and medicine at Cambridge up to 1545. After that he taught mathematics at +Oxford and practised medicine in London. His _Grounde of Artes_, published +about 1540, was the first arithmetic published in English that had any +influence. It went through many editions. The _Castle of Knowledge_ +appeared in 1551. It was a textbook on astronomy and the first to set forth +the Copernican theory in England. Like Recorde's other works it was written +on the catechism plan. His _Whetstone of Witte ... containying thextraction +of Rootes: The Cosike practise, with the rule of Equation: and the woorkes +of Surde Nombres_ appeared in 1557, and it is in this work that the modern +sign of equality first appears in print. The word "Cosike" is an adjective +that was used for a long time in Germany as equivalent to algebraic, being +derived from the Italian _cosa_, which stood for the unknown quantity. + +[610] Robert Cecil (c. 1563-1612), first Earl of Salisbury, Secretary of +State under Elizabeth (1596-1603) and under James I (1603-1612). + +[611] In America the German pronunciation is at present universal among +mathematicians, as in the case of most other German names. This is due, no +doubt, to the great influence that Germany has had on American education in +the last fifty years. + +[612] The latest transliteration is substantially K'ung-fu-tz[vu]. + +[613] The tendency seems to be, however, to adopt the forms used of +individuals or places as rapidly as the mass of people comes to be prepared +for it. Thus the spelling Leipzig, instead of Leipsic, is coming to be very +common in America. + +[614] Sir Edward Coke (1552-1634), the celebrated jurist. + +[615] Dethlef Cluvier or Cluever (d. 1708 at Hamburg) was a nephew, not a +grandson, of Philippe Cluvier, or Philipp Cluever (1580-c. 1623). Dethlef +traveled in France and Italy and then taught mathematics in London. He +wrote on astronomy and philosophy and also published in the _Acta +Eruditorum_ (1686) his _Schediasma geometricum de nova infinitorum +scientia_. _Quadratura circuli infinitis modis demonstrata_, and his +_Monitum ad geometras_ (1687). Philippe was geographer of the Academy of +Leyden. His _Introductionis in universam geographiam tam veterem quam novam +libri sex_ appeared at Leyden in 1624, about the time of his death. + +[616] See Vol. I, page 124, note 7 {248}. + +[617] Bernard Nieuwentijt (1654-1718), a physician and burgomaster at +Purmerend. His _Considerationes circa Analyseos ad quantitates infinite +parvas applicatae Principia et Calculi Differentialis usum_ (Amsterdam, +1694) was attacked by Leibnitz. He replied in his _Considerationes secundae_ +(1694), and also wrote the _Analysis Infinitorum, seu Curvilineorum +Proprietates ex Polygonorum Natura deductae_ (1695). His most famous work +was on the existence of God, _Het Regt Gebruik der Werelt Beschouwingen_ +(1718). + +[618] "From a given line to construct" etc. + +[619] "Pirates do not fight one another." + +[620] Claude Mallemens (Mallement) de Messanges (1653-1723) was professor +of philosophy at the College du Plessis, in Paris, for 34 years. The work +to which De Morgan refers is probably the _Fameux Probleme de la quadrature +du cercle, resolu geometriquement par le cercle et a ligne droite_ that +appeared in 1683. + +[621] On Tycho Brahe see Vol. I, page 76, note 3 {112}. + +[622] Wilhelm Frederik von Zytphen also published the _Tidens Stroem_, a +chronological table, in 1840. The work to which De Morgan refers, the +_Solens Bevaegelse i Verdensrummet_, appeared first in 1861. De Morgan seems +to have missed his _Nogl Ord om Cirkelens Quadratur_ which appeared in +1865, at Copenhagen. + +[623] James Joseph Sylvester (1814-1897), professor of natural philosophy +at University College, London (1837-1841), professor of mathematics at the +University of Virginia (1841-1845), actuary in London (1845-1855), +professor of mathematics at Woolwich (1877-1884) and at Johns Hopkins +University, Baltimore (1877-1884), and Savilian professor of geometry at +Oxford (1884-1894). + +[624] See Vol. I, page 76, note 3 {112}. + +[625] See Vol. II, page 205, note 349. + +[626] See Vol. I, page 76, note 3 {112}. + +[627] See Vol. I, page 46, note 1 {42}. + +[628] See Vol. II, page 183, note 318. + +[629] See Vol. I, page 321, note 2 {691}. + +[630] James Mill, born 1773, died 1836. + +[631] See Vol. II, page 3, note 11. + +[632] See Vol. II, page 3, note 13. + +[633] See Vol. II, page 3, note 14. + +[634] This anecdote is printed at page 4 (Vol. II); but as it is used in +illustration here, and is given more in detail, I have not omitted +it.--S.E. De M. + +[635] See Vol. II, page 4, note 15. + +[636] See Vol. I, page 382, note 13 {786}. + +[637] "Monsieur, (a + b^{n})/n = x, whence God exists; answer that!" + +[638] "Monsieur, you know very well that your argument requires the +development of x according to integral powers of n." + +[639] See Vol. I, page 153, note 4 {337}. + +[640] Thomas Love Peacock (1785-1866) an English novelist and poet. + +[641] Perhaps Dr. Samuel Warren (1807-1877), the author of _Ten Thousand a +Year_ (serially in Blackwood's in 1839; London, 1841). + +[642] See Vol. I, page 255, note 6 {584}. + +[643] "From many, one; much in little; Ultima Thule (the most remote +region); without which not." + +[644] Spurius Maelius (fl. 440 B. C.), who distributed corn freely among the +poor in the famine of 440 B. C. and was assassinated by the patricians. + +[645] Spurius Cassius Viscellinus, Roman consul in 502, 493, and 486 B. C. +Put to death in 485. + +[646] "O what a fine bearing, he said, that has no brain." + +[647] Sir William Rowan Hamilton. See Vol. I, page 332, note 4 {709}. + +[648] William Allen Whitworth, the author of the well-known _Choice and +Chance_ (Cambridge, 1867), and other works. + +[649] James Maurice Wilson, whose _Elementary Geometry_ appeared in 1868 +and went through several editions. + +[650] See Vol. II, page 183, note 315. + +[651] "Force of inertia conquered," and "Victory in the whole heavens." + +[652] "With all his might." + +[653] George Berkeley (1685-1753), Bishop of Cloyne, the idealistic +philosopher and author of the _Principles of Human Knowledge_ (1710), _The +Analyst, or a Discourse addressed to an Infidel Mathematician_ (1734), and +_A Defense of Freethinking in Mathematics_ (1735). He asserted that space +involves the idea of movement without the sensation of resistance. Space +sensation less than the "minima sensibilia" is, therefore, impossible. From +this he argues that infinitesimals are impossible concepts. + +[654] See Vol. I, page 85, note 2 {129}. + +[655] See Vol. I, page 81, note 6 {120}. + +[656] Edwin Dunkin revised Lardner's _Handbook of Astronomy_ (1869) and +Milner's _The Heavens and the Earth_ (1873) and wrote _The Midnight Sky_ +(1869). + +[657] Michael Faraday (1791-1867) the celebrated physicist and chemist. He +was an assistant to Sir Humphrey Davy (1813) and became professor of +chemistry at the Royal Institution, London, in 1827. + +[658] "If you teach a fool he shows no joyous countenance; he cordially +hates you; he wishes you buried." + +[659] "Every man is an animal, Sortes is a man, therefore Sortes is an +animal." + +[660] + + "May some choice patron bless each grey goose quill; + May every Bavius have his Bufo still."--POPE, _Prologue to the Satires._ + +Bavius has become proverbial as a bad poet from the lines in Vergil's +_Eclogues_ (III, 90): + + "Qui Bavium non odit, amet tua carmina, Maevi, + Atque idem jungat vulpes, et mulgeat hircos." + +"He who does not hate Bavius shall love thy verses, O Maevius; and the same +shall yoke foxes and shall milk he-goats." + +Bavius and Maevius were the worst of Latin poets, condemned by Horace as +well as Vergil. + +[661] See Vol. II, page 158, note 279. + +[662] "Honest," "useful," "handsome," "sweet." + +[663] "Let not the fourth man attempt to speak." + +[664] + + "In those old times,--ah + 'Twas just like this, ah!" + +[665] See Vol. I, page 382, note 12 {785}. + +[666] These remarks were never written.--S. E. De M. + +[667] + + "Fleas, flies, and friars, are masters who sadly the people abuse, + And thistles and briars are sure growing grains to abuse. + O Christ, who hatest strife and slayst all things in peace, + Destroy where'er are rife, briars, friars, flies and fleas. + Fleas, flies, and friars foul fall them these fifteen years + For none that there is loveth fleas, flies, nor freres." + +[668] "It is my plan to restore to an unskilled race the worthy arts of a +better life." + +[669] The first sentences of the first oration of Cicero against Catiline: +"Quo usque tandem abutere, Catilina, patientia nostra?" (How long, O +Catiline, will you abuse our patience?) "Quamdiu etiam furor iste tuus nos +eludet?" (How long will this your madness baffle us?) "Nihilne te nocturnum +praesidium Palati, ... nihil horum ora voltusque moverunt?" (Does the night +watch of the Palatium, ... do the faces and expressions of all these men +fail to move you?) "In te conferri ..." (This plague should have been +inflicted upon you long ago, which you have plotted against us so long.) + +[670] "Beware of the things that are marked." + +[671] "Farewell, ye teachers without learning! See to it that at our next +meeting we may find you strong in body and sound in mind." + +[672] See Vol. I, page 336, note 8 {713}. + +[673] See Vol. I, page 229, note 2 {515}. + +[674] This proof, although capable of improvement, is left as in the +original. Those who may be interested in the mathematics of the question, +may consult F. Enriques, _Fragen der Elementargeometrie_ (German by +Fleischer), Leipsic, 1907, Part II, p. 267; F. Rudio, _Archimedes_, +_Huygens_, _Lambert_, _Legendre_. _Vier Abhandlungen ueber die +Kreismessung_, Leipsic, 1892; F. Klein, _Famous Problems of Elementary +Geometry_ (English by Beman and Smith), Boston, 1895; J. W. A. Young, +_Monographs on Modern Mathematics_, New York, 1911, Chap. IX (by the editor +of the present edition of De Morgan.) + +[675] See Vol. I, page 69, note 2 {95}. + +[676] See Vol. I, page 137, note 8 {286}. + +[677] Joseph Allen Galbraith who, with Samuel Haughton, wrote the Galbraith +and Haughton's _Scientific Manuals_. (Euclid, 1856; Algebra, 1860; +Trigonometry, 1854; Optics, 1854, and others.) + +[678] This note on Carlyle (1795-1881) is interesting. The translation of +Legendre appeared in the same year (1824) as his translation of Goethe's +_Wilhelm Meister_. + +[679] Michael Stifel (1487-1567), also known as Stiefel, Styfel, and +Stifelius, was an Augustine monk but became a convert to Lutheranism. He +was professor of mathematics at Jena (1559-1567). His edition of the _Coss_ +appeared at Koenigsberg in 1553, the first edition having been published in +1525. The + and - signs first appeared in print in Widman's arithmetic of +1489, but for purposes of algebra this book was one of the first to make +them known. + +[680] Christoff Rudolff was born about 1500 and died between 1540 and 1552. +_Die Coss_ appeared in 1525 and his arithmetic in 1526. + + * * * * * + + +Corrections made to printed original. + +Page 9, "long-fostered prejudice": 'perjudice' in original. + +Page 73, "Pensees, ch. 7": 'Pansees' in original. + +Page 127, "and pulled out a plum": 'und' in original. + +Page 147, "did not come forward": 'forword' in original. + +Page 172, "come into general circulation": 'circulalation' in original. + +Ibid., "the more difficult fractions which we have got": 'he have got' in +original. + +Page 192, "it has been stated": 'started' in original. + +Page 216, "the obsolete word tetch of the same meaning": 'meaing' in +original. + +Page 228, "[Greek: dioklasianos]": 'dioklalasianos' in original. + +Page 233. After `Henry E. Manning' were printed two paragraphs `Shilling +versus Franc.' and `Teutonic Long Hundred 120 versus 100 or the Decimal +question.' These appear to have been set in error, there is no applicable +context. + +Page 316, "in a manner depending upon the difference": 'maner' in original. + +Page 322, "neither what Newton did, nor what was done before him.": 'not' +(for 'nor') in original. + +Page 344, "Victoria toto coelo": 'tolo' in original. + +Page 368, "cannot be brought up to 1": 'up to +-' in original. + +Page 371, "Q_2=b_2 Q_1+a_2": 'Q_2=b_2 Q_1-a_2' in original. + +Note 50, "all who were not in the road to Heaven were excommunicated": +'excomunicated' in original. + +Note 372, "[Greek: he alazoneia biou]": 'alaxoneia' in original. + +Ibid., "Iapetos": 'Ispetos' in original. + +Ibid., "Papeiskos": 'Paspeisoks' in original. + +Ibid., "[Greek: dioklasianos]": 'dioklalasianos' in original. + + + +***END OF THE PROJECT GUTENBERG EBOOK A BUDGET OF PARADOXES, VOLUME II (OF +II)*** + + +******* This file should be named 26408.txt or 26408.zip ******* + + +This and all associated files of various formats will be found in: +http://www.gutenberg.org/dirs/2/6/4/0/26408 + + + +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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