GIFT OF 
 MICHAEL REESE 
 
BUDGET OF PAEADOXES. 
 
LONDON : PRINTED BT 
 
 6POTTISWOODE AND CO., NEW-STREET SQUARE 
 AND PARLIAMENT STREET 
 
BUDGET OF PARADOXES. 
 
 BY 
 
 AUGUSTUS DE MOKGAN, 
 
 F.E.A.S. & C.P.S. 
 
 OF TRINITY COLLEGE, CAMBRIDGE, 
 
 {REPRINTED, WITH THE AUTHOR'S ADDITIONS, FROM THE ' 
 
 * Ut agendo snrgamus arguendo gustamua.' 
 
 PTOCHODOKIARCHUS AN AG R AMM ATISTES. 
 
 LONDON : 
 
 LONGMANS, GEEEN, AND CO. 
 1872. 
 
 All rights reserved. 
 
EDITOR'S PREFACE. 
 
 IT is not without hesitation that I have taken upon myself 
 the editorship of a work left avowedly imperfect by the 
 author, and, from its miscellaneous and discursive character, 
 difficult of completion with due regard to editorial limita- 
 tions by a less able hand. 
 
 Had the author lived to carry out his purpose he would 
 have looked through his Budget again, amplifying and 
 probably rearranging some of its contents. He had collected 
 materials for further illustration of Paradox of the kind 
 treated of in this book ; and he meant to write a second 
 part, in which the contradictions and inconsistencies of 
 orthodox learning would have been subjected to the same 
 scrutiny arid castigation as heterodox ignorance had already 
 received. 
 
 It will be seen that the present volume contains more 
 than the Atlienceum Budget. Some of the additions formed 
 a Supplement to the original articles. These supplementary 
 paragraphs were, by the author, placed after those to which 
 they respectively referred, being distinguished from the rest 
 of the text by brackets. I have omitted these brackets as 
 useless, except where they were needed to indicate sub- 
 sequent writing. 
 
vi EDITOR'S PREFACE. 
 
 Another and a larger portion of the work consists of 
 discussion of matters of contemporary interest, for the 
 Budget was in some degree a receptacle for the author's 
 thoughts on any literary, scientific, or social question. 
 Having grown thus gradually to its present size, the book 
 as it was left was not quite in a fit condition for publication, 
 but the alterations which have been made are slight and 
 few, being in most cases verbal and such as the sense 
 absolutely required, or transpositions of sentences to secure 
 coherence with the rest, in places where the author, in his 
 more recent insertion of them, had overlooked the connexion 
 in which they stood. In no case has the meaning been in 
 any degree modified or interfered with. 
 
 One rather large omission must be mentioned here. It 
 is an account of the quarrel between Sir James South and 
 Mr. Troughton on the mounting, &c. of the equatorial 
 telescope at Campden Hill. At some future time when the 
 affair has passed entirely out of the memory of living 
 Astronomers, the appreciative sketch, which is omitted in 
 this edition of the Budget, will be an interesting piece of 
 history and study of character. 
 
 A very small portion of Mr. James Smith's circle-squaring 
 has been left out, with a still smaller portion of Mr. De 
 Morgan's answers to that Gyclometrical Paradoxer. 
 
 In more than one place repetitions, which would have 
 disappeared under the author's revision, have been allowed 
 to remain, because they could not have been taken away 
 without leaving a hiatus, not easy to fill up without damage 
 to the author's meaning. 
 
EDITOR'S PREFACE. vii 
 
 I give these explanations in obedience to the rules laid 
 down for the guidance of editors at page 11. If any apology 
 for the fragmentary character of the book be thought 
 necessary, it may be found in the author's own words 
 at page 438. 
 
 The publication of the Budget could not have been 
 delayed without lessening the interest attaching to the 
 writer's thoughts upon questions of our own day. I trust 
 that, incomplete as the work is compared with what it 
 might have been, I shall not be held mistaken in giving it 
 to the world. Bather let me hope that it will be welcomed 
 as an old friend returning under great disadvantages, but 
 bringing a pleasant remembrance of the amusement which 
 its weekly appearance in the Athenaeum gave to both writer 
 and reader. 
 
 The Paradoxes are dealt with in chronological order. 
 This will be a guide to the reader, and with the alphabetical 
 Index of Names, &c., will, I trust, obviate all difficulty of 
 reference. 
 
 SOPHIA DE MORGAN. 
 
 6 MERTON ROAD, PRIMROSE HILL. 
 
Erratum. 
 
 Page 40, line 27, for Litchfield read Lichfield. 
 
p5j,f2?^ 
 
 ' -aiHVERSITY 
 
 Jpf PA| IP 
 
 A BUDGET 
 
 OF 
 
 PARADOXES 
 
 INTRODUCTORY. 
 
 IF I had before me a fly and an elephant, having rever seen 
 more than one such magnitude of either kind ; and if the fly 
 were to endeavour to persuade me that he was larger than the 
 elephant, I might by possibility be placed in a difficulty. The 
 apparently little creature might use such arguments about the 
 effect of distance, and might appeal to such laws of sight and 
 hearing as I, if unlearned in those things, might be unable 
 wholly to reject. But if there were a thousand flies, all buzzing, 
 to appearance, about the great creature ; and, to a fly, declaring, 
 each one for himself, that he was bigger than the quadruped ; 
 and all giving different and frequently contradictory reasons ; and 
 each one despising and opposing the reasons of the others I 
 should feel quite at my ease. I should certainly say. My little 
 friends, the case of each one of you is destroyed by the rest. I 
 intend to show flies in the swarm, with a few larger animals, for 
 reasons to be given. 
 
 In every age of the world there has been an established system, 
 which has been opposed from time to time by isolated and dis- 
 sentient reformers. The established system has sometimes fallen, 
 slowly and gradually : it has either been upset by the rising in- 
 fluence of some one man, or it has been sapped by gradual change 
 of opinion in the many. 
 
 I have insisted on the isolated character of the .dissentients, as 
 an element of the a priori probabilities of the case. Show me a 
 schism, especially a growing schism, and it is another thing. The 
 homoeopathists, for instance, shall > be, if any one so thinlf, a|$ 
 
A BUDGET OF PARADOXES. 
 
 wrong as St. John Long ; but an organised opposition, supported 
 by the efforts of many acting in concert, appealing to common 
 arguments and experience, with perpetual succession and a com- 
 mon seal, as the Queen says in the charter, is, be the merit of the 
 schism what it may, a thing wholly different from the case of the 
 isolated opponent in the mode of opposition to it which reason 
 points out. 
 
 During the last two centuries and a half, physical knowledge 
 has been gradually made to rest upon a basis which it had not 
 before. It has become mathematical. The question now is, not 
 whether this or that hypothesis is better or worse to the pure 
 thought, but whether it accords with observed phenomena in 
 those consequences which can be shown necessarily to follow from 
 it, if it be true. Even in those sciences which are not yet under 
 the dominion of mathematics, and perhaps never will be, a 
 working copy of the mathematical process has been made. This 
 is not known to the followers of those sciences who are not them- 
 selves mathematicians, and who very often exalt their horns against 
 the mathematics in consequence. They might as well be squaring 
 the circle, for any sense they show in this particular. 
 
 A great many individuals, ever since the rise of the mathematical 
 method, have, each for himself, attacked its direct and indirect 
 consequences. I shall not here stop to point out how the very 
 accuracy of exact science gives better aim than the preceding 
 state of things could give. I shall call each of these persons a 
 ' paradoxer, and his system a paradox. I use the word in the old 
 sense : a paradox is something which is apart from general 
 opinion, either in subject-matter, method, or conclusion. 
 
 Many of the things brought forward would now be called 
 crotchets, which is the nearest- word we have to old paradox. But 
 there is this difference, that by calling a thing a crotchet we mean 
 to speak lightly of it ; which was not the necessary sense of para- 
 dox. Thus in the sixteenth century many spoke of the earth's 
 motion as the paradox of Copernicus, who held the ingenuity of 
 that theory in very high esteem, and some, I think, who even in- 
 clined towards it. In the seventeenth century, the depravation 
 of meaning took place, in England at least. Phillips says paradox 
 is ' a thing which seemeth strange ' here is the old meaning : 
 after a colon, he proceeds ' and absurd, and is contrary to common 
 opinion,' which is an addition due to his own time. 
 
 Some of my readers are hardly inclined to think that the word 
 paradox could once have had no disparagement in its meaning ; 
 still less that persons could have applied it to themselves. I 
 
INTRODUCTORY. 3 
 
 chance to have met with a case in point against them. It is 
 Spinoza's 'Philosophia Scripturse Interpres, Exercitatio Paradoxa,' 
 printed anonymously at Eleutheropolis, in 1666. This place 
 was one of several cities in the clouds, to which the cuckoos re- 
 sorted who were driven away by the other birds ; that is, a feigned 
 place of printing, adopted by those who would have caught it if 
 orthodoxy could have caught them. Thus, in 1656, the works of 
 Socinus could only be printed at Irenopolis. The author deserves 
 his self-imposed title, as in the following : 
 
 Quanto sane satius fuisset illam [Trinitatem] pro mysterio non 
 habuisse, et Philosophise ope, antequam quod essefc statuerent, secun- 
 dum verse logices praecepta quid esset cum 01. Keckermanno inves- 
 tigasse ; tanto fervore ac labore in profundissimas speluncas et 
 obscurissimos metaphysicarum speculationum atque fictionum recessus 
 se recipere ut ab adversariorum telis sententiam suam in tuto collo- 
 carent. Profecto magnus ille vir . . . dogma illud, quamvis apud 
 theologos eo nomine non multum gratiae iniverit, ita ex immotis 
 Philosophise fundamentis explicat ac demonstrat, ut paucis tantum 
 immutatis, atque additis, nihil amplius animus veritate sincere deditus 
 desiderare possit. 
 
 This is properly paradox, though also heterodox. It supposes, 
 contrary to all opinion, orthodox and heterodox, that philosophy 
 can, with slight changes, explain the Athanasian doctrine so as to 
 be at least compatible with orthodoxy. The author would stand 
 almost alone, if not quite ; and this is what he meant. I have 
 met with the counter-paradox. I have heard it maintained that 
 the doctrine as it stands, in all its mystery, is a priori more 
 likely than any other to have been Eevelation, if such a thing 
 were to be ; and that it might almost have been predicted. 
 
 After looking into books of paradoxes for more than thirty 
 years, and holding conversation with many persons who have 
 written them, and many who might have done so, there is one 
 point on which my mind, is fully made up. ) The manner in 
 which a paradoxer will show himself, as to sense or nonsense, will 
 not depend upon what he maintains, but upon whether he has or 
 has not made a sufficient knowledge of what has been done by 
 others, especially as to the mode of doing it, a preliminary to in- 
 venting knowledge for himself. That a little knowledge is a 
 dangerous thing is one of the most fallacious of proverbs. A 
 person of small knowledge is in danger of trying to make his 
 little do the work of more ; but a person without any is in more 
 danger of making his no knowledge do the work of someJ[ Take 
 the speculations on the tides as an instance. Persons with nothing 
 
4 A BUDGET OF PARADOXES. 
 
 but a little geometry have certainly exposed themselves in their 
 modes of objecting to results which require the higher mathe- 
 matics to be known before an independent opinion can be formed 
 on sufficient grounds. But persons with no g'eometry at all have 
 done the same thing much more completely. 
 
 There is a line to be drawn which is constantly put aside in the 
 arguments held by parodoxers in favour of their right to instruct 
 the world. Most persons must, or at least will, like the lady in 
 Cadogan Place, 1 form and express an immense variety of opinions 
 on an immense variety of subjects ; and all persons must be their 
 own guides in many things. So far all is well. But there are 
 many who, in carrying the expression of their own opinions beyond 
 the usual tone of private conversation, whether they go no fur- 
 ther than attempts at oral proselytism, or whether they commit 
 themselves to the press, do not reflect that they have ceased^ to 
 stand upon the ground on which their process is defensible. ^ As-1 
 fpiring to lead others, they have never given themselves the fair 
 chance of being first led by other others into something better 
 than they can start for themselves ; and that they should first 
 do this is what both those classes of others have a fair right to 
 expect. New knowledge, when to any purpose, must come by 
 contemplation of old knowledge, in every matter which concerns 
 thought ; mechanical eontrivanee sometimes, not very often, 
 escapes this rule. All the men who are now called discoverers, in 
 every matter ruled by thought, have been men versed in the minds 
 of their predecessors, and learned in what had been before them. 
 There is not one exception. I do not say that every man has 
 made direct acquaintance with the whole of his mental ancestry ; 
 many have, as I may say, only known their grandfathers by the 
 report of their fathers. But even on this point it is remarkable 
 how many of the greatest names in all departments of knowledge 
 have been real antiquaries in their several subjects. 
 
 I may cite, among those who have wrought strongly upon 
 opinion or practice in science, Aristotle, Plato, Ptolemy, Euclid, 
 Archimedes, Eoger Bacon, Copernicus, Francis Bacon, Kamus, 
 Tycho Brahe, Gralileo, Napier, Descartes, Leibnitz, Newton, 
 Locke. I take none but names known out of their fields of work ; 
 and all were learned as well as sagacious. I have chosen my 
 instances : if any one will undertake to show a person of little or 
 , no knowledge who has established himself in a great matter of 
 [pure thought, let him bring forward his man, and we shall see. J 
 
 This is the true way of putting off those who plague others 
 
 1 Mrs. Wititterly, in Nicholas NicMeby. 
 
 \ 
 
INTRODUCTOKY. 5 
 
 with their great discoveries. The first demand made should be 
 Mr. Moses, before I allow you to lead me over the Eed Sea, I 
 must have you show that you are learned in all the wisdom of the 
 Egyptians upon your own subject. The plea that it is unlikely 
 that this or that unknown person should succeed where Newton, 
 &c. have failed, or should show Newton, &c. to be wrong, is utterly 
 null and void. It was worthily versified by Sylvanus Morgan 
 (the great herald who in his ' Sphere of Gentry ' gave coat armour 
 to 4 Gentleman Jesus J as he said), who sang of Copernicus as 
 follows (1652): 
 
 If Telhis winged be, 
 The earth a motion round ; 
 Then much deceived are they 
 Who nere before it found. 
 Solomon was the wisest, 
 His wit nere this attained ; 
 Cease, then, Copernicus, 
 Thy hypothesis vain. 
 
 Newton, &c. were once* unknown ; but they made themselves 
 known by what they knew, and then brought forward what they 
 could do ; which I see is as good verse as that of Herald Sylvanus. 
 The demand for previous knowledge disposes of twenty-nine cases 
 out of thirty, and the thirtieth is worth listening to. 
 
 I have not set down Copernicus, Galileo, &c. among the para- 
 doxers, merely because everybody knows them ; if my list were 
 quite complete, they would have been in it. But the reader will 
 find Gilbert, the great precursor of sound magnetical theory ; and 
 several others on whom no censure can be cast, though some of 
 their paradoxes are inadmissible, some unproved, and some capital 
 jokes, true or false : the author of the 'Vestiges of Creation' is an 
 instance. I expect that my old correspondent. General Perronet 
 Thompson, will admit that his geometry is part and parcel of my 
 plan ; and also that, if that plan embraced politics, he would 
 claim a place for his ' Catechism on the Corn Laws,' a work at one 
 time paradoxical, but which had more to do with the abolition of 
 the bread-tax than Sir Eobert Peel. 
 
 My intention in publishing this Budget in the Athenceum is 
 to enable those who have been puzzled by one or two discoverers 
 to see how they look in Hie lump. The only question is, has the 
 selection been fairly made ? To this my answer is, that no selec- 
 tion at all has been made. The books are, without exception, 
 those which I have in my own library ; and I have taken all I 
 mean all of the kind : Heaven forbid that I should be supposed 
 
6 A BUDGET OF PARADOXES. 
 
 to have no other books ! But I may have been a collector, in- 
 fluenced in choice by bias ? I answer that I never have collected 
 books of this sort that is, I have never searched for them, never 
 made up my mind to look out for this book or that. 1 have 
 bought what happened to come in my way at shop or auction ; I 
 have retained what came in as part of the undescribed portion of 
 miscellaneous auction lots ; I have received a few from friends 
 who found them among what they called their rubbish ; and I 
 have preserved books sent to me for review. In not a few in- 
 stances the books have been bound up with others, unmentioned 
 at the back ; and for years I knew no more I had them than I 
 knew I had Lord Macclesfield's speech on moving the change of 
 Style, which, after I had searched shops, &c. for it in vain, I 
 found had been reposing on my own shelves for many years, at 
 the end of a summary of Leibnitz's philosophy. Consequently, I 
 may positively affirm that the following list is formed by accident 
 and circumstance alone, and that it truly represents the casualties 
 of about a third of a century. For instance, the large proportion 
 of works on the quadrature of the circle is not my doing : it is 
 the natural share of this subject in the actual run of events. 
 
 [I keep to my plan of inserting only such books as I possessed 
 in 1863, except by casual notice in aid of my remarks. I have 
 found several books on my shelves which ought to have been 
 inserted. These have their titles set out at the commencement 
 of their articles, in leading paragraphs ; the casuals are without 
 this formality. 1 ] 
 
 Before proceeding to open the Budget, I say something on my 
 personal knowledge of the class of discoverers who square the 
 circle, upset Newton, &c. I suspect I know more of the English 
 class than any man in Britain. I never kept any reckoning ; but 
 I know that one year with another and less of late years than in 
 earlier time I have talked to more than live in each year, giving 
 more than a hundred and fifty specimens. Of this I am sure, 
 that it is my own fault if they have not bsen a thousand. Nobody 
 knows how they swarm, except those to v/hom they naturally 
 resort. They are in all ranks and occupations, of all . ages and 
 characters. They are very earnest people, and their purpose is 
 bonafide the dissemination of their paradoxes. A great many 
 the mass, indeed are illiterate, and a great many waste their 
 means, and are in or approaching penury. But I must say that 
 never, in any one instance, has the quadrature of the circle, of 
 
 1 The brackets mean that the paragraph is substantially from some one of the 
 Mhenceum Supplements. (ED.) 
 
INTRODUCTORY. 7 
 
 the like, been made a pretext for begging ; even to be asked to 
 purchase a book is of the very rarest occurrence it has happened, 
 and that is all. 
 
 These discoverers despise one another : if there were the concert 
 among* them which there is among foreign mendicants, a man 
 who admitted one to a conference would be plagued to death. I 
 once gave something to a very genteel French applicant, who 
 overtook me in the street, at my own door, saying he had picked 
 up my handkerchief : whether he picked it up in my pocket for 
 an introduction, I know not. But that day week came another 
 Frenchman to iny house, and that day fortnight a French lady ; 
 both failed, and I had no more trouble. The same thing hap- 
 pened with Poles. It is not so with circle-squarers, &c. : they 
 know nothing of each other. Some will read this list, and will 
 say I am right enough, generally speaking, but that there is an 
 exception, if I could but see it. 
 
 I do not mean, by my confession of the manner in which I 
 have sinned against the twenty-four hours, to hold myself out as 
 accessible to personal explanation of new plans. Quite the con- 
 trary : I consider myself as having made my report, and being 
 discharged from further attendance on the subject. I will not, 
 from henceforward, talk to any squarer of the circle, trisector of 
 the angle, duplicator of the cube, constructor of perpetual motion, 
 subverter of gravitation, stagnator of the earth, builder of the 
 universe, &c. I will receive any writings or books which require 
 no answer, and read them when I please : I will certainly preserve 
 them this list may be enlarged at some future time. 
 
 There are three subjects which I have hardly anything upon; 
 astrology, mechanism, and the infallible way of winning at play. 
 I have never cared to preserve astrology. The mechanists make 
 models, and not books. The infallible winners though I have 
 seen a few think their secret too valuable, and prefer mutare 
 quadrata rotundis to turn dice into coin at the gaming-house : 
 verily they have their reward. 
 
 I shall now select, to the mystic number se\ 3n, instances of my 
 personal knowledge of those who think they have discovered, in 
 illustration of as many misconceptions. 
 
 1. Attempt by help of the old philosophy, the discoverer not 
 being in possession of modern knowledge. A poor schoolmaster, 
 in rags, introduced himself to a scientific friend with whom I was 
 talking, and announced that he had found out the composition of 
 the sun. 4 How was that done ? ' ' By consideration of the four 
 elements.' c What are they ? ' ' Of course, fire, air, earth, and 
 
8 A BUDGET OF PAKADOXES. 
 
 water.' c Did you not know that air, earth, and water, have long 
 been known to be no elements at all, but compounds ? ' ' What 
 do you mean, sir ? Who ever heard of such a thing ? ' 
 
 2. The notion that difficulties are enigmas, to be overcome in 
 a moment by a lucky thought. A nobleman of very high rank, 
 now long dead, read an article by me oil the quadrature, in an 
 early number of the Penny Magazine. He had, I suppose, school 
 recollections of geometry. He put pencil to paper, drew a circle, 
 and constructed what seemed likely to answer, and, indeed, was 
 as he said certain, if only this bit were equal to that ; which of 
 course it was not. He forwarded his diagram to the Secretary of 
 the Diffusion Society, to be handed to the author of the article, in 
 case the difficulty should happen to be therein overcome. 
 
 3. Discovery at all hazards, to get on in the world. Thirty 
 years ago, an officer of rank, just come from foreign service, and 
 trying for a decoration from the Crown, found that his claims were 
 of doubtful amount, and was told by a friend that so and so, who 
 had got the order, had the additional claim of scientific distinc- 
 tion. Now this officer, while abroad, had bethought himself one 
 day, that there really could be no difficulty in finding the circum- 
 ference of a circle : if a circle were rolled upon a straight line 
 until the undermost point came undermost again, there would be 
 the straight line equal to the circle. He came to me, saying that 
 "he did not feel equal to the statement of his claim in this respect, 
 but that if some clever fellow would put the thing in a proper 
 light, he thought his affair might be managed. I was clever 
 enough to put the thing in a proper light to himself, to this extent 
 at least, that, though perhaps they were wrong, the advisers of the 
 Crown would never put the letters K.C.B.. to such a circle as his. 
 
 4. The notion that mathematicians cannot find the circle for 
 common purposes. A working man measured the altitude of a 
 cylinder accurately, and I think the process of Archimedes was 
 one of his proceedings found its bulk. He then calculated the 
 ratio of the circumference to the diameter, and found it answered 
 very well on other modes of trial. His result was about 3*14. 
 He came to London, and somebody sent him to me. Like many 
 others of his pursuit, he seemed to have turned the whole force of 
 his mind upon one of his points, on which alone he would be open 
 to refutation. He had read some of Kater's experiments, and had 
 got the Act of 1825 on weights and measures. Say what I would, 
 he had for a long time but one answer c Sir ! I go upon Captain 
 Kater and the Act of Parliament.' But I fixed him at last. I 
 happened to^have on the table a proof-sheet of the Astronomical 
 
. INTRODUCTORY. 9 
 
 ^ in which were a large number of observed places of the 
 planets compared with prediction, and asked him whether it could 
 be possible that persons who did not know the circle better than 
 he had found it could make the calculations, of which I gave him 
 a notion, so accurately ? He was perfectly astonished, and took 
 the titles of some books which he said he would read. 
 
 5. Application for the reward from abroad. Many years ago, 
 about twenty-eight, I think, a Jesuit came from South America, 
 with a quadrature, and a cutting from a newspaper, announcing 
 that a reward was ready for the discovery in England. On this 
 evidence he came over. After satisfying him that nothing had 
 ever been offered here, I discussed his quadrature, which was of 
 no use. I succeeded better when I told him of Eichard White, 
 also a Jesuit, and author of a quadrature published before 1648, 
 under the name of Chi^yscespis, of which I can give no account, 
 having never seen it. This White (Albius) is the only quad- 
 rator who was ever convinced of his error. My Jesuit was struck 
 by the instance, and promised to read more geometry he was 
 no Clavius before he published his book. He relapsed, how- 
 ever, for I saw his book advertised in a few days. I may say, as 
 sufficient proof of my being no collector, that I had not the 
 curiosity to buy this book ; and my friend the Jesuit did not 
 send me a copy, which he ought to have done, after the hour I 
 had given him. 
 
 6. Application for the reivard at home. An agricultural 
 labourer squared the circle, and brought the proceeds to London. 
 He left his papers with me, one of which was the copy of a letter 
 to the Lord Chancellor, desiring his Lordship to hand over 
 forthwith 100,000?., the amount of the alleged offer of reward. 
 He did not go quite so far as M. de Vausenville, who, I think 
 in 1778, brought an action against the Academy of Sciences to 
 recover a reward to which he held himself entitled. I returned 
 the papers, with a note, stating that he had not the knowledge 
 requisite to see in what the problem consisted. I got for answer 
 a letter in which I was told that a person who could not see that 
 he had done the thing should ' change his business, and appro- 
 priate his time and attention to a Sunday-school, to learn what 
 he could, and keep the title children from dwrting their close.' 
 I also received a letter from a friend of the quadrator, informing 
 me that I knew his friend had succeeded, and had been heard to 
 say so. These letters were printed without the names of the 
 writers for the amusement of the readers of Notes and Queries, 
 First Series, xii. 57, and they will appear again in the sequel. 
 
10 A BUDGET OF PARADOXES. 
 
 [There are many who have such a deep respect for any attempt 
 at thought that they are shocked at ridicule even of those who 
 have made themselves conspicuous by pretending to lead the 
 world in matters which they have not studied. Among my 
 anonymes is a gentleman who is angry at my treatment of 
 the ' poor but thoughtful ' man who is described in my intro- 
 duction as recommending me to go to a Sunday-school because I 
 informed him that he did not know in what the difficulty of 
 quadrature consisted. My impugner quite forgets that this 
 man's ; thoughtfulness ' chiefly consisted in his demanding a 
 hundred thousand pounds from the Lord Chancellor for his dis- 
 covery ; and I may add, that his greatest stretch of invention 
 was finding out that ' the clergy ' were the means of his modest 
 request being unnoticed. I mention this letter because it affords 
 occasion to note a very common error, namely, that men unread 
 in their subjects have, by natural wisdom, been great benefactors 
 of mankind. My critic says, 4 Shakspeare, whom the Pro r (sic) 
 may admit to be a wisish man, though an object of contempt as 
 to learning. . . .' Shakspeare an object of contempt as to 
 learning ! Though not myself a thoroughgoing Shakspearean 
 and adopting the first half of the opinion given by George III., 
 6 What! is there not sad stuff? only one must not say so' I 
 am strongly of opinion that he throws out the masonic signs of 
 learning in almost every scene, to all who know what they are. 
 And this over and above every kind of direct evidence. First, 
 foremost, and enough, the evidence of Ben Jon son that he had 
 4 little Latin and less Greek ; ' then Shakspe.are had as much 
 Greek as Jonson would call some, even when he was depreciating. 
 To have any Greek at all was in those days exceptional. In 
 Shakspeare's youth St. Paul's and Merchant Taylors' schools were 
 to have masters learned in good and clean Latin literature, and 
 also in Greek if such may be gotten. When Jonson spoke as 
 above, he intended to put Shakspeare low among the learned, 
 but not out of their pale ; and he spoke as a rival dramatist, who 
 was proud of his own learned sock ; and it may be a subject of 
 inquiry how much Latin he would call little. If Shakspeare's 
 learning on certain points be very much less visible than Jonson's, 
 it is partly because Shakspeare's writings hold it in chemical 
 combination, Jonson's in mechanical aggregation.] 
 
 7. An elderly man came to me, to show me how the universe 
 was created. There-was one molecule, which by vibration became 
 Heaven knows how ! the Sun. Further vibration produced 
 Mercury, and so on. I suspect the nebular hypothesis had got 
 
INTKODUCTOEY. 11 
 
 into the poor man's head by reading, in some singular mixture 
 with what it found there. Some modifications of vibration gave 
 heat, electricity, &e. I listened until my informant ceased to 
 vibrate which is always the shortest way and then said, ' Our 
 knowledge of elastic fluids is imperfect.' ' Sir ! ' said he, ' I 
 see you perceive the truth of what I have said, and I will 
 reward your attention by telling you what I seldom disclose, 
 never, except to those who can receive my theory the little 
 molecule whose vibrations have given rise to our solar system is 
 the Logos of St. John's Grospel ! ' He went away to Dr. Lardner, 
 who would not go into the solar system at all the first molecule 
 settled the question. So hard upon poor discoverers are men of 
 science who are not antiquaries in their subject ! On leaving, 
 he said, ' Sir, Mr. De Morgan received me in a very different 
 way ; he heard me attentively, and I left him perfectly satisfied 
 of the truth of my system.' I have had much reason to think 
 that many discoverers, of all classes, believe they have convinced 
 every one who is not peremptory to the verge of incivility. 
 
 My list is given in chronological order. My readers will 
 understand that my general expressions, where slighting or 
 contemptuous, refer to the ignorant, who teach before they 
 have learnt. In every instance, those of whom I am able to 
 speak with respect, whether as right or wrong, have sought 
 knowledge in the subject they were to handle before they com- 
 pleted their speculations. I shall further illustrate this at the 
 conclusion of my list. 
 
 Before I begin the list, I give prominence to the following 
 letter, addressed by me to the Correspondent of October 28, 1865. 
 Some of my paradoxers attribute to me articles in this or that 
 journal; and others may think I know some do think they 
 know me as the writer of reviews of some of the very books 
 noticed here. The following remarks will explain the way in 
 which they may be right, and in which they may be wrong : 
 
 THE EDITORIAL SYSTEM. 
 
 SIR, I have reason to think that many persons have a very in- 
 accurate notion of the Editorial system. What I call by this name has 
 grown up in the last centenary a word I may use to. signify the 
 hundred years now ending, and to avoid the ambiguity of century. It 
 cannot conveniently be explained by editors themselves, and edited 
 journals generally do not like to say much about it. In your paper 
 perhaps, in which editorial duties differ somewhat from those of 
 ordinary journals, the common system may be freely spoken of. 
 
12 A BUDGET OF PARADOXES. 
 
 When a reviewed author, as very often happens, writes to the 
 editor of the reviewing journal to complain of what has been said of 
 him, he frequently even more often than not complains of 'your 
 reviewer.' He sometimes presumes that ' you ' have, ' through 
 inadvertence ' in this instance, ' allowed some incompetent person to 
 lower the character of your usually accurate pages.' Sometimes he 
 talks of 'your scribe,' and, in extreme cases, even of 'your hack.' All 
 this shows perfect ignorance of the journal system, except where it is 
 done under the notion of letting the editor down easy. But the editor 
 never accepts the mercy. 
 
 All that is in a journal, except what is marked as from a corre- 
 spondent, either by the editor himself or by the correspondent's real 
 or fictitious signature, is published entirely on editorial responsibility, 
 as much as if the editor had written it himself. The editor, therefore, 
 may claim, and does claim and exercise, unlimited right of omission, 
 addition, and alteration. This is so well understood that the editor 
 performs his last function on the last revise without the ' contributor ' 
 knowing what is done. The word contributor is the proper one : it 
 implies that he furnishes materials without stating what he furnishes 
 or how much of it is accepted, or whether he be the only contributor. 
 All this applies both to political and literary journals. No editor 
 acknowledges the right of a contributor to withdraw an article, if he 
 should find alterations in the proof sent to him for correction which 
 would make him wish that the article should not appear. If the 
 demand for suppression were made I say nothing about what might 
 be granted to request the answer would be, ' It is tiot your article, 
 but mine ; I have all the responsibility ; if it should contain a libel, I 
 could not give you up, even at your own desire. You have furnished 
 me with materials, on the known and common understanding that I 
 was to use them at my discretion, and you have no right to impede my 
 operations by making the appearance of the article depend on your 
 approbation of my use of your materials.' 
 
 There is something to be said for this system, and something against 
 it I mean simply on its own merits. But the all- conquering argu- 
 ment in its favour is, that the only practicable alternative is the 
 modern French plan of no articles without the signature of the writers. 
 I need not discuss this plan ; there is no collective party in favour of 
 it. Some may think it is not the only alternative ; they have not pro- 
 duced any intermediate proposal in which any dozen of persons have 
 concurred. Many will say, Is not all this, though perfectly correct, 
 well known to be matter of form ? Is it not practically the course of 
 events that an engaged contributor writes the article, and sends it to 
 the editor, who admits it as written substantially, at least ? And is 
 it not often very well known, by style and in other ways, who it was 
 wrote the article ? This system is matter of form just as much as 
 loaded pistols are matter of form so long as the wearer is not assailed 
 but matter of form takes the form of matter in the pulling of a trigger, 
 
INTRODUCTORY. 18 
 
 so soon as the need arises. Editors and contributors who can work 
 together find each other out by elective affinity, so that the common 
 run of events settles down into most articles appearing much as they 
 are written. And there are two safety-valves ; that is, when judicious 
 persons come together. In the first place, the editor himself, when he 
 has selected his contributor, feels that the contributor is likely to know 
 his business better than an editor can teach him ; in fact, it is on 
 that principle that the selection is made. But he feels that he is more 
 competent than the writer to judge questions of strength and of tone, 
 especially when the general purpose of the journal is considered, of 
 which the editor is the judge without appeal. An editor who meddles 
 with substantive matter is likely to be wrong, even when he knows the 
 subject ; but one who prunes what he deems excess, is likely to be 
 right, even when he does not know the subject. In the second place, 
 a contributor knows that he is supplying an editor, and learns, without 
 suppressing truth or suggesting falsehood, to make the tone of his com- 
 munications suit the periodical in which they are to appear. Hence 
 it very often arises that a reviewed author, who thinks he knows the 
 name of his reviewer, and proclaims it with expressions of dissatis- 
 faction, is only wrong in supposing that his critic has given all his 
 mind. It has happened to myself, more than once, to be announced as 
 the author of articles which I could not have signed, because they did 
 not go far enough to warrant my affixing my name to them as to a 
 sufficient expression of my own opinion. 
 
 There are two other ways in which a reviewed author may be wrong 
 about his critic. At editor frequently makes slight insertions or 
 omissions I mean slight in quantity of type as he goes over the last 
 proof; this he does in a comparative hurry, and it may chance that he 
 does not know the full sting of his little alteration, The very bit which 
 the writer of the book most complains of may not have been seen by the 
 person who is called the writer of the article until after the appearance 
 of the journal ; nay, if he be one of those few, I daresay who do not 
 read their own articles, may never have been seen by him at all. Pos- 
 sibly, the insertion or omission would not have been made if the editor 
 could have had one minute's conversation with his contributor. Some- 
 times it actually contradicts something which is allowed to remain in 
 another part of the article ; and sometimes, especially in the case of 
 omission, it renders other parts of the article unintelligible. These are 
 disadvantages of the system, and a judicious editor is not very free 
 with his unus et alter pannus. Next, readers in general, when they 
 see the pages of a journal with the articles so nicely fitting, and so 
 many ending with the page or column, have very little notion of the 
 cutting and carving which goes to the process. At the very last 
 moment arises the necessity of some trimming of this kind ; and the 
 editor, who would gladly call the writer to counsel if he could, is 
 obliged to strike out ten or twenty lines. He must do his best, but it 
 may chance that the omission selected would take from the writer the 
 
14 A BUDGET OF PARADOXES. 
 
 power of owning the article. A few years ago, an able opponent of 
 mine wrote to a journal some criticisms upon an article which he 
 expressly attributed to me. I replied as if I were the writer, which, in 
 a sense, I was. But if any one had required of me an unmodified ' Yes ' 
 or ' No ' to the question whether I wrote the article, I must, of two 
 falsehoods, have chosen ' No : ' for certain omissions, dictated by the 
 necessities of space and time, would have amounted, had my signature 
 been affixed, to a silent surrender of points which, in my own cha- 
 racter, I must have strongly insisted on, unless I had chosen to admit 
 certain inferences against what I had previously published in my own 
 name. I may here add that the forms of journalism obliged me in this 
 case to remind my opponent that it could not be permitted to me, in 
 that journal, either to acknowledge or deny the authorship of the articles. 
 The cautions derived from the above remarks are particularly wanted 
 with reference to the editorial comments upon letters of complaint. 
 There is often no time to send these letters to the contributor, 
 and even when this can be done, an editor is and very properly 
 never of so editorial a mind as when he is revising the comments of 
 a contributor upon an assailant of the article. He is then in a better 
 position as to information, and a more critical position as to responsi- 
 bility. Of course, an editor never meddles, except under notice, with 
 the letter of a correspondent, whether of a complainant, of a casual in- 
 formant, or of a contributor who sees reason to become a correspondent. 
 Omissions must sometimes be made when a grievance is too highly 
 spiced. It did once happen to me that a waggish editor made an inser- 
 tion without notice in a letter signed by me with some fiction, which 
 insertion contained the name of a friend of mine, with a satire which I 
 did not believe, and should not have written if I had. To my strong 
 rebuke, he replied ' I know it was very wrong ; but human nature 
 could not resist.' But this was the only occasion on which such a 
 thing ever happened to me. 
 
 I daresay what I have written may give some of your readers to under- 
 stand some of the pericula et commoda of modern journalism. I have 
 known men of deep learning and science as ignorant of the prevailing 
 system as any uneducated reader of a newspaper in a country town. I 
 may, perhaps, induce some writers not to be too sure about this, that, 
 or the other person. They may detect their reviewer, and they may be 
 safe in attributing to him the general matter and tone of the article. 
 But about one and another point, especially if it be a short and sting- 
 ing point, they may very easily chance to be wrong. It has happened 
 to myself, and within a few weeks to publication, to be wrong in two 
 ways in reading a past article to attribute to editorial insertion what 
 was really my own, and to attribute to myself what was really editorial 
 insertion. 
 
 What is a man to do who is asked whether he wrote an article. 
 He may, of course, refuse to answer ; which is regarded as an 
 
INTRODUCTORY. 15 
 
 admission. He may say, as Swift did to Serjeant Bettesworth, 
 ' Sir, when I was a young man, a friend of mine advised me, \ 
 whenever I was asked whether I had written a certain paper, to 
 deny it ; and I accordingly tell you that I did not write it.' He Nj 
 may say, as I often do, when charged with having invented a joke, 
 story, or epigram, 6 I want all the credit I can get, and therefore 
 I always acknowledge all that is attributed to me, truly or not ; 
 the story, &c. is mine. But for serious earnest, in the matter of 
 imputed criticism, the answer may be, ' That article was of my 
 material, but the editor has not let it stand as I gave it ; I cannot 
 own it as a whole.' He may then refuse to be particular as to 
 the amount of the editor's interference. Of this there are two 
 extreme cases. The editor may have expunged nothing but a 
 qualifying adverb. Or he may have done as follows. We all 
 remember the account of Adam which satirizes woman, but 
 eulogizes her if every second and third line be transposed. As 
 in 
 
 Adam could find no solid peace 
 
 When Eve was given him for a mate, 
 
 Till he beheld a woman's face, 
 Adam was in a happy state. 
 
 If this had been the article, and a gallant editor had made the 
 transpositions, the author could not with truth acknowledge. If 
 the alteration were only an omitted adverb, or a few things of the 
 sort, the author could not with truth deny. In all that comes 
 between, every man must be his own casuist. I stared, when I 
 was a boy, to hear grave persons approve of Sir Walter Scott's 
 downright denial that he was the author of Waverley, in answer 
 to the Prince Eegent's downright question. If I remember 
 rightly, Samuel Johnson would have approved of the same course. 
 It is known that, whatever the law gives, it also gives all that 
 is necessary to full possession ; thus a man whose land is environed 
 by the land of others has a right of way over the land of these 
 others. By analogy, it is argued that when a man has a right to 
 his secret, he has a right to all that is necessary to keep it, and 
 that is not -unlawful. If, then, he can only keep his secret by 
 denial, he has a right to denial. This I admit to be an answer as 
 against all men except the denier himself ; if conscience and self- 
 respect will allow it, no one can impeach it. But the question 
 cannot be solved on a case. That question is, A lie, is jit malum in 
 se, without reference to meaning and circumstances ? This is a 
 question with two sides to it. Cases may be invented in which a 
 
16 A BUDGET OF PARADOXES. 
 
 lie is the only way of preventing a murder, or in which a lie may 
 otherwise save a life. In these cases it is difficult to acquit, and 
 almost impossible to blame ; discretion introduced, the line be- 
 comes very hard to draw. 
 
 I know but one work which has precisely as at first appears 
 the character and object of my Budget. It is the 6 Eeview of the 
 Works of the Eoyal Society of London,' by Sir John Hill, M.D. 
 (1751 and 1780, 4to.) This man offended many: the Eoyal 
 Society, by his work ; the medical profession, by inventing and 
 selling extra-pharmacopceian doses ; Grarrick, by resenting the 
 rejection of a play. So Grarrick wrote: 
 
 For physic and farces his equal there scarce is ; 
 His farces are physic ; his physic a farce is. 
 
 I have fired at the Eoyal Society and at the medical profession, 
 but I have given a wide berth to the drama and its wits ; so 
 there is no epigram out against me, as yet. He was very able 
 and very eccentric. Dr. Thomson (Hist. Roy. Soc.) says he has 
 no humour, but Dr. Thomson was a man who never would have 
 discovered humour. 
 
 Mr. Weld (Hist. Roy. Soc.} backs Dr. Thomson, but with a re- 
 markable addition. Having followed his predecessor in observing 
 that the Transactions in Martin Folkes's time have an unusual 
 proportion of trifling and puerile papers, he says that Hill's book 
 is a poor attempt at humour, and glaringly exhibits the feelings 
 of a disappointed man. It is probable, he adds, that the points 
 told with some effect on the Society ; for shortly after its publica- 
 tion the Transactions possess a much higher scientific value. 
 
 I copy an account which I gave elsewhere. 
 
 When the Eoyal Society was founded, the Fellows set to work 
 to prove all things, that they might hold fast that which was 
 good. They bent themselves to the question whether sprats were 
 young herrings. They made a circle of the powder of a unicorn's 
 horn, and set a spider in the middle of it ; 4 but it immediately 
 ran out.' They tried several times, and the spider ' once made 
 some stay in the powder.' They enquired into Kenelm Digby's 
 sympathetic powder. ' Magnetical cures being discoursed of, Sir 
 Gilbert Talbot promised to communicate what he knew of sym- 
 pathetical cures ; and those members who had any of the powder 
 of sympathy, were desired to bring some of it at the next meeting.' 
 
 June 21, 1661, certain gentlemen were appointed ' curators of 
 the proposal of tormenting a man with the sympathetic powder ;' 
 I cannot find any record of the result. And so they went on 
 
INTRODUCTORY. 1 7 
 
 until the time of Sir John Hill's satire, in 1751. This once well- 
 known work is, in my judgment, the greatest compliment the 
 Eoyal Society ever received. It brought forward a number of 
 what are now feeble and ohildish researches in the Philosophical 
 Transactions. It showed that the inquirers had actually been 
 inquiring ; and that they did not pronounce decision about 
 ' natural knowledge' by help of ' natural knowledge.' But for 
 this, Hill would neither have known what to assail, nor how. 
 Matters are now entirely changed. The scientific bodies are far 
 too well established to risk themselves. Ibit qui zonamperdidit 
 
 Let him take castles who has ne'er a groat. 
 
 These great institutions are now without any collective purpose, 
 except that of promoting individual energy ; they print for their 
 contributors, and guard themselves by a general declaration that 
 they will not be answerable for the things they print. Of course 
 they will not put forward anything for everybody ; but a writer of 
 a certain reputation, or matter of a certain look of plausibility and 
 safety, will find admission. This is as it should be ; the pas- 
 turer of flocks and herd 3 and the hunters of wild beasts are two 
 very different bodies, "with very different policies. The scientific 
 academies are what a spiritualist might call 'publishing mediums,' 
 and their spirits fall occasionally into writing which looks as if 
 minds in the higher state were not always impervious to nonsense. 
 
 The following joke is attributed to Sir John Hill. I cannot 
 honestly say I believe it ; but it shows that his contemporaries did 
 not believe he had no humour, (rood stories are always in some 
 sort of keeping with the characters on which they are fastened. 
 Sir John Hill contrived a communication to the Eoyal Society 
 from Portsmouth, to the effect that a sailor had broken his leg in 
 a fall from the mast-head ; that bandages and a plentiful applica- 
 tion of tarwater had made him, in three days, able to use his leg 
 as well as ever. While this communication was under grave 
 discussion- it must be remembered that many then thought tar- 
 water had extraordinary remedial properties the joker contrived 
 that a second letter should be delivered, which stated that the 
 writer had forgotten, in his previous communication, to mention 
 that the leg was a wooden leg ! Horace Walpole told this story, 
 I suppose for the first time ; he is good authority for the fact of 
 circulation, but for nothing more. 
 
 Sir John Hill's book is droll and cutting satire. Dr. Maty, 
 (Sec. Royal Society) wrote thus of it in the Journal Britannique 
 (Feb. 1751), of which he was editor: 
 
18 A BUDGET OF PAEADOXES. 
 
 II est facheux que cet ingenieux Naturaliste, qui nous a deja donne 
 et qui nous prepare encore des ouvrages plus utiles, emploie a cette 
 odieuse tache une plume qu'il trempe dans le fiel et dans 1'absinthe. Tl 
 est vrai que plusieurs de ses remarques sont fondees, et qu'a 1'erreur 
 qu'il indique, il joint en meme terns la correction. Mais il n'est pas tou- 
 jours equitable, et ne manque jamais d'insulter. Que peut apres tout 
 prouver son livre, si ce n'est que la quarante-cinquieme partie d'un 
 tres-ample et tres-utile Recueil n'est pas exempte d'erreurs ? Devoit- 
 il confondre avec des Berivains superficiels, dont la Liberte du Corps ne 
 permet pas de restreindre la fertilite, cette foule de savans du Premier 
 ordre, dont les Merits ont orne et ornent encore les Transactions ? A-t-il 
 oublie qu'on y a vu frequemment les noms des Boyle, des Newton, 
 des Halley, des De Moivres, des Hans Sloane, etc. ? Et qu'on y trouve 
 encore ceux des Ward, des Bradley, des Graham, des Ellicot, des Watson, 
 et d'un Auteur que Mr. Hill prefere a tous les autres, je veux dire de 
 Mr. Hill lui-meme ? 
 
 This was the only answer ; but it was no answer at all. Hill's 
 object was to expose the absurdities ; he therefore collected the 
 absurdities. I feel sure that Hill was a benefactor of the Eoyal 
 Society ; and much more than he would have been if he had 
 softened their errors and enhanced their praises. No reviewer 
 will object to me that I have omitted Young, Laplace, &c. But 
 then my book has a true title. Hill should not have called his 
 a review of the ' Works.' 
 
 It was charged against Sir John Hill that he had tried to 
 become a Fellow of the Royal Society and had failed. This he 
 denied, and challenged the production of the certificate which a 
 candidate always sends in, and which is preserved. But perhaps 
 he could not get so far as a certificate that is, could not find any 
 one to recommend him ; he was a likely man to be in such a 
 predicament. As I have myself run foul of the Society on some 
 little points, I conceive it possible that I may fall under a like 
 suspicion. Whether I could have been a Fellow, I cannot know ; 
 as the gentleman said who was asked if he could play the violin, 
 I never tried. I have always had a high opinion of the Society 
 upon its whole history. A person used to historical inquiry 
 learns to look at wholes ; the Universities of Oxford and 
 Cambridge, the College of Physicians, &c. are taken in all their 
 duration. But those who are not historians I mean not 
 possessed of the habit of history hold a mass of opinions about 
 current things which lead them into all kinds of confusion when 
 they try to look back. Not to give an instance which will offend 
 any set of existing men this merely because I can do without 
 it let us take the country at large. Magna Charta for ever ! 
 
INTKODUCTOKY. 19 
 
 glorious safeguard of our liberties ! Nullus liber homo capiatur 
 aut imprisonetur. . . . aut aliquo modo destruatur, nisi per 
 judicium parium. . . . Liber homo ; frank home ; a capital 
 thing for him but how about the villeins ? Oh, there are none 
 noiv ! But there were. Who cares for villains, or barbarians, or 
 helots ? And so England, and Athens, and Sparta, were free 
 States : all the freemen in them were free. Long after Magna 
 Charta, villains were sold with their * chattels and offspring,' 
 named in that order. Long after Magna Charta, it was law that 
 c Le Seigniour poit rob, naufrer, et chastiser son villein a son 
 volunt, salve que il ne poit luy maim.' 
 
 The Royal Society was founded as a co-operative body, and co- 
 operation was its purpose. The early charters, &c. do not contain 
 a trace of the intention to create a scientific distinction, a kind 
 of Legion of Honour. It is clear that the qualification was ability 
 and willingness to do good work for the promotion of natural 
 knowledge, no matter in how many persons, nor of what position 
 in society. Charles II. gave a smart rebuke for exclusiveness, as 
 elsewhere mentioned. In time arose, almost of course, the idea 
 of distinction attaching to the title ; and when I first began 
 to know the Society, it was in this state. Gentlemen of good 
 social position were freely elected if they were really educated 
 men ; but the moment a claimant was announced as resting on 
 his science, there was a disposition to inquire whether he was 
 scientific enough. The maxim of the poet was adopted; and 
 the Fellows were practically divided into Drink-deeps and 
 Taste-nots. 
 
 I was, in early life, much repelled by the tone taken by the 
 Fellows of the Society with respect to their very mixed body. A 
 man high in science some thirty-seven years ago (about 1830) 
 gave me some encouragement, as he thought. ' We shall have you a 
 Fellow of the Royal Society in time,' said he. Umph ! thought I : 
 for I had thatday heard of some recent elections, the united science 
 of which would not have demonstrated I. 1, nor explained the action 
 of a pump. Truly an elevation to look up at ! It came, further, to 
 my knowledge that the Royal Society if I might judge by the 
 claims made by very influential Fellows considered itself as 
 entitled to the best of everything : second-best being left for the 
 newer bodies. A secretary, in returning thanks for the Royal 
 at an anniversary of the Astronomical, gave rather a lecture to 
 the company on the positive duty of all present to send the very 
 best to the old body, and the absolute right of the old body to 
 expect it. An old friend of mine, on a similar occasion, stated as 
 
 c 2 
 
20 A BUDGET OF PARADOXES. 
 
 a fact that the thing was always done, as well as that it ought to 
 be done. 
 
 Of late years this pretension has been made by a President 
 of the Society. In 1855, Lord Eosse presented a confidential 
 memorandum to the Council on the expediency of enlarging 
 their number. He says, 6 In a Council so small it is impossible 
 to secure a satisfactory representation of the leading scientific 
 Societies, and it is scarcely to be expected that, under such cir- 
 cumstances, they will continue to publish inferior papers while 
 they send the best to our Transactions.' 
 
 And, again, with all the Societies represented on the Council, 
 * even if every Science had its Society, and if they published every- 
 thing, withholding their best papers [i.e. from the Eoyal Society], 
 which they would not be likely to do, still there would remain to 
 the Eoyal Society . . .' Lord Eosse seems to imagine that the 
 minor Societies themselves transfer their best papers to the 
 Eoyal Society ; that if, for instance, the Astronomical Society 
 were to receive from A. B. a paper of unusual merit, the Society 
 would transfer it to the Eoyal Society. This is quite wrong : any 
 preference of the Eoyal to another Society is the work of the 
 contributor himself. But it shows how well hafted is the Eoyal 
 Society's claim, that a President should acquire the notion that 
 it is acknowledged and acted upon by the other Societies, in their 
 joint and corporate capacities. To the pretension thus made I 
 never could give any sympathy. When I first heard Mr. Christie, 
 Sec. E. S., set it forth at the anniversary dinner of the Astro- 
 nomical Society, I remembered the Baron in Walter Scott 
 
 Of Gilbert the Galliard a heriot he sought, 
 Saying, Give thy best steed as a vassal ought. 
 
 And I remembered the answer 
 
 Lord and Earl though thou be, I trow 
 I can rein Buek's-foot better than thou. 
 
 Fully conceding that the Eoyal Society is entitled to pre- 
 eminent rank and all the respect due to age and services, I 
 could not, nor can I now, see any more obligation in a contributor 
 to send his best to that Society than he can make out to be due 
 to himself. This pretension, in my mind, was hooked on, by 
 my historical mode of viewing things already mentioned, to my 
 knowledge of the fact that the Eoyal Society the chief fault, 
 perhaps, lying with its President, Sir Joseph Bankshad sternly 
 set itself against the formation of other societies ; the Geological 
 
INTRODUCTORY. 21 
 
 and Astronomical, for instance, though it must be added that 
 the chief rebels came out of the Society itself. And so a certain 
 not very defined dislike was generated in my mind an' anti- 
 aristocratic affair to the body which seemed to me a little too 
 uplifted. This would, I daresay, have worn off; but a more 
 formidable objection arose. My views of physical science gradu- 
 ally arranged themselves into a form which would have rendered 
 F.R.S., as attached to my name, a false representation symbol. 
 The Eoyal Society is the great fortress of general physics : and in 
 the philosophy of our day, as to general physics, there is some- 
 thing which makes the banner of the R.S. one under which I 
 cannot march. Everybody who saw the three letters after my 
 name would infer certain things as to my mode of thought which 
 would not be true inference. It would take much space to explain 
 this in full. I may hereafter, perhaps, write a budget of collected 
 results of the a priori philosophy, the nibbling at the small 
 end of omniscience, and the effect it has had on common life, 
 from the family parlour to the jury-box, from the girls'-school 
 to the vestry-meeting. There are in the Society those who 
 would, were there no others, prevent my criticism, be its con- 
 clusions true or false, from having any basis ; but they are in the 
 minority. 
 
 There is no objection to be made to the principles of philosophy 
 in vogue at the Society, when they are stated as principles ; but 
 there is an omniscience in daily practice which the principles 
 repudiate. In like manner, the most retaliatory Christians have 
 a perfect form of round words about behaviour to those who 
 injure them : none of them are as candid as a little boy I knew, 
 who, to his mother's admonition, You should love your enemies, 
 answered Catch me at it ! 
 
 Years ago, a change took place which would alone have put a 
 sufficient difficulty in the way. The co-operative body got tired 
 of getting funds from and lending name to persons who had little 
 or no science, and wanted F.E.S. to be in every case a Fellow 
 Really Scientific. Accordingly, the number of yearly elections was 
 limited to fifteen recommended by the Council, unless the general 
 body should choose to elect more ; which it does not do. The 
 election is now a competitive examination: it is no longer Are you 
 able and willing to promote natural knowledge ; it is Are you one 
 of the upper fifteen of those who make such claim. In the list of 
 candidates a list rapidly growing in number each year shows 
 from thirty to forty of those whom Newton and Boyle would have 
 gladly welcomed as fellow-labourers. And though the rejected 
 
22 A BUDGET OF PAKADOXES. 
 
 of one year may be the accepted of the next or of the next but 
 one, or but two, if self-respect will permit the candidate to hang 
 on yet the time is clearly coming when many of those who 
 ought to be welcomed will be excluded for life, or else shelved at 
 last, when past work, with a scientific peerage. Coupled with 
 this attempt to create a kind of order of knighthood is an ab- 
 surdity so glaring that it should always be kept before the general 
 eye. This distinction, this mark set by science upon successful 
 investigation, is of necessity a class-distinction. Rowan Hamilton, 
 one of the greatest names of our day in mathematical science, 
 never could attach F.E.S. to his name he could not afford it. 
 There is a condition precedent Four Eed Sovereigns. It is 
 four pounds a year, or to those who have contributed to the 
 Transactions forty pounds down. This is as it should be : the 
 Society must be supported. But it is not as it should be that a 
 kind of title of honour should be forged, that a body should take 
 upon itself to confer distinctions for science, when it is in the 
 background and kept there when the distinction is trumpeted 
 that the wearer is a man who can spare four pounds a year. I 
 am well aware that in England a person who is not gifted, either 
 by nature or art, with this amount of money power, is, with the 
 mass, a very second-rate sort of Newton, whatever he may be in 
 the field of investigation. Even men of science, so called, have 
 this feeling. I know that the scientific advisers of the Admiralty, 
 who, years ago, received lOOi. a year each for his trouble, were 
 sneered at by a wealthy pretender as ' fellows to whom a hundred 
 a year is an object.' Dr. Thomas Young was one of them. To 
 a bookish man I mean a man who can manage to collect books 
 there is no tax. To myself, for example, 40Z. worth of books 
 deducted from my shelves, and the life-use of the Society's 
 splendid library instead, would have been a capital exchange. 
 But there may be, and are, men who want books, and cannot pay 
 the Society's price. The Council would be very liberal in allow- 
 ing their books to be consulted. I have no doubt that if a known 
 investigator were to call and ask to look at certain books, the 
 Assistant-Secretary would forthwith seat him with the books 
 before him, absence of F.R.S. not in any wise withstanding. But 
 this is not like having the right to consult, any book on any day, 
 and to take it away, if farther wanted. 
 
 So much for the Royal Society as concerns myself. I must add, 
 that there is not a spark of party feeling against those who 
 wilfully remain outside. The better minds of course know better; 
 and the smaller savants look complacently on the idea of an 
 
INTRODUCTORY, 2 3 
 
 outer world which makes elite of them. I have done such a 
 thing as serve on a committee of the Society, and report on a 
 paper : they had the sense to ask, and I had the sense to see that 
 none of rny opinions were compromised by compliance. And I 
 will be of any use which does not involve the status of homo trium 
 literarum ; as I have elsewhere explained, I would gladly be 
 Fautor Realis Scientice, but I would not be taken for Falsce 
 Rationis Sacerdos. 
 
 Nothing worse will ever happen to me than the smile which 
 individuals bestow on a man who does not groove. Wisdom, like 
 religion, belongs to majorities ; who can wonder that it should be 
 so thought, when it is so clearly pictured in the New Testament 
 from one end to the other ? 
 
 The counterpart of paradox, the isolated opinion of one or of 
 few, is the general opinion held by all the rest ; and the counter- 
 part of false and absurd paradox is what is called the ' vulgar 
 error,' the pseudodox. There is one great work on this last subject, 
 the Pseudodoxia Epidemica of Sir Thomas Browne, the famous 
 author of the Religio Medici; it usually goes by the name of 
 Browne ' On Vulgar Errors ' (1st ed. 1646 ; 6th, 1672). A careful 
 analysis of this work would show that vulgar errors are frequently 
 opposed by scientific errors ; but good sense is always good sense, 
 and Browne's book has a vast quantity of it. 
 
 As an example of bad philosophy brought against bad observa- 
 tion. The Amphisbaena serpent was supposed to have two heads, 
 one at each end ; partly from its shape, partly because it runs 
 backwards as well as forwards. On this Sir Thomas Browne makes 
 the following remarks : 
 
 And were there any such species or natural kind of animal, it would 
 be hard to make good those six positions of body which, according to 
 the three dimensions, are ascribed unto every Animal ; that is, infra, 
 supra, anfe, retro, dextrosum, sinistrosum: for if (as it is determined) 
 that be the anterior and upper part wherein the senses are placed, and 
 that the posterior and lower part which is opposite thereunto, there is 
 no inferior or former part in this Animal ; for the senses, being placed 
 at both extreams, doth make both ends anterior, which is impossible ; 
 the terms being Relative, which mutually subsist, and are not without 
 each other. And therefore this duplicity was ill contrived to place one 
 head at both extreams, and had been more tolerable to have settled 
 three or four at one. And therefore also Poets have been more reason- 
 able than Philosophers, and Geryon or Cerberus less monstrous than 
 Ampliisbcena. 
 
 There may be paradox upon paradox: and there is a good 
 instance in the eighth century in the case of Virgil, an Irishman, 
 
24 A BUDGET OF PARADOXES. 
 
 Bishop of Salzburg and afterwards Saint, and his quarrels with 
 Boniface, an Englishman, Archbishop of Mentz, also afterwards 
 Saint. All we know about the matter is, that there exists a 
 letter of 748 from Pope Zachary, citing Virgil then, it seems, at 
 most a simple priest, though the Pope was not sure even of that 
 to Eome to answer the charge of maintaining that there is 
 another world (mundus) under our earth (terra}, with another 
 sun and another moon. Nothing more is known : the letter 
 contains threats in the event of the charge being true ; and there 
 history drops the matter. Since Virgil was afterwards a Bishop 
 and a Saint, we may fairly conclude that he died in the full 
 flower of orthodox reputation. It has been supposed and it 
 seems probable that Virgil maintained that the earth is peopled 
 all the way round, so that under some spots there are antipodes ; 
 that his contemporaries, with very dim ideas about the roundness 
 of the earth, and most of them with none at all, interpreted him 
 as putting another earth under ours turned the other way, 
 probably, like the second piece of bread-and-butter in a sandwich, 
 with a sun and moon of its own. In the eighth century this 
 would infallibly have led to an underground Gospel, an under- 
 ground Pope, and an underground Avignon for him to live in. 
 When, in later times, the idea of inhabitants for the planets 
 was started, it was immediately asked whether they had sinned, 
 whether Jesus Christ died for them, whether their wine and their 
 water could be lawfully used in the sacraments, &c. 
 
 On so small a basis as the above has been constructed a com- 
 panion case to the persecution of Galileo. On one side the 
 positive assertion, with indignant comment, that Virgil was 
 deposed for antipodal heresy, on the other, serious attempts at 
 justification, palliation, or mystification. Some writers say that 
 Virgil was found guilty ; others that he gave satisfactory expla- 
 nation, and became very good friends with Boniface: for all 
 which see Bayle. . Some have maintained that the antipodist was 
 a different person from the canonised bishop : there is a second 
 Virgil, made to order. When your shoes pinch, and will not 
 stretch, always throw them away and get another pair : the same 
 with your facts. Baronius was not up to the plan of a substitute : 
 his commentator Pagi (probably writing about 1690) argues for 
 rfc in a manner which I think Baronius would not have approved. 
 This Virgil was perhaps a slippery fellow. The Pope says he 
 hears that Virgil pretended licence from him to claim one of 
 some new bishoprics : this he declares is totally false. It is part 
 of the argument that such a man as this could not have been 
 
INTKODUCTOKY. 25 
 
 created a Bishop and a Saint: on this point there will be opinions 
 and opinions. 1 
 
 Lactantius, four centuries before, had laughed at the antipodes 
 in a manner which seems to be ridicule thrown on the idea of the 
 earth's roundness. Ptolemy, without reference to the antipodes, 
 describes the extent of the inhabited part of the globe in a way 
 which shows that he could have had no objection to men turned 
 opposite ways. Probably, in the eighth century, the roundness of 
 the earth was matter of thought only to astronomers. It should 
 always be remembered, especially by those who affirm persecution 
 of a true opinion, that but for our knowing from Lactantius that 
 the antipodal notion had been matter of assertion and denial 
 among theologians, we could never have had any great confidence 
 in Virgil really having maintained the simple theory of the exist- 
 ence of antipodes. And even now we are not entitled to affirm it 
 as having historical proof: the evidence goes to Virgil having 
 been charged with very absurd notions, which it seems more 
 likely than not were the absurd constructions which ignorant 
 contemporaries put upon sensible opinions of his. 
 
 One curious part of this discussion is, that neither side has 
 allowed Pope Zachary to produce evidence to character. He 
 shall have been an Urban, say the astronomers ; an Urban he 
 ought to have been, say the theologians. What sort of man was 
 Zachary ? He was eminently sensible and conciliatory ; he con- 
 trived to make northern barbarians hear reason in a way which 
 puts him high among that section of the early popes who had 
 the knack of managing uneducated swordsmen. He kept the 
 peace in Italy to an extent which historians mention with ad- 
 miration. Even Bale, that Maharajah of pope-haters, allows 
 himself to quote in favour of Zachary, that 'multa Papalem 
 dignitatem decentia, eademque prseclara (scilicet) opera confecit.' 
 And this, though so willing to find fault that, speaking of 
 Zachary putting a little geographical description of the earth 
 on the portico of the Lateran Church, he insinuates that it was 
 intended to affirm that the Pope was lord of the whole. Nor 
 can he say how long Zachary held the see, except by announcing 
 his death in 752, 'cum decem annis pestilentise sedi praefuisset.' 
 
 1 An Irish antiquary informs me that Virgil is mentioned in annals, at A.D. 784, as 
 1 Verghil, i.e. the geometer, Abbot of Achadhbo [and Bishop of Saltzburg], died in 
 Germany in the thirteenth year of his bishoprick.' No allusion is made to his 
 opinions ; but it seems he was, by tradition, a mathematician. The Abbot of Aghabo 
 (Queen's County) was canonised by Gregory IX., in 1233. The story of the second, 
 or scapegoat, Virgil would be much damaged by the character given to the real 
 bishop, if there were anything in it to dilapidate. 
 
26 A BUDGET OF PARADOXES. 
 
 There was another quarrel between Virgil and Boniface ^ which 
 is an illustration. An ignorant priest had baptised ; in nomine 
 Patrki, et Filia, et Spirituo, Sancta.' Boniface declared the 
 rite null and void ; Virgil maintained the contrary ; and Zachary 
 decided in favour of Virgil, on the ground that the absurd form 
 was only ignorance of Latin, and not heresy. It is hard to^believe 
 that this man deposed a priest for asserting the whole globe to 
 be inhabited. To me the little information that we have seems 
 to indicate but not with certainty that Virgil maintained the 
 antipodes : that his ignorant contemporaries travestied his theory 
 into that of an underground cosmos ; that the Pope cited him 
 to Eome to explain his system, which, as reported, looked like 
 what all would then have affirmed to be heresy ; that he gave 
 satisfactory explanations, and was dismissed with honour. It 
 may be that the educated Greek monk, Zachary, knew his 
 Ptolemy well enough to guess what the asserted heretic would 
 say ; we have seen that he seems to have patronised geography. 
 The description of the earth, according to historians, was a map ; 
 this Pope may have been more ready than another to prick up his 
 ears at any rumour of geographical heresy, from hope of informa- 
 tion. And Virgil, who may have entered the sacred presence as 
 frightened as Jacquard, when Napoleon I. sent for him and said, 
 with a stern voice and threatening gesture, 4 You are the man who 
 can tie a knot in a stretched string,' may have departed as well 
 pleased as Jacquard with the riband and pension which the inter- 
 view was worth to him. 
 
 A word more about Baronius. If he had been pope, as he 
 would have been but for the opposition of the Spaniards, and if 
 he had lived ten years longer than he did, and if Clavius, who 
 would have been his astronomical adviser, had lived five years 
 longer than he did, it is probable, nay almost certain, that the 
 great exhibition, the proceeding against Galileo, would not have 
 furnished a joke against theology in all time to come. For 
 Baronius was sensible and witty enough to say that in the Scrip- 
 tures the Holy Spirit intended to teach how to go to Heaven, 
 not how Heaven goes ; and Clavius, in his last years, confessed 
 that the whole system of the heavens had broken down, and 
 must be mended. 
 
 The manner in which the Galileo case, a reality, and the 
 Virgil case, a fiction, have been hawked against the Eoman see 
 are enough to show that the Pope and his adherents have not 
 cared much about physical philosophy. In truth, orthodoxy has 
 
INTRODUCTORY. 27 
 
 always had other fish to fry. Physics, which in modern times 
 has almost usurped the name philosophy, in England at least, 
 has felt a little disposed to clothe herself with all the honours 
 of persecution which belong to the real owner of the name. 
 But the bishops, &c. of the middle ages knew that the contest 
 between nominalism and realism, for instance, had a hundred 
 times more bearing upon orthodoxy than anything in astronomy, 
 &c. A wrong notion about substance might play the mischief 
 with transubstantiation. 
 
 The question of the earth's motion was the single point in 
 which orthodoxy came into real contact with science. Many 
 students of physics were suspected of magic, many of atheism : but, 
 stupid as the mistake may have been, it was bona fide the magic or 
 the atheism, not the physics, which was assailed. In the astro- 
 nomical case it was the very doctrine, as a doctrine, indepen- 
 dently of consequences, which was the corpus delicti : and this 
 because it contradicted the Bible. And so it did ; for the stability 
 of the earth is as clearly assumed from one end of the Old Testa- 
 ment to the other as the solidity of iron. Those who take the 
 Bible to be totidem verbis dictated by the . (rod of Truth can 
 refuse to believe it ; and they make strange reasons. They 
 undertake, a priori, to settle Divine intentions. The Holy Spirit 
 did not mean to teach natural philosophy : this they know before- 
 hand ; or else they infer it from finding that the earth does move, 
 and the Bible says it does not. Of course, ignorance apart, every 
 word is truth, or the writer did not mean truth. But this puts 
 the whole book on its trial : for we never can find out what the 
 writer meant, until we otherwise find out what is true. Those 
 who like may, of course, declare for an inspiration over which 
 they are to be viceroys ; but common sense will either accept 
 verbal meaning or deny verbal inspiration. 
 
28 A BUDGET OF PARADOXES. 
 
 Questiones Morales, folio, 1489 [Paris]. By T. Buridan. 
 
 This is the title from the Hartwell Catalogue of Law Books. I 
 suppose it is what is elsewhere called the ' Commentary on the 
 Ethics of Aristotle,' printed in 1489. Buridan (died about 1358) 
 is the creator of the famous ass which, as Burdin's ass, was cur- 
 rent in Burgundy, perhaps is, as a vulgar proverb. Spinoza says 
 it was a jenny ass, and that a man would not have been so foolish ; 
 but whether the compliment is paid to human or to masculine 
 character does not appear perhaps to both in one. The story 
 told about the famous paradox is very curious. The Queen of 
 France, Joanna or Jeanne, was in the habit of sewing her lovers 
 up in sacks, and throwing them into the Seine ; not for blab- 
 bing, but that they might not blab certainly the safer plan. 
 Buridan was exempted, and, in gratitude, invented the sophism. 
 What it has to do with the matter has never been explained. 
 Assuredly qui facit per alium facit per se will convict Buridan 
 of prating. The argument is as follows, and is seldom told in 
 full. Buridan was for free-will that is, will which determines 
 conduct, let motives be ever so evenly balanced. An ass is equally 
 pressed by hunger and by thirst ; a bundle of hay is on one side, 
 a pail of water on the other. Surely, you will say, he will not be 
 ass enough to die for want of food or drink ; he will then make 
 a choice that is, will choose between alternatives of equal force. 
 The problem became famous in the schools ; some allowed the 
 poor donkey to die of indecision ; some denied the possibility of 
 the balance, which was no answer at all. 
 
 The following question is more difficult, and involves free-will 
 to all who answer 6 Which you please.' If the northern hemisphere 
 were land, and all the southern hemisphere water, ought we to 
 call the northern hemisphere an island, or the southern hemisphere 
 a lake ? Both the questions would be good exercises for paradoxers 
 who must be kept employed, like Michael Scott's devils. The 
 wizard knew nothing about squaring the circle, &c., so he set 
 them to make ropes out of sea sand, which puzzled them. Stupid 
 devils ! much of our glass is sea sand, and it makes beautiful 
 thread. Had Michael set them to square the circle or to find 
 a perpetual motion, he would have done his work much better. 
 But all this is conjecture : who knows that I have not hit on the 
 very plan he adopted ? Perhaps the whole race of paradoxers 
 on hopeless subjects are Michael's subordinates, condemned to 
 transmigration after transmigration, until their task is done. 
 
THE BUDGET OPENED BUEIDAN. 29 
 
 The above was not a bad guess. A little after the time when 
 the famous Pascal papers were produced, I came into possession 
 of a correspondence which, but for these papers, I should have 
 held too incredible to be put before the world. But when one 
 sheep leaps the ditch, another will follow : so I gave the following 
 account in the AtTienceum of October 5, 1867 : 
 
 The recorded story is that Michael Scott, being bound by contract 
 to procure perpetual employment for a number of young demons, was 
 worried out of his life in inventing jobs for them, until at last he set 
 them to make ropes out of sea sand, which they never could do. We 
 have obtained a very curious correspondence between the wizard 
 Michael and his demon- slaves ; but we do not feel at liberty to say how 
 it came into our hands. We much regret that we did not receive it 
 in time for the British Association. It appears that the story, true as 
 far as it goes, was never finished. The demons easily conquered the 
 rope difficulty, by the simple process of making the sand into glass, 
 and spinning the glass into thread, which they twisted. Michael, 
 thoroughly disconcerted, hit upon the plan of setting some to square 
 the circle, others to find the perpetual motion, &c. He commanded 
 each of them to transmigrate from one human body into another, until 
 their tasks were done. This explains the whole succession of cyclo- 
 meters, and all the heroes of the Budget. Some of this correspondence 
 is very recent ; it is much blotted, and we are not quite sure of its 
 meaning : it is full of figurative allusions to driving something illegible 
 down a steep into the sea. It looks like a humble petition to be 
 allowed some diversion in the intervals of transmigration ; and the 
 
 answer is 
 
 Eumpat et serpens iter institutum, 
 
 a line of Horace, which the demons interpret as a direction to come 
 athwart the proceedings of the Institute by a sly trick. Until we saw 
 this, we were suspicious of M. Libri : the unvarying blunders of the 
 correspondence look like knowledge. To be always out of the road 
 requires a map : genuine ignorance occasionally lapses into truth. We 
 thought it possible M. Libri might have played the trick to show how 
 easily the French are deceived ; but with our present information, our 
 minds are at rest on the subject. We see M. Chasles does not like to 
 avow the real source of information : he will not confess himself a 
 spiritualist. 
 
30 A BUDGET OF PAKADOXES. 
 
 Philo of Gradara is asserted by Montucla, on the authority of 
 Eutocius, the commentator on Archimedes, to have squared the 
 circle within the ten-thousandth part of a unit, that is, to four 
 places of decimals. A modern classical dictionary represents it as 
 done by Philo to ten thousand places of decimals. Lacroix com- 
 ments on Montucla to the effect that myriad (in Greek ten thou- 
 sand) is here used as we use it, vaguely, for an immense number. 
 On looking into Eutocius, I find that not one definite word is 
 said about the extent to which Philo carried the matter. I give 
 a translation of the passage : 
 
 We ought to know that Apollonius Pergaeus, in his Ocytocium [this 
 work is lost], demonstrated the same by other numbers, and came 
 nearer, which seems more accurate, but has nothing to do with 
 Archimedes ; for, as before said, he aimed only at going near enough 
 for the wants of life. Neither is Porus of Nicaea fair when he takes 
 Archimedes to task for not giving a line accurately equal to the 
 circumference. He says in his Cerii that his teacher, Philo of Gadara, 
 had given a more accurate approximation (etc aKpifievrfpovc apiftpovg 
 ayayeii') than that of Archimedes, or than 7 to 22. But all these [the 
 rest as well as Philo] miss the intention. They multiply and divide by 
 tens of thousands j which no one can easily do, unless he be versed in 
 the logistics [fractional computation] of Magnus [now unknown]. 
 
 Montucla, or his source, ought not to have made this mistake. 
 He had been at the Greek to correct Philo Gadetanus, as he had 
 often been called, and he had brought away and quoted airo 
 TaSapcov. Had he read two sentences further, he would have 
 found the mistake. 
 
 We here detect a person quite unnoticed hitherto by the 
 moderns, Magnus the arithmetician. The phrase is ironical ; it 
 is as if we should say, 4 To do this a man must be deep in Cocker.' 
 Accordingly, Magnus, Baveme, and Cocker, are three personifica- 
 tions of arithmetic ; and there may be more. 
 
 Aristotle, treating of the category of relation, denies that the 
 quadrature has been found, but appears to assume that it can be 
 done. Boethius, in his comment on the passage, says that it 'has 
 been done since Aristotle, but that the demonstration is too long 
 for him to give. Those who have no notion of the quadrature 
 question may look at the English Cyclopaedia, art. 'Quadrature 
 of the Circle.' 
 
EAELY CIRCLE SQUARERS. 31 
 
 Tetragonisrnus. Id est circuli quadratura per Campanum, 
 Arehimedem Syracusanum, atque Boetium mathematics per- 
 spicacissimos adinventa. At the end, Impressum Yenetiis per 
 loan. Bapti. Sessa. Anno ab incarnatione Domini, 1503. Die 
 28 Augusti. 
 
 This book has never been noticed in the history of the subject, 
 and I cannot find .any mention of it. The quadrature of Campanus 
 takes the ratio of Archimedes, 7 to 22, to be absolutely correct ; 
 the account given of Archimedes is not a translation of his book ; 
 and that of Boetius has more than is in Boet/iius. This book 
 must stand, with the next, as the earliest in print on the subject, 
 until further showing : Murhard and Kastner have nothing so 
 early. It is edited by Lucas Grauricus, who has given a short 
 preface. Luca Graurico, Bishop of Civita Ducale, an astrologer 
 of astrologers, published this work at about thirty years of age, 
 and lived to eighty-two. His works are collected in folios, but I 
 do not know whether they contain this production. The poor fellow 
 could never tell his own fortune, because his father neglected to 
 note the hour and minute of his birth. But if there had been 
 anything in astrology, he could have worked back, as Adams and 
 Leverrier did when they caught Neptune : at sixty he could have 
 examined every minute of his day of birth, by the events of his 
 life, and so would have found the right minute. He could then 
 have gone on, lay rules of prophecy. Grauricus was the mathe- 
 matical teacher of Joseph Scaliger, who did him no credit, as we 
 shall see. 
 
 In hoc opere contenta Epitome Liber de quadratura 
 
 Circuli Paris, 1503, folio. 
 
 The quadrator is Charles Bovillus, who adopted the views of 
 Cardinal Cusa, presently mentioned. Montucla is hard on his 
 compatriot, who, he says, was only saved from the laughter of 
 geometers by his obscurity. Persons must guard against most 
 historians of mathematics in one point : they frequently attribute 
 to his own age the obscurity which a writer has in their own time. 
 This tract was printed by Henry Stephens, at the instigation of 
 Faber Stapulensis, and is recorded by Dechales, &c. It was also 
 introduced into the ; Margarita Philosophica' of 1815, in the 
 same appendix with the new perspective from Viator. This is not 
 extreme obscurity, by any means. The quadrature deserved it ; 
 but that is another point. 
 
32 A BUDGET OF PARADOXES. 
 
 It is stated by Montucla that Bovillus makes TT = x/10. But 
 Montucla cites a work of 1507, Introductorium Geometricum, 
 which I have never seen. He finds in it an account which 
 Bovillus gives of the quadrature of the peasant labourer, and 
 describes it as agreeing with his own. But the description makes 
 TT = 3, which it thus appears Bovillus could not distinguish 
 from VIO. It seems also that this 3, about which we shall see 
 so much in the sequel, takes its rise in the thoughtful head of a 
 poor labourer. It does him great honour, being so near the truth, 
 and he having no means of instruction. In our day, when an 
 ignorant person chooses to bring his fancy forward in opposition 
 to demonstration which he will not study, he is deservedly 
 laughed at. 
 
 Mr. James Smith, of Liverpool hereinafter notorified attri- 
 butes the first announcement of 3 to M. Joseph Lacomme, a 
 French well-sinker, of whom he gives the following account : 
 
 In the year 1836, at which time Lacomme could neither read nor 
 write, he had constructed a circular reservoir and wished to know the 
 quantity of stone that would be required to pave the bottom, and for 
 this purpose called on a professor of mathematics. On putting his 
 question and giving the diameter, he was surprised at getting the 
 following answer from the Professor ' Qu'il lui &ait impossible de le lui 
 dire au juste, attendu quepersonne n'avait encore pu trouver d'une maniere 
 exacte le rapport de la cir -conference au diametre.' From this he was 
 led to attempt the solution of the problem. His first process was 
 purely mechanical^ and he was so far convinced he had made the dis- 
 covery that he took to educating himself, and became an expert 
 arithmetician, and then found that arithmetical results agreed with his 
 mechanical experiments. He appears to have eked out a bare existence 
 for many years by teaching arithmetic, all the time struggling to get a 
 hearing from some of the learned societies, but without success. In 
 the year 1855 he found his way to Paris, where, as if by accident, he 
 made the acquaintance of a young gentleman, son of M. Winter, a 
 commissioner of police, and taught him his peculiar methods of calcu- 
 lation. The young man was so enchanted that he strongly recom- 
 mended Lacomme to his father, and subsequently through M. Winter 
 he obtained an introduction to the President of the Society of Arts and 
 Sciences of Paris. A committee of the society was appointed to 
 examine and report upon his discovery, and the society at its seance 
 of March 17, 1856, awarded a silver medal of the first class to 
 M. Joseph Lacomme for his discovery of the true ratio of diameter 
 to circumference in a circle. He subsequently received three other 
 medals from other societies. While writing this I have his likeness 
 before me, with his medals on his breast, which stands as a frontispiece 
 
NICHOLAS OF CUSA AORIPPA. 33 
 
 to a short biography of this extraordinary man, for which I am in- 
 debted to the gentleman who did me the honour to publish a French 
 translation of the pamphlet I distributed at the meeting of the British 
 Association for the Advancement of Science, at Oxford, in 1860. 
 Correspondent, May 3, 1866. 
 
 My inquiries show that the story of the medals is not incredible. 
 There are at Paris little private societies which have not so much 
 claim to be exponents of scientific opinion as our own Mechanics' 
 Institutes. Some of them were intended to give a false lustre : as 
 the ' Institut Historique," the members of which are ' Membre de 
 1'Institut Historique.' That M. Lacomme should have got four 
 medals from societies of this class is very possible : that he should 
 have received one from any society at Paris which has the least 
 claim to give one is as yet simply incredible. 
 
 Nicolai de Cusa Opera Omnia. Venice, 1514. 3 vols. folio. 
 
 The real title is 'Hsec accurata recognitio trium voluminum 
 operum clariss. P. Nicolai Cusae . , . proxime sequens pagina 
 monstrat.' Cardinal Cusa, who died in 1 464, is one of the earliest 
 modern attempters. His quadrature is found in the second 
 volume, and is now quite unreadable. In these early days every 
 quadrator found a geometrical opponent, who finished him. 
 Regiomontanus did this office for the Cardinal. 
 
 De Occulta Philosophia libri III. By Henry Cornelius Agrippa. 
 
 Lyons, 1550, 8vo. 
 De incertitudine et vanitate scientiarum. By the same. Cologne, 
 
 1531, 8vo. 
 
 The first editions of these works were of 1530, as well as I can 
 make out; but the first was in progress in 1510. In the second 
 work Agrippa repents of having wasted time on the magic of the 
 first ; but all those who actually deal with demons are destined 
 to eternal fire with Jamnes and Mambres and Simon Magus. 
 This means, as is the fact, that his occult philosophy did not actu- 
 ally enter upon black magic, but confined itself to the power of 
 the stars, of numbers, &c. The fourth book, which appeared after 
 the death of Agrippa, and really concerns dealing with evil spirits, 
 is undoubtedly spurious. It is very difficult to make out what 
 Agrippa really believed on the subject. I have introduced his 
 books as the most marked specimens of treatises on magic, a 
 paradox of our day, though not far from orthodoxy in his ; and 
 here I should have ended my notice, if I had not casually found 
 something more interesting to the reader of our day. 
 
34 A BUDGET OF PARADOXES. 
 
 Walter Scott, it is well known, was curious on all matters 
 connected with magic, and has used them very widely. But it is 
 hardly known how much pains he has taken to be correct, and to 
 give the real thing. The most decided detail of a magical pro- 
 cess which is found in his writings is that of Dousterswivel in 
 4 The Antiquary ' ; and it is obvious, by his accuracy of process, 
 that he does not intend the adept for a mere impostor, but for 
 one who had a lurking belief in the efficacy of his own processes, 
 coupled with intent to make a fradulent use of them. The 
 materials for the process are taken from Agrippa. I first quote 
 Mr. Dousterswivel : 
 
 ... I take a silver plate when she [the moon] is in her fifteenth 
 mansion, which mansion is in de head of Libra, and I engrave upon one 
 side de worts 8chedbarschemoth Schartachan \_cli should be t\ dat is, 
 de Intelligence of de Intelligence of de moon and I make his picture 
 like a flying serpent with a turkey-cock's head vary well Then upon 
 this side I make de table of de moon, which is a square of nine, 
 multiplied into itself, with eighty-one numbers [nine] on every side, 
 and diameter nine. . . . 
 
 In the'De Occulta Philosophia,' p. 290, we find that the 
 fifteenth mansion of the moon incipit capite Librae, and is good 
 pro extrahendis thesauris, the object being to discover hidden 
 treasure. In p. 246, we learn that a silver plate must be used 
 with the moon. In p. 248, we have the words which denote the 
 Intelligence, &c. But, owing to the falling of a number into a 
 wrong line, or the misplacement of a line, one or other which 
 takes place in all the editions I have examined Scott has, sad 
 to say, got hold of the wrong words ; he has written down the 
 demon of the demons of the moon. Instead of the gibberish 
 above, it should have been Malcha betharsisim hed beruah sche- 
 hakim. In p. 253, we have the magic square of the moon, with 
 eighty-one numbers, and the symbol for the Intelligence, which 
 Scott likens to a flying serpent with a turkey-cock's head. He 
 was obliged to say something ; but I will stake my character 
 and so save a woodcut on the scratches being more like a pair 
 of legs, one shorter than the other, without a body, jumping over 
 a six-barred gate placed side uppermost. Those who thought 
 that Scott forged his own nonsense, will henceforth stand corrected. 
 As to the spirit Peolphan, &c., no doubt Scott got it from the 
 authors he elsewhere mentions, Nicolaus Eemigius and Petrus 
 Thyracus ; but this last word should be Thyrgeus. 
 
 The tendency of Scott's mind towards prophecy is very marked, 
 
OEONTIUS FINAEUS-UKSUS. 35 
 
 and it is always fulfilled. Hyder, in his disguise, calls out to 
 
 Tippoo ' Cursed is the prince who barters justice for lust ; he 
 
 shall die in the gate by the sword of the stranger.' Tippoo was 
 killed in a gateway at Seringapatam. 
 
 Orontii Finaei. . . Quadratura Circuli. Paris, 1544, 4to. 
 
 Orontius squared the circle out of all comprehension ; but he 
 was killed by a feather from his own wing. His former pupil, 
 John Buteo, the same who I believe for the first time calculated 
 the question of Noah's ark, as to its power to hold all the animals 
 and stores, unsquared him completely. Orontius was the author 
 of very many works, and died in 1555. Among the laudatory 
 verses which, as was usual, precede this work, there is one of a 
 rare character : a congratulatory ode to the wife of the author. 
 The French now call this writer Oronce Finee ; but there is much 
 difficulty about delatinisation. Is this more correct than Oronce 
 Fine, which the translator of De Thou uses ? Or than Horonce 
 Phine, which older writers give ? I cannot understand why M. 
 de Viette should be called Viete, because his Latin name is Vieta. 
 It is difficult to restore Buteo ; for not only now is butor a block- 
 head as well as a bird, but we really cannot know what kind of 
 bird Buteo stood for. We may be sure that Madame Fine was 
 Denise Blanche ; for Dionysia Candida can mean nothing else. 
 Let her shade rejoice in the fame which Hubertus Sussannseus 
 has given her. 
 
 I ought to add that the quadrature of Orontius, and solutions 
 of all the other difficulties, were first published in c De Rebus 
 Mathematicis Hactenus Desideratis,' of which I have not the date. 
 
 Nicolai Raymari Ursi Dithmarsi Fundamentum Astronomicum, 
 id est, nova doctrina sinuum et triangulorum. . . . Strasburg, 
 1588, 4to. 
 
 People choose the name of this astronomer for themselves : I 
 take Ursus, because he was a bear. This book gave the quadra- 
 ture of Simon Duchesne, or a Quercu, which excited Peter Metius, 
 as presently noticed. It also gave that unintelligible reference to 
 Justus Byrgius which has been used in the discussion about the 
 invention of logarithms. 
 
 The real name of Duchesne is Van der Eycke. "I have met 
 with a tract in Dutch, Letterkundige Aanteekeningen, upon Van 
 Eycke, Van Ceulen, &c., by J. J. Dodt van Flensburg, which I 
 make out to be since 1841 in date. I should much like a trans- 
 
 D 2 
 
36 A BUDGET OF PAKADOXES. 
 
 lation of this tract to be printed, say in the Phil. Mag. Dutch 
 would be clear English if it were properly spelt. For example, 
 learn-master would be seen at once to be teacher ; but they will 
 spell it leermeester. Of these they write as van deze; widow 
 they make weduwe. All this is plain to me, who never saw a 
 Dutch dictionary in my life ; but many of their mispellings are 
 quite unconquerable. 
 
 Jacobus Falco Valentinus, miles Ordinis Montesiani, hanc circuli 
 quadraturam invenit. Antwerp, 1589, 4to. 
 
 The attempt is more than commonly worthless ; but as Mon- 
 tucla and others have referred to the verses at the end, and as the 
 tract is of the rarest, I will quote them : 
 
 Circulus loquitur. 
 
 Vocabar ante circulus 
 Eramque curvus nndique 
 Ut alta solis orbita 
 Et arcus ille nubium. 
 Eram figura nobilis 
 Carensque sola origine 
 Carensque sola termino. 
 Modo indecora prodeo 
 Novisque foedor angulis. 
 Nee hoc peregit Archytas 
 Neque Icari pater neque 
 Tims lapete films. 
 Quis ergo casus aut Deus 
 Meam quadravit aream ? 
 
 Respondet auctor. 
 
 Ad alta Turias ostia 
 Lacumque limpidissimum 
 Sita est beata civitas 
 Parum Saguntus abfuit 
 Abestque Sucro plusculum. 
 Hie est poeta quispiam 
 Libenter astra consulens 
 Sibique semper arrogans 
 Negata doctioribus. 
 Senex ubique cogitans 
 Sui frequenter immemor 
 Nee explicare circinum 
 
PETER BUNaUS. 37 
 
 Nee exarare lineas 
 Sciens nt ipse preedicat. 
 Hie ergo bellus artifex 
 Tuam quadravit aream. 
 
 Falco's verses are pretty, if the ^ " mysteries be correct ; but of 
 these things I have forgotten what I knew. [One mistake has 
 been pointed out to me : it is Archytas]. 
 
 As a specimen of the way in which history is written, I copy 
 the account which Montucla who is accurate when he writes 
 about what he has seen gives of these verses. He gives the date 
 1587 ; he places the verses at the beginning instead of the end; 
 he says the circle thanks its quadrator affectionately ; and he 
 says the good and modest chevalier gives all the glory to the 
 patron saint of his order. All of little consequence, as it happens ; 
 but writing at second-hand makes as complete mistakes about 
 more important matters. 
 
 Petri Bungi Bergomatis Numerorum mysteria. Bergomi [Ber- 
 gamo], 1591, 4to. Second Edition. 
 
 The first edition is said to be of 1585 ; the third, Paris, 1618. 
 Bungus is not for my purpose on his own score, but those who 
 gave the numbers their mysterious characters : he is but a collector. 
 He quotes or uses 402 authors, as we are informed by his list : 
 this just beats Warburton, whom some eulogist or satirist, I forget 
 which, holds up as having used 400 authors in some one work. 
 Bungus goes through 1, 2, 3, &c., and gives the account of every- 
 thing remarkable in which each number occurs ; his accounts not 
 being always mysterious. The numbers which have nothing to 
 say for themselves are omitted : thus there is a gap between 50- 
 and 60. In treating 666, Bungus, a good Catholic, could not 
 compliment the Pope with it, but he fixes it on Martin Luther 
 with a little forcing. If from A to I represent 1-10, from K to 
 S 10-90, and from T to Z 100-500, we see 
 
 MARTIN LIT TERA 
 
 30 1 80 100 9 40 20 200 100 5 80 1 
 
 which gives 666. Again, in Hebrew, Lulter does the same : 
 
 i n t> i *> 
 
 200 400 30 6 30 
 
 And thus two can play at any game. The second is better 
 than the first : to Latinise the surname and not the Christian 
 name is very unscholarlike. The last number mentioned is a 
 
38 A BUDGET OF PAKADOXES. 
 
 thousand millions ; all greater numbers are dismissed in half a 
 page. Then follows an accurate distinction between number 
 and multitude a thing much wanted both in arithmetic and 
 logic. 
 
 What may be the use of such a book as this ? The last occa- 
 sion on which it was used was the following. Fifteen or sixteen 
 years ago the Eoyal Society determined to restrict the number of 
 yearly admissions to fifteen men of science, and noblemen ad 
 libitum ; the men of science being selected and recommended by 
 the Council, with a power, since practically surrendered, to the 
 Society to elect more. This plan appears to me to be directly 
 against the spirit of their charter, the true intent of which is, 
 that all who are fit should be allowed to promote natural know- 
 ledge in association, from and after the time at which they are 
 both fit and willing. It is also working more absurdly from year 
 to year ; the tariff of fifteen per annum will soon amount to the 
 practical exclusion of many who would be very useful. This 
 begins to be felt already, I suspect. But, as appears above, the 
 body of the Society has the remedy in its own hands. When the 
 alteration was discussed by the Council, my friend the late Mr. 
 Galloway, then one of the body, opposed it strongly, and in- 
 quired particularly into the reason why fifteen, of all numbers, 
 was the one to be selected. Was it because fifteen is seven and 
 eight, typifying the Old Testament Sabbath, and the New Testa- 
 ment day of the resurrection following ? Was it because Paul 
 strove fifteen days against Peter, proving that he was a doctor 
 both of the Old and New Testament ? Was it because the prophet 
 Hosea bought a lady for fifteen pieces of silver ? Was it because, 
 according to Micah, seven shepherds and eight chiefs should 
 ^ waste the Assyrians ? Was it because Ecclesiastes commands 
 equal reverence to be given to both Testaments such was the 
 interpretation in the words c Give a portion to seven, and also 
 to eight' ? Was it because the waters of the Deluge rose fifteen 
 cubits above the mountains ? or because they lasted fifteen 
 decades of days ? Was it because Ezekiel's temple had fifteen 
 steps ? Was it because Jacob's ladder has been supposed to have 
 had fifteen steps ? Was it because fifteen years were added to 
 the life of Hezekiah ? Was it because the feast of unleavened 
 bread was on the fifteenth day of the month ? Was it because 
 the scene of the Ascension was fifteen stadia from Jerusalem ? 
 Was it because the stone-masons and porters employed in 
 Solomon's temple amounted to fifteen myriads ? &c. The Council 
 were amused and astounded by the volley of fifteens which was 
 
THE FIFTEENS OF BUNGUS. 39 
 
 fired at them ; they knowing nothing* about Bungus, of which 
 Mr. G-alloway who did not, as the French say, indicate his 
 sources possessed the copy now before me. In giving this 
 anecdote I give a specimen of the book, which is exceedingly rare. 
 Should another edition ever appear, which is not very probable, 
 he would be but a bungling Bungus who should forget the fifteen 
 of the Eoyal Society. 
 
 [I make a remark on the different colours which the same 
 person gives to one story, according to the bias under which he 
 tells it. My friend Galloway told me how he had quizzed the 
 Council of the Eoyal Society, to my great amusement. When- 
 ever I ana struck by the words of any one, I carry away a vivid 
 recollection of position, gestures, tones, &c. I do not know 
 whether this be common or uncommon. I never recall this joke 
 without seeing before me my friend, leaning against his book- 
 case, with Bungus open in his hand, and a certain half-deprecia- 
 tory tone which he often used when speaking of himself. Long 
 after his death, an F.E.S. who was present at the discussion, told 
 me the story. I did not say I had heard it, but I watched him, 
 with Gralloway at the bookcase before me. I wanted to see 
 whether the two would agree as to the fact of an enormous 
 budget of fifteens having been fired at the Council, and they 
 did agree perfectly. But when the paragraph of the Budget 
 appeared in the Athenceum, my friend, who seemed rather to 
 object to the shewing-up, assured me that the thing was grossly 
 exaggerated ; there was indeed a fifteen or two, but nothing like 
 the number I had given. I had, however, taken sharp note of 
 the previous narration. 
 
 I will give another instance. An Indian officer gave me an 
 account of an elephant, as follows. A detachment was on the 
 march, and one of the gun-carriages got a wheel off the track, 
 so that it was also off the ground, and hanging over a precipice. 
 If the bullocks had moved a step, carriages, bullocks, and all 
 must have been precipitated. No one knew what could be done 
 until some one proposed to bring up an elephant, and let him 
 manage it his own way. The elephant took a moment's survey of 
 the fix, put his trunk under the axle of the free wheel, and waited. 
 The surrounders, who saw what he meant, moved the bullocks 
 gently forward, the elephant followed, supporting the axle, until 
 there was ground un'der the wheel, when he let it quietly down. 
 From all I had heard of the elephant, this was not too much 
 to believe. But when, years afterwards, I reminded my friend 
 
 OF THK SJ r~ 
 
 TT TST T T7 V R ci f nn "V 
 
40 A BUDGET OF PARADOXES. 
 
 of his story, he assured me that I had misunderstood him, that 
 the elephant was directed to put his trunk under the wheel, and 
 saw in a moment why. This is reasonable sagacity, and very 
 likely the correct account ; but I am quite sure that, in the fit 
 of elephant-worship under which the story was first told, it was 
 told as I have first stated it.] 
 
 [Jordani Bruni Nolani de Monade, Numero et Figura . . . item de 
 Innumerabilibus, Immense, et Infigurabili. . . Frankfort, 1591, 
 8vo. 
 
 I cannot imagine how I came to omit a writer whom I have 
 known so many years, unless the following story will explain it. 
 The officer reproved the boatswain for perpetual swearing ; the 
 boatswain answered that he heard the officers swear. 6 Only in 
 an emergency,' said the officer. ; That's just it,' replied the 
 other ; c a boatswain's life is a life of 'mergency.' Giordano 
 Bruno was all paradox; and my mind was not alive to his 
 paradoxes, just as my ears might have become dead to the boat- 
 swain's oaths. He was, as has been said, a vorticist before 
 Descartes, an optimist before Leibnitz, a Copernican before 
 Galileo. It would be easy to collect a hundred strange opinions 
 of his. He was born about 1550, and was roasted alive at Eome, 
 February 17, 1600, for the maintenance and defence of the holy 
 Church, and the rights and liberties of the same. These last 
 words are from the writ of our own good James I., under which 
 Leggatt was roasted at Smithfield, in March 1612 ; and if I had a 
 copy of the instrument under which Wightman was roasted at 
 Litchfield, a month afterwards, I daresay I should find something 
 quite as edifying. I extract an account which I gave of Bruno 
 in the Comp. Aim. for 1855 : 
 
 He was first a Dominican priest, then a Calvinist ; and was roasted 
 alive at Rome, in 1600, for as many heresies of opinion, religious and 
 philosophical, as ever lit one fire. Some defender's of the papal cause 
 have at least worded their accusations so to be understood as imputing 
 to him villainous actions. But it is positively certain that his death 
 was due to opinions alone, and that retractation, even after sentence, 
 would have saved him. There exists a remarkable letter, written from 
 Home on the very day of the murder, by Scioppius (the celebrated 
 scholar, a waspish convert from Lutheranism, known by his hatred to 
 Protestants and Jesuits) to Rittershusius, a well-known Lutheran 
 writer on civil and canon law, whose works are in the index of prohi- 
 bited books. This letter has been reprinted by Libri (vol. iv. p. 407). 
 The writer informs his friend (whom he wished to convince that even a 
 Lutheran would have burnt Bruno) that all Rome would tell him that 
 
GIOKDANO BRUNO. 41 
 
 Bruno died for Lutheranism ; but this is because the Italians do not 
 know the difference between one heresy and another, in which simpli- 
 city (says the writer) may God preserve them. That is to say, they 
 knew the difference between a live heretic and a roasted one by actual 
 inspection, but had no idea of the difference between a Lutheran and a 
 Calvinist. The countrymen of Boccaccio would have smiled at the idea 
 which the German scholar entertained of them. They said Bruno was 
 burnt for Lutheranism, a name under which tbey classed all Protestants : 
 and they are better witnesses than Schopp, or Scioppius. He then 
 proceeds to describe to his Protestant friend (to whom he would 
 certainly not have omitted any act which both their Churches would 
 have condemned) the mass of opinions with which Bruno was charged ; 
 as that there are innumerable worlds, that souls migrate, that Moses 
 was a magician, that the Scriptures are a dream, that only the Hebrews 
 descended from Adam and Eve, that the devils would be saved, that 
 Christ was a magician and deservedly put to death, &c. In fact, says 
 he, Bruno has advanced all that was ever brought forward by all 
 heathen philosophers, and by all heretics, ancient and modern. A time 
 for retractation was given, both before sentence and after, which should 
 be noted, as well for the wretched palliation which it may afford, as for 
 the additional proof it gives that opinions, and opinions only, brought 
 him to the stake. In this medley of charges the Scriptures are a dream, 
 while Adam, Eve, devils, and salvation are truths, and the Saviour a 
 deceiver. We have examined no work of Bruno except the De Monade, 
 fyc., mentioned in the text. A strong though strange theism runs 
 through the whole, and Moses, Christ, the Fathers, &c., are cited in a 
 manner which excites no remark either way. Among the versions of 
 the cause of Bruno's death is atheism : but this word was very often 
 used to denote rejection of revelation, not merely in the common course 
 of dispute, but by such writers, for instance, as Brucker and Morhof. 
 Thus Morhof says of the De Monade, fyc., that it exhibits no manifest 
 signs of atheism. What he means by the word is clear enough, when 
 he thus speaks of a work which acknowledges God in hundreds of 
 places, and rejects opinions as blasphemous in several. The work of 
 Bruno in which his astronomical opinions are contained is De Monade, 
 tyc. (Frankfort, 1591, 8vo). He is the most thorough-going Copernican 
 possible, and throws out almost every opinion, true or false, which has 
 ever been discussed by astronomers, from the theory of innumerable 
 inhabited worlds and systems to that of the planetary nature of comets. 
 Libri (vol. iv.) has reprinted the most striking part of his expressions 
 of Copernican opinion. 
 
 The Satanic doctrine that a Church may employ force in aid 
 of its dogma is supposed to be obsolete in England, except as an 
 individual paradox ; but this is difficult to settle. Opinions 
 are much divided as to what the Roman Church would do in 
 
42 A BUDGET OF PARADOXES. 
 
 England, if she could : any one who doubts that she claims the 
 right does not deserve an answer. When the hopes of the 
 Tractarian section of the High Church were in bloom, before the 
 most conspicuous intellects among them had transgressed their 
 ministry, that they might go to their own place, I had the curiosity 
 to see how far it could be ascertained whether they held the 
 only doctrine which makes me the personal enemy of a sect. I 
 found in one of their tracts the assumption of a right to per- 
 secute, modified by an asserted conviction that force was not 
 efficient. I cannot now say that this tract was one of the 
 celebrated ninety ; and on looking at the collection I find it so 
 poorly furnished with contents, &c., that nothing but searching 
 through three thick volumes would decide. In these volumes I 
 find, augmenting as we go on, declarations about the character 
 and power of ' the Church ' which have a suspicious appearance. 
 The suspicion is increased by that curious piece of sophistry, 
 No. 87, on religious reserve. The queer paradoxes of that tract 
 leave us in doubt as to everything but this, that the church(man) 
 is not bound to give his whole counsel in all things, and not 
 bound to say what the things are in which he does not give it. 
 It is likely enough that some of the 6 rights and liberties ' are 
 but scantily described. There is now no fear ; but the time was 
 when, if not fear, there might be a looking for of fear to come ; 
 nobody could then be so sure as we now are that the lion was 
 only asleep. There was every appearance of a harder fight at 
 hand than was really found needful. 
 
 Among other exquisite quirks of interpretation in the No. 87 
 above mentioned is the following. Grod himself employs re- 
 serve ; he is said to be decked with light as with a garment (the 
 old or prayer-book version of Psalm civ. 2). To an ordinary 
 apprehension this would be a strong image of display, manifesta- 
 tion, revelation ; but there is something more. ' Does not a 
 garment veil in some measure that which it clothes ? Is not 
 that very light concealment ? ' 
 
 This No. 87, admitted into a series, fixes upon the managers 
 of the series, who permitted its introduction, a strong presump- 
 tion of that underhand intent with which they were charged. 
 At the same time it is honourable to our liberty that this series 
 could be published : though its promoters were greatly shocked 
 when the Essayists and Bishop Colenso took a swing on the 
 other side. When No. 90 was under discussion, Dr. Maitland, 
 the librarian at Lambeth, asked Archbishop Howley a question 
 about No. 89. * I did not so much as know there was a No. 89,' 
 
RITUALISM. 43 
 
 was the answer. I am almost sure I have seen this in print, 
 and quite sure that Dr. Maitland told it to me. It is creditable 
 that there was so much freedom ; but No. 90 was too bad, and 
 was stopped. 
 
 The Tractarian mania has now (October 1866) settled down 
 into a chronic vestment disease, complicated with fits of tran- 
 substantiation, which has taken the name of Ritualism. The 
 common sense of our national character will not put up with a 
 continuance of this grotesque folly ; millinery in all its branches 
 will at last be advertised only over the proper shops. I am told 
 that the Eitualists give short and practical sermons ; if so, they 
 may do good in the end. The English Establishment has always 
 contained those who want an excitement ; the New Testament, 
 in its plain meaning, can do little for them. Since the Ee volu- 
 tion, Jacobitism, Wesleyanism, Evangelicism, Puseyism, and 
 Eitualism, have come on in turn, and have furnished hot water 
 for those who could not wash without it. If the Eitualists should 
 succeed in substituting short and practical teaching for the 
 high-spiced lectures of the doctrinalists, they will be remembered 
 with praise. John the Baptist would perhaps not have brought 
 all Jerusalem out into the wilderness by his plain and good 
 sermons : it was the camel's hair and the locusts which got him 
 a congregation, and which, perhaps, added force to his precepts. 
 When at school I heard a dialogue, between an usher and the 
 
 man who cleaned the shoes, about Mr. , a minister, a very 
 
 corporate body with due area of waistcoat. ' He is a man of 
 great erudition,' said the first. ' Ah, yes, sir,' said Joe ; ' any- 
 one can see that who looks at that silk waistcoat.'] 
 
 [When I said at the outset that I had only taken books 
 from my own store, I should have added that I did not make any 
 search for information given as part of a work. Had I looked 
 through all my books, I might have made some curious additions. 
 For instance, in Schott's Magia Naturalis (vol. iii. pp. 756-778) 
 is an account of the quadrature of Grephyrauder, as he is mis- 
 printed in Montucla. He was Thomas Grephyrander Salicetus ; 
 and he published two editions, in 1608 and 1609 : I never even 
 heard of a copy of either. His work is of the extreme of absurdity : 
 he makes a distinction between geometrical and arithmetical frac- 
 tions, and evolves theorems from it. More curious than his quad- 
 rature is his name ; what are we to make of it ? If a German, he is 
 probably a Grerman form of Bridgeman, and Salicetus refers him to 
 Weiden. But Thomas was hardly a Grerman Christian name of his 
 
44 A BUDGET OF PARADOXES. 
 
 time ; of 526 Grerman philosophers, physicians, lawyers, and theolo- 
 gians who were biographed by Melchior Adam, only two are of this 
 name. Of these one is Thomas Erasfcus, the physician whose theolo- 
 gical writings against the Church as a separate power have given the 
 name of Erastians to those who follow his doctrine, whether they 
 have heard of him or not. Erastus is little known ; accordingly, 
 some have supposed that he must be Erastus, the friend of St. 
 Paul and Timothy (Acts xix. 22 ; 2 Tim. iv. 20 ; Eom. xvi. 23), 
 but what this gentleman did to earn the character is not hinted 
 at. Few words would have done : Graius (Eom. xvi. 23) has an 
 immortality which many more noted men have missed, given by 
 John Bunyan, out of seven words of St. Paul. I was once told 
 that the Erastians got their name from Blastus, and I could not 
 solve bl = er : at last I remembered that Blastus was a chamber- 
 lain as well as Erastus ; hence the association which caused the 
 mistake. The real heresiarch was a physician who died in 1583 ; 
 his heresy was promulgated in a work, published immediately 
 after his death by his widow, De Excommunicatione Ecclesiastica. 
 He denied the power of excommunication on the principle above 
 stated ; and was answered by Beza. The work was translated by 
 Dr. E. Lee (Edinb. 1844, 8vo). The other is Thomas Grrynaeus, 
 a theologian, nephew of Simon, who first printed Euclid in Greek ; 
 of him Adam says that of works "he published none, of learned 
 sons four. If Grephyrander were a Frenchman, his name is not so 
 easily guessed at ; but he must have been of La Saussaye. The 
 account given by Schott is taken from a certain Father Philip 
 Colbinus, who wrote against him. 
 
 In some manuscripts lately given to the Eoyal Society, 
 David Gregory, who seems to have seen Grephyrander's work, calls 
 him Salicetus Westphalus, which is probably on the title-page. 
 But the only Weiden I can find is in Bavaria. Murhard has both 
 editions in his Catalogue, but had plainly never seen the books : 
 he gives the author as Thomas Grep. Hyandrus, Salicettus West- 
 phalus. Murhard is a very old referee of mine ; but who the 
 non nominandus was to see Montucla's Gephyrauder in Murhard's 
 Gep. Hyandrus, both writers being usually accurate ?] 
 
NAPIER GILBERT BAPTISTA PORTA. 45 
 
 A plain disco verie of the whole Revelation of St. John . . . 
 whereunto are annexed certain oracles of Sibylla . . . Set Foorth 
 by John Napeir L. of Marchiston. London, 1611, 4to. 
 
 The first edition was Edinburgh, 1593, 4to. Napier always 
 believed that his great mission was to upset the Pope, and that 
 logarithms, and such things, were merely episodes and relaxations. 
 It is a pity that so many books have been written about this 
 matter, while Napier, as good as any, is forgotten and unread. 
 He is one of the first who gave us the six thousand years. ' There 
 is a sentence of the house of Eli as reserved in all ages, bearing 
 these words : The world shall stand six thousand years, and then 
 it shall be consumed by fire : two thousand yeares voide or without 
 lawe, two thousand yeares under the law, and two thousand 
 yeares shall be the daies of the Messias. . . .' 
 
 I give Napier's parting salute : it is a killing dilemma : 
 
 In summar conclusion, if thou o Howie aledges thyselfe reformed, and 
 to beleene true Christian ism e, then beleeue Saint John the Disciple, 
 whome Christ loued, publikely here in this Reuelation proclaiming thy 
 wracke, but if thou remain Ethnick in thy priuate thoghts, beleeuing 
 the old Oracles of the Sibyls reuerently keeped somtime in thy Capitol : 
 then doth here this Sibyll proclame also thy wracke. Repent therefore 
 alwayes, in this thy latter breath, as thou louest thine Eternall salvation. 
 Amen. 
 
 Strange that Napier should not have seen that this appeal could 
 not succeed, unless the prophecies of the Apocalypse were no true 
 prophecies at all. 
 
 De Magnete magneticisque corporibus, et de magno magnete 
 tenure. By William Gilbert. London, 1600, folio. There is 
 a second edition ; and a third, according to Watt. 
 
 Of the great work on the magnet there is no need to speak, 
 though it was a paradox in its day. The posthumous work of 
 Gilbert, 'De Mundo nostro sublunari philosophia nova' (Ams- 
 terdam, 1651, 4to) is, as the title indicates, confined to the 
 physics of the globe and its atmosphere. It has never excited 
 attention : I should hope it would be examined with our present 
 lights. 
 
 Elementorum Curvilineorium Libri tres. By John Baptisfca Porta. 
 
 Rome, 1610, 4to. 
 
 This is a ridiculous attempt, which defies description, except 
 that it is all about lunules. Porta was a voluminous writer. 
 
46 A BUDGET OF PARADOXES. 
 
 His printer announces fourteen works printed, and four to come, 
 besides thirteen plays printed, and eleven waiting. His name is, 
 and will be, current in treatises on physics for more reasons than 
 one. 
 
 Trattato della quadrature del cerchio. Di Pietro Antonio Cataldi. 
 Bologna, 1612, folio. 
 
 Eheticus, Vieta, and Cataldi are the three untiring computers 
 of Grermany, France, and Italy ; Napier in Scotland, and Briggs in 
 England, come just after them. This work claims a place as 
 beginning with the quadrature of Pellegrino Borello of Eeggio, 
 who will have the circle to be exactly 3 diameters and ^ T of a 
 diameter. Cataldi, taking Van Ceulen's approximation, works 
 hard at the finding of integers which nearly represent the ratio. 
 He had not then the continued fraction, a mode of representation 
 which he gave the next year in his work on the square root. He 
 has but twenty of Van Ceulen's thirty places, which he takes from 
 Clavius : and anyone might be puzzled to know whence th Italians 
 got the result ; Van Ceulen, in 1612, not having been translated 
 from Dutch. But Clavius names his comrade Grruenberger, and 
 attributes the approximation to them jointly ; c Lud. a Collen et 
 Chr. Grruenbergerus invenerunt,' which he had no right to do, 
 unless, to his private knowledge, Grruenberger had verified Van 
 Ceulen. And Grruenberger only handed over twenty of the places. 
 But here is one instance, out of many, of the polyglot character 
 of the Jesuit body, and its advantages in literature. 
 
 Philippi Lausbergii Cyclometrise Novse Libri Duo. Middleburg, 
 1616, 4to. 
 
 This is one of the legitimate quadratures, on which I shall 
 here only remark that by candlelight it is quadrature under 
 difficultieSs for all the diagrams are in red ink. 
 
 Recherches Curieuses des Mesures du Monde. By S. C. de V. 
 Paris, 1626, 8vo. (pp. 48). 
 
 It is written by some Count for his son ; and if all the French 
 nobility would have given their sons the same kind of instruction 
 about rank, the old French aristocracy would have been as pros- 
 perous at this moment as the English peerage and squireage. I 
 sent the tract to Capt. Speke, shortly after his arrival in England, 
 thinking he might like to see the old names of the Ethiopian pro- 
 vinces. But I first made a copy of all that relates to Prester John, 
 himself a paradox. The tract contains, inter alia, an account of 
 
BKESTER JOHN. 47 
 
 the four empires ; of the great Turk, the great Tartar, the great 
 Sophy, and the great Prester John. This word great (grand), 
 which was long used in the phrase c the great Turk,' is a generic 
 adjunct to an emperor. Of the Tartars it is said that ' c'est vne 
 nation prophane et barbaresque, sale et vilaine, qui mangent la 
 chair demie crue, qui boiuent du laict de jument, et qui n'vsent 
 de nappes et seruiettes que pour essuyer leurs bouches et leurs 
 mains.' Many persons have heard of Prester John, and have 
 a very indistinct idea of him. I give all that is said about him, 
 since the recent discussions about the Nile may give an interest 
 to the old notions of geography. 
 
 Le grand Prestre Jean qui est le quatriesme en rang, est Empereur 
 d'Ethiopie, et des Abyssins, et se vante d'estre issu de la race de Dauid, 
 comme estant descendu de la Royne de Saba, Royne d'Ethiopie, laquelle 
 estant venue en Hierasalem pour voir la sagesse de Salomon, enuiron 
 1'an du monde 2952, s'en retourna grosse d'vn fils qu'ils nomment 
 Moylech, duquel ils disent estre descendus en ligne directe. Et ainsi 
 il se glorifie d'estre le plus ancien Monarque de la terre, disant que son 
 Empire a dure plus de trois mil ans, ce que nul autre Empire ne peut 
 dire. Aussi inet-il en ses tiltres ce qui s'ensuit : Nous, N. Souuerain 
 en mes Royaumes, vniquement ayme de Dieu, colomne de la foy, sorty 
 de la race de luda, &c. Les limites de cet Empire touchent a la mer 
 Rouge, et aux montagnes d'Azuma vers 1'Orient, et du coste de 
 1' Occident, il est borne du fleuue du Nil, qui le separe de laNtibie, vers 
 le Septentrion il a 1'^Egypte, et au Midy les Royaumes de Congo, et de 
 Mozambique, sa longueur contenant quarante degre, qui font mille 
 vingt cinq lieues, et ce depuis Congo ou Mozambique qui sont au Midy, 
 iusqu'en ^Egypte qui est au Septentrion, et sa largeur contenant depuis 
 le Nil qui est a 1' Occident, iusqu'aux montagnes d'Azuma, qui sont a 
 V Orient, sept cens vingt cinq lieues, qui font vingfc neuf degrez. Cet 
 empire a sous soy trente grandes Prouinces, s^avoir, Medra, Gaga, 
 Alchy, Cedalon, Mantro, Finazam, Barnaquez, Ambiam, Fungy, 
 Angote, Cigremaon, Gorga Cafatez, Zastanla, Zeth, Barly, Belangana, 
 Tygra, Gorgany, Barganaza, d'Ancut, Dargaly Ambiacatina, Cara- 
 cogly, Amara- . Maon (sic), Guegiera, Bally, Dobora et Macheda. 
 Toutes ces Prouinces cy dessus sont situees iustement sous la ligne 
 equinoxiale, entres les Tropiques de Capricorne, et de Cancer. Mais 
 elles s'approchent de nostre Tropique, de deux cens cinquante lieues 
 plus qu' elles ne font de 1'autre Tropique. Ce mot de Prestre Jean 
 signifie grand Seigneur, et n'est pas Prestre comme plusieurs pense, il a 
 este tousiours Chrestien, mais souuent Schismatique : maintenant il est 
 Catholique, et reconnaist le Pape pour Souuerain Pontife. I'ay veu 
 quelqu'vn des ses Euesques, estant en Hierusalem, auec lequel i'ay 
 confere souuent par le moyen de nostre trucheman : il estoit d'vn port 
 graue et serieux, succiur (sic) en son parler, mais subtil a merueilles 
 en tout ce qu'il disoit. II prenoit grand plaisir au recit que je lay 
 
48 A BUDGET OF PARADOXES. 
 
 faisais de nos belles ceremonies, et de la granite de nos Prelats en leurs 
 habits Pontificaux, et autres choses qne je laisse pour dire, que 1'Ethi- 
 opien est ioyoux et gaillard, ne ressemblant en rien a la salete du Tar- 
 tare, ny a 1'afFreux regard du miserable Arabe, mais ils sont fins et 
 canteleux, et ne se fient en personne, soup9onneux a merueilles, et fort 
 devotieux, ils ne sont du tout noirs comme Ton croit, i'entens parler de 
 ceux qui ne sont pas sous la ligne Equinoxiale, ny trop proches d'icelle, 
 car ceux qui sont dessous sont les Mores que nous voyons. 
 
 It will be observed that the author speaks of his conversation 
 with an Ethiopian bishop, about that bishop's sovereign. Some- 
 thing must have passed between the two which satisfied the 
 writer that the bishop acknowledged his own sovereign under 
 some title answering to Prester John. 
 
 De Cometa anni 1618 dissertationes Thomge Fieni et Liberti 
 Fromondi. . . Equidem Thomge Fieni epistolica quaestio, An 
 verum sit Coelum moveri et Terram quiescere ? London, 1670, 
 8vo. 
 
 This tract of Fienus against the motion of the earth is a reprint 
 of one published in 1619. I have given an account of it as a 
 good summary of arguments of the time, in the Companion to the 
 Almanac for 1836. 
 
 Willebrordi Snellii. R. F. Cyclometricus. Ley den, 1621, 4to. 
 
 This is a celebrated work on the approximative quadrature, 
 which, having the suspicious word cydometricus, must be noticed 
 here for distinction. 
 
 1620. In this year, Francis Bacon published his 'Novum 
 Organum,' which was long held in England but not until the 
 last century to be the work which taught Newton and all his 
 successors how to philosophise. That Newton never mentions 
 Bacon, nor alludes in any way to his works, passed for nothing. 
 Here and there a parodoxer ventured not to find all this teaching 
 in Bacon, but he was pronounced blind. In our day it begins 
 to be seen that, great as Bacon was, and great as his book really 
 is, he is not the philosophical father of modern discovery. 
 
 But old prepossession will find reason for anything. A learned 
 friend of mine wrote to me that he had discovered proof that 
 Newton owned Bacon for his master : the proof was that Newton, 
 in some of his earlier writings, used the phrase experimentum 
 crucis, which is Bacon's. Newton may have read some of Bacon, 
 though no proof of it appears. I have a dim idea that I once 
 saw the two words attributed to the alchemists : if so, there is 
 
FRANCIS BACON. 49 
 
 another explanation ; for Newton was deeply read in the al- 
 chemists. 
 
 I subjoin a review which I wrote of the splendid edition of 
 Bacon by Spedding, Ellis., and Heath. All the opinions therein 
 expressed had been formed by me long before : most of the 
 materials were collected for another purpose. 
 
 The Works of Francis Bacon. Edited by James Spedding, 
 B. Leslie Ellis, and Douglas D. Heath. 5 vols. 
 
 No knowledge of nature without experiment and observation : 
 so said Aristotle, so said Bacon, so acted Copernicus, Tycho Brahe, 
 Gilbert, Kepler, Gralileo, Harvey, &c. ? before Bacon wrote. No 
 derived knowledge until experiment and observation are con- 
 cluded : so said Bacon, and no one else. We do not mean to say 
 that he laid down his principle in these words, or that he carried 
 it to the utmost extreme : we mean that Bacon's ruling idea was 
 the collection of enormous masses of facts, and then digested 
 processes of arrangement and elimination, so artistically contrived, 
 that a man of common intelligence, without any unusual sagacity, 
 should be able to announce the truth sought for. Let Bacon 
 speak for himself, in his editor's English : 
 
 But the course I propose for the discovery of sciences is such as 
 leaves but little to the acuteness and strength of wits, but places all wits 
 and understandings nearly on a level. For, as in the drawing of a straight 
 line or a perfect circle, much depends on the steadiness and practice of 
 the hand, if it be done by aim of hand only, but if with the aid of rule 
 or compass little or nothing, so it is exactly with my plan. . . For 
 my way of discovering sciences goes far to level men's wits, and leaves 
 but little to individual excellence ; because it performs everything by 
 the surest rules and demonstrations. 
 
 To show that we do not strain Bacon's meaning, we add what 
 is said by Hooke, whom we have already mentioned as his pro- 
 fessed disciple, and, we believe, his only disciple of the day of 
 Newton. We must, however, remind the reader that Hooke was 
 very little of -a mathematician, and spoke of algebra from his own 
 idea of what others had told him : 
 
 The intellect is not to be suffered to act without its helps, but is 
 continually to be assisted by some method or engine, which shall 
 be as a guide to regulate its actions, so as that it shall not be able to 
 act amiss. Of this engine, no man except the incomparable Yerulam 
 hath had any thoughts, and he indeed hath promoted it to a very good 
 pitch ; but there is yet somewhat more to be added, which he seemed 
 to want time to complete. By this, as by that art of algebra in geo- 
 
 E 
 
50 A BUDGET OF PARADOXES. 
 
 metry, 'twill be very easy to proceed in any natural inquiry, regularly 
 and certainly. . . For as 'tis very hard for the most acute wit to find 
 out any difficult problem in geometry without the help of algebra . . . 
 and altogether as easy for the meanest capacity acting by that method 
 to complete and perfect it, so will it be in the inquiry after natural 
 knowledge. 
 
 Bacon did not live to mature the whole of this plan. Are we 
 really to believe that if he had completed the ' Instauratio ' we 
 who write this and who feel ourselves growing bigger as we 
 write it should have been on a level with Newton in physical 
 discovery? Bacon asks this belief of us, and does not get it. 
 But it may be said. Your business is with what he did leave, 
 and with its consequences. Be it so. Mr. Ellis says : 6 That his 
 method is impracticable cannot, I think, be denied, if we reflect 
 not only that it never has produced any result, but also that the 
 process by which scientific truths have been established cannot 
 be so presented as even to appear to be in accordance with it.' 
 That this is very true is well known to all who have studied the 
 history of discovery : those who deny it are bound to establish 
 either that some great discovery has been made by Bacon's 
 method we mean by the part peculiar to Bacon or, better still, 
 to show that some new discovery can be made, by actually making 
 it. No general talk about induction : no reliance upon the 
 mere fact that certain experiments or observations have been 
 made ; let us see where Bacon's induction has been actually 
 used or can be used. Mere induction, enumeratio simplex, is 
 spoken of by himself with contempt, as utterly incompetent. 
 For Bacon knew well that a thousand instances may be contra- 
 dicted by the thousand and first : so that no enumeration of 
 instances, however large, is 4 sure demonstration,' so long as any 
 are left. 
 
 The immortal Harvey, who was inventing we use the word 
 in its old sense the circulation of the blood, while Bacon was in 
 the full flow of thought upon his system, may be trusted to say 
 whether, when the system appeared, he found any likeness in it 
 to his own processes, or what would have been any help to him, 
 if he had waited for the 4 Novum Organum.' He said of Bacon, 
 6 He writes philosophy like a Lord Chancellor.' This has been 
 generally supposed to be only a sneer at the sutor ultra crepidam ; 
 but we cannot help suspecting that there was more intended by 
 it. To us, Bacon is eminently the philosopher of error prevented, * 
 not of progress facilitated. When we throw off the idea of being 
 led right, and betake ourselves to that of being kept from going 
 
FRANCIS BACON. 51 
 
 wrong, we read his writings with a sense of their usefulness, his 
 genius, and their probable effect upon purely experimental science, 
 which we can be conscious of upon no other supposition. It 
 amuses us to have to add that the part of Aristotle's logic of 
 which he saw the value was the book on refutation of fallacies. 
 Now is this not the notion of things to which the bias of a 
 practised lawyer might lead him ? In the case which is before 
 the Court, generally speaking, truth lurks somewhere about the 
 facts, and the elimination of all error will show it in the residuum. 
 The two senses of the word law come in so as to look almost like 
 a play upon words. The judge can apply the law so soon as the 
 facts are settled : the physical philosopher has to deduce the law 
 from the facts. Wait, says the judge, until the facts are deter- 
 mined : did the prisoner take the goods with felonious intent ? 
 did the defendant give what amounts to a warranty ? or the like. 
 Wait, says Bacon, until all the facts, or all the obtainable facts, 
 are brought in : apply my rules of separation to the facts, and the 
 result shall come out as easily as by ruler and compasses. We think 
 it possible that Harvey might allude to the legal character of 
 Bacon's notions : we can hardly conceive so acute a man, after 
 seeing what manner of writer Bacon was, meaning only that he 
 was a lawyer and had better stick to his business. We do our- 
 selves believe that Bacon's philosophy more resembles the action 
 of mind of a common-law judge not a Chancellor than that of 
 the physical inquirers who have been supposed to follow in his 
 steps. It seems to us that Bacon's argument is, there can be 
 nothing of law but what must be either perceptible, or mechani- 
 cally deducible, when all the results of law, as exhibited in 
 phenomena, are before us. Now the truth is, that the physical 
 philosopher has frequently to conceive law which never was in his 
 previous thought to educe the unknown, not to choose among 
 the known. Physical discovery would be very easy work if the 
 inquirer could lay down his this, his that, and his t'other, and say, 
 6 Now, one of these it must be ; let us proceed to try which.' 
 Often has he done this, and failed ; often has the truth turned 
 out to be neither this, that, nor t'other. Bacon seems to us to 
 think that the philosopher is a judge who has to choose, upon 
 ascertained facts, which of known statutes is to rule the decision ; 
 he appears to us more like a person who is to write the statute- 
 book, with no guide except cases and decisions presented in all 
 their confusion and all their conflict. 
 
 Let us take the well-known first aphorism of the ' Novum 
 Organum :' 
 
52 A BUDGET OF PARADOXES. 
 
 Man being the servant and interpreter of nature, can do and under- 
 stand so much, and so much only, as he has observed in fact or in 
 thought of the course of nature : beyond this he neither knows anything 
 nor can do anything. 
 
 This aphorism is placed by Sir John Herschel at the head of 
 his 6 Discourse on the Study of Natural Philosophy : ' a book con- 
 taining notions of discovery far beyond any of which Bacon ever 
 dreamed ; and this because it was written after discovery, instead 
 of before. Sir John Herschel, in his version, has avoided the 
 translation of re vel mente observaverit, and gives us only ' by his 
 observation of the order of nature.' In making this the opening 
 of an excellent sermon, he has imitated the theologians, who 
 often employ the whole time of the discourse in stuffing matter 
 into the text, instead of drawing matter out of it. By observation 
 he (Herschel) means the whole course of discovery, observation, 
 hypothesis, deduction, comparison, &c. The type of the Baconian 
 philosopher, as it stood in his mind, had been derived from a 
 noble example, his own father, William Herschel, an inquirer 
 whose processes would have been held by Bacon to have been 
 vague, insufficient, compounded of chance work and sagacity, and 
 too meagre of facts to deserve the name of induction. In another 
 work, his treatise on Astronomy, Sir John Herschel, after noting 
 that a popular account can only place the reader on the threshold, 
 proceeds to speak as follows of all the higher departments of 
 science. The italics are his own : 
 
 Admission to its sanctuary, and to the privileges and feelings of 
 a votary, is only to be gained by one means sound and sufficient 
 'knowledge of mathematics, the great instrument of all exact inquiry, 
 without which no man can ever make such advances in this or any other 
 of the higher departments of science as can entitle him- to form an inde- 
 pendent opinion on any subject of discussion within their range. 
 
 How is this? Man can know no more than he gets from 
 observation, and yet mathematics is the great instrument of all 
 exact inquiry. Are the results of mathematical deduction results 
 of observation ? We think it likely that Sir John Herschel 
 would reply that Bacon, in coupling together observare re and 
 observare mente, has done what some wags said 'Newton afterwards 
 did in his study-door cut a large hole of exit for the large cat, 
 and a- little hole for the little cat. But Bacon did no such thing : 
 he never included any deduction under observation. To mathe- 
 matics he had a dislike. He averred that logic and mathematics 
 should be the handmaids, not the mistresses, of philosophy. He 
 meant that they should play a subordinate and subsequent part 
 
FRANCIS BACON. 53 
 
 in the dressing of the vast mass of facts by which discovery was 
 to be rendered equally accessible to Newton and to us. Bacon 
 himself was very ignorant of all that had been done by mathe- 
 matics ; and, strange to say, he especially objected to astronomy 
 being handed over to the mathematicians. Leverrier and Adams, 
 calculating an unknown planet into visible existence by enormous 
 heaps of algebra, furnish the last comment of note on this 
 specimen of the goodness of Bacon's views. The following 
 account of his knowledge of what had been done in his own day 
 or before it, is Mr. Spedding's collection of casual remarks in 
 Mr. Ellis's several prefaces : 
 
 Though he paid great attention to astronomy, discussed carefully the 
 methods in which it ought to be studied, constructed for the satisfac- 
 tion of his own mind an elaborate theory of the heavens, and listened 
 eagerly for the news from the stars brought by Galileo's telescope, he 
 appears to have been utterly ignorant of the discoveries which had 
 just been made by Kepler's calculations. Though he complained in 
 1623 of the want of compendious methods for facilitating arithmetical 
 computations, especially with regard to the doctrine of Series, and 
 fully recognized the importance of them as an aid to physical inquiries 
 he does not say a word about Napier's Logarithms, which had been 
 published only nine years before and reprinted more than once in the 
 interval. He complained that no considerable advance had been made 
 in geometry beyond Euclid, without taking any notice of what had 
 been done by Archimedes and Apollonius. He saw the importance of 
 determining accurately the specific gravities of different substances, and 
 himself attempted to form a table of them by a rude process of his own, 
 without knowing of the more scientific though still imperfect methods 
 previously employed by Archimedes, Ghetaldus, and Porta. He speaks 
 of the tvfjijKa of Archimedes in a manner which implies that he did not 
 clearly apprehend either the nature of the problem to be solved or the 
 principles upon which the solution depended. In reviewing the pro- 
 gress of mechanics, he makes no mention of Archimedes himself, or of 
 Stevinus, Galileo, Guldinus, or Ghetaldus. He makes no allusion to 
 lie theory of equilibrium. He observes that a ball of one pound weight 
 fidll fall nearly as fast through the air as a ball of two, without alluding 
 ;o the theory of the acceleration of falling bodies, which had been 
 nade known by Galileo more than thirty years before. He proposes an 
 nquiry with regard to the lever namely, whether in a balance with 
 irms of different length but equal weight the distance from the fulcrum 
 ms any effect upon the inclination, though the theory of the lever was 
 is well understood in his own time as it is now. In making an experi- 
 ment of his own to ascertain the cause of the motion of a windmill, he 
 overlooks an obvious circumstance which makes the experiment incon- 
 clusive, and an equally obvious variation of the same experiment which 
 tvould have shown him that his theory was false. He speaks of the 
 
54 A BUDGET OF PARADOXES. 
 
 poles of the earth as fixed, in a manner which seems to imply that he 
 was not acquainted with the precession of the equinoxes ; and in 
 another place, of the north pole being above and the south pole below, 
 as a reason why in our hemisphere the north winds predominate over 
 the south. 
 
 Much of this was known before, but such a summary of Bacon's 
 want of knowledge of the science of his own time was never yet 
 collected in one place. We may add, that Bacon seems to have 
 been as ignorant of Wright's memorable addition to the resources 
 of navigation as of Napier's addition to the means of calculation. 
 Mathematics was beginning to be the great instrument of exact 
 inquiry : Bacon threw the science aside, from ignorance, just at 
 the time when his enormous sagacity, applied to knowledge, 
 would have made him see the part it was to play. If Newton 
 had taken Bacon for his master, not he, but somebody else, would 
 have been Newton. 
 
 There is an attempt at induction going on, which has yielded 
 little or no fruit, the observations made in the meteorological 
 observatories. This attempt is carried on in a manner which 
 would have caused Bacon to dance for joy ; for he lived in times 
 when Chancellors did dance, Eussia, says M. Biot, is covered by 
 an army of meteorographs, with generals, high officers, subalterns, 
 and privates with fixed and defined duties of observation. .Other 
 countries have also their systematic observations. And what has 
 come of it ? Nothing, says M. Biot, and nothing will ever come 
 of it ; the veteran mathematician and experimental philosopher 
 declares, as does Mr, Ellis, that no single branch of science has 
 ever been fruitfully explored in this way. There is no special 
 object, he says. Any one would suppose that M. Biot's opinion, 
 given to the French Government upon the proposal to construct 
 meteorological observatories in Algeria (Comptes Rendus, vol. xli, 
 Dec. 31, 1855), was written to support the mythical Bacon, modern 
 physics, against the real Bacon of the ' Novum Organum.' There 
 is no special object. In these words lies the difference between 
 the two methods. 
 
 [In the report to the Greenwich Board of Visitors for 1867, 
 Mr. Airy, speaking of the increase of meteorological observatories, 
 remarks < Whether the effect of this movement will be that 
 millions of useless observations will be added to the millions that 
 already exist, or whether something may be expected to result 
 which will lead to a meteorological theory, I cannot hazard a 
 conjecture,' This is a conjecture, and a very obvious one: if 
 
FRANCIS BACON. 55 
 
 Mr. Airy would have given 2%d. for the chance of a meteorological 
 theory formed by masses of observations, he would never have 
 said what I have quoted,] 
 
 Modern discoveries have not been made by large collections of 
 facts, with subsequent discussion, separation, and resulting de- 
 duction of a truth thus rendered perceptible. A few facts have 
 suggested an hypothesis, which means a supposition, proper to 
 explain them. The necessary results of this supposition are 
 worked out, and then, and not till then, other facts are examined 
 to see if these ulterior results are found in nature. The trial of 
 the hypothesis is the special object : prior to which, hypothesis 
 must have been started, not by rule, but by that sagacity of 
 which no description can be given, precisely because the very 
 owners of it do not act under laws perceptible to themselves. 
 The inventor of hypothesis, if pressed to explain his method, must 
 answer as did Zerah Colburn, when asked for his mode of instan- 
 taneous calculation. When the poor boy had been bothered for 
 some time in this manner, he cried out in a huff, ' God put it 
 into my head, and I can't put it into yours.' Wrong hypotheses, 
 rightly worked from, have produced more useful results than 
 unguided observation. But this is not the Baconian plan. 
 Charles the Second, when informed of the state of navigation, 
 founded a Baconian observatory at Greenwich, to observe, observe, 
 observe away at the moon, until her motions were known suf- 
 ficiently well to render her useful in guiding the seaman. And 
 no doubt Flamsteed's observations, twenty or thirty of them 
 at least, were of signal use. But how? A somewhat fanciful 
 thinker, one Kepler, had hit upon the approximate orbits of the 
 planets by trying one hypothesis after another : he found the 
 ellipse, which the Platonists, well despised of Bacon, and who 
 would have despised him as heartily if they had known him, had 
 investigated and put ready to hand nearly 2,000 years before. 
 The sun in the focus, the motions of the planet more and more 
 rapid as tbey approach the sun, led Kepler and Bacon would 
 have reproved him for his rashness to imagine that a force re- 
 siding in the sun might move the planets, a force inversely as the 
 distance. Bouillaud, upon a fanciful analogy, rejected the inverse 
 distance, and, rejecting the force altogether, declared that if such 
 a thing there were, it would be as the inverse square of the 
 distance. Newton, ready prepared with the mathematics of the 
 subject, tried the fall of the moon towards the earth, away from 
 her tangent, and found that, as compared with the fall of a stone, 
 
56 A BUDGET OF PARADOXES. 
 
 the law of the inverse square did hold for the moon. He deduced 
 the ellipse, he proceeded to deduce the effect of the disturbance 
 of the sun upon the moon, upon the assumed theory of universal 
 gravitation. He found result after result of his theory in con- 
 formity with observed fact: and, by aid of Flamsteed's obser- 
 vations, which amended what mathematicians call his constants, 
 he constructed his lunar theory. Had it not been for Newton, 
 the whole dynasty of Greenwich astronomers, from Flamsteed of 
 happy memory, to Airy whom Heaven preserve, might have 
 worked away at nightly observation and daily reduction, without 
 any remarkable result : looking forward, as to a millennium, to 
 the time when any man of moderate intelligence was to see 
 the whole explanation. What are large collections of facts for ? 
 To make theories from, says Bacon : to try ready-made theories 
 by, says the history of discovery : it's all the same, says the 
 idolater : nonsense, say we ! 
 
 Time and space run short : how odd it is that of the three 
 leading ideas of mechanics, time, space, and matter, the first two 
 should always fail a reviewer before the third. We might dwell 
 upon many points, especially if we attempted a more descriptive 
 account of the valuable edition before us. No one need imagine 
 that the editors, by their uncompromising attack upon the notion 
 of Bacon's influence common even among mathematicians and 
 experimental philosophers, have lowered the glory of the great 
 man whom it was, many will think, their business to defend 
 through thick and thin. They have given a clearer notion of his 
 excellencies, and a better idea of the power of his mind, than ever 
 we saw given before. Such a correction as theirs must have come, 
 and soon, for as Hallam says after noting that the 'Novum 
 Organum' was never published separately in England, Bacon has 
 probably been more read in the last thirty years now forty than 
 in the two hundred years which preceded. He will now be more 
 read than ever he was. The history of the intellectual world is 
 the history of the worship of one idol after another. No sooner 
 is it clear that a Hercules has appeared among men, than all 
 that imagination can conceive of strength is attributed to him, 
 and his labours are recorded in tne heavens. The time arrives 
 when, as in the case of Aristotle, a new deity is found, and the 
 old one is consigned to shame and reproach. A reaction may 
 afterwards take place, and this is now happening in the case of 
 the Greek philosopher. The end of the process is, that the oppo- 
 sing deities take their places, side by side, in a Pantheon dedicated 
 pot to gods, but to heroes. 
 
COPERNICUS AND THE POPE. 57 
 
 Passing over the success of Bacon's own endeavours to improve 
 the details of physical science, which was next to nothing, and of 
 his method as a whole, which has never been practised, we might 
 say much of the good influence of his writings. Sound wisdom ? 
 set in sparkling wit, must instruct and amuse to the end of time :^ 
 and, as against error, we repeat that Bacon is soundly wise, so far 
 as he goes. There is hardly a form of human error within his 
 scope which he did not detect, expose, and attach to a satirical 
 metaphor which never ceases to sting. He is largely indebted to 
 a very extensive reading ; but the thoughts of others fall into his 
 text with such a close-fitting compactness that he can make even 
 the words of the Sacred Writers pass for his own. A saying of 
 the prophet Daniel, rather a hackneyed quotation in our day, 
 Multi pertransibunt, et augebitur scientia, stands in the title-page 
 of the first edition of Montucla's ' History of Mathematics ' as a 
 quotation from Bacon and it is not the only place in which this 
 mistake occurs. When the truth of the matter, as to Bacon's 
 system, is fully recognized, we have little fear that there will be 
 a reaction against the man. First, because Bacon will always 
 live to speak for himself, for he will not cease to be read : 
 secondly,- because those who seek the truth will find it in the 
 best edition of his works, and will be most ably led to know what 
 Bacon was, in the very books which first showed at large what he 
 was not. 
 
 In this year (1620) appeared the corrections under which the 
 Congregation of the Index i.e. the Committee of Cardinals 
 which superintended the Index of forbidden books proposed to 
 allow the work of Copernicus to be read. I insert these con- 
 ditions in full, because they are often alluded to, and I know of 
 no source of reference accessible to a twentieth part of those who 
 take interest in the question. 
 
 By a decree of the Congregation of the Index, dated March 5, 
 1616, the work of Copernicus, and another of Didacus Astunica, 
 are suspended donee corrigantur, as teaching : 
 
 4 Falsam illam doctrinam Pythagoricam,divine que Scriptures omnino 
 adversantem, de mobilitate Terra3 et immobilitate Solis.' 
 
 But a work of the Carmelite Foscarini is : 
 
 ' Omnino prohibendurn atque damnandum, 'because 'ostendere conatur 
 pra3fatam doctrinam . ^ , , consonam esse veritati et non adversari 
 Sacn Script ur.' 
 
 Works which teach the false doctrine of the earth's motion 
 
58 A BUDGET OF PABADOXES. 
 
 are to be corrected ; those which declare the doctrine conformable 
 to Scripture are to be utterly prohibited. 
 
 In a ' Monitum ad Nicolai Copernioi lectorem, ej usque emen- 
 datio, permissio, et correctio,' dated 1620 without the month or 
 day, permission is given to reprint the work of Copernicus with 
 certain alterations ; and, by implication, to read existing copies 
 after correction in writing. In the preamble the author is called 
 nobilis astrologu8\ not a compliment to his birth, which was 
 humble, but to his fame. The suspension was because : 
 
 * Sacrce Scripturee, ejusque verea et Catholicre interpretation! repug- 
 nantia (quod in homine Christiano minime tolerandum) non per hypo- 
 thesin tractare, sed ut verissima adstruere non dubitat ! 
 
 And the corrections relate : 
 
 ' Locis in quibus non ex hypothesi, sed asserendo de situ et motu Terrss 
 disputat.' 
 
 That is, the earth's motion may be an hypothesis for eluci- 
 dation of the heavenly motions, but must not be asserted as a 
 fact. 
 
 (In Pref. circa finem.) ' Copernicus. Si fortasse erunt /uarcuoXoyot, 
 qui cum omnium Mathematum ignari sint, tamen de illis judicium sibi 
 summunt, propter aliquem locum scriptures, male ad suum propositum 
 detortum, ausi fuerint meum hoc institutum reprehendere ac insec- 
 tari : illos nihil moror adeo ut etiam illorum judicium tanquam 
 temerarium contemnam. Non enim obscurum est Laetantium, celebrem 
 alioqui scriptorem, sed Mathematicum parum, admodum pueriliter de 
 forma terrae loqui, cum deridet eos, qui terram globi formam habere 
 prodiderunt. Itaque non debet mirum videri studiosis, si qui tales nos 
 etiam videbunt. Mathemata Mathematicis scribuntnr, quibus et hi 
 nostri labores, si me non fallit opinio, videbuntur etiam Reipub. eccle- 
 siastices conducere aliquid . . . Emend. Ibi si fortasse dele omnia, 
 usque ad verbum hi nostri labores et sic accommoda Cceterum hi nostri 
 labores. 1 
 
 All the allusion to Lactantius, who laughed at the notion of the 
 earth being round, which was afterwards found true, is to be 
 struck out. 
 
 (Cap. 5. lib. i. p. 3.) ' Copernicus. Si tamen attentius rem consider- 
 emus, videbitur haec queestio nondum absoluta, et idcirco minime 
 contemnenda. Emend. Si tamen attentius rem consideremus, nihil 
 refert an Terram in medio Mundi, an extra Medium existere, quoad sol- 
 yendas coDlestium motuum apparentias existimemus.' 
 
 We must not say the question is not yet settled, but only that 
 
COPERNICUS AND THE POPE, 59 
 
 it may be settled either way, so far as mere explanation of the 
 celestial motions is concerned. 
 
 (Cap. 8. lib. i.) ' Totum hoc caput potest expungi, quia ex professo 
 tractat de veritate motus Terree, dum solvit veterum rationes probantes 
 ejus quietem. Cam tamen problematice videatur loqui ; ut studiosis 
 satisfiat, seriesque et ordo libri integer man eat ; emendetur ut infra.' 
 
 A chapter which seems to assert the motion should perhaps be 
 expunged ; but it may perhaps be problematical ; and, not to 
 break up the book, must be amended as below. 
 
 (p. 6.) l Copernicus. Cui ergo hesitamus adhuc, nobilitatem illi formee 
 sure a natura congruentem concedere, magisquam quod totus labatur 
 mundus, cujus finis ignoratur, soirique nequit, neque fateamur ipsius 
 cotidianse revolutionis in coelo apparentiam esse, et in terra veritatem ? 
 Et heec perinde se habere, ac si diceret Virgilianus ^Eneas : Provehimur 
 portu .... Emend. Cur ergo non possum mobilitatem illi formaa 
 sua3 concedere, magisque quod totus labatur mundus, cujus finis 
 ignoratur scirique nequit, et quse apparent in coelo, perinde se habere, 
 ac si . . . .' 
 
 ' Why should we hesitate to allow the earth's motion,' must be 
 altered into * I cannot concede the earth's motion.' 
 
 (p. 7.) ' Copernicus. Ad do etiam, quod satis absurdum videretur, 
 continenti sive locanti motum adscribi, et non potius contento et 
 locate, quod est terra. Emend. Addo etiam difficilius non esse 
 contento et locato, quod est Terra, motum adscribere, quam continenti. 1 
 
 We must not say it is absurd to refuse motion to the contained 
 and located, and to give it to the containing and locating ; say 
 that neither is more difficult than the other. 
 
 (p. 7.) ' Copernicus. Vides ergo quod ex his omnibus probabilior sit 
 mobilitas Terree, quam ejus quies, prsesertim in cotidiana revolutione, 
 tanquam terras maxime propria. Emend. Vides . . . delendus est 
 usque ad finem capitis.' 
 
 Strike out the whole of the chapter from this to the end ; it 
 says that the motion of the earth is the most probable hypothesis. 
 
 (Cap. 9. lib. i. p. 7.) ' Copernicus. Cum igitur nihil prohibeat mobili- 
 tatem Terree, videndum nunc arbitror, an etiam plures illi motus 
 conveniant, ut possit una errantium syderum existimari. Emend. Cum 
 igitur Terrain moveri assumpserim, videndum nunc arbitror, an etiam 
 illi plures possint convenire motus.' 
 
 We must not say that nothing prohibits the motion of the 
 earth, only that having assumed it, we may inquire whether our 
 explanations require several motions. 
 
60 A BUDGET OF PAKADOXES. 
 
 (Cap. 10. lib. 1. p. 9.) c Copernicus. Non pudet nosfateri .... hoc 
 potius in mobijitate terras verificari. Emend. Kon pudet nos assumere 
 .... hoc consequenter in mobilitate verificari.' 
 
 (Cap. 10. lib. i. p. 10.) ' Copernicus. Tanta niniirum est divina hasc 
 Opt. Max. fabrica. Emend. Dele ilia verba postrema.' 
 
 (Cap. ii. lib. i.) ' Copernicus. De tripliei motu telluris demonstratio. 
 Emend. De hypothesi triplicis motus Terra, ejusque demonstratione.' 
 
 (Cap. 10. lib. iv. p. 122.) ' Copernicus. De magnitudine horum trium 
 siderum, Soils, Lunge, et Terras. Emend. Dele verba horum trium 
 siderum 9 quia terra non est sidus, ut facit earn Copernicus. ' 
 
 We must not say we are not ashamed to acknowledge ; assume 
 is the word. We must not call this assumption a Divine work. 
 A chapter must not be headed demonstration, but hypothesis. 
 The earth must not be called a star ; the word implies motion. 
 
 It will be seen that it does not take much to reduce Copernicus 
 to pure hypothesis. No personal injury being done to the author 
 who indeed had been 17 years out of reach the treatment of 
 his book is now an excellent joke. It is obvious that the Car- 
 dinals of the Index were a little ashamed of their position, and 
 made a mere excuse of a few corrections. Their mode of deal- 
 ing with chap. 8, this problematice videtur loqui,ut studiosis satis- 
 fiat, is an excuse to avoid corrections. But they struck out the 
 stinging allusion to Lactantius in the preface, little thinking, 
 honest men, for they really believed what they said that the 
 light of Lactantius would grow dark before the- brightness of 
 their own. 
 
 1622. I make no reference to the case of Galileo, except this. 
 I have pointed out (Penny Cyd. Suppl. ' Galileo ; ' Engl. Cyd. 
 6 Motion of the Earth ') that it is clear the absurdity was the act 
 of the Italian Inquisition for the private and personal pleasure 
 of the Pope, who knew that the course he took would not commit 
 him as Pope and not of the body which calls itself the Church. 
 Let the dirty proceeding have its right name. The Jesuit 
 Eiccioli, the stoutest and most learned Anti-Copernican in 
 Europe, and the Puritan Wilkins, a strong Copernican and 
 Pope-hater, are equally positive that the Koman Church never 
 pronounced any decision : and this in the time immediately fol- 
 lowing the ridiculous proceeding of the Inquisition. In like 
 manner a decision of the Convocation of Oxford is not a law of 
 the English Church ; which is fortunate, for that Convocation, 
 in 1622, came to a decision quite as absurd, and a great deal 
 more wicked than the declaration against the motion of the earth. 
 The second was a foolish mistake : the first was a disgusting 
 
KNIGHT AND THE OXFORD CONVOCATION. 61 
 
 surrender of right feeling. The story is told without disappro- 
 bation by Anthony Wood, who never exaggerated anything 
 against the university of which he is writing eulogistic history. 
 
 In 1622, one William Knight put forward in a sermon preached 
 before the University certain theses which, looking at the state 
 of the times, may have been improper and possibly of seditious 
 intent. One of them was that the bishop might excommunicate 
 the civil magistrate : this proposition the clerical body could not 
 approve, and designated it by the term erronea, the mildest 
 going. But Knight also declared as follows 
 
 Subditis mere privatis, si Tyrannus tanquam latro aut stuprator 
 in ipsos faciat impetum, et ipsi nee potestatem ordinariam 
 implorare, nee alia ratione effugere periculum possint, in presenti 
 periculo se et suos contra tyrannum, sicut contra privatum gras- 
 satorem, defendere licet. 
 
 That is, a man may defend his purse or a woman her honour, 
 against the personal attack of a king, as against that of a private 
 person, if no other means of safety can be found. The Convoca- 
 tion sent Knight to prison, declared the proposition 'falsa, 
 periculosa, et impia, and enacted that all applicants for degrees 
 should subscribe this censure, and make oath that they would 
 neither hold, teach, nor defend Knight's opinions. 
 
 The thesis, in the form given, was unnecessary and improper. 
 Though strong opinions of the king's rights were advanced at the 
 time, yet no one ventured to say that, ministers and advisers 
 apart, the king might personally break the law; and we know 
 that the first and only attempt which his successor made brought 
 on the crisis which cost him his throne and his head. But the 
 declaration that the proposition was false far exceeds in all that 
 is disreputable the decision of the Inquisition against the earth's 
 motion. We do not mention this little matter in England. 
 Knight was a Puritan, and Neal gives a short account of his ser- 
 mon. From comparison with Wood, I judge that the theses, as 
 given, were not Knight's words, but the digest which it was 
 customary to make in criminal proceedings against opinion. 
 This heightens the joke, for it appears that the qualifiers of the 
 Convocation took pains to present their condemnation of Knight 
 in the terms which would most unequivocally make their censure 
 condemn themselves. This proceeding took place in the interval 
 between the two proceedings against Gralileo : it is left undeter- 
 mined whether we must say pot-kettle-pot or kettle-pot-kettle. 
 
62 A BUDGET OF PARADOXES. 
 
 Libert! Fromondi . . ". Ant-Aristarchus, sive orbis terrse immo- 
 bilis. Antwerp, 1631, 8vo. 
 
 This book contains the evidence of an ardent opponent of 
 Galileo to the fact, that Eoman Catholics of the day did not con- 
 sider the decree of the Index or of the Inquisition as a declara- 
 tion of their Church. Fromond would have been glad to say as 
 much, and tries to come near it, but confesses he must abstain. 
 See Penny Cyclop. Suppl. 6 Gralileo,' and Eng. Cycl. ' Motion 
 of the Earth.' The author of a celebrated article in the Dublin 
 Review., in defence of the Church of Borne, seeing that Drink- 
 water Bethune makes use of the authority of Fromondus, but for 
 another purpose, sneers at him for bringing up a 4 musty old Pro- 
 fessor.' If he had known Fromondus, and used him he would have 
 helped his own case, which is very meagre for want of knowledge. 1 
 
 Advis a Monseigneur 1'eminentissirae Cardinal Due de Richelieu, 
 sur la Proposition faicte par le Sieur Morin pour 1'invention des 
 longitudes. Paris, 1634, 8vo. 
 
 This is the Official Eeport of the Commissioners appointed by 
 the Cardinal, of whom Pascal is the one now best known, to consider 
 Morin's plan. See the full account in Delambre, Hist. Astr. 
 Mod. ii. 236, &c. 
 
 Arithmetica et Geometria pracfcica. By Adrian Metius. Ley- 
 den, 1640, 4to. 
 
 This book contains the celebrated approximation guessed at by 
 his father. Peter Metius, namely, that the diameter is to the 
 circumference as 113 to 355. The error is at the rate of about a 
 foot in 2,000 miles. Peter Metius, having his attention called 
 to the subject by the false quadrature of Duchesne, found that 
 the ratio lay between ^f and -J-J^. He then took the liberty of 
 taking the mean of both numerators and denominators, giving 
 ^3. He had no right to presume that this mean was better than 
 either of the extremes ; nor does it appear positively that he did so. 
 He published nothing : but his son Adrian, when Van Ceulen's work 
 showed how near his father's result came to the truth, first made 
 it known in the work above. (See Eng. Cyclop, art. < Quadrature.') 
 
 A discourse concerning a new world and another planet, in two 
 
 books. London, 1640, 8vo. 
 Cosrnotheoros : or conjectures concerning the planetary worlds 
 
 1 The article referred to is about thirty years old : since it appeared another has 
 been given (Dubl. Rev. Sept. 1865) which is of much greater depth. In it will also be 
 found the Roman view of Bishop Virgil (ante, p. 24). 
 
PLUKALITY OF WORLDS. 63 
 
 and their inhabitants. Written in Latin, by Christianas Huy- 
 ghens. This translation was first published in 1698. Glasgow 
 1757, 8vo. [The original is also of 1698.] 
 
 The first work is by Bishop Wilkins, being the third edition, [first 
 in 1638] of the first book, 'That the Moon maybe a Planet;' and the 
 first edition of the second work, ' That the Earth may be a Planet.' 
 [See more under the reprint of 1802.] Whether other planets be 
 inhabited or not, that is, crowded with organisations, some of 
 them having consciousness, is not for me to decide ; but I should 
 be much surprised if, on going to one of them, I should find it 
 otherwise. The whole dispute tacitly assumes that, if the stars 
 and planets be inhabited, it must be by things of which we can 
 form some idea. But for aught we know, what number of such 
 bodies there are, so many organisms may there be, of which we 
 have no way of thinking nor of speaking. This is seldom re- 
 membered. In like manner it is usually forgotten that the matter 
 of other planets may be of different chemistry from ours. There 
 may be no oxygen and hydrogen in Jupiter, which may have gens 
 of its own. But this must not be said : it would limit the omni- 
 science of the a priori school of physical inquirers, the larger half 
 of the whole, and would be very imphilosophical. Nine-tenths 
 of my best paradoxers come out from among this larger half, 
 because they are just a little more than of it at their entrance. 
 
 There was a discussion on the subject some years ago, which 
 began with 
 
 The plurality of worlds : an Essay. London, 1853, 8vo. [By Dr. 
 Wm. Whewell, Master of Trinity College^ Cambridge]. A 
 dialogue on the plurality of worlds, being a supplement to the 
 Essay on that subject. [First found in the second edition, 1854 ; 
 removed to the end in subsequent editions, and separate copies 
 issued.] 
 
 A work of sceptical character, insisting on analogies which pro- 
 hibit the positive conclusion that the planets, stars, &c., are what 
 we should call inhabited worlds. It produced several works and 
 a large amount of controversy in reviews. The last predecessor 
 of whom I know was 
 
 Plurality of Worlds. . . . By Alexander Maxwell. Second Edition. 
 
 London, 1820, Svo. 
 
 This work is directed against the plurality by an author who 
 does not admit modern astronomy. It was occasioned by Dr. Chal- 
 mers's celebrated discourses on religion in connexion with astro- 
 nomy. The notes contain many citations on the gravity controversy, 
 
64 A BUDGET OF PARADOXES. 
 
 from authors now very little read : and this is its present value. I 
 find no mention of Maxwell, not even in Watt. He communicated 
 with mankind without the medium of a publisher ; and, from Vieta 
 till now, this method has always been favourable to loss of books. 
 
 A correspondent informs me that Alex. Maxwell, who wrote on 
 the plurality of worlds, in 1820, was a law-bookseller and pub- 
 lisher (probably his own publisher) in Bell Yard. He had pecu- 
 liar notions, which he was fond of discussing with his customers. 
 He was a bit of a Swedenborgian. 
 
 There is a class of hypothetical creations which do not belong 
 to my subject, because they are acknowledged to be fictions, as 
 those of Lucian, Eabelais, Swift, Francis Godwin, Voltaire, &c. 
 All who have more positive notions as to either the composition 
 or organisation of other worlds, than the reasonable conclusion 
 that our Architect must be quite able to construct millions of 
 other buildings on millions of other plans, ought to rank with 
 the writers just mentioned, in all but self-knowledge. Of every 
 one of their systems I say, as the Irish Bishop said of Grulliver's 
 book, I don't believe half of it. Huyghens had been precede- 1 
 by Fontenelle, who attracted more attention. Huyghens is very 
 fanciful and very positive ; but he gives a true account of his 
 method. ' But since there's no hopes of a Mercury to carry us 
 such a journey, we shall e'en be contented with what's in our 
 power : we shall suppose ourselves there. . . .' And yet he says, 
 ' We have proved that they live in societies, have hands and 
 feet. . . .' Kircher had gone to the stars before him, but would 
 not find any life in them, either animal or vegetable. 
 
 The question of the inhabitants of a particular planet is one 
 which has truth on one side or the other: either there are some 
 inhabitants, or there are none. Fortunately, it is of no conse- 
 quence which is true. But there are many cases, where the 
 balance is equally one of truth and falsehood, in which the choice 
 is a matter of importance. My work selects, for the most part, 
 sins against demonstration : but the world is full of questions of 
 fact or opinion, in which a struggling minority will become a 
 majority, or else will be gradually annihilated : and each of the 
 cases subdivides into results of good, and results of evil. What is 
 to be done ? 
 
 Periculosum est credere et non credere ; 
 Hippolitus obiit qnia novercge creditum est ; 
 Cassandrse quia non creditum ruit Ilium : 
 Ergo exploranda est veritas multum prius 
 Quam stulta prove judicet sententia. 
 
VENETIAN PARADOXERS. LONGOMONTANUS. 65 
 
 Nova Demonstratio imniobilitatis terra3 petita ex virtute mag- 
 netica. By Jacobus Grandamicus. Flexise (La Fleche), 1645, 
 4to. 
 
 No magnetic body can move about its poles : the earth is a 
 magnetic body, therefore, &c. The iron and its magnetism are 
 typical of two natures in one person ; so it is said, ' Si exaltatus 
 fuero a terra, omnia traham ad me ipsum.' 
 
 Le glorie degli incogniti, o vero gli huomini illustri dell* ac- 
 cademia de' signori incogniti di Venetia. Venice, 1 647, 4to. 
 
 This work is somewhat like a part of my own : it is a budget 
 of Venetian nobodies who wished to be somebodies ; but paradox 
 is not the only means employed. It is of a serio-comic character, 
 gives genuine portraits in copper-plate, and grave lists of works ; 
 but satirical accounts. The astrologer Andrew Argoli is there, 
 and his son ; both of whom, with some of the others, have place in 
 modern works on biography. Argoli's discovery that logarithms 
 facilitate easy processes, but increase the labour of difficult ones, 
 is worth recording. 
 
 ControversiaB de vera circtili mensura . . , inter ........ 
 
 C. S. Longomontanum et Jo. Pellium. Amsterdam, 1647, 4to. 
 
 Longomontanus, a Danish astronomer of merit, squared the 
 circle in 1644 : he found out that the diameter 43 gives the square 
 root of 18252 for the circumference; which gives 3'14185 . . . 
 for the ratio. Pell answered him, and being a kind of circulating 
 medium, managed to engage in the controversy names known and 
 unknown, as Roberval, Hobbes, Carcavi, Lord Charles Cavendish, 
 Pallieur, Mersenne, Tassius, Baron Wolzogen, Descartes, Cavalieri 
 and Grolius. Among them, of course, Longomontanus was made 
 mincemeat : but he is said to have insisted on the discovery in his 
 epitaph. 
 
 The great circulating mediums, who wrote to everybody, heard 
 from everybody, and sent extracts to everybody else, have been 
 Father Mersenne, John Collins, and the late Prof, Schumacher : 
 all 'late' no doubt, but only the last recent enough to be so 
 styled. If M.C.S. should ever again stand for ' Member of the 
 Corresponding Society,' it should raise an acrostic thought of the 
 three. There is an allusion to Mersenne's occupation in Hobbes's 
 reply to him. He wanted to give Hobbes, who was very ill at 
 Paris, the Roman Eucharist: but Hobbes said, 4 I have settled all 
 
 F 
 
66 A BUDGET OF PARADOXES. 
 
 that long ago ; when did you hear from Grassendi ?' We are re- 
 minded of William's answer to Burnet. John Collins disseminated 
 Newton, among others. Schumacher ought to have been called 
 the postmaster-general of astromony, as Collins was called the 
 attorney-general of mathematics. 
 
 A late discourse. ... by Sir Kenelme Digby . . . Rendered into 
 English by R. White. London, 1658, 12mo. 
 
 On this work see Notes and Queries, 2nd series, vii. 231, 299, 
 445, viii. 190. It contains the celebrated sympathetic powder. I 
 am still in much doubt as to the connexion of Digby with this 
 tract. Without entering on the subject here, I observe that in 
 Birch's 'History of the Royal Society,' to which both Digby and 
 White belonged, Digby, though he brought many things before 
 the Society, never mentioned the powder, which is connected only 
 with the names of Evelyn and Sir Gilbert Talbot. The sym- 
 pathetic powder was that which cured by anointing the weapon 
 with its salve instead of the wound. I have long been convinced 
 that it was efficacious. The directions were to keep the wound 
 clean and cool, and to take care of diet, rubbing the salve on the 
 knife or sword. If we remember the dreadful notions upon drugs 
 which prevailed, both as to quantity and quality, we shall readily 
 see that any way of not dressing the wound would have been use- 
 ful. If the physicians had taken the hint, had been careful of 
 diet, &c. , and had poured the little barrels of medicine down the 
 throat of a practicable doll, they would have had their magical 
 cures as well as the surgeons. Matters are much improved now ; 
 the quantity of medicine given, even by orthodox physicians, 
 would have been called infinitesimal by their professional ances- 
 tors. Accordingly, the College of Physicians has a right to 
 abandon its motto, which is ATS long a, vita brevis, meaning 
 \ Practice is long, so life is short. 
 
 Examinatio et emendatio Mathematics Hodiernae. By Thomas 
 Hobbes. London, 1666, 4to. 
 
 In six dialogues : the sixth contains a quadrature of the circle. 
 But there is another edition of this work, without place or date 
 on the title-page, in which the quadrature is omitted. This 
 seems to be connected with the publication of another quadra- 
 ture, without date, but about 1670, as may be judged from its 
 professing to answer a tract of Wallis, printed in 1669. The 
 title is < Quadratura circuli, cubatio sphsersB, duplicatio cubi,' 4to . 
 
THOMAS HOBBES. SCALIGER. 67 
 
 Hobbes, who began in 1655, was very wrong in his quadrature ; 
 but, though not a Gregory St. Vincent, he was not the ignoramus 
 in geometry that he is sometimes supposed. His writings, erro- 
 neous as they are in many things, contain acute remarks on points 
 of principle. He is wronged by being coupled with Joseph 
 Scaliger, as the two great instances of men of letters who have 
 come into geometry to help the mathematicians out of their diffi- 
 culty. I have never seen Scaliger's quadrature, except in the 
 answers of Adrianus Romanus, Vieta and Clavius, and in the 
 extracts of Kastner. Scaliger had no right to such strong oppo- 
 nents : Erasmus or Bentley might just ay well have tried the 
 problem, and either would have done much better in any twenty 
 minutes of his life. 
 
 Scaliger inspired some mathematicians with great respect for 
 his geometrical knowledge. Vieta, the first man of his time, who 
 answered him, had such regard for his opponent as made him 
 conceal Scaliger's name. Not that he is very respectful in his 
 manner of proceeding : the following dry quiz on his opponent's 
 logic must have been very cutting, being true. 4 In grammaticis, 
 dare navibus Austros, et dare naves Austris, sunt seque significantia. 
 Sed in Geometricis, aliud est adsumpsisse circulum BCD non esse 
 majorem triginta sex segmentis BCDF, aliud circulo BCD non esse 
 majora triginta sex segmenta BCDF. Ilia adsumptiuncula vera est, 
 hsec falsa.' Isaac Casaubon, in one of his letters to De Thou, 
 relates that, he and another paying a visit to Vieta, the conversa- 
 tion fell upon Scaliger, of whom the host said that he believed 
 Scaliger was the only man who perfectly understood mathematical 
 writers, especially the Greek ones : and that he thought more of 
 Scaliger when wrong than of many others when right ; pluris se 
 Scaligerum vel errantem facere quam multos Karop&ovvras. This 
 must have been before Scaliger's quadrature (1594). There is an 
 old story of some one saying, ' Mallem cum Scaligero errare, quam 
 cum Clavio recte sapere.' This I cannot help suspecting to have 
 been a version of Vieta's speech with Clavius satirically inserted, 
 on account of the great hostility which Vieta showed towards 
 Clavius in the latter years of his life. 
 
 Montucla could not have read with care either Scaliger's quadra- 
 ture or Clavius's refutation. He gives the first a wrong date : he 
 assures the world that there is no question about Scaliger's quad- 
 rature being wrong, in the eyes of geometers at least : and he 
 states that Clavius mortified him extremely by showing that it 
 made the circle less than its inscribed dodecagon, which is, of 
 course, equivalent to asserting that a .straight line is not always 
 
 F 2 
 
68 A BUDGET OF PARADOXES. 
 
 the shortest distance between two points. Did Clavius show 
 this ? No, it was Scaliger himself who showed it, boasted 
 of it, and declared it to be a ' noble paradox ' that a theorem 
 false in geometry is true in arithmetic ; a thing, he says with 
 great triumph, not noticed by Archimedes himself! He says in 
 so many words that the periphery of the dodecagon is greater 
 than that of the circle ; and that the more sides there are to the 
 inscribed figure, the more does it exceed the circle in which it is. 
 And here are the words, on the independent testimonies of Clavius 
 and Kastner : 
 
 Ambitus dodecagoni circulo inscribendi plus potest quam circuli am- 
 bitus. Et quanto deineeps pluriuin laterum fuerit po]ygonum circulo 
 inscribendum, tanto plus poterit ambitus polygoni quam ambitus 
 circuli. 
 
 There is much resemblance between Joseph Scaliger and 
 William Hamilton, in a certain impetuosity of character, and in- 
 aptitude to think of quantity. Scaliger maintained that the arc 
 of a circle is less than its chord in arithmetic, though greater in 
 geometry ; Hamilton arrived at two quantities which are identi- 
 cal, but the greater the one the less the other. But, on the whole, 
 I liken Hamilton rather to Julius than to Joseph. On this last 
 hero of literature I repeat Thomas Edwards, who says that a man 
 is unlearned who, be his other knowledge what it may, does not 
 understand the subject he writes about. And now one of many 
 instances in which literature gives to literature character in 
 science. Anthony Teissier, the learned annotator of De Thou's 
 biographies, says of Finaeus, c II se vanta sans raison avoir trouve 
 la quadrature du cercle ; la gloire de cette admirable decouverte 
 etait reservee a Joseph Scaliger, comme 1'a ecrit Scevole de 
 St. Marthe.' 
 
 Natural and Political Observations . . . upon the Bills of 
 Mortality. By John Graunt, citizen of London. London, 1662, 
 4to. 
 
 This is a celebrated book, the first great work upon mortality. 
 But the author, going ultra crepidam, has attributed to the 
 motion of the moon in her orbit all the tremors which she gets 
 from a shaky telescope. But there is another paradox about this 
 book : the above absurd opinion is attributed to that excellent 
 mechanist. Sir William Petty, who passed his days among the 
 astronomers. Graunt did not write his own book ! Anthony Wood 
 hints that Petty ' assisted, or put into a way ' his old benefactor : 
 no doubt the two friends talked the matter over many a time. 
 
JOHN GRAUNT. GADBURY ON COMETS. 69 
 
 Burnet and Pepys state that Petty wrote the book. It is enough 
 for me that Graunt, whose honesty was never impeached, uses the 
 plainest incidental professions of authorship throughout ; that he 
 was elected into the Eoyal Society because he was the author ; 
 that Petty refers to him as author in scores of places, and published 
 an edition, as editor, after Graunt's death, with Graunt's name of 
 course. The note on Graunt in the ' Biographia Britannica ' may 
 be consulted ; it seems to me decisive. Mr. C. B. Hodge,, an able 
 actuary, has done the best that can be done on the other side in the 
 Assurance Magazine, viii. 234. If I may say what is in my mind, 
 without imputation of disrespect, I suspect some actuaries have 
 a bias : they would rather have Petty the greater for their Cory- 
 phaeus than Graunt the less. 
 
 Pepys is an ordinary gossip : but Burnet's account has an ani- 
 mus which is of a worse kind. He talks of ' one Graunt, a Papist, 
 under whose name Sir William Petty published his observations 
 on the bills of mortality.' He then gives the cock without a bull 
 story of Graunt being a trustee of the New Eiver Company, and 
 shutting up the cocks and carrying off their keys, just before the 
 lire of London, by which a supply of water was delayed. It was 
 one of the first objections made to Burnet's work, that Graunt was 
 not a trustee at the time ; and Maitland, the historian of London, 
 ascertained from the books of the Company that he was not 
 admitted until twenty-three days after the breaking out of the 
 fire. Graunt's first admission to the Company took place on the 
 very day on which a committee was appointed to inquire into the 
 cause of the fire. So much for Burnet. I incline to the view that 
 Graunt's setting London on fire strongly corroborates his having 
 written on the bills of mortality : every practical man takes stock 
 before he commences a grand operation in business. 
 
 De Cometis : or a discourse of the natures and effects of 
 Comets, as they are philosophically, historically, and astrologi- 
 cally considered. With a brief (yet full) account of the III late 
 Comets, or blazing stars, visible to all Europe. And what (in a 
 natural way of judicature) they portend. Together with some 
 observations on the nativity of the Grand Seignior. By John 
 Gadbury, ^tXo/mS^juariKo'c. London, 1665, 4to. 
 
 Gadbury, though his name descends only in astrology, was a well- 
 informed astronomer. D'Israeli sets down Gadbury, Lilly, Wharton, 
 Booker, &c., as rank rogues : I think him quite wrong. The easy 
 belief in roguery and intentional imposture which prevails in 
 educated society is, to my mind, a greater presumption against the 
 
70 A BUDGET OF PAEADOXES. 
 
 honesty of mankind than all the roguery and imposture itself. 
 Putting aside mere swindling for the sake of gain, and looking at 
 speculation and paradox, I find very little reason to suspect wilful 
 deceit. My opinion of mankind is founded upon the mournful fact 
 that, so far as I can see, they find within themselves the means of 
 believing in a thousand times as much as there is to believe in, 
 judging by experience. I do not say anything against Isaac 
 D'Israeli for talking his time. We are all in the team, and we all 
 go the road, but we do not all draw. 
 
 An essay towards a real character and a philosophical language. 
 By John Wilkins [Dean of Ripon, afterwards Bishop of 
 Chester]. London, 1668, folio. 
 
 This work is celebrated, but little known. Its object gives it 
 a right to a place among paradoxes. It proposes a language if 
 that be the proper name in which things and their relations 
 shall be denoted by signs, not words : so that any person, what- 
 ever may be his mother tongue, may read it in his own words. 
 This is an obvious possibility, and, I am afraid, an obvious im- 
 practicability. One man may construct such a system Bishop 
 Wilkins has done it but where is the man who will learn it ? 
 The second tongue makes a language, as the second blow makes a 
 fray. There has been very little curiosity about his performance, 
 the work is scarce ; and I do not know where to refer the reader for 
 any account of its details, except to the partial reprint of Wilkins 
 presently mentioned under 1802, in which there is an unsatisfac- 
 tory abstract. There is nothing in the 4 Biographia Britannica,' 
 except discussion of Anthony Wood's statement that the hint was 
 derived from Dalgarno's book, ' De Signis,' 1661. Hamilton 
 (' Discussions,' Art. 5,< Dalgarno ') does not say a word on this point, 
 beyond quoting Wood ; and Hamilton, though he did now and 
 then write about his countrymen with a rough-nibbed pen, knew 
 perfectly well how to protect their priorities. 
 
 Problema Austriacnm. Plus ultra Quadratura Circuli. Auctore 
 P. Gregorio a Sancto Vincentio Soc. Jesu., Antwerp, 1647, 
 folio. Opus Geometricum posthumum ad Mesolabium. By the 
 same. Gandavi [Ghent], 1668, folio. 
 
 The first book has more than 1200 pages, on all kinds of 
 geometry. Gregory St. Vincent is the greatest of circle-squarers, 
 and his investigations led him into many truths : he found the 
 property of the area of the hyperbola which led to Napier's loga- 
 rithms being called hyperbolic, Montucla says of him, with sly 
 
THE MESOLABUM. GEOMETRICAL QUADRATURE. 71 
 
 truth, that no one has ever squared the circle with so much genius, 
 or, excepting his principal object, with so much success. His 
 reputation, and the many merits of his work, led to a sharp con- 
 troversy on his quadrature, which ended in its complete exposure 
 by Huyghens and others. He had a small school of followers, 
 who defended him in print. 
 
 Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liege], 
 1668, 4to. 
 
 The Mesolabum is the solution of the problem of finding two 
 mean proportionals, which Euclid's geometry does not attain. 
 Slusius is a true geometer, and uses the ellipse, &c.: but he is 
 sometimes ranked with the trisectors, for which reason I place him 
 here, with this explanation. 
 
 The finding of two mean proportionals is the preliminary to the 
 famous old problem of the duplication of the cube, proposed by 
 Apollo (not Apollonius) himself. D'Israeli speaks of the ' six 
 follies of science,' the quadrature, the duplication, the perpetual 
 motion, the philosopher's stone, magic, and astrology. He might 
 as well have added the trisection, to make the mystic number seven : 
 but had he done so, he would still have been very lenient ; only 
 seven follies in all .science, from mathematics to chemistry! 
 Science might have said to such a judge as convicts used to say 
 who got seven years, expecting it for life, 4 Thank you, my Lord, 
 and may you sit there till they are over,' may the Curiosities of 
 Literature outlive the Follies of Science ! 
 
 1668. In this year James Gregory, in his Vera Circuli et 
 Hyperbolce Quadratures, held himself to have proved that the 
 geometrical quadrature of the circle is impossible. Few mathe- 
 maticians read this very abstruse speculation, and opinion is 
 somewhat divided. The regular circle-squarers attempt the 
 arithmetical quadrature, which has long been prove 1 to be impos- 
 sible. Very few attempt the geometrical quadrature. One of 
 the last is Malacarne, an Italian, who published his Solution 
 Geometrique, at Paris, in 1825. His method would make the 
 circumference less than three times the diameter. 
 
 La .Geometric Francoise, ou la Pratique aisee ... La qnadracture 
 du cercle. Par le Sieur de Beaulieu, Ingenieur, Geographe du 
 Hoi . . . Paris, 1676, 8vo. [not Pontault de Beaulieu, the cele- 
 brated topographer ; he died in 1674]. 
 
 If this book had been a fair specimen, I might have pointed 
 to it in connection with contemporary English works, and made 
 
72 A BUDGET OF PARADOXES. 
 
 a scornful comparison. But it is not a fair specimen. Beaulieu 
 was attached to the Eoyal Household, and throughout the century 
 it may be suspected that the household forced a royal road to 
 geometry. Fifty years before, Beaugrand, the king's secretary, 
 made a fool of himself, and [so?] contrived to pass for a geometer. 
 He had interest enough to get Desargues, the most powerful 
 geometer of his time, the teacher and friend of Pascal, prohibited 
 from lecturing. See some letters on the History of Perspective, 
 which I wrote in the Athenceum, in October and November, 
 1861. Montucla, who does not seem to know the true secret of 
 Beaugrand's greatness, describes him as 4 un certain M. de Beau- 
 grand, mathematicien, fort mal traite par Descartes, et a ce qu'il 
 paroit avec justice.' 
 
 Beaulieu's quadrature amounts to a geometrical construction 
 which gives TT= VIO. His depth may be ascertained from the 
 following extracts. First, on Copernicus : 
 
 Copernic, Allemand, ne s'esfc pas moms rendu ilhistre par ses doctes 
 ecrits ; et nous pourrions dire de luy, qu'il seroit le seul et unique en 
 la force de ses Problemes, si sa trop grande presomption ne 1'avoit 
 porte a avancer en cette Science une proposition aussi absurde, qu'elle 
 est centre la Foy et raison, en faisant la circonference d'un Cercle fixe, 
 immobile, et le centre mobile, sur lequel principe Geometrique, il a 
 avance en son Traitte Astrologique le Soleil fixe, et la Terre mobile. 
 
 I digress here to point out that though our quadrators, &c., 
 very often, and our historians sometimes, assert that men of the 
 character of Copernicus, &c. were treated with contempt and 
 abuse until their day of ascendancy came, nothing can be more 
 incorrect. From Tycho Brahe to Beaulieu, there is but one 
 expression of admiration for the genius of Copernicus. There is 
 an exception, which, I believe, has been quite misunderstood. 
 Maurolycus, in his 'De Sphaera,' written many years before its 
 posthumous publication in 1575, and which it is not certain he 
 would have published, speaking of the safety with which various 
 authors may be read after his cautions, says, ' Toleratur et 
 Mcolaus Copernicus qui Solem fixum et Terram in girum 
 circumverti posuit: et scutica potius, aut flagello, quam repre- 
 hensione dignus est.' Maurolycus was a mild and somewhat 
 contemptuous satirist, when expressing disapproval : as we should 
 now say, he pooh-poohed his opponents ; but, unless the above 
 be an instance, he was never savage nor impetuous. I am fully 
 satisfied that the meaning of the sente'nce is, that Copernicus, 
 who turned the earth like a boy's top, ought rather to have a whip 
 given him wherewith to keep up his plaything than a serious 
 
ff 
 
 J UNI 
 BEAULIEU'S ALGEBRA. SIR M. HALE. 73 
 
 ^ 
 
 refutation. To speak of tolerating a person as being more worthy 
 of a flogging than an argument, is almost a contradiction. 
 I will now extract Beaulieu's treatise on algebra, entire. 
 
 L'Algebre est la science curieuse des S9avans et specialement d'rra. 
 General d'Armee on Capitaine, pour promptement ranger une Armee 
 en bataille, et nombre de Monsquetaires et Piqniers qui composent les 
 bataillons d'icelle, outre les figures de I'Arithmetique. Cette science a 
 5 figures particulieres en cette sorte. P signifie plus au commerce, et 
 a 1' Armee Piquiers. M signifie moins, et Mousquetaire en 1'Art des 
 bataillons. [It is quite true that P and M were used for plus and minus 
 in a great many old works.] R signifie ratine en la mesure du Cube, 
 et en 1' Armee rang. Q signifie quare en 1'un et Fautre usage. 
 signifie cube en la mesure, et Cavallerie en la composition des bataillons 
 et escadrons. Quant a 1'operation de cette science, c'est d'additionner 
 un plus d'avec plus, la somme sera plus, et moins d'avec plus, on 
 soustrait le moindre du plus, et la reste est la somme requise ou nombre 
 trouve. Je dis seulement cecy en passant pour ceux qui n'en savent 
 rien du tout. 
 
 This is the algebra of the Eoyal Household, seventy-three years 
 after the death of Vieta. Quaere, is it possible that the fame of 
 Vieta, who himself held very high stations in the household all 
 his life, could have given people the notion that when such an 
 officer chose to declare himself an algebraist, he must be one 
 indeed ? This would explain Beaugrand, Beaulieu, and all the 
 beaux. Beaugrand not only secretary to the king, but c mathe- 
 matician ' to the Duke of Orleans I wonder what his 'fool 'could 
 have been like, if indeed he kept the offices separate, would 
 have been in my list if I had possessed his Geostatique, pub- 
 lished about 1638. He makes bodies diminish in weight as they 
 approach the earth, because the effect of a weight on a lever is 
 less as it approaches the fulcrum. 
 
 Remarks upon two late ingenious discourses . . . By Dr. Henry 
 More. London, 1676, 8vo. 
 
 In 1673 and 1675, Matthew Hale, then Chief Justice, published 
 two tracts, an ' Essay touching Gravitation,' and ' Difficiles Nugse' 
 on the Torricellian experiment. Here are the answers by the 
 learned and voluminous Henry More. The whole would be 
 useful to any one engaged in research about ante-Newtonian 
 notions of gravitation. 
 
74 A BUDGET OF PARADOXES, 
 
 Observations touching the principles of natural motions ; and 
 especially touching rarefaction and condensation . . . By the 
 author of Difficiles Nugce. London, 1677, 8vo. 
 
 This is another tract of Chief Justice Hale, published the year 
 after his death. The reader will remember that motion, in old 
 philosophy, meant any change from state to state : what we now 
 describe as motion was local motion. This is a very philosophical 
 book, about flux and materia prima, virtus activa and essentialis, 
 and other fundamentals. I think Stephen Hales, the author of 
 the ; Vegetable Statics,' has the writings of the Chief Justice 
 sometimes attributed to him, which is very puny justice indeed. 
 Matthew Hale died in 1676, and from his devotion to science it 
 probably arose that his famous Pleas of the Crown and other law 
 works did not appear until after his death. One of his con- 
 temporaries was the astronomer Thomas Street, whose Caroline 
 Tables were several times printed : another contemporary was 
 his brother judge. Sir Thomas Street. But of the astronomer 
 absolutely nothing is known : it is very unlikely that he and the 
 judge were the same person, but there is not a bit of positive evi- 
 dence either for or against, so far as can be ascertained. Halley 
 no less a person published two editions of the 'Caroline Tables,' no 
 doubt after the death of the author : strange indeed that neither 
 Halley nor any one else should leave evidence that Street was 
 born or died. 
 
 Matthew Hale gave rise to an instance of the lengths a lawyer 
 will go when before a jury who cannot detect him. Sir Samuel 
 Shepherd, the Attorney General, in opening Hone's first trial, 
 calls him ' one who was the most learned man that ever adorned 
 the Bench, the most even man that ever blessed domestic life, the 
 most eminent man that ever advanced the progress of science, 
 and one of the [very moderate] best and most purely religious 
 men that ever lived. 
 
 Basil Valentine his triumphant Chariot of Antimony, with 
 annotations of Theodore Kirkringius, M.D. With the true book 
 of the learned Synesius, a Greek abbot, taken out of the 
 Emperour's library, concerning the Philosopher's Stone. 
 London, 1678, 8vo. 
 
 There are said to be three Hamburg editions of the collected 
 works of Valentine, who discovered the common antimony, and 
 is said to have given the name antimoine, in a curious way. 
 Finding that the pigs of his convent throve upon it, he gave it 
 
BASIL VALENTINE. THE ALCHEMISTS. 75 
 
 to his brethren, who died of it. The impulse given to chemistry 
 by E. Boyle seems to have brought out a vast number of transla- 
 tions, as in the following tract : 
 
 Collectanea Gliymica : A collection of ten several treatises in 
 chymistry, concerning the liquor Alkehest, the Mercury of 
 Philosophers, and other curiosities worthy the perusal. Written 
 by Eir. Philaletha, Anonymus, J. B. Van-Helmont, Dr. Fr. 
 Antonie, Bernhard Earl of Trevisan, Sir Geo. Bipley, Rog. 
 Bacon, Geo. Starkie, Sir Hugh Platt, and the Tomb of Semira- 
 mis. See more in the contents. London, 1684, 8vo. 
 
 In the advertisements at the ends of these tracts there are 
 upwards of a hundred English tracts, nearly all of the period, 
 and most of them translations. Alchemy looks up since the 
 chemists have found perfectly different substances composed of 
 the same elements and proportions. It is true the chemists 
 cannot yet transmute ; but they may in time : they poke about 
 most assiduously. It seems, then, that the conviction that 
 alchemy must be impossible was a delusion: but we do not 
 mention it. 
 
 The astrologers and the alchemists caught it in company in 
 the following, of which I have an unreferenced note. 
 
 Mendacem et futilem hominem nominare qui volunt, calenda- 
 riographum dicunt ; at qui sceleratum simul ac impostorem, 
 chimicum. 
 
 Crede ratem ventis, corpus ne crede chimistis ; 
 Est qusevis chimica tutior aura fide. 
 
 Among the smaller paradoxes of the day is that of the Times 
 newspaper, which always spells it chymistry : but so, I believe, 
 do Johnson, Walker, and others. The Arabic word is very likely 
 formed from the Greek : but it may be connected either with 
 or with 
 
 Lettre d'un gentil-homme de province a une dame de qualite, 
 sur l.e sujet de la Comete. Paris, 1681, 4to. 
 
 An opponent of astrology, whom I strongly suspect to have 
 been one of the members of the Academy of Sciences under the 
 name of a country gentleman, writes very good sense on the 
 tremors excited by comets. 
 
76 A BUDGET OF PARADOXES. 
 
 The Petitioning- Comet : or, a brief Chronology of all the famous 
 Comets and their events, that have happened from the birth of 
 Christ to this very day. Together with a modest enquiry into 
 this present comet, London, 1681, 4to. 
 
 A satirical tract against cometic prophecy : 
 
 1 This present comet (it's true) is of a menacing aspect, but if the 
 new parliament (for whose convention so many good men pray) continue 
 long to sit, I fear not but the star will lose its virulence and malignancy, 
 or at least its portent be averted from this our nation ; which being 
 the humble request to God of all good men, makes me thus entitle it, 
 a Petitioning- Comet. 
 
 The following anecdote is new to me : 
 
 Queen Elizabeth (1558) being then at "Richmond, and being 
 disswaded from looking on a comet which ,did then appear, made 
 answer, jacta est alea, the dice are thrown ; thereby intimating that 
 the pre-order'd providence of God was above the influence of any star 
 or comet. 
 
 The argument was worth nothing : for the comet might have 
 been on the dice with the event ; the astrologers said no more, 
 at least the more rational ones, who were about half oF the 
 whole. 
 
 An astrological and theological discourse upon this present 
 great conjunction (the like whereof hath not (likely) been in 
 some ages) ushered in by a great comet. London, 1682, 4to. 
 By C. N. 
 
 The author foretells the approaching ' sabbatical jubilee,' but 
 will not fix the date : he recounts the failures of his predeces- 
 sors. 
 
 A judgment of the comet which became first generally visible 
 to us in Dublin, December 13, about 15 minutes before 5 in the 
 evening, A.D. 1680. By a person of quality. Dublin, 1682, 
 4to. 
 
 The author argues against cometic astrology with great ability . 
 
 A prophecy on the conjunction of Saturn and Jupiter in this 
 present year 1682. With some prophetical predictions of what 
 is likely to ensue therefrom in the year 1684. By John Case, 
 Student in physic and astrology. London, 1682, 4to. 
 
 According to this writer, great conjunctions of Jupiter and 
 Saturn occur ' in the fiery trigon,' about once in 800 years. Of 
 
MAECELIS. MATHEMATICAL THEOLOGY. 77 
 
 these there are to be seven : six happened in the several times 
 of Enoch, Noah, Moses, Solomon, Christ, Charlemagne. The 
 seventh, which is to happen at 6 the lamb's marriage with the 
 bride,' seems to be that of 1682 ; but this is only vaguely hinted. 
 
 De Quadrature van de Circkel. By Jacob Marcelis. Amsterdam, 
 
 1698, 4to. 
 Ampliatie en demonstrate wegens de Quadrature . . . By Jacob 
 
 Marcelis. Amsterdam, 1699, 4to. 
 Eenvoudig vertoog briev-wys geschrevem am J. Marcelis . . 
 
 Amsterdam, 1702, 4to. 
 De sleutel en openinge van de quadrature. . . . Amsterdam, 
 
 1704, 4to. 
 
 Who shall contradict Jacob Marcelis ? He says the circum- 
 ference contains the diameter exactly times 
 
 S 1QQ8449Q87377541679894282184894 
 6997T83637540819440035239271702 
 
 But he does not come very near, as the young arithmetician will 
 find. 
 
 Theologize Christianse Principia Mathematica. Auctore Johanne 
 Craig. London, 1699, 4to. 
 
 This is a celebrated speculation, and has been reprinted abroad, 
 and seriously answered. Craig is known in the early history of 
 fluxions, and was a good mathematician. He professed to calcu- 
 late, on the hypothesis that the suspicions against historical 
 evidence increase with the square of the time, how long it will 
 take the evidence of Christianity to die out. He finds, by 
 formulae, that had it been oral only, it would have gone out 
 A.D. 800 ; but, by aid of the written evidence, it will last till 
 A.D. 3150. At this period he places the second coming, which is 
 deferred until the extinction of evidence, on the authority of the 
 question ' When the Son of Man cometh, shall he find faith on 
 the earth ? ' It is a pity that Craig's theory was not adopted : it 
 would have spared a hundred treatises on the end of the world, 
 founded on no better knowledge than his, and many of them 
 falsified by the event. The most recent (October, 1863) is a 
 tract in proof of Louis Napoleon being Antichrist, the Beast, the 
 eighth Head, &c.; and the present dispensation is to close soon 
 after 1864. 
 
 In order rightly to judge Craig, who added speculations on the 
 variations of pleasure and pain treated as functions of time, it is 
 
78 A BUDGET OF PARADOXES. 
 
 necessary to remember that in Newton's day the idea of force, as a 
 quantity to be measured, and as following a law of variation, was 
 very new : so likewise was that of probability, or belief, as an object 
 of measurement. The success of the 4 Principia ' of JSTewtonput it 
 into many heads to speculate about applying notions of quantity 
 to other things not then brought under measurement. Craig 
 imitated Newton's title, and evidently thought he was making 
 a step in advance : but it is not every one who can plough with 
 Samson's heifer. 
 
 It is likely enough that Craig took a hint, directly or in- 
 directly, from Mahometan writers, who make a reply to the 
 argument that the Koran has not the evidence derived from 
 miracles. They say that, as evidence of Christian miracles is 
 daily becoming weaker, a time must at last arrive when it will 
 fail of affording assurance that they were miracles at all : 
 whence would arise the necessity of another prophet and other 
 miracles. Lee, the Cambridge orientalist, from whom the above 
 words are taken, almost certainly never heard of Craig or his 
 theory. 
 
 Copernicans of all sort s convicted ... to which is added a Treatise 
 of the Magnet. By the Hon. Edw. Howard, of Berks. London, 
 1705, 8vo. 
 
 Not all the blood of all the Howards will gain respect for a 
 writer who maintains that eclipses admit no possible explanation 
 under the Copernican hypothesis, and who asks how a man can 
 'go 200 yards to any place if the moving superficies of the earth 
 does carry it from him ? ' Horace Walpole, at the beginning of 
 his ' Eoyal and Noble Authors,' has mottoed his book with the 
 Cardinal's address to Ariosto, 'Dove diavolo, Messer Ludovico, 
 avete pigliato tante coglionerie ? ' Walter Scott says you could 
 hardly pick out, on any principle of selection except badness 
 itself, he means of course the same number of plebeian authors 
 whose works are so bad. But his implied satire on aristocratic 
 writing forgets two points. First, during a large period of our 
 history, when persons of rank condescended to write, they veiled 
 themselves under ' a person of honour,' 4 a person of quality,' and 
 the like, when not wholly undescribed. Not one of these has 
 Walpole got ; he omits, for instance, Lord Brounker's translation 
 of Descartes on Music. Secondly, Walpole only takes the heads 
 of houses: this cuts both ways; he equally eliminates the Hon. 
 Robert Boyle and the precious Edward Howard. This last writer 
 is hardly out of the time in which aristocracy suppressed its 
 
WHISTON, DITTON, AND SWIFT. 79 
 
 names ; the avowal was then usually meant to make the author's 
 greatness useful to the book. In our day, literary peers and 
 honourables are very favourably known, and contain an eminent 
 class. They rough it like others, and if such a specimen as Edw. 
 Howard were now to appear, he would be greeted with 
 
 Hereditary noodle ! knowest thou not, 
 
 Who would be wise, himself must make him so ? 
 
 A new and easy method to find the longitude at land or sea. 
 London, 1710, 4to. 
 
 This tract is a little earlier than the great epoch of such publi- 
 cations (1714), and professes to find the longitude by the observed 
 altitudes of the moon and two stars. 
 
 A new method for discovering the longitude both at sea and 
 land, humbly proposed to the consideration of the public. By 
 Wm. Whiston and Humphry Ditton. London, 1714, 8vo. 
 
 This is the celebrated tract, written by the two Arian heretics. 
 Swift, whose orthodoxy was as undoubted as his meekness, wrote 
 upon it the epigram if, indeed, that be epigram of which the 
 point is pious wish which has been so often recited for the 
 purity of its style, a purity which transcends modern printing. 
 Perhaps some readers may think that Swift cared little for Whiston 
 and Ditton, except as a chance hearing of their plan pointed them 
 out as good marks. But it was not so : the clique had their eye 
 on the guilty pair before the publication of the tract. The pre- 
 face is dated July 7 ; and ten days afterwards Arbuthnot writes 
 as follows to Swift : 
 
 Whiston has at last published his project of the longitude ; the most 
 ridiculous thing that ever was thought on. But a pox on him ! he has 
 spoiled one of my papers of Scriblerus, which was a proposition for the 
 longitude not very unlike his, to this purpose ; that since there was no 
 pole for east and west, that all the princes of Europe should join and 
 build two prodigious poles, upon high mountains, with a vast lighthouse 
 to serve for -a polestar. I was thinking of a calculation of the time, 
 charges, and dimensions. Now you must understand his project is by 
 lighthouses, and explosion of bombs at a certain hour. 
 
 The plan was certainly impracticable ; but Whiston%nd Ditton 
 might have retorted that they were nearer to the longitude than 
 their satirist to the kingdom of heaven, or even to a bishopric. 
 Arbuthnot, I think, here and elsewhere, reveals himself as the 
 calculator who kept Swift right in his proportions in the matter 
 
80 A BUDGET OF PAKADOXES. 
 
 of the Lilliputians, Brobdingnagians, &c. Swift was very ignorant 
 about things connected with number. He writes to Stella that 
 he has discovered that leap-year comes every four years, and that 
 all his life he had thought it came every three years. Did he 
 begin with the mistake of Caesar's priests ? Whether or no, when 
 I find the person who did not understand leap-year inventing 
 satellites of Mars in correct accordance with Kepler's third law, 
 I feel sure he must have had help. 
 
 An essay concerning the late apparition in the heavens on the 
 6th of March. Proving by mathematical, logical, and moral 
 arguments, that it cou'd not have been produced meerly by the 
 ordinary course of nature, but must of necessity be a prodigy. 
 Humbly offered to the consideration of the Royal Society. 
 London, 1716, 8vo. 
 
 The prodigy, as described, was what we should call a very 
 decided and unusual aurora borealis. The inference was, that 
 men's sins were bringing on the end of the world. The author 
 thinks that if one of the old ' threatening prophets ' were then 
 alive, he would give ' something like the following.' I quote a 
 few sentences of the notion which the author had of the way in 
 which Ezekiel, for instance, would have addressed his Maker in 
 the reign of George the First : 
 
 Begin ! Begin ! Sovereign, for once, with an effectual clap of 
 thunder. . . . O Deity ! either thunder to us no more, or when you 
 thunder, do it home, and strike with vengeance to the mark. . . . "Pis 
 not enough to raise a storm, unless you follow it with a blow, and the 
 thunder without the bolt, signifies just nothing at all. . . . Are then 
 your lightnings of so short a sight, that they don't know how to hit, 
 unless a mountain stands like a barrier in their way ? Or perhaps so 
 many eyes open in the firmament make you lose your aim when you 
 shoot the arrow? Is it this? No\ but, my J dear Lord, it is your 
 custom never to take hold of your arms till you have first bound round 
 your majestic countenance with gathered mists and clouds. 
 
 The principles of the Philosophy of the Expansive and Con- 
 tractive Forces. ... By Robert Greene, M.A., Fellow of Clare 
 Hall. Cambridge, 1727, folio. 
 
 Sanderson writes to Jones : * The gentleman has been reputed 
 mad for these two years last past, but never gave the world such 
 ample testimony of it before.' This was said of a former work of 
 Greene's, on solid geometry, published in 1712, in which he gives 
 
NEWTON'S APPLE. gj_ 
 
 a quadrature. He gives the same or another, I do not know 
 which, in the present work, in which the circle is 3 diameters. 
 This volume is of 981 good folio pages, and treats of all things, 
 mental and material. The author is not at all mad, only wrong 
 on many points. It is the weakness of the orthodox follower of 
 any received system to impute insanity to the solitary dissentient : 
 which is voted (in due time) a very wrong opinion about Coper- 
 nicus, Columbus, or Galileo, but quite right about Robert Greene. 
 If misconceptions, acted on by too much self-opinion, be sufficient 
 evidence of madness, it would be a curious inquiry what is the 
 laast per-centage of the reigning school which has been insane at 
 any one time. Greene is one of the sources for Newton being led 
 to think of gravitation by the fall of an apple : his authority is 
 the gossip of Martin Folkes. Probably Folkes had it from 
 Newton's niece, Mrs. Conduitt, whom Voltaire acknowledges as 
 his authority. It is in the draft found among Conduitt's papers 
 of memoranda to be sent to Fontenelle. But Fontenelle, though 
 a great retailer of anecdote, does not mention it in his eloge of 
 Newton ; whence it may be suspected that it was left out in the 
 copy forwarded to France. D'Israeli has got an improvement on 
 the story : the apple * struck him a smart blow on the head : ' no 
 doubt taking him just on the organ of causality. He was ' surprised 
 at the force of the stroke ' from so small an apple : but then the 
 apple had a mission ; Homer would have said it was Minerva in 
 the form of an apple. 6 This led him to consider the accelerating 
 motion of falling bodies,' which Galileo had settled long before : 
 4 from whence he deduced the principle of gravity,' which many 
 had considered before him, but no one had deduced anything from 
 it. I cannot imagine whence D'Israeli got the rap on the head, 
 I mean got it for Newton : this is very unlike his usual accounts 
 of things. The story is pleasant and possible : its only defect is 
 that various writings^ well known to Newton, a very learned 
 mathematician, had given more suggestion than a whole sack of 
 apples could have done, if they had tumbled on that mighty head 
 all at once. And Pemberton, speaking from Newton himself, 
 says nothing more than that the idea of the moon being retained 
 by the same force which causes the fall of bodies struck him for 
 the first time while meditating in a garden. One particular tree 
 at Woolsthorpe has been selected as the gallows of the apple- 
 shaped goddess: it died in 1820, and Mr. Tumor kept the wood; 
 but Sir D. Brewster brought away a bit of root in 1814, and must 
 have had it on his conscience for 43 years that he may have killed 
 the tree. Kepler's suggestion of gravitation with the inverse 
 
 G 
 
82 A BUDGET OF PARADOXES. 
 
 distance, and Bouillaud's proposed substitution of the inverse 
 square of the distance, are things which Newton knew better than 
 his modern readers. I discovered two anagrams on his name, 
 which are quite conclusive : the notion of gravitation was not 
 new; but Newton went on. Some wandering spirit, probably, 
 whose business it was to resent any liberty taken with Newton's 
 name, put into the head of a friend of mine eighty-one anagrams 
 on my own pair, some of which hit harder than any apple. 
 
 This friend, whom I must not name, has since made it up to 
 about 800 anagrams on my name, of which I have seen about 
 650. Two of them I have joined in the title-page : the reader 
 may find the sense. A few of the others are personal remarks. 
 
 Great gun ! do us a sum ! 
 is a sneer at my pursuits : but, 
 
 Go ! great sum ! fa u du 
 
 is more dignified. 
 
 Sunt agro ! gaudemus, 
 
 is happy as applied to one of whom it may be said : 
 
 Ne'er out of town ; 'tis such a horrid life : 
 Bat duly sends his family and wife. 
 
 Ad sum, nugator, suge ! 
 
 is addressed to a student who continues talking after the lecture 
 has commenced : oh ! the rascal ! 
 
 Graduatus sum ! nego 
 applies to one who declined to subscribe for an M.A. degree. 
 
 Usage mounts guard 
 symbolises a person of very fixed habits. 
 
 Gus ! Gus ! a mature don ! 
 
 August man ! sure, god ! 
 And Gus must argue, O ! 
 
 Snug as mud to argue, 
 Must argue on gauds. 
 
 A mad rogue stung us. 
 Gag a numerous stud. 
 
 Go ! turn us ! damage us ! 
 Tug us ! O drag us ! Amen. 
 
 Grudge us ! moan at us ! 
 Daunt us ! gag us more ! 
 
 T3og-ear us, man ! gut us ! 
 D us ! a rogue tugs ! 
 
TKEATISE ASCEIBED TO NEWTON. 83 
 
 are addressed to me by the circle-squarers ; and, 
 O ! Gus ! tug a mean surd ! 
 
 is smart upon my preference of an incommensurable value of IT 
 to 3^, or some such simple substitute. While, 
 Gus ! Gus ! at 'em a' round ! 
 
 ought to be the backing of the scientific world to the author of 
 the ' Budget of Paradoxes.' 
 
 The whole collection commenced existence in the head of a 
 powerful mathematician during some sleepless nights. Seeing 
 how large a number was practicable, he amused himself by in- 
 venting a digested plan of finding more. 
 
 Is there any one whose name cannot be twisted into either 
 praise or satire ? I have had given to me, 
 
 Thomas Babington Macaulay 
 Mouths big : a Cantab anomaly. 
 
 A treatise of the system of the world. By Sir Isaac Newton- 
 Translated into English. London, 1728, 8vo. 
 
 I think I have a right to one little paradox of my own : I 
 greatly doubt that Newton wrote this book. Castiglione, in his 
 c Newtoni Opuscula,' gives it in the Latin which appeared in 1731, 
 not for the first time ; he says Angli omnes Newtono tribuunt. It 
 appeared just after Newton's death, without the name of any 
 editor, or any allusion to Newton's recent departure, purporting 
 to be that popular treatise which Newton^ at the beginning of 
 the third book of the ' Principia,' says he wrote, intending it to 
 be the third book. It is very possible that some observant turn- 
 penny might construct such a treatise as this from the third book, 
 that it might be ready for publication the moment Newton could 
 not disown it. It has been treated with singular silence : the 
 name of the editor has never been given. Eigaud mentions it 
 without a word : I cannot find it in Brewster's Newton, nor in the 
 6 Biographia Britannica.' There is no copy in the Catalogue of 
 the Royal Society's Library, either in English or Latin, except in 
 Castiglione. I am open to correction ; but I think nothing from 
 Newton's acknowledged works will prove as laid down in the 
 suspected work that he took Numa's temple of Vesta, with a 
 central fire, to be intended to symbolise the sun as the centre of 
 our system, in the Copernican sense. 
 
 Mr.Edleston gives an account of the lectures ' de motu corporum,' 
 and gives the corresponding pages of the Latin ' De Systemate 
 
 o 2 
 
84 A BUDGET OF PARADOXES. 
 
 Mundi' of 1731. But no one mentions the English of 1728. 
 This English seems to agree with the Latin ; but there is a mystery 
 about it. The preface says, 4 That this work as here published is 
 genuine will so clearly appear by the intrinsic marks it bears, that 
 it will be but losing words and the reader's time to take pains in 
 giving him any other satisfaction.' Surely fewer words would 
 have been lost if the prefator had said at once that the work was 
 from the manuscript preserved at Cambridge. Perhaps it was a 
 mangled copy clandestinely taken and interpolated. 
 
 Lord Bacon not the author of 'The Christian Paradoxes,' being 
 a reprint of ' Memorials of Godliness and Christianity,' by 
 Herbert Palmer, B.D. With Introduction, Memoir, and Notes, 
 by the Rev. Alexander B. Grosart, Kenross. (Private, circulation, 
 1864). 
 
 I insert the above in this place on account of a slight con- 
 nexion with the last. Bacon's Paradoxes, so attributed were 
 first published as his in some asserted ' Eemains,' 1648. They 
 were admitted into his works in 1730, and remain there to this 
 day. The title is 4 The Character of a believing Christian, set 
 forth in paradoxes and seeming contradictions.' The following is 
 a specimen : 
 
 He believes three to be one and one to be three ; a father not to be 
 older than his son ; a son to be equal with his father ; and one pro- 
 ceeding from both to be equal with both : he believes three persons in 
 
 one nature, and two natures in one person He believes the God 
 
 of all grace to have been angry with one that never offended Him ; and 
 that God that hates sin to be reconciled to himself though sinning con- 
 tinually, and never making or being able to make Him any satisfaction. 
 He believes a most just God to have punished a most just person, and 
 to have justified himself, though a most ungodly sinner. He believes 
 himself freely pardoned, and yet a sufficient satisfaction was made for 
 him. 
 
 Who can doubt that if Bacon had written this, it must have 
 been wrong? Many writers, especially on the Continent, have 
 taken him as sneering at (Athanasian) Christianity right and left. 
 Many Englishmen have taken him to be quite in earnest, and to 
 have produced a body of edifying doctrine. More than a century 
 ago the Paradoxes were published as a penny tract ; and, again, at 
 the same price, in the ' Penny Sunday Header,' vol. vi. No. 148, a 
 few passages were omitted, as too strong. But all did not agree : 
 in my copy of Peter Shaw's edition (vol. ii. p. 283) the Paradoxes 
 have been cut out by the binder, who has left the backs of the 
 leaves. I never had the curiosity to see whether other copies of 
 
BACON'S PARADOXES. SOCINIANS AND UNITARIANS. 85 
 
 the edition have been served in the same way. The Keligious 
 Tract Society republished them recently in ' Selections from the 
 Writings of Lord Bacon,' (no date; bad plan; about 1863, I 
 suppose). No omissions were made, so far as I find. 
 
 I never believed that Bacon wrote this paper ; it has neither his 
 sparkle nor his idiom. I stated my doubts even before I heard 
 that Mr. Spedding, one of Bacon's editors, was of the same mind. 
 (Athenceum.) July 16, 1864). I was little moved by the wide con- 
 sent of orthodox men : for I knew how Bacon, Milton, Newton, 
 Locke, &c., were always claimed as orthodox until almost the 
 present day. Of this there is a remarkable instance. 
 
 Among the books which in my younger day were in some 
 orthodox publication lists I think in the list of the Christian 
 Knowledge Society, but I am not sure was Locke's ' Eeason- 
 ableness of Christianity.' It seems to have come down from the 
 eighteenth century, when the battle was belief in Christ against 
 unbelief, simpliciter, as the logicians say. Now, if ever there 
 were a Socinian 1 book in the world, it is this work of Locke. 
 ' These two,' says Locke, ' faith and repentance, i.e. believing 
 Jesus to be the Messiah, and a good life, are the indispensable 
 conditions of the new covenant, to be performed by all those who 
 would obtain eternal life.' All the book is amplification of this 
 doctrine. Locke, in this and many other things, followed Hobbes, 
 whose doctrine / in the Leviathan, is fidem, quanta ad salutem 
 necessaria est, contineri in hoc articulo, Jesus est Christus. For 
 this Hobbes was called an atheist, which many still believe him 
 to have been : some of his contemporaries called him, rightly, 
 
 1 I use the word Socinian because it was so much used in Locke's time ; it is used 
 in our own day by the small fry, the unlearned clergy and their immediate followers, 
 as a term of reproach for all Unitarians. I suspect they have a kind of liking for the 
 word ; it sounds like so sinful. The learned clergy and the higher laity know better : 
 they know that the bulk of the modern Unitarians go farther than Socinus, and are 
 not correctly named as his followers. The Unitarians themselves neither desire nor 
 deserve a name which puts them one point nearer to orthodoxy than they put 
 themselves. That point is the doctrine that direct prayer to Jesus Christ is lawful 
 and desirable : this Socinus held, and the modern Unitarians do not hold, Socinus, 
 in treating the subject in his own Institutio, an imperfect catechism which he left, lays 
 much more stress on John xiv. 13 than on xv. 16 and xvi. 23. He is not disinclined to 
 think that Patr&m should be in the first citation, where some put it ; but he says 
 that to ask the Father in the name of the Son is nothing but praying to the Son in 
 prayer to the Father. He labours the point with obvious wish to secure a conclusive 
 sanction. In the Racovian Catechism, of which Faustus Soeinus probably drew the 
 first sketch, a clearer light is arrived at. The translation says : ' But wherein con- 
 sists the divine honour due to Christ? In adoration likewise and invocation. For 
 we ought at all times to adore Christ, and may in our necessities address our prayers 
 to him as often as we please; and there are many reasons to induce us to do t]i:$ 
 freely.' There are some who like accuracy, even in aspersion. 
 
86 A BUDGET OF PARADOXES. 
 
 a Socinian. Locke was known for a Socinian as soon as his work 
 appeared : Dr. John Edwards, his assailant, says he is ; Socin- 
 ianized all over.' Locke, in his reply, says 'there is not one 
 word of Socinianism in it : ' and he was right : the positive 
 Socinian doctrine has not one word of Socinianism in it ; So- 
 cinianism consists in omissions. Locke and Hobbes did not dare 
 deny the Trinity : for such a thing Hobbes might have been 
 roasted, and Locke might have been strangled. Accordingly, the 
 well known way of teaching Unitarian doctrine was the collection 
 of the asserted essentials of Christianity, without naming the 
 Trinity, &c. This is the plan Newton followed, in the papers which 
 have at last been published. 
 
 So I, for one, thought little about the general tendency of 
 orthodox writers to claim Bacon by means of the Paradoxes. I 
 knew that, in his ' Confession of Faith ' he is a Trinitarian of a 
 heterodox stamp. * His second Person takes human nature before 
 he took flesh, riot for redemption, but as a condition precedent of 
 creation. ' God is so holy, pure, and jealous, that it is impossible 
 for him to be pleased in any creature, though the work of his 
 
 own hands [Genesis i. 10, 12, 18, 21, 25, 31, freely 
 
 rendered]. But purposing to become a Creator, and to commu- 
 nicate to his creatures, he ordained in his eternal counsel that 
 one person of the Godhead should be united to one nature, and 
 to one particular of his creatures ; that so, in the person of 
 the Mediator, the true ladder might be fixed, whereby God 
 might descend to his creatures and his creatures might ascend 
 to God ' 
 
 This is republished by the Eeligious Tract Society, and seems 
 to suit their theology, for they confess to having omitted some 
 things of which they disapprove. 
 
 In 1864, Mr. Grosart published his discovery that the Paradoxes 
 are by Herbert Palmer; that they were first published surrep- 
 titiously, and immediately afterwards by himself, both in 1645; 
 that the ' Eemains ' of Bacon did not appear until 1 648 ; that 
 from 1645 to 1708, thirteen editions of the ' Memorials' were 
 published, all containing the Paradoxes. In spite of this, the 
 Paradoxes were introduced into Bacon's w r orks in 1730, where they 
 have remained. 
 
 Herbert Palmer was of good descent, and educated as a Puri- 
 tan. He was an accomplished man, one of the few of his day who 
 could speak P^rench as well as English. He went into the Church, 
 and was beneficed by Laud, in spite of his puritanism ; he sat in 
 the Assembly of Divines, and was finally President of Queens' 
 
CIKCLE SQUAKEKS. WHISTON ON THE LONGITUDE. 87 
 
 College, Cambridge, in which post he died, August 13, 1647, in the 
 46th year of his age. 
 
 Mr. Grrosart says, speaking of Bacon's 4 Eemains,' c All who have 
 had occasion to examine our early literature* are aware that it was 
 a common trick to issue imperfect, false, and unauthorised writings 
 under any recently deceased name that might be expected to take. 
 The Puritans, down to John Bunyan, were perpetually expos- 
 tulating and protesting against such procedure.' I have met with 
 instances of all this ; but I did not know that there was so much 
 of it : a good collection would be very useful. The work of 1728, 
 attributed to Newton, is likely enough to be one of the class. 
 
 Demonstration de 1'immobilitez de la Terre. . . . Par M. de la 
 Jonchere, Ingenieur Fran9ais. Londres, 1728, 8vo. 
 
 A synopsis which is of a line of argument belonging to the 
 beginning of the preceding century. 
 
 The Circle squared ; together with the Ellipsis and several re- 
 flections on it. The finding two geometrical mean proportionals, 
 or doubling the cube geometrically. By Richard Locke. .... 
 London, no date, probably about 1730, 8vo. 
 
 According to Mr. Locke, the circumference is three diameters, 
 three-fourths the difference of the diameter and the side of the 
 inscribed equilateral triangle, and three- fourths the difference 
 between seven-eighths of the diameter and the side of the same 
 triangle. This gives, he says, 3*18897. There is an addition to 
 this tract, being an appendix to a book on the longitude. 
 
 The Circle squar'd. By Thos. Baxter, Crathorn, Cleaveland, 
 Yorkshire-. London, 1732, 8vo. 
 
 Here TT = 3*0625. No proof is offered. 
 
 The longitude discovered by the Eclipses, Occultations, and Con- 
 junctions of Jupiter's planets. By William Whiston. London, 
 
 1738. 
 
 This tract has, in some copies, the celebrated preface contain- 
 ing the account of Newton's appearance before the Parliamentary 
 Committee on the longitude question, in 1714 (Brewster, ii. 257 
 266). This < historical preface,' is an insertion, and is dated ^pril 
 28, 1741, with four additional pages dated August 10, 1741. The 
 short ; preface ' is by the publisher, John Whiston, the author's 
 son. 
 
88 A BUDGET OF PAKADOXES. 
 
 A description and draught of a new-invented machine for carrying 
 vessels or ships out of, or into any harbour, port, or river, 
 against wind and ti 'e, or in a calm. For which, His Majesty 
 has granted letters patent, for the sole benefit of the author, for 
 the space of fourteen years. By Jonathan Hulls. London : 
 printed for the author, 1737. Price sixpence (folding plate and 
 pp. 48, beginning from title). 
 
 (I ought to have entered this tract in its place. It is so rare 
 that its existence was once doubted. It is the earliest description 
 of steam-power applied to navigation. The plate shows a barge, 
 with smoking funnel, and paddles at the stem, towing a ship of 
 war. The engine, as described, is Newcomen's. 
 
 In 1855, John Sheepshanks, so well known as a friend of Art 
 and a public donor, reprinted this tract, in fac-simile, from his own 
 copy ; twenty-seven copies of the original 12mo. size, and twelve 
 on old paper, small 4to. I have an original copy, wanting the 
 plate, and with ' Price sixpence ' carefully erased, to the honour of 
 the book. 
 
 It is not known whether Hulls actually constructed a boat. In 
 all probability his tract suggested to Symington, as Symington did 
 to Fulton.) 
 
 Le vrai systeme de physique generale de M. Isaac Newton ex- 
 pose et analyse en parallele avec celui de Descartes. By 
 Louis Castel [Jesuit and F.R.S.]. Paris, 1743, 4to. 
 
 This is an elaborate correction of Newton's followers, and of 
 Newton himself, who it seems did not give his own views with 
 perfect fidelity. Father Castel, for instance, assures us that New- 
 ton placed the sun at rest in the centre of the system. Newton left 
 the sun to arrange that matter with the planets and the rest of the 
 universe. In this volume of 500 pages there is right and wrong, 
 both clever. 
 
 A dissertation on the .^Ether of Sir Isaac Newton. By Bryan 
 Robinson, M.D. Dublin, 1743, 8vo. 
 
 A mathematical work, professing to prove that the assumed 
 ether causes gravitation. 
 
 Mathematical principles of theology, or the existence of God 
 geometrically demonstrated. By Richard Jack, teacher of 
 .Mathematics. London, 1747, 8vo. 
 
 Propositions arranged after the manner of Euclid, with beings 
 represented by circles anct squares. But these circles and squares 
 
JOHN BERNOULLI AND DE FAUBE. 89 
 
 are logical symbols, not geometrical ones. I brought this book 
 forward to the Eoyal Commission on the British Museum as an 
 instance of the absurdity of attempting a classed catalogue from 
 the titles of books. The title of this book sends it either to theo- 
 logy or geometry : when, in fact, it is a logical vagary. Some of 
 the houses which Jack built were destroyed by the fortune of war 
 in 1745, at Edinburgh : who will say the rebels did no good what- 
 ever ? I suspect that Jack copied the ideas of J. B. Morinus, 
 c Quod Deus sit,' Paris, 1636, 4to., containing an attempt of the 
 same kind, but not stultified with diagrams. 
 
 Dissertation, decouverte, et demonstrations de la quadrature 
 mathematique du cercle. Par M. de Faure, geometre. [s. L, 
 probably Geneva] 1747, 8vo. 
 
 Analyse de la Quadrature du Cercle. Par M. de Faure, 
 Gentilhomme Suisse. Hague, 1749, 4to. 
 
 According to this octavo geometer and quarto gentleman, a 
 diameter of 81 gives a circumference of 256. There is an amusing 
 circumstance about the quarto which -has been overlooked, if 
 indeed the book has ever been examined. John Bernoulli (the 
 one of the day) and Koenig have both given an attestation : my 
 mathematical readers may stare as they please, such is the fact. 
 But, on examination, there will be reason to think the two sly 
 Swiss played their countryman the same trick as the medical man 
 played Miss Pickle, in the novel of that name. The lady only 
 wanted to get his authority against sousing her little nephew, and 
 said, ' Pray, doctor, is it not both dangerous and cruel to be the 
 means of letting a poor tender infant perish by sousing it in water 
 as cold as ice ? ' ' Downright murder, I affirm,' said the doctor ; 
 and certified accordingly. De Faure had built a tremendous 
 scaffolding of equations, quite out of place, and feeling cock-sure 
 that his solutions, if correct, would square the circle, applied to 
 Bernoulli and Koenig who after his tract of two years before, 
 must have known what he was at for their approbation of the 
 solutions. . And he got it, as follows, well guarded : 
 
 Suivant les suppositions posees dans ce Memoire, il est si evident 
 que t doit etre 84, y = 1, et z = 1, que cela n'a besoin ni de preuve 
 ni d'autorite pour etre reconnu par tout le monde, 
 
 a Basle le 7e Mai 1749. JEAN BERNOULLI. 
 
 Je souscris au jugement de M**. Bernoulli, en consequence de ces 
 suppositions. 
 
 a la Haye le 21 Juin 1749. S. KOENIG. 
 
 On which de Faure remarks with triumph as I have no doufyt 
 
90 A BUDGET OF PARADOXES. 
 
 it was intended he should do 4 il const e clairement par ma 
 presente Analyse et Demonstration, qu'ils y ont deja reconnu et 
 approuve parfaitement que la quadrature du cercle^est mathema- 
 tiquement demontree.' It should seem that it is easier to square 
 the circle than to get round a mathematician. 
 
 An attempt to demonstrate that all the Phenomena in Nature 
 may be explained by two simple active principles, Attraction 
 and Repulsion, wherein the attractions of Cohesion, Gravity 
 and Magnetism are shown to be one and the same. By Go win 
 Knight. London, 1748, 4to. 
 
 Dr. Knight was Mr. Panizzi's archetype, the first Principal 
 Librarian of the British Museum. He was celebrated for his 
 magnetical experiments. This work was long neglected ; but is 
 now recognised as of remarkable resemblance to modern specula- 
 tions. 
 
 An original theory or Hypothesis of the Universe. By Thomas 
 Wright of Durham. London, 4to. 1750. 
 
 Wright is a speculator whose thoughts are now part of our 
 current astronomy. He took that view or most of it of the 
 milky way which afterwards suggested itself to William Herschel. 
 I have given an account of him and his work in the Philosophi- 
 cal Magazine for April, 1848. 
 
 Wright was mathematical instrument maker to the King; and 
 kept a shop in Fleet Street. Is the celebrated business of Trough- 
 ton & Simms, also in Fleet Street, a lineal descendant of that of 
 Wright ? It is likely enough, more likely than that as I find 
 him reported to have affirmed Prester John was the descendant 
 f Solomon and the Queen of Sheba. Having settled it thus, it 
 struck me that I might apply to Mr. Simms, and he informs me 
 that it is as I thought, the line of descent being Wright, Cole, 
 John Troughton, Edward Troughton, Troughton & Simms. 
 
 The theology and *" philosophy in Cicero's 8 omnium Scipionis 
 explained. Or, a brief attempt to demonstrate, that the 
 Newtonian system is perfectly agreeable to the notions of the 
 wisest ancients : and that mathematical principles are the only 
 sure ones. [By Bishop Home, at the age of nineteen.] 
 London, 1751, 8vo. 
 
 This tract, which was not printed in the collected works, and is 
 mow excessively rare, is mentioned in Notes and Queries, 1st S., 
 
BISHOP HORNE AND OLD BEN MARTIN. 91 
 
 v. 490, 573 ; 2nd S., ix. 15. The boyish satire on Newton is 
 amusing- Speaking of old Benjamin Martin, he goes on as 
 follows : 
 
 But the most elegant account of the matter [attraction] is by that 
 homiiiiform animal, Mr. Benjamin Martin, who having attended 
 Dr. Desaguliers' fine, raree, gallanty shew for some years [Desa- 
 guliers was one of the first who gave public experimental lectures, 
 before the saucy boy was born] in the capacity of a turnspit, has, it 
 seems, taken it into his head to set up for a philosopher. 
 
 Thus is preserved the fact, unknown to his biographers, that 
 Benj. Martin was an assistant to Desaguliers in his lectures. 
 Hutton says of him, that ' he was well skilled in the whole circle 
 of the mathematical and philosophical sciences, and wrote useful 
 books on every one of them' : this is quite true ; and even at this 
 day he is read by twenty where Home is read by one ; see the 
 stalls, passim. All that I say of him, indeed my knowledge of 
 the tract, is due to this contemptuous mention of a more durable 
 man than himself. My assistant secretary at the Astronomical 
 Society, the late Mr. Epps, bought the copy at a stall because his 
 eye was caught by the notice of ' Old Ben Martin,' of whom he 
 was a great reader. Old Ben could not be a Fellow of the Eoyal 
 Society, because he kept a shop : even though the shop sold 
 nothing but philosophical instruments. Thomas Wright, similarly 
 situated as to shop and goods, never was a Fellow. The Society 
 of our day has greatly degenerated : those of the old time would 
 be pleased, no doubt, that the glories of their day should be 
 commemorated. In the early days of the Society, there was a 
 similar difficulty about Grraunt, the author of the celebrated work 
 on mortality. But their royal patron, 4 who never said a foolish 
 thing,' sent them a sharp message, and charged them if they 
 found any more such tradesmen, they should 'elect them without 
 more ado.' 
 
 Home's first pamphlet was published when he was but twenty- 
 one years old. Two years afterwards, being then a Fellow of his 
 college, and having seen more of the world, he seems to have felt 
 that his manner was a little too pert. He endeavoured, it is said, 
 to suppress his first tract : and copies are certainly of extreme 
 rarity. He published the following as his maturer view : 
 
92 A BUDGET OF PARADOXES. 
 
 A fair, candid, and impartial state of the case between Sir 
 Isaac Newton and Mr. Hutohinson. In which is shown how- 
 far a system of physics is capable of mathematical demonstra- 
 tion; how far Sir Isaac's, as such a system, has that demon- 
 stration ; and consequently, what regard Mr. Hutchinson's claim 
 may deserve to have paid to it. By George Home, M.A. 
 Oxford, 1753, 8vo. 
 
 It must be remembered that the successors of Newton were 
 very apt to declare that Newton had demonstrated attraction as a 
 physical cause : he had taken reasonable pains to show that he 
 did not pretend to this. If any one had said to Newton, I hold 
 that every particle of matter is a responsible being of vast intel- 
 lect, ordered by the Creator to move as it would do if every other 
 particle attracted it, and gifted with power to make its way in 
 true accordance with that law, as easily as a lady picks her way 
 across the street ; what have you to say against it ? Newton 
 must have replied, Sir ! if you really undertake to maintain this 
 as demonstrable, your soul had better borrow a little power from 
 the particles of which your body is made : if you merely ask me 
 to refute it, I tell you that I neither can nor need do it ; for 
 whether attraction comes in this way or in any other, it comes, 
 and that is all I have to do with it. 
 
 The reader should remember that the word attraction, as used 
 by Newton and the best of his followers, only meant a drawing 
 towards, without any implication as to the cause. Thus whether 
 they said that matter attracts matter, or that young lady attracts 
 young gentleman, they were using one word in one sense. Newton 
 found that the law of the first is the inverse square of the dis- 
 tance : I am not aware that the law of the second has been 
 discovered ; if there be any chance, we shall see it at the year 
 1856 in this list. 
 
 In this point young Home made a hit. He justly censures 
 those who fixed upon New'ton a more positive knowledge of what 
 attraction is than he pretended to have. 'He has owned over 
 and over he did not know what he meant by it it might be this, 
 or it might be that, or it might be anything, or it might be 
 nothing.' With the exception of the nothing clause, this is true, 
 though Newton might have answered Home by ' Thou hast said 
 
 it; 
 
 (Tthought everybody knew the meaning of ' Thou hast said it :' 
 I was mistaken. In three of the evangelists %v \tyst,s is the 
 
HOKNE OX NEWTON. WEYMAN LEE. 93 
 
 answer to ' Art thou a king ? ' The force of this answer, as always 
 understood, is ' That is your way of putting it.' The Puritans, 
 who lived in Bible phrases, so understood it : and Walter Scott, 
 who caught all peculiarities of language with great effect, makes 
 a marked instance, * Were you armed ? I was not I went in my 
 calling, as a preacher of (rod's word, to encourage them that drew 
 the sword in His cause. In other words, to aid and abet the 
 rebels, said the Duke. Thou hast spoken it, replied the prisoner.') 
 
 Again, Home quotes Eowning as follows : 
 
 Mr. Rowning, pt. 2 p. 5 in a note, has a very pretty conceit upon 
 this same subject of attraction, about every particle of a fluid being 
 intrenched in three spheres of attraction and repulsion, one within 
 another, ' the innermost of which (he says) is a sphere of repulsion, 
 which keeps them from approaching into contact ; the next, a sphere 
 of attraction, diffused around this of repulsion, by which the particles 
 are disposed to run together into drops ; and the outermost of all, a 
 sphere of repulsion, whereby they repel each other, when removed out 
 of the attraction.' So that between the urginys, and sollicitations, of 
 one and t'other, a poor unhappy particle must ever be at his wit's end, 
 not knowing which way to turn, or whom to obey first. 
 
 Eowning has here started the notion which Boscovich afterwards 
 developed. 
 
 I may add to what precedes that it cannot be settled' that, as 
 G-ranger says, Desaguliers was the first who gave experimental 
 lectures in London. William Whiston gave some, and Francis 
 Hauksbee made the experiments. The prospectus, as we should 
 now call it, is extant, a quarto tract of plates and descriptions, 
 without date. Whiston, in his life, gives 1714 as the first date 
 of publication, and therefore, no doubt, of the lectures. Desagu- 
 liers removed to London soon after 1712, and commenced his 
 lectures soon after that. It will be rather a nice point to settle 
 which lectured first; probabilities seem to go in favour ot 
 Whiston. 
 
 An Essay to ascertain the value of leases, and annuities for 
 years and lives. By W[eyman] L[ee]. London, 1737, 8vo. 
 
 A valuation of Annuities and Leases certain, for a single life. 
 By Weyman Lee, Esq. of the Inner Temple. London, 1751, 
 8vo. Third edition, 1773. 
 
 Every branch of exact science has its paradoxer. The world at 
 large cannot tell with certainty who is right in such questions as 
 squaring the circle, &c. Mr. Weyman Lee was the assailant of 
 
94 A BUDGET OF PARADOXES. 
 
 what all who had studied called demonstration in the question of 
 annuities. He can be exposed to the world : for his error arose 
 out of his not being able to see that the whole is the sum of all 
 its parts. 
 
 By an annuity, say of 100?., now bought, is meant that the 
 buyer is to have for his money lOQl. in a year, if he be then 
 alive, 100Z. at the end of two years, if then alive, and so 
 on. It is clear that he would buy a life annuity if he 
 should buy the first 100?. in one office, the second in another, 
 and so on. All the difference between buying the whole from 
 one office, and buying all the separate conti agent payments at 
 different offices, is immaterial to calculation. Mr. Lee would 
 have agreed with the rest of the world about the payments to be 
 made to the several different offices, in consideration of their several 
 contracts : but he differed from every one else about the sum to 
 be paid to one office. He contended that the way to value an 
 annuity is to find out the term of years which the individual has 
 an even chance of surviving, and to charge for the life annuity 
 the value of an annuity certain for that term. 
 
 It is very common to say that Lee took the average life, or ex- 
 pectation, as it is wrongly called, for his term : and this I have 
 done myself, taking the common story. Having exposed the 
 absurdity of this second supposition, taking it for Lee's, in my 
 'Formal Logic,' I will now do the same with the first. 
 
 A mathematical truth is true in its extreme cases. Lee's prin- 
 ciple is that an annuity on a life is the annuity made certain for 
 the term within which it is an even chance the life drops. If, 
 then, of a thousand persons, 500 be sure to die within a year, and 
 the other 500 be immortal, Lee's price of an annuity to any one 
 of these persons is the present value of one payment : for one year 
 is the term which each one has an even chance of surviving and 
 not surviving. But the true value is obviously half that of a 
 perpetual annuity : so that at 5 per cent. Lee's rule would give 
 less than the tenth of the true value. It must be said for the 
 poor circle-squarers, that they never err so much as this. 
 
 Lee would have said, if alive, that I have put an extreme case : 
 but any universal truth is true in its extreme cases. It is not 
 fair to bring forward an extreme case against a person who is 
 speaking as of usual occurrences : but it is quite fair when, as 
 frequently happens, the proposer insists upon a perfectly general 
 acceptance of his assertion. And yet many who go the whole hog- 
 protest against being tickled with the tail. Counsel in court are 
 good instances: they are paradoxers by trade. June 13, 1849, at 
 
MONTUCLA'S HISTORY OF CIRCLE SQUARING. 95 
 
 Hertford, there was an action about a ship, insured against a total 
 loss : some planks were saved, and the underwriters refused to pay. 
 Mr. Z. (for deft.) 'There can be no degrees of totality; and some 
 timbers were saved.' L. C. B. 'Then if the vessel were burned to 
 the water's edge, and some rope saved in the boat, there would be 
 no total loss.' Mr. Z. 'This is putting a very extreme case.' 
 L. C. B. 'The argument would go that length.' What would 
 Judge Z. as he now is say to the extreme case beginning some- 
 where between six planks and a bit of rope ? 
 
 Histoire des recherches sur la quadrature da cercle. . . . avec 
 une addition concernant les problemes de la duplication du 
 cube et de la trisection de Tangle. Paris, 1754, 12mo. [By 
 Montucla.] 
 
 This is the history of the subject. It was a little episode to 
 the great history of mathematics by Montucla, of which the first 
 edition appeared in 1758. There was much addition at the end 
 of the fourth volume of the second edition ; this is clearly by 
 Montucla, though the bulk of the volume is put together, with 
 help from Montucla's papers, by Lalande. There is also a second 
 edition of the history of the quadrature, Paris, 1831, 8vo, 
 edited, I think, by Lacroix ; of which it is the great fault that it 
 makes hardly any use of the additional matter just mentioned. 
 
 Montucla is an admirable historian when he is writing from his 
 own direct knowledge : it is a sad pity that he did not tell us 
 when he was depending on others. We are not to trust a quarter 
 of his book, and we must read many other books to know which 
 quarter. The fault is common enough, but Montucla's good 
 three-quarters is so good that the fault is greater in him than in 
 most others : I mean the fault of not acknowledging ; for an 
 historian cannot read everything. But it must be said that 
 mankind give little encouragement to candour on this point. 
 Hallam, in his ' History of Literature,' states with his own usual 
 instinct of honesty every case in which he depends upon others : 
 Montucla does not. And what is the consequence ? Montucla is 
 trusted, and believed in, and cried up in the bulk ; while the 
 smallest talker can lament that Hallam should be so unequal and 
 apt to depend on others, without remembering to mention that 
 Hallam himself gives the information. As to a universal history 
 of any great subject being written entirely upon primary know- 
 ledge, it is a thing of which the possibility is not yet proved by 
 an example. Delambre attempted it with astronomy, and was 
 removed by death before it was finished, to say nothing of the 
 gaps he left. 
 
96 A BUDGET OF PAKADOXES. 
 
 Montucla was nothing of a bibliographer, and his descriptions 
 of books in the first edition were insufficient. The Abbe Eive 
 fell foul of him, and as the phrase is, gave it him. Montucla 
 took it with great good humour, tried to mend, and, in his second 
 edition, wished his critic had lived to see the vernis de biblio- 
 graphe which he had given himself. 
 
 I have seen Montucla set down as an esprit fort, more than 
 once : wrongly, I think. When he mentions Barrow's address to 
 the Almighty, he adds, ' On voit, au reste, par la, que Barrow 
 etoit un pauvre philosophe ; car il croyait en 1'immortalite de 
 1'ame, et en une Divinite autre que la nature universelle.' This 
 is irony, not an expression of opinion. In the book of mathe- 
 matical recreations which Montucla constructed upon that of 
 Ozanam, and Ozanam upon that of Van Etten, now best known in 
 England by Hutton's similar treatment of Montucla, there is an 
 amusing chapter on the quadrators. Montucla refers to his own 
 anonymous book of 1754 as a curious book published by Jombert. 
 He seems to have been a little ashamed of writing about circle- 
 squarers : what a slap on the face for an unborn Budgeteer ! 
 
 Montucla says, speaking of France, that he finds three notions 
 prevalent among the cyclometers : 1. that there is a large reward 
 offered for success ; 2. that the longitude problem depends on 
 that success ; 3. that the solution is the great end and object of 
 geometry. The same three notions are equally prevalent among 
 the same class in England. No reward has ever been offered by 
 the government "of either country. The longitude problem in 
 no way depends upon perfect solution : existing approximations 
 are sufficient to a point of accuracy far beyond what can be 
 wanted. And geometry, content with what exists, has long passed 
 on to other matters. Sometimes a cyclometer persuades a skipper 
 who has made land in the wrong place that the astronomers are in 
 fault, for using a wrong measure of the circle ; and the skipper 
 thinks it a very comfortable solution ! And this is the utmost 
 that the problem ever has to do with longitude. 
 
 Antinewtonianismus. By Caelestino Cominale, M.D. Naples, 
 1754 and 1756, 2 vols. 4to. 
 
 The first volume upsets the theory oF light ; the second 
 vacuum, vis inertise, gravitation, and attraction. I confess I 
 never attempted these big Latin volumes, numbering 450 closely- 
 printed quarto pages. The man who slays Newton in a pamphlet 
 is the man for me. But I will lend them to anybody who will 
 
EEWAED FOE QUADEATUEE. 97 
 
 give security, himself in 500., and two sureties in 250?. each, that 
 he will read them through, and give a full abstract ; and I will 
 not exact security for their return. I have never seen any 
 mention of this book : it has a printer, but not a publisher, as 
 happens with so many unrecorded books. 
 
 1755. The French Academy of Sciences came to the deter- 
 mination not to examine any more quadratures or kindred 
 problems. This was the consequence, no doubt, of the publication 
 of Montucla's book : the time was well chosen ; for that book was 
 a full justification of the resolution. The Eoyal Society followed 
 the same course, I believe, a few years afterwards. When our 
 Board of Longitude was in existence, most of its time was con- 
 sumed in listening to schemes, many of which included the 
 quadrature of the circle. It is certain that many quadrators have 
 imagined the longitude problem to be connected with theirs : and 
 no doubt the notion of a reward being offered by Government for 
 a true quadrature is a result of the reward offered for the longi- 
 tude. Let it also be noted that this longitude reward was not 
 a premium upon excogitation of a mysterious difficulty. The 
 legislature was made to know that the rational hopes of the 
 problem were centred in the improvement of the lunar tables and 
 the improvement of chronometers. To these objects alone, and 
 by name, the offer was directed : several persons gained rewards 
 for both ; and the offer was finally repealed. 
 
 Fundamentalis Figura Georaetrica, primas tantum lineas circuli 
 quadrature possibilitatis ostendens. By Niels Erichsen 
 (Nicolaus Ericius), shipbuilder, of Copenhagen. Copenhagen, 
 1755, 12mo. 
 
 This was a gift from my oldest friend who was not a relative, 
 Dr. Samuel Maitland of the 'Dark Ages.' He found it among 
 his books, and could not imagine how he came by it : I could 
 have told him. He once collected interpretations of the Apo- 
 calypse : and auction lots of such books often contain quadratures. 
 The wonder is he never found more than one. 
 
 The quadrature is not worth notice. Erichsen is the only 
 squarer I have met with who has distinctly asserted the particulars 
 of that reward which has been so frequently thought to have been 
 offered in England. He says that, in 1747, the Koyal Society, on 
 the 2nd of June, offered to give a large reward for the quadrature of 
 the circle and a true explanation of magnetism, in addition to 
 30,000^ previously promised for the same. I need hardly say that 
 
98 A BUDGET OF PAKADOXES. 
 
 the Royal Society had not 30,000?. at that time, and would not, if 
 it had had such a sum, have spent it on the circle, nor on magnetic 
 theory ; nor would it have coupled the two things. On this book, 
 see Notes and Queries^ 1st S. xii. 306. Perhaps Erichsen meant 
 that the 30,OOOL had been promised by the Government, and the 
 addition by the Eoyal Society. 
 
 October 8, 1866. I receive a letter from a cyclometer who 
 understands that a reward is offered to any one who will square 
 the circle, and that all competitors are to send their plans to me. 
 The hoaxers have not yet failed out of the land. 
 
 Theoria Philosophic Naturalis redacta ad imicam legem virium 
 in natura existentium. Editio Veneta prima. By Roger Joseph 
 Boscovich. Venice, 1763, 4to. 
 
 The first edition is said to be of Vienna, 1758. This is a 
 celebrated work on the molecular theory of matter, grounded on 
 the hypothesis of spheres of alternate attraction and repulsion. 
 Boscovich was a Jesuit of varied pursuit. During his measure- 
 ment of a degree of the meridian, while on horseback or waiting 
 for his observations, he composed a Latin poem of about five 
 thousand verses on eclipses, with notes, which he dedicated to the 
 Royal Society : ' De Solis et Lunae defectibus,' London, Millar 
 and Dodsley, 1760, 4to. 
 
 Traite de paix entre Des Cartes et Newton, precede des vies 
 Ijtteraires de ces deux chefs de la physique moderiie. . . . By 
 Aime Henri Paulian. Avignon, 1763, 12mo. 
 
 I have had these books for many a year without feeling the 
 least desire to see how a lettered Jesuit would atone Descartes 
 and Newton. On looking at my two volumes, I find that one 
 contains nothing but the literary life of Des Cartes ; the other 
 nothing but the literary life of Newton. The preface indicates 
 more : and Watt mentions three volumes. I dare say the first 
 two contain all that is valuable. On looking more attentively at 
 the two volumes, I find them both readable and instructive ; the 
 account of Newton is far above that of Voltaire, but not so 
 popular. But he should not have said that Newton's family 
 came from Newton in Ireland. Sir Rowland Hill gives fourteen 
 Newtons in Ireland : twice the number of the cities that con- 
 tended for the birth of Homer may now contend for the origin of 
 Newton, on the word of Father Paulian. 
 
BAILLY'S LETTERS TO VOLTAIRE. 99 
 
 Philosophical Essays, in three parts. By R. Lovett, Lay 
 Clerk of the Cathedral Church of Worcester. Worcester, 1766, 
 8vo. 
 
 The Electrical Philosopher: containing a new system of 
 physics founded upon the principle of an universal Plenum 
 of elementary fire ... By R. Lovett. Worcester, 1774, 8vo. 
 
 Mr. Lovett was one of those ether philosophers who bring in 
 elastic fluid as an explanation by imposition of words, without 
 deducing any one phenomenon from what we know of it. And 
 yet he says that attraction has received no support from geome- 
 try ; though geometry, applied to a particular law of attraction, 
 had shown how to predict the motions of the bodies of the solar 
 system. He, and many of his stamp, have not the least idea of 
 the confirmation of a theory by accordance of deduced results 
 with observation posterior to the theory. 
 
 Lettres sur 1'Atlantide de Platon, et sur Tancien Histoire de 
 TAsie, pour servir de suite aux lettres sur 1'origine des Sciences, 
 adressees a M. de Voltaire, par M. Bailly. London and Paris, 
 1779, 8vo. 
 
 I might enter here all Bailly's histories of astronomy. The 
 paradox which runs through them all more or less, is the doctrine 
 that astronomy is of immense antiquity, coming from some 
 forgotten source, probably the drowned island of Plato, peopled 
 by a race whom Bailly makes, as has been said, to teach us 
 everything except their existence and their name. These books, 
 the first scientific histories which belong to readable literature, 
 made a great impression by power of style : Delambre created a 
 strong reaction, of injurious amount, in favour of history founded 
 on contemporary documents, which early astronomy cannot 
 furnish. These letters are addressed to Voltaire, and continue 
 the discussion. There is one letter of Voltaire, being the fourth, 
 dated Feb. 27, 1777, and signed < le vieux malade de Ferney, V. 
 puer centum annorum.' Then begin Bailly's letters, from 
 January 16 to May 12, 1778. From some ambiguous expressions 
 in the Preface, it would seem that these are fictitious letters, sup- 
 posed to be addressed to Voltaire at their dates. Voltaire went 
 to Paris February 10, 1778, and died there May 30. Nearly all 
 this interval was his closing scene, and it is very unlikely that 
 Bailly would have troubled him with these letters. 
 
 H 2 
 
100 A BUDGET OF PAEADOXES. 
 
 An inquiry into the cause of motion, or a general theory of 
 physics. By S. Miller. London, 1781, 4 to. 
 
 Newton all wrong : matter consists of two kinds of particles, 
 one inert, the other elastic and capable of expanding themselves 
 ad infinitum. 
 
 Des Erreurs et de la Verite, ou les hommes rappeles an prin- 
 cipe universe! de la science ; ouvrage dans lequel, en faisant 
 reinarquer aux observateurs 1'incertitude de leurs recherches, 
 et leurs meprises continuelles, on leur indique la route qu'ils 
 auroient du suivre, pour acquerir 1'evidence physique sur 
 1'origine du bien et du mal, sur 1'homme, sur la nature materielle, 
 et la nature sacree ; sur la base des gouvernements politiques, 
 sur 1'autorite des souverains, sur la justice civile et criminelle, 
 sur les sciences, les langues, et les arts. Par un Ph. . . . 
 Inc. ... A Edimbourg. 1782. Two vols. 8vo. 
 
 This is the famous work of Louis Claude de Saint-Martin 
 (1743-1 803), for whose other works, vagaries included, the reader 
 must look elsewhere : among other things, he was a translator of 
 Jacob Behmen. The title promises much, and the writer has 
 smart thoughts now and then ; but the whole is the wearisome 
 omniscience of the author's day and country, which no reader of 
 our time can tolerate. Not that we dislike omniscience ; but 
 we have it of our own country, both home-made and imported ; 
 and fashions vary. But surely there can be but one omniscience ? 
 Must a man have but one wife ? Nay, may not a man have a 
 new wife while the old one is living ? There was a famous 
 instrumental professor forty years ago, who presented a friend to 
 
 Madame . The friend started, and looked surprised ; for, 
 
 not many weeks before, he had been presented to another lady, 
 with the same title, at Paris. The musician observed his 
 
 surprise, and quietly said, ' Celle-ci est Madame de Lon- 
 
 dres.' In like manner we have a London omniscience now 
 current, which would make any one start who only knew the old 
 French article. 
 
 The book was printed at Lyon, but it was a trick of French 
 authors to pretend to be afraid of prosecution : it made a book 
 look wicked-like to have a feigned place of printing, and stimu- 
 lated readers. A Government which had undergone Voltaire 
 would never have drawn its sword upon quiet Saint-Martin. To 
 make himself look still worse, he was only phplosophe] Inc. . . , 
 which is generally read Inconnu, but sometimes Incredule : 
 
SAINT-MAKTIN. 101 
 
 most likely the ambiguity was intended. There is an awful 
 paradox about the book, which explains, in part, its leaden same- 
 ness. It is all about Vhomme, rhomme, Vhomme, except as much 
 as treats of les hommes, les hommes, les hommes ; but not one 
 single man is mentioned by name in its 500 pages. It reminds 
 one of 
 
 Water, water, everywhere, 
 
 And not a drop to drink. 
 
 Not one opinion of any other man is referred to, in the way of 
 agreement or of opposition. Not even a town is mentioned : 
 there is nothing which brings a capital letter into the middle of a 
 sentence, except, by the rarest accident, such a personification as 
 Justice. A likely book to want an Edimbourg godfather ! 
 
 Saint-Martin is great in mathematics. The number four 
 essentially belongs to straight lines, and nine to curves. The 
 object of a straight line is to perpetuate ad infinitum the pro- 
 duction of a point from which it emanates. A circle O bounds 
 the production of all its radii, tends to destroy them, and is in 
 some sort their enemy. How is it possible that things so distinct 
 should not be distinguished in their number as well as in their 
 action ? If this important observation had been made earlier, 
 immense trouble would have been saved to the mathematicians, 
 who would have been prevented from searching for a common 
 measure to lines which have nothing in common. But, though 
 all straight lines have the number four, it must not be supposed 
 that they are all equal, for a line is the result of its law and its 
 number ; but though both are the same for all lines of a sort, 
 they act differently, as to force, energy, and duration, in different 
 individuals ; which explains all differences of length, &c. I 
 congratulate the reader who understands this ; and I do not pity 
 the one who does not. 
 
 Saint-Martin and his works are now as completely forgotten as 
 if they had never been born, except so far as this, that some one 
 may take up one of the works as of heretical character, and lay it 
 down in disappointment, with the reflection that it is as dull as 
 orthodoxy. For a person who was once in some vogue, it would 
 be difficult to pick out a more fossil writer, from Aa to Zypoeus, 
 except, though it is unusual for (, ) to represent an interval of 
 more than a year his unknown opponent. This opponent, in the 
 very year of the 4 Des Erreurs . . . .' published a book in two 
 parts with the same fictitious place of printing ; 
 
102 A BUDGET OF PAEADOXES. 
 
 Tableau Naturel des Rapports qui existent entre Dieu, rHoinme, 
 et I'Univers. A Edimbourg, 1782, 8vo. 
 
 There is a motto from the Des Erreurs itself, c Expliquer les 
 choses par I'homme, et non Thomme par les choses. Des Erreurs 
 et de la Verite, par un PH. . . . INC. . . ., p. 9.' This work is set 
 down in various catalogues and biographies as written by the 
 PH. . . . INC. . . . himself. But it is not usual for a writer to 
 publish two works in the same year, one of which takes a motto 
 from the other. And the second work is profuse in capitals and 
 italics, and uses Hebrew learning : its style differs much from the 
 first work. The first work sets out from man, and has nothing 
 to do with God : the second is religious and raps the knuckles of 
 the first as follows : c Si nous voulons nous preserver de toutes 
 les illusions, et surtout des amorces de 1'orgueil par lesquelles 
 Thomme est si sou vent seduit, ne prenons jamais les hommes, 
 mais toujours Dieu pour notre terme de comparaison.' The first 
 uses four and nine in various ways, of which I have quoted one : 
 the second says, 6 Et ici se trouve deja uiie explication des 
 nombres quatre et neuf, qui ont peu embarrasse dans 1'ouvrage deja 
 cite. L'homme s'est egare en allant de quatre a neuf . . . .' 
 The work cited is the Erreurs, &c., and the citation is in the 
 motto, which is the text of the opposition sermon. 
 
 Method to discover the difference of the earth's diameters ; 
 proving its true ratio to be not less variable than as 45 is to 46, 
 and shortest in its pole's axis 174 miles . . . likewise a method 
 for fixing an universal standard for weights and measures. By 
 Thomas Williams. London, 1788, 8vo. 
 
 Mr. Williams was a paradoxer in his day, and proposed what 
 was, no doubt, laughed at by some. He proposed the sort of plan 
 which the French independently of course carried into effect a 
 few years after. He would have the 52nd degree of latitude 
 divided into 100,000 parts and each part a geographical yard. 
 The geographical tun was to be the cube of the geographical 
 yard filled with sea-water taken some leagues from land. All 
 multiples and subdivisions were to be decimal. 
 
 I was beginning to look up those who had made similar 
 proposals, when a learned article on the proposal of a metrical 
 system came under my eye in the Times of Sept. 15, 1863. The 
 author cites Mouton, who would have the minute of a degree 
 divided into 10,000 virgulce; James Cassini, whose foot was to be 
 
PAINE WOLLSTONECEAFT PAKE. 103 
 
 six thousandths of a minute ; and Paucton, whose foot was the 
 400,000th of a degree. I have verified the first and third state- 
 ments ; surely the second ought to be the six-thousandth. 
 
 An inquiry into the Copernican system . . . wherein it is 
 proved, in the clearest manner, that the earth has only her 
 diurnal motion . . . with an attempt to point out the only true 
 way whereby mankind can receive any real benefit from the 
 study of the heavenly bodies. By John Cunningham. London, 
 1 789, 8vo. 
 
 The * true way ' appears to be the treatment of heaven and 
 earth as emblematical of the Trinity. 
 
 Cosmology. An inquiry into the cause of what is called gra- 
 vitation or attraction, in which the motions of the heavenly 
 bodies, and the preservation and operations of all nature, are 
 deduced from an universal principle of efflux and reflux. By 
 T. Vivian, vicar of Corn wood, Devon. Bath, 1792, 12mo. 
 
 Attraction, an influx of matter to the sun ; centrifugal force, 
 the solar rays; cohesion, the pressure of the atmosphere. The 
 confusion about centrifugal force, so called, as demanding an 
 external agent, is very common. 
 
 The rights of MAN, being an answer to Mr. Burke's attack on 
 
 the French Revolution. By Thomas Paine. In two parts. 
 
 1791-1792. 8vo. (Various editions.) 
 A vindication of the rights of WOMAN, with strictures on 
 
 political and moral subjects. By Mary Wollstonecraft. 1792. 
 
 8vo. 
 A sketch of the rights of BOYS and GIRLS. By Launcelot 
 
 Light, of Westminster School ; and Lsetitia Lookabout, of 
 
 Queen's Square, Bloomsbury. [By the Rev. Samuel Parr, 
 
 LL.D.] 1792. 8vo. (pp. 64). 
 
 When did we three meet before ? The first work has sunk into 
 oblivion : had it merited its title, it might have lived. It is what 
 the French call a pi&ce de circonstance ; it belongs in time to the 
 French Revolution, and in matter to Burke's opinion of that 
 movement. Those who only know its name think it was really 
 an attempt to write a philosophical treatise on what we now call 
 socialism. Silly government prosecutions gave it what it never 
 could have got for itself. 
 
 Mary Wollstonecraft seldom has her name spelt right. I 
 suppose the ! ! character she got made her Woolstonecraft. 
 
104 A BUDGET OF PARADOXES. 
 
 Watt gives double insinuation, for his cross-reference sends us to 
 Goodwin. No doubt the title of the book was an act of disciple- 
 ship to Paine's 6 Eights of Man ' ; but this title is very badly 
 chosen. The book was marred by it, especially when the authoress 
 and her husband assumed the right of dispensing with legal 
 sanction until the approach of offspring brought them to a sense 
 of their child's interest. Not a hint of such a claim is found in 
 the book, which is mostly about female education. The right 
 claimed for woman is to have the education of a rational human 
 being, and not to be considered as nothing but woman throughout 
 youthful training. The maxims of Mary Wollstonecraft are now, 
 though not derived from her, largely followed in the education of 
 girls, especially in home education : just as many of the political 
 principles of Tom Paine, again not derived from him, are the 
 guides of our actual legislation. I remember, forty years ago, 
 an old lady who used to declare that she disliked girls from the 
 age of sixteen to five-and-twenty. ' They are full,' said she, ' of 
 femabities.' She spoke of their behaviour to women as well as to 
 men. She would have been shocked to know that she was a 
 follower of Mary Wollstonecraft, and had packed half her book 
 into one sentence. 
 
 The third work is a satirical attack on Mary Wollstonecraft and 
 Tom Paine. The details of the attack would convince any one 
 that neither has anything which would now excite reprobation. 
 It is utterly unworthy of Dr. Parr, and has quite disappeared 
 from lists of his works, if it were ever there. That it was written 
 by him I take to be evident, as follows. Nichols, who could not 
 fail to know, says (Anecd., vol. ix. p. 120): 'This is a playful 
 essay by a first-rate scholar, who is elsewhere noticed in this 
 volume, but whose name I shall not bring forward on so trifling 
 an occasion.' Who the scholar was is made obvious by Master 
 Launcelot being ma.de to talk of Bellendenus. Further, the 
 same boy is made to say, c Let Dr. Parr lay his hand' upon his 
 heart, if his conscience will let him, and ask himself how many 
 thousands of waggon-loads of this article [birch] he has cruelly 
 misapplied.' How could this apply to Parr, with his handful of 
 private pupils, and no reputation for severity ? Any one except 
 himself would have called on the head-master of Westminster or 
 Eton. I doubt whether the name of Parr could be connected 
 with the rod by anything in print, except the above and an 
 anecdote of his pupil, Tom Sheridan. The Doctor had dressed 
 for a dinner visit, and was ready a quarter of an hour too soon to 
 set off. ' Tom,' said he, 4 1 think I had better whip you now ; 
 
SAMUEL PARR. 105 
 
 you are sure to do something while I am out.' c I wish you would, 
 sir ! ' said the boy ; ' it would be a letter of licence for the whole 
 evening.' The Doctor saw the force of the retort : my two 
 tutelaries will see it by this time. They paid in advance ; and I 
 have given liberal interpretation to the order. 
 
 The following story of Dr. Parr was told me and others, about 
 1829, by the late Leonard Homer, who knew him intimately. 
 Parr was staying in a house full of company, I think in the 
 north of England. Some gentlemen from America were among 
 the guests, and after dinner they disputed some of Parr's asser- 
 tions or arguments. So the Doctor broke out with 6 Do you 
 know what country you come from ? You come from the place 
 to which we used to send our thieves ! ' This made the host 
 angry, and he gave Parr such a severe rebuke as sent him from 
 the room in ill-humour. The rest walked on the lawn, amusing 
 the Americans with sketches of the Doctor. There was a dark 
 cloud overhead, and from that cloud presently came a voice 
 which called Tham (Parr-lisp for Sarti). The company were 
 astonished for a moment, but thought the Doctor was calling his 
 servant in the house, and that the apparent direction was an 
 illusion arising out of inattention. But presently the sound was 
 repeated, certainly from the cloud, 
 
 And nearer, clearer, deadlier than before. 
 
 There was now a little alarm : where could the Doctor have got 
 to ? They ran to his bedroom, and there they discovered a 
 sufficient rather than satisfactory explanation. The Doctor had 
 taken his pipe into his bedroom, and had seated himself, in sulky 
 mood, upon the higher bar of a large and deep old-fashioned 
 grate with a high mantelshelf. IJere he had tumbled backwards, 
 and doubled himself up between the bars and the back of the 
 grate. He was fixed tight, and when he called for help, he could 
 only throw his voice up the chimney. The echo from the cloud 
 was the warning which brought his friends to the rescue. 
 
 Days of political paradox were coming, at which we now stare. 
 Cobbett said, about 1830, in earnest, that in the country every 
 man who did not take off his hat to the clergyman was suspected, 
 and ran a fair chance of having something brought against him. 
 I heard this assertion canvassed, when it was made, in a party of 
 elderly persons. The Eadicals backed it, the old Tories rather 
 denied it, but in a way which satisfied me they ought to have 
 denied it less if they could not deny it more. But it must be 
 said that the Governments stopped far short of what their 
 
106 A BUDGET OF PAKADOXES. 
 
 partisans would have had them do. All who know Robert 
 Kobinson's very quiet assault on church-made festivals in hL 
 6 History and Mystery of (rood Friday' (1777) will hear or 
 remember with surprise that the British Critic pronounced it 
 a direct, unprovoked, and malicious libel on the most sacred 
 institutions of the national Church. It was reprinted again and 
 again: in 1811 it was in a cheap form at 6s 6d. a hundred. 
 When the Jacobin day came, the State was really in a fright : 
 people thought twice before they published what would now be 
 quite disregarded. I examined a quantity of letters addressed to 
 George Dyer (Charles Lamb's G.D.) and what between the auto- 
 graphs of Thelwall, Hardy, Home Tooke, and all the rebels, 
 put together a packet which produced five guineas, or there- 
 abouts, for the widow. Among them were the following verses, 
 sent by the author who would not put his name, even in a 
 private letter, for fear of accidents for consultation whether they 
 could safely be sent to an editor : and they were not sent. The 
 occasion was the public thanksgiving at St. Paul's for the naval 
 victories, December 19, 1797. 
 
 God bless me ! what a thing ! 
 Have you heard that the King 
 
 Goes to St. Paul's ? 
 Good Lord ! and when he's there, 
 He'll roll his eyes in prayer, 
 To make poor Johnny stare 
 
 At this fine thing. 
 
 No doubt the plan is wise 
 To blind poor Johnny's eyes 
 
 By this grand show ; 
 For should he once suppose 
 That he's led by the nose, 
 Down the whole fabric goes, 
 
 Church, lords, and king. 
 
 As he shouts Duncan's praise, 
 Mind how supplies they'll raise 
 
 In wondrous haste.* 
 For while upon the sea 
 We gain one victory, 
 John still a dupe will be 
 
 .And taxes pay. 
 
 Till from his little store 
 Three-fourths or even more 
 Goes to the Crown. 
 
WILLIAM HONE'S TRIALS, 107 
 
 Ah, John ! you little think 
 How fast we downward sink 
 And touch the fatal brink 
 At which we're slaves. 
 
 I would have indicted the author for not making his thirds 
 and sevenths rhyme. As to the rhythm, it is not much better 
 than what the French sang in the Calais theatre, when the Duke 
 of Clarence took over Louis XVIII. in 1814. 
 
 God save noble Clarence, 
 
 Who brings our king to France ; 
 
 God save Clarence ! 
 He maintains the glory 
 Of the British navy. 
 &c. &c. 
 
 Perhaps had this been published, the Government would have 
 assailed it as a libel on the church service. They got into the 
 way of defending themselves by making libels on the Church, of 
 what were libels, if on anything, on the rulers of the State ; until 
 the celebrated trials of Hone settled the point for ever, and 
 established that juries will not convict for one offence, even 
 though it have been committed, when they know the prosecution 
 is directed at another offence and another intent. 
 
 The results of Hone's trials (William Hone, 1779-1842) are 
 among the important constitutional victories of our century. He 
 published parodies on the Creeds, the Lord's Prayer, the Cate- 
 chism, &c., with intent to bring the Ministry into contempt : 
 everybody knew that was his purpose. The Government indicted 
 him for impious, profane, blasphemous intent, but not for 
 seditious intent. They hoped to wear him out by proceeding day 
 by day. December 18, 1817, they hid themselves under the 
 Lord's Prayer, the Creed, and the Commandments; December 19, 
 under the Litany ; December 20, under the Athanasian Creed, 
 an odd place for shelter when they could not find it in the previous 
 places. Hone defended himself for six, seven, and eight hours on 
 the several days : and the jury acquitted him in 15, 105, and 20 
 minutes. In the second trial tta offence was laid both as pro- 
 fanity and as sedition, which seems to have made the jury hesitate. 
 And they probably came to think that the second count was false 
 pretence : but the length of their deliberation is a satisfactory 
 addition to the value of the whole. In the first trial the Attorney- 
 General (Shepherd) had the impudence to say that the libel 
 had nothing of a political tendency about it, but was avowedly 
 
108 A BUDGET OF PAKADOXES 
 
 set off against the religion and worship of the Church of England. 
 The whole is political in every sentence ; neither more nor less 
 political than the following, which is part of the parody on the 
 Catechism. 4 What is thy duty towards the Minister ? My duty 
 towards the Minister is, to trust him as much as I can ; to honour 
 him with all my words, with all my bows, with all my scrapes, 
 and with all my cringes ; to flatter him ; to give him thanks ; to 
 give up my whole soul to him ; to idolize his name, and obey his 
 word, and serve him blindly all the days of his political life.' 
 And the parody on the Creed begins, ' I believe in George, the 
 Regent almighty, maker of new streets and Knights of the Bath.' 
 This is what the Attorney- General said had nothing of a political 
 tendency about it. But this was on the first trial : Hone 
 was not know r n. The first day's trial was under Justice Abbott 
 (afterwards C. J. Tenterden). It was perfectly understood, when 
 Chief Justice Ellenborough appeared in Court on the second day, 
 that he was very angry at the first result, and put his junior aside 
 to try his own rougher dealing. But Hone tamed the lion. An 
 eye-witness told me that when he implored of Hone not to detail 
 his own father Bishop Law's views on the Athanasian Creed, which 
 humble petition Hone kindly granted, he held by the desk for 
 support. And the same when which is not reported the 
 Attorney-General appealed to the Court for protection against a 
 stinging attack which Hone made on the Bar : he held on, and 
 said, c Mr. Attorney, what can I do ! ' I was a boy of twelve years 
 old, but so strong was the feeling of exultation at the verdicts 
 that boys at school were not prohibited from seeing the parodies, 
 which would have been held at any other time quite unfit to 
 meet their eyes. I was not able to comprehend all about the 
 Lord Chief Justice until I read and heard again in after years. 
 In the meantime, Joe Miller had given me the story of the 
 leopard which was sent home on board a ship of war, and was in 
 two days made as docile as a cat by the sailors. ' You have got 
 that fellow well under,' said an officer. 'Lord bless your honour !' 
 said Jack, ' if the Emperor of Marocky would send us a cock 
 rhinoceros, we'd bring him to his bearings in no time ! ' When I 
 came to the subject again, it pleased me to entertain the question 
 whether, if the Emperor had sent a cock rhinoceros to preside on 
 the third day in the King's Bench, Hone would have mastered 
 him : I forget how I settled it. There grew up a story that Hone 
 caused Lord Ellenborough's death, but this could not have been 
 true. Lord Ellenborough resigned his seat in a few months, and 
 
SUBSCRIPTIONS FOE HONE. 109 
 
 died just a year after the trials ; but sixty-eight years may have 
 had more to do with it than his defeat. 
 
 A large subscription was raised for Hone, headed by the Duke 
 of Bedford for 105?. Many of the leading ante-ministerialists 
 joined : but there were many of the other side who avowed their 
 disapprobation of the false pretence. Many could not venture 
 their names. In the list I find : A member of the House of Lords, 
 an enemy to persecution, and especially to religious persecution 
 employed for political purposes No parodist, but an enemy to 
 persecution A juryman on the third day's trial Ellen Borough 
 My name would ruin me Oh ! minions of Pitt Oil for the 
 Hone The Ghosts of Jeffries a.nd Sir William Eoy [Ghosts of 
 Jeffries in abundance] A conscientious Jury and a conscientious 
 Attorney, ll. 6s. 8d. To Mr. Hone, for defending in his own 
 person the freedom of the press, attacked for a political object, 
 under the old pretence of supporting Eeligion. A cut at corruption 
 An Earldom for myself and a translation for my brother One 
 who disapproves of parodies, but abhors persecution From a 
 schoolboy who wishes Mr. Hone to have a very grand subscription 
 ' For delicacy's sake forbear,' and ' Felix trembled ' ' I will go 
 myself to-morrow ' Judge Jeffries' works rebound in calf by Law 
 Keep us from Law, and from the Shepherd's paw I must not 
 give you my name, but God bless you ! As much like Judge 
 Jeffries as the present times will permit May Jeffries' fame 
 and Jeffries' fate on every modern Jeffries wait No parodist, 
 but an admirer of the man who has proved the fallacy of the 
 Lawyer's Law, that when a man is his own advocate he has a fool 
 for his client A Mussulman who thinks it would not be an impious 
 libel to parody the Koran May the suspenders of the Habeas 
 Corpus Act be speedily suspended Three times twelve for thrice- 
 tried Hone, who cleared the cases himself alone, and won three 
 heats by twelve to one, ll. 16s. A conscientious attorney, 
 ll. 6s. Sd. Kev. T. B. Morris, rector of Shelfanger, who dis- 
 approves of the parodies, but abhors the making an affected zeal 
 for religion the pretext for political persecution A Lawyer 
 opposed in principle to Law For the Hone that set the razor 
 that shaved the rats Eev. Dr. Samuel Parr, who most seriously 
 disapproves of all parodies upon the hallowed language of Scripture 
 and the contents of the Prayer-book, but acquits Mr. Hone of 
 intentional impiety, admires his talents and fortitude, and 
 applauds the good sense and integrity of his juries Eeligion 
 without hypocrisy, and Law without partiality Law ! Law I 
 Law ! 
 
110 A BUDGET OF PARADOXES, 
 
 These are specimens of a great many allusive mottoes. The 
 subscription was very large, and would have bought a handsome 
 annuity, but Hone employed it in the bookselling trade, and did 
 not thrive. His 'Everyday Book' and his 'Apocryphal New 
 Testament' are useful books. On an annuity he would have 
 thriven as an antiquarian writer and collector. It is well that 
 the attack upon the right to ridicule Ministers roused a dormant 
 power which was equal to the occasion. Hone declared, on his 
 honour, that he had never addressed a meeting in his life, nor 
 spoken a word before more than twelve persons. Had he which 
 however could not then be done employed counsel, and had a 
 guilty defence made for him, he would very likely have been 
 convicted, and the work would have been left to be done by 
 another. No question that the parodies disgusted all who 
 reverenced Christianity, and who could not separate the serious and 
 the ludicrous, and prevent their existence in combination. 
 
 My extracts, &c., are from the nineteenth, seventeenth, and six- 
 teenth editions of the three trials, which seem to have been con- 
 temporaneous (all in 1818) as they are made up into one book, 
 with additional title over all, and the motto 4 Thrice the brindled 
 cat hath mew'd.' They are published by Hone himself, who I 
 should -have said was a publisher as well as was to be. And 
 though the trials only ended Dec. 20, 1817, the preface attached 
 to this common title is dated Jan. 23, 1818. 
 
 The spirit which was roused against the false dealing of 
 the Government, i.e. the pretence of prosecuting for impiety 
 when all the world knew the real offence was, if anything, sedi- 
 tion was not got up at the moment : there had been previous 
 exhibitions of it. For example, in the spring of 1818 Mr. Eussell, 
 a little printer in Birmingham, was indicted for publishing the 
 Political Litany on which Hone was afterwards tried. He took 
 his witnesses to the summer Warwick assizes, and was told that 
 the indictment had been removed by certiorari into the King's 
 Bench. He had notice of trial for the spring assizes at Warwick: 
 he took his witnesses there, and the trial was postponed by the 
 Crown. He then had notice for the summer assizes at Warwick ; 
 and so on. The policy seems to have been to wear out the ob- 
 noxious parties, either by delays or by heaping on trials. The 
 Government was odious, and knew it could not get verdicts against 
 ridicule, and could get verdicts against impiety. No difficulty 
 was found in convicting the sellers of Paine's works, and the like. 
 When Hone was held to bail it was seen that a crisis was at hand. 
 All parties in politics furnished him with parodies in proof of 
 
PEOFANITY OF LORD BYEON. Ill 
 
 religious persons having made instruments of them. The parodies 
 by Addison and Luther were contributed by a Tory lawyer, who 
 was afterwards a judge. 
 
 Hone had published, in 1817, tracts of purely political ridicule: 
 ; official account of the noble lord's bite,' ' trial of the dog for 
 biting the noble lord,' &c. These were not touched. After the 
 trials, it is manifest that Hone was to be unassailed, do what he 
 might. 4 The Political House that Jack built,' in 1 8 1 9 ; < The Man 
 in the Moon,' 1820 ; 6 The Queen's Matrimonial Ladder,' c Non mi 
 ricordo,' 'The K 1 fowls,' 1820 ; 'The Political Showman at home,' 
 with plates by Gr. Cruickshank, 1821 [he did all the plates] ; < The 
 Spirit of Despotism,' 1821 would have been legitimate marks 
 for prosecution in previous years. The biting caricature of 
 several of these works are remembered to this day. c The Spirit 
 of Despotism ' was a tract of 1795, of which a few copies had been 
 privately circulated with great secrecy. Hone reprinted it, and 
 prefixed the following address to ' Robert Stewart, alias Lord 
 Castlereagh ' ' It appears to me that if, unhappily, your counsels 
 are allowed much longer to prevail in the Brunswick Cabinet, 
 they will bring on a crisis, in which the king may be dethroned 
 or the people enslaved. Experience has shown that the people 
 will not be enslaved the alternative is the affair of your em- 
 ployers.' Hone might say this without notice. 
 
 In 1819 Mr. Murray published Lord Byron's 'Don Juan,' and 
 Hone followed it with 6 Don John, or Don Juan unmasked,' a 
 little account of what the publisher to the Admiralty was allowed 
 to issue without prosecution. The parody on the Commandments 
 was a case very much in point : and Hone makes a stinging 
 allusion to the use of the ' unutterable Nvme, with a profane 
 levity unsurpassed by any other two lines in the English language.' 
 The lines are 
 
 'Tis strange the Hebrew noun which means * I am/ 
 The English always use to govern d n. 
 
 Hone ends, with : 6 Lord Byron's dedication of " Don Juan " to Lord 
 Castlereagh was suppressed by Mr. Murray from delicacy to 
 Ministers. Q. Why did not Mr. Murray suppress Lord Byron's 
 parody on the Ten Commandments? A. Because it contains 
 nothing in ridicule of Ministers, and therefore nothing that they 
 could suppose would lead to the displeasure of Almighty God.' 
 
 The little matters on which I have dwelt will never appear in 
 history from their political importance, except in a few words of 
 result. As a mode of thought, silly evasions of all kinds belong 
 
112 A BUDGET OF PARADOXES, 
 
 to such a work as the present. Ignorance, which seats itself in 
 the chair of knowledge, is a mother of revolutions in politics, and 
 of unread pamphlets in circle-squaring. From 1815 to 1830 the 
 question of revolution or no revolution lurked in all our English 
 discussions. The high classes must govern ; the high classes 
 shall not govern ; and thereupon issue was to be joined. In 1828- 
 1833 the question came to issue; and it was, Revolution with or 
 without civil war ; choose. The choice was wisely made ; and 
 the Eeform Bill started a new system so well dovetailed into the 
 old that the joinings are hardly visible. And now, in 1867, the 
 thing is repeated with a marked subsidence of symptoms ; and the 
 party which has taken the place of the extinct Tories is carrying 
 through Parliament a wider extension of the franchise than their 
 opponents would have ventured. Napoleon used to say that a 
 decided nose was a sign of power : on which it has been remarked 
 that he had good reason to say so before the play was done. And 
 so had our country ; it was saved from a religious war, and from 
 a civil war, by the power of that nose over its colleagues. 
 
 The Commentaries of Proclus* Translated by Thomas Taylor. 
 London, 1792, 2 vols. 4to. 
 
 The reputation of ' the Platonist ' begins to grow, and will 
 continue to grow. The most authentic account is in the Penny 
 Cyclopaedia, written by one of the few persons who knew him 
 well, and one of the fewer who possess all his works. At page 
 Ivi. of the Introduction is Taylor's notion of the way to find the 
 circumference. It is not geometrical, for it proceeds on the 
 motion of a point: the words ' on account of the simplicity of the 
 impulsive motion, such a line must be either straight or circular' 
 will suffice to show how Platonic it is. Taylor certainly professed 
 a kind of heathenism. D'Israeli said, 'Mr. T. Taylor, the Platonic 
 philosopher and the modern Plethon, consonant to that philosophy, 
 professes polytheism.' Taylor printed this in large type, in a 
 page by itself after the dedication, without any disavowal. I 
 have seen the following, Greek and translation both, in his hand- 
 writing : ' TLas dyoQos 77 dyaSos sQvitcos* KCLI iras xpianavos ij 
 'Xpicrnavos Kafco?. Every good man, so far as he is a good man, 
 is a heathen ; and every Christian, so far as he is a Christian, is a 
 bad man.' Whether Taylor had in his head the Christian of the 
 New Testament, or whether he drew from those members of the 
 6 religious world ' who make manifest the religious flesh and the 
 religious devil, cannot be decided by us, and perhaps was not 
 known to himself. If a heathen, he was a virtuous one. 
 
HANNAH MOKE -MISS BURNEY. 113 
 
 (1795.) This is the date of a very remarkable paradox. The 
 religious world to use a name claimed by a doctrinal sect 
 had long set its face against amusing literature, and all works of 
 imagination. Bunyan, Milton, and a few others were irresis- 
 tible ; but a long face was pulled at every attempt to produce 
 something readable for poor people and poor children. In 
 1795, a benevolent association began to circulate the works of 
 a lady who had been herself a dramatist, and had nourished a 
 pleasant vein of satire in the society of Grarrick and his friends ; 
 all which is carefully suppressed in some biographies. Hannah 
 More's Cheap Repository Tracts, which were bought by millions 
 of copies, destroyed the vicious publications with which the 
 hawkers deluged the country, by the simple process of furnishing 
 the hawkers with something more saleable. 
 
 Dramatic fiction, in which the characters are drawn by them- 
 selves, was, at the middle of the last century, the monopoly of 
 writers who required indecorum, such as Fielding and Smollett. 
 All, or nearly all, which could be permitted to the young, was 
 dry narrative, written by people who could not make their 
 personages talk character ; they all spoke alike. The author 
 of the Rambler is ridiculed, because his young ladies talk 
 Johnsonese ; but the satirists forget that all the presentable novel- 
 writers were equally incompetent ; even the author of 4 Zeluco ' 
 (1789) is the strongest possible case in point. 
 
 Dr. Moore, the father of the hero of Corunna, with good narra- 
 tive power, some sly humour, and much observation of character, 
 would have been, in our day, a writer of the Peacock family. 
 Nevertheless, to one who is accustomed to our style of things, 
 it is comic to read the dialogue of a jealous husband, a suspected 
 wife, a faithless maid-servant, a tool of a nurse, a wrong-headed 
 pomposity of a priest, and a sensible physician, all talking Dr. 
 Moore through their masks. Certainly an Irish soldier does say 
 by Jasus, and a cockney footman this here and that there ; and 
 this and the like is all the painting of characters which is effected 
 out of the mouths of the bearers by a narrator of great power. 
 I suspect that some novelists repressed their power under a rule 
 that a narrative should narrate, and that the dramatic should be 
 confined to the drama. 
 
 I make no exception in favour of Miss Burney ; though she was 
 the forerunner of a new era. Suppose a country in which dress 
 is always of one colour ; suppose an importer who brings in cargoes 
 of blue stuff, red stuff, green stuff, &c., and exhibits dresses of 
 these several colours, that person is the similitude of Miss 
 
 i 
 
114 A BUDGET OF PAKADOXES. 
 
 Burney. It would be a delightful change from a universal dull 
 brown, to see one person all red, another all blue, &c. ; but the 
 real inventor of pleasant dress would be the one who could mix 
 his colours and keep down the bright and gaudy. Miss Burney's 
 introduction was so charming, by contrast, that she nailed such men 
 as Johnson, Burke, Grarrick, &c., to her books. But when a 
 person who has read them with keen pleasure in boyhood, as I 
 idid, comes back to them after a long period, during which he 
 has made acquaintance with the great novelists of our century, 
 three-quarters of the pleasure is replaced by wonder that he had 
 not seen he was at a puppet-show, not at a drama. Take some 
 labelled characters out of our humourists, let them be put 
 together into one piece, to speak only as labelled : let there be 
 a Dominie with nothing but 'Prodigious ! ' a Dick Swiveller with 
 nothing but adapted quotations ; a Dr. Folliott with nothing 
 but sneers at Lord Brougham ; and the whole will pack up into 
 one of Miss Burney's novels. 
 
 Maria Edgeworth, Sydney Owenson (Lady Morgan), Jane 
 Austen, Walter Scott, &c., are all of our century ; as are, I 
 believe, all the Minerva Press novels, as they were called, which 
 show some of the power in question. Perhaps dramatic talent 
 found its best encouragement in the drama itself. But I cannot 
 ascertain that any such power was directed at the multitude, 
 whether educated or uneducated, with natural mixture of 
 character, under the restraints of decorum, until the use of it 
 by two religious writers of the school called c evangelical,' Han- 
 nah More and Eowland Hill. The Village Dialogues, though 
 not equal to the Repository Tracts^ are in many parts an ap- 
 proach, and perhaps a copy ; there is frequently humorous satire, 
 in that most effective form, self-display. They were published in 
 1800, and, partly at least, by the Keligious Tract Society, the 
 lineal successor of the Repository association, though knowing 
 nothing about its predecessor. I think it right to add that 
 Eowland Hill here mentioned is not the regenerator of the 
 Post Office. Some do not distinguish accurately ; I have heard 
 of more than one who took me to have had a logical controversy 
 with a diplomatist who died some years before I was born. 
 
 A few years ago, an attempt was made by myself and others 
 to collect some information about the Cheap Repository (see 
 Notes and Queries, 3rd Series, vi. 241, 290, 353 ; Christ'ian 
 Observer, Dec. 1864, pp. 944-49). It appeared that after the 
 Keligious Tract Society had existed more than fifty years, a friend 
 presented it with a copy of the original prospectus of the Reposi- 
 
THE KELIGIOUS TEACT SOCIETY. 115 
 
 tory, a thing the existence of which was not known. In this 
 prospectus it is announced that from the plan ' will be carefully 
 excluded whatever is enthusiastic, absurd, or superstitious.' The 
 6 evangelical' party had, from the foundation of the Eeligious 
 Tract Society, regretted that the Repository Tracts 'did not 
 contain a fuller statement of the great evangelical principles ;' 
 while in the prospectus it is also stated that c no cause of any 
 particular party is intended to be served by it, but general 
 Christianity will be promoted upon practical principles.' This 
 explains what has often been noticed, that the tracts contain a 
 mild form of the ' evangelical ' doctrine, free from that more 
 ftrvid dogmitism which appears in the Village Dialogues; and 
 such as H. More's friend, Bishop Porteus a great promoter of 
 the scheme might approve. The Eeligious Tract Society (in 
 1863) republished some of H. More's tracts, with alterations, 
 additions, and omissions ad libitum. This is an improper way 
 of dealing with the works of the dead ; especially when the 
 reprints are of popular works. A small type addition to the 
 preface contains : ' Some alterations and abridgments have been 
 made to adapt them to the present times and the aim of the 
 Eeligious Tract Society.' I think every publicity ought to be 
 given to the existence of such a practice ; and I reprint what I 
 said on the subject in Notes and Queries. 
 
 Alterations in works which the Society republishes are a neces- 
 sary part of their plan, though such notes as they should judge 
 to be corrective would be the best way of proceeding. But the 
 fact of alteration should be very distinctly announced on the title 
 of the work itself, not left to a little bit of small type at the end 
 of the preface, in the place where trade advertisements, or direc- 
 tions to the binder, are often found. And the places in which 
 alteration has been made should be pointed out, either by marks 
 of omission, when omission is the alteration, or by putting the 
 altered sentences in brackets, when change has been made. May 
 any one alter the works of the dead at his own discretion ? We 
 all know that readers in general will take each sentence to be 
 that of the author whose name is on the title; so that a correcting 
 republisher makes use of his author's name to teach his own 
 variation. The tortuous logic of 4 the trade,' which is content 
 when ' the world ' is satisfied, is not easily answered, any more 
 than an eel is easily caught; but the Eeligious Tract Society may 
 be convinced [in the old sense] in a sentence. On which course 
 would they feel most safe in giving their account to the God of 
 truth ? * In your own conscience, now ? ' 
 
 i 2 
 
116 A BUDGET OF PARADOXES. 
 
 I have tracked out a good many of the variations made by the 
 Keligious Tract Society in the recently published volume of 
 Repository Tracts. Most of them are doctrinal insertions or 
 amplifications, to the matter of which Hannah More would not 
 have objected all that can be brought against them is the want 
 of notice. But I have found two which the respect I have for the 
 Keligious Tract Society, in spite of much difference on various 
 points, must not prevent my designating as paltry. In the story 
 of Mary Wood, a kind-hearted clergyman converses with the poor 
 girl who has ruined herself by lying. In the original, he < assisted 
 her in the great work of repentance ; ' in the reprint it is to be 
 shown in some detail how he did this. He is to begin by pointing 
 out that c the heart is deceitful above all things and desperately 
 wicked.' Now the clergyman's name is HeartwM : so to prevent 
 his name from contradicting his doctrine, he is actually cut down 
 to Harwell. Hannah More meant this good man for one of those 
 described in Acts xv. 8, 9, and his name was appropriate. 
 
 Again, Mr. Flatterwell, in persuasion of Parley the porter to 
 let him into the castle, declares that the worst he will do is to 
 < play an innocent game of cards just to keep you awake, or sing 
 a cheerful song with the maids.' Oh fie ! Miss Hannah More ! 
 and you a single lady too, and a contemporary of the virtuous 
 Bowdler ! Though Flatterwell be an allegory of the devil, this 
 is really too indecorous, even for him. Out with the three last 
 words ! and out it is. 
 
 The Society cuts a poor figure before a literary tribunal. 
 Nothing was wanted except an admission that the remarks made by 
 me were unanswerable, and this was immediately furnished by the 
 Secretary (N. and Q. 3 S. vi. 290). In a reply of which six parts 
 out of seven are a very amplified statement that the Society did 
 not intend to reprint all Hannah More's tracts, the remaining 
 seventh is as follows : 
 
 I am not careful [perhaps this should be careful not] to notice 
 Professor De Morgan's objections to the changes in ' Mary Wood ' or 
 4 Parley the Porter/ but would merely reiterate that the tracts were 
 neither designed nor announced to be ' reprints * of the originals 
 [design is only known to the designers ; as to announcement, the title is 
 'Tis all for the best, The Shepherd of Salisbury Plain, and other 
 narratives, by Mrs. Hannah More '] ; and much less [this must be 
 careful not; further removed from answer than not careful^ can I 
 occupy your space by a treatise on the Professor's question : ' May 
 any one alter the works of the dead at his own discretion ? ' 
 
 To which I say Thanks for help ! 
 
WILLIAM FEEND'S ALGEBKA. 117 
 
 I predict that Hannah More's Cheap Repository Tracts will 
 somewhat resemble the Pilgrim's Progress in their fate. Written 
 for the cottage, and long remaining in their original position, 
 they will become classical works of their kind. Most assuredly 
 this will happen if my assertion cannot be upset, namely That 
 they contain the first specimens of fiction addressed to the world 
 at large, and widely circulated, in which dramatic as distin- 
 guished from puppet power is shown, and without indecorum. 
 
 According to some statements I have seen, but which I have 
 not verified, other publishing bodies, such as the Christian 
 Knowledge Society, have taken the same liberty with the names 
 of the dead as the Keligious Tract Society. If it be so, the 
 impropriety is the work of the smaller spirits, who have not been 
 sufficiently overlooked. There must be an overwhelming majority 
 in the higher councils to feel that, whenever altered works are 
 published, the fact of alteration should be made as prominent as 
 the name of the author. Everything short of this is suppression 
 of truth, and will ultimately destroy the credit of the Society. 
 Equally necessary is it that the alterations should be noted. 
 When it comes to be known that the author before him is altered, 
 he knows not where nor how nor by whom, the lowest reader will 
 lose his interest. 
 
 The principles of Algebra. By William Trend. London, 1796, 
 8vo. Second Part, 1799. 
 
 This Algebra, says Dr. Peacock, shows ' great distrust of the 
 results of algebraical science which were in existence at the time 
 when it was written.' Truly it does ; for, as Dr. Peacock had 
 shown by full citation, it makes war of extermination upon all 
 that distinguishes algebra from arithmetic. Eobert Simson and 
 Baron Maseres were Mr. Frend's predecessors in this opinion. 
 
 The genuine respect which I entertained for my father-in-law 
 did not prevent my canvassing with perfect freedom his anti- 
 algebraical and anti-Newtonian opinions, in a long obituary 
 memoir read at the Astronomical Society in February 1842, 
 which was written by me. It was copied into the Athenceum of 
 March 19. It must be said that if the manner in which algebra 
 was presented to the learner had been true algebra, he would 
 have been right : and if he had confined himself to protesting 
 against the imposition of attraction as a fundamental part of the 
 existence of matter, he would have been in unity with a great 
 many, including Newton himself. I wish he had preferred 
 
US A BUDGET OF PARADOXES. 
 
 amendment to rejection when lie was a college tutor : lie wrote 
 and spoke English with a clearness which is seldom equalled. 
 
 His anti-Newtonian discussions are confined to the preliminary 
 chapters of his fc Evening Amusements,' a series of astronomical 
 lessons in nineteen volumes, following the moon through a period 
 of the golden numbers. 
 
 There is a mistake about him which can never be destroyed. 
 It is constantly said that, at his celebrated trial in 1792, for 
 sedition and opposition to the Liturgy, &c., he was expelled the 
 University. He was banished. People cannot see the difference; 
 but it made all the difference to Mr. Frend. He held his fellow- 
 ship and its profits till his marriage in 1808, and was a member 
 of the University and of its Senate till his death in 1841, as any 
 Cambridge Calendar up to 1841 will show. That they would have 
 expelled him if they could, is perfectly true ; and there is a funny 
 story also perfectly true about their first proceedings being 
 under a statute which would have given the power, had it not been 
 discovered during the proceedings that the statute did not exist. 
 It had come so near to existence as to be entered into the Vice- 
 Chancellor's book for his signature, which it wanted, as was not 
 seen till Mr. Frend exposed it : in fact, the statute had never 
 actually passed. 
 
 There is an absurd mistake in Gunning's 4 Keminiscences of 
 Cambridge.' In quoting a passage of Mr. Frend's pamphlet, 
 which was very obnoxious to the existing Government, it is 
 printed that the poor market-women complained that they were 
 to be scotched a quarter of their wages by taxation; and attention 
 is called to the word by its being three times printed in italics. 
 In the pamphlet it is ' sconced ' ; that very common old word for 
 fined or mulcted. 
 
 Lord Lyndhurst, who has [1863] just passed away under a load 
 of years and honours, was Mr. Frend's private pupil at Cambridge. 
 At the time of the celebrated trial, he and two others amused 
 themselves, and vented the feeling which was very strong among 
 the undergraduates, by chalking the walls of Cambridge with 
 c Frend for ever!' While thus engaged in what, using the term 
 legally, we are probably to call his first publication, he and his 
 friends were surprised by the proctors. Flight and chase followed 
 of course : Copley and one of the others, Serjeant Eough, 
 escaped ; the third, whose name I forget, but who afterwards, I 
 have been told, was a bishop, 1 being lame, was captured and 
 impositioned. Looking at the Cambridge Calendar to verify the 
 
 1 Herbert Marsh, afterwards Bishop of Peterborough, a relation of my father, (Ed.) 
 
FRANCIS PLACE WILLIAM COBBETT. 119 
 
 fact that Copley was an undergraduate at the time, I find that 
 there are but two other men in the list of honours of his year 
 whose names are now widely remembered. And they were both 
 celebrated schoolmasters ; Butler of Harrow, and Tate of Richmond. 
 
 But Mr. Frend had another noted pupil. I once had a con- 
 versation with a very remarkable man, who was generally called 
 c Place, the tailor,' but who was politician, political economist, 
 &c., &c. He sat in the room above his shop he was then a 
 thriving master tailor at Charing Cross surrounded by books 
 enough for nine, to shame a proverb. The blue books alone, cut 
 up into strips, would have measured Great Britain for oh-no-we- 
 never-mention-'erns, the Highlands included. I cannot find a 
 biography of this worthy and able man. I happened to mention 
 William Frend, and he said, 6 Ah ! my old master, as I always 
 call him. Many and many a time, and year after year, did he 
 come in every now and then to give me instruction, while I was 
 sitting on the board, working for rny living, you know.' 
 
 Place, who really was a sound economist, is joined with 
 Cobbett, because they were together at one time, and because he 
 was, in 1800, &c., a great Radical. But for Cobbett he had a 
 great contempt. He told me the following story. He and others 
 were advising with Cobbett about the defence he was to make on 
 a trial for seditious libel which was coming on. Said Place, 4 You 
 must put in the letters you have received from Ministers, 
 members of the Commons from the Speaker downwards, &c., 
 about your Register, and their wish to have subjects noted. You 
 must then ask the jury whether a person so addressed must be 
 considered as a common sower of sedition, &c. You will be 
 acquitted ; nay, if your intention should get about, very likely 
 they will manage to stop proceedings.' Cobbett was too much 
 
 disturbed to listen ; he walked about the room ejaculating 6 D 
 
 the prison ! ' and the like. He had not the sense to follow the 
 advice, and was convicted. 
 
 Cobbett, to go on with the chain, was a p}litical acrobat, ready 
 for any kind of posture. A friend of mine gave me several times 
 an account of a mission to him. A Tory member those who 
 know the old Tory world may look for his initials in initials of 
 two consecutive words of ' Pay his money with interest ' who 
 was, of course, a political opponent, thought Cobbett had been 
 hardly used, and determined to subscribe handsomely towards the 
 expenses he was incurring as a candidate. My friend was com- 
 missioned to hand over the money a bag of sovereigns, that notes 
 might not be traced. He went into Cobbett's committee-room, 
 
120 A BUDGET OF PARADOXES. 
 
 told the patriot his errand, and put the money on the table. 
 ' And to whom, sir, am I indebted ? ' said Cobbett. ' The donor,' 
 was the answer, ' is Mr. Andrew Theophilus Smith,' or some such 
 unlikely pair of baptismals. ' Ah ! ' said Cobbett, ' I have known Mr. 
 A. T. S. a long time! he was always a true friend of his country! 5 
 To return to Place. He is a noted instance of the advantage 
 of our jury system, which never asks a man's politics, &c. The 
 late King of Hanover, when Duke of Cumberland, being unpopular, 
 was brought under unjust suspicions by the suicide of his valet : 
 he must have seduced the wife and murdered the husband. The 
 charges were as absurd as those brought against the Englishman 
 in the Frenchman's attempt at satirical verses upon him : 
 
 The Englishman is a very bad man ; 
 He drink the beer and lie steal the can : 
 He kiss the wife and he beat the man ; 
 And the Englishman is a very G d . 
 
 The charges were revived in a much later day, and the defence 
 might have given some trouble. But Place, who had been the 
 foreman at the inquest, came forward, and settled the question in 
 A few lines. Everyone knew that the old Eadical was quite free 
 / of all disposition to suppress truth from wish to curry favour with 
 royalty. 
 
 John Speed, the author of the English History (1632) which 
 Bishop Nicolson calls the best chronicle extant, was a man, like 
 Place, of no education but what be gave himself. The bishop 
 says he would have done better if he had had better training : 
 but what, he adds, could have been expected from a tailor ! This 
 Speed was, as well as Place. But he was released from manual 
 labour by Sir Fulk Grevil, who enabled him to study. 
 
 I have elsewhere noticed that those who oppose the mysteries 
 of algebra do not ridicule them ; this I want the cyclometers to 
 do. Of the three who wrote against the great point, the negative 
 quantity, and the uses of which are connected with it, only 
 one could fire a squib. That Eobert Simson should do such a 
 thing will be judged impossible by all who admit tradition. I 
 do not vouch for the following ; I give it as a proof of the 
 impression which prevailed about him : 
 
 He used to sit at his open window on the ground floor, as deep 
 in geometry as a Eobert Simson ought to be. Here he would be 
 accosted by beggars, to whom he generally gave a trifle , he 
 roused himself to hear a few words of the story, made his dona- 
 tion, and instantly dropped down into his depths. Some wags 
 
MASEKES ON THE NEGATIVE SIGN. 121 
 
 one day stopped a mendicant who was on his way to the window, 
 with ' Now, my man, do as we tell you, and you will get some- 
 thing from that gentleman, and a shilling from us besides. You 
 will go and say you are in distress, he will ask you who you are, 
 and you will say you are Robert Simson, son of John Simson of 
 Kirktonhill.' The man did as he was told ; Simson quietly gave 
 him a coin, and dropped off. The wags watched a little, and saw 
 him rouse himself again, and exclaim ' Eobert Simson, son of 
 John Simson of Kirktonhill ! why, that is myself. That man 
 must be an impostor.' Lord Brougham tells the same story, with 
 some difference of details. 
 
 Baron Maseres was, as a writer, dry ; those who know his 
 writings will feel that he seldom could have taken in a joke or 
 issued a pun. Maseres was the fourth wrangler of 1752, and 
 first Chancellor's medallist (or highest in classics) ; his second 
 was Porteus (afterwards Bishop of London). Waring carne five 
 years after him : he could not get Maseres through the second 
 page of his first work on algebra ; a negative quantity stood 
 like a lion in the way. In 1758 he published his 4 Dissertation 
 on the Use of the Negative Sign,' 4to. There are some who care 
 little about + and , who would give it house-room for the sake 
 of the four words 6 Printed by Samuel Eichardson. 5 
 
 Maseres speaks as follows : < A single quantity can never be 
 marked with either of those signs, or considered as either affirma- 
 tive or negative ; for if any single quantity, as 6, is marked 
 either with the sign -f or with the sigh without assigning 
 some other quantity, as a, to which it is to be added, or from 
 which it is to be subtracted, the mark will have no meaning or 
 signification : thus if it be said that the square of 5, or the 
 product of 5 into 5, is equal to +25, such an assertion must 
 either signify no more than that 5 times 5 is equal to 25 without 
 any regard to the signs, or it must be mere nonsense and unin- 
 telligible jargon. I speak according to the foregoing definition, 
 by which the affirmativeness or negativeness of any quantity 
 implies a relation to another quantity of the same kind to which 
 it is added, or from which it is subtracted ; for it may perhaps be 
 very clear and intelligible to those who have formed to them- 
 selves some other idea of affirmative and negative quantities 
 different from that above defined.' 
 
 Nothing can be more correct, or more identically logical : -f 5 
 and 5, standing alone, are jargon if -f 5 and 5 are to be 
 understood as without reference to another quantity. But those 
 who have c formed to themselves sfcme other idea ' see meaning 
 
122 A BUDGET OF PARADOXES. 
 
 enough. The great difficulty of the opponents of algebra lay in 
 want of power or will to see extension of terms. Maseres is right 
 when he implies that extension, accompanied by its refusal, 
 makes jargon. One of my paradoxers was present at a meeting 
 of the Eoyal Society (in 1864, I think) and asked permis- 
 sion to make some remarks upon a paper. He rambled into 
 other things, and, naming me, said that I had written a 
 book in which two sides of a triangle are pronounced equal to 
 the third. So they are, in the sense in which the word is used 
 in complete algebra; in which A-fB = c makes A, B, c, three 
 sides of a triangle, and declares that going over A and B, one after 
 the other, is equivalent, in change of place, to going over c at 
 once. My critic, who might, if he pleased, have objected to 
 extension, insisted upon reading me in unextended meaning. 
 
 On the other hand, it must be said that those who wrote on 
 the other idea wrote very obscurely about it, and justified Des 
 Cartes (De Methodo) when he said : ' Algebram vero, ut solet 
 doceri, animadverti certis regulis et numerandi formulis ita esse 
 contentam, ut videatur potius ars qusedam confusa, cujus usu 
 ingenium quodam modo turbatur et obscuratur, quam scientia 
 qua excolatur et perspicacius reddatur.' Maseres wrote this 
 sentence on the title of his own copy of his own work, now before 
 me ; he would have made it his motto if he had found it earlier. 
 There is, I believe, in Cobbett's c Annual Register,' an account 
 of an interview between Maseres and Cobbett when in prison. 
 
 The conversation of Maseres was lively, and full of serious anec- 
 dote : but only one attempt at humorous satire is recorded of 
 him; it is an instructive one. He was born in 1731 (Dec. 15), 
 and his father was a refugee. French was the language of the 
 house, with the pronunciation of the time of Louis XIV. He 
 lived until 1824 (May 19), and saw the race of refugees who 
 were driven out by the first Eevolution. Their pronunciation 
 differed greatly from his own ; and he used to amuse himself by 
 mimicking them. Those who heard him and them had the two 
 schools of pronunciation before them at once; a thing which 
 seldom happens. It might even yet be worth while to examine 
 the Canadian pronunciation. 
 
 Maseres went as Attorney-General to Quebec; and was ap- 
 pointed Cursitor Baron of our Exchequer in 1773. There is a 
 curious story about his mission to Canada, which I have heard as 
 good tradition, but have never seen in print. The reader shall 
 have it as cheap as I ; and I confess I rather believe it. Maseres 
 was inveterately honest ; he could not, at the bar, bear to see his 
 
BAEON MASEEES. 123 
 
 own client victorious, when he knew his cause was a bad one. 
 On a certain occasion he was in a cause which he knew would 
 go against him if a certain case were quoted. Neither the judge 
 nor the opposite counsel seemed to remember this case, and 
 Ma seres could not help dropping an allusion which brought it 
 out. His business as a barrister fell off, of course. Some time 
 after, Mr. Pitt (Chatham) wanted a lawyer to send to Canada on 
 a private mission, and wanted a very honest man. Some one 
 mentioned Maseres, and told the above story : Pitt saw that he 
 had got the man he wanted. The mission was satisfactorily per- 
 formed, and Maseres remained as Attorney-General. 
 
 The 'Doctrine of Life Annuities' (4to. 726 pages, 1783) is a 
 strange paradox. Its size, the heavy dissertations on the national 
 debt, and the depth of algebra supposed known, put it out of 
 the question as an elementary work, and it is unfitted for the 
 higher student by its elaborate attempt at elementary character, 
 shown in its rejection of forms derived from chances in favour of 
 the average, and its exhibition of the separate values of the 
 years of an annuity, as arithmetical illustrations. It is a climax 
 of unsaleability, unreadability, and inutility. For intrinsic 
 nullity of interest, and dilution of little matter with much ink, 
 I can compare this book to nothing but that of Claude de St. 
 Martin, elsewhere mentioned, or the lectures 6 On the Nature and 
 Properties of Logarithms,' by James Little, Dublin, 1830, 8vo. 
 (254 heavy pages of many words and few symbols), a wonderful 
 weight of weariness. 
 
 The stock of this work on annuities, very little diminished, 
 was given by the author to William Frend, who paid warehouse 
 room for it until about 1835, when he consulted me as to its 
 disposal. As no publisher could be found who would take it 
 as a gift, for any purpose of sale, it was consigned, all but a few 
 copies, to a buyer of waste paper. 
 
 Baron Maseres's republications are well known : the Scriptores 
 Logarithmici is a set of valuable reprints, mixed with much 
 which might better have entered into another collection. It is 
 not so well known that there is a volume of optical reprints, 
 Scriptores Optici, London, 1823, 4to, edited for the veteran of 
 ninety-two by Mr. Babbage at twenty-nine. This excellent 
 volume contains James Gregory, Des Cartes, Halley, Barrow, 
 and the optical writings of Huyghens, the Principia of the 
 undulatory theory. It also contains, by the sort of whim in 
 which such men as Maseres, myself, and some others are apt 
 to indulge, a reprint of c The great and new Art of weighing 
 
124 A BUDGET OF PAKADOXKS. 
 
 Vanity,' by M. Patrick Mathers, Arch-Bedel to the University of 
 St. Andrews, Glasgow, 1672. Professor Sinclair, of Glasgow, a 
 good man at clearing mines of the water which they did not 
 want, and furnishing cities with the water which they did want, 
 seems to have written absurdly about hydrostatics, and to have 
 attacked a certain Sanders, M.A. So Sanders, assisted by James 
 Gregory, published a heavy bit of jocosity about him. This 
 story of the authorship rested on a note made in his copy 
 by Eobert Gray, M.D. ; but it has since been fully confirmed by 
 a letter of James Gregory to Collins, in the Macclesfield Corre- 
 spondence. 4 There is one Master Sinclair, who did write the 
 Ars Magna et Nova, a pitiful ignorant fellow, who hath lately 
 written horrid nonsense in the hydrostatics, and hath abused a 
 master in the University, one Mr. Sanders, in print. This Mr. 
 Sanders ... is resolved to cause the Bedel of the University 
 to write against him. . . . We resolve to make excellent sport 
 with him.' 
 
 On this I make two remarks : First, I have learnt from ex- 
 perience that old notes, made in books by their possessors, are 
 statements of high authority : they are almost always confirmed. 
 I do not receive them without hesitation ; but I believe that 
 of all the statements about books which rest on one authority, 
 there is a larger percentage of truth in the written word than in 
 the printed word. Secondly, I mourn to think that when the 
 New Zealander picks up his old copy of this book, and reads it 
 by the associations of his own day, he may, in spite of the many 
 assurances I have received that my Athenceum Budget was 
 amusing, feel me to be as heavy as I feel James Gregory and 
 Sanders. But he will see that I knew what was coming, which 
 Gregory did not. 
 
 It was left for William Frend to prove that an impugner of 
 algebra could attempt ridicule. He was, in 1803, editor of a 
 periodical The Gentleman's Monthly Miscellany, which lasted 
 a few months. To this, among other things, he contributed the 
 following, in burlesque of the use made of 0, to which he ob- 
 jected. The imitation of Eabelais, a writer in whom he de- 
 lighted, is good : to those who have never dipped, it may give 
 such a notion as they would not easily get elsewhere. The point 
 of the satire is not so good. But in truth it is not easy to make 
 pungent scoffs upon what is common sense to all mankind. Who 
 can laugh with effect at six times nothing is nothing, as false or 
 unintelligible ? In an article intended for that undistinguishing 
 know-0 the ' general reader,' there would have been no force of 
 
IMITATION OF EABELAIS. 125 
 
 satire, if division by had been separated from multiplication 
 by the same. 
 
 I have followed the above by another squib, by the same 
 author, on the English language. The satire is covertly aimed at 
 theological phraseology; and any one who watches this subject 
 will see that it is a very just observation that the Greek words 
 are not boiled enough, 
 
 PANTAGRUEL'S DECISION of the QUESTION about NOTHING. 
 
 PANTAGRUEL determined to Lave a snug afternoon with Epistemon and 
 Panurge. Dinner was ordered to be set in a small parlonr, and a 
 particular batch of Hermitage with some choice Burgundy to be drawn 
 from a remote corner of the cellar upon the occasion. By way of 
 lunch, about an hour before dinner, Pantagruel was composing his 
 stomach with German sausages, reindeer's tongues, oysters, brawn, and 
 half a dozen different sorts of English beer just come into fashion, when 
 a most thundering knocking was heard at the great gate, and from the 
 noise they expected it to announce the arrival at least of the First 
 Consul, or king Gargantua. Panurge was sent to reconnoitre, and 
 after a quarter of an hour's absence, returned with the news that the 
 University of Pontemaca was waiting his highness' s leisure in the 
 great hall, to propound a question which had turned the brains of 
 thirty-nine students, and had flung twenty-seven more into a high 
 fever. With all my heart, says Pantagruel, and swallowed down three 
 quarts of Burton ale ; but remember, it wants but an hour of dinner 
 time, and the question must be asked in as few words as possible ; for 
 I cannot deprive myself of the pleasure I expected to enjoy in the 
 company of my good friends for a set of mad-headed masters. I wish 
 brother John was here to settle these matters with the black gentry. 
 
 Having said or rather growled this, he proceeded to the hall of 
 ceremony, and mounted his throne ; Epistemon and Panurge standing 
 on each side, but two steps below him. Then advanced to the throne 
 the three beadles of the University of Pontemaca with their silver 
 staves on their shoulders, and velvet caps on their heads, and they 
 were followed by three times three doctors, and thrice three times 
 three masters of art ; for everything was done in Pontemaca by the 
 number three, and on this account the address was written on parch- 
 ment, one foot in breadth, and thrice three times thrice three feet in 
 length. The beadles struck the ground with their heads arid their 
 staves three times in approaching the throne ; the doctors struck the 
 ground with their heads thrice three times, and the masters did the 
 same thrice each time, beating the ground with their heads thrice 
 three times. This was the accustomed form of approaching the throne, 
 time out of mind, and it was said to be emblematic of the usual pros- 
 tration of science to the throne of greatness. 
 
120 A BUDGET OF PARADOXES. 
 
 The mathematical professor, after having spit, and hawked, and 
 cleared his throat, and blown his nose on a handkerchief lent to him, 
 for he had forgotten to bring his own, began to read the address. In 
 this he was assisted by three masters of arts, one of whom, with a 
 silver pen, pointed out the stops ; the second with a small stick rapped 
 his knuckles when he was to raise or lower his voice ; and a third 
 pulled his hair behind when he was to look Pantagruel in the face. 
 Pantagruel began to chafe like a lion : he turned first on one side, then 
 on the other : he listened and groaned, and groaned and listened, and 
 was in the utmost cogitabundity of cogitation. His countenance 
 began to brighten, when, at the end of an hour, the reader stammered 
 out these words : 
 
 * It has therefore been most clearly proved, that as all matter may 
 be divided into parts infinitely smaller than the infinitely smallest part 
 of the infinitesimal of nothing, so nothing has all the properties of 
 something, and may become, by just and lawful right, susceptible of 
 addition, subtraction, multiplication, division, squaring, and cubing : 
 that it is to all intents and purposes as good as anything that has 
 been, is, or can be taught in the nine universities of the land, and to 
 deprive it of its rights is a most cruel innovation and usurpation, 
 tending to destroy all just subordination in the world, making all 
 universities superfluous, levelling vice-chancellors, doctors, and proctors, 
 masters, bachelors, and scholars, to the mean and contemptible state of 
 butchers and tallow*chandlers, bricklayers and chimney-sweepers, who, 
 if it were not for these learned mysteries, might think that they knew 
 as much as their betters. Every one then, who has the good of science 
 at heart, must pray for the interference of his highness to put a stop 
 to all the disputes about nothing, and by his decision to convince all 
 gainsayers that the science of nothing is taught in the best manner in 
 the universities, to the great edification and improvement of all the 
 youth in the land.' 
 
 Here Pantagruel whispered in the ear of Panurge, who nodded to 
 Epistemon, and they two left the assembly, and did not return for an 
 hoar, till the orator had finished his task. The three beadles had 
 thrice struck the ground with their heads and staves, the doctors had 
 finished their compliments, and the masters were making their twenty- 
 seven prostrations. Epistemon and Panurge went up to Pantagruel, 
 whom they found fast asleep and snoring ; nor could he be roused but 
 by as many tugs as there had been bowings from the corps of learning. 
 At last he opened his eyes, gave a good stretch, made half a dozen 
 yawns, and called for a stoup of wine. I thank you, my masters, says 
 he ; so sound a nap I have not had since I came from the island of 
 Priestfolly. Have you dined, my masters ? They answered the 
 question by as many bows as at entrance ; but his highness left them 
 to the care of Panurge, and retired to the little parlour with Epistemon, 
 where they burst into a fit of laughter, declaring that this learned 
 }>:n-agouin about nothing was just as intelligible as the lawyer's 
 
IMITATION OF KABELAIS. 127 
 
 Galimathias. Panurge conducted the learned body into a large saloon, 
 and each in his way hearing a clattering of plates and glasses, con- 
 gratulated himself on his approaching good cheer. There they were 
 left by Panurge, who took his chair by Pantagruel just as the soup 
 was removed, but he made up for the want of that part of his dinner 
 by a pint of Champagne. The learning of the university had whetted 
 their appetites ; what they each ate it is needless to recite ; good wine, 
 good stories, and hearty laughs went round, and three hours elapsed 
 before one soul of them recollected the hungry students of Pontemaca. 
 Epistemon reminded them of the business in hand, and orders were 
 given for a fresh dozen of hermitage to be put upon table, and the 
 royal attendants to get ready. As soon as the dozen bottles were- 
 emptied, Pantagruel rose from table, the royal trumpets sounded, and 
 he was accompanied by the great officers of his court into the large 
 dining hall, where was a table with forty-two covers. Pantagruel sat 
 at the head, Epistemon at the bottom, and Panurge in the middle, 
 opposite an immense silver tureen, which would hold fifty gallons of 
 soup. The wise men of Pontemaca then took their seats according to 
 seniority. Every countenance glistened with delight ; the music struck 
 up ; the dishes were uncovered. Panurge had enough to do to handle 
 the immense silver ladle : Pantagruel and Epistemon had no time for 
 eating, they were fully employed in carving. The bill of fare announced 
 the names of a hundred different dishes. From Panurge's ladle came 
 into the soup plate as much as he took every time out of the tureen ; 
 and as it was the rule of the court that every one should appear to eat, 
 as long as he sat at table, there was the clattering of nine and thirty 
 spoons against the silver soup-plates for a quarter of an hour. They 
 were then removed, and knives and forks were in motion for half an 
 hour. Glasses were continually handed round in the mean time, and 
 then everything was removed, except the great tureen of soup. The 
 second course was now served up, in dispatching which half an hour 
 was consumed ; and at the conclusion the wise men of Pontemaca had 
 just as much in their stomachs as Pantagruel in his head from their 
 address : for nothing was cooked up for them in every possible shape 
 that Panurge could devise. 
 
 Wine-glasses, large decanters, fruit dishes, and plates were now set 
 on. Pantagruel and Epistemon alternately gave bumper toasts : the 
 University of Pontemaca, the eye of the woild, the mother of taste and 
 good sense and universal learning, the patroness of utility, and the 
 second only to Pantagruel in wisdom and virtue (for these were her 
 titles), was drank standing with thrice three times three, and huzzas 
 and clatterings of glasses ; but to such wine the wise men of Pontemaca 
 had not been accustomed ; and though Pantagruel did not suffer one 
 to rise from table till the eighty-first glass had been emptied, not even 
 the weakest headed master of arts felt his head in the least indisposed. 
 The decanters indeed were often removed, but they were brought back 
 replenished, filled always with nothing. 
 
128 A BUDGET OF PAKADOXEa 
 
 Silence was now proclaimed, and in a trice Panurge leaped into the 
 large silver tureen. Thence lie made his bows to Pantagruel and the 
 whole company, and commenced an oration of signs, which lasted an 
 hour and a half, and in which he went over all the matter contained 
 in the Pontemacan address ; and though the wise men looked very 
 serious during the whole time, Pantagruel himself and his whole court 
 could not help indulging in repeated bursts of laughter. It was 
 universally acknowledged that he excelled himself, and that the ar- 
 guments by which he beat the English masters of arts at Paris were 
 nothing to the exquisite selection of attitudes which he this day 
 assumed. The greatest shouts of applause were excited when he was 
 running thrice round the tureen on its rim, with his left hand holding 
 his nose, and the other exercising itself nine and thirty times on his 
 back. In this attitude he concluded with his back to the pro- 
 fessor of mathematics ; and at the instant he gave his last flap, by a 
 sudden jump, and turning heels over head in the air, he presented 
 himself face to face to the professor, and standing on his left leg, with 
 his left hand holding his nose, he presented to him, in a white satin 
 bag, Pantagruel's royal decree. Then advancing his right leg, he 
 fixed it on the professor's head, and after three turns, in which he 
 clapped his sides with both hands thrice three times, down he 
 leaped, and Pantagruel, Epistemon, and himself took their leaves of the 
 wise men of Pontemaca. 
 
 The wise men now retired, and by royal orders were accompanied 
 by a guard, and according to the etiquette of the court, no one having 
 a royal order could stop at any public house till it was delivered. The 
 procession arrived at Pontemaca at nine o'clock the next morning, and 
 the sound of bells from every church and college announced their 
 arrival. The congregation was assembled ; the royal decree was 
 saluted in the same manner as if his highness had been there in 
 person ; and after the proper ceremonies had been performed, the 
 satin bag was opened exactly at twelve o'clock. A finely emblazoned 
 roll was drawn forth, and the public orator read to the gaping assembly 
 the following words : 
 
 * They who can make something out of nothing shall have nothing 
 to eat at the court of PANTAGRUEL.' 
 
 ORIGIN of the ENGLISH LANGUAGE, related by a SWEDE. 
 
 SOME months ago in a party in Holland, consisting of natives of various 
 countries, the merit of their respective languages became a topic of 
 conversation. A Swede, who had been a great traveller, and could 
 converse in most of the modern languages of Europe, laughed very 
 heartily at an Englishman, who had ventured to speak in praise of the 
 tongue of his dear country. I never had any trouble, says he, in learning 
 English. To my very great surprise, the moment I sat foot on shore 
 
ORIGIN OF ENGLISH; A FABLE. 129 
 
 at Gravesend, I found out, that I could understand, with very little 
 trouble, every word that was said. It was a mere jargon, made up of 
 German, French, and Italian, with now and then a word from the 
 Spanish, Latin, or Greek. I had only to bring my mouth to their 
 mode of speaking, which was done with ease in less than a week, and 
 I was every where taken for a true-born Englishman ; a privilege by 
 the way of no small importance in a country, where each man, God 
 knows why, thinks his foggy island superior to any other part of the 
 world: and though his door is never free from some dun or other 
 coming for a tax, and if he steps out of it he is sure to be knocked 
 down or to have his pocket picked, yet he has the insolence to think 
 every foreigner a miserable slave, and his country the seat of every 
 thing wretched. They may talk of liberty as they please, but Spain 
 or Turkey for my money : barring the bowstring and the inquisition, 
 they are the most comfortable countries under heaven, and you need 
 not be afraid of either, if you do not talk of religion and polities. I do 
 not see much difference too in this respect in England, for when I was 
 there, one of their most eminent men for learning was put in prison 
 for a couple of years, and got his death for translating one of ^Esop's 
 fables into English, which every child in Spain and Turkey is taught, 
 as soon as he comes out of his leading strings. Here all the company 
 unanimously cried out against the Swede, that it was impossible : for in 
 England, the land of liberty, the only thing its worst enemies could 
 say against it, was, that they paid for their liberty a much greater 
 price than it was worth. Every man there had a fair trial accord- 
 ing to laws, which every body could understand ; and the judges were 
 cool, patient, discerning men, who never took the part of the crown 
 against the prisoner, but gave him every assistance possible for his 
 defence. 
 
 The Swede was borne down, but not convinced ; and he seemed 
 determined to spit out all his venom. Well, says he, at any rate you 
 will not deny that the English have not got a language of their own, 
 and that they came by it in a very odd way. Of this at least I am 
 certain, for the whole history was related to me by a witch in Lapland, 
 whilst I was bargaining for a wind. Here the company were all in 
 unison again for the story. 
 
 In antient times, said the old hag$ the English occupied a spot in 
 Tartary, where they lived sulkily by themselves, unknowing and un- 
 known. By a great convulsion that took place in China, the inhabit- 
 ants of that and the adjoining parts of Tartary were driven from their 
 seats, and after various wanderings took up their abode in Germany. 
 During this time no body could understand th^ English, for they did 
 not talk, but hissed like so many snakes. The poor people felt uneasy 
 under this circumstance, and in one of their parliaments, or rather 
 hissing meetings, it was determined to seek for a remedy : and an 
 embassy was sent to some of our sisterhood then living on Mount 
 Hecla. They were put to a nonplus, and summoned the Devil to their 
 
 K 
 
130 A BUDGET OF PAEADOXES. 
 
 relief. To him the English presented their petitions, and explained 
 their sad case ; and he, upon certain conditions, promised to befriend 
 them, and to give them a language. The poor Devil was little aware 
 of what he had promised ; but he is, as all the world knows, a man of 
 too much honour to break his word. Up and down the world then he 
 went in quest of this new language : visited all the universities, and 
 all the schools, and all the courts of law, and all the play-houses, and 
 all the prisons ; never was poor devil so fagged. It would have made 
 your heart bleed to see him. Thrice did he go round the earth in 
 every parallel of latitude ; and at last, wearied and jaded out, back 
 came he to Hecla in despair, and would have thrown himself into the 
 volcano, if he had been made of combustible materials. Luckily at 
 that time our sisters were engaged in settling the balance of Europe ; 
 and whilst they were looking over projects, and counter-projects, and 
 ultimatums, and post ultimatums, the poor Devil, unable to assist them, 
 was groaning in a corner and ruminating over his sad condition. 
 
 On a sudden, a hellish joy overspread his countenance; up he 
 jumped, and, like Archimedes of old, ran like a madman amongst the 
 throng, turning over tables, and papers, and witches, roaring out for a 
 full hour together nothing else but 'tis found, 'tis found ! Away were 
 sent the sisterhood in every direction, some to traverse all corners of 
 the earth, and others to prepare a larger caldron than had ever yet 
 been set upon Hecla. The affairs of Europe were at a stand: its 
 balance was thrown aside ; prime ministers and ambassadors were 
 every where in the utmost confusion ; and, by the way, they have 
 never been able to find the balance since that time, and all the fine 
 speeches upon the subject, with which your newspapers are every now 
 and then filled, are all mere hocus-pocus and rhodomontade. How- 
 ever, the caldron was soon set on, and the air was darkened by witches 
 riding on broomsticks, bringing a couple of folios under each arm, and 
 across each shoulder. I remember the time exactly: it was just as the 
 council of Nice had broken up, so that they got books and papers there 
 dog cheap ; but it was a bad thing for the poor English, as these were 
 the worst materials that entered into the caldron. Besides, as the 
 Devil wanted some amusement, and had not seen an account of the 
 transactions of this famous council, he had all the books brought from 
 it laid before him, and split his sides almost with laughing, whilst he 
 was reading the speeches and decrees of so many of his old friends and 
 acquaintance. All this while the witches were depositing their loads 
 in the great caldron. There were books from the Dalai Lama, and 
 from China : there were books from the Hindoos, and tallies from the 
 Cafires : there were paintings from Mexico, and rocks of hieroglyphics 
 from Egypt : the last country supplied besides the swathings of two 
 thousand mummies, and four-fifths of the famed library of Alexandria. 
 Bubble ! bubble ! toil and trouble ! never was a day of more labour 
 and anxiety ; and if our good master had but flung in the Greek books 
 at the proper time, they would have made a complete job of it. He 
 
EAKLY GENIUS. 131 
 
 was a little too impatient : as the caldron frothed up, he skimmed it 
 off with a great ladle, and filled some thousands of our wind-bags 
 with the froth, which the English with great joy carried back to their 
 own country. These bags were sent to every district : the chiefs first 
 took their fill, and then the common people ; hence they now speak 
 a language which no foreigner can understand, unless he has learned 
 half a dozen other languages ; and the poor people, not one in ten, 
 understand a third part of what is said to them. The hissing, how- 
 ever, they have not entirely got rid of, and every seven years, when 
 the Devil, according to agreement, pays them a visit, they entertain 
 him at their common halls and county meetings with their original 
 language. 
 
 The good natured old hag told me several other circumstances, 
 relative to this curious transaction, which, as there is an Englishman 
 in company, it will be prudent to pass over in silence : but I cannot 
 help mentioning one thing which she told me as a very great secret. 
 You know, says she to me, that the English have more religions among 
 them than any other nation in Europe, and that there is more teaching 
 and sermonizing with them than in any other country. The fact is 
 this ; it matters not who gets up to teach them, the hard words of the 
 Greek were not sufficiently boiled, and whenever they get into a 
 sentence, the poor people's brains are turned, and they know no more 
 what the preacher is talking about, than if he harangued them in 
 Arabic. Take my word for it if you please ; but if not, when you get 
 to England, desire the bettermost sort of people that you are acquainted 
 with to read to you an act of parliament, which of course is written in 
 the clearest and plainest stile in which any thing can be written, and 
 you will find that not one in ten will be able to make tolerable sense 
 of it. The language would have been an excellent language, if it had 
 not been for the council of Nice, and the words had been well boiled. 
 
 Here the company burst out into a fit of laughter. The Englishman 
 got up and shook hands with the Swede : si non e vero, said he, e ben 
 trovato. But, however I may laugh at it here, I would not advise 
 you to tell this story on the other side of the water. So here's a 
 bumper to Old England for ever, and God save the king/ 
 
 * The accounts given of extraordinary children and adolescents 
 frequently defy credence. I will give two well-attested instances. 
 The celebrated mathematician, Alexis Claude Clairault (now 
 Clairaut) was certainly born in May, 1713. His treatise on 
 curves of double curvature (printed in 1731) received the appro- 
 bation of the Academy of Sciences, August 23, 1729. Fontenelle, 
 in his certificate of this, calls the author sixteen years of age, and 
 
 K 2 
 
132 A BUDGET OF PARADOXES. 
 
 does not strive to exaggerate the wonder, as he might have done, 
 by reminding his readers that this work, of original and sustained 
 mathematical investigation, must have been coming from the pen 
 at the ages of fourteen and fifteen. The truth was, as attested 
 by De Molieres, Clairaut had given public proofs of his power at 
 twelve years old. His age being thus publicly certified, all doubt 
 is removed : say he had been though great wonder would still 
 have been left twenty-one instead of sixteen, his appearance, 
 and the remembrances of his friends, schoolfellows, &c., would 
 have made it utterly hopeless to knock off five years of that age 
 while he was on view in Paris as a young lion. De Molieres, who 
 examined the work officially for the Garde des Sceaux, is trans- 
 ported beyond the bounds of official gravity, and says that it 6 ne 
 merite pas seulement d'etre imprime, mais d'etre admire comme 
 un prodige d'imagination, de conception, et de capacite.' 
 
 That Blaise Pascal was born in June, 1623, is perfectly well 
 established and uncontested. That he wrote his conic sections at 
 the age of sixteen might be difficult to establish, though tolerably 
 well attested, if it were not for one circumstance, for the book 
 was not published. The celebrated theorem, Pascal's hexagram, 
 makes all the rest come very easy. Now Curabelle, in a work 
 published in 1644, sneers at Desargues, whom he quotes, for 
 having, in 1 642, deferred a discussion until cette grande proposi- 
 tion nommee la Pascale verra le jour. That is, by the time 
 Pascal was nineteen, the hexagram was circulating under a name 
 derived from the author. The common story about Pascal, 
 given by his sister, is an absurdity which no doubt has prejudiced 
 many against tales of early proficiency. He is made, when quite 
 a boy, to invent geometry in the order of Euclid's propositions : 
 as if that order were natural sequence of investigation. The 
 hexagram at ten years old would be a hundred times less un- 
 likely. 
 
 The instances named are painfully astonishing : I give one 
 which has fallen out of sight, because it will preserve an imperfect 
 biography. John Wilson is Wilson of that Ilk, that is, of 
 Wilson's Theorem. It is this : If p be a prime number, the 
 product of all the numbers up to p -1, increased by 1, is divisible 
 without remainder by p. All mathematicians know this as 
 Wilson's theorem, but few know who Wilson was. He was born 
 August 6, 1741, at the Howe in Applethwaite, and he was heir 
 to a small estate at Troutbeck in Westmoreland. He was sent to 
 Peterhouse, at Cambridge, and, while an undergraduate was 
 considered stronger in algebra than any one in the University, 
 
JOHN WILSON WILLIAM MORGAN MRS. FRY. 133 
 
 except Professor Waring, one of the most powerful algebraists of 
 the century. 1 He was the senior wrangler of 1761, and was then 
 for some time a private tutor. When Paley, then in his third 
 year, determined to make a push for the senior wranglership, 
 which he got, Wilson was recommended to him as a tutor. Both 
 were ardent in their work, except that sometimes Paley, when he 
 came for his lesson, would find gone a fishing written on his 
 tutor's outer door : which was insult added to injury, for Paley 
 was very fond of fishing. Wilson soon left Cambridge, and went 
 to the bar. He practised on the northern circuit with great 
 success ; and, one day, while passing his vacation on his little 
 property at Troutbeck, he received information, to his great 
 surprise, that Lord Thurlow, with whom he had no acquaintance, 
 had recommended him to be a Judge of the Court of Common 
 Pleas. He died, Oct. 18, 1793, with a very high reputation 
 as a lawyer and a Judge. These facts are partly from Meadley's 
 ' Life of Paley,' no doubt from Paley himself, partly from the 
 Gentleman's Magazine, and from an epitaph written by Bishop 
 Watson. Wilson did not publish anything : the theorem by 
 which he has cut his name in the theory of numbers was com- 
 municated to Waring, by whom it was published. He married, 
 in 1788, a daughter of Serjeant Adair, and left issue. Had a 
 family, many will say : but a man and his wife are a family, even 
 without children. An actuary may be allowed to be accurate in 
 this matter, of which I was reminded by what an actuary wrote 
 of another actuary. William Morgan, in the life of his uncle 
 Dr. Richard Price, says that the Doctor and his wife were 4 never 
 blessed with an addition to their family.' I never met with such 
 accuracy elsewhere. Of William Morgan I add that my surname 
 and pursuits have sometimes, to my credit be it said, made a 
 confusion between him and me. Dates are nothing to the 
 mistaken ; the last three years of Morgan's life were the first 
 three years of my actuary-life (1830-33). The mistake was to 
 my advantage as well as to my credit. I owe to it the acquaint- 
 ance of one of the noblest of the human race, I mean Elizabeth 
 Fry, who came to me for advice about a philanthropic design, 
 which involved life questions, under a general impression that 
 some Morgan had attended to such things. 2 
 
 1 He wrote, in 1 760, a tract in defence of Waring, a point of whose algebra had 
 been assailed by a Dr. Powell. Waring wrote another tract of the same date. 
 
 2 Mrs. Fry certainly believed that the writer was the old actuary of the Equitable, 
 when she first consulted him upon the benevolent Assurance project ; but we were 
 introduced to her by our old and dear friend Lady Noel Byron, by whom she had 
 
134 A BUDGET OF PARADOXES. 
 
 A treatise on the sublime science of heliography, satisfactorily 
 demonstrating our great orb of light, the sun, to be absolutely 
 no other than a body of ice ! Overturning all the received 
 systems of the universe hitherto extant ; proving the celebrated 
 and indefatigable Sir Isaac Newton, in his theory of the solar 
 system, to be as far distant from the truth, as any of the 
 heathen authors of Greece or Rome. By Charles Palmer, Gent. 
 London, 1798, 8vo. 
 
 Mr. Palmer burned some tobacco with a burning glass, saw 
 that a lens of ice would do as well, and then says 
 
 4 If we admit that the sun could be removed, and a terrestrial body 
 of ice placed in its stead, it would produce the same effect. The sun 
 is a crystaline body receiving the radience of God, and operates on this 
 earth in a similar manner as the light of the sun does when applied to 
 a convex mirror or glass.' 
 
 Nov. 10, 1801. The Eev. Thomas Cormouls, minister of 
 Tettenhall, addressed a letter to Sir Wm. Herschel, from which I 
 extract the following : 
 
 Here it may be asked, then, how came the doctrines of Newton to 
 solve all astronomic Phenomina, and all problems concerning the same, 
 both a parte ante and a parte post. It is answered that he certainly 
 wrought the principles he made use of into strickt analogy with the 
 real Phenomina of the heavens, and that the rules and results arizing 
 from them agree with them and resolve accurately all questions con- 
 cerning them. Though they are not fact and true, or nature, but 
 analogous to it, in the manner of the artificial numbers of logarithms, 
 sines, &c. A very important question arises here, Did Newton mean 
 to impose upon the world ? By no means : he received and used the 
 doctrines reddy formed ; he did a little extend and contract his prin- 
 ciples when wanted, and commit a few oversights of consequences. But 
 when he was very much advanced in life, he suspected the fundamental 
 nullity of them : but I have from a certain anecdote strong ground to 
 believe that he knew it before his decease, and intended to have re- 
 'tracted his error. But, however, somebody did deceive, if not wilfully, 
 neglently at least. That was a man to whom the world has great 
 obligations too. It was no less a philosopher than Galileo. 
 
 That Newton wanted to retract before his death, is a notion 
 not uncommon among paradoxers. Nevertheless, there is no 
 
 been long known and venerated, and who referred her to Mr. De Morgan for advice. 
 An -unusual degree of confidence in, and appreciation of each other, arose on their 
 first meeting between the two, who had so much that was externally different, and so 
 much that was essentially alike, in their natures. (Ed.) 
 
BISHOP WILKINS'S WORKS, 135 
 
 retraction in the third edition of the ' Principia,' published when 
 Newton was eighty-four years old ! The moral of the above is, 
 that a gentleman who prefers instructing William Herschel to 
 learning how to spell, may find a proper niche in a proper place, 
 for warning to others. It seems that gravitation is not truth, 
 but only the logarithm of it. 
 
 The mathematical and philosophical works of the Right Rev. 
 John Wilkins ... In two volumes. London, 1802, 8vo. 
 
 This work, or at least part of the edition all for aught I know 
 - is printed on wood ; that is, on paper made from wood-pulp. 
 It has a rough surface, and when held before a candle is of very 
 unequal transparency. There is in it a reprint of the works on 
 the earth and moon. The discourse on the possibility of going 
 to the moon, in this and the edition of 1640, is incorporated : 
 but from the account in the life prefixed, and a mention by 
 D'Israeli, I should suppose that it had originally a separate title- 
 page, and some circulation as a separate tract. Wilkins treats 
 this subject half seriously, half jocosely; he has evidently not 
 quite made up his mind. He is clear that ' arts are not yet come 
 to their solstice,' and that posterity will bring hidden things to 
 light. As to the difficulty of carrying food, he thinks, scoffing 
 Puritan that he is, the Papists may be trained to fast the voyage, 
 or may find the bread of their Eucharist ' serve well enough for 
 their viaticum? He also puts the case that the story of Do- 
 mingo Gonsales may be realized, namely, that wild geese find 
 their way to the moon. It will be remembered to use the 
 usual substitute for, It has been forgotten that the posthumous 
 work of Bishop Francis Godwin of Llandaff was published in 
 1638, the very year of Wilkins's first edition, in time for him to 
 mention it at the end. Godwin makes Domingo Gronsales get to 
 the moon in a chariot drawn by wild geese, and, as old books 
 would say, discourses fully on that head. It is not a little 
 amusing that Wilkins should have been seriously accused of 
 plagiarizing Godwin, Wilkins writing in earnest, or nearly so, 
 and Godwin writing fiction. It may serve to show philosophers 
 how very near pure speculation comes to fable. From the 
 Sublime to the ridiculous there is but a step : which is the sub- 
 lime, and which the ridiculous, every one must settle for himself. 
 With me, good fiction is the sublime, and bad speculation the 
 ridiculous. The number of bishops in my list is small. I 
 might, had I possessed the book, have opened the list of quad- 
 rators with an Archbishop of Canterbury, or at least with a 
 
136 A BUDGET OF PARADOXES. 
 
 divine who was not wholly not archbishop. Thomas Bradwardine 
 (Bragvardinus, Bragadinus) was elected in 1348 ; the Pope put 
 in another, who died unconsecrated ; and Bradwardine was again 
 elected in 1 349, and lived five weeks longer, dying, I suppose, 
 unconfirmed and unconsecrated. Leland says he held the see a 
 year, unus tantum annulus, which seems to be a confusion : 
 the whole business, from the first election, took about a year. 
 He squared the circle, and his performance was printed at Paris 
 in 1494. I have never seen it, nor any work of the author, 
 except a tract on proportion. 
 
 As Bradwardine's works are very scarce indeed, I give two titles 
 from one of the Libri catalogues. 
 
 * ARITHMETIC. BEAUAEDINI (Thorns) Arithmetica speculativa revisa 
 et correcta a Petro Sanchez Ciruelo Aragonesi, black letter, 
 elegant woodcut title-page, VERY RARE, folio. Parisiis, per Thomam 
 Anguelast (jpro Olivier Senant), s.a. circa 1510. 
 
 ' This book, by Thomas Bradwardine, Archbishop of Canterbury, 
 must be exceedingly scarce as it has escaped the notice of Pro- 
 fessor De Morgan, who, in his Arithmetical Books, speaks of a 
 treatise of the same author on proportions, printed at Vienna in 
 1515, but does not mention the present work. 
 
 ' Bradwardine (Archbp. T.). Brauardini (Thomas) Geometrla 
 speculativa, cum Tractatu de Quadratura Circuli bene revisa a 
 Petro Sanchez Ciruelo, SCARCE, folio. Parisiis, J. Petit, 1511. 
 
 ' In this work we find the polygones etoiles, see Chasles (Aperqu, 
 pp. 480, 487, 521, 523, &c.) on the merit of the discoveries of 
 this English mathematician, who was Archbishop of Canterbury 
 in the xivth Century (tempore Edward III. A.D. 1349) ; and 
 who applied geometry to theology. M. Chasles says that the 
 present work of Bradwardine contains " Une theorie nouvelle qui 
 doit faire honneur au xive Siecle." ' 
 
 The titles do not make it quite sure that Bradwardine is the 
 quadrator ; it may be Peter Sanchez after all. 
 
 Nouvelle theorie des paralleles. Par Adolphe Kircher [so signed 
 at the end of the appendix]. Paris, 1803, 8vo. 
 
 An alleged emendation of Legendre. The author refers to 
 attempts by Hoffman, 1801, by Hauff, 1799, and to a work of 
 Karsten, or at least a theory of -Karsten, contained in < Tentamen 
 novse parallelarum theorise notione situs fundatse ; auctore Gr. C. 
 
ROSSI W. SPENCE PANICS. 137 
 
 Schwal, StuttgardsB, 1801, en 8 volumes.' Surely this is a mis- 
 print ; eight volumes on the theory of parallels ? If there be 
 such a work, I trust I and it may never meet, though ever so 
 far produced. 
 
 Soluzione . . . della quadratura del Circolo. By Gaetano Rossi. 
 London, 1804, 8vo. 
 
 The three remarkable points of this book are, that the house- 
 hold of the Prince of Wales took ten copies, Signora Grassini 
 sixteen v and that the circumference is 3^ diameters. That is, 
 the appetite of Grassini for quadrature exceeded that of the 
 whole household (loggia) of the Prince of Wales in the ratio in 
 which the semi-circumference exceeds the diameter. And these 
 are the first two in the list of subscribers. Did the author see 
 this theorem ? 
 
 Britain independent of commerce ; or proofs, deduced from an in- 
 vestigation into the true causes of the wealth of nations, that our 
 riches, prosperity, and power are derived from sources inherent 
 in ourselves, and would not be affected, even though our 
 commerce were annihilated. By Wm. Spence. 4th edition, 
 1808, 8vo. 
 
 A patriotic paradox, being in alleviation of the Commerce 
 panic which the measures of Napoleon I. who felt our Commerce, 
 while Mr. Spence only saw it had awakened. In this very 
 month (August, 1866), the Pres. Brit. Assoc. has applied a 
 similar salve to the coal panic ; it is fit that science, which 
 rubbed the sore, should find a plaster. We ought to have an 
 iron panic and a timber panic ; and a solemn embassy to the 
 Americans, to beg them not to whittle, would be desirable. 
 There was a gold panic beginning, before the new fields were 
 discovered. For myself, I am the unknown and unpitied victim 
 of a chronic gutta-percha panic: I never could get on without 
 it ; to me, gutta percha and Eowland Hill are the great dis- 
 coveries of our day; and not unconnected either, gutta percha 
 being to the submarine post what Eowland Hill is to the super- 
 terrene. I should be sorry to lose cow-choke I gave up trying 
 to spell it many years ago but if gutta percha go, I go too. 
 I think, that perhaps when, five hundred years hence, the people 
 say to the Brit. Assoc. (if it then exist) ; Pray, gentlemen, is it 
 not time for the coal to be exhausted ? ' they will be answered out 
 of Moliere (who will certainly then exist) : Cela etait autrefois 
 ainsi, mais nous avons change tout cela. A great many people 
 
138 A BUDGET OF PAEADOXES. 
 
 think that if the coal be used up, it will be announced some 
 unexpected morning by all the yards being shut up and written 
 notice outside, c Coal all gone ! ' just like the < Please, ma'am, 
 there ain't no more sugar,' with which the maid servant damps 
 her mistress just at breakfast-time. But these persons should 
 be informed that there is every reason to think that there will 
 be time, as the city gentleman said, to venienti the occurrite 
 morbo. 
 
 An appeal to the republic of letters in behalf of injured science, 
 from the opinions and proceedings of some modern authors of 
 elements of geometry. By George Douglas. Edinburgh, 
 1810, 8vo. 
 
 Mr. Douglas was the author of a very good set of mathematical 
 tables, and of other works. He criticizes Simson, Playfair, and 
 others, sometimes, I think, very justly. There is a curious 
 phrase, which occurs more than once. When he wants to say 
 that something or other was done before Simson or another was 
 born, he says ' before he existed, at least as an author.' He 
 seems to reserve the possibility of Simson's pre-existence, but at 
 the same time to assume that he never wrote anything in his 
 previous state. Tell me that Simson pre-existed in any other 
 way than as editor of some pre-existent Euclid ? Tell Apella ! 
 
 1810. In this year Jean Wood, Professor of Mathematics in 
 the University of Virginia (Richmond), addressed a printed 
 circular to 'Dr. Herschel, Astronomer, Greenwich Observatory.' 
 No mistake was more common than the natural one of imagining 
 that the Private Astronomer of the king was the Astronomer 
 Royal. The letter was on the difference of velocities of the two 
 sides of the earth, arising from the composition of the rotation 
 and the orbital motion. The paradox is a fair one, and 
 deserving of investigation ; but, perhaps it would not be easy to 
 deduce from it tides, trade-winds, aerolithes, &c., as Mr. Wood 
 thought he had done in a work from which he gives an extract, 
 and which he describes as published. The composition of rota- 
 tions, &c., is not for the world at large : the paradox of the 
 non-rotation of the moon about her axis is an instance. How 
 many persons know that when a wheel rolls on the ground, the 
 lowest point is moving upwards, the highest point forwards, and 
 the intermediate points in all degrees of betwixt and between ? 
 This is too short an explanation, with some good difficulties. 
 
PAKADOX WITHOUT STOPPING. 139 
 
 The Elements of Geometry. In 2 vols. [By the Rev. J. Dobson, 
 B.D.] Cambridge, 1815. 4to. 
 
 Of this unpunctuating paradoxer I shall give an account in his 
 own way : he would not stop for any one ; why should I stop for him ? 
 It is worth while to try how unpunctuated sentences will read. 
 
 The reverend J Dobson BD late fellow of saint Johns college 
 Cambridge was rector of Brandesburton in Yorkshire he was 
 seventh wrangler in 1798 and died in 1847 he was of that sort of 
 eccentricity which permits account of his private life if we may 
 not rather say that in such cases private life becomes public there 
 is a tradition that he was called Death Dobson on account of his 
 head and aspect of countenance being not very unlike the 
 ordinary pictures of a human skull his mode of life is reported 
 to have been very singular whenever he visited Cambridge he was 
 never known to go twice to the same inn he never would sleep at 
 the rectory with another person in the house some ancient char- 
 woman used to attend to the house but never slept in it he has 
 been known in the time of coach travelling to have deferred his 
 return to Yorkshire on account of his disinclination to travel 
 with a lady in the coach he continued his mathematical studies 
 until his death and till his executors sold the type all his tracts 
 to the number of five were kept in type at the university press 
 none of these tracts had any stops except full stops at the end of 
 paragraphs only neither had they capitals except one at the 
 beginning of a paragraph so that a full stop was generally 
 followed by some white as there is not a single proper name in 
 the whole of the book I have I am not able to say whether he 
 would have used capitals before proper names I have inserted 
 them as usual for which I hope his spirit will forgive me if I be 
 wrong he also published the elements of geometry in two 
 volumes quarto Cambridge 1815 this book had also no stops 
 except when a comma was wanted between letters as in the 
 straight lines AB 5 BC I should also say that though the title is 
 unpunctuated in the author's part it seems the publishers would 
 not stand it in their imprint this imprint is punctuated as usual 
 and Deighton and Sons to prove the completeness of their allegi- 
 ance have managed that comma semicolon colon and period 
 shall all appear in it why could they not have contrived interro- 
 gation and exclamation this is a good precedent to establish the 
 separate right of the publisher over the imprint it is said that 
 only twenty of the tracts were printed and very few indeed of the 
 book on geometry it is doubtful whether any were sold there is a 
 
140 A BUDGET OF PARADOXES. 
 
 copy of the geometry in the university library at Cambridge and 
 I have one myself the matter of the geometry differs entirely 
 from Euclid and is so fearfully prolix that I am sure no mortal 
 except the author ever read it the man went on without stops 
 and without stop save for a period at the end of a paragraph this 
 is the unpunctuated account of the unpunctuating geometer 
 suum cuique tribuito Mrs Thrale would have been amused at a 
 Dobson who managed to come to a full stop without either of the 
 three warnings. 
 
 I do not find any difficulty in reading Dobson's geometry ; and 
 I have read more of it to try reading without stops than I should 
 have done had it been printed in the usual way. Those who dip 
 into the middle of my paragraph may be surprised for a moment 
 to see that ' on account of his disinclination to travel with a 
 lady in the coach he continued his mathematical studies until 
 his death and [further, of course] until his executors sold the 
 type.' But a person reading straight through would hardly take 
 it so. I should add that, in order to give a fair trial, I did not 
 compose as I wrote, but copied the words of the correspondent 
 who gave me the facts, so far as they went. 
 
 Philosophia Sacra, or the principles of natural Philosophy. Ex- 
 tracted from Divine Revelation. By the Rev. Samuel Pike. 
 Edited by the Rev. Samuel Kittle. Edinburgh, 1815, 8vo. 
 
 This is a work of modified Hutchinsonianism, which I have 
 seen cited by several. Though rather dark on the subject, it 
 seems not to contradict the motion of the earth, or the doctrine 
 of gravitation, Mr. Kittle gives a list of some Hutchinsonians, 
 as Bishop Home ; Dr. Stukeley ; the Rev. W. Jones, author of 
 6 Physiological Disquisitions ; ' Mr. Spearman, author of ' Letters 
 on the Septuagint' and editor of Hutchinson ; Mr. Barker, 
 author of ' Reflexions on Learning ' ; Dr. Catcott, author of a 
 work on the creation, &c. ; Dr. Robertson, author of a * Treatise 
 on the Hebrew Language ; ' Dr. Hollo way, author of ' Originals, 
 Physical and Theological ; ' Dr. Walter Hodges, author of a work 
 on Elohim ; Lord President Forbes (ob. 1747). 
 
 The Rev. William Jones, above mentioned, (1726-1800), the 
 friend and biographer of Bishop Home, and his stout defender, 
 is best known as William Jones of Nay land, who (1757) pub- 
 lished the 6 Catholic Doctrine of the Trinity ; ' he was also strong 
 for the Hutchinsonian physical trinity of fire, light, and spirit. 
 This well-known work was generally recommended, as the de- 
 fence of the orthodox system, to those who could not go into the 
 
TRINITARIAN CONTROVERSY. 141 
 
 learning of the subject. There is now a work more suited to 
 our time : c The Eock of Ages,' by the Rev. E. H. Bickersteth, 
 now published by the Religious Tract Society, without date, 
 answered by the Rev. Dr. Sadler, in a work (1859) entitled Gloria 
 Patri, in which, says Mr. Bickersteth, 'the author has not 
 even attempted to grapple with my main propositions.' I have 
 read largely on the controversy, and I think I know what this 
 means. Moreover, when I see the note ' There are two other 
 passages to which Unitarians sometimes refer, but the deduction 
 they draw from them is, in each case, refuted by the context' 
 I think I see why the two texts are not named. Nevertheless, 
 the author is a little more disposed to yield to criticism than his 
 foregoers ; he does not insist on texts and readings which the 
 greatest editors have rejected. And he writes with courtesy, both 
 direct and oblique, towards his antagonists ; which, on his side 
 of this subject, is like letting in fresh air. So that I suspect the 
 two books will together make a tolerably good introduction to 
 the subject for those who cannot go deep. Mr. Bickersteth's 
 book is well arranged and indexed, which is a point of superiority 
 to Jones of Nayland. There is a point which I should gravely 
 recommend to writers on the orthodox side. The Unitarians in 
 England have frequently contended that the method of proving 
 the divinity of Jesus Christ from the New Testament would 
 equally prove the divinity of Moses. I have not fallen in the 
 way of any orthodox answers specially directed at the repeated 
 tracts written by Unitarians in proof of their assertion. If there 
 be any, they should be more known ; if there be none, some 
 should be written. Which ever side may be right, the treatment 
 of this point would be indeed coming to close quarters. The 
 heterodox assertion was first supported, it is said, by John Bidle 
 or Biddle (1615-1662) of Magdalen College, Oxford, the earliest 
 of the English Unitarian writers, previously known by a transla- 
 tion of part of Virgil and part of Juvenal. But I cannot find 
 that he wrote on it. It is the subject of ' aipsa-scov dvacrrao-is, or a 
 new way of deciding old controversies. By Basanistes. Third 
 edition, enlarged,' London, 1815, 8vo. It is the appendix to the 
 amusing, 4 Six more letters to Granville Sharp, Esq., . . . By 
 Gregory Blunt, Esq. 5 London, 8vo., 1803. This much I can 
 confidently say, that the study of these tracts would prevent 
 orthodox writers from some curious slips, which are slips obvious 
 to all sides of opinion. The lower defenders of orthodoxy fre- 
 quently vex the spirits of the higher ones. 
 
 Since writing the above I have procured Dr. Sadler's answer. 
 
142 A BUDGET OF PAEADOXES. 
 
 I thought I knew what the challenger meant when he said the 
 respondent had not grappled with his main propositions. I 
 should say that he is clung on to from beginning to end. But 
 perhaps Mr. B. has his own meaning of logical terms, such as 
 proposition : he certainly has his own meaning of cumulative. 
 He says his evidence is cumulative ; not a catena, the strength of 
 which is in its weakest part, but distinct and independent lines, 
 each of which corroborates the other. This is the very opposite 
 of cumulative : it is distributive. When different arguments are 
 each necessary to a conclusion, the evidence is cumulative ; when 
 any one will do, even though they strengthen each other, it is 
 distributive. The word cumulative is a synonym of the law word 
 constructive ; a whole which will do made out of parts which 
 separately will not. Lord Strafford opens his defence with the 
 use of both words : ' They have invented a kind of accumulated 
 or constructive evidence ; by which many actions, either totally 
 innocent in themselves, or criminal in a much inferior degree, 
 shall, when united, amount to treason.' The conclusion is, that 
 Mr. B. is a Cambridge man ; the Oxford men do not confuse the 
 elementary terms of logic. dear old Cambridge ! when the 
 New Zealander comes let him find among the relics of your later 
 sons some proof of attention to the elementary laws of thought. 
 A little-go of logic, please ! 
 
 Mr. B. ? though apparently not a Hutchinsonian, has a nibble 
 at a physical Trinity. 4 If, as we gaze on the sun shining in the 
 firmament, we see any faint adumbration of the doctrine of the 
 Trinity in the fontal orb, the light ever generated, and the heat 
 proceeding from the sun and its beams threefold and yet one, 
 the sun, its light, and its heat, that luminous globe, and the 
 radiance ever flowing from it, are both evident to the eye ; but the 
 vital warmth is felt, not seen, and is only manifested in the life 
 it transfuses through creation. The proof of its real existence is 
 self-demonstrating.' 
 
 We shall see how Kevilo 1 illustrates orthodoxy by mathematics. 
 It was my duty to have found one of the many illustrations from 
 physics ; but perhaps I should have forgotten it if this instance 
 had not come in my way. It is very bad physics. The sun, 
 apart from its light, evident to the eye ! Heat more self-demon- 
 strating than light, because felt ! Heat only manifested by the 
 life it diffuses I Light implied not necessary to life I But the 
 theology is worse than Sabellianism. To adumbrate i.e. make 
 
 1 The name assumed by a writer who professed to give a mathematical explanation 
 of the Trinity, see farther on. (Ed.) 
 
TRINITARIAN CONTROVERSY SIR RICHARD PHILLIPS, 143 
 
 a picture of the orthodox doctrine, the sun must be heavenly 
 body, the light heavenly body, the heat heavenly body : and 
 yet, not three heavenly bodies, but one heavenly body. The 
 truth is, that this illustration and many others most strik- 
 ingly illustrate the Trinity of fundamental doctrine held by the 
 Unitarians, in all its differences from the Trinity of persons held 
 by the Orthodox. Be right which may, the right or wrong of 
 the Unitarians shines out in the comparison. Dr. Sadler confirms 
 me by which I mean that I wrote the above before I saw what 
 he says in the following words : 4 The sun is one object with two 
 properties, and these properties have a parallel not in the second 
 and third persons of the Trinity, but in the attributes of Deity.' 
 
 The letting light alone, as self-evident, and making heat self- 
 demonstrating, because felt i.e. perceptible now and then has 
 the character of the Irishman's astronomy : 
 
 Long life to the moon, for a dear noble cratur, 
 Which serves us for lamplight all night in the dark, 
 While the sun only shines in the day, which, by natur, 
 Wants no light at all, as ye all may remark. 
 
 Sir Richard Phillips (born 1768) was conspicuous in 1793, 
 when he was sentenced to a year's imprisonment for selling 
 Paine's 4 Eights of Man;' and again when, in 1807, he was 
 knighted as Sheriff of London. As a bookseller, he was able to 
 enforce his astronomical opinions in more ways than others. 
 For instance, in James Mitchell's 'Dictionary of the Mathe- 
 matical and Physical Sciences,' 1823, 12mo., which, though he 
 was not technically a publisher, was printed for him a book I 
 should recommend to the collector of works of reference there 
 is a temperate description of his doctrines, which one may almost 
 swear was one of his conditions previous to undertaking the work. 
 Phillips himself was not only an anti-Newtonian, but carried to a 
 fearful excess the notion that statesmen and Newtonians were 
 in league to deceive the world. He saw this plot in Mrs. Airy's 
 pension, and in Mrs. Somerville's. In 1836, he did me the 
 honour to attempt my conversion. In his first letter he says : 
 
 Sir Richard Phillips has an inveterate abhorrence of all the pre- 
 tended wisdom of philosophy derived from the monks and doctors of 
 the middle ages, and not less of those of higher name who merely 
 sought to make the monkish philosophy more plausible, or so to dis- 
 guise it as to mystify the mob of small thinkers. 
 
 So little did his writings show any knowledge of antiquity, 
 that I strongly suspect, if required to name one of the monkish 
 
144 A BUDGET OF PARADOXES. 
 
 doctors, lie would have answered Aristotle. These schoolmen, 
 and the c philosophical trinity of gravitating force, projectile 
 force, and void space,' were the bogies of his life. 
 
 I think he began to publish speculations in the Monthly 
 Magazine (of which he was editor) in July 1817 : these he 
 republished separately in 1818. In the Preface, perhaps judging 
 the feelings of others by his own, he says that he * fully expects 
 to be vilified, reviled, and anathematized, for many years to 
 come.' Poor man! he was let alone. He appeals with con- 
 fidence to the ' impartial decision of posterity ; ' but posterity 
 does not appoint a hearing for one per cent, of the appeals which 
 are made ; and it is much to be feared that an article in such a 
 work of reference as this will furnish nearly all her materials fifty 
 years hence. The following, addressed to M. Arago, in 1835, 
 will give posterity as good a notion as she will probably need : 
 
 Even the present year has afforded EVER-MEMORABLE examples, 
 paralleled only by that of the Romish Conclave which persecuted 
 Galileo. Policy has adopted that maxim of Machiavel which teaches 
 that it is more prudent to reward partisans than to persecute opponents. 
 Hence, a bigot/ted party had influence enough with the late short-lived 
 administration [I think he is wrong as to the administration] of 
 Wellington, Peel, &c., to confer munificent royal pensions on three 
 writers whose sole distinction was their advocacy of the Newtonian 
 philosophy. A Cambridge professor last year published an elaborate 
 volume in illustration of Gravitation, and on him has been conferred a 
 pension of 300 L per annum. A lady has written a light popular view 
 of the Newtonian Dogmas, and she has been complimented by a pension 
 of 200L per annum. And another writer, who has recently published 
 a volume to prove that the only true philosophy is that of Moses, has 
 been endowed with a pension of 200Z. per annum. Neither of them 
 were needy persons, and the political and ecclesiastical bearing of the 
 whole was indicated by another pension of 300Z. bestowed on a political 
 writer, the advocate of all abuses and prejudices. Whether the con- 
 duct of the Romish Conclave was more base for visiting with legal 
 penalties the promulgation of the doctrines that the Earth turns on its 
 axis and revolves around the Sun ; or that of the British Court, for its 
 craft in conferring pensions on the opponents of the plain corollary, 
 that all the motions on the Earth are ' part and parcel ' of these great 
 motions, and those again and all like them consecutive displays of 
 still greater motions in equality of action and reaction, is A QUESTION 
 which must be reserved for the casuists of other generations. . . I 
 cannot expect that on a sudden you and your friends will come to my 
 conclusion, that the present philosophy of the Schools and Univer- 
 sities of Europe, based on faith in witchcraft, magic, &c., is a system 
 of execrable nonsense, by which quacks live on the faith of fools ; but I 
 desire a free and fair examination of my Aphorisms, and if a few are 
 
PHILLIPS WOOD -SATIRICAL PARADOX. 145 
 
 admitted to be true, merely as courteous concessions to arithmetic, my 
 purpose will be effected, for men will thus be led to think ; and if they 
 think, then the fabric of false assumptions, and degrading superstitions 
 will soon tumble in ruins. 
 
 This for posterity. For the present time I ground the fame of 
 Sir E. Phillips on his having squared the circle without knowing 
 it, or intending to do it. In the Protest presently noted he 
 discovered that * the force taken as 1 is equal to the sum of all 
 its fractions .... thus 1 = + i- -f T *g- + -gV? ^ C -J can 'i e( i to in- 
 finity.' This the mathematician instantly sees is equivalent to 
 the theorem that the circumference of any circle is double of the 
 diagonal of the cube on its diameter. 
 
 I have examined the following works of Sir E. Phillips, and 
 heard of many others : 
 
 Essays on the proximate mechanical causes of the general phe- 
 nomena of the Universe, 1818, 12mo. 
 
 Protest against the prevailing principles of natural philosophy, 
 with the development of a common sense system (no date, 
 8vo. pp. 16). 
 
 Four dialogues between an Oxford Tutor and a disciple of the 
 common-sense philosophy, relative to the proximate causes of 
 material phenomena. 8vo. 1824. 
 
 A century of original aphorisms on the proximate causes of the 
 phenomena of nature, 1835, 12mo. 
 
 Sir Eichard Phillips had four valuable qualities ; honesty, 
 zeal, ability, and courage. He applied them all to teaching 
 matters about which he knew nothing ; and gained himself an 
 uncomfortable life and a ridiculous memory. 
 
 Astronomy made plain ; or only way the true perpendicular dis- 
 tance of the Sun, Moon, or Stars, from this earth, can be 
 obtained. By Wm. Wood. Chatham, 1819, 12mo. 
 
 If this theory be true, it will follow, of course, that this earth is the 
 only one God made, and that it does not whirl round the sun, but vice 
 versa, the sun round it. 
 
 Historic doubts relative to Napoleon Buonaparte. London, 1 819, 
 8vo. 
 
 This tract has since been acknowledged by Archbishop 
 Whately and reprinted. It is certainly a paradox : but differs 
 from most of those in my list as being a joke, and a satire upon 
 the reasoning of those who cannot receive narrative, no matter 
 
 L 
 
146 A BUDGET OF PAKADOXES. 
 
 what the evidence, which is to them utterly improbable a priori. 
 But had it been serious earnest, it would not have been so absurd 
 as many of those which I have brought forward. The next on 
 the list is not a joke. 
 
 The idea of the satire is not new. Dr. King, in the dispute 
 on the genuineness of Phalaris, proved with humour that Bentley 
 did not write his own dissertation. An attempt has lately been 
 made, for the honour of Moses, to prove, without humour, that 
 Bishop Colenso did not write his own book. This is intolerable : 
 anybody who tries to use such a weapon without banter, plenty 
 and good, and of form suited to the subject, should get the 
 drubbing which the poor man got in the Oriental tale for striking 
 the dervishes with the wrong hand. 
 
 The excellent and distinguished author of this tract has ceased 
 to live. I call him the Paley of our day : with more learning, 
 and more purpose than his predecessor ; but perhaps they might 
 have changed places if they had changed centuries. The clever 
 satire above named is not the only work which he published 
 without his name. The following was attributed to him, I 
 believe rightly : 6 Considerations on the Law of Libel, as relating 
 to Publications on the subject of Eeligion, by John Search.' 
 London, 1833, 8vo. This tract excited little attention: for those 
 who should have answered, could not. Moreover, it wanted a 
 prosecution to call attention to jt : the fear of calling such atten- 
 tion may have prevented prosecutions. Those who have read it 
 will have seen why. 
 
 The theological review elsewhere mentioned attributes .the 
 pamphlet of John Search on blasphemous libel to Lord Brougham. 
 This is- quite absurd : the writer states points of law on credence 
 where the judge must have spoken with authority. Besides which, 
 a hundred points of style are decisive between the two. I think 
 any one who knows Whately's writings will soon arrive at my 
 conclusion. Lord Brougham himself informs me that he has no 
 knowledge whatever of the pamphlet. 
 
 It is stated in Notes and Queries (3 S. xi. 511) that Search 
 was answered by the Bishop of Ferns as S.N., with a rejoinder by 
 Blanco White. These circumstances increase the probability that 
 Whately was written 'against and for. 
 
 Voltaire Chretien ; preuves tirees de ses onvrages. Paris, 1820, 
 12mo. 
 
 If Voltaire have not succeeded in proving himself a strong 
 theist and a strong anti-revelationist, who is to succeed in proving 
 
THE WORD CHRISTIAN. 147 
 
 himself one thing or the other in any matter whatsoever ? By 
 occasional confusion between theism and Christianity; by taking 
 advantage of the formal phrases of adhesion to the Eoman 
 Church, which very often occur, and are often the happiest bits 
 of irony in an ironical production ; by citations of his morality, 
 which is decidedly Christian, though often attributed to Brah- 
 mins ; and so on the author makes a fair case for his paradox, 
 in the eyes of those who know no more than he tells them. If 
 he had said that Voltaire was a better Christian than himself 
 knew of, towards all mankind except men of letters, I for one 
 should have agreed with him. 
 
 Christian! the word has degenerated into a synonym of man, 
 in what are called Christian countries. So we have the parrot 
 who ' swore for all the world like a Christian,' and the two dogs 
 who ' hated each other just like Christians.' When the Irish 
 duellist of the last century, whose name may be spared in 
 consideration of its historic fame and the worthy people who 
 bear it, was (June 12, 1786) about to take the consequence of 
 his last brutal murder, the rope broke, and the criminal got up, 
 
 and exclaimed, ' By Mr. Sheriff, you ought to be ashamed 
 
 of yourself ! this rope is not strong enough to hang a dog, far 
 less a Christian ! ' But such things as this are far from the worst 
 depravations. As to a word so defiled by usage, it is well to 
 know that there is a way of escape from it, without renouncing 
 the New Testament. I suppose any one may assume for himself 
 what I have sometimes heard contended for, that no New Testa- 
 ment word is to be used in religion in any sense except that of 
 the New Testament. This granted, the question is settled. 
 The word Christian, which occurs three times, is never recog- 
 nised as anything but a term of contempt from those without 
 the pale to those within. Thus, Herod Agrippa, who was deep in 
 Jewish literature, and a correspondent of Josephus, says to Paul, 
 (Acts xxvi. 28) ' Almost thou persuadest me to be (what I and 
 other followers of the state religion depise under the name) 
 a Christian.' Again, (Acts xi. 26) ' The disciples (as they called 
 themselves) were called (by the surrounding heathens) Christians 
 first in Antioch.' Thirdly, (1 Peter iv. 16) ' Let none of you 
 suffer as a murderer. . . . But if as a Christian (as the heathen 
 call it by whom the suffering comes), let him not be ashamed.' 
 That is to say, no disciple ever called himself a Christian, or 
 applied the name, as from himself, to another disciple, from one 
 end of the New Testament to the other ; and no disciple need 
 
 L 2 
 
148 A BUDGET OF PARADOXES. 
 
 apply that name to himself in our day, if he dislike the associa- 
 tions with which the conduct of Christians has clothed it. 
 
 Address of M. Hoene Wronski to the British Board of Longitude, 
 
 upon the actual state of the mathematics, their reform, and 
 
 upon the new celestial mechanics, giving the definitive solution 
 
 of the problem of longitude. London, 1820, 8vo. 
 
 M. Wronski was the author of seven quartos on mathematics, 
 
 showing very great power of generalization. He was also deep in 
 
 the transcendental philosophy, and had the Absolute at his 
 
 fingers' ends. All this knowledge was rendered useless by a 
 
 persuasion that he had greatly advanced beyond the whole world, 
 
 with many hints that the Absolute would not be forthcoming, 
 
 unless prepaid. He was a man of the widest extremes. At 
 
 one time he desired people to see all possible mathematics in 
 
 Fx = A O -f Ajfl, f A 2 H 2 4- A 3 O 3 + &c. 
 
 which he did not explain, though there is meaning to it in the 
 quartos. At another time he was proposing the general solution 
 of the fifth degree by help of 625 independent equations of one 
 form and 125 of another. The first separate memoir from any 
 Transactions that T ever possessed was given to me when at 
 Cambridge; the refutation (1819) of this asserted solution, 
 presented to the Academy of Lisbon by Evangelista Torriano. 
 I cannot say I read it. The tract above is an attack on modern 
 mathematicians in general, and on the Board of Longitude, and 
 Dr. Young. 
 
 1820. In this year died Dr. Isaac Milner, President of Queens' 
 College, Cambridge, .one of the class of rational paradoxers. 
 Under this name I include all who, in private life, and in matters 
 which concern themselves, take their own course, and suit their 
 own notions, no matter what other people may think of them. 
 These men will put things to uses they were never intended for, 
 to the great distress and disgust of their gregarious friends. I 
 am one of the class, and I could write a little book of cases in 
 which I have incurred absolute reproach for not ' doing as other 
 people do.' I will name two of my atrocities : I took one of 
 those butter-dishes which have for a top a dome with holes in 
 it, which is turned inward, out of reach of accident, when not in 
 use. Turning the dome inwards, I filled the dish with water, 
 and put a sponge in the dome : the holes let it fill with water, 
 and I had a penwiper, always moist, and worth its price five 
 times over. 4 Why ! what do you mean ? It was made to hold 
 
MILNER'S LAMP. 149 
 
 butter. You are always at some queer thing or other ! ' I 
 bought a leaden comb, intended to dye the hair, it being sup- 
 posed that the application of lead will have this effect, I did 
 not try : but I divided the comb into two, separating the part 
 of closed prongs from the other; and thus I had two ruling 
 machines. The lead marks paper, and by drawing the end of 
 one of the machines along a ruler, I could rule twenty lines at 
 a time, quite fit to write on. I thought I should have killed a 
 friend to whom I explained it : he could not for the life of him 
 understand how leaden lines on paper would dye the hair. 
 
 But Dr, Milner went beyond me. He wanted a seat suited to 
 his shape, and he defied opinion to a fearful point. He spread a 
 thick block of putty over a wooden chair and sat in it until it 
 had taken a ceroplast copy of the proper seat. This he gave to 
 a carpenter to be imitated in wood. One of the few now living 
 who knew him my friend, General Perronet Thompson 
 answers for the wood, which was shown him by Milner himself ; 
 but he does not vouch for the material being putty, which was 
 in the story told me at Cambridge ; William Frend also re- 
 membered it. Perhaps the Doctor took off his great seal in 
 green wax, like the Crown ; but some soft material he certainly 
 adopted ; and very comfortable he found the wooden copy. 
 
 The same gentleman vouches for Milner's lamp : but this had 
 visible science in it ; the vulgar see 
 no science in the construction of the 
 chair. A hollow semi-cylinder, but 
 not with a circular curve, revolved on 
 pivots. The curve was calculated on 
 the law that, whatever quantity of oil 
 might be in the lamp, the position of 
 equilibrium just brought the oil up to 
 the edge of the cylinder, at which a 
 bit of wick was placed. As the wick 
 exhausted the oil, the cylinder slowly 
 revolved about the pivots so as to 
 keep the oil always touching the wick. 
 
 Great discoveries are always laughed at : but it is very often 
 not the laugh of incredulity ; it is a mode of distorting the sense 
 of inferiority into a sense of superiority, or a mimicry of supe- 
 riority interposed between the laugher and "his feeling of in- 
 feriority. Two persons in conversation agreed that it was often 
 
150 A BUDGET OF PARADOXES. 
 
 a nuisance not to be able to lay hands on a bit of paper to mark 
 the place in a book, every bit of paper on the table was sure to 
 contain something not to be spared. I very quietly said that I 
 always had a stock of bookmarkers ready cut, with a proper place 
 for them : my readers owe many of my anecdotes to this absurd 
 practice. My two colloquials burst into a fit of laughter ; about 
 what ? Incredulity was out of the question ; and there could be 
 nothing foolish in my taking measures to avoid what they knew 
 was an inconvenience. I was in this matter obviously their 
 superior, and so they laughed at me. Much more candid was 
 the Royal Duke of the last century, who was noted for slow ideas. 
 ' The rain comes into my mouth,' said he, while riding. ' Had 
 not your Eoyal Highness better shut your mouth ? ' said the 
 equerry. The Prince did so, and ought, by rule, to have laughed 
 heartily at his adviser ; instead of this, he said quietly, ' It 
 doesn't come in now.' 
 
 De Attentionis mensura causisque primariis. By J. F. Herbart. 
 Koenigsberg, 1822, 4to. 
 
 This celebrated philosopher maintained that mathematics 
 ought to be applied to psychology, in a separate tract, published 
 also in 1822 : the one above seems, therefore, to be his challenge 
 on the subject. It is on attention, and I think it will hardly 
 support Herbart's thesis. As a specimen of his formula, let t be 
 the time elapsed since the consideration began, /3 the whole 
 perceptive intensity of the individual, (/> the whole of his mental 
 force, and z the force given to a notion by attention during the 
 time t. Then, 
 
 Now for a test. There is a jactura, v, the meaning of which I 
 do not comprehend. If there be anything in it, my mathe- 
 matical readers ought to interpret it from the formula 
 
 and to this task I leave them, wishing them better luck than 
 mine. The time may come when other manifestations of mind, 
 besides belief ', shall be submitted to calculation : at that time, 
 should it arrive, a final decision may be passed upon Herbart. 
 
THE WHIZGIG MYTHOLOGICAL ASTKONOMY. 151 
 
 The theory of the Whizgig considered ; in as much as it mechani- 
 cally exemplifies the three working properties of nature ; which 
 are now set forth under the guise of this toy, for children of all 
 ages. London, 1822, 12mo. (pp. 24, B. McMillan, Bow Street, 
 Co vent Garden.) 
 
 The toy called the whizgig will be remembered by many. The 
 writer is a follower of Jacob Behmen, William Law, Eichard 
 Clarke, and Eugenius Philalethes. Jacob Behmen first an- 
 nounced the three working properties of nature, which Newton 
 stole, as described in the Gentleman's Magazine? July, 1782, 
 p. 329. These laws are illustrated in the whizgig. There is the 
 harsh astringent, attractive compression ; the bitter compunction, 
 repulsive expansion ; and the stinging anguish, duplex motion. 
 The author hints that he has written other works, to which he 
 gives no clue. I have heard that Behmen was pillaged by New- 
 ton, and Swedenborg by Laplace, and Pythagoras by Copernicus, 
 and Epicurus by Dalton, &c. I do not think this mention will 
 revive Behm en ; but it may the whizgig, a very pretty toy, and 
 philosophical withal, for few of those who used it could ex- 
 plain it. 
 
 A Grammar of infinite forms ; or the mathematical elements of 
 ancient philosophy and mythology. By Wm. Howison. Edin- 
 burgh, 1823, 8vo. 
 
 A curious combination of geometry and mythology. Perseus, 
 for instance, is treated under the head, 6 the evolution of diminish- 
 ing hyperbolic branches.' 
 
 The Mythological Astronomy of the Ancients ; part the second : 
 or the key of Urania, the wards of which will unlock all the 
 mysteries of antiquity. Norwich, 1823, 12mo. 
 
 A Companion to the Mythological Astronomy, &c., containing 
 remarks on recent publications. . . Norwich, 1824, 12mo. 
 
 A new Theory of the Earth and of planetary motion ; in which it 
 is demonstrated that the Sun is vicegerent of his own system. 
 Norwich, 1825, 12mo. 
 
 The analyzation of the writings of the Jews, so far as they are 
 found to have any connection with the sublime science of 
 astronomy. [This is pp. 97-180 of some other work, being all 
 I have seen.] 
 
 These works are all by Sampson Arnold Mackey, for whom see 
 Notes and Queries, 1st S. viii. 468, 565, ix. 89, 179. Had it 
 
152 A BUDGET OF PAKADOXES. 
 
 not been for actual quotations given by one correspondent only 
 (1st S. viii. 565), that journal would have handed him down as 
 a man of some real learning. An extraordinary man he certainly 
 was : it is not one illiterate shoemaker in a thousand who could work 
 upon such a singular mass of Sanscrit and Greek words, without 
 showing evidence of being able to read a line in any language 
 but his own, or to spell that correctly. He was an uneducated 
 Godfrey Higgins. A few extracts will put this in a strong light : 
 one for history of science, one for astronomy, and one for philo- 
 logy: 
 
 ' Sir Isaac Newton was of opinion that " the atmosphere of the earth 
 was the sensory of God ; by which he was enabled to see quite round 
 the earth :" which proves that Sir Isaac had no idea that God could 
 see through the earth. 
 
 Sir Richard [Phillips] has given the most rational explanation of 
 the cause of the earth's elliptical orbit that I have ever seen in print. 
 It is because the earth presents its watery hemisphere to the sun at 
 one time and that of solid land the other ; but why has he made his 
 Oxonian astonished at the coincidence ? It is what I taught in my 
 attic twelve years before. 
 
 Again, admitting that the Eloim were powerful and intelligent beings 
 that managed these things, we would accuse them of being the authors 
 of all the sufferings of Chrisna. And as they and the constellation of 
 Leo were below the horizon, and consequently cut off from the end of 
 the zodiac, there were but eleven constellations of the zodiac to be 
 seen ; the three at the end were wanted, but those three would be 
 accused of bringing Chrisna into the troubles which at last ended in 
 his death. All this would be expressed in the Eastern language by 
 saying that Chrisna was persecuted by those Judoth Ishcarioth 1 ! ! ! ! 
 [the five notes of exclamation are the author's]. But the astronomy 
 of those distant ages, when the sun was at the south pole in winter, 
 would leave five of those Decans cut off from our view, in the latitude 
 of twenty-eight degrees; hence Chrisna died of wounds from five 
 Decans, but the whole five may be included in Judoth Ishcarioth ! for 
 the phrase means the men that are wanted at the extreme parts. Ish- 
 carioth is a compound of ish, a man, and carat wanted or taken away, 
 and oth the plural termination, more ancient than im. . . ' 
 
 I might show at length how Michael is the sun, and the 
 D'-ev-'l, in French Di-ob-al, also 'L-evi-ath-an the evi being the 
 radical part both of devil and leviathan is the Nile, which the 
 sun dried up for Moses to pass : a battle celebrated by Jude. 
 Also how Moses, the same name as Muses, is from mesha, drawn 
 out of the water, 6 and hence we called our land which is saved 
 from the water by the name of marshS But it will be of more use 
 to collect the character of S. A. M. from such correspondents of 
 
A TEANSCENDENTAL PHILOSOPHEE. 153 
 
 Notes and Queries as have written after superficial examination. 
 Great astronomical and philological attainments ; much ability 
 and learning; had evidently read and studied deeply; remark- 
 able for the originality of his views upon the very abstruse 
 subject of mythological astronomy, in which he exhibited great 
 sagacity. Certainly his views were original ; but their sagacity, 
 if it be allowable to copy his own mode of etymologizing, is of an 
 ori-gin-ale cast, resembling that of a person who puts to his 
 mouth liquors both distilled and fermented. 
 
 Principles of the Kantesian, or transcendental philosophy. By 
 Thomas Wirgman. London, 1824, 8vo. 
 
 Mr. Wirgman's mind was somewhat attuned to psychology ; 
 but he was cracky and vagarious. He had been a fashionable 
 jeweller in St. James's Street, no doubt the son or grandson of 
 Wirgman at 'the well-known toy-shop in St. James's Street,' 
 where Sam Johnson smartened himself with silver buckles. 
 (Boswell, set. 69). He would not have the ridiculous large ones 
 in fashion ; and he would give no more than a guinea a pair ; 
 such, says Boswell, in Italics, were the principles of the business : 
 and I think this may be the first place in which the philo- 
 sophical word was brought down from heaven to mix with men. 
 However this may be, f my Wirgman sold snuff-boxes, among 
 other things, and fifty years ago a fashionable snuff-boxer would 
 be under inducement, if not positively obliged, to have a stock 
 with very objectionable pictures. So it happened that Wirgman 
 by reason of a trifle too much candour came under the notice 
 of the Suppression Society, and ran considerable risk. Mr. 
 Brougham was his counsel ; and managed to get him acquitted. 
 Years and years after this, when Mr. Brougham was deep in the 
 formation of the London University (now University College), 
 Mr. Wirgman called on him. ' What now ? ' said Mr. B. with his 
 most sarcastic look a very perfect thing of its kind c you're 
 in a scrape again, I suppose 1 ' ' No ! indeed ! ' said W., < my present 
 object is to ask your interest for the chair of Moral Philosophy 
 in the new University ! ' He had taken up Kant ! 
 
 Mr. Wirgman, an itinerant paradoxer, called on me in 1831 : he 
 came to convert me. ' I assure you,' said he, ' I am nothing but 
 an old brute of a jeweller ; ' and his eye and manner were of the 
 extreme of jocosity, as good in their way, as the satire of his 
 former counsel. I mention him as one of that class who go away 
 quite satisfied that they have wrought conviction. ' Now,' said he, 
 
154 A BUDGET OF PARADOXES. 
 
 ' I'll make it clear to you ! Suppose a number of gold-fishes in a 
 glass bowl you understand ? Well ! I come with my cigar, 
 and go puff, puff, puff, over the bowl, until there is a little cloud 
 of smoke : now, tell me, what will the gold-fishes say to that ? ' 
 6 1 should imagine,' said I, < that they would not know what to make 
 of it.' ' By Jove ! you're a Kantian ; ' said he, and with this and 
 the like, he left me, vowing that it was delightful to talk to so 
 intelligent a person. The greatest compliment Wirgman ever 
 received was from James Mill, who used to say he did not under- 
 stand Kant. That such a man as Mill should think this worth 
 saying is a feather in the cap of the jocose jeweller. 
 
 Some of my readers will stare at my supposing that Boswell 
 may have been the first down-bringer of the word principles into 
 common life ; the best answer will be a prior instance of the 
 word as true vernacular ; it has never happened to me to notice 
 one. Many words have very common uses which are not old. 
 Take the following from Nichols ( Anecd. ix. 263) : < Lord 
 Thurlow presents his best respects to Mr. and Mrs. Thicknesse, 
 and assures them that he knows of no cause to complain of any 
 part of Mr. Thicknesse's carriage ; least of all the circumstance of 
 sending the head to Ormond Street.' Surely Mr. T. had lent 
 Lord T. a satisfactory carriage with a moveable head, and the 
 above is a polite answer to inquiries. Not a bit of it! carriage 
 is here conduct, and the head, is a. bust. The vehicles of the 
 rich, at the time, were coaches, chariots, chaises, &c., never 
 carriages, which were rather carts, (ribbon has the word for 
 baggage-waggons. In Jane Austen's novels the word carriage is 
 established. 
 
 John Walsh, of Cork (1786-1847). This discoverer has had 
 the honour of a biography from Prof. Boole, who, at my request, 
 collected information about him on the scene of his labours. 
 It is in the Philosophical Magazine for November, 1851, and 
 will, I hope, be transferred to some biographical collection where 
 it may find a larger class of readers, It is the best biography of 
 a single hero of the kind that I know. Mr. Walsh introduced 
 himself to me, as he did to many others, in the anterowlandian 
 days of the Post-office ; his unpaid letters were double, treble, 
 &c. They contained his pamphlets, and cost their weight in 
 silver : all have the name of the author, and all are in octavo or 
 in quarto letter-form : most are in four pages, and all dated from 
 Cork. I have the following by me : 
 
JOHN WALSH'S DELUSIONS. 155 
 
 The Geometric Base. 1825. The theory of plane angles. 1827. 
 Three Letters to Dr. Francis Sadleir. 1838. The invention of 
 polar geometry. By Irelandus. 1839. The theory of partial 
 functions. Letter to Lord Brougham. 1839. On the invention 
 of polar geometry. 1839. Letter to the Editor of the Edin- 
 burgh Review. 1840. Irish Manufacture. A new method of 
 tangents. 1841. The normal diameter in curves. 1843. 
 Letter to Sir R. Peel. 1845. [Hints that Government should 
 compel the introduction of Walsh's Geometry into Universities.] 
 Solution of Equations of the higher orders. 1845. 
 
 Besides these, there is a 4 Metalogia,' and I know not how many 
 others. 
 
 Mr. Boole, who has taken the moral and social features of 
 Walsh's delusions from the commiserating point of view, which 
 makes ridicule out of place, has been obliged to treat Walsh as 
 Scott's Alan Fairford treated his client Peter Peebles ; namely, 
 keep the scarecrow out of court while his case was argued. My 
 plan requires me to bring him in : and when he comes in at the 
 door, pity and sympathy fly out at the window. Let the reader 
 remember that he was not an ignoramus in mathematics : lie 
 might have won his spurs if he could have first served as an 
 esquire. Though so illiterate that even in Ireland he never 
 picked up anything more Latin than Irelandus, he was a very 
 pretty mathematician spoiled in the making by intense self- 
 opinion. 
 
 This is part of a private letter to me at the back of a page of 
 print : I had never addressed a word to him : 
 
 ' There are no limits in mathematics, and those that assert there are, 
 are infinite ruffians, ignorant, lying blackguards. There is no dif- 
 ferential calculus, no Taylor's theorem, no calculus of variations, &c. 
 in mathematics. There is no quackery whatever in mathematics ; no 
 equal to anything. What sheer ignorant blackguardism that ! 
 
 In mechanics the parallelogram of forces is quackery, and is danger- 
 ous ; for nothing is at rest, or in uniform, or in rectilinear motion, in 
 the universe. Variable motion is an essential property of matter. 
 Laplace's demonstration of the parallelogram of forces is a begging of 
 the question ; and the attempts of them all to show that the difference 
 of twenty minutes between the sidereal and actual revolution of the 
 earth round the sun arises from the tugging of the Sun and Moon at 
 the pot-belly of the earth, without being sure even that the earth has 
 a pot-belly at all, is perfect quackery. The said difference arising 
 from and demonstrating the revolution of the Sun itself round some 
 distant centre. 1 
 
156 A BUDGET OF PARADOXES. 
 
 In the letter to Lord Brougham we read as follows : 
 ' I ask the Royal Society of London, I ask the Saxon crew of that 
 crazy hulk, where is the dogma of their philosophic god now ? . . . 
 "When the Royal Society of London, and the Academy of Sciences of 
 Paris, shall have read this memorandum, how will they appear ? Like 
 two cur dogs in the paws of the noblest beast of the forest . . . Just 
 as this note was going to press, a volume lately published by you was 
 put into my hands, wherein you attempt to defend the fluxions and 
 Principia of Newton. Man ! what are you about ? You come forward 
 now with your special pleading, and fraught with national prejudice, 
 to defend, like the philosopher Grassi, the persecutor of Galileo, prin- 
 ciples and reasoning which, unless you are actually insane, or an 
 ignorant quack in mathematics, you know are mathematically false. 
 What a moral lesson this for the students of the University of London 
 from its head ! Man ! demonstrate corollary 3, in this note, by the 
 lying dogma of Newton, or turn your thoughts to something you 
 understand/ 
 
 'WALSH IRELANDUS.' 
 
 Mr. Walsh honour to his memory once had the considera- 
 tion to save me postage by addressing a pamphlet under cover to 
 a Member of Parliament, with an explanatory letter. In that 
 letter he gives a candid opinion of himself : 
 
 (1838.) * Mr. Walsh takes leave to send the enclosed corrected 
 copy to Mr. Hutton as one of the Council of the University of London, 
 and to save postage for the Professor of Mathematics there. He will 
 find in it geometry more deep and subtle, and at the same time more 
 simple and elegant, than it was ever contemplated human genius could 
 invent.' 
 
 He then proceeds to set forth that a certain c tomfoolery 
 lemma,' with its c tomfoolery ' superstructure, ' never had exist- 
 ence outside the shallow brains of its inventor,' Euclid. He then 
 proceeds thus : 
 
 ' The same spirit that animated those philosophers who sent Galileo 
 to the Inquisition animates all the philosophers of the present day 
 without exception. If anything can free them from the yoke of error, 
 it is the [Walsh] problem of double tangence. But free them it will, 
 how deeply soever they may be sunk into mental slavery and God 
 knows that is deeply enough ; and they bear it with an admirable 
 grace ; for none bear slavery with a better grace than tyrants. The 
 lads must adopt my theory ... It will be a sad reverse for all our 
 great professors to be compelled to become schoolboys in their gray 
 years. But the sore scratch is to be compelled, as they had before 
 been compelled one thousand years ago, to have recourse to Ireland 
 for instruction.' 
 
PROGRESS OF FREE THOUGHT. 157 
 
 The following < Impromptu ' is no doubt by Walsh himself: he 
 was more of a poet than of an astronomer : 
 
 * Through ages unfriended, 
 
 With sophistry blended, 
 Deep science in Chaos had slept ; 
 
 Its limits were fettered, 
 
 Its voters unlettered, 
 Its students in movements but crept. 
 
 Till, despite of great foes, 
 
 Great WALSH first arose, 
 And with logical might did unravel 
 
 Those mazes of knowledge, 
 
 Ne'er known in a college, 
 Though sought for with unceasing travail. 
 
 With cheers we now hail him, 
 
 May success never fail him, 
 In Polar Geometrical mining ; 
 
 Till his foes be as tamed 
 
 As his works are far-famed 
 For true philosophic refining.' 
 
 Walsh's system is, that all mathematics and physics are wrong : 
 there is hardly one proposition in Euclid which is demonstrated. 
 His example ought to warn all who rely on their own evidence to 
 their own success. He was not, properly speaking, insane ; he 
 only spoke his mind more freely than many others of his class. 
 The poor fellow died in the Cork union, during the famine. He 
 had lived a happy life, contemplating his own perfections, like 
 Brahma on the lotos-leaf. 
 
 The year 1825 brings me to about the middle of my Athe- 
 nceum list : that is, so far as mere number of names mentioned 
 is concerned. Freedom of opinion, beyond a doubt, is gaining 
 ground, for good or for evil, according to what the speaker 
 happens to think : admission of authority is no longer made in 
 the old way. If we take soul-cure and body-cure, divinity and 
 medicine, it is manifest that a change has come over us. Time 
 was when it was enough that dose or dogma should be certified 
 by ; II a ete ordonne, Monsieur, il a ete ordonne,' as the apothe- 
 cary said when he wanted to operate upon poor de Porceaugnac. 
 Very much changed : but whether for good or for evil does not 
 now matter ; the question is, whether contempt of demonstration 
 such as our paradoxers show has augmented with the rejection of 
 dogmatic authority. It ought to be just the other way : for the 
 
158 A BUDGET OF PARADOXES. 
 
 worship of reason is the system on which, if we trust them, the 
 deniers of guidance ground their plan of life. The following 
 attempt at an experiment on this point is the best which I can 
 make ; and, so far as I know, the first that ever was made. 
 
 Say that my list of paradoxers divides in 1825 : this of itself 
 proves nothing, because so many of the earlier books are lost, or 
 not likely to be come at. It would be a fearful rate of increase 
 which would make the number of paradoxes since 1825 equal to 
 the whole number before that date. Let us turn now to another 
 collection of mine, arithmetical books, of which I have published 
 a list. The two collections are similarly circumstanced as to 
 new and old books ; the paradoxes had no care given to the 
 collection of either ; the arithmetical books equal care to both. 
 The list of arithmetical books, published in 1847, divides at 
 1735; the paradoxes, up to 1863, divide at 1825. If we take 
 the process which is most against the distinction, and allow every 
 year from 1847 to 1863 to add a year to 1735, we should say 
 that the arithmetical writers divide at 1751. This rough pro- 
 cess may serve, with sufficient certainty, to show that the pro- 
 portion of paradoxes to books of sober demonstration is on the 
 increase ; and probably, quite as much as the proportion of 
 heterodoxes to books of orthodox adherence. So that divinity 
 and medicine may say to geometry, Don't you sneer : if ration- 
 alism, homoeopathy, and their congeners are on the rise among 
 us, your enemies are increasing quite as fast. But geometry 
 replies Dear friends, content yourselves with the rational in- 
 ference that the rise of heterodoxy within your pales is not 
 conclusive against you, taken alone ; for it rises at the same 
 time within mine. Store within your garners the precious 
 argument that yoii are not proved wrong by increase of dissent ; 
 because there is increase of dissent against exact science. But 
 do not therefore even yourselves to me : remember that you, 
 Dame Divinity, have inflicted every kind of penalty, from the 
 stake to the stocks, in aid of your reasoning ; remember that 
 you, Mother Medicine, have, not many years ago applied to 
 Parliament for increase of forcible hindrance of antipharma- 
 copoeal drenches, pills, and powders. Who ever heard of my 
 asking the legislature to fine blundering circle-squarers ? Ee-. 
 member that the D in dogma is the D in decay ; but the D in 
 demonstration is the D in durability. 
 
 I have known a medical man a young one who was seriously 
 of opinion that the country ought to be divided into medical 
 parishes, with a practitioner appointed to each, and a penalty 
 
MEDICAL EEFOEM. 159 
 
 for calling in any but the incumbent curer. How should people 
 know how to choose ? The hair-dressers once petitioned Par- 
 liament for an act to compel people to wear wigs. My own 
 opinion is of the opposite extreme, as in the following letter 
 (Examiner, April 5, 1856) ; which, to my surprise, I saw reprinted 
 in a medical journal, as a plan not absolutely to be rejected. 
 I am perfectly satisfied that it would greatly promote true 
 medical orthodoxy, the predominance of well educated thinkers, 
 and the development of their desirable differences. 
 
 SIR. The Medical Bill and the medical question generally is 
 one on which experience would teach, if people would be taught. 
 
 The great soul question took three hundred years to settle : the 
 little body question might be settled in thirty years, if the deci- 
 sions in the former question were studied. 
 
 Time was when the State believed, as honestly as ever it 
 believed anything, that it might, could, and should find out 
 true doctrine for the poor ignorant community ; to which, like 
 a worthy honest state, it added would. Accordingly, by the 
 assistance of a Church, which undertook the physic, the surgery, 
 and the pharmacy of sound doctrine all by itself, it sent forth 
 its legally qualified teachers into every parish, and woe to the 
 man who called in any other. They burnt that man, they 
 whipped him, they imprisoned him, they did everything but what 
 was Christian to him, all for his soul's health and the amendment 
 of his excesses. 
 
 But men would not submit. To the argument that the State 
 was a father to the ignorant, they replied that it was at best the 
 ignorant father of an ignorant son, and that a blind man could 
 find his way into a ditch without another blind man to help him. 
 And when the State said But here we have the Church, which 
 knows all about it, the ignora.nt community declared that it had 
 a right to judge that question, and that it would judge it. It 
 also said that the Church was never one thing long, and that it 
 progressed, on the whole, rather more slowly than the ignorant 
 community. 1 
 
 The end of it was, in this country, that every one who chose 
 taught all who chose to let him teach, on condition only of an open 
 and true registration. The State was allowed to patronise one 
 particular Church, so that no one need trouble himself to choose 
 a pastor from the mere necessity of choosing. But every church 
 is allowed its colleges, its studies, its diplomas ; and every man 
 is allowed his choice. There is no proof that our souls are 
 
160 A BUDGET OF PARADOXES. 
 
 worse off than in the sixteenth century ; and, judging by fruits, 
 there is much reason to hope they are better off. 
 
 Now the little body question is a perfect parallel to the great 
 soul question in all its circumstances. The only things in which 
 the parallel fails are the following : Every one who believes in a 
 future state sees that the soul question is incomparably more 
 important than the body question, and every one can try the 
 body question by experiment to a larger extent than the soul 
 question. The proverb, which always has a spark of truth at the 
 bottom, says that every man of forty is either a fool or a 
 physician ; but did even the proverb maker ever dare to say that 
 every man is at any age either a fool or a fit teacher of religion ? 
 
 Common sense points out the following settlement of the 
 medical question : and to this it will come sooner or later. 
 
 Let every man who chooses subject to one common law of 
 manslaughter for all the crass cases doctor the bodies of all 
 who choose to trust him, and recover payment according to 
 agreement in the courts of law. . Provided always that every 
 person practising should be registered at a moderate fee in a 
 register to be republished every six months. 
 
 Let the register give the name, address, and asserted qualifica- 
 tion of each candidate as licentiate, or doctor, or what not, of 
 this or that college, hall, university, &c., home or foreign. Let 
 it be competent to any man to describe himself as qualified by 
 study in public schools without a diploma, or by private study, 
 or even by intuition or divine inspiration, if he please. But 
 whatever he holds his qualification to be, that let him declare. 
 Let all qualification which of its own nature admits of proof be 
 proved, as by the diploma or certificate, &c., leaving things which 
 cannot be proved, as asserted private study, intuition, inspiration, 
 &c., to work their own way. 
 
 Let it be highly penal to assert to the patient any qualification 
 which is not in the register, and let the register be sold very 
 cheap. Let the registrar give each registered practitioner a copy 
 of the register in his own case ; let any patient have power to 
 demand a sight of this copy ; and let no money for attendance 
 be recoverable in any case in which there has been false repre- 
 sentation. 
 
 Let any party in any suit have a right to produce what medi- 
 cal testimony he pleases. Let the medical witness produce his 
 register, and let his evidence be for the jury, as is that of an 
 engineer or a practitioner of any art which is not attested by 
 diplomas. 
 
MEDICAL REFORM REV. R. TAYLOR. 161 
 
 Let any man who practises without venturing to put his name 
 on the register be liable to fine and imprisonment. 
 
 The consequence would be that, as now, anybody who pleases 
 might practise ; for the medical world is well aware that there 
 is no power of preventing what they call quacks from practising. 
 But very different from what is now, every man who practises 
 would be obliged to tell the whole world what his claim is, and 
 would run a great risk if he dared to tell his patient in private 
 anything different from what he had told the whole world. 
 
 The consequence would be that a real education in anatomy, 
 physiology, chemistry, surgery, and what is known of the thing 
 called medicine, would acquire more importance than it now 
 has. 
 
 It is curious to see how completely the medical man of the 
 nineteenth century squares with the priest of the sixteenth cen- 
 tury. The clergy of all sects are now better divines and better 
 men than they ever were. They have lost Bacon's reproach that 
 they took a smaller measure of things than any other educated 
 men ; and the physicians are now in this particular the rear- 
 guard of the learned world ; though it may be true that the rear 
 in our day is further on in the march than the van of Bacon's 
 day. Nor will they ever recover the lost position until medicine 
 is as free as religion. 
 
 To this it must come. To this the public, which will decide 
 for itself, has determined it shall come. To this the public has t 
 in fact, brought it, but on a plan which it is not desirable to 
 make permanent. We will be as free to take care of our bodies 
 as of our souls and of our goods. This is the profession of all 
 who sign as I do, and the practice of most of those who would not 
 like the name HETEROPATH.' 
 
 The motion of the Sun in the Ecliptic, proved to be uniform in a 
 circular orbit . . . with preliminary observations on the fallacy 
 of the Solar System. By Bartholomew Prescott, 1825, 8vo. 
 
 The author had published, in 1803, a < Defence of the Divine 
 System,' which I never saw ; also, ' On the inverted scheme of 
 Copernicus.' The above work is clever in its satire. 
 
 Manifesto of the Christian Evidence Society, established Nov. 12, 
 1824. Twenty- four plain questions to honest men. 
 
 These are two broadsides of August and November, 1826, 
 signed by Robert Taylor, A.B., Orator of the Christian Evidence 
 
 M 
 
162 A BUDGET OF PAKADOXES. 
 
 Society. This gentleman was a clergyman, and was convicted of 
 blasphemy in 1827, for which he suffered imprisonment, and got 
 the name of the DeviVs Chaplain. The following are quota- 
 tions : 
 
 4 For the book of Revelation, there was no original Greek at all, bat 
 Erasmus wrote it himself in Switzerland, in the year 1516. Bishop 
 Marsh, vol. i. p. 320.'' * Is not God the author of your reason ? Can he 
 then be the author of anything which is contrary to your reason ? If 
 reason be a sufficient guide, why should God give you any other ? if it 
 be not a sufficient guide, why has he given you that ? ' 
 
 I remember a votary of the Society being asked to substitute for 
 reason ' the right leg,' and for guide ' support,' and to answer the 
 two last questions : he said there must be a quibble, but he did 
 not see what. It is pleasant to reflect that the argumentum a 
 carcere is obsolete. One great defect of it was that it did not go 
 far enough : there should have been laws against subscriptions 
 for blasphemers, against dealing at their shops, and against rich 
 widows marrying them. 
 
 Had I taken in theology, I must have entered books against 
 Christianity. I mention the above, and Paine's c Age of Eeason,' 
 simply because they are the only English modern works that 
 ever came in my way without my asking for them. The three 
 parts of the 4 Age of Eeason ' were published in Paris 1793, Paris 
 1795, and New York 1807. Carlile's edition is of London, 
 1818, 8vo. It must be republished when the time comes, to show 
 what stuff governments and clergy were afraid of at the begin- 
 ning of this century. I should never have seen the book, if it 
 had not been prohibited : a bookseller put it under my nose with 
 a fearful look round him ; and I could do no less, in common 
 curiosity, than buy a work which had been so complimented by 
 church and state. And when I had read it, I said in my mind to 
 church and state, Confound you ! you have taken me in worse 
 than any reviewer I ever met with. I forget what I gave for 
 the book, but I ought to have been able to claim compensation 
 somewhere. 
 
 Cabbala Algebraica. Auctore Gul. Lud. Christmann. Stuttgard, 
 1827, 4to. 
 
 Eighty closely printed pages of an attempt to solve equations 
 of every degree, which has a process called by the author cabbala. 
 An anonymous correspondent spells cabbala as follows, ^a/3/3a\X, 
 and makes 666 out of its letters. This gentleman has sent me. 
 
CABBALA ALPHABETICA. 163 
 
 since my Budget commenced, a little heap of satirical communi- 
 cations, each having a 666 or two ; for instance, alluding to my 
 remarks on the spelling of chemistry, he finds the fated number in 
 ^i/jLSLa. With these are challenges to explain them, and hints about 
 the end of the world. All these letters have different fantastic 
 seals ; one of them with the legend ' keep your temper,' another . 
 bearing ' bank token five pence.' The only signature is a triangle 
 with a little circle in it, which I interpret to mean that the 
 writer confesses himself to be the round man stuck in the three- 
 cornered hole, to be explained as in Sydney Smith's joke. 
 
 There is a kind of Cabbala Alphabetica which the investigators 
 of the numerals in words would do well to take up : it is the 
 formation of sentences which contain all the letters of the alphabet, 
 and each only once. No one has done it with v and j treated as 
 consonants ; but you and I can do it. Dr. Whewell and I amused 
 ourselves, some years ago, with attempts. He could not make 
 sense, though he joined words : he gave me 
 
 Phiz, styx, wrong, buck, flame, quid. 
 
 I gave him the following, which he agreed was * admirable 
 sense : ' I certainly think the words would never have come 
 together except in this way : 
 
 I, quartz pyx, who fling muck beds. 
 
 I long thought that no human being could say this under any 
 circumstances. At last I happened to be reading a religious 
 writer as he thought himself who threw aspersions on his 
 opponents thick and threefold. Heyday ! came into my head, 
 this fellow flings muck beds ; he must be a quartz pyx. And then 
 I remembered that a pyx is a sacred vessel, and quartz is a hard 
 stone, as hard as the heart of a religious foe-curser. So that the 
 line is the motto of the ferocious sectarian, who turns his religious 
 vessels into mud-holders, for the benefit of those who will not 
 see what he sees. 
 
 I can find no circumstances for the following, which I 
 received from another : 
 
 Fritz ! quick ! land ! hew gypsum box, 
 From other quarters I have the following : 
 Dumpy quiz ! whirl back fogs next. 
 This might be said in time of haze to the queer little figure in 
 
 M 2 
 
164 A BUDGET OF PAKADOXES. 
 
 the Dutch weather-toy, which comes out or goes in with the 
 change in the atmosphere. Again, 
 
 Export my fund ! Quiz black whigs. 
 
 This Squire Western might have said, who was always afraid of 
 the whigs sending the sinking-fund over to Hanover. But the 
 following is the best : it is good advice to a young man, very well 
 expressed under the circumstances : 
 
 Get nymph ; quiz sad brow ; fix luck, 
 
 Which in more sober English would be, Marry ; be cheerful ; 
 watch your business. There is more edification, more religion in 
 this than in all the 666-interpretations put together. 
 
 Such things would make excellent writing copies, for they 
 secure attention to every letter ; v and j might be placed at the 
 end. 
 
 The Celtic Druids. By Godfrey Higgins, Esq. of Skellow Grange, 
 
 near Doncaster. London, 1827, 4to. 
 Anacalypsis, or an attempt to draw aside the veil of the Saitic 
 
 Isis : or an inquiry into the origin of languages, nations, and 
 
 religions. By Godfrey Higgins, &c London, 1836, 
 
 2 vols. 4to. 
 
 The first work had an additional preface and a new index in 
 1829. Possibly, in future time, will be found bound up with 
 copies of the second work two sheets which Mr. Higgins circu- 
 lated among his friends in 1831 : the first a ' Kecapitulation,' the 
 second ' Book vi. ch. 1.' 
 
 The system of these works is that 
 
 The Buddhists of Upper India (of whom the Phenician Canaanite, 
 Melchizedek, was a priest), who built the Pyramids, Stonehenge 
 Carnac, &c. will be shown to have founded all the ancient mythologies 
 of the world, which, however varied and corrupted in recent times, 
 were originally one, and that one founded on principles sublime, 
 beautiful, and true. 
 
 These works contain an immense quantity of learning, very 
 honestly put together. I presume the enormous number of facts, 
 and the goodness of the index, to be the reasons why the Ana- 
 calypsis found a permanent place in the old reading-room of the 
 British Museum, even before the change which greatly increased 
 the number of books left free to the reader in that room. 
 
 Mr. Higgins, whom I knew well in the last six years of his life, 
 and respected as a good, learned, and (in his own vf^y) pious man, 
 
GODFREY HIGGINS. 165 
 
 was thoroughly and completely the man of a system. He had 
 that sort of mental connection with his theory that made his 
 statements of his authorities trustworthy : for, besides perfect 
 integrity, he had no bias towards alteration of facts : he saw his 
 system in the way the fact was presented to him by his authority, 
 be that what it might. 
 
 He was very sure of a fact which he got from any of his 
 authorities : nothing could shake him. Imagine a conversation 
 between him and an Indian officer who had paid long attention 
 to Hindoo antiquities and their remains : a third person was 
 present, ego qui scribo. G. H. ' You know that in the temples 
 of I-forget-who the Ceres is always sculptured precisely as in 
 
 Greece.' Col. , 'I really do not remember it, and I have 
 
 seen most of these temples.' G. H. ; It is so, I assure you, 
 
 especially at I-forget- where.' Col. , ; Well, I am sure ! I 
 
 was encamped for six weeks at the gate of that very temple, and, 
 except a little shooting, had nothing to do but to examine its 
 details, which I did, day after day, and I found nothing of the 
 kind.' It was of no use at all. 
 
 Godfrey Higgins began life by exposing and conquering, at 
 the expense of two years of his studies, some shocking abuses 
 which existed in the York Lunatic Asylum. This was a pro- 
 ceeding which called much attention to the treatment of the 
 insane, and produced much good effect. He was very resolute 
 and energetic. The magistracy of his time had scruples about 
 using the severity of law to people of such station as well-to-do 
 farmers, &c. : they would allow a great deal of resistance, and 
 endeavour to mollify the rebels into obedience. A young farmer 
 flatly refused to pay under an order of affiliation made upon him 
 by Godfrey Higgins. He was duly warned ; and persisted : he 
 shortly found himself in gaol. He went there sure to conquer 
 the Justice, and the first thing he did was to demand to see his 
 lawyer. He was told, to his horror, that as soon as he had been 
 cropped and prison-dressed, he might see as many lawyers as he 
 pleased, to be looked at, laughed at, and advised that there was 
 but one way out of the scrape. Higgins was, in his speculations, 
 a regular counterpart of Bailly ; but the celebrated Mayor of Paris 
 had not his nerve. It is impossible to say, if their characters had 
 been changed, whether the unfortunate crisis in which Bailly was 
 not equal to the occasion would have led to very different results 
 if Higgins had been in his place : but assuredly constitutional 
 liberty would have had one chance more. There are two works 
 of his by which he was known, apart from his paradoxes. 
 
166 A BUDGET OF PARADOXES. 
 
 First, ' An apology for the life and character of the celebrated 
 prophet of Arabia, called Mohamed, or the Illustrious.' London, 
 8vo. 1829. The reader will look at this writing of our English 
 Buddhist with suspicious eye, but he will not be able to avoid 
 confessing that the Arabian prophet has some reparation to 
 demand at the hands of Christians. Next, ' Horse Sabbaticae ; or 
 an attempt to correct certain superstitions and vulgar errors 
 respecting the Sabbath. Second edition, with a large appendix.' 
 London, 12mo. 1833. This book was very heterodox at the 
 time, but it has furnished material for some of the clergy of our 
 day. 
 
 I never could quite make out whether Godfrey Higgins took 
 that system which he traced to the Buddhists to have a Divine 
 origin, or to be the result of good men's meditations. Himself a 
 strong theist, and believer in a future state, one would suppose 
 that he would refer a universal religion, spread in different forms 
 over the whole earth from one source, directly to the universal 
 Parent. And this I suspect he did, whether he knew it or not. 
 The external evidence is balanced. In his preface he says 
 
 ' 1 cannot help smiling when I consider that the priests have objected 
 to admit my former book, " the Celtic Druids," into libraries, because 
 it was antichristian ; and it has been attacked by Deists, because it 
 was superfluously religious. The learned Deist, the Rev. R. Taylor 
 [already mentioned], has designated me as the religious Mr. Higgins.' 
 
 The time will come when some profound historian of literature 
 will make himself much clearer on the point than I am. 
 
 The triumphal Chariot of Friction : or a familiar elucidation of 
 the origin of magnetic attraction, &c. &c. By William Pope. 
 London, 1829, 4to. 
 
 Part of this work is on a dipping-needle of the author's con- 
 struction. It must have been under the impression that a book 
 of naval magnetism was proposed, that a great many officers, the 
 Royal Naval Club, &c. lent their names to the subscription list. 
 How must they have been surprised to find, right opposite to the 
 list of subscribers, the, plate presenting ' the three emphatic letters, 
 J. A. 0.' And how much more when they saw it set forth that if 
 a square be inscribed in a circle, a circle within that, then a 
 square again, &c., it is impossible to have more than fourteen 
 circles, let the first circle be as large as you please. From this 
 the seven attributes of God are unfolded ; and further, that all 
 matter was moral, until Lucifer churned it into physical ; as far 
 
JACOTOT TRACT ON PROBABILITY. 167 
 
 as the third circle in Deity ' : this Lucifer, called Leviathan in 
 Job, being thus the moving cause of chaos. I shall say no more, 
 except that the friction of the air is the cause of magnetism. 
 
 Remarks on the Architecture, Sculpture, and Zodiac of Palmyra ; 
 with a Key to the Inscriptions. By B. Prescot. London, 
 1830, 8vo. 
 Mr. Prescot gives the signs of the zodiac a Hebrew origin. 
 
 Epitome de mathematiques. Par F. Jacotot, Avocat. 3ieme edition. 
 
 Paris, 1830, 8vo. (pp. 18). 
 Methode Jacotot. Choix de propositions mathematiques. Par 
 
 P. Y. de Sepres. 2nde edition. Paris, 1830, 8vo. (pp. 82). 
 
 Of Jacotot's method, which had some vogue in Paris, the 
 principle was Tout est dans tout, and the process Apprendre 
 quelque chose, et a y rapporter tout le reste. The first tract has 
 a proposition in conic sections and its preliminaries : the second 
 has twenty exercises, of which the first is finding the greatest 
 common measure of two numbers, and the last is the motion of a 
 point on a surface, acted on by given forces. This is topped up 
 with -the problem of sound in a tube, and a slice of Laplace's 
 theory of the tides. All to be studied until known by heart, and 
 all the rest will come, or at least join on easily when it comes. 
 There is much truth in the assertion that new knowledge hooks 
 on easily to a little of the old, thoroughly mastered. The day is 
 coming when it will be found out that crammed erudition, got up 
 for examinations, does not cast out any hooks for more. 
 
 Lettre a MM. les Membres de 1'Academie E-oyale des Sciences, 
 contenant un developpement de la refutation du systeme de la 
 gravitation universelle, qui leur a ete presentee le 30 aout, 1830. 
 Par Felix Passot. Paris, 1830, 8vo. 
 
 Works of this sort are less common in France than in England. 
 In France there is only the Academy of Sciences to go to : in 
 England there is a reading public out of the Eoyal Society, &c. 
 
 About 1830 was published, in the Library of Useful Know- 
 ledge, the tract on Probability, the joint work of the late Sir 
 John Lubbock and Mr. Drinkwater (Bethune). It is one of the 
 best elementary openings of the subject. A binder put my name 
 on the outside (the work was anonymous) and the consequence 
 was that nothing could drive out of people's heads that it was 
 
168 A BUDGET OF PARADOXES. 
 
 written by me. I do not know how many denials I have made, 
 from a passage in one of my own works to a letter in the Times : 
 and I am not sure that I have succeeded in establishing the 
 truth, even now. I accordingly note the fact once more. But 
 as a book has no right here unless it contain a paradox or thing 
 counter to general opinion or practice I will produce two small 
 ones. Sir John Lubbock, with whom lay the executive arrange- 
 ment, had a strong objection to the last word in ' Theory of 
 Probabilities,' he maintained that the singular probability ', should 
 be used ; and I hold him quite right. 
 
 The second case was this : My friend Sir J. L., with a large 
 cluster of intellectual qualities, and another of social qualities, 
 had one point of character which I will not call bad and cannot 
 call good ; he never used a slang expression. To such a length 
 did he carry his dislike, that he could not bear head and tail, 
 even in a work on games of chance : so he used obverse and reverse. 
 I stared when I first saw this : but, to my delight, I found that 
 the force of circumstances beat him at last. He was obliged to 
 take an example from the race-course, and the name of one of 
 the horses was Bessy Bedlam ! And he did not put her down as 
 Elizabeth Bethlehem, but forced himself to follow the jockeys. 
 
 [Almanach B-omain sur la Loterie Royale de France, on les 
 Etrennes necessaires anx Actionnaires et Reeevenrs de la dite 
 Loterie. Par M. Menut de St.-Mesmin. Paris, 1830. 12mo. 
 
 This book contains all the drawings of the French lottery (two 
 or three, each month) from 1758 to 1830. It is intended for 
 those who thought they could predict the future drawings from 
 the past : and various sets of sympathetic numbers are given to 
 help them. The principle is, that anything which has not 
 happened for a long time must be soon to come. At rouge et 
 noir, for example, when the red has won five times running, 
 sagacious gamblers stake on the .black, for they think the turn 
 which must come at last is nearer than it was. So it is : but 
 observation would have shown that if a large number of those 
 cases had been registered which show a run of five for the red, 
 the next game would just as often have made the run into six 
 as have turned in favour of the black. But the gambling 
 reasoner is incorrigible : if he would but take to squaring the 
 circle, what a load of misery would be saved. A writer of 1823, 
 who appeared to be thoroughly acquainted with the gambling of 
 Paris and London, says that the gamesters by profession are 
 haunted by a secret foreboding of their future destruction, and 
 
PARADOXES OF CHANCE. 169 
 
 seem as if they said to the banker at the table, as the gladiators 
 said to the emperor, Morituri te salutant. 
 
 In the French lottery, five numbers out of ninety were drawn 
 at a time. Any person, in any part of the country, might stake 
 any sum upon any event he pleased, as that 27 should be drawn ; 
 that 42 and 81 should be drawn; that 42 and 81 should be 
 drawn, and 42 first ; and so on up to a quine determine, if he 
 chose, which is betting on five given numbers in a given order. 
 Thus, in July, 1821, one of the drawings was 
 
 8 46 16 64 13. 
 
 A gambler had actually predicted the five numbers (but not 
 their order), and won 131,350 francs on a trifling stake. M. 
 Menut seems to insinuate that the hint what numbers to choose 
 was given at his own office. Another won 20,852 francs on the 
 quaterne 8, 16, 46, 64, in this very drawing. These gains, of 
 course, were widely advertised : of the multitudes who lost 
 nothing was said. The enormous number of those who played 
 is proved to all who have studied chances arithmetically by the 
 numbers of simple quaternes which were gained : in 1 822, four- 
 teen ; in 1823, six ; in 1824, sixteen; in 1825, nine, &c. 
 
 The paradoxes of what is called chance, or hazard, might them- 
 selves make a small volume. All the world understands that 
 there is a long run, a general average ; but great part of the 
 world is surprised that this general average should be computed 
 and predicted. There are many remarkable cases of verification ; 
 and one of them relates to the quadrature of the circle. I give 
 some account of this and another. Throw a penny time after 
 time until head arrives, which it will do before long : let this 
 be called a set. Accordingly, H is the smallest set, TH the next 
 smallest, then TTH, &c. For abbreviation, let a set in which 
 seven tails occur before head turns up be T 7 H. In an immense 
 number of trials of sets, about half will be H ; about a quarter 
 TH; about an eighth, T 2 H. BufTon tried 2,048 sets; and 
 several have followed him. It will tend to illustrate the prin- 
 ciple if I give all the results ; namely, that many trials will 
 with moral certainty show an approach and the greater the 
 greater the number of trials to that average which sober reason- 
 ing predicts. In the first column is the most likely number of 
 the theory : the next column gives Buffon's result ; the three 
 next are results obtained from trial by correspondents of mine. 
 In each case the number of trials is 2,048. 
 
170 A BUDGET OF PAKADOXES. 
 
 H . 1,024 . 1,061 . 1,048 . 1,017 . 1,039 
 
 TH . 
 
 512 . 
 
 494 . 
 
 507 . 
 
 547 . 
 
 480 
 
 T 2 H . 
 
 256 . 
 
 232 . 
 
 248 . 
 
 235 . 
 
 267 
 
 T 3 H , 
 
 128 . 
 
 137 . 
 
 99 . 
 
 118 . 
 
 126 
 
 T 4 H . 
 
 64 . 
 
 56 . 
 
 71 . 
 
 72 . 
 
 67 
 
 T*H . 
 
 32 .. 
 
 29 . 
 
 38 . 
 
 32 . 
 
 33 
 
 T 6 H . 
 
 16 
 
 25 . 
 
 17 . 
 
 10 . 
 
 19 
 
 T 7 H . 
 
 8 . 
 
 8 . 
 
 9 . 
 
 9 . 
 
 10 
 
 T 8 H . 
 
 4 . 
 
 6 . 
 
 5 . 
 
 3 . 
 
 3 
 
 T 9 H . 
 
 2 . 
 
 
 3 . 
 
 2 . 
 
 4 
 
 T 10 H . 
 
 1 . 
 
 
 1 . 
 
 1 
 
 
 T U H 
 
 
 
 . 
 
 1 
 
 
 T 12 H 
 
 
 
 . 
 
 
 
 
 T 13 H 
 
 1 . 
 
 
 1 . 
 
 
 
 
 T 14 H 
 
 
 
 . 
 
 
 
 
 T 15 H 
 
 
 
 1 . 
 
 1 
 
 
 &G. 
 
 
 
 . 
 
 
 
 
 2,048 . 2,048 . 2,048 . 2,048 . 2,048 
 
 In very many trials, then, we may depend upon something like 
 the predicted average. Conversely, from many trials we may 
 form a guess at what the average will be. Thus, in Buffon's 
 experiment the 2,048 first throws of the sets gave head in 1,061 
 cases : we have a right to infer that in the long run something 
 like 1,061 out of 2,048 is the proportion of heads, even before 
 we know the reasons for the equality of chance, which tell us that 
 1,024 out of 2,048 is the real truth. I now come to the way in 
 which such considerations have led to a mode in which mere 
 pitch-and-toss has given a more accurate approach to the quadra- 
 ture of the circle than has been reached by some of my para- 
 doxers. What would my friend 1 in No. 14 have said to this? 
 The method is as follows : Suppose a planked floor of the usual 
 kind, with thin visible seams between the planks. Let there be 
 a thin straight rod, or wire, not so long as the breadth of the 
 plank. This rod, being tossed up at hazard, will either fall quite 
 clear of the seams, or will lay across one seam. Now Buffon, 
 and after him Laplace, proved the following : That in the long 
 run the fraction of the whole number of trials in which a seam 
 is intersected will be the fraction which twice the length of the 
 rod is of the circumference of the circle having the breadth of a 
 plank for its diameter. In 1855 Mr. Ambrose Smith, of Aber- 
 deen, made 3,204 trials with a rod three-fifths of the distance 
 between the planks: there were 1,213 clear intersections, and 
 11 contacts on which it was difficult to decide. Divide these 
 
 1 See p. 172. This article was a supplement to No. 14 in the Athcnceum Budget. 
 
THE INTERMINABLE FRACTION TT. 171 
 
 contacts equally, and we have 1,218^ to 3,204 for the ratio of 6 
 to 57T, presuming that the greatness of the number of trials gives 
 something near to the final average, or result in the long run : 
 this gives 7r = 3'1553. If all the 11 contacts had been treated as 
 intersections, the result would have been 77 = 3* 141 2, exceedingly 
 near. A pupil of mine made 600 trials with a rod of the length 
 between the seams, and got TT = 3*137. 
 
 This method will hardly be believed until it has been re- 
 peated so often that 4 there never could have been any doubt 
 about it.' 
 
 The first experiment strongly illustrates a truth of the theory, 
 well confirmed by practice : whatever can happen will happen if we 
 make trials enough. Who would undertake to throw tail eight 
 times running? Nevertheless, in the 8,192 sets tail 8 times 
 running occurred 17 times; 9 times running, 9 times ; 10 times 
 running, twice; 11 times and 13 times, each once; and 15 times, 
 twice.] 
 
 1830. The celebrated interminable fraction 3*14159. . . , which 
 the mathematician calls TT, is the ratio of the circumference to 
 the diameter. But it is thousands of things besides. It is con- 
 stantly turning up in mathematics : and if arithmetic and algebra 
 had been studied without geometry, TT must have come in some- 
 how, though at what stage or under what name must have 
 depended upon the casualties of algebraical invention. This will 
 readily be seen when^it is stated that TT is nothing but four times 
 the series ^ 
 
 1 JL_i-JL J_4 JL_- *-4-. 
 3^5 7^9 Tl ^ 
 
 ad infinitum. It would be wonderful if so simple a series had 
 but one kind of occurrence. As it is, our trigonometry being 
 founded on the circle, TT first appears as the ratio stated. If, for 
 instance, a deep study of probable fluctuation from the average 
 had preceded geometry, TT might have emerged as a number 
 perfectly indispensable in such problems as What is the chance 
 of the number of aces lying between a million -f x and a million 
 a, when six million of throws are made with a die ? I have not 
 gone into any detail of all those cases in which the paradoxer 
 finds out, by his unassisted acumen, that results of mathematical 
 investigation cannot be : in fact, this discovery is only an accom- 
 paniment, though a necessary one, of his paradoxical statement of 
 that which must be. Logicians are beginning to see that the 
 notion of horse is inseparably connected with that of non-horse : 
 that the first without the second would be no notion at all. And 
 it is clear that the positive affirmation of that which contradicts 
 
172 A BUDGET OF PARADOXES. 
 
 mathematical demonstration cannot but be accompanied by a 
 declaration, mostly overtly made, that demonstration is false. If 
 the mathematician were interested in punishing this indiscretion, 
 he could make his denier ridiculous by inventing asserted results 
 which would completely take him in. 
 
 More than thirty years ago I had a friend, now long gone, who 
 was a mathematician, but not of the higher branches : he was, 
 inter alia, thoroughly up in all that relates to mortality, life 
 assurance, &c. One day, explaining to him how it should be 
 ascertained what the chance is of the survivors of a large number 
 of persons now alive lying between given limits of number at the 
 end of a certain time, I came, of course, upon the introduction of 
 TT, which I could only describe as the ratio of the circumference 
 of a circle to its diameter. 6 Oh, my dear friend ! that must be 
 a delusion ; what can the circle have to do with the numbers 
 alive at the end of a given time ? ' c I cannot demonstrate it to 
 you; but it is demonstrated.' ' Oh ! stuff! I think you can 
 prove anything with your differential calculus : figment, depend 
 upon it.' I said no more ; but, a few days afterwards, I went to 
 him and very gravely told him that I had discovered the law of 
 human mortality in the Carlisle Table, of which he thought very 
 highly. I told him that the law was involved in this circum- 
 stance. Take the table of expectation of life, choose any age, 
 take its expectation and make the nearest integer a new age, do 
 the same with that, and so on ; begin at what age you like, you 
 are sure to end at the place where the age past is equal, or most 
 nearly equal, to the expectation to come. ' You don't mean that 
 this always happens ? ' 6 Try it.' He did try, again and again ; 
 and found it as I said. < This is, indeed, a curious thing ; this is 
 a discovery.' I might have sent him about trumpeting the law 
 of life : but I contented myself with informing him that the same 
 thing would happen with any table whatsoever in which the first 
 column goes up and the second goes down ; and that if a pro- 
 ficient in the higher mathematics chose to palm a figment upon 
 him, he could do without the circle : a corsaire, corsaire et demi, 
 the French proverb says. ' Oh ! ' it was remarked, ' I see, this was 
 Milne ! ' It was not Milne : I remember well showing the formula 
 to him some time afterwards. He raised no difficulty about TT ; 
 he knew the forms of Laplace's results, and he was much in- 
 terested. Besides, Milne never said stuff ! and figment I And he 
 would not have been taken in : he would have quietly tried it 
 with the Northampton and all the other tables, and would have 
 got at the truth. 
 
EUCLID WITHOUT AXIOMS. 173 
 
 The first book of Euclid's Elements. With alterations and 
 familiar notes. Being an attempt to get rid of axioms alto- 
 gether ; and to establish the theory of parallel lines, without 
 the introduction of any principle not common to other parts of 
 the elements. By a member of the University of Cambridge. 
 Third edition. In usum serenissimge filiolae. London, 1830. 
 
 The author was Lieut. -Col. (now General) Perronet Thompson, 
 the author of the ' Catechism on the Corn Laws.' I reviewed the 
 fourth edition which had the name of ' Geometry without 
 Axioms,' 1833 in the quarterly Journal of Education for 
 January, 1834. Col. Thompson, who then was a contributor to 
 if not editor of the Westminster Review, replied in an article 
 the authorship of which could not be mistaken. 
 
 Some more attempts upon the problem, by the same author, 
 will be found in the sequel. They are all of acute and legitimate 
 speculation ; but they do not conquer the difficulty in the manner 
 demanded by the conditions of the problem. The paradox of 
 parallels does not contribute much to my pages : its cases are to 
 be found for the most part in geometrical systems, or in notes to 
 them. Most of them consist in the proposal of additional pos- 
 tulates ; some are attempts to do without any new postulate. 
 Gen. Perronet Thompson, whose paradoxes are always constructed 
 on much study of previous writers, has collected in the work 
 above-named, a budget of attempts, the heads of which are in the 
 Penny and English Cyclopaedias, at ' Parallels.' He has given 
 thirty instances, selected from what he had found. 
 
 Lagrange, in one of the later years of his life, imagined that he 
 had overcome the difficulty. He went so far as to write a paper, 
 which he took with him to the Institute, and began to read it. 
 But in the first paragraph something struck him which he had 
 not observed : he muttered II faut que fy songe encore, and put 
 the paper in his pocket. 
 
 The following paragraph appeared in the Morning Post, 
 May 4, 1831 : 
 
 t We understand that although, owing to circumstances with which 
 the public are not concerned, Mr. Goulburn declined becoming a 
 candidate for University honours, that his scientific attainments are 
 far from inconsiderable. He is well known to be the author of an 
 essay in the Philosophical Transactions on the accurate rectification of 
 a circular arc, and of an investigation of the equation of a lunar 
 
174 A BUDGET OF PARADOXES. 
 
 caustic a problem likely to become of great use in nautical as- 
 tronomy.' 
 
 This hoax which would probably have succeeded with any 
 journal was palmed upon the Morning Post, which supported 
 Mr. Goulburn, by some Cambridge wags who supported Mr. 
 Lubbock, the other candidate for the University of Cambridge. 
 Putting on the usual concealment, I may say that I always sus- 
 pected Dr-nkw-t-r B-th-n- of having a share in the matter. The 
 skill of the hoax lies in avoiding the words ; quadrature of the 
 circle,' which all know, and speaking of ' the accurate rectification 
 of a circular arc,' which all do not know for its synonyme. The 
 Morning Post next day gave a reproof to hoaxers in general, 
 without referring to any particular case. It must be added, 
 that although there are caustics in mathematics, there is no 
 lunar caustic. 
 
 So far as Mr. Goulburn was concerned, the above was poetic 
 justice. He was the minister who, in the old time, told a depu- 
 tation from the Astronomical Society that the Government 4 did 
 not care twopence for all the science in the country.' There may 
 be some still alive who remember this : I heard it from more than 
 one of those who were present, and are now gone. Matters are 
 much changed. I was thirty years in office at the Astronomical 
 Society ; and, to my certain knowledge, every Government of that 
 period, Whig and Tory, showed itself ready to help with influence 
 when wanted, and with money whenever there was an answer for 
 the House of Commons. The following correction subsequently 
 appeared. Referring to the hoax about Mr. Goulburn, Messrs. C. 
 H. and Thompson Cooper have corrected an error, by stating that 
 the election which gave rise to the hoax was that in which Messrs. 
 Goulburn and Yates Peel defeated Lord Palmerston and Mr. 
 Cavendish. They add that Mr. Gunning, the well-known Esquire 
 Bedell of the University, attributed the hoax to the late Eev. E. 
 Sheepshanks, to whom, they state, are also attributed certain clever 
 fictitious biographies of public men, as I understand it which 
 were palmed upon the editor of the Cambridge Chronicle, who 
 never suspected their genuineness to the day of his death. Being 
 inmost confidential intercourse with Mr. Sheepshanks, both at the 
 time and all the rest of his life (twenty-five years j, and never 
 having heard him allude to any such things which were not in 
 his line, though he had satirical power of quite another kind I 
 feel satisfied he had nothing to do with them. I may add that 
 others, his nearest friends, and also members of his family, never 
 
SCIENTIFIC ELECTION SQUIB, 175 
 
 heard him allude to these hoaxes as their author, and disbelieve 
 his authorship as much as I do myself. I say this not as imputing 
 any blame to the true author, such hoaxes being fair election 
 jokes in all time, but merely to put the saddle off the wrong horse, 
 and to give one more instance of the 'insecurity of imputed 
 authorship. Had Mr. Sheepshanks ever told me that he had 
 perpetrated the hoax, I should have had no hesitation in giving 
 it to him. I consider all clever election squibs, free from bitter- 
 ness and personal imputation, as giving the multitude good 
 channels for the vent of feelings which but for them would cer- 
 tainly find bad ones. 
 
 [ But I now suspect that Mr. Babbage had some hand in the 
 hoax. He gives it in his ' Passages, &c.' and is evidently writing 
 from memory, for he gives the wrong year. But he has given the 
 paragraph, though not accurately, yet with such a recollection of 
 the points as brings suspicion of the authorship upon him, perhaps 
 in conjunction with D. B. Both were on Cavendish's committee. 
 Mr. Babbage adds, that ' late one evening a cab drove up in hot 
 haste to the office of the Morning Post, delivered the copy as 
 coming from Mr. Groulburn's committee, and at the same time 
 ordered fifty extra copies of the Post to be sent next morning to 
 their committee-room. I think the man the only one I ever 
 heard of who knew all about the cab and the extra copies must 
 have known more.] 
 
 Demonville. A Frenchman's Christian name is his own secret, 
 unless there be two of the surname. M. Demonville is a very 
 good instance of the difference between a French and English 
 discoverer. In England there is a public to listen to discoveries 
 in mathematical subjects made without mathematics : a public 
 which will hear, and wonder, and think it possible that the pre- 
 tensions of the discoverer have some foundation. The unnoticed 
 man may possibly be right : and the old country-town reputation 
 which I once heard of, attaching to a man who ' had written a 
 book about, the signs of the zodiac which all the philosophers in 
 London could not answer,' is fame as far as it goes. Accordingly, 
 we have plenty of discoverers who, even in astronomy, pronounce 
 the learned in error because of mathematics. In France, beyond 
 the sphere of influence of the Academy of Sciences, there is no 
 one to cast a thought upon the matter : all who take the least 
 interest repose entire faith in the Institute. Hence the French 
 discoverer turns all his thoughts to the Institute, and looks for 
 
176 A BUDGET OF PARADOXES. 
 
 his only hearing in that quarter. He therefore throws no slur 
 upon the means of knowledge, hut would say, with M. Demon- 
 ville ' A Tegard de M. Poisson, j'envie loyalement la millieme 
 partie de ses connaissances mathematiques, pour prouver mon 
 systeme d'astronomie aux plus incredules.' This system is that 
 the only bodies of our system are the earth, the sun, and the 
 moon ; all the others being illusions, caused by reflexion of the 
 sun and moon from the ice of the polar regions. In mathematics, 
 addition and subtraction are for men ; multiplication and division, 
 which are in truth creation and destruction, are prerogatives of 
 Deity. But nothing multiplied by nothing is one. M. Demon- 
 ville obtained an introduction to William the Fourth, who desired 
 the opinion of the Eoyal Society upon his system : the answer 
 was very brief. The King was quite right ; so was the Society : 
 the fault lay with those who advised His Majesty on a matter 
 they knew nothing about. The writings of M. Demonville in my 
 possession are as follows. The dates which were only on covers 
 torn off in binding were about 1831-34 : 
 
 * Petit cours d'astronomie' followed by * Sur 1'unite mathematique.' 
 Principes de la physique de la creation implicitement admis dans la 
 notice sur le tonnerre par M. Arago. Question de longitude sur 
 nier. Vrai systeme du monde (pp. 92). Same title, four pages, small 
 type. Same title, four pages, addressed to the British Association. 
 Same title, four pages, addressed to M. Mathieu. Same title, four 
 pages, on M. Bouvard's report. Resume de la physique de la crea- 
 tion ; troisieine partie du vrai systeme du monde. 
 
 The quadrature of the circle discovered, by Arthur Parsey, author 
 of the 'art of miniature painting.' Submitted to the consider- 
 ation of the Royal Society, on whose protection the author 
 humbly throws himself. London, 1832, 8vo. 
 
 Mr. Parsey was an artist, who also made him?elf conspicuous 
 by a new view of perspective. Seeing that the sides of a tower, 
 for instance, would appear to meet in a point if the tower were 
 high enough, he thought that these sides ought to slope to one 
 another in the picture. On this theory he published a small 
 work, of which I have not the title, with a Grecian temple in the 
 frontispiece, stated, if I remember rightly, to be the first picture 
 which had ever been drawn in true perspective. Of course the 
 building looked very Egyptian, with its sloping sides. The 
 answer to his notion is easy enough. What is called the picture 
 is not the picture from which the mind takes its perception ; that 
 picture is on the retina. The intermediate picture, as it may be 
 called the human artist's work is itself seen perspectively. If 
 
PERSPECTIVE RITCHIE'S GEOMETRY. 177 
 
 the tower were so high that the sides, though parallel, appeared 
 to meet in a point, the picture must also be so high that the 
 picture-sides, though parallel, would appear to meet in a point. 
 I never saw this answer given, though I have seen and heard the 
 remarks of artists on Mr. Parsey's work. I am inclined to think 
 it is commonly supposed that the artist's picture is the represen- 
 tation which comes before the mind : this is not true ; we might 
 as well say the same of the object itself. In July 1831, reading 
 an article on squaring the circle, and finding that there was a 
 difficulty, he set to work, got a light denied to all the mathe- 
 maticians in some would say through a crack, and advertised 
 in the Times that he had done the trick. He then prepared this 
 work, in which, those who read it will see how, he showed that 
 
 3-14159 should be 3-0625, He might have found out his 
 
 error by stepping a draughtsman's circle with the compasses. 
 
 Perspective has not had many paradoxes. The only other one 
 I remember is that of a writer on perspective, whose name I 
 forget, and whose four pages I do not possess. He circulated 
 remarks on my notes on the subject, published in the Athenaeum? 
 in which he denies that the stereographic projection is a case of 
 perspective, the reason being that the whole hemisphere makes 
 too large a picture for the eye conveniently to grasp at once. 
 That is to say, it is no perspective because there is too much 
 perspective. 
 
 Principles of Geometry familiarly illustrated. By the Rev. W, 
 
 Ritchie, LL.D. London, 1833, 12mo. 
 A new Exposition of the system of Euclid's Elements, being an 
 
 attempt to establish his work on a different basis. By Alfred 
 
 Day, LL.D. London, 1839, 12mo. 
 
 These works belong to a small class which have the peculiarity 
 of insisting that in the general propositions of geometry a propo- 
 sition gives its converse : that * Every B is A' follows from 4 Every 
 A is B.' Dr. Ritchie says, * If it be proved that the equality of 
 two of the angles of a triangle depends essentially upon the 
 equality of the opposite sides, it follows that the equality of the 
 opposite sides depends essentially on the equality of the angles.* 
 Dr. Day puts it as follows : 
 
 ' That the converses of Euclid, so called, where no particular limit- 
 ation is specified or implied in the leading proposition, more than in 
 the converse, must be necessarily true ; for as by the nature of the 
 reasoning the leading proposition must be universally ti'ue, should the 
 converse not be so, it cannot be so universally, but has ao least all tho 
 
 N 
 
178 A BUDGET OF PARADOXES. 
 
 exceptions conveyed in the leading proposition, and the case is therefore 
 unadapted to geometric reasoning ; or, what is the same thing, by the 
 very natnre of geometric reasoning, the particular exceptions to the 
 extended converse must be identical with some one or other of the 
 cases under the universal affirmative proposition with which we set 
 forth, which is absurd/ 
 
 On tins I cannot help transferring to my reader the words of the 
 Pacha when he orders the bastinado, May it do you good ! A 
 rational study of logic is much wanted to show many mathema- 
 ticians, of all degrees of proficiency, that there is nothing in the 
 reasoning of mathematics which differs from other reasoning. 
 Dr. Day repeated his argument in c A Treatise on Proportion/ 
 London, 1840, 8vo. Dr. Kitchie was a very clear-headed man. 
 He published, in 1818, a work on arithmetic, with rational ex- 
 planations. This was too early for such an improvement, and 
 nearly the whole of this excellent work was sold as waste paper. 
 His elementary introduction to the Differential Calculus was 
 drawn up while he was learning the subject late in life. Books 
 of this sort are often very effective on points of difficulty. 
 
 Letter to the Royal Astronomical Society in refutation of Mistaken 
 Notions held in common, by the Society, and by all the New- 
 tonian philosophers. By Capt. Forman, R.N. Shepton-Mallet, 
 1833, 8vo. 
 
 Capt. Forman wrote against the whole system of gravitation, 
 and got no notice. He then wrote to Lord Brougham, Sir J. 
 Herschel, and others I suppose, desiring them to procure notice 
 of his books in the reviews : this not being acceded to, he wrote 
 (in print) to Lord John Eussell to complain of their < dishonest' 
 conduct. He then sent a manuscript letter to the Astronomical 
 Society, inviting controversy : he was answered by a recommen- 
 dation to study dynamics. The above pamphlet was the con- 
 sequence, in which, calling the Council of the Society ' craven 
 dunghill cocks,' he set them right about their doctrines. From 
 all I can learn, the life of a worthy man and a creditable officer 
 was completely embittered by his want of power to see that no 
 person is bound in reason to enter into controversy with every 
 one who chooses to invite him to the field. This mistake is not 
 peculiar to philosophers, whether of orthodoxy or paradoxy; a 
 majority of educated persons imply, by their modes of proceeding, 
 that no one has a right to any opinion which he is not prepared 
 to defend against all comers. 
 
INSPIRED PARADOXERS. 179 
 
 David and Goliath, or an attempt to prove that the Newtonian 
 system of Astronomy is directly opposed' to the Scriptures. 
 By Wm. Lauder, Sen., Mere, Wilts. Mere, 1833, 12mo. 
 
 Newton is Groliath ; Mr. Lauder is David. David took five 
 pebbles ; Mr. Lauder takes five arguments. He expects oppo- 
 sition ; for Paul and Jesus both met with it. 
 
 Mr. Lauder, in his comparison, seems to put himself in the 
 divinely inspired class. This would not be a fair inference in 
 every case ; but we know not what to think when we remember 
 that a tolerable number of cyclometers have attributed their 
 knowledge to direct revelation. The works of this class are very 
 scarce ; I can only mention one or two from Montucla. Alphonso 
 Cano de Molina, in the last century, upset all Euclid, ani squared 
 the circle upon the ruins ; he found a follower, Janson, who 
 translated him from Spanish into Latin. He declared that he 
 believed in Euclid, until Grod, who humbles the proud, taught 
 him better. One Paul Yvon, called from his estate de la Leu, 
 a merchant at Eochelle, supported by his book-keeper, M. Pujos, 
 and a Scotchman, John Dunbar, solved the problem by divine 
 grace, in a manner which was to convert all Jews, Infidels, &c. 
 There seem to have been editions of his work in 1619 and 1628, 
 and a controversial 'Examen' in 1630, by Eobert Sara. There 
 was a noted discussion, in which Mydorge, Hardy, and others 
 took part against de la Leu. I cannot find this name either in 
 Lipenius or Murhard, and I should not have known the dates if 
 it had not been for one of the keenest bibliographers of any time, 
 my friend Prince Balthasar Boncompagni, who is trying to find 
 copies of the works, and has managed to find copies of the titles. 
 In 1750, Henry Sullamar, an Englishman, squared the circle by 
 the number of the Beast : he published a pamphlet every two or 
 three years ; but I cannot find any mention of him in English 
 works. In France, in 1753, M. de Causans, of the Guards, cut a 
 circular piece of turf, squared it, and deduced original sin and 
 the Trinity. He found out that the circle was equal to the 
 square in which it is inscribed ; and he offered a reward for 
 detection of any error, and actually deposited 10,000 francs as 
 earnest of 300,000. But the courts would not allow any one to 
 recover. 
 
 1834. In this year Sir John Herschel set up his telescope at 
 Feldhausen, Cape of (rood Hope. He did much for astronomy, 
 
 N 2 
 
180 A BUDGET OF PARADOXES. 
 
 but not much for the Budget of Paradoxes. He gives me, how- 
 ever, the following story. He showed a resident a remarkable 
 blood-red star, and some little time after he heard of a sermon 
 preached in those parts in which it was asserted that the state- 
 ments of the Bible must be true, for that Sir J. H. had seen in his 
 telescope 4 the very place where wicked people go/ 
 
 But red is not ' always the colour. Sir J. Herschel has in his 
 possession a letter written to his father, Sir W. H., dated April 
 3, 1787, and signed ' Eliza Cumyns,' begging to know if any of 
 the stars be indigo in colour, 6 because, if there be, I think it 
 may be deemed a strong conjectural illustration of the expression, 
 so often used by our Saviour in the Holy Gospels, that " the 
 disobedient shall be cast into outer darkness ; " for as the Almighty 
 Being can doubtless confine any of his creatures, whether cor- 
 poreal or spiritual, to what part of his creation He pleases, if 
 therefore any of the stars (which are beyond all doubt so many 
 suns to other systems) be of so dark a colour as that above 
 mentioned, they may be calculated to give the most insufferable 
 *heat to those dolorous systems dependent upon them (and to 
 reprobate spirits placed there), without one ray of cheerful light ; 
 and may therefore be the scenes of future punishments.' This 
 letter is addressed to Dr. Heirschel at Slow. Some have placed 
 the infernal regions inside the earth, but others have filled this 
 internal cavity for cavity they will have with refulgent light, 
 and made it the abode of the blessed. It is difficult to build 
 without knowing the number to be provided for. A friend of 
 mine heard the following (part) dialogue between two strong 
 Scotch Calvinists : ' Noo ! hoo manny d'ye thank there are of 
 the alact on the arth at this moment ? Eh ! mabbee a doozen 
 Hoot ! mon ! nae -so mony as thot 1 ' 
 
 1834. From 1769 to 1834 the Nautical Almanac was pub- 
 lished on a plan which gradually fell behind what was wanted. 
 In 1834 the new series began, under a new superintendent (Lieut. 
 W. S. Stratford). There had been a long scientific controversy, 
 which would not be generally intelligible. To set some of the 
 points before the reader, I reprint a cutting which I have by me. 
 It is from the Nautical Magazine, but I did hear that some had 
 an idea that it was in the Nautical Almanac itself. It certainly 
 was not, and I feel satisfied the Lords of the Admiralty would 
 not have permitted the insertion ; they are never in advance of 
 their age. The Almanac for 1834 was published in July 1833. 
 
COUNCIL OF THE SOLAR SYSTEM. 181 
 
 THE NEW NAUTICAL ALMANAC. Extract from the * Primum Mobile,' 
 and * Milky Way Gazette.* Communicated by AEEOLITH. 
 
 A meeting of the different bodies composing the Solar System 
 was this day held at the Dragon's Tail, for the purpose of taking 
 into consideration the alterations and amendments introduced 
 into the New Nautical Almanac. The honourable luminaries 
 had been individually summoned by fast-sailing comets, and 
 there was a remarkably full attendance. Among the visitors we 
 observed several nebulae, and almost all the stars whose proper 
 motions would admit of their being present. 
 
 The SUN was unanimously called to the focus. The small 
 planets took the oaths, and their places, after a short discussion, 
 in which it was decided that the places should be those of the 
 Almanac itself, with leave reserved to move for corrections. 
 
 Petitions were presented from a and 8 Urs86 Minoris, com- 
 plaining of being put on daily duty, and praying for an increase of 
 salary. Laid on the plane of the ecliptic. 
 
 The trustees of the eccentricity 1 and inclination funds re- 
 ported a balance of *00001 in the former, and a deficit of 0"*009 
 in the latter. This announcement caused considerable surprise, 
 and a committee was moved for, to ascertain which of the bodies 
 had more or less than his share. After some discussion, in 
 which the small planets offered to consent to a reduction, if 
 necessary, the motion was carried. 
 
 The FOCAL BODY then rose to address the meeting. He re- 
 marked that the subject on which they were assembled was one 
 of great importance to the routes and revolutions of the heavenly 
 bodies. For himself, though a private arrangement between two 
 of his honourable neighbours (here he looked hard at the Earth 
 and Venus) had prevented his hitherto paying that close atten- 
 tion to the predictions of the Nautical Almanac which he de- 
 clared he always had wished to do ; yet he felt consoled by 
 knowing that the conductors of that work had every disposition 
 to take his peculiar circumstances into consideration. He de- 
 clared that he had never passed the wires of a transit without 
 deeply feeling his inability to adapt himself to the present state 
 of his theory ; a feeling which he was afraid had sometimes caused 
 a slight tremor in his limb. Before he sat down, he expressed a 
 hope that honourable luminaries would refrain as much as 
 possible from eclipsing each other, or causing mutual perturba- 
 
 1 See Sir J. Herschel's Astronomy, p. 369. 
 
182 A BUDGET OF PARADOXES. 
 
 tions. Indeed, he should be very sorry to see any interruption of 
 the harmony of the spheres. (Applause.) 
 
 The several articles of the New Nautical Almanac were then 
 read over without any comment ; only we observed that Saturn 
 shook his ring at every novelty, and Jupiter gave his belt a 
 hitch, and winked at the satellites at page 21 of each month. 
 
 The MOON rose, to propose a resolution. No one, he said, 
 would be surprised at his bringing this matter forward in the 
 way he did, when it was considered in how complete and satis- 
 factory a manner his motions were now represented. He must 
 own he had trembled when the Lords of the Admiralty dissolved 
 the Board of Longitude, but his tranquillity was more than re- 
 established by the adoption of the new system. He did not 
 know but that any little assistance he could give in Nautical 
 Astronomy was becoming of less and less value every day, owing 
 to the improvement of chronometers. But there was one thing, 
 of which nothing could deprive him he meant the regulation of 
 the tides. And, perhaps, when his attention was not occupied by 
 more than the latter, he should be able to introduce a little 
 more regularity into the phenomena. (Here the honourable 
 luminary gave a sort of modest libration, which convulsed the 
 meeting with laughter.) They might laugh at his natural 
 infirmity if they pleased, but he could assure them it arose only 
 from the necessity he was under, when young, of watching the 
 motions of his worthy primary. He then moved a resolution 
 highly laudatory of the alterations which appeared in the New 
 Nautical Almanac. 
 
 The EARTH rose, to second the motion. His honourable satel- 
 lite had fully expressed his opinions on the subject. He joined 
 his honourable friend in the focus in wishing to pay every 
 attention to the Nautical Almanac, but, really, when so impor- 
 tant an alteration had taken place in his magnetic pole 1 (hear) 
 and there might, for aught he knew, be a successful attempt to 
 reach his pole of rotation, he thought he could not answer for 
 the preservation of the precession in its present state. (Here 
 the hon. luminary, scratching his side, exclaimed, as he sat down, 
 4 More steam-boats confound 'em F) 
 
 An honourable satellite (whose name we could not learn) pro- 
 posed that the resolution should be immediately despatched, cor- 
 rected for refraction, when he was called to order by the Focal 
 Body, who reminded him that it was contrary to the moving 
 
 1 Captain Ross had just stuck a bit of brass there. 
 
COUNCIL OF THE SOLAR SYSTEM. 183 
 
 orders of the system to take cognizance of what passed inside the 
 atmosphere of any planet. 
 
 SATURN and PALLAS rose together. (Cries of ' New member ! ' 
 and the former gave way.) The latter, in a long and eloquent 
 speech, praised the liberality with which he and his colleagues had 
 at length been relieved from astronomical disqualifications. He 
 thought that it was contrary to the spirit of the laws of gravita- 
 tion to exclude any planet from office on account of the eccen- 
 tricity or inclination of his orbit. Honourable luminaries need 
 not talk of the want of convergency of his series. What had 
 they to do with any private arrangements between him and the 
 general equations of the system ? (Murmurs from the opposi- 
 tion.) So long as he obeyed the laws of motion, to which he had 
 that day taken a solemn oath, he would ask, were old planets, 
 which were now so well known that nobody trusted them, 
 to .... 
 
 The FOCAL BODY said he was sorry to break the continuity of 
 the proceedings, but he thought that remarks upon character, 
 with a negative sign, would introduce differences of too high an 
 order. The honourable luminary must eliminate the expression 
 which he had brought out, in finite terms, and use smaller in- 
 equalities in future. (Hear, hear.) 
 
 PALLAS explained, that he was far from meaning to reflect upon 
 the orbital character of any planet present. He only meant to 
 protest against being judged by any laws but those of gravitation, 
 and the differential calculus : he thought it most unjust that 
 astronomers should prevent the small planets from being ob- 
 served, and then reproach them with the imperfections of the 
 tables, which were the result of their own narrow-minded policy. 
 (Cheers.) 
 
 SATURN thought that, as an old planet, he had not been 
 treated with due respect. (Hear, from his satellites.) He had 
 long foretold the wreck of the system from the friends of inno- 
 vation. Why, he might ask, were his satellites to be excluded, 
 when small planets, trumpery comets, which could not keep their 
 mean distances (cries of oh ! oh !), double stars, with graphical 
 approximations, and such obscure riff-raff of the heavens (great 
 uproar) found room enough. So help him Arithmetic, nothing 
 could come of it, but a stoppage of all revolution. His hon. 
 friend in the focus might smile, for he would be a gainer by such 
 an event ; but as for him (Saturn), he had something to lose, 
 and hon. luminaries well knew that, whatever they might think 
 under an atmosphere, above it continual revolution was the only 
 
184 A BUDGET OF PARADOXES. 
 
 way of preventing perpetual anarchy. As to the hon. luminary 
 who had risen before him, he was not surprised at his remarks, 
 for he had invariably observed that he and his colleagues allowed 
 themselves too much latitude. The stability of the system re- 
 quired that they should be brought down, and he, for one, would 
 exert all his powers of attraction to accomplish that end. If 
 other bodies would cordially unite with him, particularly his 
 noble friend next him, than whom no luminary possessed greater 
 weight 
 
 JUPITER rose to order. He conceived his noble friend had no 
 right to allude to him in that manner, and was much surprised at 
 his proposal, considering the matters which remained in dispute 
 between them. In the present state of affairs, he would take 
 care never to be in conjunction with his hon. neighbour one 
 moment longer than he could help. (Cries of 4 Order, order, no 
 long inequalities/ during which he sat down.) 
 
 SATURN proceeded to say, that he did not know till then that a 
 planet with a ring could affront one who had only a belt, by pro- 
 posing mutual co-operation. He would now come to the subject 
 under discussion. He should think meanly of his hon. col- 
 leagues if they consented to bestow their approbation upon a 
 mere astronomical production. Had they forgotten that they 
 once were considered the arbiters of fate, and the prognosticators 
 of man's destiny ? What had lost them that proud position ? 
 Was it not the infernal march of intellect, which, after having 
 turned the earth topsy-turvy, was now disturbing the very 
 universe. For himself (others might do as they pleased), but he 
 stuck to the venerable Partridge, and the Stationers' Company, 
 and trusted that they would outlive infidels and anarchists, whether 
 of Astronomical or Diffusion of Knowledge Societies. (Cries of 
 oh! oh!) 
 
 MARS said he had been told, for he must confess he had not 
 seen the work, that the places of the planets were given for 
 Sundays. This, he must be allowed to say, was an indecorum 
 he had not expected ; and he was convinced the Lords of the 
 Admiralty had given no orders to that effect. He hoped this 
 point would be considered in the measure which had been intro- 
 duced in another place, and that some one would move that the 
 prohibition against travelling on Sundays extend to the heavenly 
 as well as earthly bodies. 
 
 Several of the stars here declared, that they had been much 
 annoyed by being observed on Sunday evenings, during the hours 
 of divine service. 
 
COUNCIL OF THE SOLAR SYSTEM. 185 
 
 The room was then cleared for a division, but we are unable to 
 state what took place. Several comet s-at-arms were sent for, and 
 we heard rumours of a personal collision having taken place 
 between two luminaries in opposition. We were afterwards told, 
 that the resolution was carried by a majority, and the luminaries 
 elongated at 2 h. 15 m. 33,41 s. sidereal time. 
 
 * # * It is reported, but we hope without foundation, that 
 Saturn, and several other discontented planets, have accepted an 
 invitation from Sirius to join his system, on the most liberal 
 appointments. We believe the report to have originated in 
 nothing more than the discovery of the annual parallax of Sirius 
 from the orbit of Saturn ; but we may safely assure our readers 
 that no steps have as yet been taken to open any communica- 
 tion. 
 
 We are also happy to state, that there is no truth in the 
 rumour of the laws of gravitation being about to be repealed. 
 We have traced this report, and find it originated with a gentle- 
 man living near Bath (Captain Forman, E.N.), whose name we 
 forbear to mention. 
 
 A great excitement has been observed among the nebulae, 
 visible to the earth's southern hemisphere, particularly among 
 those which have not yet been discovered from thence. We are 
 at a loss to conjecture the cause, but we shall not fail to report 
 to our readers the news of any movement which may take place. 
 (Sir J. Herschel's visit. He could just see this before he went 
 out.) 
 
 A Treatise on the Divine System of the Universe, by Captain 
 Woodley, R.N., and as demonstrated by his Universal Time- 
 piece, and universal method of determining a ship's longitude 
 by the apparent true place of the moon ; with an introduction 
 refuting the solar system of Copernicus, the Newtonian philo- 
 sophy, and mathematics. 1834. 8vo. 
 
 Description of the Universal Time-piece. (4 pp. 12 mo.) 
 
 I think this divine system was published several years before, 
 and was republished with an introduction in 1834. Capt. 
 Woodley was very sure that the earth does not move : he pointed 
 out to me, in a conversation I had with him, something I forget 
 what in the motion of the Great Bear, visible to any eye, which 
 could not possibly be if the earth moved. He was exceedingly 
 ignorant, as the following quotation from his account of the usual 
 opinion will show : 
 
186 A BUDGET OF PARADOXES. 
 
 The north pole of the Earth's axis deserts, they say, the north star 
 or pole of the Heavens, at the rate of 1 in 71| years . . . The fact is, 
 nothing can be more certain than that the Stars have not changed 
 their latitudes or declinations one degree in the last 71 j years. 
 
 This is a strong specimen of a class of men by whom all ac- 
 cessible persons who have made any name in science are hunted. 
 It is a pity that they cannot be admitted into scientific societies, 
 and allowed fairly to state their cases, and stand quiet cross- 
 examination, being kept in their answers very close to the 
 questions, and the answers written down. I am perfectly satisfied 
 that if one meeting in the year were devoted to the hearing of 
 those who chose to come forward on such conditions, much good 
 would be done. But I strongly suspect few would come forward 
 at first, and none in a little while : and I have had some ex- 
 perience of the method I recommend, privately tried. Capt. 
 Woodley was proposed, a little after 1834, as a Fellow of the 
 Astronomical Society ; and, not caring whether he moved the sun 
 or the earth, or both I could not have stood neither I signed 
 the proposal. I always had a sneaking kindness for paradoxers, 
 such a one, perhaps, as Petit Andre had for his lambs, as he called 
 them. There was so little feeling against his opinions, that he 
 only failed by a fraction of a ball. Had I myself voted, he would 
 have been elected ; but being engaged in conversation, and not 
 having heard the slightest objection to him, I did not think it 
 worth while to cross the room for the purpose. I regretted this 
 at the time, but had I known how ignorant he was I should not 
 have supported him. Probably those who voted against him 
 knew more of his books than I then did. 
 
 I remember no other instance of exclusion from a scientific 
 society on the ground of opinion, even if this be one ; of which it 
 may be that ignorance had more to do with it than paradoxy. 
 Mr. Frend, a strong anti-Newtonian, was a Fellow of the Astro- 
 nomical Society, and for some years in the Council. Lieut. 
 Kerigan was elected to the Eoyal Society at a time when his 
 proposers must have known that his immediate object was to put 
 F.R.S. on the title-page of a work against the tides. To give all 
 I know, I may add that the editor of some very ignorant bombast 
 about the c forehead of the solar sky, T who did not know the 
 difference between Bailly and Baily, received hints which induced 
 him to withdraw his proposal for election into the Astronomical 
 Society. But this was an act of kindness ; for if he had seen Mr. 
 Baily in the chair, with his head on, he might have been political 
 historian enough to faint away. 
 
FEANCIS BAILY. FLAMSTEED. 187 
 
 De la formation des Corps. Par Paul Laurent. Nancy, 1834, 8vo. 
 
 Atoms, and ether, and ovules or eggs, which are planets, and 
 their eggs, which are satellites. These speculators can create 
 worlds, in which they cannot be refuted ; but none of them dare 
 attack the problem of a grain of wheat, and its passage from a 
 seed to a plant, bearing scores of seeds like what it was itself. 
 
 An account of the Rev. John Flamsteed, the First Astronomer- 
 Eoyal ... By Francis Baily, Esq. London, 1835, 4to. Supple- 
 ment, London, 1837, 4to. 
 
 My friend Francis Baily was a paradoxer : he brought forward 
 things counter to universal opinion. That Newton was impeccable 
 in every point was the national creed ; and failings of temper and 
 conduct would have been utterly disbelieved, if the paradox had 
 not come supported by very unusual evidence. Anybody who 
 impeached Newton on existing evidence might as well have been 
 squaring the circle, for any attention he would have got. About 
 this book I will tell a story. It was published by the Admiralty 
 for distribution ; and the distribution was entrusted to Mr. Baily. 
 On the eve of its appearance, rumours of its extraordinary reve- 
 lations got about, and persons of influence applied to the Admiralty 
 for copies. The Lords were in a difficulty : but on looking at 
 the list they saw names, as they thought, which were so obscure 
 that they had a right to assume Mr. Baily had included persons 
 who had no claim to such a compliment as presentation from the 
 Admiralty. The Secretary requested Mr. Baily to call upon him. 
 6 Mr. Baily, my Lords are inclined to think that some of the 
 persons in this list are perhaps not of that note which would 
 justify their Lordships in presenting this work.' ; To whom does 
 your observation apply, Mr. Secretary?' 'Well, now, let us 
 examine the list ; let me see ; now, now, now, come ! here's 
 Gauss who's Gauss V 'Grauss, Mr. Secretary, is the oldest 
 mathematician now living, and is generally thought to be the 
 greatest.' < 0-o-oh ! Well, Mr. Baily, we will see about it, and I 
 will write you a letter.' The letter expressed their Lordships' 
 perfect satisfaction with the list. 
 
 There was a controversy about the revelations made in this 
 work ; but as the eccentric anomalies took no part in it, there is 
 nothing for my purpose. The following valentine from Mrs. 
 Flamsteed, which I found among Baily's papers, illustrates some 
 of the points : 
 
188 A BUDGET OF PARADOXES. 
 
 '3 Astronomers' How, Paradise : February 14, 1836. 
 
 ' Dear Sir, I suppose you hardly expected to receive a letter from 
 me, dated from this place ; but the truth is, a gentleman from our 
 street was appointed guardian angel to the American Treaty, in which 
 there is some astronomical question about boundaries. He has got 
 leave to go back to fetch some instruments which he left behind, and 
 I take this opportunity of making your acquaintance. That America 
 has become a wonderful place since I was down among you ; you have 
 no idea how grand the fire at New York looked up here. Poor dear 
 Mr. Flamsteed does not know I am writing a letter to a gentleman on 
 Valentine's day ; he is walked out with Sir Isaac Newton (they are 
 pretty good friends now, though they do squabble a little sometimes) 
 and Sir William Herschel, to see a new nebula. Sir Isaac says he 
 can't make out at all how it is managed ; and I am sure I cannot help 
 him. I never bothered my head about those things down below, and 
 I don't intend to begin here. 
 
 I have just received the news of your having written a book about 
 my poor dear man. It's a chance that I heard it at all ; for the truth 
 is, the scientific gentlemen are somehow or other become so wicked, 
 and go so little to church, that very few of them are considered fit 
 company for this place. If it had not been for Dr. Brinkley, who 
 came here of course, I should not have heard about it. He seems a 
 nice man, but is not yet used to our ways. As to Mr. Halley, he is of 
 course not here ; which is lucky for him, for Mr. Flamsteed swore the 
 moment he caught him in a place where there are no magistrates, he 
 would make a sacrifice of him to heavenly truth. It was very generous 
 in Mr. F. not appearing against Sir Isaac when he came up, for I am 
 told that if he had, Sir Isaac would not have been allowed to come in 
 at all. I should have been sorry for that, for he is a companionable 
 man enough, only holds his head rather higher than he should do. I 
 met him the other pay walking with Mr. Whiston, and disputing about 
 tte deluge. " Well, Mrs. Flamsteed," says he, " does old Poke-the- 
 Stars understand gravitation yet ? " Now you must know'that is rather 
 a sore point with poor dear Mr. Flamsteed. He says that Sir Isaac is 
 as crochetty about the moon as ever ; and as to what some people say 
 about what has been done since his time, he says he should like to see 
 somebody who knows something about it of himself. For it is very 
 singular that none of the people who have carried on Sir Isaac's notions 
 have been allowed to come here. 
 
 I hope you have not forgotten to tell how badly Sir Isaac used 
 Mr. Flamsteed about that book. I have never quite forgiven him ; as 
 for Mr. Flamsteed, he says that as long as he does not come for ob- 
 servations, he does not care about it, and that he will never trust him 
 with any papers again as long as he lives. I shall never forget what 
 a rage he came home in when Sir Isaac had called him a puppy. He 
 struck the stairs all the way up with his crutch, and said puppy at 
 
MRS. FLAMSTEED'S VALENTINE. 189 
 
 every step, and all the evening, as soon as ever a star appeared in the 
 telescope, he called it puppy. I could not think what was the matter, 
 and when I asked, he only called me puppy. 
 
 I shall be very glad to see you if you come our way, Pray keep up 
 some appearances, and go to church a little. St. Peter is always 
 uncommonly civil to astronomers, and indeed to all scientific persons, 
 and never bothers them with many questions. If they can make any- 
 thing out of a case, he is sure to let them in. Indeed, he says, it is 
 perfectly out of the question expecting a mathematician to be as 
 religious as an apostle, but that it is as much as his place is worth to 
 let in the greater number of those who come. So try if you cannot 
 manage it, for I am very curious to know whether you found all the 
 letters. I remain, dear sir, your faithful servant, 
 
 MARGARET FLAMSTEED. 
 
 Francis Baily, Esq. 
 
 P.S. Mr. Elamsteed has come in, and says he left Sir Isaac riding 
 cockhorse upon the nebula, and poring over it as if it were a book. 
 He has brought in his old acquaintance Ozanam, who says that it was 
 always his maxim on earth, that " il appartient aux docteurs de 
 Sorbonne de disputer, au Pape de prononcer, et au mathematicien 
 d'aller en Paradis en ligne perpendiculaire." * 
 
 The Secretary of the Admiralty was completely extinguished. 
 I can recall but two instances of demolition as complete, though 
 no doubt there are many others. The first is in 
 
 Simon Stevin and M. Dumortier. Nieuport, 1845, 12mo. 
 
 M. Dumortier was a member of the Academy of Brussels : there 
 was a discussion, I believe, about a national Pantheon for Bel- 
 gium, The name of Stevinus suggested itself as naturally as 
 that of Newton to an Englishman ; probably no Belgian is better 
 known to foreigners as illustrious in science. Stevinus is great 
 in the Mecanique Analytique of Lagrange ; Stevinus is great in 
 the Tristram Shandy of Sterne. M. Dumortier, who believed 
 that not one Belgian in a thousand knew Stevinus, and who 
 confesses with ironical shame that he was not the odd man, 
 protested against placing the statue of an obscure man in the 
 Pantheon, to give foreigners the notion that Belgium could show 
 nothing greater. The work above named is a slashing retort : 
 any one who knows the history of science ever so little may 
 imagine what a dressing was given, by mere extract from foreign 
 writers. The tract is a letter signed J. du Fan, but this is a 
 pseudonym of Mr. Van de Weyer. The Academician says 
 Stevinus was a man who was not without merit for the time at 
 
190 A BUDGET OF PARADOXES. 
 
 which he lived : Sir ! is the answer, he was as much before his 
 . own time as you are behind yours. How came a man who 
 had never heard of Stevinus to be a member of the Brussels 
 Academy? 
 
 The second story was told me by Mr. Crabb Eobinson, who was 
 long connected with the Times, and intimately acquainted with 
 Mr. W***. When W*** was an undergraduate at Cambridge, 
 taking a walk, he came to a stile, on which sat a bumpkin who 
 did not make way for him : the gown in that day looked down 
 on the town. 4 Why do you not make way for a gentleman ? ' 
 c Eh ? ' 4 Yes, why do you not move ? You deserve a good 
 hiding, and you shall get it if you don't take care ? ' The 
 bumpkin raised his muscular figure on its feet, patted his 
 menacer on the head, and said, very quietly, 4 Young man ! I'm 
 Cribb.' W*** seized the great pugilist's hand, and shook it 
 warmly, got him to his own rooms in college, collected some 
 friends, and had a symposium which lasted until the large end of 
 the small hours. 
 
 God's Creation of the Universe as it is, in support of the Scriptures. 
 By Mr. Finleyson. Sixth Edition, 1835, 8vo. 
 
 This writer, by his own account, succeeded in delivering the 
 famous Lieut. Eichard Brothers from the lunatic asylum, and 
 tending him, not as a keeper but as a disciple, till he died. 
 Brothers was, by his own account, the nephew of the Almighty, 
 and Finleyson ought to have been the nephew of Brothers. For 
 Napoleon came to him in a vision, with a broken sword and an 
 arrow in his side, beseeching help: Finleyson pulled out the 
 arrow, but refused to give a new sword ; whereby poor Napoleon, 
 though he got off with life, lost the battle of Waterloo. This 
 story was written to the Duke of Wellington, ending with ' I 
 pulled out the arrow, but left the broken sword. Your Grace 
 can supply the rest, and what followed is amply recorded in 
 history.' The book contains a long account of applications to 
 Government to do three things : to pay 2,000?. for care taken of 
 Brothers, to pay 10,000?. for discovery of the longitude, and to 
 prohibit the teaching of the Newtonian system, which makes God 
 a liar. The successive administrations were threatened that they 
 would have to turn out if they refused, which, it is remarked, 
 came to pass in every case. I have heard of a joke of Lord 
 Macaulay, that the House of Commons must be the Beast of the 
 Eevelations, since 658 members, with the officers necessary for 
 the action of the House, make 666. Macaulay read most things, 
 
RICHAED BROTHERS, PROPHET AND POET. 191 
 
 and the greater part of the rest : so that he might be suspected 
 of having appropriated as a joke one of Finley son's serious points 
 'I wrote Earl Grey upon the 13th of July, 1831, informing 
 him that his Eeform Bill could not be carried, as it reduced the 
 members below the present amount of 658, which, with the 
 eight principal clerks or officers of the House, make the number 
 666.' But a witness has informed me that Macaulay's joke was 
 made in his hearing a great many years before the Eeform Bill 
 was proposed ; in fact, when both were students at Cambridge. 
 Earl Grey was, according to Finleyson, a descendant of Uriah 
 the Hittite. For a specimen of Lieut. Brothers, this book would 
 be worth picking up. Perhaps a specimen of the Lieutenant's 
 poetry may be acceptable : Brothers loquitur, remember : 
 
 Jerusalem ! Jerusalem ! shall be built again ! 
 
 More rich, more grand than ever ; 
 And through it shall Jordan flow ! (!) 
 
 My people's favourite river. 
 There I'll erect a splendid throne, 
 
 And build on the wasted place ; 
 To fulfil my ancient covenant 
 
 To King David and his race. 
 ****** 
 
 Euphrates' stream shall flow with ships, 
 
 And also my wedded Nile ; 
 And on my coast shall cities rise, 
 
 Each one distant but a mile. 
 
 * * * * * # 
 
 My friends the Russians on the north 
 
 With Persees and Arabs round, 
 Do show the limits of my land, 
 
 Here ! Here ! then I mark the ground. 
 
 Among the paradoxers are some of the theologians who in 
 tlieir own organs of the press venture to criticise science. These 
 may hold their ground when they confine themselves to the 
 geology of long past periods and to general cosmogony : for it is 
 the tug of Greek against Greek ; and both sides deal much in 
 what is grand when called hypothesis, petty when called supposi- 
 tion. And very often they are not conspicuous when they 
 venture upon things within knowledge ; wrong, but not quite 
 wrong enough for a Budget of Paradoxes. One case, however, 
 is destined to live, as an instance of a school which finds writers, 
 editors, and readers. The double stars have been seen from the 
 seventeenth century, and diligently observed by many from the 
 
192 A BUDGET OF PARADOXES. 
 
 time of Wm. Herschel, who first devoted continuous attention to 
 them. The year 1836 was that of a remarkable triumph of 
 astronomical prediction. The theory of gravitation had been 
 applied to the motion of binary stars about each other, in elliptic 
 orbits, and in that year the two stars of 7 Virginis, as had been 
 predicted should happen within a few years of that time for 
 years are small quantities in such long revolutions the two 
 stars came to their nearest : in fact, they appeared to be one as 
 much with the telescope as without it. This remarkable turn- 
 ing-point of the history of a long and widely-known branch of 
 astronomy was followed by an article in the Church of England 
 Quarterly Review for April 1837, written against the Useful 
 Knowledge Society. The notion that there are any such things 
 as double stars is (p. 460) implied to be imposture or delusion, 
 as in the following extract. I suspect that I myself am the 
 Sidrophel, and that my companion to the maps of the stars, 
 written for the Society and published in 1836, is the work to 
 which the writer refers : 
 
 We have forgotten the name of that Sidrophel who lately discovered 
 that the fixed stars were not single stars, but appear in the heavens, 
 like soles at Billingsgate, in pairs ; while a second astronomer, under 
 the influence of that competition in trade which the political economists 
 tell us is so advantageous to the public, professes to show us, through 
 his superior telescope, that the apparently single stars are really three. 
 Before such wondrous mandarins of science, how continually must 
 homunculi like ourselves keep in the background, lest we come between 
 the wind and their nobility. 
 
 If the homunculus who wrote this be still above ground, how 
 devoutly must he hope he may be able to keep in the back- 
 ground ! But the chief blame falls on the editor. The title of 
 the article is 
 
 The new school of superficial pantology ; a speech intended to be 
 delivered before a defunct Mechanics' Institute. By Swallow Swift, 
 late M.P. for the Borough of Cockney- Cloud, Witsbury : reprinted 
 Balloon Island, Bubble year, month Ventose. Long live Charlatan ! 
 
 As a rule, orthodox theologians should avoid humour, a weapon 
 which all history shows to be very difficult to employ in favour 
 of establishment, and which, nine times out of ten, leaves its 
 wielder fighting on the side of heterodoxy. Theological argu- 
 ment, when not enlivened by bigotry, is seldom worse than 
 narcotic : but theological fun, when not covert heresy, is almost 
 always sialagogue. The article in question is a craze, which no 
 editor should have admitted, except after severe inspection by 
 
SATIRICAL CRITICISM. 193 
 
 qualified persons. The author of this wit committed a mistake 
 which occurs now and then in old satire, the confusion between 
 himself and the party aimed at. He ought to be reviewing this 
 fictitious book, but every now and then the article becomes the 
 book itself; not by quotation, but by the writer forgetting that 
 he is not Mr. Swallow Swift, but his reviewer. In fact, he and 
 Mr. S. Swift had each had a dose of the Devil's Elixir. A novel 
 so called, published about forty years ago, proceeds upon a 
 legend of this kind. If two parties both drink of the elixir, 
 their identities get curiously intermingled ; each turns up in 
 the character of the other throughout the three volumes, without 
 having his ideas clear as to whether he be himself or the other. 
 There is a similar confusion in the answer made to the famous 
 Epistolce Obscurorum Virorum: it is headed Lamentationes 
 Obscurorum Virorum. This is not a retort of the writer, throw- 
 ing back the imputation : the obscure men who had been 
 satirized are themselves made, by name, to wince under the 
 disapprobation which the Pope had expressed at the satire upon 
 themselves. 
 
 Of course the book here reviewed is a transparent forgery. 
 But I do not know how often it may have happened that the 
 book, in the journals which always put a title at the head, may 
 have been written after the review. About the year 1830 a 
 friend showed me the proof of an article of his on the malt tax, 
 for the next number of the Edinburgh Revieiv. Nothing was 
 wanting except the title of the book reviewed ; I asked what it 
 was. He sat down, and wrote as follows at the head, ' The 
 Maltster's Guide (pp. 1 24), ' and said that would do. as well as 
 anything. 
 
 But I myself, it will be remarked, have employed such humour 
 as I can command 'in favour of establishment/ What it is 
 worth I am not to judge ; as usual in such cases, those who are of 
 my cabal pronounce it good, but cyclometers and other paradoxers 
 either call it very poor, or commend it as sheer buffoonery. Be 
 it one or the other, I observe that all the effective ridicule is, in 
 this subject, on the side of establishment. This is partly due to 
 the difficulty of quizzing plain and sober demonstration ; but so 
 much, if not more, to the ignorance of the paradoxers. For that 
 which cannot be ridiculed, can be turned into ridicule by those 
 who know how. But by the time a person is deep enough in 
 negative quantities, and impossible quantities, to be able to satirise 
 them, he is>aught, and being inclined to become a user, shrinks 
 from being an abuser. Imagine a person with a gift of ridicule. 
 
194 A BUDGET OF PAEADOXES. 
 
 and knowledge enough, trying his hand on the junction of the 
 assertions which he will find in various books of algebra. First, 
 that a negative quantity has no logarithm ; secondly, that a 
 negative quantity has no square root ; thirdly, that the first non- 
 existent is to the second as the circumference of a circle to its 
 diameter. One great reason of the allowance of such unsound 
 modes of expression is the confidence felt by the writers that V-l 
 and log (-1) will make their way, however inaccurately described. 
 I heartily wish that the cyclometers had knowledge enough to 
 attack the weak points of algebraical diction : they would soon 
 work a beneficial change. 
 
 Recueil de ma vie, mes ouvrages et mes pensees. Par Thomas 
 
 Ignace Marie Forster. Brussels, 1836, 12mo. 
 Mr. Forster, an Englishman settled at Bruges, was an observer 
 in many subjects, but especially in meteorology. He communi- 
 cated to the Astronomical Society, in 1848, the information that, 
 in the registers kept by his grandfather, his father, and himself, 
 beginning in 1767, new moon on Saturday was followed, nineteen 
 times out of twenty, by twenty days of rain and wind. This 
 statement being published in the Athenceum, a cluster of corres- 
 pondents averred that the belief is common among seamen, in all 
 parts of the world, and among landsmen too. Some one quoted 
 a distich 
 
 ' Saturday's moon and Sunday's full 
 Never were fine and never wull.' 
 Another brought forward 
 
 ' If a Saturday's moon 
 Comes once in seven years it comes too soon/ 
 
 Mr. Forster did not say he was aware of the proverbial character 
 of the phenomenon. He was a very eccentric man. He treated 
 his dogs as friends, and buried them with ceremony. He quar- 
 relled with the cure of his parish, who remarked that he could 
 not take his dogs to heaven with him. I will go nowhere, said 
 he, where I cannot take my dog. He was a sincere Catholic : but 
 there is a point beyond which even churches have no influence. 
 
 The following is some account of the announcement of 1849. 
 The Athenaeum (Feb. 17), giving an account of the meeting of 
 the Astronomical Society in December, 1858, says: 
 
 ' Dr. Forster of Bruges, who is well known as a meteorologist, made 
 a communication at which our readers will stare : he declares that by 
 journals of the weather kept by his grandfather, father, and himself, 
 ever since 1767, to the present time, whenever the new moon has fallen 
 on a Saturday y the following twenty days have leen wet and windy, in 
 
A SATURDAY'S MOON. 195 
 
 nineteen cases out of twenty. In spite of our friend Zadkiel and the 
 others who declare that we would smother every truth that does not 
 happen to agree with us, we are glad to see that the Society had 
 the sense to publish this communication, coming, as it does, from a 
 veteran observer, and one whose love of truth is undoubted. It must 
 be that the fact is so set down in the journals, because Dr. Forster 
 says it : and whether it be only a fact of the journals, or one of the 
 heavens, can soon be tried. The new moon of March next, falls on 
 Saturday the 24th, at 2 in the afternoon. We shall certainly look out.! 
 
 The following appeared in the number of March 31 : 
 
 * The first Saturday Moon since Dr. Forster's announcement came off 
 ~a week ago. We had previously received a number of letters from 
 different correspondents all to the effect that the notion of new moon 
 on Saturday bringing wet weather is one of widely extended currency. 
 One correspondent (who gives his name) states that he has constantly 
 heard it at sea, and among the farmers and peasantry in Scotland, 
 Ireland, and the North of England. He proceeds thus : " Since 1826, 
 nineteen years of the time. I have spent in a seafaring life. I have 
 constantly observed, though unable to account for, the phenomenon. 
 I have also heard the stormy qualities of a Saturday's moon remarked 
 by American, French, and Spanish seamen ; and, still more distant, 
 a Chinese pilot, who was once doing duty on board my vessel seemed 
 to be perfectly cognizant of the fact." So that it seems we have, in 
 giving currency to what we only knew as a very curious communica- 
 tion from an earnest meteorologist, been repeating what is common 
 enough among sailors and farmers. Another correspondent affirms 
 that the thing is most devoutly believed in by seamen ; who would as 
 soon sail on a Friday as be in the Channel after a Saturday moon. 
 After a tolerable course of dry weather, there was some snow, accom- 
 panied by wind on Saturday last, here in London ; there were also 
 heavy louring clouds. Sunday was cloudy and cold, with a little rain ; 
 Monday was louring; Tuesday unsettled; Wednesday quite over- 
 clouded, with rain in the morning. The present occasion shows only 
 a general change of weather, with a tendency towards rain. If Dr. 
 Forster's theory be true, it is decidedly one of the minor instances, 
 as far as London weather is concerned. It will take a good deal of 
 evidence to .make us believe in the omen of a Saturday Moon. But, 
 as we have said of the Poughkeepsie Seer, the thing is very curious 
 whether true or false. Whence comes this universal proverb and a 
 hundred others while the meteorological observer cannot, when he 
 puts down a long series of results, detect any weather cycles at all ? 
 One of our correspondents wrote us something of a lecture for en- 
 couraging, he said, the notion that names could influence the weather. 
 He mistakes the question. If there be any weather cycles depending 
 on the moon, it is possible that one of them may be so related to the 
 week cycle of seven days, as to show recurrences which are of the kind 
 
 o 2 
 
196 A BUDGET OF PAEADOXES. 
 
 stated, or any other. For example, we know that if the new moon of 
 March fall on a Saturday in this year, it will most probably fall on 
 a Saturday nineteen years hence. This is not connected with the 
 spelling of Saturday but with the connexion between the motions of 
 the sun and moon. Nothing but the Moon can settle the question 
 and we are willing to wait on her for further information. If the 
 adage be true, then the philosopher has missed what lies before his 
 eyes ; if false, then the world can be led by the nose in spite of the 
 eyes. Both these things happen sometimes; and we are willing to 
 take whichever of the two solutions is borne out by future facts. In 
 the mean time, we announce the next Saturday Moon for the 18th 
 of August.' 
 
 How many coincidences are required to establish a law of 
 connexion ? It depends on the way in which the mind views the 
 matter in question. Many of the paradoxers are quite set up by 
 a very few instances. I will now tell a story about myself, and 
 then ask them a question. 
 
 So far as instances can prove a law, the following is proved : no 
 failure has occurred. Let a clergyman be known to me, whether 
 by personal acquaintance or correspondence, or by being frequently 
 brought before me by those with whom I ain connected in private 
 life : that clergyman does not, except in few cases, become a 
 bishop ; but, if he become a bishop, h'e is sure, first or last, to 
 become an arch-bishop. This has happened in every case. As 
 follows : 
 
 1 . My last schoolmaster, a former Fellow of Oriel, was a very 
 intimate college friend of Kiehard Whately, a younger man. 
 Btruck by his friend's talents, he used to talk of him perpetually, 
 and predict his future eminence. Before I was sixteen, and 
 before Whately had even given his Bampton Lectures, I was very 
 familiar with his name, and some of his sayings. I need not say 
 that lie became Archbishop of Dublin. 
 
 2. When I was a child, a first cousin of John Bird Sunnier 
 married a sister of my mother. I cannot remember the time 
 when I first heard his name, but it was made very familiar to me. 
 In time lie became Bishop of Chester, and then, Archbishop of 
 Canterbury. My reader may say that Dr. C. E. Sumner, Bishop 
 of Winchester, has just as good a claim : but it is not so : those 
 connected with me had more knowledge of Dr. J. B. Sumner ; 
 and said nothing, or next to nothing, of the other. Humour says 
 that the Bishop of Winchester has declined an Archbishopric : if 
 so, my rule is a rule of gradations. 
 
 3. Thomas Musgrave, Fellow of Trinity College, Cambridge, 
 was Dean of the college when I was an undergraduate : this 
 
ACCIDENT, OK LAW? 197 
 
 brought me into connexion with him, he giving impositions for 
 not going to chapel, I writing them out according. We had 
 also friendly intercourse in after life ; I forgiving, he probably 
 forgetting. Honest Tom Musgrave, as he used to be called, 
 became Bishop of Hereford, and Archbishop of York. 
 
 4. About the time when I went to Cambridge, I heard a great 
 deal about Mr. C. T. Longley, of Christchurch, from a cousin 
 of my own of the same college, long since deceased, who spoke of 
 him much, and most affectionately. Dr. Longley passed from 
 Durham to York, and thence to Canterbury. I cannot quite make 
 out the two Archbishoprics ; I do not remember any other private 
 channel through which the name came to me : perhaps Dr. 
 Longley, having two strings to his bow, would have been one 
 Archbishop if I had never heard of him. 
 
 5. When Dr. Wm. Thomson was appointed to the see of 
 Gloucester in 1861, he and I had been correspondents on the 
 subject of logic on which we had both written for about 
 fourteen years. On his elevation I wrote to him, giving the pre- 
 ceding instances, and informing him that he would certainly be 
 an Archbishop. The case was a strong one, aad the law acted 
 rapidly; for Dr. Thomson's elevation to the see of York took 
 place in 1862. 
 
 Here are five cases ; and there is no opposing instance. I have 
 searched the almanacs since 1828, and can find no instance of a 
 Bishop not finally Archbishop of whom I had known through 
 private sources, direct or indirect. Now what do my paradoxers 
 say ? Is this a pre-'established harmony, or a chain of coinci- 
 dences ? And how many instances will it require to establish a 
 law? 
 
 Some account of the great astronomical discoveries lately made 
 by Sir John Herschel at the Cape of Good Hope. Second 
 Edition. London, 12mo. 1836. 
 
 This is a curious hoax, evidently written by a person versed in 
 astronomy and clever at introducing probable circumstances and 
 undesigned coincidences. It first appeared in a newspaper. It 
 makes Sir J. Herschel discover men, animals, &c. in the moon, of 
 which much detail is given. There seems to have been a French 
 edition, the original, and English editions in America, whence 
 the work came into Britain : but whether the French was pub- 
 lished in America or at Paris I do not know. There is no doubt 
 that it was produced in the United States, by M. Mcollet, an 
 astrenomer, once of Paris, and a fugitive of some kind. About 
 
198 A BUDGET OF PARADOXES. 
 
 him I have heard two stories. First, that he fled to America 
 with funds not his own, and that this book was a mere device to 
 raise the wind. Secondly, that he was a protege of Laplace, and 
 of the Polignac party, and also an outspoken man. That after 
 the revolution he was so obnoxious to the republican party that 
 he judged it prudent to quit France ; which he did in debt, 
 leaving money for his creditors, but not enough, with M. Bouvard. 
 In America he connected himself with an assurance office. The 
 moon-story was written, and sent to France, chiefly with the 
 intention of entrapping M. Arago, Nieollet's especial foe, into the 
 belief of it. And those who narrate this version of the story 
 wind up by saying that M. Arago was entrapped, and circulated 
 the wonders through Paris, until a letter from Nicollet to M. 
 Bouvard explained the hoax. I have no personal knowledge of 
 either story : but as the poor man had to endure the first, it is 
 but right that the second should be told with it. 
 
 The Weather Almanac for the Year 1838. By P. Murphy, Esq. 
 
 M.N.S. 
 
 By M.N.S. is meant member of no society. This almanac bears 
 on the title-page two recommendations. The Morning Post calls 
 it one of the most important-if-true publications of our gene- 
 ration. The Times says : c If the basis of his theory prove sound, 
 and its principles be sanctioned by a more extended experience, 
 it is not too much to say that the importance of the discovery 
 is equal to that of the longitude.' Cautious journalist ! Three 
 times that of the longitude would have been too little to say. 
 That the landsman might predict the weather of all the year, at 
 its beginning, Jack would cheerfully give up astronomical longi- 
 tude the problem altogether, and fall back on chronometers 
 with the older Ls, lead, latitude, and look-out, applied to dead- 
 reckoning. Mr. Murphy attempted to give the weather day by 
 day : thus the first seven days of March bore Changeable ; Eain ; 
 Eain ; Kain-wmc? ; Changeable ; Fair ; Changeable. To aim at 
 such precision as to put a fair day between two changeable ones 
 by weather theory was going very near the wind and weather too. 
 Murphy opened the year with cold and frost ; and the weather 
 did the same. But Murphy, opposite to Saturday, January 20, 
 put down 'Fair, Probable lowest degree of winter temperature.' 
 When this Saturday came, it was not merely the probably cold- 
 est of 1838, but certainly the coldest of many consecutive years. 
 Without knowing anything of Murphy, I felt it prudent to cover 
 my nose with my glove as I walked the street at eight in the 
 
MATHEMATICAL THEOLOGY. 199 
 
 morning. The fortune of the Almanac was made. Nobody 
 waited to see whether the future would dement the prophecy : 
 the shop was beset in a manner which brought the police to keep 
 order; and it was said that the Almanac for 1838 was a gain of 
 5,000i. to the owners. It very soon appeared that this was only 
 a lucky hit : the weather-prophet had a modified reputation for a 
 few years ; and is now no more heard of. A work of his will 
 presently appear in the list. 
 
 Letter from Alexandria on the evidence of the practical appli- 
 cation of the quadrature of the circle in the great pyramids of 
 Gizeh. By H. C. Agnew, Esq. London, 1838, 4to. 
 
 Mr. Agnew detects proportions which he thinks were suggested 
 by those of the circumference and diameter of a circle. 
 
 The creed of St. Athanasius proved by a mathematical parallel. 
 Before you censure, condemn, or approve ; read, examine, and 
 understand. E. B. REVILO. London, 1839, 8vo. 
 
 This author really believed himself, and was in earnest. He is 
 not the only person who has written nonsense by confounding the 
 mathematical infinite (of quantity) with what speculators now 
 more correctly express by the unlimited, the unconditioned, or 
 the absolute. This tract is worth preserving, as the extreme case 
 of a particular kind. The following is a specimen. Infinity 
 being represented by oo , as usual, and/, s, #, being finite integers, 
 the three Persons are denoted by oo r , (m oo )', oo , the finite 
 fraction m representing human nature, as opposed to oo . The 
 clauses of the Creed are then given with their mathematical 
 parallels. I extract a couple : 
 
 But the Godhead of the Father, It has been shown that oo^, oo*, 
 of the Son, and of the Holy Ghost, and (m oo ) *, together, are but oo , 
 is all one : the glory equal, the and that each is oo , and any magni- 
 Majesty co-eternal. tude in existence represented by oo 
 
 always was and always will be : for 
 it cannot be made, or destroyed, and 
 yet exists. 
 
 Equal to the Father, as touching (m oo )* is equal to oo^as touch- 
 his Godhead: and inferior to the ing oo , but inferior to oo^as touch- 
 Father, as touching his Manhood, ing m : because m is not infinite. 
 
 I might have passed this over, as beneath even my present 
 subject, but for the way in which I became acquainted with it. 
 A bookseller, not the publisher, handed it to* me over his counter: 
 one who had published mathematical works. He said, with an 
 
200 A BUDGET OF PARADOXES. 
 
 air of important communication. Have you seen this, Sir I In 
 
 reply, I recommended him to show it to my friend Mr. , for 
 
 whom he had published mathematics. Educated men, used to 
 books, and to the converse of learned men, look with mysterious 
 wonder on such productions as this : for which reason I have 
 made a quotation which many will judge had better have been 
 omitted. But it would have been an imposition on the public if 
 I were, omitting this and some other uses of the Bible and 
 Common Prayer, to pretend that I had given a true picture of 
 my school. 
 
 [Since the publication of the above, it has been stated that the 
 author is Mr. Oliver Byrne, the author of the Dual Arithmetic 
 mentioned further on : E. B. Eevilo seems to be obviously a 
 reversal.] 
 
 Old and new logic contrasted : being an attempt to elucidate, for 
 ordinary comprehension, how Lord Bacon delivered the human 
 mind from its 2,000 years' enslavement under Aristotle. By 
 Justin Brenan. London, 1839, 12mo. 
 
 Logic, though the other exact science, has not had the sort of 
 assailants who have clustered about Mathematics. There is a 
 sect which disputes* the utility of logic, but there are no special 
 points, like the quadrature of the circle, which excite dispute 
 among those who admit other things. The old story about 
 Aristotle having one logic to trammel us, and Bacon another to 
 set us free, always laughed at by those who really knew either 
 Aristotle or Bacon, now begins to be understood by a large 
 section of the educated world. The author of this tract connects 
 the old logic with the indecencies of the classical writers, and the 
 new with moral purity : he appeals to women, who, ' when they 
 see plainly the demoralizing tendency of syllogistic logic, they 
 will, no doubt, exert their powerful influence against it, and 
 support the Baconian method.' This is the only work against 
 logic which I can introduce, but it is a rare one, I mean in 
 contents. I quote the author's idea of a syllogism : 
 
 The basis of this system is the syllogism. This is a form of couch- 
 ing the substance of your argument or investigation into one short 
 line or sentence then corroborating or supporting it in another, and 
 drawing your conclusion or proof in a third. 
 
 On this definition he gives an example, as follows : ' Every sin 
 deserves death,' the substance of the < argument or investigation.' 
 Then comes, ' Every unlawful wish is a sin,' which ' corroborates 
 or supports ' the preceding : and, lastly, 4 therefore every unlaw- 
 
LOGIC; SIR WILLIAM HAMILTON. 201 
 
 ful wish deserves death,' which is the ' conclusion or proof.' We 
 learn, also, that ' sometimes the first is called the premises (sic), 
 and sometimes the first premiss ; ' as also that ' the first is some- 
 times called the proposition, or subject, or affirmative, and the 
 next the predicate, and sometimes the middle term.' To which 
 is added, with a mark of exclamation at the end, ' but, in analyz- 
 ing the syllogism, there is a middle term, and a predicate too, in 
 each of the lines ! ' It is clear that Aristotle never enslaved this 
 mind. 
 
 I have said that logic has no paradoxers, but I was speaking of 
 old time. This science has slept until our own day : Hamilton 
 says there has been 4 no progress made in the general develop- 
 ment of the syllogism since the time of Aristotle ; and in regard 
 to the few partial improvements, the professed historians seem 
 altogether ignorant.' But in our time, the paradoxer, the oppo- 
 nent of common opinion, has appeared in this field. I do not 
 refer to Prof. Boole, who is not a paradoxer, but a discoverer : 
 his system could neither oppose nor support common opinion, 
 for its grounds were not within the conception of any one. I 
 speak especially of two others, who fought like cat and dog : 
 one was dogmatical, the other categorical. The first was Hamil- 
 ton himself Sir William Hamilton of Edinburgh, -the meta- 
 physician, not Sir William Rowan Hamilton of Dublin, the 
 mathematician, a combination of peculiar genius with unprece- 
 dented learning, erudite in all he could want except mathematics, 
 for which he had no turn, and in which he had not even a school- 
 boy's knowledge, thanks to the Oxford of his younger day. The 
 other was the author of this work, so fully described in Hamil- 
 ton's writings that there is no occasion to describe him here. I 
 shall try to say a few words in common language about the para- 
 doxers. 
 
 Hamilton's great paradox was the quantification of the predi- 
 cate ; a fearful phrase, easily explained. We all know that when 
 we say ' Men are animals,' a form wholly unquantified in phrase, 
 we speak of all men, but not of all animals : it is some or ally 
 some may be all for aught the proposition says. This some-may- 
 be-all-for-aught-we-say, or not-none, is the logician's some. One 
 would suppose that ; all men are some animals,' would have been 
 the logical phrase in all time : but the predicate never was 
 quantified. The few who alluded to the possibility of such a 
 thing found reasons for not adopting it over and above the great 
 reason, that Aristotle did not adopt it. For Aristotle never ruled 
 in physics or metaphysics in the old time with near so much of 
 
202 A BUDGET OF PAKADOXES. 
 
 absolute sway as he has ruled in logic down to our own time. 
 The logicians knew that in the proposition c all men are animals ' 
 the 6 animal ' is not universal, but particular : yet no one dared 
 to say that all men are some animals, and to invent the phrase, 
 6 some animals are all men ' until Hamilton leaped the ditch, 
 and not only completed a system of enunciation, but applied it to 
 syllogism. 
 
 My own case is as peculiar as his : I have proposed to intro- 
 duce mathematical thought into logic to an extent which makes 
 the old stagers cry 
 
 St. Aristotle ! what wild notions ! 
 Serve a ne exeat regno on him ! 
 
 Hard upon twenty years ago, a friend and opponent, who stands 
 high in these matters, and who is not nearly such a sectary of 
 Aristotle and establishment as most, wrote to me as follows : 
 4 It is said that next to the man who forms the taste of a nation, 
 the greatest genius is the man who corrupts it. I mean therefore 
 no disrespect, but very much the reverse, when I say that I 
 have hitherto always considered you as a great logical heresiarch.' 
 Coleridge says he thinks that it was Sir Joshua Keynolds who 
 made the remark : which, to copy a bull I once heard, I cannot 
 deny, because I was not there when he said it. My friend did 
 not call me to repentance and reconciliation with the church : 
 I think he had a guess that I was a reprobate sinner. My 
 offences at that time were but small : I went on spinning syllo- 
 gism systems, all alien from the common logic, until I had six, 
 the initial letters of which, put together, from the names I gave 
 before I saw what they would make, bar all repentance by the 
 words 
 
 RUE NOT ! 
 
 leaving to the followers of the old school the comfortable option 
 of placing the letters thus : 
 
 TRUE ? NO ! 
 
 It should however be stated that the question is not about 
 absolute truth or falsehood. No one denies that anything I call 
 an inference is an inference : they say that my alterations are 
 extra-logical ; that they are material, not formal ; and that logic 
 is a formal science. 
 
 The distinction between material and formal is easily made, 
 where the usual perversions are not required. A form is an 
 empty machine, such as 6 Every X is Y ; ' it may be supplied 
 with matter, as in 6 Every man is animal.' The logicians will 
 
LOGIC ; THE HAMILTON CONTROVERSY. 203' 
 
 not see that their formal proposition, 'Every X is Y,' is material 
 in three points, the degree of assertion, the quantity of the 
 proposition, and the copula. The purely formal proposition is 
 c There is the probability a that X stands in the relation L to 
 Y.' The time will come when it will be regretted that logic 
 went without paradoxers for two thousand years : and when much 
 that has been said on the distinction of form and matter will 
 breed jokes. 
 
 I give one instance of one mood of each of the systems, in the 
 order of the letters first written above. 
 
 Relative. In this system the formal relation is taken, that is, 
 the copula may be any whatever. As a material instance, in 
 which the relations are those of consanguinity (of men under- 
 stood ), take the following : X is the brother of Y ; X is not the 
 uncle of Z ; therefore, Z is not the child of Y. The discussion of 
 relation, and of the objections to the extension, is in the Cam- 
 bridge Transactions, vol. x, part 2 ; a crabbed conglomerate. 
 
 Undecided. In this system one premise, and want of power 
 over another, infer want of power over a conclusion. As ' Some 
 men are not capable of tracing consequences ; we cannot be sure 
 that there are beings responsible for consequences who are in- 
 capable of tracing consequences ; therefore, we cannot be sure 
 that all men are responsible for the consequences of their ac- 
 tions.' 
 
 Exemplar. This, long after it suggested itself to me as a 
 means of correcting a defect in Hamilton's system, I saw to be 
 the very system of Aristotle himself, though his followers have 
 drifted into another. It makes its subject and predicate ex- 
 amples, thus : Any one man is an animal ; any one animal is a 
 mortal ; therefore, any one man is a mortal. 
 
 Numerical. Suppose 100 Ys to exist: then if 70 Xs be Ys, 
 and 40 Zs be Ys, it follows that 10 Xs (at least) are Zs. Hamil- 
 ton, whose mind could not generalize on symbols, saw that the 
 word most would come under this system, and admitted, as valid, 
 such a syllogism as ' most Ys are Xs ; most Ys are Zs ; therefore, 
 some Xs are Zs.' 
 
 Onymatic. This is the ordinary system much enlarged in 
 propositional forms. It is fully discussed in my Syllabus of 
 Logic. 
 
 Transposed. In this syllogism the quantity in one premise is 
 transposed into the other. As, some Xs are not Ys ; for every X 
 there is a Y which is Z ; therefore, some Zs are not Xs. 
 
 Sir William Hamilton of Edinburgh was one of the best 
 
204 A BUDGET OF PARADOXES. 
 
 friends and allies I ever had. When I first began to publish 
 speculation on this subject, he introduced me to the logical 
 world as having plagiarized from him. This drew their attention : 
 a mathematician might have written about logic under forms 
 which had something of mathematical look long enough before the 
 Aristotelians would have troubled themselves with him : as was 
 done by John Bernoulli, James Bernoulli, Lambert, and Grergonne ; 
 who, when our discussion began, were not known even to omnile- 
 gent Hamilton. He retracted his accusation of wilful theft in 
 a manly way when he found it untenable ; but on " this point he 
 wavered a little, and was convinced to the last that I had taken 
 his principle unconsciously. He thought I had done the same 
 with Ploucquet and Lambert. It was his pet notion that I did 
 not understand the commonest principles of logic, that I did not 
 always know the difference between the middle term of a syllo- 
 gism and its conclusion. It went against his grain to imagine 
 that a mathematician could be a logician. So long as he 
 took me to be riding my own hobby, he laughed consumedly : 
 but when he thought he could make out that I was mounted 
 behind Ploucquet or Lambert, the current ran thus : ' It would 
 indeed have been little short of a miracle had he, ignorant even 
 of the common principles of logic, been able of himself to rise to 
 generalization so lofty and so accurate as are supposed in the 
 peculiar doctrines of both the rival logicians, Lambert and 
 Ploucquet how useless soever these may in practice prove to be. J 
 All this has been sufficiently discussed elsewhere : ' but, masters, 
 remember that I am an ass.' 
 
 I know that I never saw Lambert's work until after all 
 Hamilton supposed me to have taken was written : he himself, 
 who read almost everything, knew nothing about it until after I 
 did. I cannot prove what I say about my knowledge of Lambert : 
 but the means of doing it may turn up. For, by the casual 
 turning up of an old letter, I have found the means of clearing 
 myself as to Ploucquet. Hamilton assumed that (unconsciously) 
 I took from Ploucquet the notion of a logical notation in which 
 the symbol of the conclusion is seen in the joint symbols of the 
 premises. For example, in my own fashion I write down ()()' 
 two symbols of premises. By these symbols I see that there is a 
 valid conclusion, and that it may be written in symbol by striking 
 out the two middle parentheses, which gives ( . . ) and reading 
 the two negative dots as an affirmative. And so I see in (.)(.) 
 that ( ) is the conclusion. This, in full, is the perception that 
 c all are either Xs or Ys ' and ; all are either Ys or Zs ' necessitates 
 'some Xs are Zs.' Now in Ploucquet's book of 1763, is found. 
 
CONTKOVEKSY WITH HAMILTON. 205 
 
 'Deleatur in prsemissis medius ; id quod restat indicat con- 
 clusionem.' In the paper in which I explain my symbols which 
 are altogether different from Ploucquet's there is found c Erase 
 the symbols of the middle term ; the remaining symbols show 
 the inference.' There is very great likeness : and I would have 
 excused Hamilton for his notion if he had fairly given reference to 
 the part of the book in which his quotation was found. For I 
 had shown in my Formal Logic what part of Ploucquet's book I 
 had used : and a fair disputant would either have strengthened 
 his point by showing that I had been at his part of the book, or 
 allowed me the advantage of it being apparent that I had not 
 given evidence of having seen that part of the book. My good 
 friend, though an honest man, was sometimes unwilling to allow 
 due advantage to controversial opponents. 
 
 But to my point. The only work of Ploucquet I ever saw was 
 lent me by my friend Dr. Logan, with whom I have often corres- 
 ponded on logic, &c. I chanced (in 1865) to turn up the letter 
 which he sent me (Sept. 12, 1847) with the book. Part of it 
 runs thus : c I congratulate you on your success in your logical 
 researches [that is, in asking for the book, I had described some 
 results]. Since the reading of your first paper I have been 
 satisfied as to the possibility of inventing a logical notation in 
 which the rationale of the inference is contained in the symbol, 
 though I never attempted to verify it [what I communicated, 
 then, satisfied the writer that I had done and communicated what 
 he, from my previous paper, suspected to be practicable]. I 
 send you Ploucquet's dissertation. . . .' 
 
 It now being manifest that I cannot be souring grapes which 
 have been taken from me, I will say what I never said in print 
 before. There is not the slightest merit in making the symbols 
 of the premises yield that of the conclusion by erasure : the thing 
 must do itself in every system which symbolises quantities. For 
 in every syllogism (except the inverted Bramantip of the Aristo- 
 telians) the conclusion is manifest in this way without symbols. 
 This Bramantip destroys system in the Aristotelian lot : and 
 circumstances which I have pointed out destroy it in Hamilton's 
 own collection. But in that enlargement of the reputed Aristo- 
 telian system which I have called onymatic, and in that correction 
 of Hamilton's system which I have called exemplar ', the rule of 
 erasure is universal, and may be seen without symbols. 
 
 Our first controversy was in 1846. In 1847, in my Formal 
 Logic, I gave him back a little satire for satire, just to show, as 
 I stated, that I could employ ridicule if I pleased. He was so 
 
206 A BUDGET OF PARADOXES. 
 
 offended with the appendix in which this was contained, that he 
 would not accept the copy of the book I sent him, but returned 
 it. Copies of controversial works, sent from opponent to opponent, 
 are not presents, in the usual sense : it was a marked success to 
 make him angry enough to forget this. It had some effect how- 
 ever : during the rest of his life I wished to avoid provocation ; for 
 I could not feel sure that excitement might not produce con- 
 sequences. I allowed his slashing account of me in the Discus- 
 sions to pass unanswered : and before that, when he proposed to 
 open a controversy in the Athenceum upon my second Cambridge 
 paper, I merely deferred the dispute until the next edition of my 
 Formal Logic. I cannot expect the account in the Discussions 
 to amuse an unconcerned reader as much as it amused myself : 
 but for a cut-and-thrust, might-and-main, tooth-and-nail, ham- 
 mer-and-tongs assault, I can particularly recommend it. I never 
 knew, until I read it, how much I should enjoy a thundering 
 onslaught on myself, done with racy insolence by a master hand, 
 to whom my good genius had whispered Ita feri ut se sentiat 
 emori. Since that time I have, as the Irishman said, become * dry 
 moulded for want of a bating.' Some of my paradoxers have 
 done their best : but theirs is mere twopenny ' small swipes,' as 
 Peter Peebles said. Brandy for heroes ! I hope a reviewer or two 
 will have mercy on me, and will give me as good discipline as 
 Straff ord would have given to Hampden and his set: 'much 
 beholden,' said he, c should they be to any one that should 
 thoroughly take pains with them in that kind ' meaning objective 
 flagellation. And I shall be the same to any one who will serve 
 me so but in a literary and periodical sense : my corporeal 
 cuticle is as thin as my neighbours-'. 
 
 Sir W. H. was suffering under local paralysis before our con- 
 troversy commenced : and though his mind was quite unaffected, 
 a retort of as downright a character as the attack might have 
 produced serious effect upon a person who had shown himself 
 sensible of ridicule. Had a second attack of his disorder followed 
 an answer from me, I should have been held to have caused it : 
 though, looking at Hamilton's genial love of combat, I strongly 
 suspected that a retort in kind 
 
 Would cheer his heart, and warm his blood, 
 And make him fight, and do him good. 
 
 But I could not venture to risk it. So all I did, in reply to the 
 article in the Discussions, was to write to him the following note : 
 which, as illustrating an etiquette of controversy, I insert. 
 
LETTEE TO HAMILTON DOGGEEL. 207 
 
 ' I beg to acknowledge and thank you for ... It is necessary that I 
 should say a word on my retention of this work, with reference to 
 your return of the copy of my ' Formal Logic/ which I presented to 
 you on its publication : a return made on the ground of your disap- 
 proval of the account of our controversy which that work contained. 
 According to my view of the subject, any one whose dealing with the 
 author of a book is specially attacked in it, has a right to expect from 
 the author that part of the book in which the attack is made, together 
 with so much of the remaining part as is fairly context. And I hold 
 that the acceptance by the party assailed of such work or part of a work 
 does not imply any amount of approval of the contents, or of want of 
 disapproval. On this principle (though I am not prepared to add the 
 word alone) I forwarded to you the whole of my work on " Formal 
 Logic ' ' and my second Cambridge Memoir. And on this principle I 
 should have held you wanting in due regard to my literary rights if 
 you had not forwarded to me your asterisked pages, with all else that 
 was necessary to a full understanding of their scope and meaning, so 
 far as the contents of the book would furnish it. For the remaining 
 portion, which it would be a hundred pities to separate from the pages 
 in which I am directly concerned, I am your debtor on another princi- 
 ple ; and shall be glad to remain so if you will allow me to make a 
 feint of balancing the account by the offer of two small works on sub- 
 jects as little connected with our discussion as the " Epistolse Obscuro- 
 rum Virorum," or the Lutheran dispute. I trust that by accepting 
 my " Opuscula " you will enable me to avoid the use of the knife, and 
 leave me to cut you up with the pen as occasion shall serve, I remain, 
 &c. (April 21, 1852).' 
 
 I received polite thanks, but not a word about the body of the 
 letter : my argument, I suppose, was admitted. 
 
 I find among my miscellaneous papers the following jeu 
 d'csprit, or jeu de betise, whichever the reader pleases I care 
 not intended, before I saw ground for abstaining, to have, as the 
 phrase is, come in somehow. I think I could manage to bring- 
 any thing into anything : certainly into a Budget of Paradoxes. 
 Sir W. H. rather piqued himself upon some caniculars, or doggrel 
 verses, which he had put together in memoriam [technicam] of 
 the way in which A E I are used in logic : he added U, Y, for 
 the addition of meet, &c. to the system. I took the liberty of 
 concocting some counter-doggrel, just to show that a mathema- 
 tician may have architectonic power as well as a metaphysician. 
 
208 A BUDGET OF PAEADOXES. 
 
 DOGGREL. 
 BY SIR W. HAMILTON. 
 
 A it affirms of this, these, all, 
 
 Whilst E der ies of any ; 
 I it affirms (whilst denies) 
 
 Of some (or few, or many). 
 
 Thus A affirms, as E denies, 
 
 And definitely either ; 
 Thus I affirms, as denies, 
 
 And definitely neither. 
 
 A half, left semidefinite, 
 
 Is worthy of its score ; 
 U, then, affirms, as Y denies, 
 
 This, neither less nor more. 
 
 Indefinito-definites, 
 
 I, UI, YO, last we come ; 
 And this affirms, as that denies 
 
 Of more, most (half, plus, some). 
 
 COUNTER DOGGREL. 
 
 BY PROF. DE MORGAN. 
 (1847.) 
 
 GREAT A affirms of all ; 
 
 Sir William does so too : 
 When the subject is * my suspicion/ 
 
 And the predicate ' must be true.' 
 
 Great E denies of all ; 
 
 Sir William of all but one : 
 When he speaks about this present time, 
 
 And of those who in logic have done. 
 
 Great I takes up but some ; 
 
 Sir William ! my dear soul ! , 
 
 Why then in all your writings, 
 
 Does ' Great I ' fill l the whole ! 
 
 1 A very truculently unjust assertion : for Sir W. was as great a setter up of some 
 as he was a puller down of others. His writings are a congeries of praises and 
 blames, both cruel smart, as they say in the States. But the combined instigation of 
 
LOGICAL DOGGREL. 209 
 
 Great O says some are not ; 
 
 Sir William's readers catch, 
 That some (modern) Athens is not without 
 
 An Aristotle to match, 
 
 A half, left semi-definite, 
 
 Is worthy of its score : ' 
 This looked very much like balderdash, 
 
 And neither less nor more. 
 
 It puzzled me like anything ; 
 
 In fact, it puzzled me worse : 
 Isn't schoolman's logic hard enough, 
 
 Without being in Sibyl's verse ? 
 
 At last, thinks I, 'tis German ; 
 
 And I'll try it with some beer 1 
 The landlord asked what bothered me so, 
 
 And at once he made it clear, 
 
 Itf s half-and-half, the gentleman means ; 
 
 Don't you see he talks of score ? 
 That's the bit of a memorandum 
 
 That we chalk behind the door. 
 
 Semi-definite 's outlandish ; 
 
 But I see, in half a squint, 
 That he speaks of the lubbers who call for a quart, 
 
 When they can't manage more than a pint. 
 
 Now Til read it into English, 
 
 And then you'll answer me this : 
 If it isn't good logic all the world round, 
 
 I should like to know what is ? 
 
 When you call for a pot of half-and-half, 
 
 If you're lost to sense of shame, 
 You may leave it semi-definite, 
 
 But you pay for it all just the same. 
 
 I am unspeakably comforted when I look over the above in 
 remembering that the question is not whether it be Pindaric or 
 
 prose, rhyme, and retort would send Aristides himself to Tartarus, if it were not 
 pretty certain that Minos would grant a stet processus under the circumstances. The 
 first two verses are exaggerations standing on a basis of truth. The fourth verse is 
 quite true : Sir W. H. was an Edinburgh Aristotle, with the differences of ancient and 
 modern Athens well marked, especially the perfervidum ingtnium Scotorum, 
 
 P 
 
210 A BUDGET OF PARADOXES. 
 
 Horatian, but whether the copy be as good as the original. And 
 I say it is : and will take no denial. 
 
 Long live long will live the glad memory of William 
 Hamilton, Good, Learned, Acute, and Disputatious! He fought 
 upon principle : the motto of his book is 
 
 Truth, like a torch, the more it's shook it shines. 
 
 There is something in this ; but metaphors, like puddings, 
 quarrels, rivers, and arguments, always have two sides to them. 
 For instance, 
 
 Truth, like a torch, the more it 's shook it shines ; 
 
 But those who want to use it, hold it steady. 
 They shake the flame who like a glare to gaze at, 
 
 They keep it still who want a light to see by. 
 
 Theory of Parallels. The proof of Euclid's axiom looked for in 
 the properties of the Equiangular Spiral. By Lieut- Col. G. Per- 
 ronet Thompson. The same, second edition, revised and cor- 
 rected. The same, third edition, shortened, and freed from 
 dependence on the theory of limits. The same, fourth edition, 
 ditto, ditto. All London, 1840, 8vo. 
 
 To explain these editions it should be noted that General 
 Thompson rapidly modified his notions, and republished his tracts 
 accordingly. 
 
 Vestiges of the Natural History of Creation. London, 1840, 12mo. 
 
 This is the first edition of this celebrated work. Its form is a 
 case of the theory : the book is an undeniable duodecimo, but the 
 size of its paper gives it the look of not the smallest of octavos. 
 Does not this illustrate the law of development, the gradation of 
 families, the transference of species, and so on ? If so, I claim 
 the discovery of this esoteric testimony of the book to its own 
 contents ; I defy any one to point out the reviewer who has 
 mentioned it. The work itself is described by its author as 6 the 
 first attempt to connect the natural sciences into a history of 
 creation.' The attempt was commenced, and has been carried 
 on, both with marked talent, and will be continued. Great 
 advantage will result : at the worst we are but in the alchemy of 
 some new chemistry, or the astrology of some new astronomy. 
 Perhaps it would be as well not to be too sure on the matter, 
 until we have an antidote to possible consequences as ex- 
 
THE VESTIGES OF CREATION. 211 
 
 hibited under another theory, on which it is as reasonable to 
 speculate as on that of the ' Vestiges.' I met long ago with a 
 splendid player on the guitar, who assured me, and was confirmed 
 by his friends, that he never practised, except in thought, and 
 did not possess an instrument : he kept his fingers acting in his 
 mind, until they got their habits ; and thus he learnt the most 
 difficult novelties of execution, Now what if this should be a 
 minor segment of a higher law ? What if, by constantly think- 
 ing of ourselves as descended from primaeval monkeys, we should, 
 if this be true actually get our tails again ? What if the 
 first man who was detected with such an appendage should be 
 obliged to confess himself the author of the ; Vestiges ' a person 
 yet unknown who would naturally get the start of his species 
 by having had the earliest habit of thinking on the matter ? I 
 confess I never hear a man of note talk fluently about it without a 
 curious glance at his proportions, to see whether there may be 
 ground to conjecture that he may have more of ' mortal coil ' 
 than others, in anaxyridical concealment. I do not feel sure 
 that even a paternal love for his theory would induce him, in the 
 case I am supposing, to exhibit himself at the British Associa- 
 tion, 
 
 With a hole behind which his tail peeped through. 
 
 The first sentence of this book (1840) is a cast of the log, which 
 shows our rate of progress. * It is familiar knowledge that the 
 earth which we inhabit is a globe of somewhat less than 8,000 
 miles in diameter, being one of a series of eleven which revolve at 
 different distances around the sun.' The eleven I Not to mention 
 the Iscariot which Le Verrier and Adams calculated into existence, 
 there is more than a septuagint of new planetoids. 
 
 The Constitution and Rules of the Ancient and Universal * Benefit 
 Society ' established by Jesus Christ, exhibited, and its advan- 
 tages and claims maintained, against all Modern and merely 
 Human Institutions of the kind : A Letter very respectfully ad- 
 dressed to the Rev. James Everett, and occasioned by certain 
 remarks made by him, in a speech to the Members of the 
 * Wesleyan Centenary Institute ' Benefit Society. Dated York, 
 Dec. 7, 1840. By Thomas Smith. i2ino. (pp. 8.) 
 
 The Wesleyan minister addressed had advocated provision 
 against old age, &c. : the writer declares all private provision 
 unchristian. After decent maintenance and relief of family 
 claims of indigence, he holds that all the rest is to go to the 
 6 Benefit Society,' of which he draws up the rules, in technical 
 
 p 2 
 
212 A BUDGET OF PAKADOXES. 
 
 form, with chapters of ' Officers,' c Contributors,' &c., from the 
 Acts of the Apostles, &c., and some of the early Fathers. He 
 holds that a Christian may not ' make a private provision against 
 the contingencies of the future : ' and that the great ' Benefit 
 Society ' is the divinely-ordained recipient of all the surplus of 
 his income ; capital, beyond what is necessary for business, he 
 is to have none. A real good speculator shuts his eyes by 
 instinct, when opening them would not serve the purpose : he 
 has the vizor of the Irish fairy tale, which fell of itself over the 
 eyes of the wearer the moment he turned them upon the en- 
 chanted light which would have destroyed him if he had caught 
 sight of it. c Whiles it remained, was it not thine own ? and 
 after it was sold, was it (the purchase-money) not in thine own 
 power?' would have been awkward to quote, and accordingly 
 nothing is stated except the well-known result, which is rule 3, 
 cap. 5, 6 Prevention of Abuses.' By putting his principles to- 
 gether, the author can be made, logically, to mean that the 
 successors of the apostles should put to death all contributors who 
 are detected in not paying their full premiums. 
 
 I have known one or two cases in which policy-holders have 
 surrendered their policies through having arrived at a conviction 
 that direct provision is unlawful. So far as I could make it out, 
 these parties did not think it unlawful to lay by out of income, 
 except when this was done in a manner which involved calcula- 
 tion of death-chances. It is singular they did not see that the 
 entrance of chance of death was the entrance of the very principle 
 of the benefit society described in the Acts of the Apostles. The 
 family of the one who died young received more in proportion to 
 premiums paid than the family of the one who died old. Every 
 one who understands life assurance sees that bonus apart the 
 difference between an assurance office and a savings bank consists 
 in the adoption, pro tanto, of the principle of community of 
 goods. In the original constitution of the oldest assurance office, 
 the Amicable Society, the plan with which they started was 
 nothing but this : persons of all ages under forty-five paid one 
 common premium, and the proceeds were divided among the 
 representatives of those who died within the year. 
 
 [I omitted from its proper place a manuscript quadrature 
 (3*1416 exactly) addressed to an eminent mathematician, dated 
 in 1842 from the debtors' ward of a country gaol. The unfortu- 
 nate speculator says, ' I have laboured many years to find the 
 precise ratio.' I have heard of several cases in which squaring 
 
PERPETUAL MOTION GRAVITATION AND MAGNETISM. 213 
 
 the circle has ' produced an inability to square accounts. I re- 
 mind those who feel a kind of inspiration to employ native 
 genius upon difficulties, without gradual progression from ele- 
 ments, that the call is one which becomes stronger and stronger, 
 and may lead, as it has led, to abandonment of the duties of life, 
 and all the consequences.] 
 
 1842. Provisional Prospectus of the Double Acting Rotary Engine 
 Company. Also Mechanic's Magazine, March 26, 1842. 
 
 Perpetual motion by a drum with one vertical half in mercury, 
 the other in a vacuum : the drum, I suppose, working round for 
 ever to find an easy position. Steam to be superseded : steam 
 and electricity convulsions of nature never intended by Provi- 
 dence for the use of man. The price of the present engines, 
 as old iron, will buy new engines that will work without fuel 
 and at no expense. Guaranteed by the Count de Predaval, the 
 discoverer. I was to have been a Director, but my name got no 
 further than ink, and not so far as official notification of the 
 honour, partly owing to my having communicated to the 
 Mechanic's Magazine information privately given to me, which 
 gave premature publicity, and knocked up the plan. 
 
 An Exposition of the Nature, Force, Action, and other properties 
 of Gravitation on the Planets. London, 1842, 12mo. 
 
 An Investigation of the principles of the Rules for determining the 
 Measures of the Areas and Circumferences of Circular Plane 
 Surfaces . . . London, 1844, 8vo. 
 
 These are anonymous ; but the author (whom I believe to be 
 Mr. Denison, presently noted) is described as author of a new 
 system of mathematics, and also of mechanics. He had need 
 have both, for he shows that the line which has a square equal 
 to a given circle, has a cube equal to the sphere on the same 
 diameter : that is, in old mathematics, the diameter is to the 
 circumference as 9 to 16! Again, admitting that the velocities 
 of planets in circular orbits are inversely as the square roots of 
 their distances, that is, admitting Kepler's law, he manages to 
 prove that gravitation is inversely as the square root of the 
 distance : and suspects magnetism of doing the difference be- 
 tween this and Newton's law. Magnetism and electricity are, in 
 physics, the member of parliament and the cabman at every 
 man's bidding, as Henry Warburton said. 
 
214 A BUDGET OF PARADOXES. 
 
 The above is an outrageous quadrature. In the preceding year, 
 1841, was published what I suppose at first to be a Maori quadra- 
 ture, by Maccook. But I get it from a cutting out of some 
 French periodical, and I incline to think that it must be by a 
 Mr. M'Cook. He maks TT to be 2 + 2 V(& V2- 11). 
 
 Refutation of a Pamphlet written by the Rev. John Mackey, 
 R.C.P., entitled * A method of making a cube double of a cube, 
 founded on the principles of elementary geometry,' wherein his 
 principles are proved erroneous, and the required solution not 
 yet obtained. By Robert Murphy. Mallow, 18*24, 12mo. 
 
 This refutation was the production of an Irish boy of eighteen 
 years old, self-educated in mathematics, the son of a shoemaker 
 at Mallow. He died in 1843, leaving a name which is well 
 known among mathematicians. His works on the theory of 
 equations and on electricity, and his papers in the Cambridge 
 Transactions, are all of high genius. The only account of him 
 which I know of is that which I wrote for the Supplement of the 
 Penny Cyclopaedia. He was thrown by his talents into a good 
 income at Cambridge, with no social training except penury, and 
 very little intellectual training except mathematics. He fell 
 into dissipation, and his scientific career was almost arrested : 
 but he had great good in him, to my knowledge. A sentence in 
 a letter from the late Dean Peacock to me giving some advice 
 about the means of serving Murphy sets out the old case : 
 ' Murphy is a man whose special education is in advance of his 
 general, and such men are almost always difficult subjects to 
 manage.' This article having been omitted in its proper place, 
 I put it at 1843, the date of Murphy's death. 
 
 The Invisible Universe disclosed ; or, the real Plan and Govern- 
 ment of the Universe. By Henry Coleman Johnson, Esq. 
 London, 1843, 8vo. 
 
 The book opens abruptly with 
 
 " First demonstration. Concerning the centre : showing that, be- 
 cause the centre is an innermost point at an equal distance between 
 two extreme points of a right line, and from every two relative and 
 opposite intermediate points, it is composed of the two extreme in- 
 ternal points of each half of the line ; each extreme internal point 
 attracting towards itself all parts of that half to which it belongs ..." 
 
THE COMET OF 1843. 215 
 
 Of course the circle is squared : and the circumference is 3 J^ 
 diameters. 
 
 Combination of the Zodiacal and Cometical Systems. Printed for 
 the London Society, Exeter Hall. Price Sixpence, (n.d. 1843.) 
 
 What this London Society was, or the ' combination,' did not 
 appear. There was a remarkable comet in 1843, the tail of 
 which was at first confounded with what is called the zodiacal 
 light* This nicely-printed little tract^ evidently got up with 
 less care for expense than is usual in such works, brings together 
 all the announcements of the astronomers, and adds a short head 
 and tail piece, which I shall quote entire. As the announce- 
 ments are very ordinary astronomy, the reader will be able to 
 detect, if detection be possible, what is the meaning and 
 force of the < Combination of the Zodiacal and Cometical Sys- 
 tems ' : 
 
 " Premonition. It has pleased the AUTHOR OF CREATION to cause (to 
 His human and reasoning Creatures of this generation, by a ' combined ' 
 appearance in His Zodiacal and Cometical systems) a ' warning Crisis ' 
 of universal concernment to this our GLOBE. It is this ' Crisis ' that 
 has so generally ' BOUSED ' at this moment the ' nations throughout the 
 Earth ' that no equal interest has ever before been excited by MAN ; 
 unless it be in that caused by the ' PAGAN-TEMPLE IN ROME/ which 
 is recorded by the elder Pliny, ' Nat. Hist. 1 i. 23. iii. 3. HARDOUIN." 
 
 After the accounts given by the unperceiving astronomers, comes 
 what follows : 
 
 " Such has been (hitherto) the only object discerned by the ' Wise of 
 this World,' in this twofold union of the ' Zodiacal ' and c Cometical ' 
 systems: yet it is nevertheless a mcst * Thrilling Warning,' to all the 
 inhabitants of this precarious and transitory EARTH. We have no 
 authorized intimation, or reasonable prospective contemplation, of 
 * current time ' beyond a year 1860, of the present century ; or rather, 
 except ' the interval which may now remain from the present year 1843, 
 to a year I860' (///icpag E^HKONTA 'threescore or sixty days' <J 
 have appointed each " DAY " for a " YEAR," ' Ezek. iv. 6) : and we know, 
 from our * common experience,' how speedily such a measure of time 
 will pass away. 
 
 No words can be l more explicit ' than these of OUR BLESSED LORD : 
 viz. * THIS GOSPEL of the Kingdom shall be preached in ALL the EARTH, 
 for a Witness to ALL NATIONS ; AND THEN, shall the END COME.' The 
 ' next 18 years ' must therefore supply the interval of the ' special 
 Episcopal forerunners.' 
 
 (Matt. xxiv. 14.) - 
 
 See the * JEWISH INTELLIGENCER ' of the present month (April) 
 
216 A BUDGET OF PARADOXES. 
 
 p. 153, for the 'Delates in Parliament,' respecting the BISHOP OP 
 JERUSALEM, viz. Dr. Bowring, Mr. Hume, Sif E. Inglis, Sir R. Peel, 
 Viscount Palm erst on." 
 
 I have quoted this at length, to show the awful threats which 
 were published at a time of some little excitement about the 
 phenomenon, under the name of the London Society. The 
 assumption of a corporate appearance is a very unfair trick : and 
 there are junctures at which harm might be done by it. 
 
 Wealth the name and number of the Beast, 666, in the Book of 
 
 Revelation. [By John Taylor.] London, 1844, 8vo. 
 Whether Junius or the Beast be the more difficult to identify, 
 must be referred to Mr. Taylor, the only person who has at- 
 tempted both. His cogent argument on the political secret is 
 not unworthily matched in his treatment of the theological 
 riddle. He sees the solution in sv-jropia, which occurs in the 
 Acts of the Apostles as the word for wealth in one of its most 
 disgusting forms, and makes 666 in the most straightforward 
 way. This explanation has as good a chance as any other. The 
 work contains a general attempt at explanation of the Apoca- 
 lypse, and some history of opinion on the subject. It has not 
 the prolixity which is so common a fault of apocalyptic com- 
 mentators. 
 
 A practical Treatise on Eclipses . . . with remarks on the anom- 
 alies of the present Theory of the Tides. By T. Kerigan, F.R.S. 
 1844, 8vo. 
 
 Containing also a refutation of the theory of the tides, and after- 
 wards increased by a supplement, ' Additional facts and argu- 
 ments against the theory of the tides,' in answer to a short notice 
 in ihe^Athenceum journal. Mr. Kerigan was a lieutenant in the 
 Navy: he obtained admission to the Eoyal Society just before 
 the publication of his book. 
 
 A new theory of Gravitation. By Joseph Denison, Esq. London, 
 
 1844, 12mo. 
 Commentaries on the Principia. By the author of ' A new theory 
 
 of Gravitation.' London, 1846, 8vo. 
 
 Honour to the speculator who can be put in his proper place 
 by one sentence, be that place where it may. 
 
 ' But we have shown that the velocities are inversely as the square 
 roots of the mean distances from the sun ; wherefore, by equality of 
 ratios, the forces of the sun's gravitation upon them are also inversely 
 as the square roots of their distances from the sun.' 
 
EASTER DAY PARADOXERS. 217 
 
 In the years 1818 and 1845 the full moon fell on Easter Day, 
 having been particularly directed to fall before it in the act for 
 the change of style, and in the English missals and prayer-books 
 of all time : perhaps it would be more correct to say that Easter 
 Day was directed to fall after the full moon ; c but the principle 
 is the same.' No explanation was given in 1818, but Easter was 
 kept by the tables, in defiance of the rule, and of several protests. 
 A chronological panic was beginning in December 1844, which 
 was stopped by the Times newspaper printing extracts from an 
 article of mine in the Companion to the Almanac for 1845, which 
 had then just appeared. No one had guessed the true reason, 
 which is that the thing called the moon in the Gregorian Calendar 
 is not the moon of the heavens, but a fictitious imitation put 
 wrong on purpose, as will presently appear, partly to keep Easter 
 out of the way of the Jews' Passover, partly for convenience of 
 calculation. The apparent error happens but rarely ; and all the 
 work will perhaps have to be gone over next time. I now give 
 two bits of paradox. 
 
 Some theologians were angry at this explanation. A review 
 called the Christian Observer (of which Christianity I do not 
 know) got up a crushing article against me. I did not look at it, 
 feeling sure that an article on such a subject which appeared on 
 January 1, 1845, against a publication made in December 1844, 
 must be a second-hand job. But some years afterwards (Sept. 10, 
 1850), the reviews, &c. having been just placed at the disposal of 
 readers in the old reading-room of the Museum, I made a tour of 
 inspection, came upon my critic on his perch, and took a look at 
 him. I was very glad to remember this, for, though expecting 
 only second-hand, yet even of this there is good and bad ; and 
 I expected to find some hints in the good second-hand of a 
 respectable clerical publication. I read on, therefore, attentively, 
 but not long : I soon came to the information that some additions 
 to Delambre's statement of the rule for finding Easter, belonging 
 to distant years, had been made by Sir Harris Nicolas ! Now as I 
 myself furnished my friend Sir H. N. with Delambre's digest of 
 Clavius's rule, which I translated out of algebra into common 
 language for the purpose, I was pretty sure this was the ignorant 
 reading of a person to whom Sir H. N. was the highest arith- 
 metical authority on the subject. A person pretending to 
 chronology, without being able to distinguish the historical 
 points so clearly as they stand out in which Sir H. N. speaks 
 with authority, from the arithmetical points of pure reckoning on 
 which he does not pretend to do more than directly repeat others, 
 
213 A BUDGET OF PAKADOXES. 
 
 must be as fit to talk about the construction of Easter Tables as 
 the Spanish are to talk French. I need hardly say that the 
 additions for distant years are as much from Clavius as the rest : 
 my reviewer was not deep enough in his subject to know that 
 Clavius made and published, from his rules, the full table up to 
 A.D. 5000, for all the moveable feasts of every year ! I gave only 
 a glance at the rest : I found I was either knave or fool, with a 
 leaning to the second opinion ; and I came away satisfied that my 
 critic was either ignoramus or novice, with a leaning to the first. 
 I afterwards found an ambiguity of expression in Sir H. N.'s 
 account whether his or mine I could not tell which might 
 mislead a novice or content an ignoramus, but would have been 
 properly read or further inquired into by a competent person. 
 
 The second case is this. Shortly after the publication of my 
 article, a gentleman called at my house, and, finding I was not at 
 home, sent up his card with a stylish west-end club on it to 
 my wife, begging for a few words on pressing business. With 
 many well-expressed apologies, he stated that he had been alarmed 
 by hearing that Prof. De M. had an intention of altering Easter 
 next year. Mrs. De M. kept her countenance, and assured him 
 that I had no such intention, and further, that she greatly 
 doubted my having the power to do it. Was she quite sure ? 
 his authority was very good : fresh assurances given. He was 
 greatly relieved, for he had some horses training for after Easter, 
 which would not be ready to run if it were altered the wrong 
 way. A doubt comes over him : would Mrs. De M., in the event 
 of her being mistaken, give him the very earliest information ? 
 Promise given ; profusion of thanks ; more apologies ; and de- 
 parture. 
 
 Now, candid reader ! or uncandid either I which most 
 deserves to be laughed at ? A public instructor, who undertakes 
 to settle for the world whether a reader of Clavius, the constructor 
 of the Gregorian Calendar, is fool or knave, upon information 
 derived from a compiler in this matter of his own day ; or a 
 gentleman of horse and dog associations who, misapprehending 
 something which he heard about a current topic, infers that the 
 reader of Clavius had the ear of the Government on a proposed 
 alteration. I suppose the querist had heard some one say, 
 perhaps, that the day ought to be set right, and some one else 
 remark that I might be consulted, as the only person who had 
 discussed the matter from the original source of the Calendar. 
 
 To give a better chance of the explanation being at once 
 produced, next time the real full moon and Easter Day shall fall 
 
THE EASTER QUESTION. 219 
 
 together, I insert here a summary which was printed in the Irish 
 Prayer-book of the Ecclesiastical Society. If the amusement 
 given by paradoxers should prevent a useless discussion some years 
 hence, I and the paradoxers shall have done a little good between 
 us at any rate, I have done my best to keep the heavy weight 
 afloat by tying bladders to it. I think the next occurrence will 
 be in 1875. 
 
 EASTER DAY. 
 
 In the years 1818 and 1845, Easter Day, as given by the rules in 
 24 Geo. II. cap. 23. (known as the act for the change of style) contra- 
 dicted the precept given in the preliminary explanations. The precept 
 is as follows : 
 
 * Easter Day, on which the rest ' of the moveable feasts * depend, is 
 always the First Sunday after the Full Moon, which happens upon or 
 next after the Twenty-first Day of March ; and if the Full Moon hap- 
 pens upon a Sunday, Easier Day is the Sunday after.' 
 
 But in 1818 and 1845, the full moon fell on a Sunday, and yet the 
 rules gave that same Sunday for Easter Day. Much discussion was 
 produced by this circumstance in 1818 : but a repetition of it in 1845 
 was nearly altogether prevented by a timely * reference to the inten- 
 tion of those who conducted the Gregorian reformation of the Calendar. 
 Nevertheless, seeing that the apparent error of the Calendar is due to 
 the precept in the Act of Parliament, which is both erroneous and in- 
 sufficient, and that the difficulty will recur so often as Easter Day falls 
 on the day of full moon, it may be advisable to select from the two 
 articles cited in the note such of their conclusions and rules, without 
 proof or controversy, as will enable the reader to understand the main 
 points of the Easter question, and, should he desire it, to calculate for 
 himself the Easter of the old or new style, for any given year. 
 
 1 . In the very earliest age of Christianity, a controversy arose as 
 to the mode of keeping Easter, some desiring to perpetuate the Passover, 
 others to keep the festival of the Resurrection. The first afterwards 
 obtained the name of Quartadecimans, from their Easter being always 
 kept on the fourteenth day of the moon (Exod. xii. 18, Levit. xxiii. 5.). 
 But though it is unquestionable that a Judaizing party existed, it is 
 also likely that many dissented on chronological grounds. It is clear 
 that no perfect anniversary can take place, except when the fourteenth 
 
 1 In the Companion to the Almanac for 1845 is a paper by Professor De Morgan, 
 ' On the Ecclesiastical Calendar,' the statements of which, so far as concerns the 
 Gregorian Calendar, are taken direct from the work of Clavius, the principal agent in 
 the arrangement of the reformed reckoning. This was followed, in the Companion to 
 the Almanac for 1846, by a second paper, by the same author, headed 'On the Earliest 
 Printed Almanacs,' much of which is written in direct supplement to the former 
 article. 
 
220 . A BUDGET OF PAKADOXES. 
 
 of the moon, and with it the passover, falls on a Friday. Suppose, for 
 instance, it falls on a Tuesday : one of three things must be done. 
 Either (which seems never to have been proposed) the crucifixion and 
 resurrection must be celebrated on Tuesday and Sunday, with a wrong 
 interval ; or the former on Tuesday, the latter on Thursday, aban- 
 doning the first day of the week ; or the former on Friday, and the 
 latter on Sunday, abandoning the paschal commemoration of the 
 crucifixion. 
 
 The last mode has been, as every one knows, finally adopted. The 
 disputes of the first three centuries did not turn on any calendar 
 questions. The Easter question was merely the symbol of the strug- 
 gle between what we may call the Jewish and Gentile sects of 
 Christians : and it nearly divided the Christian world, the Easterns, 
 for the most part, being Quartadecimans. It is very important to 
 note that there is no recorded dispute about a method of predicting the 
 new moon, that is, no general dispute leading to formation of sects : 
 there may have been difficulties, and discussions about them. The 
 Metonic cycle, presently mentioned, must have been used by many, 
 perhaps most, churches. 
 
 2. The question came before the Nicene Council (A.D. 325) not 
 as an astronomical, but as a doctrinal, question : it was, in fact, this, 
 Shall the passover l be treated as a part of Christianity ? The Council 
 resolved this question in the negative, and the only information on its 
 premises and conclusion, or either, which comes from itself, is contained 
 in the following sentence of the synodical epistle, which epistle is pre- 
 served by Socrates and Theodoret. ' We also send you the good news 
 concerning the unanimous consent of all in reference to the celebration 
 of the most solemn feast of Easter, for this difference also has been 
 made up by the assistance of your prayers : so that all the brethren in 
 the East, who formerly celebrated this festival at the same time as the 
 Jews, will in future conform to the Romans and to us, and to all who 
 have of old observed our manner of celebrating Easter/ This is all 
 that can be found on the subject : none of the stories about the Coun- 
 cil ordaining the astronomical mode of finding Easter, and introducing 
 the Metonic cycle into ecclesiastical reckoning, have any contemporary 
 evidence : the canons which purport to be those of the Nicene Council 
 do not contain a word about Easter ; and this is evidence, whether we 
 suppose those canons to be genuine or spurious. 
 
 3. The astronomical dispute about a lunar cycle for the predic- 
 tion of Easter either commenced, or became prominent, by the ex- 
 tinction of greater ones, soon after the time of the Nicene Council. 
 Pope Innocent I. met with difficulty in 414. S. Leo, in 454, ordained 
 that Easter of 455 should be April 24 ; which is right. It is useless to 
 
 1 It may "be necessary to remind some English readers that in Latin and its derived 
 European languages, what we call Easter is called the passover (pascha). The 
 Quartadecimans had the name on their side : a possession which often is, in this world, 
 nine points of the law. 
 
THE EASTER QUESTION. 221 
 
 record details of these disputes in a summary : the result was, that in 
 the year 463, Pope Hilarius employed Yictorinus of Aquitaine to 
 correct the Calendar, and Victorinus formed a rule which lasted until 
 the sixteenth century. He combined the Metonic cycle and the solar 
 cycle, presently described. But this cycle bears the name of Dionysius 
 Exiguus, a Scythian settled at Home, about A.D. 530, who adapted 
 it to his new yearly reckoning, when he abandoned the sera of Dio- 
 cletian as a commencement, and constructed that which is now in 
 common use. 
 
 4. With Dionysius, if not before, terminated all difference as to 
 the mode of keeping Easter which is of historical note : the increasing 
 defects of the Easter Cycle produced in time the remonstrance of 
 persons versed in astronomy, among whom may be mentioned Roger 
 Bacon, Sacrobosco, Cardinal Cusa, Regiomontanus, &c. From the 
 middle of the sixth to that of the sixteenth century, one rule was 
 observed. 
 
 5. The mode of applying astronomy to chronology has always 
 involved these two principles. First, the actual position of the 
 heavenly body is not the object of consideration, but what astronomers 
 call its mean place, which may be described thus. Let a fictitious sun 
 or moon move in the heavens, in such manner as to revolve among the 
 fixed stars at an average rate, avoiding the alternate accelerations and 
 retardations which take place in every planetary motion. Thus the 
 fictitious (say mean) sun and moon are always very near to the real 
 sun and moon. The ordinary clocks show time by the mean, not the 
 real, sun : and it was always laid down that Easter depends on the 
 opposition (or full moon) of the mean sun and moon, not of the real 
 ones. Thus we see that, were the Calendar ever so correct as to the 
 mean moon, it would be occasionally false as to the true one : if, for 
 instance, the opposition of the mean sun and moon took place at one 
 second before midnight, and that of the^ real bodies only two seconds 
 afterwards, the calendar day of full moon would be one day before 
 that of the common almanacs. Here is a way in which the discussions 
 of 1818 and 1845 might have arisen : the British legislature has de- 
 fined the moon as the regulator of the paschal calendar. But this was 
 only a part of the mistake. 
 
 6. Secondly, in the absence of perfectly accurate knowledge of the 
 solar and lunar motion (and for convenience, even if such knowledge 
 existed), cycles are, and always have been taken, which serve to 
 represent those motions nearly. The famous Metonic cycle, which is 
 introduced into ecclesiastical chronology under the name of the cycle 
 of the golden numbers, is a period of 19 Julian 1 years. This period, 
 in the old Calendar, was taken to contain exactly 235 lunations, or 
 intervals between new moons, of the mean moon. Now the state of 
 the case is 'this : 
 
 1 The Julian year is a year of the Julian Calendar, in which there is leap year every 
 fourth year. Its average length is therefore 365 days and a quarter. 
 
222 A BUDGET OF PAEADOXES. 
 
 19 average Julian years make 6939 days 18 hours. 
 
 235 average lunations make 6939 days 16 hours 31 minutes. 
 
 So that successive cycles of golden numbers, supposing the first to 
 start right, amount to making the new moons fall too late, gradually, 
 so that the mean moon of this cycle gains 1 hour 29 minutes in 19 
 years upon the mean moon of the heavens, or about a day in 300 
 years. When the Calendar was reformed, the calendar new moons 
 were four days in advance of the mean moon of the heavens : so that, 
 for instance, calendar full moon on the 18th usually meant real full 
 moon on the 14th. 
 
 7. If the difference above had not existed, the moon of the 
 heavens (the mean moon at least), would have returned permanently 
 to the same days of the month in 19 years ; with an occasional slip 
 arising from the unequal distribution of the leap years, of which a 
 period contains sometimes five and sometimes four. As a general rule, 
 the days of new and full moon in any one year would have been also 
 the days of new and full moon of a year having 19 more units in its 
 date. Again, if there had been no leap years, the days of the month 
 would have returned to the same days of the week every seven years. 
 The introduction of occasional 29ths of February disturbs this, and 
 makes the permanent return of month days to week days occur only 
 after 28 years. If all had been true, the lapse of 28 times 19, or 532 
 years, would have restored the year in every point : that is, A.D. 1, for 
 instance, and A.D. 533, would have had the same almanac in every 
 matter relating to week days, month days, sun, and moon (mean sun 
 and moon at least). And on the supposition of its truth, the old 
 system of Dionysius was framed. Its errors are, first, that the mo- | 
 ments of mean new moon advance too much by Ih. 29m. in 19 average I 
 Julian years ; secondly, that the average Julian year of 365^ days is 
 too long by llm. 10s. 
 
 8. The Council of Trent, moved by the representations made on 
 the state of the Calendar, referred the consideration of it to the Pope- 
 In 1577, Gregory XIII. submitted to the Roman Catholic Princes and 
 Universities a plan presented to him by the representatives of Aloysius 
 Lilius, then deceased. This plan being approved of, the Pope nomi 
 nated a commission to consider its details, the working member of 
 which was the Jesuit Clavius. A short work was prepared by Clavius, 
 descriptive of the new Calendar: this was published 1 in 1582, with 
 the Pope's bull (dated February 24, 1581) prefixed. A larger work 
 was prepared by Clavius, containing fuller explanation, and entitled 
 ' Romani Calendarii a Gregorio XIII. Pontifice Maximo restituti Ex- 
 plicatio.' This was published at Rome in 1603, and again in the col- 
 lection of the works of Clavius in 1612. 
 
 1 The title of this work, which is the authority on all points of the new Calendar, is 
 * Kalendarium Gregoriamim Perpetuum. Cum Privilegio Summi Pontificis Et Alio- 
 rum Principum. Romae, Ex Officina Dominici Basse. MDLXXXII. Cum Licentia 
 Superiorum ' (quarto, pp. 60). 
 
THE EASTER QUESTION. 223 
 
 9. The following extracts from Clavins settle the question of the 
 meaning of the term moon, as used in the Calendar : 
 
 * Who, except a few who think they are very sharp- sighted in this 
 matter, is so blind as not to see that the 14th of the moon and the full 
 moon are not the same things in the Church of God ? . . . Although 
 the Church, in finding the new moon, and from it the 14th day, uses 
 neither the true nor the mean motion of the moon, but measures only 
 according to the order of a cycle, it is nevertheless undeniable that 
 the mean full moons found from astronomical tables are of the greatest 
 use in determining the cycle which is to be preferred . . . the new 
 moons of which cycle, in order to the due celebration of Easter, should 
 be so arranged that the 14th days of those moons, reckoning from the 
 day of new moon inclusive, should not fall two or more days before the 
 mean full moon, but only one day, or else on the very day itself, or 
 not long after. And even thus far the Church need not take very 
 great pains . . . for it is sufficient that all should reckon by the 14th 
 day of the moon in the cycle, even though sometimes it should be more 
 than one day before or after the mean full moon . . . We have taken 
 pains that in our cycle the new moons should follow the real new 
 moons, so that the 14th of the moon should fall either the day before 
 the mean full moon, or on that day, or not long after ; and this was 
 done on purpose, for if the new moon of the cycle fell on the same day 
 as the mean new moon of the astronomers, it might chance that we 
 should celebrate Easter on the same day as the Jews or the Quarta- 
 deciman heretics, which would be absurd, or else before them, which 
 would be still more absurd/ 
 
 From this it appears that Clavius continued the Calendar of his 
 predecessors in the choice of the fourteenth day of the moon. Our 
 legislature lays down the day of the full moon : and this mistake 
 appears to be rather English than Protestant ; for it occurs in missals 
 published in the reign of Queen Mary. The calendar lunation being 
 29 J- days, the middle day is the fifteenth day, and this is and was 
 reckoned as the day of the full moon. There is every right to presume 
 that the original passover was a feast of the real full moon : but it is 
 most probable that the moons were then reckoned, not from the astro- 
 nomical conjunction with the sun, which nobody sees except at an 
 eclipse, but from the day of first visibility of the new moon. In fine 
 climates this would be the day or two days after conjunction ; and the 
 fourteenth day from that of first visibility inclusive, would very often 
 be the day of full moon. The following is then the proper correction 
 of the precept in the Act of Parliament : 
 
 Easter Day, on which the rest depend, is always the First Sunday 
 after the fourteenth day of the calendar moon which happens upon or 
 next after the Twenty-first day of March, according to the rules laid 
 down for the construction of the Calendar ; and if the fourteenth day 
 happens upon a Sunday, Easter Day is the Sunday after. 
 
 10. Further, it appears that Clavius valued the celebration of the 
 
224 A BUDGET OF PARADOXES. 
 
 festival after tlie Jews, &c., more than astronomical correctness. He 
 gives comparison tables which would startle a believer in the astrono- 
 mical intention of his Calendar : they are to show that a calendar in 
 which the moon is always made a day older than by him, represents the 
 heavens better than he has done, or meant to do. But it must be ob- 
 served that this diminution of the real moon's age has a tendency to 
 make the English explanation often practically accordant with the 
 Calendar. For the fourteenth day of Clavius is generally the fifteenth 
 day of the mean moon of the heavens, and therefore most often that of 
 the real moon. But for this, 1818 and 1845 would not have been the 
 only instances of our day in which the English precept would have 
 contradicted the Calendar. 
 
 11. In the construction of the Calendar, Clavius adopted the ancient 
 cycle of 532 years, but, we may say, without ever allowing it to run 
 out. At certain periods, a shift is made from one part of the cycle 
 into another. This is done whenever what should be Julian leap year 
 is made a common year, as in 1700, 1800, 1900, 2100, &c. It is also 
 done at certain times to correct the error of Ih. 19m., before referred 
 to, in each cycle of golden numbers : Clavius, to meet his view of the 
 amount of that error, put forward the moon's age a day 8 times in 
 2,500 years. As we cannot enter at full length into the explanation, 
 we must content ourselves with giving a set of rules, independent of 
 tables, by which the reader may find Easter for himself in any year, 
 either by the old Calendar or the new. Any one who has much oc- 
 casion to find Easters and moveable feasts should procure Francceur's l 
 tables. 
 
 1 2. Rule for determining Easter Day of the Qregorian Calendar in any 
 year of the new style. To the several parts of the rule are annexed, by 
 way of example, the results for the year 1849. 
 
 I. Add 1 to the given year. (1850). 
 
 II. Take the quotient of the given year divided by 4, neglecting the remainder. 
 (462). 
 
 III. Take 16 from the centurial figures of the given year, if it can be done, and 
 
 take the remainder. (2). 
 
 IV. Take the quotient of III. divided by 4, neglecting the remainder. (0). 
 V. From the sum of L, II., and IV., substract III. (2310). 
 
 VI. Find the remainder of V. divided by 7. (0). 
 
 VII. Subtract VI. from 7 ; this is the number of the dominical letter ^ ?????? 
 
 1 J o 4 o o 7 
 (7; dominical letter G-). 
 
 VIII. Divide I. by 19, the remainder (or 19, if no remainder) is the golden number. 
 (7). 
 
 1 ' Manuel s-Roret. Theorie du Calendrier et collection de tous les Calendriers des 
 Annees passees et futures. . . .ParL. B. Francceur, . . .Paris, a la librairie encyclope- 
 dique de Roret, rue Hautefeuille, 10 bis. 1842.' (12mo.) In this valuable manual, 
 the 35 possible almanacs are given at length, with such preliminary tables as will 
 enable any one to find, by mere inspection, which almanac he is to choose for any 
 year, whether of old or new style. [1866. I may now refer to my own 'Book of 
 Almanacs,' for the same purpose]. 
 
RULE FOR FINDING EASTER DAY. 
 
 225 
 
 IX. From the centurial figures of the year subtract 17, divide by 25, and keep the 
 
 quotient. (0). 
 
 X. Subtract IX. and 15 from the centurial figures, divide by 3, and keep the 
 quotient. (1). 
 
 XI. To VIII. add ten times the next less number, divide by 30, and keep the 
 
 remainder. (7). 
 
 XII. To XI. add X. and IV., and take away III., throwing out thirties, if any. If 
 this give 24, change it into 25. If 25, change it into 26, whenever the 
 golden number is greater than 11. If 0, change it into 30. Thus we have 
 the epact, or age of the Calendar moon at the beginning of the year. (6). 
 
 When the Epact is 23, or less. 
 
 XIII. Subtract XII., the epact, from 45. 
 
 (39). 
 
 XIV. Subtract the epact from 27, divide 
 
 by 7, and k^ep the remainder, or 
 7, if there be no remainder. (7). 
 
 When the Epact is greater than 23. 
 
 XIII. Subtract XII., the epact, from 
 75. 
 
 XIV. Subtract the epact from 57, divide 
 by 7, and keep the remainder, 
 or 7, if there be no remainder. 
 
 XV. To XIII. add VII., the dominical number, (and 7 besides, if XIV. be greater 
 than VII.,) and subtract XIV., the result is the day of March, or if more 
 than 31, subtract 31, and the result is the day of April, on which Easter 
 Sunday falls. (39 ; Easter Day is April 8). 
 
 In the following examples, the several results leading to the final con- 
 clusion are tabulated. 
 
 Given year 
 
 1592 
 
 1637 
 
 1723 
 
 1853 
 
 2018 
 
 4686 
 
 I. 
 
 1593 
 
 1638 
 
 1724 
 
 1854 
 
 2019 
 
 4687 
 
 II. 
 
 398 
 
 409 
 
 430 
 
 463 
 
 504 
 
 1171 
 
 III. 
 
 
 
 
 
 1 
 
 2 
 
 4 
 
 30 
 
 IV. 
 
 
 
 
 
 
 
 
 
 1 
 
 r r 
 
 V. 
 
 1991 
 
 2047 
 
 2153 
 
 2315 
 
 2520 
 
 5835 
 
 VI. 
 
 3 
 
 3 
 
 4 
 
 5 
 
 
 
 4 
 
 VII. 
 
 4 
 
 4 
 
 3 
 
 2 
 
 7 
 
 3 
 
 VIII. 
 
 16 
 
 4 
 
 14 
 
 11 
 
 5 
 
 13 
 
 IX. 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 X. 
 
 
 
 
 
 
 
 1 
 
 1 
 
 10 
 
 XI. 
 
 16 
 
 4 
 
 24 
 
 21 
 
 15 
 
 13 
 
 XII. 
 
 16 
 
 4 
 
 23 
 
 20 
 
 13 
 
 say 30 
 
 XIII. 
 
 29 
 
 41 
 
 22 
 
 25 
 
 32 
 
 45 
 
 XIV. 
 
 4 
 
 2 
 
 4 
 
 7 
 
 7 
 
 6 
 
 XV. 
 
 29 
 
 43 
 
 28 
 
 27 
 
 32 
 
 49 
 
 Easter Day. 
 
 Mar. 29 
 
 Apr. 12 
 
 Mar. 28 
 
 Mar. 27 
 
 Apr. 1 
 
 Apr. 18 
 
 13. 'Rule for determining Easter Day of the Antegregorian Calendar in 
 any year of the old style. To the several parts of the rule are annexed, 
 by way of example, the results for the year 1287. The steps are 
 numbered to correspond with the steps of the Gregorian rule, so that 
 ifc can be seen what augmentations the latter requires. 
 
 I. Set down the given year. (1287). 
 II. Take the quotient of the given year divided by 4, neglecting the remainder 
 
 (321). 
 
 V. Take 4 more than the sum of I. and II. (1612). 
 VI. Find the remainder of V. divided by 7. (2). 
 
 VII. Subtract VI. from 7 ; this is the number of the dominical letter 
 (5 ; dominical letter E)^ 
 
 Q 
 
226 A BUDGET OP PARADOXES. 
 
 VIII. Divide one more than the given year by 19, the remainder (or 19 if no re- 
 mainder) is the golden number. (15). 
 
 XII. Divide 3 less than 11 times VIII. by 30 ; the remainder (or 30 if there be no 
 remainder) is the epact. (12). 
 
 When the Epact is 23, or less. 
 
 XIII. Subtract XII., the epact, from 45, 
 
 (33). 
 
 XIV. Subtract the epact, from 27, divide 
 
 by 7, and keep the remainder, or 
 7, if there be no remainder. (1). 
 
 When the Epact is greater than 23. 
 
 XIII. Subtract XII., the epact, from 
 
 75. 
 
 XIV. Subtract the epact from 57, divide 
 
 by 7, and keep the remainder, 
 or 7, if there be no remainder. 
 
 XV. To XIII. add VII., the dominical number, (and 7 besides if XIV. be greater 
 than VII.,) and subtract XIV., the result is the day of March, or if more 
 than 31, subtract 31, and the result is the day of April, on which Easter 
 Sunday (old style) falls. (37 ; Easter Day is April 6). 
 
 These rules completely represent the old and new Calendars, so far 
 as Master is concerned. For further explanation we must refer to the 
 articles cited at the commencement. 
 
 The annexed is the table of new and full moons of the 
 Gregorian Calendar, cleared of the errors made for the purpose 
 of preventing Easter from coinciding with the Jewish Passover. 
 
 The second table (page 228) contains epacts, or ages of the 
 moon at the beginning of the year : thus in 193 3, the epact is 22 : 
 in 1868 it is 6. This table goes from 1850 to 1999 : should the 
 New Zealander not have arrived by that time, and should the 
 churches of England and Home then survive, the epact table may 
 be continued from their liturgy-books. The way of using the table 
 is as follows : Take the epact of the required year, and find it 
 in the first or last column of the first table, in line with it are 
 seen the calendar days of new and full moon. Thus, when the 
 epact is 17, the new and full moons of March fall on the 13th 
 and 28th. The result is, for the most part, correct : but in a 
 minority of cases there is an error of a day. When this happens, 
 the error is almost always a fraction of a day much less than 
 twelve hours. Thus, when the table gives full moon on the 27th, 
 and the real truth is the 28th, we may be sure it is early on 
 the 28th. For example, the year 1867. The epact is 25, and 
 we find in the table : 
 
 Jv F. M. Ap. M, Ju. Jl> An. & 0. K. D. 
 
 New. ..5+4 5+4 3+2 1,31 29 28- 27 26 25 
 Full ... 20 19-20 19-18 17 16 15 13- 13 11 + 11 
 
 When the truth is the day after *-f is written after the date ; 
 when the day before, . Thus, the new moon of Marches on 
 the 6th ; the full moon of April is on the 18th. 
 
Table of New and Full Moon. 
 
 
 Jan. 
 
 Feb. 
 
 Mar. 
 
 Apr. 
 
 May 
 
 June 
 
 July 
 
 Aug. 
 
 Sep.! 
 
 Oct. 
 
 Nov. 
 
 Dec. 
 
 
 _{ 
 
 29 
 14 
 
 27 
 13 
 
 29 
 14 
 
 27 
 13 
 
 27 
 12 
 
 25 
 11 
 
 25 
 
 10 
 
 23 
 9 
 
 22 1 
 7 1 
 
 21 
 
 7 
 
 20 
 5 
 
 11 
 
 } i 
 
 3 (1 
 
 28 
 13 
 
 26 
 12 
 
 28 
 13 
 
 26 
 12 
 
 26 
 11 
 
 24 
 10 
 
 24 
 9 
 
 22 
 
 8 
 
 21 
 
 6 
 
 20 
 6 
 
 19 
 4 
 
 18 
 4 
 
 } 
 
 "{ 
 
 27 
 12 
 
 25 
 11 
 
 27 
 12 
 
 25 
 11 
 
 25 
 10 
 
 23 
 9 
 
 23 
 8 
 
 21 
 
 7 
 
 20 
 5 
 
 19 
 5 
 
 18 
 3 
 
 17 
 3 
 
 > 
 
 *{ 
 
 26 
 11 
 
 24 
 10 
 
 26 
 11 
 
 24 
 10 
 
 24 
 9 
 
 22 
 8 
 
 22 
 
 7 
 
 20 
 6 
 
 19 
 4 
 
 18 
 4 
 
 17 
 2 
 
 16 
 2,31 
 
 }* 
 
 '{ 
 
 25 
 10 
 
 23 
 9 
 
 25 
 10 
 
 23 
 9 
 
 23 
 8 
 
 21 
 
 7 
 
 21 
 6 
 
 19 
 5 
 
 18 
 3 
 
 17 
 3 
 
 16 
 1 
 
 15 
 1,30 
 
 } <> 
 
 <>{ 
 
 24 
 9 
 
 22 
 
 8 
 
 24 
 9 
 
 22 
 8 
 
 22 
 
 7 
 
 20 
 6 
 
 20 
 5 
 
 18 
 4 
 
 17 
 2 
 
 16 
 2,31 
 
 15 
 
 30 
 
 14 
 
 29 
 
 } 
 
 '{ 
 
 23 
 8 
 
 21 
 
 7 
 
 23 
 8 
 
 21 
 
 7 
 
 21 
 6 
 
 19 
 5 
 
 19 
 4 
 
 17 
 3 
 
 16 
 1 
 
 15 
 
 1,30 
 
 14 
 29 
 
 13 
 
 28 
 
 } i 
 
 P 
 
 22 
 7 
 
 20 
 6 
 
 22 
 
 7 
 
 20 
 6 
 
 20 
 5 
 
 18 
 4 
 
 18 
 3 
 
 16 
 2,31 
 
 15 
 30 
 
 14 
 29 
 
 13 
 
 28 
 
 12 
 
 27 
 
 }8 
 
 o 
 
 21 
 6 
 
 19 
 5 
 
 21 
 
 6 
 
 19 
 5 
 
 19 
 4 
 
 17 
 3 
 
 17 
 
 2 
 
 15 
 1,30 
 
 14 
 29 
 
 13 
 
 28 
 
 12 
 
 27 
 
 11 
 26 
 
 }_ 
 
 10{ 
 
 20 
 5 
 
 18 
 4 
 
 20 
 5 
 
 18 
 4 
 
 18 
 3 
 
 16 
 2 
 
 16 
 1,31 
 
 1! 
 29 
 
 13 
 
 28 
 
 12 
 27 
 
 11 
 26 
 
 10 
 25 
 
 }10 
 
 {l 
 
 19 
 4 
 
 17 
 3 
 
 19 
 4 
 
 17 
 3 
 
 17 
 2 
 
 15 
 
 1,30 
 
 15 
 30 
 
 13 
 28 
 
 12 
 
 27 
 
 11 
 26 
 
 10 
 25 
 
 9 
 24 
 
 } 
 
 13 {| 
 
 18 
 
 3 
 
 16 
 2 
 
 18 
 3 
 
 16 
 2 
 
 16 
 
 1,31 
 
 14 
 
 29 
 
 14 
 
 29 
 
 12 
 
 27 
 
 11 
 26 
 
 10 
 25 
 
 9 
 24 
 
 8 
 23 
 
 }! 
 
 ( 
 
 17 
 2 
 
 15 
 1 
 
 17 
 2 
 
 15 
 
 1,30 
 
 15 
 30 
 
 13 
 28 
 
 13 
 28 
 
 11 
 26 
 
 10 
 25 
 
 9 
 24 
 
 8 
 23 
 
 7 
 22 
 
 } 
 
 { 
 
 16 
 1,31 
 
 14 
 
 16 
 1,31 
 
 14 
 29 
 
 14 
 29 
 
 12 
 27 
 
 12 
 
 27 
 
 10 
 25 
 
 9 
 24 
 
 8 
 23 
 
 7 
 22 
 
 6 
 21 
 
 }14 
 
 15 { 
 
 15 
 
 30 
 
 13 
 28 
 
 15 
 
 30 
 
 13 
 
 28 
 
 13 
 
 28 
 
 11 
 26 
 
 11 
 
 26 
 
 9 
 24 
 
 8 
 23 
 
 7 
 22 
 
 6 
 21 
 
 5 
 20 
 
 }15 
 
 16 { 
 
 14 
 
 29 
 
 12 
 
 27 
 
 14 
 29 
 
 12 
 27 
 
 12 
 27 
 
 10 
 25 
 
 10 
 25 
 
 8 
 23 
 
 7 
 22 
 
 6 
 21 
 
 5 
 20 
 
 4 
 19 
 
 }16 
 
 17 { 
 
 13 
 
 28 
 
 11 
 26 
 
 13 
 
 28 
 
 11 
 26 
 
 11 
 26 
 
 9 
 24 
 
 9 
 24 
 
 7 
 22 
 
 6 
 21 
 
 5 
 20 
 
 4 
 19 
 
 3 
 18 
 
 }17 
 
 18 { 
 
 12 
 
 27 
 
 10 
 25 
 
 12 
 
 27 
 
 10 
 25 
 
 10 
 25 
 
 8 
 23 
 
 8 
 23 
 
 6 
 21 
 
 5 
 
 20 
 
 4 
 19 
 
 3 
 18 
 
 2 
 17 
 
 }18 
 
 19 { 
 
 11 
 26 
 
 9 
 24 
 
 11 
 26 
 
 9 
 24 
 
 9 
 24 
 
 7 
 22 
 
 7 
 22 
 
 5 
 20 
 
 4 
 19 
 
 3 
 18 
 
 2 
 17 
 
 1,31 
 16 
 
 }j? 
 
 20 { 
 
 10 
 25 
 
 8 
 23 
 
 10 
 25 
 
 8 
 23 
 
 8 
 23 
 
 6 
 21 
 
 6 
 21 
 
 4 
 19 
 
 3 
 18 
 
 2 
 17 
 
 1,31 
 16 
 
 30 
 15 
 
 } 20 
 
 21 { 
 
 9 
 24 
 
 7 
 22 
 
 9 
 24 
 
 7 
 22 
 
 7 
 22 
 
 5 
 
 20 
 
 5 
 20 
 
 3 
 18 
 
 2 
 17 
 
 1,31 
 16 
 
 29 
 15 
 
 29 
 14 
 
 } 
 
 22 { 
 
 8 
 23 
 
 6 
 21 
 
 8 
 23 
 
 6 
 21 
 
 6 
 
 21 
 
 4 
 19 
 
 4 
 19 
 
 2 
 17 
 
 1,30 
 16 
 
 30 
 15 
 
 28 
 14 
 
 28 
 13 
 
 } 22 
 
 23 { 
 
 7 
 22 
 
 5 
 
 20 
 
 7 
 22 
 
 5 
 
 20 
 
 5 
 
 20 
 
 3 
 
 18 
 
 3 
 
 18 
 
 1,31 
 16 
 
 29 
 15 
 
 29 
 14 
 
 27 
 13 
 
 27 
 12 
 
 } 23 
 
 24 { 
 
 6 
 21 
 
 5 
 19 
 
 6 
 21 
 
 5 
 19 
 
 4 
 19 
 
 3 
 
 17 
 
 2 
 17 
 
 1,30 
 15 
 
 29 
 14 
 
 28 
 13 
 
 27 
 12 
 
 26 
 11 
 
 } 24 
 
 25 { 
 
 5 
 
 20 
 
 4 
 19 
 
 5 
 
 20 
 
 4 
 19 
 
 3 
 
 18 
 
 2 
 
 17 
 
 1,31 
 16 
 
 29 
 15 
 
 28 
 13 
 
 27 
 13 
 
 26 
 11 
 
 25 
 
 11 
 
 } 25 
 
 26 { 
 
 4 
 19 
 
 3 
 
 18 
 
 4 
 19 
 
 3 
 
 18 
 
 2 
 17 
 
 1,30 
 16 
 
 30 
 15 
 
 28 
 14 
 
 27 
 12 
 
 26 
 12 
 
 25 
 10 
 
 24 
 10 
 
 } 26 
 
 27 { 
 
 3 
 18 
 
 2 
 
 17 
 
 3 
 18 
 
 2 
 
 17 
 
 1,31 
 16 
 
 29 
 15 
 
 29 
 14 
 
 27 
 13 
 
 26 
 11 
 
 25 
 11 
 
 24 
 9 
 
 ,23 
 9 
 
 } 27 
 
 28 { 
 
 2 
 17 
 
 1 
 16 
 
 2 
 17 
 
 1,30 
 16 
 
 30 
 15 
 
 28 
 14 
 
 28 
 13 
 
 26 
 12 
 
 25 
 10 
 
 24 
 10 
 
 23 
 8 
 
 22 
 8 
 
 !} 
 
 29 { 
 
 1,31 
 16 
 
 15 
 
 1,31 
 16 
 
 29 
 15 
 
 29 
 14 
 
 27 
 13 
 
 27 
 12 
 
 25 
 11 
 
 24 
 9 
 
 23 
 9 
 
 22 
 
 7 
 
 21 
 
 ts 
 
 30 { 
 
 1 30 
 ! 15 
 
 28 
 14 
 
 30 
 15 
 
 28 
 14 
 
 28 
 13 
 
 26 
 12 
 
 26 
 11 
 
 24 
 10 
 
 23 
 
 8 
 
 22 
 8 
 
 21 
 6 
 
 20 
 6 
 
 11 3 
 
 
 .Tan. 
 
 Feb. 
 
 Mar. 
 
 Apr. 
 
 May 
 
 June 
 
 July 
 
 Aug. 
 
 Sep. 
 
 Oct. 
 
 Nov. 
 
 ' Dec. 
 
 
 Q 2 
 
228 
 
 A BUDGET OF PABADOXES. 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 I 6 
 
 7 
 
 8 
 
 9 
 
 185 
 
 17 
 
 28 
 
 19 
 
 20 
 
 2 
 
 12 
 
 23 
 
 4 
 
 15 
 
 26 
 
 186 
 
 7 
 
 18 
 
 30 
 
 11 
 
 22 
 
 3 
 
 14 
 
 25 
 
 6 
 
 17 
 
 187 I 28 
 
 9 
 
 20 
 
 1 
 
 12 
 
 23 
 
 4 
 
 15 
 
 26 
 
 7 
 
 188 
 
 18 
 
 30 
 
 11 
 
 22 
 
 3 
 
 14 
 
 25 
 
 6 
 
 17 
 
 28 
 
 189 
 
 9 
 
 21 
 
 1 
 
 12 
 
 23 
 
 4 
 
 15 
 
 26 
 
 7 
 
 18 
 
 190 
 
 29 
 
 10 
 
 21 
 
 2 
 
 13 
 
 24 
 
 5 
 
 16 
 
 27 
 
 8 
 
 191 
 
 19 
 
 30 
 
 11 
 
 22 
 
 3 
 
 14 
 
 26 
 
 6 
 
 17 
 
 29 
 
 192 
 
 10 
 
 21 
 
 2 
 
 13 
 
 24 
 
 5 
 
 16 
 
 27 
 
 8 
 
 19 
 
 193 
 
 30 
 
 11 
 
 22 
 
 3 
 
 14 
 
 26 
 
 6 
 
 17 
 
 29 
 
 10 
 
 194 
 
 21 
 
 2 
 
 13 
 
 24 
 
 5 16 
 
 27 
 
 8 
 
 19 
 
 30 
 
 195 
 
 11 
 
 22 
 
 3 
 
 14 
 
 26 
 
 6 
 
 17 
 
 29 
 
 10 
 
 21 
 
 196 
 
 2 
 
 13 
 
 24 
 
 5 
 
 16 
 
 27 
 
 8 
 
 19 
 
 30 
 
 11 
 
 197 
 
 22 
 
 3 
 
 14 
 
 26 
 
 6 
 
 17 
 
 29 
 
 10 
 
 21 
 
 2 
 
 198 
 
 13 
 
 24 
 
 5 
 
 16 
 
 27 
 
 8 
 
 19 
 
 30 
 
 11 
 
 22 
 
 199 
 
 3 
 
 14 
 
 26 
 
 6 
 
 17 
 
 29 
 
 10 
 
 21 
 
 2 
 
 13 
 
 I now introduce a small paradox of my own : and as I am not 
 able to prove it, I am compelled to declare that any one who 
 shall dissent must be either very foolish or very dishonest, and 
 will make me quite uncomfortable about the state of his soul. 
 This being settled o"nce for all, I proceed to say that the necessity 
 of arriving at the truth about the assertions that the Nicene 
 Council laid down astronomical tests led me to look at Fathers, 
 Church histories, &c. to an extent which I never dreamed of 
 before. One conclusion which I arrived at was, that the Nicene 
 Fathers had a knack of sticking to the question which many later 
 councils could not acquire. In our own day, it is not permitted 
 to Convocation seriously to discuss any one of the points which 
 are bearing so hard upon their resources of defence the cursing 
 clauses of the Athanasian Creed, for example. And it may be 
 collected that the prohibition arises partly from fear that there 
 is no saying where a beginning, if allowed, would end. There 
 seems to be a suspicion that debate, once let loose, would play 
 up old Trent with the liturgy, and bring the whole book to book. 
 But if any one will examine the real Nicene Creed, without the 
 augmentation, he will admire the way in which the framers stuck 
 to the point, and settled what they had to decide, according to 
 
EASTER AND PASSOVER CLAVIUS. 229 
 
 their view of it. With such a presumption of good sense in 
 their favour, it becomes easier to believe in any claim which may 
 be made on their behalf to tact or sagacity in settling any other 
 matter. And I strongly suspect such a claim may be made for 
 them on the Easter question. 
 
 I collect from many little indications, both before and after 
 the Council, that the division of the Christian world into Judai- 
 cal and Grentile, though not giving rise to a sectarian distinction 
 expressed by names, was of far greater force and meaning than 
 historians prominently admit. I took note of many indications 
 of this, but not notes, as it was not to my purpose. If it were 
 so, we must admire the discretion of the Council. The Easter 
 question was the fighting ground of the struggle : the Eastern 
 or Judaical Christians, with some varieties of usage and meaning, 
 would have the Passover itself to be the great feast, but taken in 
 a Christian sense ; the Western or Gentile Christians, would have 
 the commemoration of the Kesurrection, connected with the 
 Passover only by chronology. To shift the Passover in time, 
 under its name, Pascha, without allusion to any of the force of 
 the change, was gently cutting away the ground from under the 
 feet of the Conservatives. And it was done in a very quiet way : no 
 allusion to the precise character of the change ; no hint that the 
 question was about two different festivals : * all the brethren in 
 the East, who formerly celebrated this festival at the same time 
 as the Jews, will in future conform to the Romans and to us.' 
 The Judaizers meant to be keeping the Passover as a Christian 
 feast : they are gently assumed to be keeping, not the Passover, 
 but a Christian feast ; and a doctrinal decision is quietly, but 
 efficiently, announced under the form of a chronological ordin- 
 ance. Had the Council issued theses of doctrine, and excom- 
 municated all dissentients, the rupture of the East and West 
 would have taken place earlier by centuries than it did. The 
 only place in which I ever saw any part of my paradox ad- 
 vanced, was in an article in the Examiner newspaper, towards 
 the end of 1866, after the above was written. 
 
 A story about Christopher Clavius, the workman of the new 
 Calendar. I chanced to pick up ' Albertus Pighius Campensis de 
 sequinoctiorum solsticiorumque inventione .... Ejusdem de 
 ratione Paschalis celebrationis, De que Restitutione ecclesiastic! 
 Kalendarii,' Paris, 1520, folio. On the title-page were decayed 
 words followed by < . . hristophor . . C . . ii, 1556 (or 8),' the 
 last blank not entirely erased by time, but showing the lower 
 halves of an I and of an a, and rather too much room for a v. 
 It looked very like E Libris Christophori Clavii 1556. By the 
 
230 A BUDGET OF PAKADOXES. 
 
 courtesy of some members of the Jesuit body in London, I 
 procured a tracing of the signature of Clavius from Rome, and 
 the shapes of the letters, and the modes of junction and disjunc- 
 tion, put the matter beyond question. Even the extra space 
 was explained ; he wrote himself Clauius. Now in 1556, 
 Clavius was nineteen years old : it thus appears probable that 
 the framer of the Gregorian Calendar was selected, not merely 
 as a learned astronomer, but as one who had attended to the 
 calendar, and to works on its reformation, from early youth. 
 When on the subject I found reason to think that Clavius had 
 really read this work, and taken from it a phrase or iwo and a 
 notion or two. Observe the advantage of writing the baptismal 
 name at full length. 
 
 The discovery of a general resolution of all superior finite equa- 
 tions, of every numerical both algebraick and transcendent 
 form. By A. P. Vogel, mathematician at Leipzick. Leipzick 
 and London, 1845, 8vo. 
 
 This work is written in the English of a German who has not 
 mastered the idiom : but it is always intelligible. It professes to 
 solve equations of every degree c in a more extent sense, and till 
 to every degree of exactness.' The general solution of equations 
 of all degrees is a vexed question, which cannot have the mys- 
 terious interest of the circle problem, and is of a comparatively 
 modern date. Mr. Vogel announces a forthcoming treatise in 
 which are resolved the ; last impossibilities of pure mathematics.' 
 
 Elective Polarity the Universal Agent. By Frances Barbara 
 Burton, authoress of t Astronomy familiarized,' * Physical As 
 tronoruy/ &c. London, 1845, 8vo. 
 
 The title gives a notion of the theory. The first sentence 
 states, that 12,500 years ago a Lyrao was the pole-star, and 
 attributes the immense magnitude of the now fossil animals to a 
 star of such 'polaric intensity as Vega pouring its magnetic 
 streams through our planet.' Miss Burton was a lady of property, 
 and of very respectable acquirements, especially in Hebrew ; she 
 was eccentric in all things. 
 
 1867. Miss Burton is revived by the writer of a book on 
 meteorology which makes use of the planets : she is one of his 
 leading minds. 
 
 In the year 1845 the old Mathematical Society was merged in 
 the Astronomical Society. The circle-squarers, &c., thrive more 
 
SPECULATIVE THOUGHT IN ENGLAND. 231 
 
 in England than in any other country : there are most weeds 
 where there is the largest crop. Speculation, though not en- 
 couraged by our Government so much as by those of the Conti- 
 nent, has had, not indeed such forcing, but much wider diffusion : 
 few tanks, but many rivulets. On this point I quote from the 
 preface to the reprint of the work of Eamchundra, which I 
 superintended for the late Court of Directors of the East India 
 Company. 
 
 4 That sound judgment which gives men well to know whafc is best 
 for them, as well as that faculty of invention which leads to develop, 
 ment of resources and to the increase of wealth and comfort, are both 
 materially advanced, perhaps cannot rapidly be advanced without, a 
 great taste for pure speculation among the general mass of the people, 
 down to the lowest of those who can read and write. England is a 
 marked example. Many persons will be surprised at this assertion. 
 They imagine that our country is the great instance of the refusal of 
 all unpractical knowledge in favour of what is useful. I affirm, on the 
 contrary, that there is no country in Europe in which there has been 
 so wide a diffusion of speculation, theory, or what other unpractical 
 word the reader pleases. In our country, the scientific society is 
 always formed and maintained by the people ; in every other, the 
 scientific academy most aptly named has been the creation of the 
 government, of which it has never ceased to be the nursling. In all 
 the parts of England in which manufacturing pursuits have given the 
 artisan some command of time, the cultivation of mathematics and 
 other speculative studies has been, as is well known, a very frequent 
 occupation. In no other country has the weaver at his loom bent over 
 the Principia of Newton ; in no other country has the man of weekly 
 wages maintained his own scientific periodical. With us, since the 
 beginning of the last century, scores upon scores perhaps hundreds, 
 for I am far from knowing all of annuals have run, some their ten 
 years, some their half-century, some their century and a half, con- 
 taining questions to be answered, from which many of our examiners 
 in the Universities have culled materials for the academical contests. 
 And these questions have always been answered, and in cases without 
 number by the lower order of purchasers, the mechanics, the weavers, 
 and the printers' workmen. I cannot here digress to point out the 
 manner in which the concentration of manufactures, and the general 
 diffusion of education, have affected the state of things ; I speak of the 
 time during which the present system took its rise, and of the circum- 
 stances under which many of its most effective promoters were trained. 
 In all this there is nothing which stands out, like the state-nourished 
 academy, with its few great names and brilliant single achievements. 
 This country has differed from all others in the wide diffusion of the 
 disposition to speculate, which disposition has found its place among 
 the ordinary habits of life, moderate in its action, healthy in its 
 amount.' 
 
232 A BUDGET OF PARADOXES. 
 
 Among the most remarkable proofs of the diffusion of specu- 
 lation was the Mathematical Society, which flourished from 1717 
 to 1845. Its habitat was Spitalfields, and I think most of its 
 existence was passed in Crispin Street, It was originally a plain 
 society, belonging to the studious artisan. The members met for 
 discussion once a week ; and I believe I am correct in saying that 
 each man had his pipe, his pot, and his problem. One of their 
 old rules was that, ' If any member shall so far forget himself and 
 the respect due to the Society as in the warmth of debate to 
 threaten or offer personal violence to any other member, he shall 
 be liable to immediate expulsion, or to pay such fine as the 
 majority of the members present shall decide.' But their great 
 rule, printed large on the back of the title page of their last book 
 of regulations, was ' By the constitution of the Society, it is the 
 duty of every member, if he be asked any mathematical or philo- 
 sophical question by another member, to instruct him in the 
 plainest and easiest manner he is able.' We shall presently see 
 that, in old time, the rule had a more homely form. 
 
 I have been told that De Moivre was a member of this Society, 
 This I cannot verify : circumstances render it unlikely ; even 
 though the French refugees clustered in Spitalfields ; many of 
 them were of the Society, which there is some reason to think 
 was founded by them. But Dollond, Thomas Simpson, Saun- 
 derson, Crossley, and others of known name, were certainly 
 members. The Society gradually declined, and in 1845 was 
 reduced to nineteen members. An arrangement was made by 
 which sixteen of these members, who were not already in the 
 Astronomical Society became Fellows without contribution, all 
 the books and other property of the old Society being transferred 
 to the new one. I was one of the committee which made the 
 preliminary inquiries, and the reason of the decline was soon 
 ^manifest. The only question which could arise was whether the 
 members of the society of working men for this repute still 
 continued were of that class of educated men who could as- 
 sociate with the Fellows of the Astronomical Society on terms 
 agreeable to all parties. We found that the artisan element had 
 been extinct for many years ; there was not a man but might, as 
 to education, manners, and position, have become a Fellow in the 
 usual way. The fact was that life in Spitalfields had become 
 harder : and the weaver could only live from hand to mouth, and 
 not up to the brain. The material of the old Society no longer 
 existed. 
 
THE OLD MATHEMATICAL SOCIETY. 233 
 
 In 1798, experimental lectures were given, a small charge for 
 admission being taken at the door : by this hangs a tale and a 
 song. Many years ago, I found among papers of a deceased friend, 
 who certainly never had anything to do with the Society, and 
 who passed all his life far from London, a song, headed 6 Song 
 sung at a Mathematical Society in London, at a dinner given to 
 Mr. Fletcher, a solicitor, who had defended the Society gratis.' 
 Mr. Williams, the Assistant Secretary of the Astronomical Society, 
 formerly Secretary of the Mathematical Society, remembered that 
 the Society had had a solicitor named Fletcher among the 
 members. Some years elapsed before it struck me that my old 
 friend Benjamin Grompertz, who had long been a member, might 
 have some recollection of the matter. The following is an extract 
 of a letter from him (July 9, 1861) : 
 
 As to the Mathematical Society, of which I was a member when 
 only 18 years of age, [Mr. G. was borii in 1779], having been, contrary 
 to the rules, elected under the age of 21. How I came to be a 
 member of that Society and continued so until it joined the Astro- 
 nomical Society, and was then the President was : I happened to 
 pass a bookseller's small shop, of second-hand books, kept by a poor 
 taylor, but a good mathematician, John Griffiths. I was very pleased 
 to meet a mathematician, and I asked him if he would give me some 
 lessons ; and his reply was that I was more capable to teach him, but 
 he belonged to a society of mathematicians, and he would introduce 
 me. I accepted the offer, and I was elected, and had many scholars 
 then to teach, as one of the rules was, if a member asked for informa- 
 tion, and applied to any one who could give it, he was obliged to give 
 it, or fine one penny. Though I might say much with respect to the 
 Society which would be interesting, I will for the present reply only to 
 your question. I well knew Mr. Fletcher, who was a very clever and 
 very scientific person. He did, as solicitor, defend an action brought 
 by an informer against the Society I think for 5,OOOL for giving 
 lectures to the public in philosophical subjects [i.e. for unlicensed 
 public exhibition with money taken at the doors]. I think the price 
 for admission was one shilling, and we used to have, if I rightly 
 recollect, from two to three hundred visitors. Mr. Fletcher was suc- 
 cessful in his defence, and we got out of our trouble. There was a 
 collection made to reward his services, but he did not accept of any 
 reward : and I think we gave him a dinner, as you state, and enjoyed 
 ourselves ; no doubt with astronomical songs and other songs ; but my 
 recollection does not enable me to say if the astronomical song was a 
 drinking song. I think the anxiety caused by that action was the 
 cause of some of the members' death. [They had, no doubt, broken 
 the law in ignorance ; and by the sum named, the informer must have 
 been present, and sued for a penalty on every shilling he could prove 
 to have been taken]. 
 
234 A BUDGET OF PARADOXES. 
 
 I by no means guarantee that the whole song I proceed to give 
 is what was sung at the dinner : I suspect, by the completeness of 
 the chain, that augmentations have been made. My deceased 
 friend was just the man to add some verses, or the addition may 
 have been made before it came into his hands, or since his decease, 
 for the scraps containing the verses passed through several hands 
 before they came into mine. We may, however, be pretty sure 
 that the original is substantially contained in what is given, and 
 that the character is therefore preserved. I have had myself to 
 repair damages every now and then, in the way of conjectural 
 restoration of defects caused by ill-usage. 
 
 THE ASTRONOMER'S DRINKING- SONG. 
 
 * WHOE'ER would search the starry sky, 
 
 Its secrets to divine, sir, 
 Should take his glass I mean, should try 
 
 A glass or two of wine, sir ! 
 True virtue lies in golden mean, 
 
 And man must wet his clay, sir ; 
 Join these two maxims, and 'tis seen 
 
 He should drink his bottle a day, sir ! 
 
 Old Archimedes, reverend sage ! 
 
 By trump of fame renowned, sir, 
 Deep problems solved in every page, 
 
 And the sphere's curved surface found, sir: 
 Himself he would have far outshone, 
 
 And borne a wider sway, sir, 
 Had he our modern secret known, 
 
 And drank his bottle a day, sir ! 
 
 When Ptolemy, now long ago, 
 
 Believed the earth stood still, sir, 
 He never would have blundered so, 
 
 Had he but drunk his fill, sir : 
 He'd then have felt 1 it circulate, 
 
 And would have learnt to say, sir, 
 The true way to investigate 
 
 Is to drink your bottle a day, sir ! 
 
 Copernicus, that learned wight, 
 
 The glory of his nation, 
 With draughts of wine refreshed his sight, 
 
 And saw the earth's rotation ; 
 
 1 Dr. Whewell, when I communicated this song to him, started the opinion, which 
 I had before him, that this was a very good idea, of which too little was made. 
 
THE ASTKONOMER'S DKINKING-SONG. 235 
 
 Each planet then its orb described, 
 
 The moon got under way, sir ; 
 These truths from nature he imbibed 
 
 For he drank his bottle a day, sir ! 
 
 The noble 1 Tycho placed the stars, 
 
 Each in its due location ; 
 He lost his nose 2 by spite of Mars, 
 
 But that was no privation : 
 Had he but lost his mouth, I grant 
 
 He would have felt dismay, sir, 
 Bless you ! he knew what he should want 
 
 To drink his bottle a day, sir ! 
 
 Cold water makes no lucky hits ; 
 
 On mysteries the head runs : 
 Small drink let Kepler time his wits 
 
 On the regular polyhedrons : 
 He took to wine, and it changed the chime, 
 
 His genius swept away, sir, 
 Through area varying 3 as the time 
 
 At the rate of a bottle a day, sir ! 
 
 Poor Galileo, forced to rat 
 
 Before the Inquisition, 
 JG/ pur si muove was the pat 
 
 He gave them in addition : 
 He meant, whate'er you think you prove, 
 
 The earth must go its way, sirs ; 
 Spite of your teeth I'll make it move, 
 
 For I'll drink my bottle a day, sirs ! 
 
 Great Newton, who was never beat 
 
 Whatever fools may think, sir ; 
 Though sometimes he forgot to eat, 
 
 He never forgot to drink, sir : 
 Descartes 4 took nought but lemonade, 
 
 To conquer him was play, sir ; 
 The first advance that Newton made 
 
 Was to drink his bottle a day, sir ! 
 
 1 The common epithet of rank: nobilis Tycho, as he was a nobleman. The writer 
 had been at history. 
 
 2 He lost it in a duel, with Manderupius Pasbergius. A contemporary, T. B. 
 Laurus, insinuates that they fought to settle which was the best mathematician ! 
 This seems odd, but it must be remembered they fought in the dark, ' in tenebris 
 densis ' ; and it is a nice problem to shave off a nose in the dark, without any other 
 harm. 
 
 8 Keferring to Kepler's celebrated law of planetary motion. He had previously 
 wasted his time on analogies between the planetary orbits and the polyhedrons. 
 
 4 As great a lie as ever was told: but in 1800 a compliment to Newton without a 
 fling at Descartes would have been held a lopsided structure. 
 
236 A BUDGET OF PARADOXES. 
 
 D'Alembert, Euler, and Clairaut, 
 
 Though they increased our store, sir, 
 Much further had been seen to go 
 
 Had they tippled a little more, sir ! 
 Lagrange gets mellow with Laplace, 
 
 And both are wont to say, sir, 
 The philosophe who's not an ass 
 
 Will drink his bottle a day, sir ! 
 
 Astronomers ! what can avail 
 
 Those who calumniate us ; 
 Experiment can never fail 
 
 With such an apparatus : 
 Let him who'd have his merits known 
 
 Remember what I say, sir ; 
 Fair science shines on him alone 
 
 Who drinks his bottle a day, sir ! 
 
 How light we reck of those who mock 
 
 By this we'll make to appear, sir, 
 We'll dine by the sidereal * clock 
 
 For one more bottle a year, sir : 
 But choose which pendulum you will, 
 
 You'll never make your way, sir, 
 Unless you drink and drink your fill, 
 
 At least a bottle a day, sir ! ' 
 
 Old times are changed, old manners gone ! 
 
 There is a new Mathematical Society, and I am, at this present 
 writing (1866), its first President. We are very high in the 
 newest developements, and bid fair to take a place among the 
 scientific establishments. Benjamin Grompertz, who was President 
 of the old Society when it expired, was the link between the old 
 and new body : he was a member of ours at bis death. But not 
 a drop of liquor is seen at our meetings, except a decanter of 
 water : all our heavy is a fermentation of symbols ; and we do not 
 draw it mild. There is no penny fine for reticence or occult 
 science ; and as to a song ! not the ghost of a chance. 
 
 1826. The time may have come when the original documents 
 connected with the discovery of Neptune may be worth revising. 
 The following are extracts from the Athenceum of October 3 and 
 October 17 : 
 
 1 The sidereal day is about four minutes short of the solar ; there are 366 sidereal 
 days in the year. 
 
LETTER FROM SIR JOHN IIERSCHEL. 237 
 
 LE VERRIER'S PLANET. 
 
 We have received, at the last moment before making up for 
 press, the following letter from Sir John Herschel, in reference 
 to the matter referred to in the communication from Mr. Hind 
 given below : 
 
 Collingwood, Oct. 1. 
 
 * In my address to the British Association assembled at Southampton, 
 on the occasion of my resigning the chair to Sir R. Murchison, I stated, 
 among the remarkable astronomical events of the last twelvemonth, 
 that it had added a new planet to our list, adding, " it has done more, 
 it has given us the probable prospect of the discovery of another. 
 We see it as Columbus saw America from the shores of Spain. Its 
 movements have been felt, trembling along the far- reaching line of our 
 analysis, with a certainty hardly inferior to that of ocular demonstra- 
 tion." These expressions are not reported in any of the papers which 
 profess to give an account of the proceedings, but I appeal to all pre- 
 sent whether they were not used. 
 
 Give me leave to state my reasons for this confidence ; and, in so 
 doing, to call attention to some facts which deserve to be put on record 
 in the history of this noble discovery. On July 12, 1842, the late 
 illustrious astronomer, Bessel, honoured me with a visit at my present 
 residence. On the evening of that day, conversing on the great work 
 of the planetary reductions undertaken by the Astronomer Royal then 
 in progress, and since published, 1 M. Bessel remarked that the mo- 
 tions of Uranus, as he had satisfied himself by careful examination of 
 the recorded observations, could not be accounted for by the pertur- 
 bations of the known planets ; and that the deviations far exceeded any 
 possible limits of error of observation. In reply to the question, 
 Whether the deviations in question might not be due to the action 
 of an unknown planet ? he stated that he considered it highly pro- 
 bable that such was the case, being systematic, and such as might 
 be produced by an exterior planet. I then inquired whether he had 
 attempted, from the indications afforded by these perturbations, to 
 discover the position of the unknown body, in order that " a hue and 
 cry " might be raised for it. From his reply, the words of which I do 
 not call to mind, I collected that he had not then gone into that in- 
 quiry ; but proposed to do so, having now completed certain works 
 which had occupied too much of his time. And, accordingly, in a 
 letter which I received from him after his return to Konigsberg, dated 
 November 14, 1842, he says, " In reference to our conversation at 
 Collingwood, I announce to you (melde ich Ihnen) that Uranus is not 
 forgotten." Doubtless, therefore, among his papers will be found some 
 researches on the subject. 
 
 1 The expense of this magnificent work was defrayed by Government grants, ob- 
 tained, at the instance of the British Association, in Ib33, 
 
233 A BUDGET OF PARADOXES. 
 
 The remarkable calculations of M. Le Yerrier which have pointed 
 out, as now appears, nearly the true situation of the new planet, by 
 resolving the inverse problem of the perturbations if uncorroborated 
 by repetition of the numerical calculations by another hand, or by 
 independent investigation from another quarter, would hardly justify- 
 so strong an assurance as that conveyed by my expressions above 
 alluded to. But it was known to me, at that time, (I will take the 
 liberty to cite the Astronomer Royal as my authority) that a similar 
 investigation had been independently entered into, and a conclusion as 
 to the situation of the new planet very nearly coincident with M. Le 
 Verrier's arrived at (in entire ignorance of his conclusions), by a young 
 Cambridge mathematician, Mr. Adams ; who will, I hope, pardon this 
 mention of his name (the matter being one of great historical moment), 
 and who will, doubtless, in his own good time and manner, place his 
 calculations before the public, 
 
 J. F. W. HERSCHEL.' 
 
 Discovery of Le Vermeils Planet. 
 
 Mr. Hind announces to the Times that he has received a letter 
 from Dr. Briinnow, of the Eoyal Observatory at Berlin, giving the 
 very important information that Le Verrier's planet was found by 
 M. Galle, on the night of September 23. ' In announcing this 
 grand discovery,' he says, ' I think it better to copy Dr. Briinnow's 
 letter.' 
 
 . Berlin, Sept. 25. 
 
 * My dear Sir, M. Le Terrier's planet was discovered here the 23rd 
 of September, by M. Galle. It is a star of the 8th magnitude, but 
 with a diameter of two or three seconds. Here are its places : 
 
 h. m. s. R. A. Declination. 
 
 Sept. 23, 12 14-6 M.T. 328 19' 16-0" 13 24' 8-2" 
 Sept. 24, 8 54 4O9 M.T. 328 18' 14-3" 13 24' 297" 
 
 The planet is now retrograde, its motion amounting daily to four 
 seconds of time. 
 
 Yours most respectfully, 
 
 4 This discovery,' Mr. Hind says, c may be justly considered one 
 of the greatest triumphs of theoretical Astronomy ; ' and he adds, 
 in a postscript, that the planet was observed at Mr. Bishop's 
 Observatory, in the Regent's Park, on Wednesday night, not- 
 withstanding the moonlight and hazy sky. < It appears bright,' 
 he says, ' and with a power of 320 I can see the disc. The 
 following position is the result of instrumental comparisons with 
 33 Aquarii : 
 
THE DISCOVERY OF NEPTUNE. 239 
 
 Sept. 30, at 8h. 16m. 21s. Greenwich mean time 
 
 Bight ascension of planet V . 21h. 52m. 47*15s. 
 South declination . > V ' V 13 27' 20".' 
 
 THE NEW PLANET. 
 
 Cambridge Observatory, Oct. 15. 
 
 The allusion made by Sir John Herschel, in his letter contained in 
 the Athenceum of October 3, to the theoretical researches of Mr. 
 Adams, respecting the newly- discovered planet, has induced me to 
 request that you would make the following communication public. It 
 is right that I should first say that I have Mr. Adams's permission to 
 make the statements that follow, so far as they relate to his labours. 
 I do not propose to enter into a detail of the steps by which Mr. Adams 
 was led, by his spontaneous and independent researches, to a conclusion 
 that a planet must exist more distant than Uranus. The matter is of 
 too great historical moment not to receive a more formal record than 
 it would be proper to give it here. My immediate object is to show, 
 while the attention of the scientific public is more particularly directed 
 to the subject, that, with respect to this remarkable discovery, English 
 astronomers may lay claim to some merit. 
 
 Mr. Adams formed the resolution of trying, by calculation, to account 
 for the anomalies in the motion of Uranus on the hypothesis of a more 
 distant planet, when he was an undergraduate in this University, and 
 when his exertions for the academical distinction, which he obtained 
 in January 1843, left him no time for pursuing the research. In the 
 course of that year, he arrived at an approximation to the position of 
 the supposed planet ; which, however, he did not consider to be worthy 
 of confidence, on account of his not having employed a sufficient numlcM. 
 of observations of Uranus. Accordingly, he requested my intervention 
 to obtain for him the early Greenwich observations, then in course of 
 reduction ; which the Astronomer Royal immediately supplied, in the 
 kindest possible manner. This was in February, 1844. In September, 
 1845, Mr. Adams communicated to me values which he had obtained 
 for the heliocentric longitude, excentricity of orbit, longitude of peri- 
 helion, and mass, of an assumed exterior planet, deduced entirely 
 from unaccounted-for perturbations of Uranus. The same results, 
 somewhat corrected, he communicated, in October, to the Astronomer 
 Royal. M. Le Yerrier, in an investigation which was published in 
 June of 1846, assigned very nearly the same heliocentric longitude for 
 the probable position of the planet as Mr. Adams had arrived at, but 
 gave no results respecting its mass and the form of its orbit. The 
 coincidence as to position from two entirely independent investigations 
 naturally inspired confidence ; and the Astronomer Royal shortly after 
 suggested the .employing of the Northumberland telescope of this 
 Observatory in a systematic search after the hypothetical planet ; re- 
 commending, at the same time, a definite plan of operations. I under- 
 
240 A BUDGET OF PARADOXES. 
 
 took to make the search, and commenced observing on July 29. 
 The observations were directed, in the first instance, to the part of the 
 heavens which theory had pointed out as the most probable place of 
 the planet ; in selecting which I was guided by a paper drawn up for 
 me by Mr. Adams. Not having hour xxi. of the Berlin star-maps of 
 the publication of which I was not aware I had to proceed on the 
 principle of comparison of observations made at intervals. On July 30, 
 I went over a zone 9' broad, in such a manner as to include all stars 
 to the eleventh magnitude. On August 4, I took a broader zone, 
 and recorded a place of the planet. My next observations were on 
 August 12 ; when I met with a star of the eighth magnitude in the 
 zone which I had gone over on July 30, and which did not then 
 contain this star. Of course, this was the planet ; the place of which 
 was, thus, recorded a second time in four days of observing. A com- 
 parison of the observations of July 30 and August 12 would, according 
 to the principle of search which I employed, have shown me the planet. 
 I did not make the comparison till after the detection of it at Berlin 
 partly because I had an impression that a much more extensive search 
 was required to give any probability of discovery and partly from the 
 press of other occupation. The planet, however, was secured, and two 
 positions of it recorded six weeks earlier here than in any other 
 observatory, and in a systematic search expressly undertaken for that 
 purpose. I give now the positions of the planet on August 4 and 
 August 12. 
 
 Greenwich mean time, 
 
 A A IOT Q* OK /R.A. 21h. 58m. 1470s. 
 
 Aug. 4, 13h. 36m. 25s. , v ( N .p. D . 102 o 6? / 32 . 2 /, 
 
 A 10 mi, Q 9a fK.A. 21h. 57m.26'13s. 
 
 Aug. 12, 13h. 3m. 26s. , ^ t | N .PJD. 103 2' 02" 
 
 From these places compared with recent observations Mr. Adams 
 has obtained the following results : 
 
 Distance of the planet from the sun . . . 30 '05 
 
 Inclination of the orbit . . . % ; .\.'",. . 1 45' 
 
 Longitude of the descending node . . V '..'' , . 309 43' 
 
 Heliocentric longitude, Aug. 4 < ' , V V * . . ~' -^ 326 39' 
 
 The present distance from the sun is, therefore, thirty times the earth's 
 mean distance ; which is somewhat less than the theory had indicated. 
 The other elements of the orbit cannot be approximated to till the 
 observations shall have been continued for a longer period. 
 
 The part taken by Mr. Adams in the theoretical search after this 
 planet will, perhaps, be considered to justify the suggesting of a name. 
 With his consent, I mention Oceanus as one which may possibly receive 
 the votes of astronomers, I have authority to state that Mr. Adams's 
 investigations will, in a short time, be published in detail. 
 
 J. CHALLIS.' 
 
DISCOVERY OF NEPTUNE 241 
 
 ASTRONOMICAL POLICE REPORT. 
 
 " An ill-looking kind of body, who declined to give any name, 
 was brought before the Academy of Sciences, charged with having 
 assaulted a gentleman of the name of Uranus in the public 
 highway. The prosecutor was a youngish looking person, wrapped 
 up in two or three great coats ; and looked chillier than any- 
 thing imaginable, except the prisoner, whose teeth absolutely 
 shook, all the time. 
 
 Policeman Le Yerrier stated that he saw the prosecutor walking 
 along the pavement, and sometimes turning sideways, and 
 sometimes running up to the railings and jerking about in a 
 strange way. Calculated that somebody must be pulling his 
 coat, or otherwise assaulting him. It was so dark that he could 
 not see ; but thought, if he watched the direction in which the 
 next odd move was made, he might find out something. When 
 the time came, he set Briinnow, a constable in another division 
 of the same force, to watch where he told him; and Briinnow 
 caught the prisoner lurking about in the very spot, trying to 
 look as if he was minding his own business. Had suspected for 
 a long time that somebody was lurking about in the neighbour- 
 hood. Briinnow was then called, and deposed to his catching the 
 prisoner as described. 
 
 M. Arago. Was the prosecutor sober ? 
 
 Le Verrier. Lord, yes, your worship ; no man who had a drop 
 in him ever looks so cold as he did. 
 
 M. Arago. Did you see the assault ? 
 
 Le Verrier. I can't say I did ; but I told Briinnow exactly 
 how he'd be crouched down, just as he was. 
 
 M. Arago (to Briinnow). Did you see the assault ? 
 
 Briinnow. No, your worship ; but I caught the prisoner. 
 
 M. Arago. How do you know there was any assault at all ? 
 
 Le Verrier. I reckoned it could'nt be otherwise, when I saw 
 the prosecutor making those odd turns on the pavement. 
 
 M. Arago. You reckon and you calculate ! Why, you'll tell 
 me, next, that you policemen may sit at home and find out all 
 that's going on in the streets by arithmetic. Did you ever bring 
 a case of this kind before me till now ? 
 
 Le Verrier. Why, you see, your worship, the police are grow- 
 ing cleverer and cleverer every day. We can't help it : it grows 
 upon us. 
 
242 A BUDGET OF PAKABOXES. 
 
 M. Arago. You're getting too clever for me. What does the 
 prosecutor know about the matter ? 
 
 The prosecutor said, all he knew was that he was pulled behind 
 by somebody several times. On being further examined, he said 
 that he had seen the prisoner often, but did not know his name, 
 nor how he got his living; but had understood he was called 
 Neptune. He himself had paid rates and taxes a good many 
 years now. Had a family of six, two of whom got their own 
 living. 
 
 The prisoner, being called on for his defence, said that it was 
 a quarrel. He had pushed the prosecutor and the prosecutor 
 had pushed him. They had known each other a long time, and 
 were always quarrelling ; he did not know why. It was their 
 nature, he supposed. He further said, that the prosecutor had 
 given a false account of himself; that he went about under 
 different names. Sometimes he was called Uranus, sometimes 
 Herschel, and sometimes Greorgium Sidus ; and he had no 
 character for regularity in the neighbourhood. Indeed, he was 
 sometimes not to be seen for a long time at once. 
 
 The prosecutor, on being asked, admitted, after a little hesita- 
 tion, that he had pushed and pulled the prisoner too. In the 
 altercation which followed, it was found very difficult to make 
 out which began : and the worthy magistrate seemed to think 
 they must have begun together. 
 
 M. Arago. Prisoner, have you any family ? 
 
 The prisoner declined answering that question at present. He 
 said he thought the police might as well reckon it out whether 
 he had or not. 
 
 M. Arago said he didn't much differ from that opinion. He 
 Jien addressed both prosecutor and prisoner ; and told them that 
 if they couldn't settle their differences without quarrelling in 
 the streets, he should certainly commit them both next time. 
 In the meantime, he called upon both to enter into their own 
 recognizances ; and directed the police to have an eye upon both, 
 observing that the prisoner would be likely to want it a long 
 time, and the prosecutor would be not a hair the worse for it." 
 
 This squib was written by a person who was among the astrono- 
 mers : and it illustrates the fact that Le Verrier had sole posses- 
 sion of the field until Mr. Challis's letter appeared. Sir John 
 Herschel's previous communication should have paved the way : 
 but the wonder of. the discovery drove it out of many heads, 
 is an excellent account of the whole matter in Professor 
 
THE MOON AND THE TIDES. 243 
 
 Grant's ' History of Physical Astronomy.' The squib scandalized 
 some grave people, who wrote severe admonitions to the editor. 
 There are formalists who spend much time in writing propriety 
 to journals, to which they serve as foolometers. In a letter to 
 the Athenceum, speaking of the way in which people hawk fine 
 terms for common things, I said that these people ought to have 
 a new translation of the Bible, which should contain the verse 
 4 gentleman and lady, created He them.' The editor was hand- 
 somely fired and brimstoned ! 
 
 A new theory of the tides : in which the errors of the usual theory 
 are demonstrated ; and proof shewn that the full moon is not 
 the cause of a concomitant spring tide, but actually the cause of 
 the neaps ... By Comm r . Debenham, R.N. London, 1846, 
 8vo. 
 
 The author replied to a criticism in the Athenceum, and I 
 remember how, in a very few words, he showed that he had 
 read nothing on the subject. The reviewer spoke of the forces of 
 the planets (i.e. the Sun and Moon) on the Ocean, on which the 
 author remarks, ; But N.B. the Sun is no planet, Mr. Critic.' 
 Had he read any of the actual investigations on the usual theory, 
 he would have known that to this day the sun and moon con- 
 tinue to be called planets though the phrase is disappearing 
 in speaking of the tides ; the sense, of course, being the old one, 
 wandering bodies. 
 
 A large class of the paradoxers, when they meet with some- 
 thing which taken in their sense is absurd, do not take the 
 trouble to find out the intended meaning, but walk off with the 
 words laden with their own first construction. Such men are 
 hardly fit to walk the streets without an interpreter. I was 
 startled for a moment, at the time when a recent happy and 
 more recently happier marriage occupied the public thoughts, 
 by seeing in a haberdasher's window, in staring large letters, an 
 unpunctuated sentence which read itself to me as 'Princess 
 Alexandra! collar and cuff!' It immediately occurred to me 
 that had I been any one of some scores out of my paradoxers, 
 I should, no doubt, have proceeded to raise the mob against 
 the unscrupulous person who dared to hint to a young bride such 
 maleficent or at least immellificent conduct towards her new 
 lord. But, as it was, certain material contexts in the shop 
 window suggested a less savage explanation. A paradoxer should 
 not stop at reading the advertisements of Newton or Laplace : he 
 should learn to look at the stock of goods* 
 
 E 2 
 
244 A BUDGET OF PAKADOXES. 
 
 I think I must have an eye for double readings, when pre- 
 sented : though I never guess riddles. On the day on which I 
 first walked into the Panizzi reading room as it ought to be 
 called at the Museum, I began my circuit of the wall-shelves 
 at the ladies' end : and perfectly coincided in the propriety of 
 the Bibles and theological works being placed there. But the 
 very first book I looked on the back of had, in flaming gold 
 letters, the following inscription ; Blast the Antinomians ! ' If 
 a line had been drawn below the first word, Dr. Blast's history 
 of the Antinomians would not have been so fearfully misinter- 
 preted. It seems that neither the binder nor the arranger of the 
 room had caught my reading. The book was removed before the 
 catalogue of books of reference was printed. 
 
 Two systems of astronomy : first, the Newtonian system, showing 
 the rise and progress thereof, with a short historical account ; 
 the general theory with a variety of remarks thereon : second, 
 the system in accordance with the Holy Scriptures, showing 
 the rise and progress from Enoch, the seventh from Adam, the 
 prophets, Moses, and others, in the first Testament ; our Lord 
 Jesus Christ, and his apostles, in the new or second Testament ; 
 Reeve and Muggleton, in the third and last Testament ; with 
 a variety of remarks thereon. By Isaac Frost. London, 1846, 
 4to. 
 
 A very handsomely printed volume, with beautiful plates. 
 Many readers who have heard of Muggleton ians have never had 
 any distinct idea of Lodowick Muggleton, the inspired tailor, 
 (1608-1698) who about 1650 received his commission from 
 heaven, wrote a Testament, founded a sect, and descended to 
 posterity. Of Eeeve less is usually said ; according to Mr. Frost, 
 he and Muggleton are the two 'witnesses.' I shall content 
 myself with one specimen of Mr. Frost's science : 
 
 " I was once invited to hear read over ' Guthrie on Astronomy/ and 
 when the reading was concluded I was asked my opinion thereon ; 
 when I said, ' Doctor,, it appears to me that Sir I. Newton has only 
 given two proofs in support of his theory of the earth revolving round 
 the sun : all the rest is assertion without any proofs/ * What are 
 they ? ' inquired the Doctor. ' Well,' I said, * they are, first, the 
 power of attraction to keep the earth to the sun ; the second is the 
 power of repulsion, by virtue of the centrifugal motion -of the earth : 
 all the rest appears to me assertion without proof.' The Doctor con- 
 sidered a short time, and then said, l It certainly did appear so.' I 
 said, ' Sir Isaac has certainly obtained the credit of completing the 
 system, but really he has only half done his work.' 'How is that,' 
 
MUaOLETON GEOKGE FOX. 245 
 
 inquired my friend the Doctor. My reply was this: 'You will 
 observe his system shows the earth traverses round the sun on an 
 inclined plane ; the consequence is, there are four powers required to 
 make his system complete : 
 
 1st. The power of attraction. 
 
 2ndly. The power of repulsion. 
 
 Srdly. The power of ascending the inclined plane. 
 
 4thly. The power of descending the inclined plane. 
 
 You will thus easily see the four powers required, and Newton has 
 only accounted for two ; the work is therefore only half done.' Upon 
 due reflection the Doctor said, ' It certainly was necessary to have 
 these four points cleared up before the system could be said to be 
 complete. 1 " 
 
 I have no doubt that Mr. Frost, and many others on my list, 
 have really encountered doctors who could be puzzled by such 
 stuff as this, or nearly as bad, among the votaries of existing 
 systems, and have been encouraged thereby to print their ob- 
 jections. But justice requires me to say that from the words 
 6 power of repulsion by virtue of the centrifugal motion of the 
 earth,' Mr. Frost may be suspected of having something more 
 like a notion of the much-mistaken term ' centrifugal force ' 
 than many paradoxers of greater fame. The Muggletonian sect 
 is not altogether friendless : over and above this handsome 
 volume, the works of Eeeve and Muggleton were printed, in 1832, 
 in three quarto volumes. See Notes and Queries, 1st Series, v. 
 80 ; 3rd Series, iii, 303. 
 
 [The system laid down by Mr. Frost, though intended to be 
 substantially that of Lodowick Muggleton, is not so vagari- 
 ous. It is worthy of note how very different have been the 
 fates of two contemporary paradoxers, Muggleton and George 
 Fox. They were friends and associates, and commenced their 
 careers about the same time, 1647-1650. The followers of Fox 
 have made their sect an institution, and deserve to be called 
 the pioneers of philanthropy. But though there must still be 
 Muggletonians, since expensive books are published by men who 
 take the name, no sect of that name is known to the world. 
 Nevertheless, Fox and Muggleton are men of one type, developed 
 by the same circumstances : it is for those who investigate such 
 men to point out why their teachings have had fates so different. 
 Macaulay says it was because Fox found followers of more sense 
 than himself. True enough : but why did Fox find such 
 followers and not Muggleton ? The two were equally crazy, to 
 
246 A BUDGET OF PARADOXES. 
 
 all appearance : and the difference required must be sought in 
 the doctrines themselves. 
 
 Fox was not a rational man : but the success of his sect and 
 doctrines entitles him to a letter of alteration of the phrase 
 which I am surprised has not become current. When Conduitt, 
 the husband of Newton's half-niece, wrote a circular to Newton's 
 friends, just after his death, inviting them to bear their parts in 
 a proper biography, he said, 4 As Sir I. Newton was a national 
 man, I think every one ought to contribute to a work intended 
 to do him justice.' Here is the very phrase which is often 
 wanted to signify that celebrity which puts its mark, good or 
 bad, on the national history, in a manner which cannot be 
 asserted of many notorious or famous historical characters. Thus 
 Greorge Fox and Newton are both national men. Dr. Koget's 
 Thesaurus gives more than fifty synonyms colleagues would be 
 the better word of 4 celebrated] any one of which might be 
 applied, either in prose or poetry, to Newton or to his works, no 
 one of which comes near to the meaning which Conduitt's ad- 
 jective immediately suggests. 
 
 The truth is, that we are too monarchical to be national. 
 We have the Queen's army, the Queen's navy, the Queen's high- 
 way, the Queen's English, &c. ; nothing is national except the 
 debt. That this remark is not new is an addition to its force ; 
 it has hardly been repeated since it was first made. It is some 
 excuse that nation is not vernacular English : the country is our 
 word, and country man is appropriated.] 
 
 Astronomical Aphorisms, or Theory of Nature ; founded on the 
 immutable basis of Meteoric Action. By P. Murphy, Esq. 
 London, 1847, 12mo. 
 
 This is by the framer of the Weather Almanac, who appeals to 
 that work as corroborative of his theory of planetary temperature, 
 years after all the world knew by experience that this meteorolo- 
 gical theory was just as good as the others. 
 
 The conspiracy of the Bullionists as it affects the present system 
 of the money laws. By Caleb Quotem. Birmingham, 1847, 
 8vo. (pp. 16). 
 
 This pamphlet is one of a class of which I know very little, 
 in which the effects of the laws relating to this or that political 
 bone of contention are imputed to deliberate conspiracy of one 
 class to rob another of what the one knew ought to belong to the 
 
THEISM INDEPENDENT OF REVELATION. 247 
 
 other. The success of such writers in believing what they have 
 a bias to believe, would, if they knew themselves, make them 
 think it equally likely that the inculpated classes might really 
 believe what it is their interest to believe. The idea of a guilty 
 understanding existing among fundholders, or landholders, or 
 any holders, all the country over, and never detected except by 
 bouncing pamphleteers, is a theory which should have been left 
 for Cobbett to propose, and for Apella to believe. 
 
 [August, 1866. A pamphlet shows how to pay the National 
 Debt. Advance paper to railways, &c., receivable in payment of 
 taxes. The railways pay interest and principal in money, with 
 which you pay your national debt, and redeem your notes. 
 Twenty -five years of interest redeems the notes, and then the 
 principal pays the debt. Notes to be kept up to value by penal- 
 ties.] 
 
 The Reasoner. No. 45. Edited by G. J. Holyoake. Price 2d. 
 Is there sufficienj proof of the existence of God ? 8vo. 1847. 
 
 This acorn of the holy oak was forwarded to me with a manu- 
 script note, signed by the editor, on the part of the 4 London 
 Society of Theological Utilitarians,' who say 6 they trust you 
 may be induced to give this momentous subject your considera- 
 tion.' The supposition that a middle-aged person, known as a 
 student of thought on more subjects than one, had that particular 
 subject yet to begin, is a specimen of what I will call the as- 
 sumption-trick of controversy, a habit which pervades all sides 
 of all subjects. The tract is a proof of the good policy of letting 
 opinions find their level, without any assistance from the Court 
 of Queen's Bench. Twenty years earlier the thesis would have 
 been positive, ' There is sufficient proof of the non-existence of 
 God,' and bitter in its tone. As it stands, we have a moderate 
 and respectful treatment wrong only in making the opponent 
 argue absurdly, as usually happens when one side invents the 
 other of a question in which a great many Christians have 
 agreed with the atheist : that question being Can the existence 
 of God be proved independently of revelation? Many very 
 religious persons answer this question in the negative, as well 
 as Mr. Holyoake. And, this point being settled, all who agree 
 in the negative separate into those who can endure scepticism, 
 and those who cannot : the second class find their way to Chris- 
 tianity. This very number of ' The Eeasoner ' announces the 
 secession of one of its correspondents, and his adoption of the 
 Christian faith. This would not have happened twenty years 
 
248 A BUDGET OF PAKADOXES. 
 
 before : nor, had it happened, would it have been respectfully 
 announced. 
 
 There are people who are very unfortunate in the expres- 
 sion of their meaning. Mr. Holyoake, in the name of the 
 'London Society,' &c., forwarded a pamphlet on the existence 
 of God, and said that the Society trusted I ; may be induced to 
 give ' the subject my ' consideration.' How could I know the 
 Society was one person, who supposed I had arrived at a conclu- 
 sion, and wanted a ' guiding word ' ? But so it seems it was : 
 Mr. Holyoake, in the English Leader of October 15, 1864, and in 
 a private letter to me, writes as follows : 
 
 " The gentleman who was the author of the argument, and who asked 
 me to send it to Mr. De Morgan, never assumed that that gentleman 
 had c that particular subject to begin ' on the contrary, he supposed 
 that one whom we all knew to be eminent as a thinker had come to a 
 conclusion upon it, and would perhaps vouchsafe a guiding word to 
 one who was, as yet, seeking the solution of the Great Problem of 
 Theology. I told my friend that ' Mr, De Morgan was doubtless pre- 
 occupied, and that he must be content to wait. On some day of 
 courtesy and leisure he might have the kindness to write.' Nor was 
 I wrong the answer appears in your pages at the lapse of seventeen 
 years." 
 
 I suppose Mr. Holyoake's way of putting his request was the 
 stylus curice of the Society. A worthy Quaker who was sued 
 for debt in the King's Bench was horrified to find himself 
 charged in the declaration with detaining his creditor's money 
 by force and arms, contrary to the peace of our Lord the King, 
 &c. It's only the stylus curice, said a friend: I don't know 
 curice, said the Quaker, but he shouldn't style us peace-breakers. 
 The notion that the -noTi-existence of God can be proved, has 
 died out under the light of discussion : had the only lights 
 shone from the pulpit and the prison, so great a step would never 
 have been made. The question now is as above. The dictum 
 that Christianity is ; part and pare 3! of the law of the land 5 is 
 also abrogated : at the same time, and the coincidence is not 
 an accident, it is becoming somewhat nearer the truth that the 
 law of the land is part and parcel of Christianity. It must also 
 be noticed that Christianity was part and parcel of the articles 
 of war ; and so was duelling. Any officer speaking against 
 religion was to be cashiered ; and any officer receiving an affront 
 without, in the last resort, attempting to kill his opponent, was 
 also to be cashiered. Though somewhat of a book-hunter, I 
 have never been able to ascertain the date of the collected 
 
LOST EPISCOPAL PEOTEST. 249 
 
 remonstrances of the prelates in the House of Lords against this 
 overt inculcation of murder, under the soft name of satisfaction : 
 it is neither in Watt, nor in Lowndes, nor in any edition of 
 Brunet ; and there is no copy in the British Museum. Was the 
 collected edition really published ? 
 
 [The publication of the above in the Athenceum has not pro- 
 duced reference to a single copy. The collected edition seems 
 to be doubted. I have even met one or two persons who doubt 
 the fact of the Bishops having remonstrated at all : but their 
 doubt was founded on an absurd supposition, namely, that it was 
 TIO business of theirs ; that it was not the business of the prelates 
 of the Church in union with the State to remonstrate against 
 the Crown commanding murder! Some say that the edition 
 was published, but under an irrelevant title, which prevented 
 people from knowing what it was about. Such things have 
 happened: for example, arranged extracts from Wellington's 
 general orders, which would have attracted attention, fell 
 dead under the title of 'Principles of War.' It is surmised 
 that the book I am looking for also contains the protests of 
 the Eeverend bench against other things besides the Thou-shalt- 
 do-murder of the Articles (of war), and is called ' First Elements 
 of Eeligion ' or some similar title. Time clears up all things.] 
 
 With the general run of the philosophical atheists of the last 
 century the notion of a Grod 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 super- 
 intendent. In the works of Laplace, who is sometimes called 
 an atheist from his writings, there is nothing from which such 
 an inference can be drawn : unless indeed a Eeverend Fellow of 
 the Eoyal Society may be held to be the fool who said in his 
 heart, &c. &c., if his contributions to the Philosophical Trans- 
 actions 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 Grod, and who was fond of putting embarrassing questions, 
 received it with c 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 
 
250 A BUDGET OF PARADOXES. 
 
 his philosophy or religion (ex. gr. even under Charles X. he 
 never concealed his dislike of the priests), drew himself up, and 
 answered bluntly, ' Je n'avais pas besoin de cette hypothese-la.' 
 Napoleon, greatly amused, told this reply to Lagrange, who 
 exclaimed, ' Ah ! c'est une belle hypothese ; pa explique beaucoup 
 de choses.' 
 
 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.' This looks like a parody on Newton's pebbles : 
 the following is the true account ; it comes to me through one 
 remove from Poisson. 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 dest que tout cela ! 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 repu au Bureau des 
 Longitudes une lettre d'Allemagne annoncant que M. Bessel 
 a verifie par 1'observation vos decouvertes theoriques sur les 
 satellites de Jupiter.' Laplace opened his eyes and answered 
 with deep gravity, ' L'homme ne poursuit que des chimeres? 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 was a believer in Grod, downright and straightforward. 
 The following story is told by Thiebault, in his Souvenirs de 
 vingt ans de sejour a Berlin, published in his old age, about 
 1 804. This volume was fully received as trustworthy ; and 
 Marshal Mollendorff told the Due de Bassano in 1 807 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 that it was believed throughout the whole of the 
 
ROTATION OF THE MOON. 251 
 
 north of Europe. Diderot 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 pos- 
 session of an algebraical demonstration of the existence of Grod, 
 and would give it him before all the Court, if he desired to hear 
 it. Diderot gladly consented : though the name of the mathe- 
 matician is not given, it was Euler. He advanced towards 
 Diderot, and said gravely, and in a tone of perfect conviction : 
 
 Monsieur, = #, done Dieu existe ; repondez I Diderot, 
 
 n 
 
 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. 
 
 An examination of the Astronomical doctrine of the Moon's rota- 
 tion. By J. L. 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. A writer on astronomy 
 said of Mr. Jeilinger Symons, l 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 Eome will not cast his tiara and keys at the feet 
 of the c 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. 
 
252 A BUDGET OF PABADOXES. 
 
 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 astrono- 
 mising upon ignorant geometry and false logic, and comparing to 
 blockheads those who expose his nonsense. Their comparison is 
 as foolish as supposing 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 asser- 
 tions 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, &c., 
 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 pro- 
 positions in the theory of chances to the Christian miracles. 
 By Protimalethes. Cambridge, 1847, 8vo. 
 
 The theory, as may be supposed, is carried further than most 
 students of the subject would hold defensible. 
 
THE PLANET NEPTUNE STEAM BALLOONS. 
 
 An astronomical Lecture. By the Rev. R. Wilson. Greenock, 
 1847, 12mo. 
 
 Against the moon's rotation on her axis. 
 
 [Handed about in the streets in 1847 : I quote the whole :] Im- 
 portant discovery in astronomy, communicated to the Astrono- 
 mer Royal, December 21st, 1846. That the Sun revolve round 
 the Planets in 25748f 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, of Shrewsbury, published some remarks tending to 
 impeach the fact that Neptune, the planet found by Grail e, really 
 was the planet which Le Verrier and Adams had a right to claim. 
 This was followed (September 14) by two pages, separately circu- 
 lated, 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, con- 
 tended that the planet actually discovered was an intruder ; and 
 the future histories of the discovery must contain some account of 
 this little after-piece. Tim Linkinwater's theory that there is no 
 place like London for coincidences, would have been utterly over- 
 thrown in favour of what they used to call the celestial spaces, if 
 there had been a planet which by chance was put near the place 
 assigned to Neptune at the time when the discovery was made. 
 
 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 had proposed what he called an 
 aeronaut steam-engine, and a Bill was brought in to incorporate 
 an c Aerial Transit Company.' The present plan is altogether 
 different, the moving power being the explosion of mixed hydro- 
 gen and air* Nothing came of it not even a Bill. What the 
 final destiny of the balloon may be no one knows: it may reason- 
 ably be suspected that difficulties will at last be overcome. 
 Darwin, in his 'Botanic Garden' (1781), has the following 
 prophecy : 
 
254 A BUDGET OF PAKADOXES. 
 
 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, when he spoke of 
 dragging the slow barge : it is only very receotly 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 be something of a character which we cannot imagine, 
 even with the two prophecies and their fulfilments to help us. 
 (/WT ff n* W'S*^ r^ U&vS& 
 
 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 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, c I am very much obliged to your Lordship for intro- 
 ducing me to Mr. - ; he has convinced me 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 candour and 
 sense, which infected those who came within reach : he would 
 have done so, if anybody, 
 
THE ANGLE TRISECTED. 255 
 
 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). 
 
 4 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 tra- 
 versing round and at an equal distance from a given point, called 
 a centre, 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 a line 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 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). 
 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,' and ' Dangers along a coast by correcting (as it is 
 called) a ship's reckoning by bearings of the land at night lall, or in 
 a fog, nearly out of print. Subscriptions are requested for a new 
 edition/ 
 
256 A BUDGET 'OF PARADOXES. 
 
 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. The author, as Q. E. D., was in controversy 
 with the Athenceum 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 Athenceum published but without some Italics, for 
 which the editor was sharply reproved, as a sufficient 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. 
 
 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 geometri- 
 cally solved. By W. Upton, B.A. 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 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 
 
TEISECTION OF THE ANGLE. 257 
 
 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. Dis- 
 honesty sometimes follows, The speculators are, as a class, very 
 apt to imagine that the mathematicians are in fraudulent con- 
 federacy 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 - = 1 -f ^(4-sin 2 0) 
 o 
 
 which is certainly false. 
 
 In 1852 I examined a terrific construction, at the request of 
 the late Dr. Wallich, who was anxious to persuade a poor country- 
 man 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, 
 being any angle, the cosine of its third part is 
 
 o/i 50 . o/i 50 
 
 sin 30 . cos + sin 2 sin . 
 
 2 2 
 
 divided by the square root of ^ 
 
 2 50 
 
 sin 2 30 cos - - + sin 4 + sin 30 . sin 50 . sin 2 
 2t 
 
 This is from my rough notes, and I believe it is correct. It 
 is so nearly true, unless the angle be very obtuse, that common 
 drawing, applied to the construction, will not detect the error. 
 
 8 
 
258 A BUDGET OF PARADOXES. 
 
 There are many formula of this kind : and I have several times 
 found a speculator who has discovered the corresponding con- 
 struction, 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 be one. 
 At least I discovered that two parts of the diagram were incom- 
 patible 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 or 180. 
 
 Aug. 22, 1866. Mr. Upton sticks to his subject. He has just 
 published ; The Uptonian Trisection. Kespectfully 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 mean 
 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 tri sector 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 of Bonnycastle into Turkish. 
 This Englishman was Eichard Baily, brother of Francis Baily the 
 astronomer, who emigrated to Turkey in his youth, and adopted 
 
LETTEE FEOM A CYCLOMETER 259 
 
 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 labourer and his 
 friend, described in page 9. 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 yon 
 
 Brute Creation may perhaps enjoy the faculty of behold- 
 ing 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* merit & ability aught to be appreciated 
 and valued In proportion to its worth & utility 
 
 In whatever State or Circumstances they may fortunately or un- 
 fortunately 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 ex- 
 plained by words and Letters and mathematacally 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 possesion 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 Desirious of heaping Disonors upon my own nation. But 
 
 3 9, 
 
260 A BUDGET OF PARADOXES. 
 
 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 such tho' lowly his origiiie; 
 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 l that the mind is the standard of the man,' has 
 laid before you and asked your opinion of his extraordinary perform- 
 ance, 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 ac- 
 knowledge 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 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 ac- 
 knowledge that he is right. 
 
 I was asked my opinion and I gave it unhesitatingly in the affirm- 
 mative and I am backed in my opinion not only by Mr. a mathe- 
 matician and watchmaker residing in the boro of South wark but by 
 
 no less an authority than the Erofessor 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 MOON'S ROTATION. 261 
 
 the nursery of the 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. 
 
 I am, sir, yours ' 
 
 Dr. Morgan. 
 
 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 attri- 
 buted to each of the words. (No date nor place, but by Mr. Peri- 
 gal, 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 
 6 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 ; 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 
 
262 A BUDGET OF PAEADOXES. 
 
 and an anonymous opponent ; and I think there have been 
 others. 
 
 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 Mathematical 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 propound 
 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 Eotate ? ' in Sanscrit and English. The arguments are 
 much the same as those of the discussion at home. 
 
 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 
 
MILNER'S 'END OF RELIGIOUS CONTROVERSY.' 263 
 
 (of good), &c. 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 ; L the 
 second is a robber. In theology, the Greek Church is Orthodox, 
 the Eoman is Catholic, the modern Puritan is Evangelical, &c. 
 
 The word Christian (ante, p. 147) 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 
 Heathens, who knew little or nothing about the Jewish hope, 
 would naturally apply the term Christian 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, &c., are well enough as mere nomen- 
 clature ; and the world falls for the most part, into any names 
 which parties choose to give themselves. Silly people found in- 
 ferences on , this concession ; and, as usually happens, they can 
 cite some of their betters, St. Augustine, a freakish arguer, or, 
 to put it in the way of an old writer, lectorem ne multiloquii 
 tcedio fastidiat, Punicis quibusdam argutiis recreare solet, 
 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, in a work (first published in 1801 or 
 1802) which I suppose still circulates, 'The End of Keligious 
 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 
 
 1 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. 
 
264 A BUDGET OF PARADOXES. 
 
 have been a worthy soul, though many, even of his own sect, will 
 not admire some of his logic, speaks as follows : 
 
 6 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 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, 1 am a PEOTESTANT! 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, 
 4 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 recognised 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 
 emitter 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 c hope l 
 
 1 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 
 
THE BURIAL SERVICE. 265 
 
 is not assurance. 9 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 isjike a dwarf.' Sad to say, 
 a theologian must be illogical : I fe1| 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 (lib. i. c. 12, de nomine 
 Sacrce Ecclesice, p. 87 of the Venice folio of 1537). I am told 
 that there is a Rituale in the Index Expur gator ius, 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 Eoman 
 Christians should deny its existence. 1 
 
 It amuses me to give, at a great distance of time, a small 
 Eowland for a small Oliver, which I received, de par VEglise, so 
 far as lay in the Oliver-carrier more than twenty years ago. The 
 following contribution of mine to Notes and Queries (3rd Ser. vi. 
 
 brother is declared to be taken to Grod, 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, and could not have the 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 demon- 
 stratively 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 Man- 
 chester 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 dcor 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. 
 
 1 This derivation has been omitted (ED.). 
 
266 A BUDGET OF PAKADOXES. 
 
 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 etymo- 
 logical meaning, and applied to those who give the higher and 
 final authority to the declaration ex cathedra of the Pope. 
 See Dr. Wiseman's article. Catholic Church, in the Penny Cyclo- 
 paedia. 
 
 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 favours any assumption made 
 by those to whom it is given, and not granted by those who give 
 it. Thus the subdivision which calls itself distinctively Evan- 
 gelical 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 unobjec- 
 tionable, since the Eoman 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 3rd S. iv. \_Notes and Queries']. Here we find 
 'Platts (Eev. 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 
 
KELIGIOUS NOMENCLATUKE. FIDES. 267 
 
 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 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 ; 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 Gruillim 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 Eoman 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. 
 
 The mention of Dr. Wiseman reminds me of another word, 
 appropriated by Christians to themselves : fides ; the Eoman faith 
 is fides, and nothing else ; and the adherents are fideles. 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 vindi- 
 cata was chosen : this may be read either in a Popish or heretical 
 
268 A BUDGET OF PARADOXES. 
 
 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. 1 If a Latin writer had had 
 to make a legend signifying c 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 Eoman 
 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, or/civSaircros a word meaning a 
 four stringed instrument played with a quill was an exclamation 
 of contemptuous dissent. How the wits of different races jump ! 
 
 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 Eoman 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 I How is that, said the rest ? Why, read 
 his name backwards, and you will see. As thus read it was 
 No grub ! 
 
 To return to Notes and Queries. The substitution in the 
 (editorial) index of 4 Unitarian teacher,' for the contributor's 
 c 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 contributor! al, 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, (3rd S. 
 vii. p. 36) the following was the editorial answer to the question 
 
 1 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 rock, and other words, come to moan reliance and in 
 another, a little string. 
 
THE WOKD CHURCH. 269 
 
 when the establishment was first called the c Church of England 
 and Ireland : ' 
 
 1 That unmeaning clause, "The United Church of England and 
 Ireland," which occurs on the title-page of The Boole 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, 4 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 Tract- 
 arian the tendency of his construction. 
 
 This word Church is made to have a very mystical meaning. 
 The following dialogue between Ecclesiastes and Hsereticus, 
 which I cannot vouch for, has often taken place in spirit, if not 
 in letter : E. The word Church (sKK\r]aia) 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. 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 /c\7icria is binding upon you und me ? E. 
 Certainly, unless we would 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 cry- 
 ing, Great is Diana of the Ephesians ! E. What do you mean ? 
 H. You ought to know the solemn service of the KK\rjcrt,a 
 
270 A BUDGET OF PARADOXES. 
 
 (Acts xix. 32, 41), atEphesus; 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 Kecorder. E. I see 
 your meaning : it is true, there is that one exception ! H. Why, 
 the Kecorder's sermon itself contains another, the iwojj,os 
 s/c/cXrjaia, 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 ceternum peribo ; not for their presump- 
 tion 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 ever- 
 lastingly, especially A. De Morgan.' But I hold, with the school- 
 men, that ' Omnis homo est animal' in conjunction with ' Sortes 
 est homo ' amounts to ' Sortes est animal.' But they do not 
 mean it personally ! Every universal proposition is 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 neighbour. Which decision, except everyone 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, 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 ; 
 
PROTESTANT AND PAPAL CHRISTENDOM. 271 
 
 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. 
 
 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 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 Eoman 
 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 Koman Church is one glorious compound 
 of everything that could make Heraclitus sob and Democritus 
 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 Eoman 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 Eoman 
 forge can be compared with the Protestant loom. The picking, 
 the patching, the piecing, which goes to the Protestant termini 
 ad quern, would be as remarkable to the general eye, as the 
 Eoman manufacture of termini a quo, 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 deifica- 
 cation 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, when he 
 cannot find it totidem verbis. This is Protestant method : the 
 Eoman plan is viam faciam ; the Protestant plan is viam 
 inveniam. 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, &c. The time will come when the same public will 
 begin to see the ways of wriggling in. But one thing at a time : 
 
272 A BUDGET OF PARADOXES. 
 
 neither Papal Eome nor Protestant Eome 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 Eoman sects on one side, the Protestant sects on the 
 other, must all have churches : the Greek and Eoman sects pour 
 the New Testament into their churches ; the Protestant sects 
 pour their churches into the New Testament. The Greek and 
 Eoman 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 
 somewhere ; and each says I have it. The doctrine is true : 
 and can be verified by anyone 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 colour the rest ; it matters nothing 
 that the stains are shaped into what are meant for saints and 
 angels. 
 
 But there is another side of 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 
 
THEOLOGY AND PHILOSOPHY. 273 
 
 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 Testa- 
 ment is a system of psychology ; and the philosopher writes a 
 Christianity which is utterly unintelligible as to the question 
 whether the Eesurrection 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. 
 
 Eeligion 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 gpeak 
 especially of Grreat 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 peek of pepper, 
 
 Where is the peck of pepper Peter Piper picked ? 
 
 If Eeligion and Philosophy be the two poles of a battery, whose 
 is the battery Eeligion 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 1 turned out ? 
 Has he been put under restriction ? A fool may ask more 
 questions than twenty sages can answer : but there is hope ; for 
 
 1 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.' 
 
 T 
 
274 A BUDGET OF PAKADOXES. 
 
 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 pericida, 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 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 on St. John Long ; the usual pronuncia- 
 tion of whose name must be noted 
 
 Behold ! ye quacks, the vengeance strong 
 
 On deeds like yours impinging : 
 For here below lies St. John Long Xj^'Ji 
 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 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 ! Gro 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 organisation 
 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 explana- 
 tion : 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 
 
SCIENTIFIC MATERIALISM. 275 
 
 organisms from a very few, if not from one. The better heads 
 abovementioned know that their theory, if true, does not bear 
 upon morals. The formation of solar systems from a nebular 
 hypothesis, followed by organisations 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 without 
 any such necessity. With Occam 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 your's 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, Grod 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 philoso- 
 phers 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 dis- 
 misses 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 im- 
 possibility ? If all the mind we know be from nerve-tissue, how 
 does it appear that mind in other planets may not be another 
 
 T 2 
 
276 A BUDGET OF PARADOXES. 
 
 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 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 of Fahrenheit, and the 
 pressure of the atmosphere ; and this oxygen was infinitely rare- 
 fied ; and this oxygen became God.' For myself, my aspirations 
 as to this system are Manichsean. 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 de- 
 duction 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 solar system truly solved : demonstrating by the perfect 
 harmony of the planets, founded on the four universal laws, the 
 Sun to be an electrical space ; and a source of every natural 
 production displayed throughout the solar system. By James 
 Hopkins. 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 satis- 
 factorily established, I have an undoubted claim to the credit of my 
 theory, That the Sun is an Electric Space, fed and governed by the 
 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 wonder- 
 ful a conception ! How beautiful, how magnificent an arrangement ! 
 
 ' O Centre ! O Space ! Electric Space ! ' 
 
 1849. Joseph Ady is entitled to a place in this list of dis- 
 coverers : his great fault, like that of some others, lay in pushing 
 his method too far. He began by detecting unclaimed dividends. 
 
JOSEPH ADY ZADKIEL. 277 
 
 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 favoured 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 and all other 
 aldermen ' ; which was nearly true, 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 : 
 
 1 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 charac- 
 ter : 
 
 ' 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 ISTaboth 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.' 
 
 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, R.N. London (s. a.) 
 
 12mo. 
 
 Lieut. Morrison is Zadkiel Tao Sze, and declares himself in 
 real earnest an astrologer. There are a great many books on 
 
278 A BUDGET OF PAKADOXES. 
 
 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 experi- 
 ment. Many make the mistake which M. le Marquis made when 
 he came too late, and hoped M. Cassini 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 differ- 
 ence : 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 favour, 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 Astronomical Society 
 about a matter on which the writer says 4 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 
 prophecies are fulfilled. It is related of Flamsteed that an old 
 woman came to know the whereabouts of a bundle of linen which 
 
ASTEOLOGY COINCIDENCES. 2 79 
 
 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 -veiy place. 
 
 The late Baron Zach received a letter from Pons, 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 humour, told him that no spots had been seen 
 
 on the sun for about the same time which was true, and 
 
 assured him that y^hen the spots came back, the comets would 
 
 come with them. Some time after he got a letter 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 connexion between these 
 
 spots and the earth's magnetism. 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-estab- 
 lished 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 sensa- 
 tion, 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 connexion 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. Philoso- 
 phers 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 from the Decretals, Facinora ostendi dum punientur, 
 flagitia autem abscondi debent. 
 
 The great ghost-paradox, and its theory of coincidences, will 
 
280 A BUDGET OF PAKADOXES. 
 
 rise to the surface in the mind of everyone. 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 simul- 
 taneous. Of course A is here a death, and B the spectral appear- 
 ance 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 coinci- 
 dence 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 re- 
 mains 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 connexion in time of the death, and the 
 simultaneous appearance of the dead. Any person the least used 
 to the theory of probabilities will see that purely casual coinci- 
 dence, 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, of the French Institute, 
 wrote to me to the effect that Fresnel had sent to England, in or 
 shortly after 1824, a paper for translation and insertion in the 
 
CUEIOUS COINCIDENCES. 281 
 
 European Review, which shortly afterwards expired. The 
 question was what had become of that paper. I examined 
 the Eeview 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 Eoad 
 at the junction with Edward Street, on the opposite side of which 
 is a bookstall. Lounging for a moment over the exposed books, 
 sieut meus est mos, 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) 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 4 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 Eichard 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 of omnipresence and indivisibi- 
 lity 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 
 
282 A BUDGET OF PAKADOXES. 
 
 in from a bookseller containing Heywood's ' Analysis of Kant's 
 Critick,' 1844. On turning over the leaves I found (p. 109) the 
 
 i 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. 
 Hey wood 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 Eoman Catholic priest was intro- 
 duced by P. M. A. C. F. The chain was this : the Duchess of 
 Portsmouth 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. Now the letters are a verbal acrostic of Pere Mansuete 
 a Cordelier Friar, and a syllabic acrostic of Ports Mouth and 
 Chi/Finch. 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 4 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 connexion 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 Gentle- 
 man'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 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 
 P 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 
 
COINCIDENCE BETTING. 283 
 
 should not consider any danger short of one like the above, suffi- 
 cient 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 Self- 
 conceit king. At the other end we have those who see some- 
 thing 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, 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, 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, before 1800, saw the tobacconist's carriage with a sample 
 of tobacco in a shield, and the motto Quid rides (N & Q., 3rd S. i. 
 245). His father was able to tell him all about it. The tobac- 
 conist 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 Eobinson remembers the King's Counsel 
 (Samuel Marryat) who took the motto Causes produce effects, 
 when his success enabled him to start a carriage. 
 
284 A BUDGET OF PAKADOXES. 
 
 The coincidences of errata are sometimes very remarkable : it 
 may be that the misprint has a sting. The death of Sir W. 
 Hamilton of Edinburgh was known in London on a Thursday, and 
 the editor of the Athenceum wrote to 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 4 addition to 
 Stewart' require 'for addition to read edition of.' This represents 
 what had been insisted on by the Edinburgh publisher, who, 
 frightened by the edition of Eeid, had stipulated for a simple 
 reprint without notes. Again ' principles of logic and mathe- 
 matics ' 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 mysti- 
 cal 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 pass for living's 
 preaching though a person to whom it was presented as such 
 would say that most likely the head and tail would make some- 
 thing 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 speci- 
 mens 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 c I will judge between cattle 
 and cattle, that use their tongues.' 
 
PEKPETUAL MOTION. 285 
 
 The figure of the earth. By J. L. Murphy, 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. 6 If the philosopher's 
 conclusion be right, then the pole is the centre 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. 
 
 1851. The following letter was written by one of a class of 
 persons whom, after much experience of them, I 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 
 realised : 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, &c. ' 
 
 To the Directors of the 
 London University, Gower Street. 
 
286 A BUDGET OF PARADOXES. 
 
 The Divine Drama of History and Civilisation. By the Rev. 
 James Smith, M.A. London, 1854, 8vo. 
 
 I have several books on that great paradox of our day, Spiri- 
 tualism, 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 true ? Are they caused 
 by spirits ? These I shall not enter upon : I shall merely re- 
 commend 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 6 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 Eev. 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 shoemakers 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. 
 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 : 
 
KEV. JAMES SMITH. 287 
 
 (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, Eoman, Anglican, Scotch, Lutheran, Calvinist, 
 Established and Territorial, with Baronial Bishops, and Non- 
 established 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 favoured 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 re- 
 semblance to revelation, and thus gradually open the mind of 
 the philosophical and infidel classes, as well as the professed 
 believers of thai 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 in- 
 corporated churches in England, all formed from the New Testa- 
 ment 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 : 
 
 (P. 592.) < Joanna Southcott 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 
 
288 A BUDGET OF PARADOXES. 
 
 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 the 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 develop- 
 ment of the organ of imperception.] 
 
 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 of Thales, the 
 Milesian, they came into Greece, where they were improved very much 
 by Pythagoras, Anaxagoras, and Anopides of Chios. These were 
 followed by Briso, Antipho, [two circle- squarers ; where is Euclid?] 
 and Hippocrates, but the excellence of the algebraic art was begun by 
 Geber, an Arabian astronomer, and was carried on by Cardanus, Tarta- 
 glia, Clavius, Stevinus, Ghctaldus, Herigenius, Fran, Van Schooten 
 [meaning Francis Yan Schooten], Florida de Beaurae, &c. 
 
 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 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, &c. 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 for another. This last gentleman ascer- 
 tained, 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 
 
ST. VITUS, PATRON OF CYCLOMETERS. 289 
 
 double of the equilateral triangle. He was let out of linibo by 
 Lacroix, in a note to his edition of Montucla's History of Quad- 
 rature. 
 
 Quadrature del cerchio, trisezione dell* angulo, et duplicazione del 
 
 cubo, problem! geometricamente risolute e dimostrate dal 
 
 Reverendo Arciprete di San Yito D. Domenico Anghera. 
 
 Malta, 1854, 8vo. 
 Equazioni geometriclie, estratte dalla lettera del Rev. Arciprete . . 
 
 al Professore Pullicino sulla quadratura del cerchio. Milan, 
 
 1855 or 1856, 8vo. 
 II 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. Aoghera, 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 has an arch- 
 priest. 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, 
 with whom the said circle-squarer often has nothing to do. And 
 he must not put himself under the first saint with a slanten- 
 dicular reference to the other, as is much to be feared was done 
 by the Cardinal who came to govern England with a title con- 
 taining St. Pudentiana, 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^ diameters. He is active and able, with nothing wrong about 
 him except his paradoxes. In the second tract named he has 
 given the ^testimonials of crowned heads and ministers, &c. as 
 follows. Louis-Napoleon gives thanks. The minister at Turin 
 refers it to the Academy of Sciences, and hopes so much labour 
 will be judged degna di pregio. 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 
 
 U 
 
290 A BUDGET OF PABADOXES. 
 
 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 apprecia- 
 tion. The University of Salamanca gives infinite thanks, and 
 feels true satisfaction in having the book. Lord Palrnerston 
 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 trans- 
 lated 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 
 Eibadeneira in his lives of the Saints, and that Baronius, in his 
 Martyrologium Romanum, refers to several authors who have 
 written concerning him. There is an account in Mrs. Jameson's 
 '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 
 himself, there is no crower like the circle-squarer. 
 
 The following is an extract from the English Cyclopaedia, 
 Art. TABLES : 
 
 1 1853. William Shanks, " Contributions to Mathematics, com- 
 prising chiefly the Rectification of the Circle to 607 Places of Tables," 
 London, 1853. (QUADRATURE OP 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 deci- 
 mals ; and the value of the modulus '4342. . . . to 136 decimals ; with 
 the 13th, 25th, 37th ... up to the 721st powers of 2. These tremen- 
 dous stretches of calculation at least we so call them in our day are 
 useful in several respects ; they prove more than the capacity of this 
 or that computer for labour 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 
 
MR. SHANKS' QUADRATURE. 291 
 
 tliat 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 TT has been carried have 
 been indications of a general increase in the power to calculate, and in 
 courage to face the labour. Here is a comparison of two different 
 times. In the day of Cocker, the pupil was directed to perform a 
 common subtraction with a voice- accompaniment of this kind: " 7 from 
 4 1 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, &c." 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 2nd, 4th, 8th, &c., 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 2nd, 32nd, 64th, 
 128th, 256th, and 512th powers are given at the back of the announce- 
 ment, 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 having discovered, on some grounds of 
 theological 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' 608 figures .of the value 
 of TT 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; 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 ! 
 
 TT 2 
 
292 A BUDGET OF PARADOXES. 
 
 If the cyclometers and the apocalyptics would lay their heads 
 together until they come to a unanimous verdict on this pheno- 
 menon, 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 notices that 3 is 
 the number of most frequency, and that 3^- is the nearest approxi- 
 mation to it in simple digits. Prof. Smyth himself, whose word 
 on Egypt is paradox of a very high order, backed by a great 
 quantity of useful labour, the results of which will be made 
 available by those who do not receive the paradoxes, is inclined 
 to see confirmation for some of his theory in these phenomena. 
 
 These paradoxes of calculation sometimes appear as illustrations 
 of the value of a new method. In 1863, Mr. Gr. Suffield, M.A. 
 and Mr. J. E. Lunn, 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 paradoxical length, in 
 order to illustrate a method, is the solution of x 3 2#=5, the 
 example given of Newton's method, on which all improvements 
 have been tested. In 1831, Fourier's posthumous work on equa- 
 tions showed 33 figures of solution, got with enormous labour. 
 Thinking this a good opportunity to illustrate the superiority of 
 the method of W. Gr. Homer, not then known in France, and 
 not much known in 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 John- 
 ston, of Dundalk, and of the Excise Office, went to 101 decimal 
 places. To test the accuracy of this, I reqviested 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 connexion, 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. 
 
HOBNER'S METHOD COMETS. 293 
 
 In 1851, another pupil of mine, Mr. J. Power Hicks, 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. Gr. Homer written at length, until I applied to a 
 relative of his, who told me that he was, as I supposed, Win. 
 George, but that he was named after a relative of that surname. 
 
 The square root of 2, to 110 decimal places, was given me in 
 1852 by my pupil, Mr. William Henry Colvill, now (1867) Civil 
 Surgeon at Baghdad. It was 
 
 1-4142135623730950488016887242096980785696 
 7187537694807317667973799073247846210703 
 885038753432 764157273501384623 
 
 Mr. James Steel of Birkenhead verified this by actual multipli- 
 cation, and produced 
 
 o __ 2580413 
 
 10 117 
 as the square. 
 
 Calcolo decidozzinale del Barone Silvio Ferrari. Turin, 1854, 4 to. 
 
 This is a serious proposal to alter our numeral system and to 
 count by twelves. Thus 10 would be twelve, 11 thirteen, &c., 
 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 : but the one I shall 
 presently describe beats it so completely in that point, that I 
 have not a smile left for this one. 
 
 The successful and therefore probably true theory of Comets. 
 London, 1854. (4 pp. duodecimo.) 
 
 The author is the late Mr. Peter Legh, of Norbury Booths 
 Hall, Knutsford, who published for eight or ten years the Ombro- 
 logical 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 
 
294 A BUDGET OF PARADOXES. 
 
 become capable of having their returns predicted, is not ex- 
 plained. 
 
 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, 6 Mormon creed. Mind your own business. 
 Brigham Young ; ' on the right, ' Given by inspiration of GTod. 
 Joseph Smith.' A leading article on the discoveries of Prof. 
 Orson Pratt 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 Prof. Pratt's ' Law of Planetary Eota- 
 tion.' 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 and commented on. Dated 
 GK S. L. City, Utah Ter., Aug. 1, 1855. If the creed, as above, 
 be correctly given, no wonder the Mormonites are in such bad 
 odour. 
 
 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, c 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. 
 
MATHEMATICAL ILLUSTKATIONS OF DOCTRINE. 295 
 
 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 the other becomes 
 infinite. In fact, the argument is a perfect non sequitur. Those 
 who propose it have in their minds, though in a cloudy and in- 
 definite form, the idea of the increase of guilt being propor- 
 tionate 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 T 7 Q- times as great as another is 
 exactly, no more and no less, 4 T 7 ^- 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 Laid, 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 c 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, who was a sound 
 and learned mathematician, adopted this dangerous kind of 
 illustration in his Letters on the Christian Eeligion. 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 Chris- 
 tianity. 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 
 
296 A BUDGET OF PARADOXES. 
 
 named has a striking defect. He talks of reducing this world 
 and the next to 6 present value,' as an actuary does with succes- 
 sive 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 mathe- 
 maticians, 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) 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.' 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 (rod, 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 
 
NOVUM ORGANUM MORALIUM. 297 
 
 been, if Dante had been the later of the two. The original idea 
 is due to the elder Arnobius, who, as cited by Bayle, speaks 
 thus : 
 
 ' Sed et ipse [Christus] quse pollicetur, non probat. Ita est. Nulla 
 enim, ut dixi, futurorum potest existere comprobatio. Cum ergo hsec 
 sit conditio futurorum, ut teneri et comprehendi nullius possint 
 anticipationis attactu ; nonne 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.' 
 
 Eeally 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.] 
 
 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 6 Suggestions on the subject of a Novum 
 Organum MoraliumJ 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 Mora- 
 lium. 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, 
 political and ecclesiastical affairs. By Tresham Dames Gregg, 
 Chaplain of St. Mary's, within the church of St. Nicholas intra 
 muros, Dublin. London 1859, 8vo. (pp. xl -t- 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," 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 
 
298 A BUDGET OF PARADOXES. 
 
 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 honour. 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 in hunting.' . . It will be sufficient for us, however, to 
 be the Columbus of these great Americi, and popularise 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 tvpr)Kaffi ! Let us hope that they will join us, and * 
 henceforth keep their right [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 popularised 
 his discoveries. We do not wish for any svprj/cao-i, and not even for 
 ivprj/cacri. For self and Boole, I point out what would have con- 
 vinced either of us that this house is divided against itself. 
 
 A being the apostolic element, 8 the doctrinal element, and 
 X the body of the faithful, the church is A 8 X, we are told. 
 Also, that if A become negative, or the Apostolicity become 
 Diabolicity [my words] ; or if 8 become negative, and doctrine 
 become heresy ; or if X become negative, that is, if the faithful 
 become unfaithful ; the church becomes negative, 4 the very 
 opposite of what it ought to be.' For self and Boole, I admit 
 this. But which is not noticed if A and 8 should both become 
 negative, diabolical origin and heretical doctrine, then the church, 
 A 8 X, is still positive, what it ought to be, unless X 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 
 
DE MORGAN AND BOOLE CORRECTED. 299 
 
 my partner are of opinion that a diabolical church with falste 
 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 6 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 Eevelation in words at length, but as 
 X&' 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 : 
 
 ' And the whole tells us just this,- that David did what he could. He 
 augmented those elements of his constitution which were (exceptis 
 excipiendis) 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 aug- 
 mented, and c x rose proportionally. The law of the variation, accord- 
 ing 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 dx . dc 
 
 . = ce h ex a-fca; 
 
 de de de 
 
 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, &c. 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, honour, wealth, and power, &c. : in 
 short, to all the attributes of majesty.' 
 
 The 6 solution of the family problem ' is of high interest. It is 
 
300 A BUDGET OF PARADOXES. 
 
 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 l e l os l the mother, &c. 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 = - ; . . . . and 
 
 c 
 
 this expression will represent his relation to the servant. Consequently, 
 
 c ex =fa + - lz j e %; otherwise f a + - l - \ 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 4 go to the full 
 justification of this 4 principle,' is only true in the sense in which 
 the Scotch use, or did use, the word justification. 
 
 [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. I had quite for- 
 gotten 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 
 
BOOLE'S LAWS OF THOUGHT. 301 
 
 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, in the time of the Commonwealth, 
 published his 6 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 re- 
 membered in connexion with one of the most important steps 
 towards the attainment of this knowledge.] 
 
 The Decimal System as a whole. By Dover Statter. London and 
 
 Liverpool, 1856, 8vo. 
 
 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, &c. 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. 
 
 The first book of Phonetic Reading, London, Fred. Pitman, 
 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 pro- 
 moters of this spirited attempt is very large indeed. 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 
 
302 A BUDGET OF PAKADOXES. 
 
 unpronouncable 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 commence- 
 ment very much by complete words, as if they were learning 
 Chinese, and be gradually accustomed to resolve the known words 
 into letters, a fraction, perhaps a considerable one, of the advan- 
 tage of the phonetic system is destroyed. It must be remem- 
 bered 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 syste- 
 matically. 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 ad* 
 monition 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 books is that they nowhere, 
 so far as I have seen, give all the symbols, in every stage of ad- 
 vancement, together, in one or following pages. It is symbols 
 and talk, more symbols and more talk, &c, A universal view of 
 the signs ought to begin the works. 
 
MAGNITUDE OF THE EAETH THE MOON. 803 
 
 Ombrological Almanac. Seventeenth year. An essay on Anemo- 
 logy and Ombrology. By Peter Legh, 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. 
 
 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, 
 which is known to be very incomplete, or that of Prof. Niemand 
 with the lections, Mrgend, 1824, 2 vols. folio ; just to see whether 
 the 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. (Private Circulation.) In five parts. London, 
 1856, 1857, 1857 ; Calcutta, 1858, 1858, 8vo. 
 
 The earth is c brought to a focus ' ; it describes a 6 looped ' 
 orbit round the sun. The eclipse of the sun is thus explained : 
 4 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 
 
304 A BUDGET OF PARADOXES. 
 
 the earth, when a darkness beyond is produced reaching to the 
 earth, and the sun becomes more or less eclipsed.' How the 
 earth is 4 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. 
 
 Times, April 6 or 7, 1856. The moon has no rotary motion. 
 
 A letter from Mr. Jellinger Symons, 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. 
 
 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 endeavoured to disentangle Mr. J. C. 
 Symons, but failed. Mr. Airy 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 per- 
 suaded of the honesty of opponents. Those who know demon- 
 stration are differently situated. I suspect a train might be laid 
 
CAMBEIDGE DISPUTATIONS. 305 
 
 for the formation of a better habit in this way. We know that 
 Suvaroif taught his Eussians at Ismail not to fear the Turks by 
 accustoming them to charge bundles of faggots dressed in 
 turbans, &c. 
 
 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, 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, 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 derived functions, and Locke on innate principles. 
 And though I took off everything, and was pronounced by the 
 moderator to have disputed magno honore, 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. 
 
 The Doctrine of the Moon's Rotation, considered in a letter to the 
 Astronomical Censor of the Athenceum. By Jones L. Mae- 
 Elshender. Edinburgh, 1856, 8vo. 
 
 This is an appeal to those cultivated persons who will read it 
 c to overrule the dicta of judges who would sacrifice truth and 
 
 x 
 
306 A BUDGET OF PARADOXES. 
 
 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 c 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 4 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 intelli- 
 gent 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 admit- 
 ted 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 just 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. ' A tog 
 is a tog,' said Jansen. ' Yes,' replied another, c we all know a 
 dog is a dog ; but the question is Is this dog a dog ? ' And this 
 question would arise upon every dog of them all. 
 
 Zetetic Astronomy : Earth not a globe. 1857 (Broadsheet). 
 
 Though only a travelling 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 conclu- 
 sions 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. 
 In this last advertisement is the following announcement : ' A 
 paper on the above subjects was read before the Council and 
 
ZETETIC ASTKONOMY. 307 
 
 Members of the Koyal Astronomical Society, Somerset House, 
 Strand, London (Sir John F. W. Herschel, 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. Groulden's 
 way of representing the following occurrence : Dec. 8, 1 848, 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 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 round- 
 ness 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 pheno- 
 mena 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 6 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, 
 &c. Why a pendulum vibrates with less velocity at the Equator than 
 at the Pole. The allowance for rotundity supposed to be made by 
 
308 A BUDGET OF PARADOXES. 
 
 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.), &c.' 
 
 I wish there were geoplatylogical lectures in every town in 
 England (platylogical, in composition, need not mean babbling). 
 The late Mr. Henry Archer 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, 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 the suggester 
 of the perforated border of the postage-stamps, and, I think, of 
 the way of doing it ; for this he got 4,000. 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," &c.' < 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 
 
MOKE ZETETIC ASTRONOMY. 309 
 
 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, 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 accurate conception as that of 
 the motions of the heavenly bodies. The author, though confi- 
 dent in the extreme, neither impeaches the honesty of those 
 whose opinions he assails, nor allots them any future incon- 
 venience : 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 4 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 6 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 LEVEL chart ! 
 
 To which I answer : 
 
 Why, really Mr. Common Sense, you've never got so far 
 
 As to think Merca tor'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 ! 
 
310 A BUDGET OF PARADOXES. 
 
 The great wish of persons who expose themselves as above, is 
 to be argued with, and to be treated as reputable and refutable 
 opponent?, 6 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. He announces himself 
 as the 49th and last Emanuel : his immediate predecessors were 
 Emanuel Washington, Emanuel Newton, and Emanuel Galileo. 
 He is to collect nations into one family. He knows the trans- 
 migrations of the whole human race. Thus Descartes became 
 William III. of England : Eoger Bacon became Boccaccio. But 
 Charles IX., 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 GKEAT PYRAMID. 311 
 
 A Letter to the members of the Anglo- Biblical Institute, dated 
 Sept. 7, 1858, and signed * Herman Heinfetter.' (Broadsheet.) 
 
 This gentleman is well known to the readers of the Athenceum, 
 in which, for nearly twenty years, he has inserted, as advertise- 
 ments, long arguments in favour of Christians keeping the Jew- 
 ish 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 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, 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 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 Dispensa- 
 tion, 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 
 
312 A BUDGET OF PAEADOXES. 
 
 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. 
 My old friend Mr. Taylor is well known as the author of the 
 argument which has convinced many, even most, that Sir Philip 
 Francis was Junius : pamphlet, 1813; supplement, 1817; second 
 edition 4 The Identity of Junius with a distinguished living cha- 
 racter established,' London, 1818, 8vo. He told me that Sir 
 Philip Francis, in a short conversation with him, made only this 
 remark, 4 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, 4 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 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 competi- 
 tor who has been named : but what the odds may be against the 
 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 bad 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 
 
MRS. ELIZABETH COTTLE. 313 
 
 very patiently before he published : and all his works are 
 valuable for their accurate learning, whichever side the reader 
 may take.) 
 
 1859. The Cottle Church. For more than twenty years printed 
 papers have been sent about in the name of Elizabeth Cottle. It 
 is not so remarkable that such papers should be concocted as that 
 they should circulate for such a length of time without attract- 
 ing public attention. Eighty years ago Mrs. Cottle might have 
 rivalled Lieut. Brothers or Joanna Southcott. 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 
 feature of our time : I therefore make a few extracts, faithfully 
 copied as to type. The Italic is from the New Testament ; the 
 Eoman is the requisite interpretation : 
 
 1 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, Clapham, 
 the then district church, before All Saints was built, read the funeral 
 service over the Sepulchre wherein never before man was laid. 
 
 4 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 PKEPARED place for you " Cottleifces 
 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, 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 /(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. " Oar Father which art (God) 
 in Heaven," hallowed be thy name, tky (Cottle) kingdom come, thy will 
 be done in earthy as it is (done) in (the new) Heaven (and new earth of 
 the new name of Cottle Rev. xxi. 1 ; iii. 12). 
 
 1 . . . 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 
 
314 A BUDGET OF PARADOXES. 
 
 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, 110 nation can invade us. 
 
 * In verse 4 the Church of St. Peter is m prison between four 
 quaternions of soldiers the Holy Alliance of 1815. B/ev. 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, 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, Jan. 1, 1842, and for ever. See book of Life, page 24. 
 Matt, xviii. 19, xxi. 13 1 6. 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. 
 
 1 1 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 in- 
 vestment of excentricity. I take it for granted that the gentle- 
 men 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 
 
THE COTTLE CHUKCH. 315 
 
 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 7379), that rideth (by rail and 
 steam over land and sea, from his holy habitation at Kirksfcall Lodge, 
 Psa. Ixxvii. 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).' 
 
 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. Eobert Cottle, 
 was accompanied by a manuscript letter from Mrs. Cottle, appa- 
 rently a circular. The date was Nov r . 1853, and the subject 
 was the procedure against Mr. Maurice 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,) &c. 
 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 change in them, much akin to the miracle of transub- 
 stantiation 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 prepara- 
 tions 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 every- 
 
316 A BUDGET OF PARADOXES. 
 
 thing 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 Eoman 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 gentle- 
 men' may be meant the clergy. I suppose my first interpretation 
 must have been suggested by context : I leave the point to the 
 reader's sagacity. 
 
 The Problem of squaring the circle solved ; or, the circumference 
 and area of the circle discovered. By James Smith. 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 emi- 
 nent 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 GKEAT CYCLOMETER 317 
 
 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. Re- 
 printed 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. 
 
 [On the relations between the dimensions and distances of the Sun, 
 Moon, and Earth ; a paper read before the Literary and Philo- 
 sophical 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 behaviour 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 ; 
 Eowan Hamilton quietly proved him wrong in a way accessible to 
 an ordinary schoolboy ; Whewell, 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 to 
 hold, the Supreme Pontiff of cyclometers, the vicegerent of St. 
 
318 A BUDGET OF PAKADOXES. 
 
 Vitus upon earth, the Mamamouchi of burlesque on inference. 
 I begin with a review of him which appeared in the Athenceum 
 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. The 
 symptoms soon took a defined form : his circumference shrank 
 into exactly 3 times his diameter, instead of close to S^-- y , which 
 the mathematican 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 c The Relations of a Circle inscribed in 
 a Square' ! The paper was thus forced upon the Association, for 
 Mr. Smith informs us that he ' 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 
 
ATHENAEUM EEVIEW OF ME. SMITH. 319 
 
 we mean in intention protested against the publication, saying, 
 c 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 publica- 
 tion, 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 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^ 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 some- 
 times 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 A C as dia- 
 meter, describe the circle D, which by hypothesis shall be equal 
 to three and one-eighth times the length of A C. ... 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 
 
320 A BUDGET OF PARADOXES. 
 
 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 Gralileo ; and to expose to the world the 
 perverse behaviour of the Astronomer Royal, on whom he wanted 
 to fasten a conversation, and who replied, 4 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 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, 
 
ATHENJEUM REVIEW CONTINUED. 321 
 
 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 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, of Houghton-le-Spring, and Dr. Eutherford 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 English Cyclo- 
 pcedia, an account of the matter which may illustrate the un- 
 imaginable, 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 : 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 
 
 Y 
 
322 A BUDGET OF PARADOXES. 
 
 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 abso- 
 lutely equal to two right angles ; no stretch of progression will 
 detect any error. 
 
 Now think of Mr. Lacomme's mathematical adviser (ante, p. 32) 
 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 de- 
 claring that it is a trifle more than 3,141^. 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 1001. Of course, if he set out with such an error he will 
 accumulate blunder upon blunder. Now, if there be a process in 
 which close knowledge of the circle is requisite, it is in the predic- 
 tion of the moon's place say, as to 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 100Z. of error in 
 his circumference, he gets within the fifth part of a farthing in 
 100?. 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 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 somehoV, 
 
ATHENE mi KEVIEW CONTINUED. 323 
 
 There is always a difficulty about the mode in which the think- 
 ing 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 differ- 
 ent 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 
 as Adam Smith was the man of things then to come, or Luther, 
 or Galileo ? It is true that there is an unanimity among mathe- 
 maticians 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 ques- 
 tions 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, how- 
 ever 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 mathe- 
 matical demonstration, may show himself utterly destitute of all 
 that distinguishes the reasoning geometrical investigator from the 
 calculator. 
 
 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 
 
 T 2 
 
324 A BUDGET OF PAKADOXES. 
 
 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^- 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 Athenceum 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 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. Eowan Hamilton a proof that 
 the circumference is more than 3|- 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. E. Hamilton's brief and easy exposure will 
 procure him notice in connexion with this celebrated problem. 
 
SIR W. ROWAN HAMILTON ON TT. 325 
 
 It is to be shown that the perimeter of a regular polygon of 20 
 sides is greater than 3|- diameters of the circle, and still more, 
 of course, is the circumference of the circle greater than 3^ 
 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 1280x1280; 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 (4x1280125) 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 125x1280 is equal to 400x400; 
 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 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 circum- 
 ference of the circle, is greater than 25 : that is, the circumference 
 is more than 3^ diameters." 
 
 The last work in the list was thus noticed in the Athenceum, 
 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 Prof. 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 
 
326 A BUDGET OF PARADOXES. 
 
 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, c 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 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, if not the horribile flagellum. 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 ?] or leave 
 
ARGUMENT EX ABSURDO, 327 
 
 myself open to the humiliating charge of mathematical ignorance 
 and folly. He has also honoured me with some private letters* 
 In the first of these he gives me a ' piece of information,' after 
 which he cannot imagine that I, 4 as an honest mathematician,' 
 can possibly have the slightest hesitation in admitting his solu- 
 tion. There is a tolerable reservoir of modest assurance in a man 
 who writes to a perfect stranger with what he takes for an argu- 
 ment, 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, ' I love Moll Cobb for her 
 impudence.' I have now done with my friend's suaviter in modo, 
 and proceed to his fortiter in re : I shall show that he has con- 
 victed himself of ignorance and folly, with an honesty and candour 
 worthy of a better value of TT. 
 
 Mr. Smith's method of proving that every circle is 3^ diameters 
 is to assume that it is so, ' if you dislike the term datum, then, 
 by hypothesis, let 8 circumferences of a circle 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 hypo- 
 thesis, when I can prove by means of it that every other value of TT 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 of a " redudio ad absurdum " 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, II a 
 perdu le droit d'etre frappe de V evidence. 
 
 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 4 piece of information ' which 
 will settle me, if I be honest. Assuming TT to be 3, he finds out 
 
328 A BUDGET OF PARADOXES. 
 
 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, 
 
 . f 25 /Arr 2 8 
 
 lf "- = ^' VU ' 
 
 This c 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 6 being any two numbers whatever, 
 we need only assume 
 
 We naturally ask what sort of glimmer can Mr. Smith have of 
 the subject which he professes to treat ? On this point lie has 
 given satisfactory information. I had mentioned the old problem 
 of finding two mean proportionals, as a preliminary to the dupli- 
 cation of the cube. On this mention Mr. Smith writes as follows. 
 I put a few w T ords in capitals ; and I write rq for the sign of the 
 square root, which embarrasses small type : 
 
 1 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 = \ (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 ^ =20 x 8 '* 25 =20 x 78125= 15-625 will 
 4 4 
 
 be the first number; as 25 : 16 : : rq 20: rq 8192: and (rq 8'192) 2 
 X = 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 evi- 
 dence 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, #, 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, #, T/, 20, x is a mean proportional 
 between 5 and 2/, and y is a mean proportional between x and 20. 
 And these means are # = 5^4, y = 5 ty 16. But Mr. Smith 
 
EXTEACT FROM CAMBRIDGE TRANSACTIONS. 329 
 
 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 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, &c. 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 
 
330 A BUDGET OF PARADOXES. 
 
 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 lie 
 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 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 80,000. at the banker's, 
 though you knew the book only showed 30,000?.? 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 6 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 
 
VALUE OF INSTANCES OF INACCURACY. 331 
 
 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 con- 
 spicuous as the speculator who, more visibly than almost any 
 other known to history, reasoned in a circle by way of reasoning 
 on- a circle. But 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 compe- 
 tent to think of the great mental disciplines. To this end I 
 should desire him to continue his efforts, to amplify and develope 
 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 4 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 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 
 
332 A BUDGET OF PARADOXES. 
 
 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 Welch- 
 men.' 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 geo- 
 metry, who are always assailing, but never taking, the Grarde 
 Douloureuse of the circle. ' At this commentary,' proceeds the 
 story, fc 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 assum- 
 ing 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. 
 
 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 Groliath, 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. The confusion of 
 images is amusing : Groliath turning himself into a snail to avoid 
 TT = 3, and James Smith, Esq., of the Mersey Dock Board : and 
 
KEFUTATION BY A CANTAB. 333 
 
 put hors de combat which should have been cache by pebbles 
 from a sling. If Goliath had crept into a snail-shell, David 
 would have cracked the Philistine with his foot. There is some- 
 thing 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 that one of the 
 letters to the Athenceum signed Nauticus is in the same hand- 
 writing. 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] endeavour to confine 
 myself to dry reasoning from incontrovertible premisses ... 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. 1 
 
 [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 
 
334 A BUDGET OF PARADOXES. 
 
 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. Hob- 
 house was sent to Newgate for a libel on the House of Commons 
 which was only intended for a libel on Lord Erskine. 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 TT 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 spelt 
 Jimm. 1 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 desig- 
 nated : it is enough if, as the Latin grammar has it, Verbum 
 personals concordat cum nominativo. 
 
 I may plead precedent for taking a liberty with the orthography 
 of Jem. An instructor of youth was scandalised at the abrupt 
 and irregular but very effective opening of Wordsworth's little 
 piece : 
 
 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 
 
 1 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. (Ei> ) 
 
MEASUKEMENT OF THE ANGLE. 335 
 
 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, 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' 141 6 or the tables must be 
 wrong. He does not know that sines, as well as TT, are inter- 
 minable 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 Athenwum : 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, and y half 
 the sine of an angle of 30 =s 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 xij ? secondly, what is the angle of which xy re- 
 presents the circular measure ? 
 
 If x represent 15 and y be , xy represents 3 45', whether 
 x y be xy or no. But, y being , x y is not xy unless x be ^, 
 that is, unless I2x or TT 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 1 
 
 Mr. Smith says that for the future he will give up what he 
 calls sarcasm, and confine himself, 4 as far as possible,' to what he 
 
336 A BUDGET OF PARADOXES. 
 
 calls dry reasoning from incontrovertible premisses. 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 
 the indefinite something in the mysterious all this. They are 
 brought to the point of suspicion that the mathematicians ought 
 not to treat 4 all this ' with such undisguised contempt, at least. 
 Now I have no fear for TT : but I do think it possible that general 
 opinion might in time demand that the crowd of circle-squarers, 
 &c. should be admitted to the honours 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 prevent- 
 ing such opinion from growing. A speculator who expressly 
 assumes what he wants to prove, and argues that all which con- 
 tradicts 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 strapp- 
 ing 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 Lave 
 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.' 
 
THE 1VJPON HOAX. 337 
 
 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 intention of bringing me, with a 
 contrite heart, and clean shaved, 4159265. . . razored down to 
 25 5 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 at- 
 tempted to treat me as the terrible Colonel would have treated 
 the inoffensive brother. 
 
 He is at liberty to try again. 
 
 The Moon-hoax ; or the discovery that the moon has a vast popu- 
 lation of human beings. By Richard Adams Locke. New 
 York, 1859, 8vo. 
 
 This is a reprint of the hoax already mentioned. I suppose 
 E. A. Locke is the name assumed by M. Nicollet. 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. 
 
 This discovery was also published under the name of A. E. 
 Grant. Sohnke's ' Bibliotheca Mathematica ' confounds this 
 Grant with Professor E. Grant of Glasgow, the author of the 
 c 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, the co-discoverer of Neptune. Sohnke 
 gives the titles of 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 E. A. Locke 
 was editor. It so much resembled a story then recently 
 published by Edgar A. Poe, in a Southern paper, c Adven- 
 tures of Hans Pfaal,' that some New York journals pub- 
 lished the two side by side. Mr. Locke, when he left the 
 New York Sun, started another paper, and discovered the 
 manuscript of Mungo Park ; 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, Mr. Harrison Ainsvvorth, 
 
338 A BUDGET OF PARADOXES. 
 
 and others. I have no doubt that M. Nicollet was the author of 
 the Moon hoax, 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. 
 Dray son. 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 time : the tele- 
 graph 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 in- 
 creases 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. 
 
 Athenceum, August 19, 1865. Notice to Correspondents. 
 
 4 R. "W. If yon 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 com- 
 mencement of my Budget ; but I have no recollection of having 
 
IMPALEMENT BY BEQUEST. 339 
 
 received it, and I cannot find it on the (nursery ? 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 abnormalised 
 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. 
 
 The Hailesean System of Astronomy. By John Davey Hailes (two 
 pages duodecimo, 1860). 
 
 He offers to take 100,00(M. to 1,OOOZ. that he shows the sun to 
 be less than seven millions of miles from the earth. The earth 
 in the centre, revolving eastward, the sun revolving westward, 
 so that they 6 meet at half the circle distance in the 24 hours.' 
 The diameter of a 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 ' 
 
340 A BUDGET OF PARADOXES. 
 
 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 name stand placed first. Do the worthy Frenchman 
 
 justice. 
 
 By awarding him the medal in a trice. 
 Give Adams 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 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. Kewards offered for astronomical problems. With 
 magnetism, &c. &c. 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, says Isaac : meaning in figures, not in ortho- 
 graphy. Mr. Hailes enters into the spirit, both positive and 
 negative, of this dictum, by giving the distance of Sidius from 
 the centre of the earth at 163,162,008 miles 10 feet 8 inches 17- 
 28ths of an inch. Of course, he is aware that the centre of figure 
 of the earth is 17'1998 inches from the centre 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 with- 
 out plurality, Deus : order II., FinUa? angels good and evil. 
 
JOHANNES VON GUMPACH. 341 
 
 The rest is all about a triune system, with a diagram. The 
 author is not aware that o>ov is not animal, but living being. 
 Aristotle has classed gods under fwa, and has been called to 
 account for it by moderns who have taken the word to mean 
 animal. 
 
 Explication dn Zodiaque de Denderah, des Pyramides, ei de 
 Genese. Par le Capitaine an longcours Justin Roblin. Caen, 
 1861. 8vo. 
 
 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 neighbours. 
 
 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. 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, ad- 
 dressed 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 recognised 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. 
 
342 A BUDGET OF PARADOXES. 
 
 Perpetuum Mobile : or Search, for self-motive Power. By Henry 
 Dircks. 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, which he 
 obtained from Kobert Stephenson. 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 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 con- 
 tempt, 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 philosophers said, 
 it will not gravitate, being in proprio loco. 
 
 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 : 
 
 4 To the legal mind, the part of [the part taken by] the Times will 
 present a primd facie case of the gravest nature, in the evident fore- 
 knowledge of the event, and the preparation to tarn it to account 
 when it should have occurred. The article printed on Saturday must 
 
SLANDER PARADOXES. 343 
 
 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 insinuations to 
 the effect that the Prince was the obstacle to Kussian 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 Eussia must have done it. Enough for this record. 
 Un sot trouve toujours un plus sot qui Vadmire : who can he be 
 in this case ? 
 
 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 now undoubted right to rank with 
 Le Verrier was made sure at the very outset by the manner in which 
 Mr. Airy, 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 pre- 
 sumption as to motive is that, had Mr. Adams been recognised, 
 6 then the discovery must have been indisputably an Englishman's, 
 and that Englishman not the Astronomer Eoyal.' Mr. Adams's 
 conclusions were ' retouched in France, and sent over the year 
 after.' The proof given is that it cannot be ' imagined ' other- 
 wise. 
 
 ' Can it then be imagined that the Astronomer Eoyal received such 
 results from Mr. Adams, supported as they were by Professor Challis's 
 valuable testimony as to their probable accuracy, and did not bring 
 
344 A BUDGET OF PARADOXES. 
 
 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 6 evidence which I con- 
 sider it difficult to refute.' He ends by calling upon certain 
 persons, of whom I am one, to 4 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 continua- 
 tion of this list, which I confidently expect, life and health per- 
 mitting, 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,' (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^ 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 Eoyal's alleged neglect 
 to give Mr. Adams that ' encouragement and protection ' which 
 was his due, and does not hint one word about the article contain- 
 ing the charge of having secretly and fraudulently transmitted 
 news of Mr. Adams's researches to France, that an Englishman 
 might not have the honour 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 
 pp. 349).] 
 
 I have said that those who are possessed with the idea of con- 
 
JAMES IVORY. 345 
 
 spiracy 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 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 unfavourable 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 pecu- 
 liarity 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 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, the Assistant Secretary, at the time when Francis Baily 
 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. Mr. Gralloway, to whom I com- 
 municated 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 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 expres- 
 sion. 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 
 
346 A BUDGET OF PAEADOXES. 
 
 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. 
 
 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 refer- 
 ence 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 cha- 
 racter of the articles ; but I am not concerned with this point. 
 Secondly, there is the journal which is supported by voluntary 
 contributions of 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 declined a cheque forwarded for an 
 article in the Quarterly, John Murray 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. 1 1 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 
 sympathise with them. Moreover, this sort of journal is more 
 accessible than others to articles conveying personal imputation : 
 
THE MECHANICS' MAGAZINE. 347 
 
 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. 
 
 Among the journals which went all lengths with contributors 
 whom they valued, was the Mechanics' Magazine in the period 
 1846-56. I cannot say that matters have not mended in the last 
 ten years : and I draw some 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 ridicu- 
 lous charge against the Astronomer Eoyal 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 illus- 
 trate ; 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 connexion with en- 
 gineering, &c., 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 communi- 
 cations, 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 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 illus- 
 tration 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 giving the review, I shall observe that 
 Mr. Adams, in whose favour the attack on the Astronomer Koyal 
 was made, did not appreciate the favour ; and of course did not 
 come forward to shield his champion. This gave deadly offence, 
 as will 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 Gonnaissance des 
 
348 A BUDGET OF PAHADOXES. 
 
 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 
 (p. 11). What precedes and follows has some criticism on the 
 Government, the Astronomer Royal, &c., but reserved in allusion, 
 oblique in sarcasm, and not fiercely uncourteous. The coarseness 
 of the passage I have quoted shews 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, c 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 pub- 
 lished 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 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, '2nd revise, December 27, 1846, at noon,' in the hand- 
 writing 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 my- 
 self, (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 
 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'ceuvre, is considered, by competent judges, 
 
EXTRACT FROM MECHANICS' MAGAZINE. 319 
 
 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 0. Halliwell, Esq., 
 F.R. and A.S.S., but the tremendous effort which the learned writer 
 then made to excel many titled competitors for honours 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 and modern usage in reckon- 
 ing ' 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. 
 
 4 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 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 foot-notes ; we give one of the 
 most interesting, taken from the learned Mr. Halliwell's profound 
 book on Nursery Rhymes a celebrated production, for which it is 
 supposed the author was made F.R.S. 
 
350 A BUDGET OF PAKADOXES. 
 
 ' One's nine, 
 Two's some, 
 Three's a many, 
 Four's a penny, 
 Five's a little hundred.' 
 
 1 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 4 EAEA 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 not, deny it. [N.B. I no 
 more doubt that he was the author than I doubt that I am the 
 author of this sentence.] * 
 
 Accordingly, * * * was withdrawn, and a discussion took 
 place, for which see the Athenceum, 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 whis- 
 perings against Adams (see ante, p. 348), and the above against 
 myself. In due time, I doubt not my name will appear as one of 
 the ames damnees of the Mechanics' Magazine. 2 
 
 First, as to Mr. Halliwell. The late Thomas Stephens Davies, 
 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 
 
 1 The subject of this criticism is of long past date, and as it has only been intro- 
 duced 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. ED. 
 
 2 The editor of the Mechanics' Magazine died soon after the above was written. ED. 
 
T. S. DAVIES ON EUCLID. 351 
 
 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 Homer's papers. His letter announcing the trans- 
 mission is dated February 2, 1850. This is a strong point; but 
 there is another quite as strong. Euclid and his writings were 
 matters on which T. S. Da vies knew neither fear nor favour: 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 2 2-column article, 'Eucleides' in Smith's Dictionary., 
 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 : 4 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 contribu- 
 tions 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 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, JL use the subjunctive 'if no man 
 
352 A BUDGET OF PARADOXES. 
 
 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 4 none, the denial of one, comes to be asso- 
 ciated with the denial of plurality,' reads as 6 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 hand- 
 writing, 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 trans- 
 lated into 4 one is not one,' that it must have been 4 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 halfpenny- 
 worth 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 en- 
 dowed 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 
 childen, 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. 
 
 1862. Mr. Smith replies to me, still signing himself Nauticus : 
 I give an extract : 
 
 4 By hypothesis [what, again !] Jet 14 24' be the chord of an arc of 
 15 [but I wont, says 14 24 / ], and consequently equal to a side of a 
 regular polygon of 24 sides inscribed in the circle. Then 4 times 
 14 24' == 57 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 
 
THE TWO J. S'S. 853 
 
 injuria 1 The other J. S., Joseph Scaliger, 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 insti- 
 tuted, but not in half a column. And J. S. the second has been 
 so tightly handled that he may now be dismissed, with an inscrip- 
 tion for his circular shield, obtained by changing Lexica contexat 
 into Circus quadrandus in an epigram of J. S. the first : 
 
 Si quern dura manet sententia judicis, olim 
 
 Damnatum serumnis suppliciisque caput, 
 
 Hunc neque fabrili lassent ergastula massa, 
 
 Nee rigidas vexent fossa metalla manus. 
 
 Circus quadrandus : nam castera quid moror ? omnes 
 
 Poenarum facies hie labor unus habet. 
 
 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 I 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 I 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 TT the letters I and g are closely related : 
 this appears in the well-known formula for the time of oscillation, 
 TT \/(l : g). Hence g may be written for i, but only once : do it 
 twice, and you require the time to be TT V (f 2 : g 2 ). This may be 
 reinforced by observing that if as a datum, or if you dislike that 
 
 A A 
 
354 A BUDGET OF PARADOXES. 
 
 word, by hypothesis, the first I be a #, it is absurd that it should 
 be an I. Write g for the first Z, 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^ 
 diameters to the circumference in 7r-glory. Oh for a drawing 
 of this scene ! Mr. De Morgan presents his compliments to 
 Mr. James Smith, and requests the honour of an exchange of 
 photographs. 
 
 July 26. Another printed letter. Mr. James Smith begs for 
 a distinct answer to the following plain question : c Have I not 
 in this communication brought under your notice truths that 
 were never before dreamed of in your geometrical and mathe- 
 matical 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 
 bee a done. 
 
 The Circle secerned from the Square ; and its area gauged in 
 terms of a triangle common to both. By Wm. Houlston, Esq. 
 London and Jersey, 1862, 4to. 
 
 Mr. Houlston squares at about four poetical quotations in a 
 page, and brings out TT= 3*14213 .... His forntispiece 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. London, 1862. 8vo. 
 
 Newton and others think that in a revolving sphere the 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. 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 notion. In 
 a more recent work 4 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 
 
BIRKS ON MATTER AND ETHER. 855 
 
 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 un- 
 learned 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 cequivocatio. The author, as a 
 physician, is accustomed to ; appeal from mere formula ' : accord- 
 ingly, 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. 
 
 On matter and ether, and the secret laws of physical change. By 
 T. K. Birks, M.A. 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. 
 
 The history of the l 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. (Private circulation.) London, 1862, 8vo. 
 
 This is much about Thorn, and its connected words, Thor, 
 Thoth, Theta, &c. 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, 
 
 A A 2 
 
356 A BUDGET OF PARADOXES. 
 
 William Thorn, M.D., is obliged to reveal himself, since it is his 
 object to prove that he himself is one 666. By using W for a 
 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 anyone who 
 reads the chapter in Ezekiel will see is quite against his com- 
 parison. 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 JNauticus, 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^ diameters 
 in circumference. The round man in the three-cornered hole, 
 finally William Thorn, M.D. takes charge of my future destiny, 
 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 
 
DE. THOEN ME. BIDEN. 357 
 
 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 ; 
 of the City of London, Grog and Magog ; of the Paradoxiad, 
 James Smith, Esq., and William Thorn, M.D. 
 
 September, 1866. Mr. James Biden has favoured 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 Bidun's. 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 wing swings in Scripture denote the flight of time. 
 Thus the beasts or living creatures of the Eevelations 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, 
 . 
 
 '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. 
 
 6 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 schoolfellows 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 
 
858 A BUDGET OF PAKADOXES. 
 
 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, &c. 
 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 Eevelations. 
 
 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. 
 
 An hi&t >rical survey of the Astronomy of the Ancients. By the 
 Et. Hon. Sir G. C. Lewis. 8vo. 1862. 
 
 There are few men of our day whom I admire more than the 
 late Sir GK 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. Maiden's Pragmatized Legends, Mr. Mansel's Phrontisterion, 
 and Sir Gr. Cornewall Lewis's Inscriptio Antiqua. In this last, 
 HEYDIDDLEDIDDLETHECATANDTHEFIDDLE &c. 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. Dens propitius [est], deus 
 [donatori] libenter fa vet. Deus in vianim juncture, ovorum dape 
 [eolitur], deus mundi. Deus in litatione voluit, benigno ammo, 
 haedum, taurum intra fines [loci sacri] portandos. Deus, bis lustratus, 
 beat fossam sacrse libationis.' 
 
 How then comes the history of astronomy among the paradoxes ? 
 Simply because the author, so admirable 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 
 
SIE O. C. LEWIS. 359 
 
 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 sup- 
 pression 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 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, as we learn from Simplicius ; 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 . . . . ly. 321d. 23h. 
 Jupiter ... 12 .... lly. 315d. 14h. 
 Saturn .... 30 .... 29y. 174d. Ih. 
 
 Upon this determination two remarks may be made. First, the error 
 with respect to Mercury and Yenus 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 Yenus 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 Yenus (130 days) is 
 not apparent. 
 
 Sir Gr. 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 
 
360 A BUDGET OF PARADOXES. 
 
 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 de- 
 partures. Say that a person not much accustomed to the distinc- 
 tion 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. a69>) [(169). See Delambre, 
 Hist. Astr. Mod. vol. i. p. 96]. It was reserved to Kepler to pro- 
 pound 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 cited, it is that the parallelism of 
 the earth's axis is a glaring part of the theory of Copernicus. 
 What Kepler did was to throw away, as unnecessary, the method 
 by which Copernicus, per fas et nefas, 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 them- 
 selves 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 parallel- 
 ism; 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 ? 
 
SIR G. 0. LEWIS. 361 
 
 * C'est done pour arriver a ce parallelisme, on pour le conserver, que 
 Copernic a cm devoir recourir a ce mouveinent egal et oppose qui 
 detruit 1'effet qn'il attribue si gratuitement au premier, de deranger le 
 parallelisme.' . 
 
 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 under- 
 values, 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 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 con- 
 fusion about astronomy. Theophrastus, who is either the culprit 
 or his historian, attributes to Meton, 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 we read about the nineteen years of 
 the shining sun 
 
 'RvveaKatfieKa KVK\CL (JxiEti'ou ^eX/oio. 
 
 Some man of letters must have turned Apollo into Phaeinus of 
 Elis ; and there he is in the histories of astronomy to this day. 
 
362 A BUDGET OF PAEADOXES. 
 
 Salmasius will have Aratus to have meant him, and proposes to 
 read rj\sioio : 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 
 criticised 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 recal the first. In 1855 I was one of a 
 deputation of about twenty persons who waited on Sir Gr. Lewis, 
 as Chancellor of the Exchequer, on the subject of the decimal 
 coinage. The deputation was one of much force : Mr. Airy, with 
 myself and others, represented mathematics ; William Brown, 
 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 com- 
 merce. There were bullionists, accountants, retailers, &c. Sir 
 Gr. 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, &c. &c. 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 c Surely there is no doubt that the 
 calculations of our books of arithmetic are easier 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, c I may be out of my depth here I ' 
 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.] 
 
 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 
 
DECIMAL COINAGE. 363 
 
 of editors I repeat of them. The preservation of a very marked 
 instance, the association of political recklessness with cyclo- 
 metrical and Apocalyptic absurdity, may have a tendency to warn, 
 not indeed any hardened publicman 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, 
 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, 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 para- 
 graphs, with the 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 is not 
 
 from the issue of florins. His for us to gainsay it. It only 
 
 only experience of their conve- proves that he is one of that 
 
 nience was, that when he ought class of men who are described 
 
 to have received half- a- crown, he in the old song, of which one 
 
864 A BUDGET OF PAHADOXPIS. 
 
 had generally received a florin, couplet runs thus : 
 
 and when he ought to have paid I sold my cow to buy me a calf; 
 
 a florin, he had generally paid I never make a bargain but I lose 
 
 half-a-crown." (Hear, hear, and half, 
 
 laughter.) With a &c. &c. &c. 
 
 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 humour decided 
 that the introduction of the florin had been " eminently successful and 
 satisfactory." 
 
 The truth is, that Mr. Lowe here attacks nothing except the co- 
 existence of the florin and half-crown. We are endeavouring 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 ever our coin in terms of the penny, 
 bought anything, who ever reck- which we abandon, instead of the 
 oned or wished to reckon in such florin, which we retain. Ee- 
 a coin as that ? " (Hear, hear.) member that this 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 the highest unit of account ; amongst others, a ma- 
 jority of the House of Commons, the Bank of England, the majority 
 of London bankers, the Chambers of Commerce in various places, &c. 
 &c. &c. 
 
 " Such a coin could never come Does 2|d. never pass from hand 
 
 into general circulation, because to hand ? And is 2-^d. so pre- 
 it represents nothing which cor- cisely the modulus of popular 
 responds with any of the wants wants, that an alteration of 4 per 
 of the people." cent, would make it useless ? Qf 
 
 all the values which 2^d. mea- 
 sures, 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, &c. &c. &c., would adapt themselves to the coin. 
 
MR. LOWE ON DECIMAL COINAGE. 
 
 365 
 
 " If the proposed system were 
 adopted, they would all be com- 
 pelled to live in decimals for 
 ever ; if a man dined at a public - 
 house he would have to pay for 
 his dinner in decimal fractions. 
 (Hear, hear.) He objected to 
 that, for he thought that a man 
 ought to be able to pay for his 
 dinner in integers. " (Hear, hear, 
 and a laugh.) 
 
 The confusion of ideas here 
 exhibited is most instructive. 
 The speaker is under the im- 
 pression that we are introducing 
 fractions : the truth is, that we 
 only want to abandon the more 
 difficult fractions which we have 
 got, and to introduce easier frac- 
 tions. Does he deny this ? Let 
 us trace his denial to its legiti- 
 mate consequences. A man ought 
 
 to pay for his dinner in integers. 
 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, &c., 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 and Walkingame, and always 
 looks down the proposed system. The word decimal is obstinately 
 associated with fractions, for which there is no need. Hence it be- 
 comes 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 endeavour, 
 Condemned to pay in decimals for ever, 
 
 "The present system, however, 
 had not yet been changed into 
 decimal system. That change 
 might appear very easy to accom- 
 plished mathematicians and men 
 of science, but it was one which 
 it would be very difficult to carry 
 out. (Hear, hear). What would 
 have to be done ? Every sum 
 would have to be reduced into a 
 vulgar fraction of a pound, and 
 then divided by the decimal of a 
 pound a pleasant sum for an 
 old applewoman to work out ! " 
 (Hear, hear, and laughter.) 
 
 A pleasant sum even for 
 an accomplished mathematician. 
 What does divided by the 
 decimal of a pound mean ? Per- 
 haps it means reduced to the 
 decimal of a pound ! Mr. Lowe 
 supposes, as many others do, 
 that, after the change, all calcu- 
 lations will be proposed in old 
 money, and then converted into 
 new. He cannot hit the idea 
 that the new coins will take the 
 place of the old. This lack of 
 apprehension will presently ap- 
 pear further. 
 
 " It would not be an agreeable Let the members be assured 
 
366 A BUDGET OF PARADOXES. 
 
 task, even for some members of that nine half-pence will be, for 
 that House, to reduce 4Jd., or every practical purpose, 18 mils, 
 nine half-pence, to mils." (Hear, But now to the fact asserted, 
 hear.) Davies Gilbert 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, Pollock, and Hume. 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 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, &c. ; 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 Gliiltern 
 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^d. 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 know- 
 nothings, those others cry Hear to the country in a transport of de- 
 light. 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 new coins are commensurable 
 scale of coins would not be com- with, and in a finite ratio to, the 
 mensurate in any finite ratio with old ones. The farthing is to the 
 anything in this new currency of mil as 25 to 24. The speaker has 
 mils." 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. 
 
ME. LOWE ON DECIMAL COINAGE. 
 
 367 
 
 " No less'than five of our present 
 coins must be called in, or else 
 which, would be worse 
 new values must be given to 
 them." 
 
 " If a poor man put a penny in 
 his pocket, it would come out a 
 coin of different value, which he 
 would not understand. Suppose 
 he owed another man a penny, 
 how was he to pay him? Was 
 he to pay him in mils ? Four 
 mils would be too little, and five 
 mils would be too much. The 
 hon. gentlemen said there would 
 be only a mil between them. 
 That was exactly it. He be- 
 lieved there would be a * mill ' be- 
 tween them." (Much laughter.) 
 
 This dreadful change of value 
 consists in sixpence farthing 
 going to the half- shilling instead 
 of sixpence, i*. Whether the new 
 farthings be called mils or not is 
 of no consequence. 
 
 Mr. Lowe, who cannot pass a 
 half-crown for more than a florin, 
 or get in a florin at less than 
 half-a-crown, has such a high 
 faith in the sterner stuff of his 
 fellow countrymen, that he be- 
 lieves any two of them would go 
 to fisty cuffs for the 25th part of 
 a farthing. He reasons thus : 
 He has often heard in the streets, 
 "I'd fight you for the fiftieth 
 part of a far den:" and having 
 (that is, 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 ^-^d., 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 pro- 
 gress. Do the Members of the House think they have all the forms to 
 themselves ? 
 
 " What would be the present 
 expression for fourpence ? Why, 
 0*166 (a laugh) ; for threepence ? 
 0125; for a penny? '004166, 
 and so on ad infinitum (a laugh) ; 
 for a half-penny? -002083 ad 
 infinitum. (A laugh). What 
 would be the present expression 
 for a farthing ? Why, '0010416 
 ad infinitum. (A laugh). And 
 this was the system which was to 
 cause such, a saving in figures, 
 and these were the quantities 
 into which the poor would have 
 to reduce the current coin of 
 the realm. (Cheers). With every 
 respect for decimal fractions, of 
 which he boasted no profound 
 knowledge, he doubted whether 
 the poor were equal to mental 
 
 We should hardly believe all 
 this to be .uttered in earnest, if 
 we had not known that several 
 persons who have not Mr. Lowe's 
 humour, nevertheless have his 
 impressions on this point. It 
 must, therefore, be answered : 
 but how is this to be done 
 seriously ? 
 
368 
 
 A BUDGET OF PAKADOXES. 
 
 arithmetic of tins kind, (hear, 
 hear) and he hoped the adoption 
 of the system would be deferred 
 until there were some proof that 
 they would be able to understand 
 it; for, after all, this was the 
 question of the poor, and the 
 whole weight of the change would 
 fall upon them. Let the rich by 
 all means have permission to per- 
 plex themselves by any division 
 of a pound they pleased ; but do 
 not let them, by any experiment 
 like this, impose difficulties upon 
 the poor, and compel men to 
 carry ready-reckoners in their 
 pocket to give them all these 
 fractional quantities." (Hear, 
 hear.) 
 
 Dialogue between a member of 
 Parliament and an orange-boy, 
 three days after the introduction of 
 the complete decimal system. The 
 member, going down to the House, 
 wants oranges to sustam Ms voice 
 in a two hours' speech on moving 
 that 100,0001. be placed at the 
 disposal of Her Majesty, to supply 
 the poor with ready-reckoners. 
 
 Boy. Fine oranges ! two a 
 penny ! two a penny ! 
 
 Member. Here, boy, two ! 
 Now, how am I to pay you ? 
 
 Boy. Give you change, your 
 honour. 
 
 Member. Ah ! but how ? 
 Where's your ready-reckoner ? 
 
 Boy. I sells a better sort nor 
 them. Mine's real Cheyny. 
 
 Member. But you see a far- 
 thing is now -001 4166666 ad 
 infinitum,, and if we multiply 
 
 this by 4 
 
 Boy. Hold hard, Guv'ner; I 
 sees what you're arter. Now, 
 what '11 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 half-a- crown for it, and I lams 
 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, its 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 out a sixpence ; well, in coorse, I 
 
DECIMAL COINAGE. 869 
 
 hands over fippence farden astead of fippence. I always gives a far den 
 more change, and takes according. 
 
 Member (in utter surprise, lets Ms oranges tumble into the gutter}. 
 Never mind ! They won't be wanted now. (Walks off one way. Soy 
 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 half- penny to the shil- 
 ling.' 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 ? 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. 
 
 Thirdly, he attributes to the' uneducated community a want of per- 
 ception 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 
 
 B B 
 
370 A BUDGET OF PARADOXES. 
 
 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 
 decide this question, with Mr. Lowe to quote the description given by 
 Basil Hall (who, by the way, was one of the Committee) of an obser- 
 vation 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 i< s 
 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, Mr. Babbage, Sir John Herschel, 
 Sir Thomas Maclear (Astronomer Royal at the Cape of Good Hope), 
 Dr. Robinson (of Armagh), Sir James South, Lord Wrottesley, and 
 myself]. 
 
 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. 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, &c. 
 for 17, 18, &c. 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 pro- 
 nounced 
 
 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. 
 
THE "TONAL" SYSTEM. 371 
 
 Surely An-month, De-month, &c. 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 I What is 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 May- days ; 
 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 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 
 Tun ni 1'autre. 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 Eostof 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, &c., 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- 
 Vis inertiee victa, or Fallacies affecting science. By James B/eddie. 
 London, 1862,' 8vo. 
 
 An attack on the Newtonian mechanics ; revolution by gravi- 
 tation demonstrably impossible; much to be said for the earth 
 being the immovable centre. A good analysis of contents at the 
 beginning, a thing seldom found. The author has followed up 
 
 B B 2 
 
372 A BUDGET OF PARADOXES. 
 
 his attack in a paper submitted to the British Association, but 
 which it appears the Association declined to consider. It is 
 entitled 
 
 Victoria Toto Ccelo ; or, Modern Astronomy recast. London, 
 1863, 8vo. 
 
 At the end is a criticism of Sir Gr. Lewis's ; History of Ancient 
 Astronomy.' 
 
 On the definition and nature of the Science of Political Economy. 
 By H. Dunning Macleod, 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 4 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, sub- 
 divided 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-intel- 
 ligent, 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 praise from great 
 names for his political economy ; but this, 1 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 Thomp- 
 son. 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 prede- 
 cessors 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 ap- 
 peared to me insipid, and not so agreeable as the effect of the 
 
DUAL ARITHMETIC. 373 
 
 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. 
 G-eneral 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 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 V - 1 ? By F. H. Laing. London, 1863, 8vo. 
 
 If I understand the author, a and -fa 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. 
 
 Dual Arithmetic. A new art. By Oliver Byrne. London, 
 1863, 8vo. 
 
 The plan is to throw numbers into the form a(l'l) 6 (1*01 ) c 
 
 (1'OOiy 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 was the 
 late Mr. Thomas Weddle, in his < New, simple, and general method 
 
374 A BUDGET OF PARADOXES. 
 
 of solving numeric equations of all orders,' 4to, 1842. The 
 Koyal Society, to which this paper was offered, declined to print 
 it : they ought to have printed an organised method, which, with- 
 out subsidiary tables, showed them, in six quarto pages, the 
 solution (#=8'367975431) of the equation 
 
 1379-664a; G22 + 2686034 x 10 43 V 53 - 17290224 x 10 51 V* + 2524156 
 
 x 10 574 = 0. 
 
 The method proceeds by successive factors of the form, a being 
 
 the first approximation, a x 1*6 x I'Oc x I'OOd In 
 
 my copy I find a few corrections made by me at the time in Mr. 
 Weddle's announcement. 6 It was read before that learned body 
 [the K. 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 remark- 
 ably simple method ' possessing ' several important advantages.' 
 Mr. Eutherford's extended value of TT 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. 
 
 I think it may be admitted that the indisposition to look at 
 and encourage improvements of calculation which once marked 
 the Royal Society is no longer in existence. But not without 
 severe lessons. They had the luck to accept Homer's now cele- 
 brated paper, containing the method which is far on the way to 
 become universal : but they refused the paper in which Homer 
 developed his views of this and other subjects : it was printed by 
 T. S. Davies after Homer'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 with- 
 drawn ; which was done. 
 
 But the severest lesson was the loss of Barrett's Method, 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 printed it. The Society is now 
 better informed : ' live and learnj meaning ' must live, so better 
 learn J ought to be the especial motto of a corporation, and is 
 generally acted on, more or less. 
 
 Homer's method begins to be introduced at Cambridge : it was 
 
HOENER'S METHOD. 375 
 
 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 Trans- 
 actions. 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, 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 Homer'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 Homer'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 Homer'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 ' 
 
 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 con- 
 gregation 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 4 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 rny own University, on the 
 Eoyal 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 the work of Mr. 'Oliver Byrne, the 
 dual arithmetician, &c. This writer published, in 1849, a method 
 
376 A BUDGET OF PARADOXES. 
 
 of calculating logarithms". First, a long list of instances in which, 
 as he alleges, foreign discoverers have been pillaged by English- 
 men, or turned into Englishmen : for example, O'Neill, so called 
 by Mr. Byrne, the rectifier of the semi-cubical parabola claimed - 
 by the Saxons under the name of Need : the grandfather of this 
 mathematician was conspicuous enough as Neal ; he was Arch- 
 bishop 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 loga- 
 rithm 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 Koyal 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 Eoyal Society played no part, good or bad, nor 
 had the option of playing a part. But I myself pars magna fui : 
 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. 
 
 The mystery of being ; or are ultimate atoms inhabited worlds ? 
 By Nicholas Odgers. Redrnth and London, 1863, 8vo. 
 
 This book, as a paradox, beats quadrature, duplication, trisec- 
 tion, philosopher's stone, perpetual motion, magic, astrology, 
 mesmerism, clairvoyance, spiritualism, homoeopathy, hydropathy, 
 kinesipathy, Essays and Keviews, and Bishop Colenso, 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, &c. 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 
 
AEE ATOMS WORLDS ? 377 
 
 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. 
 
 I have often had the notion that all the nebulas we see, in- 
 cluding our own, which we call the Milky Way, may be particles 
 of snuff in the box of a giant of a proportionately larger universe. 
 Of course the minim of time a million of years or whatever the 
 geologists make it 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 our 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 started 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 
 termination of Ersch and Gruber's Lexicon, as mere physical 
 phenomena. Against this glorious future there is a sad omen : 
 the initials of the forerunner of this discovery are NO ! 
 
378 A BUDGET OF PARADOXES. 
 
 The History of the Supernatural in all ages and nations, and in 
 all Churches, Christian and Pagan : demonstrating a universal 
 faith. By Wm. Howitt. 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 Eev. J. Smith (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 theatres 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. 
 
 From Matter to Spirit. By C. D. With a preface by A. B. 
 London, 1863, 8vo. 
 
 This is a work on Spiritual Manifestations. The author up- 
 holds 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 connexion 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 philosopher. 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 philosopher- 
 craft 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 
 
'FROM MATTER TO SPIRIT.' 379 
 
 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 behaviour 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 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 Athenceum. 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 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 
 4 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 
 uniinagined 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 c endorsed his opinion more boldly.' 
 According to this reviewer, anyone who writes ; I boldly 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 favours 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. 
 
380 A BUDGET 01? PARADOXES. 
 
 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 dis- 
 tinction, 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, &c. 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 l against one another. 
 Such a story as the following would, in our day, bring down grave 
 remarks from above : but I write of the olden (or Eldon) 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 
 
 1 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. 
 
' FKOM MATTER TO SPIRIT.' 381 
 
 enormity of their practices ? " It appeared in a wrangling conver- 
 sation 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, 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 preven- 
 tive of anything like proof. And A. B. says that his reader 6 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 unfavour- 
 
382 A BUDGET OF PARADOXES. 
 
 able 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 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 vigour 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 re- 
 turns 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 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 Moli&re, the virtus dormitiva of opium, for no other 
 reason than that opium faoit dormire. Had the medicine not 
 
KEVIEWS OF ' FKOM MATTEE TO SPIEIT.' 383 
 
 been previously known., they would, strange as it may seem to 
 modern pharmacopceists, have accorded a virtus dormitiva to the 
 new facit dormire. On this point they have often been misap- 
 prehended. They were prone to infer facit from a virtus ima- 
 gined a priori ; and they were ready in supplying facit in favour 
 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 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, be- 
 cause 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 intelli- 
 gent, 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 them- 
 selves smaller than the small of other pursuits. And how is this ? 
 
884 A BUDGET OF PARADOXES. 
 
 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 nor Harveys : 
 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 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 astonish- 
 ment,' 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 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 spirit- 
 ualism 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 Aris- 
 totle 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 
 
REVIEWS OF < FROM MATTER TO SPIRIT.' 385 
 
 no doubt was the reviewer's habit ; that is, if he ever took the 
 field 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 trans- 
 lation 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 diu^vpiSta, breeches, 
 would have turned up in the lexicon ; and kalos geusis, though 
 absurd, is not obscure. And d/jLcoo-yiTrcos, somehow or other, is 
 as easily found as dva%vpiSia. 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 eiSijs have 
 been rendered. The aneroid barometer does not use a column of 
 air in the same way as the old instrument. Now as cosies 
 properly like the atmosphere is by scientific non-scholarship 
 rendered having to do with the atmosphere ; and dvaeposiBrjs 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. 1 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 was on ! And 
 it's oh I for some Greek, just to find a word upon ! The reviewer 
 who, lexicon in hand, can neither make out anaxyridical, amos- 
 gepotical, 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 
 
 1 This "utter rejection" has been repeated (1872) by the same writer. ED. 
 
 C C 
 
386 A BUDGET OF PARADOXES. 
 
 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 intelli- he himself is outside its sacred 
 gence, or something which man has pale because he refers all these 
 never had any conception o/, proves strange phenomena to unseen 
 me to be out of the pale of the spiritual 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 6 incautious ' for giving in at once to the spirit 
 doctrine. But, it is said, they may be justified by the philo- 
 sophers, 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 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 c 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 theologi- 
 cal, 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 and vacci- 
 nation were, in a certain but very unsatisfactory way, witnesses to 
 the possible excellence of the system of St. John Long.' Of course 
 it might: and of course it is said by all people of common sense. 
 In introducing the word 6 possible,' the reviewer has hit the point : 
 I suspect that this word was introduced during revision, to put 
 
KEVIEWS OF 'FROM MATTER TO SPIRIT.' 387 
 
 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 im- 
 possiblethat is, it is possible that a derided system may be 
 right. Mark the three gradations : in medio tutissimus ibis. 
 
 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 examina- 
 tion ; 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 occur- 
 rence 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 Athenceum 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. 4 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 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. 
 
 c c 2 
 
388 A BUDGET OF PARADOXES. 
 
 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 flavour." 
 
 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 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 realised, 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 Commandenr P. J. 
 Arson. Public par ses Enfans (CEuvre 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, 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 distinguish- 
 ing day, Sunday, are too many to be distinctly thought of to- 
 gether : 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 Mon- 
 day, 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. 
 
 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 
 
CYCLOMETKY. 389 
 
 himself for himself, not to know how Mr. Patrick Cody trisects 
 the angle at Mullinavat, or Professor Kecalcati 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 benefit of the dis- 
 covery, 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 TT = 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 lias 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 un- 
 common self-knowledge. When I was an undergraduate there 
 was a little attendant in the library who gave me the following, 
 4 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 
 
390 A BUDGET OF PAKADOXES. 
 
 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 & 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 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 whicli 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, be- 
 ginning again where he ended, and ending where he begun : thus 
 verifying the old line 
 
 In girum imus nocte, ecce ! et consumimur igni. 
 
 Every mathematician knows that scores of methods, differing 
 altogether from each other in process, all end in this mys- 
 terious 3*14159 . . ., which insists on calling itself the circum- 
 ference 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. [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 TT : he 
 evidently takes me to be offering demonstration. He proceeds 
 thus : 
 
 * His first proof is traceable to the diameter of a circle 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, ifc 
 may be frankly admitted that we can arrive at the same result by 
 
CYCLOMETRY. 391 
 
 many other modes of arithmetical calculation, all of which may be 
 shown to have some sort of rt'lation 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 con- 
 clusions 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*14:159 . . . The proofs that these methods establish 
 the value of TT are for those who will read and can understand. 
 
 1. Take any diameter, double it, take l-3rd of that double, 
 2-5ths of the last, 3-7ths of the last, 4-9ths of the last, 5-llths 
 of the last, and so on. The sum of all is the circumference of 
 that diameter. The following 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 olf one figure. 
 
 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 
 
 y a 314153799 31415 9265 
 
 Here 200 &c. is double of the diameter ; 666 &c. is l-3rd of 
 200 &c.; 266 &c. is 2-5ths of 666 &c. ; 114 &c. is 3-7ths of 
 266 &c. ; 507 &c. is 4-9ths of 114 &c. ; 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. 
 
392 A BUDGET OF PARADOXES. 
 
 Square root of 3 .... 173205081 
 86602540 
 
 2-59807621 
 
 43301270 
 
 08660254 
 
 1855768 
 
 412393 
 
 93726 
 
 21629 
 
 5047 
 
 1188 
 
 281 
 
 67 
 
 16 
 
 4 
 
 1 
 
 314159265 
 
 3. Take the square root of | ; the square root of half of one 
 more than this ; the square root of half of one more 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 ^; '92390 
 for the square root of half one more than -70712 ; and so on, 
 through -98080, -99520, -99880, -99970, -99992, and -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 
 
CYCLOMETRY. 393 
 
 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 demon- 
 strations, 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 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 quadra- 
 ture, 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 quad- 
 rature is open to their ingenuity. Before attempting the 
 arithmetical problem, they ought to acquire knowledge enough 
 to read Lambert's demonstration (last given in Brewster's trans- 
 lation of Legendre's Geometry) and, if they can, to refute it. [It 
 
A BUDGET OF PARADOXES. 
 
 will be given in an Appendix.] Probably some have begun in 
 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 tuteiaries : 
 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 c 7 A, 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 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 &c. 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 any- 
 thing but a corruption of the obsolete word tetchy of the same meaning ? 
 
THE NUMBER OF THE BEAST. 395 
 
 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 c of course ' to declare 
 
 accursed those who do not respect the writer's vagary] ... If I could 
 
 bat get the tf, the Ox-head, which in old Hebrew was just the Latin 
 
 Digamma, F, out of your name, and could then Thau you with the Thau 
 
 of Ezekiel ix. 4, the x> then you would bear the number 
 
 M 40 of a man ! But this is too hard for me, although not so 
 
 O 70 for the Lord ! Jer. xxxii. 1 7 ... And now a word : is 
 
 B, 100 ridicule the right thing in so solemn a matter as the 
 
 G 6 discussion of Holy Writ ? [Is food for ridicule the right 
 
 1ST 50 thing ? Did I discuss Holy Writ ? I did not : I con- 
 
 cussed profane scribble. Even the Doctor did not discuss : 
 
 266 he only enunciated and denunciated out of the mass of 
 D = ^ 400 inferences which a mystical head has found premises for 
 in the Bible]." 
 
 [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, who handed it to 
 a Eomaii 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 - 
 
396 A BUDGET OF PARADOXES. 
 
 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 ? " 
 
 Those who think parody vulgar will be pleased to substitute for 
 the above a quotation from Butler : 
 
 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' uiicircu incised 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. 
 
 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 carte 
 and tierce : ' 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 ! 
 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 ana- 
 chronistic onset, with his repartees and his retorts, before there was 
 anything to fire at, takes what I give by way of subsequent pro- 
 vocation with a good humour which would make a convert of me 
 
THE NUMBEK OF THE BEAST. 397 
 
 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-hamraerer does nothing but grumble, except 
 when he tells a good story, which he says he had from Dr. 
 Abernethy. A Mr. James Dunlop was popping at the Papists 
 with a 666-rifled gun, when Dr. Chalmers quietly said, 'Why, 
 Dunlop, you bear it yourself,' and handed him a paper on which 
 the numerals in 
 
 IACOBYS DVNLOPVS 
 
 1 100 5 500 5 50 5 
 
 were added up. This is almost as good as the Filii Dei Vicarius, 
 the numeral 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 conun- 
 drums : and no more of the trumpery hints about future destiny 
 which it is too great a compliment to call blasphemous. If the 
 Doctor will cipher upon the letters in sv a> psrpG) fjusTpscrs /jLerprj- 
 Orjcrsrac vfjuw, 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 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 (ofjbo\o^ov^eva\ which it has always 
 been paradox not to receive ; and the controverted (avrt\^o^sva}^ 
 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, who first (1. 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 [t>00ot] let there be ranked both, the work 
 entitled the Acts of Paul, and the book called Pastor, and the 
 
393 A BUDGET OF PAKADOXES. 
 
 lation 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 voOov* and gives the book a claim to 
 rank (if you think good, again) in the controverted list. And 
 this is the impression received by 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 faggojts 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 reader, 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, who, though 
 heterodox in doctrine, tries hard to be orthodox as to the Canon, 
 is 4 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 con- 
 tinued 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, in vol. iv. p. 8. 
 of his New Testament, gives an elaborate handling of this ques- 
 tion. He concludes by saying that he cannot venture to refuse 
 his consent to the tradition that the Apostle is the author. This 
 modified adherence, or non-nonadherence, pretty well represents 
 
APOCALYPTIC PROPHECY. 399 
 
 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 follow- 
 ing. 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 6 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, &c. ? You 
 must tell him that the Greek sv Ta>X l i rendered fc shortly,' is as 
 strong a phrase as the language has to signify soon. The inter- 
 preter 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 not 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 any- 
 thing 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 sv ra^i may not be c soon,' it may 
 be ' quickly, without reference to time when : ' he continues thus, 
 4 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 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 iyyvs, which is a word of closeness, 
 in time, in place, in reckoning, in kindred, &c 
 
 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 Athenceum, 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 
 
400 A BUDGET OF PARADOXES. 
 
 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 Eevelation 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 T 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 know- 
 ledge 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 SSL ysvsaOai for ' must 
 come to pass,' and we know that LJZVSTO is what is usually trans- 
 lated ' 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 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 n 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 4 Prof. De Morgnn ' as have assigned me 
 apartment 7 A 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 7 A : 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 recog- 
 nized, 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 n 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 
 
CHILDHOOD AND PRIESTHOOD 401 
 
 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. 
 
 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 ?), personi- 
 fied 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 predomi- 
 nates over bigotry, we have the grotesque picturesque, and the 
 natural order of words gives us Mob, 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 exist- 
 ence, in which I find that as I am the Daniel who judges the 
 Magi of Babylon, it is to be pointed out that Daniel 4 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 imita- 
 tion 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 
 c I don't love you.' The proper rejoinder is, ' Very well ! then I '11 
 have pussy.' But in the case before me there is a rule of three 
 sum to do ; as baby \ pussy Dr. :: 666 \ the answer required. I 
 will work it out, if I can, 
 
 D D 
 
402 A BUDGET OF PARADOXES. 
 
 The squaring of the circle and the discovery of the Beast are 
 the two goals and gaols also of many unbalanced intellects, 
 and of a few instances of a better kind. I might have said more 
 of 666 5 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 his subject, the Rev. David Thorn, 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 criti- 
 cism which was once made on Paley's Evidences 4 Well I 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, 4 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 suffi- 
 cient 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. Thorn, 
 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 Eev. John 
 Hamilton Thorn (no relation), at or near the same time, and 
 until recently, of Eenshaw 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 c Jews, Turks, Infidels, 
 and Heretics.' So much for the distinction, which both gentle- 
 men 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 Thorn's book is 
 4 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 
 
NAMES OF THE BEAST. 403 
 
 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.) ; Diocles Augustus ; 
 Ludovicus ; Silvester Secundus ; Linus Secundus ; Vicarius Filii 
 Dei ; Doctor et Eex Latinus ; Paulo V. Vice-Deo ; Vicarius 
 Greneralis Dei in Terris ; Ipse Catholicse Ecclesiae Visibile Caput ; ** 
 Dux Cleri ; Una, Vera, Catholica, Infallibilis Ecclesia ; Auctoritas 
 politica ecclesiasticaque Papalis (Latina will also do) ; Lutherus 
 Ductor Grregis ; Calvinus tristis fidei interpres ; Die Lux ; 
 Ludyvic ; Will. Laud; Karsivos ; rj Xarivrj /3acri\eia* 9 sfctcXrjcria 
 rsirav; apvovfji\ \a/ji7rsrc9 ; oviKr)rr]$\ /ca/co$ 
 3\a/3spos ; 7ra\ai /SaTtcavos ; d/.wos dSucos ; 
 svu'as ; TSsvsSifcros ; Bozx/iJa^os' y. Traira . 
 77. s. s. a., meaning Boniface III. Pope 68th, bishop of bishops the 
 first! OV\TTIOS ; Stos si fit q fjpas; 17 fjnaa-a rj TTCLTTIK.'Y) ; \ovS:pava; 
 cra%oi>ios ; Bfa az^r^co^ (Beza) ; 77 d\aovsia ftiov ; Mao/msris ; 
 MaoyLtar^y /3. ; Oeos slfjut srri ryairjs ; laiTcTos ; ircnrsicrKos ; Sio/c\a- 
 Xaaiavos ; yzwa ; /3pacrKb ; lov TIavvs ; KOVTTOK.S (cowpox, y being 
 the vau ; certainly the vaccinated have the mark of the Beast) ; 
 HovvsTrapTT} ; N". Bor^Traprf ; svTropia, Trapa&ocris i TO psyaQrjpiov. 
 
 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 Eoman Alphabet. Some 
 Jews, according to Mr. Thorn, found it in nJ 1B Jesus of 
 Nazareth. I find on inquiry that this satire was actually put 
 forth by some mediaeval 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 Thorn's own solution hits hard at all sides : he finds 
 a 666 for both beasts ; 97 fypijv (the mind) for the first, and 
 scK\T]cricu crapuKdi (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, 
 Eoman, 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 symbol- 
 izing differences of number in the subdivisions. 
 
 It may be good to know that, even in speculations on 666, 
 
 D D 2 
 
404 A BUDGET OF PARADOXES. 
 
 4 
 
 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 
 Thorn found a young gentleman of the name of St. Claire busy 
 at the Beast number : he forthwith added the letters in ar icXaips 
 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 N into fi, solemnly referred the difficulty to the Al- 
 mighty : this was poor earnest. 
 
 I am glad I did' not notice, in time to insert it in the 
 Athenoeum, a very remarkable paradoxer brought forward by 
 Mr. Thorn, his friend Mr. Wapshare : it is a little too strong for 
 the general public. In the Athenceum 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 him- 
 self 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, I H S. 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 leasts ; 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, <fcc. and he who was Satan, the 
 Spirit of life in that body, is, in 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. Thorn prints it as convinced 
 of its piety, and c 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 para- 
 doxers. They are like the spiders who go on spinning after they 
 
IN EE rj-i. 405 
 
 have web enough to catch all the flies in the neighbourhood, 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 at 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 
 Eev. D. Thorn, 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 ,-1-j. 
 
 So that ' Zaphnath Paaneah ' may be after all the revealer of the 
 Northern Tau,' Qarepow 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 al Coptic to a 
 
 man who has not r-f- 1 , The Thau of the North, the double Yahu 1J. 
 Look at Jeremiah 3 C . 8 V . and then to Psalm 83 for ' hidden ones ' 
 njn? *>1SV 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 There will be thousands of Morgans 
 
 E = 5 who will be among the wise and 
 
 R = 100 prudent of Hosea 14 C . 9 V . when the 
 Seventh Angel sounds, let me number 
 
 A = 1 that One by Greek, Rev. 17 C . l v : 
 
 u = 400 
 
 C = 20 
 r = 10 
 
 N = 50 
 
 666 
 
400 A BUDGET OF PARADOXES. 
 
 
 S 
 
 = 
 
 200 
 
 
 E 
 
 
 
 5 
 
 X 
 
 V 
 
 
 
 6 
 
 
 E 
 
 = 
 
 5 
 
 
 N 
 
 = 
 
 50 
 
 
 T 
 
 = 
 
 300 
 
 
 H 
 
 = 
 
 8 
 
 
 
 
 =i 
 
 50 
 
 X 
 
 G 
 
 = 
 
 6 
 
 
 E 
 
 = 
 
 5 
 
 
 L 
 
 = 
 
 30 
 
 g O 
 
 x 
 
 O CO 
 
 666 
 
 London, October 29, 1866. 
 Dear Sir, 
 
 In re r-j- 1 versus *j< 
 
 However pretentious the X or ^ may be, and it is peculiarly so 
 just now in tins land ; after all it is only made of two Roman V's 
 and so is only )( (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 
 
 >J< HENEY E. MANNING. 
 
 Shilling versus Franc. 
 
 Teutonic Long Hundred 120 versus 100 or the Decimal question. 
 
MR. GLADSTONE 666. 407 
 
 By English Key. 
 
 H = 
 
 8 
 
 
 E = 
 
 5 
 
 
 N = 
 
 40 
 
 
 R = 
 
 80 
 
 'V . | a " 
 
 Y = 
 
 140 
 
 
 E = 
 
 5 
 
 1 ^ 
 
 D = 
 
 4 
 
 rS 3 
 
 W = 
 
 120 
 
 -+J 
 
 
 
 TJ O-, 
 
 A = 
 
 1 
 
 ^ txl 
 
 R = 
 
 80 
 
 ^ 
 
 
 
 JH ^ 
 
 D = 
 
 4 
 
 r 
 
 
 
 rt V?4 
 
 
 
 rj A 
 
 M = 
 
 30 
 
 r-j 
 
 A = 
 
 1 
 
 Q c^ 
 
 N = 
 
 40 
 
 I i 
 
 N = 
 
 40 
 
 o * 
 
 I == 
 
 9 
 
 ^ 
 
 N 
 
 40 
 
 ^ 
 
 G = 
 
 7 
 
 J 
 
 r-P = 
 
 12 
 
 -. 
 
 
 666 
 
 Cutting from newspaper : 
 
 ITALY. 
 
 Rome (via Marseilles), October 24. 
 Mr. Gladstone has paid a visit to the Pope. 
 
 ]3y Greek Power. 
 G = 6 
 
 L =a 30 
 A = 1 
 
 D = 4 
 
 s = 200 
 
 T = 300 
 
 o = 70 
 
 N = 50 
 
 - E = 5 
 
 666 
 And what then ^ ? 
 
408 A BUDGET OF PAKADOXE8. 
 
 In other letters John Stuart Mill is 666 if the a be left omt ; 
 Chasuble is perfect. John Brighte 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. Thorn and his 666 appeared on October 27 : 
 and on the 29th I received from the editor a copy of Mr. Thorn'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 of my diameter if 
 the signature, name and writing both, were not that of my 
 Q ding friend Mr. James Smith ! And so I have come in contact 
 with him on 666 as well as on IT I 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 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 Athenceum and Correspondent : of things new 
 there is but one. In a short preface Mr. J. S. particularly recom- 
 mends 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 Athenceum, left out of its place. In the 
 last sentence Mr. J. Smith, who had asked whether his character 
 
J. S.'S SYMBOLICAL REASONING. 
 
 as an honest Geometer and Mathematician was not at stake, is 
 warned against the fallacia plurium interrogationum. 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 had been staked years ago, 
 and lost. And thus truth has the last word. There is no occa- 
 sion 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 Athenceum and fore- 
 stall him. When I saw myself thus quoted yes ! quoted I 
 double commas, first person I felt as I suppose did Wm. Wilber- 
 force 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 of 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 cyclo- 
 meters. 
 
 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 6-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, 6 = 5 : let c = 
 658, the number of the House : let d = 666, the number of the 
 Beast. Then of necessity eZ = a + 6 + c+l;so that 1 is a 
 harmonious and logical quantification of the number of which we 
 are to take care. Now, 6, 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 demonsttumhowendum. 
 If Simpkin & Marshall have not, after my notice, to account for 
 
410 A BUDGET OF PARADOXES. 
 
 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 connexion 
 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 cegri somnia, which brings them 
 to a certain look of approach to reasoning which I can only 
 burlesque. Mr. J. S. produces something which resembles argu- 
 ment much as a chimpanzee in dolour, 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 Uni- 
 genitus 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 and Joseph Scaliger 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, (p. 89) 
 Joseph at contradictions was an ass. (p. 67) 
 Groaned Folly, I'm used up ! What shall I do 
 To make James Smith ? Grinned Momus, Join the two ! 
 As to my locus pcenitentice, 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. 
 
 Joanna Southcott 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 
 
A SCHOOLBOY'S DEFENCE. 411 
 
 to c favour 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 favour him. At the 
 very outset I told him in plain English that he has the whiphand 
 of all the reason ers in the world, and in plain French that il a 
 perdu le droit d'etre frappe de ^evidence ; I might have said 
 pendu. To which I now add, in plain Latin, Sapienti pauca, 
 indocto nikil. 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 con- 
 spiring 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 gentle- 
 man ; and the 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 inno- 
 cent 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 hist 
 
 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 thai 
 
 her presence would protect him. 
 
 My readers may expect a word on Mr. Thorn's sermons, after 
 my account of his queer doings about 666. He is evidently an 
 honest and devout man, mucli wanting in discrimination. He 
 has a sermon about private judgment, in which he halts between 
 
412 A BUDGET OF PARADOXES. 
 
 the logical and legal meanings of the word. He loathes those 
 who apply their private judgment to the word of Grod : 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. 
 
 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 : 
 
 Let x = I 
 
 Then x 2 = x 
 
 And x 2 1 = x 1 
 
 Divide both sides by x 1 ; then 
 
 #+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 favour, 
 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, because I think Mr. James Smith better fitted to be the 
 leader of an organised infatuation than anyone I know of. He 
 wants no pity, and will get none. He has energy, means, good 
 humour, strong conviction, character, and popularity in his own 
 circle. And, most indispensable point of all, he sticks at nothing ; 
 
 In ccelum jusseris, ibit. 
 
 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 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 in- 
 jury ; 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 
 
LITTLE JACK HORNER AND OTHERS. 413 
 
 you was a very simple one, as I shall make manifest at tlie proper 
 time.' 
 
 In one or more other 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 TT. 
 
 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 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 ' II ' 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 ' II ' 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 argu- 
 ments ; 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, &c., 
 
 A CAPTAIN, B,.N.' 
 
 On looking at this homoeopathic treatment of the 3 quadra- 
 ture remember, homoeopathic, similia similibus, not infinite- 
 
414 A BUDGET OF PARADOXES. 
 
 siraal 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 unproducible salvo pudore which .has classical 
 authority, modern or ancient, in its favour, 'He is a vulgar 
 fellow ; I asked him what he was upon, and what do you think he 
 answered, My legs ! ' 4 Well, and has he not justification ? what 
 do you find in Terence ? Quid agitur ? StaturS I do not even 
 blench from my principle where I find that it brings what is 
 called 6 taking a sight ' within permissible forms of expression : 
 Rabelais not only establishes its antiquity, but makes it English. 
 Our old translation * has it thus (book 2, ch. 19) : 
 
 6 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 a fist of the left hand is a 
 great addition of power, and should be followed in modern prac- 
 tice. 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 in the rear. 
 
 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 
 
 1 Lors feist 1'Anglois tel signe. La main gausche toute ouverte il leva hault en 
 1'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 poulee au lieu que fermait le petit doigt de la gausche, et les qiiatre 
 doigtz d'icelle mouvoit lentement en 1'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. 
 
DE. WHEWELL'S LETTEE. 415 
 
 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 con- 
 tempt ; 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 Athenceum. 
 
 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 favourite tutelary. I 
 have long played the cur, snapping and snarling . . . ; suddenly lost 
 my power, and become 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 l a muzzle for the Mathe- 
 matical 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 top ; and 
 tried neither]. 
 
 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 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 re- 
 minded 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, 
 
416 A BUDGET OF PARADOXES. 
 
 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 over- 
 come, by that change of manner, and apologetic mode of continu- 
 ance, 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 
 
 and oo are of number, and illustrated by an urn with 1 white 
 and n black 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 
 4 1 think ? . . . c Ugh ! you think !' was the answer. I repeated 
 my phrase, and gave as a reason the words which Lord Grey 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 pre- 
 viously 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 
 
 1 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 con- 
 sider this : In the whole course of the proof, though the word circle 
 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 
 
 annot, have proved a property of that special figure a circle ? 
 
AN M.P.'S ARITHMETIC. 417 
 
 Or you may do this : calculate tko 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 &c. Now, the arc which this side subtends is 
 according to your proposition ^~ = '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. 
 
 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 1330. 17s. 6d. 
 by 21. 13s. Sd. Six hundred and fifty-eight, answered one mem- 
 ber ; 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 I2d. contain 4cZ. ; answer three times. 
 Magnitude may be divided by number, and the answer is magni- 
 tude : I2d. is divided in four equal parts, what is each part ? 
 Answer three pence. The honourable objector, whose name I 
 suppress, trusting that he has mended his ways, gave the follow- 
 ing 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 
 21. 16s. Sd. ? (Laughter.) The question might be asked, * How many 
 times 2s. will go into 1Z. ?' but that was not dividing by money; it 
 was simply dividing 20 by 2. He might be asked, ' How many times 
 will 6s. Sd. go into a pound ? ' but it was only required to divide 240 
 by 80. If the right hon. gentleman were to ask the hon. member for 
 Brighton (Professor Fawcett), 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 my second edition, if I publish 
 one. 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 the 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 
 
 E E 
 
418 A BUDGET OE PAKADOXES. 
 
 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 the 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 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 51. 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 51. 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, Ki. Milward (Eichard,no doubt, but it cannot be proved) 
 who published Selden's 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 
 and forty times more than a man is worth.' For times read sub- 
 sidies, 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 of our 
 own day, who discovered two quantities which he avers to be 
 
ERRONEOUS ARITHMETICAL NOTIONS. 419 
 
 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. 
 
 c Shallow numerists,' as Cocker 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 tsedium 
 of a sea voyage : I have had more than one bet referred to me. 
 Because an oblong of five inches by four inches contain 5x4 
 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. 
 
 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 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 
 
 fa. 3d. 
 17 's. 4d. 
 
 As common sense gained a hearing very soon, there is no 
 occasion to say more. In 1858, it was proposed at a college ex- 
 amination, to divide 22557 days, 20 hours, 20 minutes, 48 
 seconds, by 57 minutes, 12 seconds, and also to explain the 
 fraction 
 
 32L 188. Sd. 
 
 621. 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 ? 
 
420 A BUDGET OF PARADOXES. 
 
 The phenomena of the two ends of society, when brought to- 
 gether, 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 6 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 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 Yishnoo, 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 recognised in our day : so far 
 good. But there is a bad contrary : the age is apt, in interpre- 
 tation, to upset the letter in favour of the view very often the 
 after thought of one side only. The case of John Palmer, the 
 improver of the mail coach system, is smothered. He was to 
 have an office and a salary, and 2 per cent, for life on the in- 
 creased 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 made his bargain with the 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 reach- 
 ing the turning sale of this stipulation, readily consented. But 
 it turned out that Dr. Lardner saw further than they : the re- 
 turns under this stipulation gave him a very handsome addition 
 
DECLARATION OF BELIEF. 421 
 
 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 per- 
 centage, they had all the rest ; and they would not have felt 
 aggrieved if he had received ten times as much. But govern- 
 ments, which cannot be brought to book before a sworn jury, are 
 ruled only by public opinion. John Palmer's day was also the 
 clay of Thomas Fyshe Palmer, 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. 
 
 1864-65. It often happens that persons combine to maintain 
 and enforce an opinion ; but it is, in our state of society, a para- 
 dox 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 4 sincere regret that researches 
 into 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 pro- 
 ceeded 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 Grod 
 is in the Bible, or whether the Word of God is all the Bible, 
 was quietly taken for granted in favour 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, who in refusing to sign the writ 
 sent to him, administered a rebuke in the Athenceum, 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 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 state- 
 ment, 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 
 
422 A BUDOET OF PAKADOXES. 
 
 fresh element of discord to the already too discordant relations of the 
 Christian world . . . But no nicety of wording, 110 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 gently worded 
 and apparently justifiable expression of regret, so embodied, from 
 grating on the feelings of thousands of estimable and well-intentioned 
 men with all the harshness of controversial hostility/ 
 
 Other doses were administered by Sir J. Bowring, Sir W. Eowan 
 Hamilton, 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 c solicit the favour ' 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 miscel- 
 laneous : 38 were designated as ' students of the College of 
 Chemistry,' meaning young men who attended lectures in that 
 college. But as all the Eoyal Society had been applied to, a test 
 results as follows. Of Fellows of the Koyal Society, 600 in 
 number, 62 gave their signatures ; of writers in the Philosophical 
 Transactions, 166 in number, 19 gave their signatures. Eoughly 
 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 downstairs, meaning that the 
 teapot ought to be brought up-stairs. And many of them would 
 defend it. Some would say that the two things are not contra- 
 dictory ; 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 
 
DECLARATION OF BELIEF. 
 
 423 
 
 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 under- 
 stand, 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 Eoman Olympiads. 
 But, with their usual love of indefiniteness, they have deter- 
 mined 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 Athenceum, 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. 
 
 WE, the undersigned Students 
 of the Natural Sciences, desire to 
 express our sincere regret, that 
 researches into scientific truth are 
 perverted by some in our own 
 times into occasion for casting 
 doubt upon the Truth and Au- 
 thenticity of the Holy Scriptures. 
 
 We conceive that it is impossible 
 for the Word of God, as written 
 in the book of nature, and God's 
 Word written in Holy Scripture, 
 to contradict one another, how- 
 ever much they may appear to 
 differ. 
 
 We are not forgetful that Physical 
 Science is not complete, but is 
 only in a condition of progress, 
 and that at present our finite 
 reason enables us only to see as 
 through a glass darkly, 
 
 Proposed Substitute. 
 
 WE, the undersigned Students 
 of Theology and of Nature, desire 
 to express our sincere regret, that 
 common notions of religious truth 
 are perverted by some in our own 
 times into occasion for casting 
 reproach upon the advocates of 
 demonstrated or highly probable 
 scientific theories. 
 We conceive that it is impossible 
 for the Word of God, as correctly 
 read in the Book of Nature, and 
 the Word of God, as truly inter- 
 preted out of the Holy Scripture, 
 to contradict one another, how- 
 ever much they may appear to 
 differ. 
 
 We are not forgetful that neither 
 theological interpretation nor 
 physical knowledge is* yet com- 
 plete, but that both are in a con- 
 dition of progress ; and that at 
 present our finite reason enables 
 us only to see both one and the 
 other as through a glass darkly 
 [the writers of the original de- 
 
424 
 
 A BUDGET OF PARADOXES. 
 
 and we confidently believe, that 
 a time will come when the two 
 records will be seen to agree in 
 every particular. 
 
 We cannot but deplore that Na- 
 tural Science should be looked 
 upon with suspicion by many 
 who do not make a study of it, 
 merely on account of the unad- 
 vised manner in which some are 
 placing it in opposition to Holy 
 Writ. 
 
 We believe that it is the duty of 
 every Scientific Student to inves- 
 tigate nature simply for the pur- 
 pose of elucidating truth, 
 
 and that if he finds that some of 
 his results appear to be in con- 
 tradiction to the Written Word, 
 or rather to his own interpreta- 
 tions of it, which may be erroneous, 
 he should not presumptuously 
 affirm that his own conclusions 
 must be right, and the statements 
 of Scripture wrong ; 
 
 rather, leave the two side by side 
 
 till it shall please God to allow us 
 to see the manner in which they 
 may be reconciled ; 
 and, instead of insisting updn 
 
 claration have distinctively ap- 
 plied 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 that 
 a time will come when the two 
 records will be seen to agree in 
 every particular. 
 
 We cannot but deplore that Re- 
 ligion should be looked upon 
 with suspicion by some, and 
 Science by others, of the students 
 of either who do not make a study 
 of the other, merely on account 
 of the unadvised manner in which 
 some are placing Religion in op- 
 position to Science, and some are 
 placing Science in opposition to 
 Religion. 
 
 We believe that it is the duty of 
 every theological student to in- 
 vestigate the Scripture, and of 
 every scientific student to inves- 
 tigate Nature, simply for the 
 purpose of elucidating truth. 
 And if either should find that 
 some of his results appear to 
 be in contradiction, whether to 
 Scripture or to Nature, or rather 
 to his own interpretation of one 
 or the other, which may be 
 efroneous, he should not affirm 
 as with certainty that his own 
 conclusion must be right, and 
 the other interpretation wrong : 
 but should leave the two side by 
 side for further inquiry into both, 
 until it shall please God to allow 
 us to arrive at the manner in 
 which they may be reconciled. 
 In the mean while, instead of 
 insisting, and least of all with 
 acrimony or injurious statements 
 about others, upon the seeming 
 
DECLABATION OF BELIEF. 425 
 
 the seeming differences between differences between Science and 
 Science and the Scriptures, it the Scriptures, it would be a 
 would be as well to rest in faith thousand times better to rest in 
 upon the points in which they faith as to our future state, in 
 agree. hope as to our coming know- 
 
 ledge, 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 : cvyopaLOi djovrai sy/caXsiTcocrav aXXrjXois. 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 Eogers that his appearance 
 was very like that of a corpse. The John Bull newspaper 
 suppose we now say Theodore Hook 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 ? 
 
426 A BUDGET OF PAEADOXES. 
 
 "SCKIPTUKE AND SCIENCE. 
 
 " The Writ De Hceretico Commiserando. 
 
 Nov. 14, 1864. 
 
 " THIS document was sent to me four days ago. It * solicits the 
 favour ' I thought at first it was a grocer's supplication for tea 
 and sugar patronage of my signature to expression of 4 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 abcut Scripture and Science in their real or 
 alleged discrepancies. 
 
 " No such favour 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 con- 
 clusions. Thirdly, even if I did regret, I should be ashamed to 
 put my name to bad chemistry made to do duty for good reason- 
 ing. The declaration is an awkward attempt to saturate sophism 
 with truism ; but the sophism is left largely in excess. 
 
 " 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 I thought I, if you had shown yourself to 
 be well up in Barbara Celarent, and had ever and anon astonished 
 the natives with the distinction between simpliciter and secun- 
 dum quid, no autograph-hunters would have baited a trap with 
 non sequitur 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. 
 
 u The kind of test before me is the utmost our time will allow of 
 that inquisition into opinion which has been the curse of Chris- 
 tianity ever since the State took Providence under its protection. 
 
DECLAEATION OF BELIEF. 427 
 
 The writ de hceretico commiserando is little more than the smell 
 of the empty cask : and those who issue it may represent the old 
 woman with her 
 
 suavis amma, quale in te dicam bonum 
 Antehac fuisse ; tales cum sint reliquiae. 
 
 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 Fir e-t he-faggot : 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 vigour : and 
 let charity, candour, sense, and ridicule, be ready to play upon it 
 whenever there is any chance of its extending to literature or 
 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 I 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 co-operation 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 contemplate all attempts to repress freedom 
 
428 A BUDGET OF PAEADOXES. 
 
 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 favour 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 traveller in the highway of 
 discussion, with Your signature or your silence ! " 
 
 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 fre- 
 quently saw, in the blank leaves of old books, learned books, 
 Bibles of a time when a Bible was very costly, &c., 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 Bible of 1599, I saw an inscription 
 in a child's writing, which certainly belonged to a much later 
 date. It was 4 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, 
 
BENJAMIN FEANKLIN. 429 
 
 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 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 learnt 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 (by Mose) 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, Gr. Phillips, J. Elliot, and E. Negus, book- 
 sellers in Boston, and sold at their shops. 1 719. 
 
 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 evens. 
 
 No ordinary map would decide these points : so I had to 
 apply to my friend Sir Francis Beaufort, and the charts at the 
 Admiralty decided immediately for Massachusetts. 
 
 The French are able paradoxers in their spelling of foreign 
 names. The Abbe Sabatier de Castres, 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, 
 
430 A BUDGET OF PARADOXES. 
 
 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. and Galileo, references to the works of two 
 Englishmen, the Eev. Win Worewel and the Eev. Eaden Powen. 
 [Win. Whewell and Baden Powell]. 
 
 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 burned for witchcraft in one century. Some- 
 times 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 8,852,000?. But 
 6,400,000 people pay the clergy of the Anglo-Irish Establishment 
 8,896,000?.; and 14,600,000 of other denominations pay 
 1 ,024,000?. 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.' 
 
 MyBudget 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, philo- 
 sophical 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 
 was not to blame for more than fire 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 won- 
 
AN ITINERANT LECTURER CAMBRIDGE POETS. 431 
 
 dered 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. c 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,' &c. I had never heard of Alfonso X. of Castile, 
 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 specu- 
 lation 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 pus h 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. 
 
 Sometimes a person who has a point to carry will assert a 
 singular fact or prediction for the sake of his point ; and 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, &c..' 
 (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 wakes a genuine poet's fires, 
 
 And modern Britons glory in their sires. 1 
 
 There is some account of the Eev. Greo. Richards, Fellow of Oriel 
 and Vicar of Bampton, (M.A. in 1791) in the 'Living Authors,' 
 by Watkinsand Shoberl (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 ' Abo- 
 riginal Britons' was an Oxford (special) prize poem, of 1791. 
 Charles Lamb mentions Richards as his school-fellow at Christ's 
 
 1 The ' Aboriginal Britons,' an excellent poem, by Richards. (Note by Byron.) 
 
432 A BUDGET OF PARADOXES. 
 
 Hospital, c author of the " Aboriginal Britons," the most spirited 
 of the Oxford Prize Poems : a pale, studious Grecian.' 
 
 As I" never heard of Eichards as a poet, 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 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 con- 
 spicuously 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 pro- 
 ductions, 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 Kichards, 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 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 : 
 
 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, pro- 
 
FALSIFIED PREDICTION. 433 
 
 hibited, respected, scorned, assailed, defended, asserted, denied, 
 declared utterly obscure, and universally known. It was hard 
 lines to select four 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. 
 
 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 Kev. Daniel Eivers, already 
 quoted, about Johnson's biographers. Peter Pindar may be 
 excused, as personal satire was his object, for addressing Bos well 
 and Mrs. Piozzi as follows : 
 
 Instead of adding splendour 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 : 
 6 As admirers of the learning and moral excellence of their hero, 
 we glow at almost every page with indignation that his weak- 
 nesses and his failings should be disclosed to public view . / . 
 Johnson, after the lustre 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 favour.' 
 
 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 
 
 F 
 
434 A BUDGET OF PARADOXES. 
 
 taking measures to carry on the cake-shop. I was before my age 
 in this respect : as a boy-reader of Bosweil, 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 protec- 
 tion, a male relation with a brace of pistols, and a competent 
 notion of using them. 
 
 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 
 
 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, in his Taste., translated part 
 of Gray's Bard into Greek. Some of his lines are 
 
 SfpHO. & o reyywv SaKpva 
 ov\ov 
 
 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 : 
 
 riyywv caKpva 
 
 Pindar's rtyycov 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 until aftei 
 publication. Byron was too much of a scholar to make this 
 
BYRON AND WORDSWORTH. 435 
 
 blunder himself: lie 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, 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 demeanour 
 to it, are matters far beyond me. Mr. Crabb Eobinson 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 that nobody may write poetry, unless he lives in a 
 garret.' Crabb Eobinson 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 I '" 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 6 Our 
 difference is po[li = e]tical.' 
 
 I suspect that Fielding would, if all were known, be ranked 
 among 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 6 proper to 
 
 F F 2 
 
436 A BUDGET OF PAKADOXES. 
 
 be read before the E 1 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 recognised 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 '1 geometra che tutto s' affige 
 Per misurar lo cerchio, e non ritruova, 
 Pensando qual principio ond' egli indige. 
 
 And Quarles 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 recognised, as 
 a general rule, the very common practice of throwing back the 
 accent in defiance of quantity, seen in orator, au'ditor, se'nator, 
 ca'tenary, &c. 
 
 Mad MatJiesis 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* 
 
 I have come in the way of a work, entitled ; The Grave of 
 Human Philosophies,' (1827) translated from the French of E. de 
 Becourt by A. Dalmas. It supports, but I suspect not very 
 accurately, the views of the old Hindoo books. That the sun is 
 
DE B^COURT. BEQUEST OF A QUADRATURE. 437 
 
 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 Hindoo 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 c avails himself of that opportunity ' to remove this veil 
 of darkness, &c. 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 com- 
 pliance 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 favour. 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. 
 
 There is much private history which will never come to light, 
 caret quia vote sacro, 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 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 TT 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 sweefc South 
 That breathes upon a bank of vile hits. 
 
438 A BUDGET OF PARADOXES. 
 
 The shares would be at a premium of 3 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 Arch- 
 priest of St. Vitus and 3^-, 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 expla- 
 nation 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 bequest of some 
 very good titles which only wanted treatises written to them. 
 Well I 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. 
 
 October 19, 1861. The English Cyclopaedia. Conducted by Charles 
 
 Knight. 22 vols. : viz., Geography, 4 vols. ; Biography, 6 vols. ; 
 
 Natural History, 4 vols. ; Arts and Sciences, 8 vols. (Bradbury 
 
 & Evans.) 
 The Encyclopaedia Brltannica : 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. . i 
 
 When the works are brought together, the first thing that 
 strikes the eye is the syllable of difference in the names. The 
 word Cyclopcedia is a bit of modern purism. Though e<yfcv/c\o- 
 is not absolutely Greek of Greece, we learn from both 
 
REVIEW OF CYCLOPEDIAS. 439 
 
 Pliny and Quintilian that the circle of the sciences was so called 
 by the Greeks, and Vitruvius 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 
 Kv/cXofapla, 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 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 Keisch, the same we must suppose, who 
 was confessor to the Emperor Maximilian. This is again a col- 
 lection 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 Eingelberg, 
 which is truly called an Encyclopaedia by 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, in four folio volumes, commonly bound in two ; published 
 in 1629 and again in 1649 ; the true parent of all the Encyclo- 
 paedias, 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 ' (1677); but Chambers's 
 (so called) Dictionary (1728) has a better claim. And we support 
 our proposed nomenclature by observing that Alsted accidentally 
 called his work Encyclopaedia, and Chambers simply Cyclo- 
 paedia. 
 
 We shall make one little extract from the 4 myrrour,' and one 
 from Eingelberg. 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.' Eingelberg 
 says that if the right nostril bleed, the little finger of the right 
 
440 A BUDGET OF PARADOXES. 
 
 -Land should be crooked, and squeezed with great force ; and the 
 same for the left. 
 
 We pass on to the Encyclopedia, commenced in 1751 ; the work 
 which has, in many minds, connected the word encyclopaedist with 
 that of infidel. Eeaders 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 ah ovo on account 
 of the character of its supporters was neither adapted, nor in- 
 tended, to excite any particular remark on the subject : no work 
 of which D'Alembert 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 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 6 EncyclopedieJ which he wrote 
 himself: 6 Dans le moral, il n'y a que Dieu qui doit servir de 
 modele a Phomme ; dans les arts, que la nature.' 
 
 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 Encyclopedic Methodique, which we always take 
 to be meant whether rightly or not we cannot tell when we 
 hear of the 6 great French Encyclopaedia.' This work, which takes 
 much from its predecessor, professing to correct it, was begun in 
 1792, and finished in 1832. There are 166 volumes of text, and 
 6,439 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 Grerman Cyclopaedia 
 of Ersch and Gruber, which was begun in 1818, and is still in 
 progress, will beat it in size. The great French work is a collec- 
 tion 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. 
 
KEVIEW OF CYCLOPEDIAS. 441 
 
 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- 
 cyclopsodia 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 supple- 
 mental 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 treatises ; the part called 
 Miscellaneous and Lexicographical in the Metropolitana 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 con- 
 tributors, 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 level 
 
442 A BUDGET OF PARADOXES. 
 
 there must be, is that of mediocrity, if not of absolute worthless- 
 ness : any attempt to secure equality of strength will result in 
 equality of weakness. Efficient development may be cut down 
 into meagre 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 im- 
 possible 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 develop- 
 ment 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, ad- 
 verting 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 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, &c. A respectable quarterly of the 
 theological cast, which in mercy we refrain from naming, was 
 
REVIEW OF CYCLOPEDIAS. 
 
 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 dis- 
 covered 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 con- 
 tinually must liomunculi 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 back- 
 ground ; 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 Encyclopedia is as subject as the Cyclopaedia ; 
 but it is not so easily recognised as a fault. 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 and Herschel. 
 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 
 
444 A BUDGET OF PARADOXES. 
 
 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 litera- 
 ture. 
 
 The literary excellence of these two extensive undertakings is 
 of the same high character. To many this will need justification : 
 they will not easily concede to the chea pand 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 
 Cyclopcedia of the Physical Sciences, published by Dr. Nichol 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 Cyclo- 
 paedias, I found that the scissors had become blunted through too fre- 
 quent and vigorous use. One great exception exists : viz. the Penny 
 Cyclopedia of Charles Knight. 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 obligations be felt to the intelligence and con- 
 scientiousness 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. 
 
 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 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 
 
KEVIEW OF CYCLOPAEDIAS. 445 
 
 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 T 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 tarn informations were laid against the agents 
 in various towns. 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 5001. 
 of 50,000?. : that of the two editions of the Britannica cost 41,000?. 
 But then it is to be remembered that the Britannica had matter 
 to begin upon, which had been paid for in the former editions. 
 Koughly 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 c Eome ' in 98 
 columns and ' Yorkshire ' in 86 columns. The only article which 
 can be called a treatise is the Astronomer Eoyal's 'Gravitation,' 
 
446 A BUDGET OF PARADOXES. 
 
 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 c Asia,' in 45 columns. In 
 natural history the antelopes demand 36 columns. In biography, 
 c 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 times with regard to the 
 subject. Our readers would not hit the longest article of this 
 department in twenty guesses : it is c 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 ; 
 Eailways, 18; Sculpture, 36; Steam, &c., 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 jEVicyclopaedia 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 col- 
 lection 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, 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, c 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 clear- 
 ance 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 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 corres- 
 pondent 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 : 
 
EEVIEW OF CYCLOPAEDIAS. 447 
 
 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, 17367: 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 favour [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 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 understand- 
 ing that the articles should simply set forth the accounts which 
 the sects themselves give of their own doctrines. Thus the article 
 on the Koman Church was written by Dr. Wiseman. 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 c 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 
 
418 A BUDGET OF PARADOXES. 
 
 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 remon- 
 strances on questions of absolute fact, which are beside the pre- 
 sent 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 careful what they say, for no one can tell 
 how long a misstatement may live. On this point we will give 
 the history of a pair of epithets. When the historian De Thou 
 died, and left the splendid library which was catalogued by 
 Bouillaud and the brothers Dupuis (Bullialdus and Puteanus), 
 there was a manuscript of De Thou's friend Vieta, the Harmonicon 
 Codeste, of which it is on record, under Bouillaud's hand, that he 
 himself lent it to Cosmo de' Medici, to which must be added that 
 M. Libri found it in the Magiiabecchi 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, from whom it was pro- 
 cured by some intending plagiarist, who would not give it back. 
 This was repeated by Sherburne, 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 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 ' surrep- 
 titious' acquaintance. We cannot have seen less than thirty 
 copies of these epithets. 
 
 October 18, 1862. Correspondence of Scientific Men of the Seven- 
 teenth Century, in the Collection of the Earl of Macclesfield. 2 
 vols. (Oxford, University Press.) 
 
 Though the title-page of this collection bears 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 
 
REVIEW OF MACCLESFIELD LETTERS. 449 
 
 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, 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 collec- 
 tion published, by Mr. Edleston, for Trinity College, in 1850. . 
 
 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 was in France : as early as 1671, E. Bernard addresses 
 him as ' the very Mersennus and intelligence of this age.' John 
 Collins was never more than accountant to the Excise Office, to 
 which he was promoted from teaching writing and ciphering, at 
 the Eestoration : he died in 1682. We have had a man of the 
 same office in our own day, the late Prof. Schumacher, 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 Eoyal 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 William 
 Jones, the father of the Indian Judge of the same name, who 
 
 a a 
 
450 A BUDGET OF PAKADOXES. 
 
 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 Eoyal 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, the mover and seconder, and 
 Daval, who drew the bill, were pupils of De Moivre. 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 and 
 others. Some of these papers passed into the custody of the 
 Eoyal Society : but the bulk was either bequeathed to, or pur- 
 chased 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 
 Prof. Eigaud, 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 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. Eigaud died before the work 
 was completed, and the publication was actually made by one of 
 his sons, S. Jordan Eigaud, 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 Prof. De Morgan, and an excellent 
 index by the Eev. John Eigaud. The work is now fairly started 
 on its career. 
 
 If we were charged to write a volume with the title 4 Small 
 things in their connexion 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 mathe- 
 matician who has any infusion of the history of his pursuit, are 
 Briggs, Oughtred, Charles Cavendish, Grascoigne, Seth Ward, 
 Wallis, Hu[y]gens, Collins, William Petty, Hooke, Boyle, Pell, 
 Oldenburg, Brancker, Slusius, Bertit, Bernard, Borelli, Mouton, 
 
REVIEW OF MACCLESFIELD LETTERS. 451 
 
 Pardies, Fermat, Towneley, Auzout, D. Gregory, Halley, Machin, 
 Montmort, Cotes, Jones, Saunderson, Eeyneau, Brook Taylor, 
 Maupertuis, Bouguer, La Condamine, Folkes, Macclesfield, Baker, 
 Barrow, Flamsteed, Lord Brounker, J. Gregory, Newton and 
 Keill. To these the Museum collection adds the names of 
 Thomas Digges, Dee, Tycho Brahe, Harriot, Lydyat, Briggs, 
 Warner, Tarporley, Pell, Lilly, Oldenburg, Collins, Moiiand. 
 
 The first who appears on the scene is the celebrated Oughtred, 
 who is related to have died of joy at the Eestoration : 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, 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 Eoyal on the discovery of Neptune, which 
 we printed March 20, 1847. Mr. Airy there contends, and proves 
 it both by Leverrier and by Adams, that the limited publication 
 of a private letter is more efficient than the more general pub- 
 lication 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 con- 
 tractions for the words sine, cosine, &c., prefixed to the symbol of 
 the angle. This is so very important a step, simple as it is, that 
 Euler 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 
 Simpson has chanced to know of Oughtred's < Trigonometric ' : 
 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, &c. : so often does the supplementary 
 
 remark begin with ' this letter has been printed in .' Fox* 
 
 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 
 
 G G 2 
 
452 A BUDGET OF PARADOXES. 
 
 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 Prof. Eigaud had to copy every- 
 thing 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 num- 
 bered and described ; and those would certainly not have been 
 noticed if any omissions had 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, 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 c 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, 4 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 (f> n x, when n increases 
 without limit, is a solution of <f>x = x. We have mentioned the 
 I. Newton to whom Dary looked up ; we add a word about the 
 
REVIEW OF MACCLESFIELD LETTERS. 453 
 
 one on whom he looked down. Dr. John Newton, a sedulous 
 publisher of logarithms, tables of interest, &c., 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. 
 
 The second character above alluded to is one who carried 
 mathematical researches a far greater length than Newton him- 
 self : 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 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 content- 
 ment 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 writes to Collins as follows : 
 4 Last week he sent us down the counterpart, which my father 
 has sealed, and I return up to you by the carrier, with 5Z. 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 
 
454 A BUDGET OF PARADOXES. 
 
 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 c le moyen de deux 
 egales hauteurs du soleil devant et apres diner.' 9 
 
 There is one mention of 'Mr. Cocker, 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 subsequently forged the famous Arithmetic, 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 c Arithmetical Books.' Among many other corro- 
 borative 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 an Hie ego qui 
 quondam of this kind : ' I have been instrumental to the benefit 
 of many, by virtue of those useful arts, writing and engraving ; 
 and do noiv, 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, 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 
 
REVIEW OF MACCLESFIELD LETTERS. 455 
 
 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. 
 Murphy chooses Wingate to be the name of an old merchant 
 who delights in vulgar fractions, and Cocker to be his arithmetical 
 catchword 4 You read Shakspeare ! 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. 
 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, 3rd S. 
 iv. 89.] 
 
 Collins informs James Gregory that c some of the Eoyal 
 Academy wrote over to Mr. Oldenburg, who was desired to 
 impart the same to the Council of the Eoyal Society, that the 
 French King was willing to allow pensions to one or two learned 
 Englishmen, but they never made any answer 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 
 
456 A BUDGET OF PARADOXES. 
 
 French King had attempted/ to buy a little adherence from 
 English literature and science : and the silent contempt of the 
 Eoyal Society is an honourable fact in their history. 
 
 Another little bit of politics is as follows. Oughtred is 
 informed that 'Mr. Foster, our Lecturer on Astronomy at 
 Grresham College, is put out because he will not kneel down at 
 the communion-table. A Scotsman [Mungo Murray], one that is 
 verbi bis minister, is now lecturer in Mr. Foster's place.' Ward, 
 in his work on the Grresham Professors, 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 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 it 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 4 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 Eoyal 
 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 appoint- 
 ment 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 [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 : 
 4 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 endeavour to 
 obviate it by acquainting your friends that I neither put in for 
 
KEVIEW OF MACCLESFIELD LETTERS. 457 
 
 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 
 Wardenskip. 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 opera- 
 tion 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, after- 
 wards assisted by Pell, commenced, a table of antilogarithms, of 
 the kind which Dodson afterwards constructed anew and pub- 
 lished. In the Museum collection there is inquiry after inquiry 
 from Charles Cavendish, first, as to when the Analogies, 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, and no small 
 share of my labours therein, are seazed upon, and most unmathemati- 
 cally 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 that the papers had fallen into the 
 hands of Dr. Busby, and Collins writes that they were left in the 
 hands of Dr. Thorndike, a prebendary of Westminster ; whence 
 Eigaud seems to say that Thorndike had left them to Dr. Busby. 
 Birch says that he procured for the Eoyal 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 
 
458 A BUDGET OF PARADOXES. 
 
 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 Collinses 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 West- 
 minster and the Head Master of Westminster School. If so, in 
 all probability Thorndike handed the cumbrous lot over to the 
 notorious collector of mathematical papers, blessing himself that 
 he had 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 re- 
 calculated, 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. 
 
 Redit labor actus in orbem. 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 Prof. Recalcati, already 
 mentioned. It ends with " Quelque objection qu'on fasse touch- 
 ant les raisonnements ci-dessus on tombera toujours dans 1'ab- 
 surde.' 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 
 30-7-4 = 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 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 in- 
 ability " to execute his task. Mr. William Dean, of Todmorden, 
 in 1863, announced 3^ 9 T as proved both practically and geome-v 
 
CYCLOMETKY AND STEEL PENS. 459 
 
 trically : 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, 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 anti- 
 cyclometers too, for that matter. Mr. Peters will not allow me 
 any extra-journal being : I am essentially a quotation from the 
 Athenceum ; ' A. De Morgan ' et prceterea nihil. 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 methodi- 
 cally at the beginning 'By Eoyal 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 OHllott's steel pens, with 
 engraving of his premises, and notice of novel application of his 
 unrivalled machinery. The second side begins with 'the circle 
 rectified ' by W. E. Walker, who finds 7r= 3-141594789624155 . . . 
 This is an off-shoot from an accurate geometrical rectification, 
 on which it 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 dis- 
 cordances. The ratio of the circumference to the diameter is not 
 always the same ! Not that it varies with the radius ; the geo- 
 meters 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 
 
4GO A BUDGET OF PARADOXES. 
 
 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 longi- 
 tudes, 
 
 ^=3i^ + ift> cos(A-a). 
 
 Mr. James Smith obtained his quadrature at full moon ; the 
 Arch priest 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' 141 59 . . . . , 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 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 Koyal leans towards another de- 
 pending on the date of the Queen's accession. I have no 
 patience with these men : what can the Moon's node or 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 &c. &c. &c. &c. 
 
 The following method of finding the circumference of a circle 
 (taken from a paper by Mr. S. Drach in the Phil. Mag., Jan. 
 1863, Suppl.) is as accurate as the use of 3'141 59265. 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. 
 
 Though I have met with nothing but a little tract from the 
 school of Jacob Behmen (or Bohme ; 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 4 Introduction to Theosophy [Theo 
 privative, I suppose, as in theological] ; or, the Science of the 
 Mystery of Christ,' published in 1854, mostly from the writings 
 of William Law : 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 6 a 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 in- 
 accurate accounts, one of which he quotes, as follows : ' He 
 
JACOB BEHMEN. ^ ,' v - 461 
 
 derived all his mystical and rapturous doctrine from Wood's 
 6 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, for whom see Wood's 
 &c. &c.' Even this is absurd enough : for Behmen began to 
 publish in 1610, and Fludd in 1616. Fludd was a Kosicrucian, 
 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 recognised 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 state- 
 ment of what is said of Behmen far less liable to suspicion of ex- 
 aggeration than anything I could write. I shall add a few extracts 
 from Behmen himself, in support of his right to be in my list.] 
 
 4 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 of that author. Per- 
 haps 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 meta- 
 physical system of Behmen the most perfect and only true one 
 still awaits a qualified commentator. Behmen's countryman, 
 Dionysius Andreas Freher, 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 excep- 
 tion of two, written in Grerman, 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 Prof. De Morgan, this Freher was the first 
 to philosophically expound Behmen's system, which was after- 
 wards, 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, accu- 
 
462 A BUDGET OF PARADOXES. 
 
 racy, 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 demonstra- 
 tion 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 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, 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 estab- 
 lishment 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 them- 
 selves 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 manifesta- 
 tion 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 outbirths of the circumference, along the 
 radius to the centre, 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 
 
JACOB BEHMEN. 463 
 
 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. 
 Eichardson) 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, ac- 
 cording to the spirit of this world in the third principle, which is con- 
 tinually generated out of the anguish of the will in the mind, and the 
 Brims tone- worm is the Spirit, which hath the fire and burneth : PHUR 
 is the sour wheel in itself which causeth that. 
 
 Mercurius comprehcndeth 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. RT 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 syllable US is called the burning fire, which with the spirit 
 continually driveth itself forth : and the syllable CU presseth con- 
 tinually upon the flash. 
 
 Shades of Tauler and Paracelsus, how strangely you do mix ! 
 Well may Hallam call Grermany 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 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 
 
464 A BUDGET OF PARADOXES. 
 
 all, because they can put the small end of their paradox into any 
 literary conversation whatsoever. 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, 
 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, the name given by Reuchlin 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 para- . 
 doxers 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 argu- 
 ment, he asked, ' What does Kitty say ? ' < Who's Kitty ? ' said 
 the magistrate, ' your wife, or your nurse ? ' c Sir ! I mean Kitty, 
 the celebrated lawyer.' ' Oh ! ' said the magistrate, c I suspect 
 you mean Mr. Chitty, the author of the great work on pleading.' 
 ' I do sir ! but Chitty is an Italian name, and ought to be pro- 
 nounced 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. 
 
 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 
 
KINO CUSTOM'S ADVISEES. 465 
 
 denote them in their books, or by our vernacular names. This is 
 the intelligible way of proceeding. I might, for instance (p. 31), 
 have spoken of Charles de Bovelles, of Lefevre d'Etaples, of Pelerin, 
 and of Etienne. 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 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 him- 
 self with the 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 Ehematopolis on circum- 
 stantial evidence which looks like mystery gone mad ; but, strange 
 to say, something very often comes to light after sentence 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 
 
 H H 
 
466 A BUDGET OF PARADOXES. 
 
 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 c a means 
 whereby we receive the same,' and Analogy a subordinate of 
 Etymology asked whether he thought it a great new to hear 
 that he was wrong. It was either this Fiddle-faddle, or Lindley 
 Murray his traveller, who persuaded the Miss Slipslops, of the 
 Ladies Seminary, to put 4 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 4 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, c 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 punctua- 
 tions and other signs ; he has a pepper-box full of commas 
 always by his side. He puts everything under marks of quota- 
 tion 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, 6 A lass and a lac a day ! ' If any 
 one should have the sense to leave out of his Greek the un- 
 meaning 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, 
 o 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 
 
TEST OF LANGUAGE. 467 
 
 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 
 coi^pus issuing out of another. 
 
 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 Ealeigh or of Bacon. Here arises the ques- 
 tion whether Ealeigh 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 Testa- 
 ments. I am not prepared ta 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 
 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 Eobert Eecorde 
 and his pupil in the ' Castle of Knowledge^' written before 1556. 
 When Dr. Eobert 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 9 
 and the modern spelling : with no other variation whatever. 
 
 ' Scholar. Yet the reason of that is easy enough to be con- 
 ceived, 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 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 
 
 H H 2 
 
468 A BUDGET OF PARADOXES. 
 
 makes not the Sun to shine long, neither the shortness of the 
 day causes not [_sic~] the Sun to shine the lesser time, but con- 
 trariwise 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 
 makes 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 a]l 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 con- 
 venient 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 : ' 
 Eecorde, ' the Sonne shynynge maketh the daye.' 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 Eecorde 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, Eecorde, the 
 version, and ourselves, by differences of the same character. But 
 we speak of Eecorde's conversation, and of our own. We con- 
 clurle that it is the plain and almost colloquial character of the 
 
PRONUNCIATION. 469 
 
 Authorized Version which distinguishes it from the English of 
 Bacon and Kaleigh, by approximating it to the common idiom of 
 the time. If any one will cast an eye upon the letters of instruc- 
 tion written by Cecil 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 Ealeigh by the same sort of 
 differences which distinguish the version itself. 
 
 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 7 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 : 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 re- 
 member that a pedant who was insisting on all the pronuncia- 
 tions being retained, was met by a maxim in contradiction, 
 invented at the moment, and fathered upon Kaen-foo-tzee, 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 ; Confu- 
 cius says that too. 
 
 The old English has fote, fode, loke, coke, roke, &c., for foot, 
 &c. 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 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 know the village of Kokeby (pro- 
 nounced Eookby) despise the world for not knowing how to name 
 Walter Scott's poem : that same world never asked a question 
 
470 A BUDGET OF PARADOXES. 
 
 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 Ruke-by would be right, with a little turning of the 
 Italian u towards 6 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, c Ah ! you got that out of the Athenceum ! ' 
 4 Excuse me,' said I, ( the Athenceum got that out of me ! '] 
 
 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, as the Leipzig Acts call him (probably 
 Dethleu Cluvier), grandson of the celebrated geographer, Philip 
 Cluvier. The grandson was a Fellow of the Eoyal Society, 
 elected on the same day as Halley, November 30, 1678 : I 
 suppose he lived in England. This 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, 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 
 divince 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, &c. : 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, &c. 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 3?i 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 
 adnrtted, 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 
 The only instance I recall is that of M. Cluvier, who (Phil. 
 
THE KAINBOW PARADOX. 471 
 
 Trans. 1686, No. 185) refuted M. Mallemont de Messange, who 
 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, &c. up to infinity. 
 
 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 colour. They only give it, as lenses and 
 mirrors ; and each one drop gives all the colours, 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 reflexion. How could this be, if 
 there were nothing coloured 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 colours to the eye after reflexion, at the water or the 
 looking-glass, A few years ago an artist exhibited a picture with 
 a rainbow and its apparent reflexion : he simply copied what he 
 had seen. When his picture was examined, some started the idea 
 that there could be no reflexion 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, 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. 
 
 The system of Tycho Brahe, with some alteration and addition, 
 has been revived and contended for in our own day by a Dane, 
 W. Zytphen, who has published 4 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 t><3 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 
 
472 A BUDGET OF PARADOXES. 
 
 attain the same result? In the Copernican and other systems, it is 
 well known that the Moon, abstracting from the insignificant excen- 
 tricity of the orbit, always in twenty-four hours performs an equally 
 long distance. Why has Copernicus never been denominated Funda- 
 mentus or Fundator ? Because he has never convinced anybody so 
 thoroughly that this otherwise so natural epithet has occurred to the 
 mind/ 
 
 Eeally the second question is more effective against Newton 
 than "against Copernicus ; for it upsets gravity : the first is of 
 great depth. 
 
 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 cor- 
 respondent who signed 4 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 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 &c. 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 him- 
 self 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, Jenner, Harvey, and other glorious trios, who have been 
 contemned . . .' 
 
 The writer then called upon Mr. James Smith to come 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. Keddie, Zadkiel, 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 would call a dose of capital for my 
 
LETTEK TO ATHENAEUM. 473 
 
 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 
 quite 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 
 Athenceum : 
 
 PSEUDOMATH, PHILOMATH, AND GliAPHOMATH. 
 
 December 31, 1867. 
 
 MANY thanks for the present of Mr. James Smith's letters of Sept. 28 
 and of Oct. 10 and 12. He asks where you will be if yon read and 
 digest his letters : you probably will be somewhere first. He after- 
 wards asks what the WE of the Athenceum will be if, finding it im- 
 possible to controvert, it should refuse to print. I answer for you, 
 that We-We of the Athenceum, 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 ; pseudomathetft and gmphomathete 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 lie had 
 peen 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 J 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 lengthways. 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 
 
474 A BUDGET OF PARADOXES. 
 
 a lesson to presumption. The following anecdote is found in Thiebault's 
 ' Souvenirs de vingt ans de sejour a Berlin,' published in 1804. The 
 book itself got a high character for truth. In 1807 Marshal Mollen- 
 dorff answered an inquiry of the Due de Bassano, 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. 1 
 
 Diderot 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 ex- 
 hibitions. 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 algebra- 
 ical proof of the existence of God, which he would communicate before 
 the whole Court, if agreeable. Diderot gladly consented. The ma- 
 thematician, who is not named, was Euler. He came to Diderot with 
 the gravest air, and in a tone of perfect conviction said, " Monsieur I 
 
 done Dieu existe ; repondez \ " 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 turned the 
 tables completely, by saying, < Monsieur ! vous savez bien que votre 
 raisonnement demande le developpement de x suivant les puissances 
 entieres de n.' Goldsmith could not have seen the anecdote, or he 
 might have been supposed to have drawn from ifc a hint as to the way 
 in which the Squire demolished poor Moses. 
 
 The graphomatji 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 calcu- 
 lator, Davy Ramsay, swears * by the bones of the immortal Napier. ' 
 Scott thought that the philomaths worshipped relics : so they do, in 
 one sense. Look into Hutton's Dictionary for Napier 1 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 l Headlong 
 
 1 This anecdote is printed at p. 251 ; but as it is used in illustration here, and is 
 given more in detail, I have not omitted it. EB. 
 
LETTER TO ATHENAEUM. 475 
 
 Hall ' 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, in his well-wrought 
 tale of the martyr-philosopher, was incautious enough to invent the 
 symbols by which his savant satisfied himself Laplace was right on a 
 doubtful point. And this is what he put together 
 
 - 3a 2 , CD ^ + 9 - n = 9, n x log e. 
 
 z* 
 
 Now, to Diderot and the mass of mankind this might be Laplace all 
 over : and, in a forged note of Pascal, would 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 : l Committing the destiny of the country 
 to your hands, Gentlemen, I may without fear declare, in the language 
 of the noble Roman poet, 
 
 E pluribns unum, 
 Multum in parvo, 
 Ultima Thule, 
 Sine qua non.' 
 
 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 I I 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, &c., 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 Athenceum : 
 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^- as would con- 
 vince 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 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, gust as an artist 
 makes use of a dummy for the purpose of arranging his drapery/ The 
 
476 A BUDGET OF PAKADOXES. 
 
 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. MaQlius and Sp. 
 Cassius.' Umph ! said I, surely all know that Spurius Mselius 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^ 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 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 knowledge of his subject and sense to get it. He 
 is, in fact, only a mask : of whom the fox 
 
 quanta species, inquit, cerebrum non habet. 
 
 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 mathema- 
 ticians : 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 ? JSTot the mathema- 
 tician, 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, 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 
 
ME. EEDDIE'S ASTRONOMY. 477 
 
 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 bat cliaff 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. 
 
 Nothing came of this until July 1869, when I received a 
 reprint of the above letter, with a comment, described as Ap- 
 pendix D of a work in course of publication on the geometry of 
 the circle. The Athenceum 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 Prof. Whitworth, and Mr. Wilson, 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^, and refusing acknowledgment. Mr. Wilson was 
 introduced to J. S. by a volunteer defence of his geometry from 
 the assaults of the Athenceum. 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 Athenceum and a merited 
 punishment for 'that unscrupulous critic and contemptible 
 mathematical twaddler, De Morgan.' 
 
 At p. 371 I mentioned Mr. Eeddie, the author of Vis Inertice 
 Victa and of Victoria tolo codo, which last is not an address to 
 the whole heaven, either from a Eoman Goddess or a British 
 Queen, whatever a scholar may suppose. Between these Mr. 
 Eeddie has published 4 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 what it would catch. His spe- 
 culations 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 6 truly scientific,* and would 
 
478 A BUDGET OF PAKADOXES. 
 
 be glad to have readers who have read what he controverts, i. e. 
 Newton's Principia : I wish he may get them ; I mean 1 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 
 Athenceum complaining that they are not laughed at ; although 
 they deserve it, they tell me, as much as some whom I have 
 inserted. Mr. Eeddie 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 demon- 
 strably impossible ? It would be as useless as evidence against a 
 man who has pleaded guilty. Mr. Eeddie 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, 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 to make it appear that ' he ' was advocating 
 solely a geocentric hypothesis, which is not true.' In fact, he did 
 his very 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, aftei* 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. Eeddie attaches much force to Berkeley's 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 irlade,' to copy a description 
 given in a review : though I have no doubt Mr. Eeddie got them 
 out of himself. But the whole matter comes to this : Mr. Eeddie 
 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 ; 
 
ME. EEDDIE'S ASTKONOMY. 479 
 
 because so wrong that none who could understand an answer 
 would be likely to want one. 
 
 Mr. Eeddie 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, let him be ever so wrong about New- 
 ton. 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 : 
 
 4 The third (Victoria . . .), although only published in September, 
 1863, has already had its triumph. It is the book that forced the As- 
 tronomer 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 abey- 
 ance" 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, Nov 18, 1865 : 
 
 4 ... You ought, when you came to put me in the " Budget," to 
 have been aware of the Repof't of the Council of the Royal Astronomical 
 Society, where it appears that Professor Airy, with a better appreci- 
 ation 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 How in doubt and 
 abeyance." You were culpable, as a public teacher of no little pre- 
 tensions, if you were " unaware " of this. If aware of it, you ought not 
 to have suppressed slidi an important testimony to my really having 
 been "very successful" in dr'awing the teeth of the pegtops, though 
 you thought them so firmly fixed. And if you still suppress 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 in- 
 jured you i '> - 
 
 Mr. Reddie must have been very well satisfied in his own mind 
 before he ventured such a challenge* with an answer from me 
 
480 A BUDGET OF PAKADOXES. 
 
 looming in the distance. The following is the passage of the 
 Eeport of the Council, &c., from which he quotes : 
 
 1 And yet, strange to say, notwithstanding the near coincidence of 
 all the results of the before-mentioned independent methods of investi- 
 gation, 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, 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 much the same result as Herschel. 
 Mr. E. Dunkin, 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 Sep- 
 tember, 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 
 
MR. REDDIE AND THE ASTRONOMER EOYAL. 481 
 
 Astronomer Eoyal to abandon the fact of motion of the solar 
 system by the February following. Had Mr. Eeddie, when he 
 saw that the Council were avowedly describing a memoir pre- 
 sented some time before, taken the precaution to rind 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. Eeddie 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 into the quillet that his thunderbolt had stopped 
 the chariot of the Sun and knocked the Greenwich Phaethon 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 in- 
 vestigation 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 what I had written what precedes, that 
 Mr. Airy had given a sufficient answer on the point. Mr. Eeddie 
 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. 7 
 
 Mr. Eeddie 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 
 
 i i 
 
482 A BUDGET OF PARADOXES. 
 
 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 c Sir ! I will 
 not say a word on that subject.' He would put it thus, 6 Sir! I 
 will only say ten words on that subject,' and, having thus said 
 them, would 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. Eeddie sends to be 
 noticed, shall be noticed, so far as an extract goes : 
 
 VMy connexion with this subject is, indeed, very simply explained. 
 In endeavouring to understand the laws of physical astronomy as 
 generally taught, I happened to entertain some doubt whether gravi- 
 tating 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 mag- 
 netism as opposing and correlative forces most probably suggested to 
 my mind, as to many others, by the transcendent discoveries made in 
 electro-magnetism by Professor Faraday my former doubts about 
 gravitation were revived, and I was led very naturally to try and dis- 
 cover 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. Eeddie is. It is clear that ' presumed ' is a slip of the 
 pen ; it should have been condescended. 
 
 Mr. Eeddie 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 infinite variety of a 
 system constructed on a wonderful sameness of leading character- 
 istics. And why should paradoxes be denied that collective im- 
 portance, paltry as many of them may individually be, which is 
 accorded to moths, beetles, or butterflies ? Mr. Eeddie himself 
 sees that ' there is a method in ' my 4 mode of dealing with para- 
 doxes.' 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. 
 
ME. EEDDIE'S CHALLENGE. 483 
 
 In the Introduction to a collected edition of the three works, 
 Mr. Eeddie describes his Mechanism of the Heavens, from which 
 I have just quoted, as 
 
 < a public challenge offered to the British Association and the mathe- 
 maticians 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 centre 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.' 
 
 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 stage coach ; dropping off at last 
 with c Why don't you get down and thrash us ? You're afraid, 
 you're afraid!' They will allow the public to judge for them- 
 selves, 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 den- 
 drobats : 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 
 anapsestic tetrameters your anapaest is the foot for satire to halt 
 on, both in Grreek 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 : 
 
 i i 2 
 
484 A BUDGET OF PAKADOXES. 
 
 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 ? 
 
 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 1 Deep 1 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 spirt 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 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 Ldlliput 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 
 
TIME THE SETTLEK OF PARADOX. 485 
 
 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 be- 
 tween the true answer and the new capitals and diagrams on which 
 the delighted paradoxer would declare 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. Keddie has done in his fancy about the 
 Astronomer Eoyal'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 Grue. 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 appro- 
 bation of all thinking non-claimants : there is no need of a suc- 
 cession of exposures. Time gets through the job in his own work- 
 manlike 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 which sets up the scientific 
 charlatan. Their world is large, and there are many who have that 
 moderate know] edge, 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 pre- 
 
486 A BUDGET OF PARADOXES. 
 
 tenders 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 Hubongra- 
 millposanfy 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 favourably 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. 
 
 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 recom- 
 mend 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, &c. The author is 
 evidently one whom I should delight to honour : 
 
THE BUDGETEEK CORRECT F^D. 487 
 
 4 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, &c. The work 
 is the result of thirty-five years' travel and observation, labour, ex- 
 pense, 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 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. 
 
 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] 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 honour 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 ; 
 
488 A BUDGET OF PARADOXES. 
 
 embracing points the most interesting, laws the most important, 
 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, &c. 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 
 6 profoundest respect ' to the loftiest insolence for an apocraphi- 
 cal correspondence, to use a word I find in the Prospectus : on 
 my honour it is genuine. He will be better employed in dis- 
 covering 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. 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 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 arc 
 not. So far natural, and so far good ; anything short of con- 
 cession 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. Eeddie 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- 
 
THE DOUBLE VAHU PROCESS. 480 
 
 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 news- 
 paper that he had a mane and tusks.] 
 
 My friend Dr. Thorn sees deeper into my mystery. By the way, 
 he still sends an occasional touch at the old 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 
 
 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 dis- 
 covery, 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. Eeddie : 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 pen- 
 tasyllabic 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 accusa- 
 tion] ; though Dr. Thorn declared me a competitor for fire and 
 brimstoneand my wife, too, which doubles the joke : though 
 
490 A BUDGET OF PARADOXES. 
 
 Mr. Eeddie 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 candour 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, &c., 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 allowance 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. He is the fourth who has taken elaborate 
 notice of me ; and my advice to him would be, Nee quarto, loqui 
 persona laboret. 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 favour with the Astronomer 
 Eoyal, 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 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 Athenceum : 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, &c. as not fit 
 to compete with me. I say of them what one crossing-sweeper 
 said of the rest : 4 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 
 
OKTHODOX PAKADOXES. 491 
 
 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 terns-la 
 
 C'etait deja comme $a ! 
 
 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, occa- 
 sionally, in the thoughts of sagacious investigators. At the end 
 of the 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 
 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 6 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 honour," replied the 
 Corporal. My uncle Toby gave a nod.' 
 
 I now proceed to die out. Some prefatory remarks will follow 
 in time. 1 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 contemned. 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. 
 
 1 These remarks were never written. (Ed.) 
 
492 A BUDGET OF PARADOXES. 
 
 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 : 
 
 ' " Bat, 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, per- 
 haps two out of five, we are indebted for the preservation of 
 literature, and their contemporaries for good teaching and miti- 
 gation of social 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 Eeformation : 
 
 Flen, flyys, and freris, populum domini male caedunt ; 
 Thystlis and breris crescentia gramina Isedunt. 
 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. 
 
 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 proposition gentis imperitaa 
 Artes frugi reddere melioris vitsD. 
 
 To this end I have spoken with freedom of books as books, of 
 opinions as opinions, of ignorance as ignorance, of 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 privi- 
 lege of retort, of which I have availed myself ; assaults which give 
 my readers a right of partnership in the amusement which I 
 mvself have received. 
 
CONCLUSION. 493 
 
 For the present I cut and run : a Catiline, pursued by a chorus 
 of Ciceros, with Quousque tandem ? Quamdiu nos ? Nihil ne te ? 
 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 : and I throw back at my pursuers Valete, doctores sine 
 doctrina ; facite ut proximo congressu vos salvos corporibus et 
 sanos mentibus videamus. Here ends the Budget of Paradoxes. 
 
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, in the Berlin Memoirs for 1761, and has been also given 
 in the notes to Legendre's Geometry, and to the English translation of 
 the same. Though not elementary algebra, it is within the . reach of 
 a student of ordinary books. 
 
 Let a continued fraction, such as 
 
 b + c 
 
 ~d + e_ 
 
 T+ &c., 
 
 be abbreviated into % -^ each fraction being understood 
 1+ d+ f+ &c. : 
 
 as falling down to the side of the preceding sign +. In every such 
 fraction we may suppose &, d, /, &c. positive ; a, c, e, &c. being as 
 required : and all are supposed integers. If this succession be con- 
 tinued ad infinitum, and if -, -, -, &c. all lie between 1 and 
 
 b d f 
 
 H- 1, exclusive, the limit of the fraction must be incommensurable 
 with unity ; that is, cannot be - , where A and B are integers. 
 
 B 
 
 First, whatever this limit may be, it lies between 1 and + 1. 
 
 This is obviously the case with any fraction , where w is between 
 
 q + o> 
 
 + 1 : for, -, being < 1, andp and q integer, cannot be brought up 
 to + , by the value of 01. Hence, if we take any of the fractions 
 
 a a c a c 
 6 6~-f d' b+ 5+ 
 
 say - - ^ f we have, -2- being between -f 1, so is - . so 
 * b+ d+ /+ h ' h f+ Ji 
 
 therefore is %- ~ i ; and so therefore is ^ \ . - -f . 
 d+ /+ h ^4 df /+ h 
 
496 APPENDIX. 
 
 Now, if possible, let ~ C ~ &c. be - at the limit ; A and B being 
 integers. Let 
 
 p = A r - -? &c, Q = p e - SL Ac., B = Q' I Ac. 
 d + /+ /+ h+ A* A- + 
 
 p, Q, R, &c. being integer or fractional, as may be. It is easily shown 
 that all must be integer : for 
 
 A a r 
 
 or, p = a B o A 
 
 - - - 
 B I + P 
 
 I' 
 
 - _ - 
 
 A d + Q 
 ? 
 P 
 
 - 
 
 or, Q = c A d P 
 
 &c., &c. Now, since a, B, &, A, are integers, so also is P ; and thence 
 
 Q ; and thence R, &c. But since-, -, ?, -, &c. are all between - 1 
 
 B A p Q 
 
 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 ^ ^- , &c. can have a commensurable limit. 
 
 It easily follows that the continued fraction is incommensurable if 
 ^, -, &c., being at first greater than unity become and continue less 
 
 U Cv 
 
 than unity after some one point. Say that -?, , . . . are all less 
 
 k m 
 
 than unity. Then the fraction ... is incommensurable, as 
 
 proved : let it be K. Then f is incommensurable, say X ; 
 
 h + ic / + X 
 
 is the same, say p, ; also , say v, and , say p. But p is 
 
 d + p. o + v 
 
 the fraction - - . . . itself ; which is therefore incommensurable. 
 Let (f> z represent 
 
 * 2*0 + 1) ' 2-3-^0 + 1) ( +2) 
 Let z be positive : this series is convergent for all values of a, and 
 
APPENDIX. 497 
 
 approaches without limit to unity as z increases without limit. Change 
 z into 3 -f 1, and form z </> (2 -f 1) : the following equation will 
 result 
 
 *. - * ( + 1) = 5_ 9, (* + 2) 
 
 _ a <t> (z + 1) f a <j> (z + 1) a $ (z + 2) 
 or (i . z -f~ . - ^ .. . -i \ 
 
 Z $ Z Z </> 3 3+10 (Z + i) 
 
 a = $ z ( 
 
 z + 
 
 J/ ^ being ^ ^ g i ; of which observe that it diminishes without 
 
 z 0. a 
 
 limit as z increases without limit. Accordingly, we have 
 
 a a 
 
 + + 1)+ ( +2) 
 
 And, $ (z + n) diminishing without limit, we have 
 a 6 (z + 1) _ a a a 
 
 ~ ~ "~ 
 
 Let 3 = i ; and let 4 a = - a; 2 . Then - (3 + 1) is - ^ 
 
 3 2 
 
 or cos a; : and the continued fraction is 
 
 ^ a? 2 a? 2 ^ a? 2 j a; a; 2 a; 2 
 
 +~ T" + ... " 2 TT 34^ 54 
 
 whence tan a; = 
 
 1+3+ 5+ 7+ .., 
 
 Or, as written in the usual way, 
 
 tan x = x 
 
 __ 
 
 3 - * 
 
 5 -a? 2 
 
 7- ... 
 K K 
 
498 A BUDGET OF PARADOXES. 
 
 This result may be proved in various ways : it may also be verified 
 by calculation. To do this, remember that if 
 
 ?! ?* ?2 ^ = ZB then 
 
 Ql = &i Q 2 = &2 Ql+2> Q3 = 
 
 in the case before us we have 
 
 a l = a?, a 2 = a; 2 , a 3 = a? 2 , a 4 = a? 2 , a 5 = a; 2 , &c. 
 &! = 1, 6 2 = 3, 6 3 = 5, 6 4 = 7, 6 5 = 9, Ac. 
 
 P! = x QI = 1 
 
 P 2 = 3 x Q 2 = 3 - a? 2 
 
 P 3 = 15 x a? 3 Q 3 = 15 6 x 2 
 
 p 4 = 105 x - 10 a? 3 Q 4 = 105 - ^5 a^ 2 + a 4 
 
 p 5 = 945 x - 105 a? 3 + x 5 Q 5 = 945 - 420 a 2 + 15 x 4 
 
 P 6 = 10395 x - 1260 aj 3 + 21aj 5 Q 6 = 10395 - 4725 a; 2 + 210 a; 4 - x* 
 
 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 a?, as 
 far as n terms. That series is 
 
 a? 3 2 x 5 17 x 7 62 a? 9 
 h T " h T5~ *" 315 ^ 2835 " 
 
 Take Pg, 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* 7295 78. 
 We find that when x = -1, P 6 = 1038-24021, Q 6 = 10347770999 ; 
 whence P G divided by Q 6 gives '1003346711. Now 5'729578 is 5 43' 
 46 J" ; and from the old tables of Eheticus no modern tables carry 
 the tangents so far the tangent of this angle is '1003347670. 
 
 Now let x = 5 TT ; in which case tan x = 1. If J TT be commensur- 
 
 able with the unit, let it be , m and n being integers : we know that 
 
 n 
 
 \ TT < 1. We have then 
 
 -, _ m m 2 m 2 _ m m 2 m 2 m 2 
 
 n 3 n 5 n 7 n . . . 
 
 222 
 
 Now it is clear that - , - , - , &c, must at last become and con- 
 3 n 5 n In 
 
 tinue severally less than unity. The continued fraction is therefore 
 incommensurable, and cannot be unity. Consequently ?r 2 cannot be 
 
APPENDIX. 499 
 
 commensurable : that is, TT is an incommensurable quantity, and so 
 also is 7T 2 . 
 
 I thought I should end with a grave bit of appendix, deeply mathe- 
 matical : but paradox follows me wherever I go. The foregoing is in 
 my own language from Dr. (now Sir David) Brewster's 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, then known at Edinburgh as a writer and teacher. 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. He prefixed, from his own pen, a thoughtful and iDgenious 
 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 p. 285 : Ed.) 
 
 Michael Stifelius edited, in 1554, a second edition of the Algebra 
 (I)ie CW.), of Christopher Rudolf. This is one of the earliest works 
 in which -f- and are used. 
 
 Stifelius was a queer man. He has introduced into this very work 
 of Rudolph 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 Melancthon about his astrology: he accepted the 
 conclusions, but told him to clear his mind of all the premises about 
 the Beast. Stifelius 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. 
 
 K K. 2 
 
INDEX. 
 
 (A. C.) Anti-Copernican, (Ale.) Alchemist, (A. N.) Anti-Newtonian, (Ast.) Astrologer, 
 (Cyc.) Cyclometer, (Mys.) Mystic, (Tris.) Trisector. 
 
 ABB 
 
 A BBOTT, Chief Justice, 108 
 J\. On Hone's trial, 108 
 Aboriginal Britons (Poem), 432 
 Academy of Sciences, French, 97 
 Adair, Serjeant, 133 
 Adam, Melchior, 44 
 ^Adams, J. C., discoverer of Neptune, 31.53, 
 
 211, 253, 337, 343, 344, 347, 348, 451 
 Addison, Joseph, 111 
 Ady, Joseph (begging letter writer), 276, 
 
 277 
 
 Agnew, H. C. (Pyramid Quadrature), 199 
 Agricultural Labourer (letter of), 259 
 Agrippa, Cornelius, 33, 34 
 
 King, 147 
 Ainsworth, Harrison, 337 
 
 Airy, G. B., 54, 55, 56, 343, 350, 362, 480 
 
 Mrs., 143 
 Albert, Prince, 286 
 Aldrovand, Father, 332 
 Alfonso X., of Castile, 431 
 Alford, Dean, 398 
 
 Alfred, King, (ballad of), 263 
 Aloysius Lilius (Calendar), 222 
 Ameen Bey, 258 
 
 Amicable Society (Constitution of), 212 
 Amphisbcena Serpent, 23; Sir T. Browne's 
 
 remarks on, 23 
 
 Anagrams on Author's name, 82, 83 
 Anaxagoras, 288 
 Anghera, Dr. (Cyc.), 289 
 Anopides of Chios, 288 
 Antegregorian Calendar, 225 
 Antinomians, The, 244 
 Antipho, (Cyc.), 288 
 Antiquary, The. 34 
 Antonie, Dr. Francis, 75 
 Apocalypse, The, 398, 399, 400 
 Apollonius, 30, 53, 71 
 Apparitions, 280 
 
 AUZ 
 
 Arago, M., 144, 176, 198, 241, 242 
 
 Aratus, 361, 362 
 
 Arbuthuot (to Swift), 79 
 
 Archer, Henry, (Zetetic Astronomer,) 308 
 
 Archimedes, 4, 8, 30, 31, 53, 68, 303, 389, 
 
 392, 470 
 
 Argoli, Andrew (Ast.,) 65 
 Ariosto, 78 
 Aristotle, 4, 28, 30, 49, 51, 56, 144, 200, 
 
 201, 202, 203, 204, 209, 288, 384, 385, 
 
 387, 490 
 
 Aristophanes, 356, 436 
 Arithmetical Books, De Morgan's, 136, 
 
 454 
 
 Arnobius, 297 
 
 Arson, P. J., (Calendrier Universe!,) 388 
 Articles (Thirty-nine), 427 
 Articles of War, 249 
 Assurance Magazine, 69 
 Astrology, 277,. 278, 279 
 Astronomer Eoyal, 320, 343, 445, 451, 
 
 460, 479, 480, 481 
 
 Astronomer's Drinking Song, 234, 235 
 Astronomical Committee, 370 
 
 Police Eeport, 241, 242 ; 243 
 
 Society, 19,20, 21, 178, 194, 230, 231, 
 232, 233, 307, 347, 350, 370, 449, 479, 
 480 
 
 Astunica, Didacas, 57 
 Athanasian Christianity, 84 
 
 Creed, 107, 199, 200, 228, 271, 273 
 
 Doctrine, 3 
 
 Athenaeum, The, 5, 194, 205, 216, 236, 
 239, 243, 256, 284, 311, 318, 324, 325, 
 333, 338, 387, 399, 408, 409, 421,423, 
 459, 470, 475, 477, 490 
 
 Review of James Smith, 321, et seq. 
 Augustine, St., 263 
 
 Austin, Jane, 114, 154 
 
 Auzout (Macclesneld Letters), 451 
 
502 
 
 INDEX. 
 
 BAB 
 
 "DABBAGE, Charles, 123, 175, 370 
 JD Bacon, Francis, 4, 48, 49, 50, 51, 52, 
 53, 54, 55, 56, 57, 84, 85, 86, 87, 200, 
 467, 468, 469 
 
 Bacon, Roger, 4, 75, 221, 310 
 Bailly, 99, 165, 186 
 Baily, Francis, 186, 187, 258, 374 
 Richard, (Hussein Effendi), 258 
 Baker, Thomas (Macclesfield Letters), 
 
 451, 453 
 
 Bakewell (A. N.), 354 
 Bale, 25 
 
 Banks, Sir Joseph, 20 
 Barker's Bible (Inscription in), 428 
 Barker, Mr. (Hutchinsonian), 140 
 Baronius, 24, 25, 26, 27, 290 
 Barrett's Method (Review of), 374 
 Barrow, Isaac, 123, 451 
 Basanistes, 141 
 Bassano, Due de, 250, 474 
 Bayle, 297 
 Baveme, 30 
 
 Baxter, Thomas (Cyc.), 87 
 Beaufort, Admiral Sir Francis, 429 
 Beaugrand de (Cyc.), 72, 73 
 Beaulieu, Pontault de, 71 
 Becourt, de (Hindu Philosophy), 436, 
 
 437 
 ^Behmen, Jacob, (Mys.), 100, 151, 460, 
 
 461, 462, 463, 464 
 Bentley, Richard, 67 
 Bernard (Macclesfield Letters), 449 
 
 Bernouilli, James, 204 
 
 John, 89, 204 
 
 Bertit (Macclesfield Letters), 450 
 
 Bessel, 250 
 
 Bethune, Drinkwater, 62, 167, 174 
 
 Beza, 44 
 
 Bible, The, Authorised Version, 467 
 -. Bickersteth, Rev. E. H. 141, 142 
 
 Biddle, John, 141 
 . Biden, James (Prophet), 357, 358 
 
 Biot, 54, 56 
 
 Birch (Hist, Royal Society), 66, 451, 456, 
 457 
 
 Birks, T. K. (On Matter and Ether), 355 
 
 Bishop, George (Observatory), 238 
 
 Blast, Dr. (Antinomians), 244 
 
 Blunt, Gregory, 141 
 
 Board of Longitude, 97 
 
 Boccaccio, 41 
 
 Boethius, 31 
 
 Boetius, 31 
 
 Bonaventura Piscator, 265, 268 
 
 Boncompagni, Prince Balthasar, 179 
 
 Boniface, Archbishop, 24, 25, 26 
 
 Boole, George, 154, 155, 201, 297. et seq. 
 
 Borelli (Macclesfield Letters), 450 
 
 Borello, Pellegrino (Cyc.), 46 
 
 Borron, Mrs. (on Neptune), 253 
 
 Bosanquet, Lieut., 282 
 
 Boscovich, 93, 98 
 
 CAM 
 
 Bouguer (Macclesfield Letters), 451 
 Bouillaud, 82, 448 
 Bouvard, M., 198 
 
 Report, 176 
 
 Bovillus, Charles (Cyc.\ 31, 32, 465 
 Bo wring, Sir J., 216,422 
 Boyle, Robt., 21, 75, 78, 450 
 Bradwardine (Cyc.), 136 
 Brahe", Tycho, 49, 72 
 Brancker, 450 
 
 Brandon, Jacob, (Tobacconist,) 283 
 Brennan, Justin, 200 
 Brewster, Sir David, 81, 83, 87, 393, 499 
 Briggs, 46, 450, 451 
 Bright, John, 408 
 Bryso, 288 
 
 British Association, The, 256, 318, 372, 
 478, 483 
 
 in jeopardy, 408 
 
 James Smith's letter to, 316 
 Brothers, Richard, (Mys.) 190, 191, 313 
 Brougham, Lord, 146, 153, 178 
 Brouncker, Lord, 78, 451 
 
 Browne, Sir Thomas, 23 
 
 Briicker, 41 
 
 Briinnow, Dr. (on Neptune) 238, 241 
 .^Bruno, Giordano, 41 
 
 BufFon, 170 
 
 Bungus, Peter (Mystical Numbers), 37, 
 
 38, 39 
 
 ^-Bunyan, John, 44, 87, 113 
 ^Buonaparte, Napoleon, 137, 145, 190 
 
 Burial Service, The, 264, 265 
 
 Buridan, 28, 29 
 
 Brunet, 249 
 
 Burnet, 66, 69 
 
 Burney, Fanny, 113, 114 
 
 Busby, Dr., (Westminster School,) 457 
 
 Burton, Frances Barbara, 230 
 
 Buteo, 35 
 
 Byrgius, Justus, 35 
 
 Byrne, Oliver, 200, 373, 374, 375, 376 
 
 Byron, Lady Noel, 435 
 
 Byron, Lord, 111, 431. et seq. 
 
 /CABBALA ALGEBRAIC A, 162, ct 
 
 \J seq. 
 
 Cabbala Alphabetica, 163, et seq. 
 
 Cabinet Cyclopaedia; The. 420 
 
 Caleb Quotem, 246 
 
 Calender, Harry (Wit), 283 
 
 Calendar, Ecclesiastical, 219, et seq. 
 
 Gregorian, 219, et seq. 
 
 Jewish, 219, et seq. 
 . Julian, 219, et seq. 
 
 Cambridge, Defective teaching at, 420, 
 421 
 
 Disputations, 305 
 
 Phil. Trans., 281, 329, 375 
 Campanus (Cyc.), 31 
 
INDEX. 
 
 503 
 
 CAN 
 
 DEC 
 
 Canning, George, 346 
 
 Cantab (Letter of a), 333 
 
 Carcavi, 65 
 
 Cardanus, 287 
 ^-Carlyle, Thomas, 499 
 
 Casaubon, Isaac, 67 
 
 Case, John (Ast.), 76 
 
 Cassini, James, 102, 103, 278 
 
 Castel, Father, (A.N.) 88 
 
 Castiglione, 83 
 
 Castle of Knowledge (dialogue from), 
 467 
 
 Castlereagh, Viscount, 111 
 
 Catcott, Dr., 140 
 
 Cataldis (Cyc.), 46 
 
 Catiline, 493 
 
 Cavalieri, 65 
 
 Cavendish, Charles, 65, 174, 175, 450, 
 457 
 
 Cayley, George, 446 
 ..-Celtic Druids, The, 166 
 
 Centrifugal Force, 431 
 
 Challis, Professor, 239, 240, 242, 343 
 
 Chalmers, Kev. Dr. (666), 397 
 
 Chambers's Dictionary, 439 
 
 Charles II. King, 19, 282 
 
 Charlemagne, 77 
 
 Charles IX. (of France), 310 
 
 Charles X. (of France), 250 
 
 Chasles, M., 29 
 
 Chaucer's Rhymes, 469 
 
 Chemistry (or Chymistry), 75 
 
 Chesterfield, Lord, 450 
 
 Childhood and Priesthood, 401 
 
 Chitty (or Kitty), 464 
 
 Christian Observer, The, 217 
 ..Christian (The name), 146, 147, 148 
 ^ - (The word), 263 
 
 (Roman), 266, 267, 268 
 -'Christianity and war, 249 
 
 Church, The, 270, 271, 272, 273, 274 
 
 Church of England and Ireland, The, 269 
 
 Church Times, The, 309 
 
 Cicero, 493 
 
 Circulation of the Blood, 254 
 
 Ciruelo, Petro Sanchez (Ed. of Bradwar- 
 dine), 136 
 
 Clairault, Alexis Claude, 131, 132, 236 
 
 Clarke, Richard (Mys.), 151 
 
 Clavius, Christopher, 9, 26, 46, 67, 68, 
 217, et seq., 287 
 
 Cluvier, Dethleu (Cyc.), 470 
 
 Cluvier, Philip, 470" 
 
 Cobbett, William, 105, 119, 120, 122 
 ^Cocker's Arithmetic, 30, 291, 454, 455 
 
 Cody, Patrick, (Tris.) 389 
 
 Coincidences, 279, et seq. 
 
 Coke, Chief Justice, 469 
 
 Colbinus, Father Philip, 44 
 
 Col burn, Zerah, 55 
 
 Colenso, Bishop, 52, 146 
 
 Collectanea Chymica, 75 
 
 Collins, John, 6, 66, 449, et seq. 
 
 Columbus, Chr., 81 
 
 Colvill, William Henry, 293 
 
 Comets as Volcanoes, 303 
 
 Cometic Astrology, 76 
 
 Cominale, Celestino, 96 
 
 Commercium Epistolicum, 449 
 
 Companion to the Almanac, The, 217 
 
 Comptes Rendus, 54 
 
 Conduitt, Mrs., 81 
 
 Congregation of the Index, 57 
 
 Convocation, 228 
 
 Convocation of Oxford, 60, 61 
 
 Cook, Chief Justice, 469 
 
 Copernicus, 2, 4, 5, 49, 57, 58, 59, 60, 
 
 61, 72, 81, 151, 161, 301, 360, 361 
 Cooper, Thomson, 174 
 Cormouls, Thomas, 134 
 Correspondent, The, 408, 409, 472, 478, 
 
 479, 481 
 
 Cosmo de' Medici, 448 
 Cotes, 451 
 
 Cottle Church, The, 313, et seq., 358 
 -Council of Nicsea, 220 
 . Trent, 222 
 
 Counter Doggrel, Logical, 208, 209 
 Craig, John (Mathematical Theology), 
 
 77, 78 
 
 Cribb, Tom, 190 
 Cromwell, Oliver, 470 
 Crossley, Mr., 232 
 -Cruickshank, George, 111 
 Cumberland, Duke of, 120 
 Cumyns, Eliza, 180 
 Cunningham, John (A.C.), 103 
 Cusa, Nicolaus de (Cyc.), 33, 221 
 Cyclometer's Letters, 259, 260 
 Cyclometry, (James Smith), 316, et seq. 
 
 Remarks on, 389, et seq. 
 
 Versified (Valentinus), 36 
 Cyclopaedia of Physical Science, 444 
 Cyropaedia, 439 
 
 D^DALUS BRITANNICUS (Flying 
 machine), 253 
 , ^.D'Alembert, 236, 440, 491 
 
 Dalgarno, 70 
 
 Dalmas, A., 436 
 . -Dante, 297, 436 
 
 Darwin (Botanic Garden), 253, 254 
 
 Dary, Michael, 452, 453 
 
 Dary's Problem, 456 
 
 Davies, Thomas Stephens, 350, 351, 374 
 
 Day, Dr. Alfred, 177, 178 
 
 Dean, William (Cyc.), 458 
 
 DeBeaume, 288 
 
 Debenham, Commander, R.N., (Tides), 
 243 
 
 De Castres, Sabatier, 429 
 
 Dechales, 32 
 
 Decimal Coinage, 363, 364, 365, 366 
 
504 
 
 INDEX. 
 
 DEC 
 
 Decimal System, The, 301 
 Declaration of Belief, 421, et seq. 
 
 (Proposed substitute), 423, 424, 425 
 De Causans, 179 
 
 ^-Dee, John (Ast.), 451 
 De Faure (Cyc.), 89, 410 
 De la Leu (Cyc.), 179 
 Delambre, 62, 99, 217, 360 
 De Moivre, 18, 99, 232, 4,00 
 De Molina, Alphonso, 179 
 Demonville, 175, 176 
 De Morgan, Arithmetical Books, 136, 454 
 
 Captain, 282 
 
 Baron, 352 
 
 Professor, in the Pillory, 409 
 
 and Macaulay, 455 
 Dennison, Joseph, 213, 216 
 D6saguliers, 93 
 D6sargues, 72 
 
 Descartes, 4, 40, 65, 98, 122, 123, 235, 310 
 De Sepre~s, P. Y., 167 
 De Serres, Olivier, 288 
 De Thou, 35, 67, 68, 448 
 De Vausenville, 9 
 ^- Dickens, Charles, 483 
 J)iderot (confuted by Euler), 250, 251, 
 
 474 
 
 .. Digby, Kenelme, 16, 66 
 Digges, Thomas, 451 
 Dircks, Henry, 342 
 Discoveries and Discoverers, 387 
 Disraeli, Isaac, 69, 70, 71, 81, 112, 135 
 Ditton, Humphry, 79 
 Diocletian, 221 
 Dionysius Exiguus, 221, 222 
 /Divine Mystery of Life, 341 
 Dobson, J., (The Unpunctuating), 139, 140 
 Dodson, John, 457, 458 
 Dollond, 232 
 Double Vahu, 395, et seq. 
 Drach, Solomon, 460 
 Drayson, Captain, 338, 339 
 Dryden, Religio Laici, 295 
 The Hind and Panther, 401 
 Dual Arithmetic (Oliver Byrne), 373 
 Dublin Review, The, 267 
 Duchesne, VanderEyck (Cyc.), 35, 36. 62 
 Duelling, 248, 249 
 Du Fan, 189 
 
 Duke, Sir James (Lord Mayor), 277 
 Dumortier, 189 
 Dunbar, John (Cyc.), 179 
 Dunciad, The, 436 
 Dunkin, Mr. E., 480 
 Dupuis, Peter, 448 
 Dutens, (Ed. of Leibnitz,) 308 
 Dyer, George, 106 
 
 T? ASTER-DAY, 217, et seq. 
 JLJ East India Company, 231 
 Ecclesiastical Society, 219 
 
 FOS 
 
 Sdgeworth, Maria, 114 
 Edinburgh Review, 193, 435 
 Editorial Duties (Letter on), 11, et seq. 
 Sdleston, Mr., 449 
 SdwardIL, 492 
 Edwards, Dr. John, 86 
 
 Thomas, 68 
 \KK\i\ffia, 269, 270 
 Elective Polarity, 230 
 Elephant, (Anecdote of,) 39, 40 
 Elizabeth, Queen, 76 
 Ellenborough, Lord, 108, 109 
 Ellis, Robert Leslie, 49, et seq. 
 E. M. to James Smith, 319, 331 
 Encyclopaedia Britannica, 438, 443 
 
 Metropolitana, 441, et seq. 
 
 Scientiarum Omnium, 439 
 Encyclopedic, L', 440 
 
 English Cyclopaedia (Art. on Quadrature), 
 290, 291 
 
 60, 61, 62, 293, 438, et seq. 
 English Leader, 248 
 Epacts, Table of, 228 
 
 Epistolse Obscurorum Virorum, 193 
 Epps, Mr. (See Ast. Soc.), 91 
 Erasmus, 67 
 Erastus, Thomas, 44 
 Ericksen, Niels (Cyc.), 97, 98 
 Ersch and Gruber (Cyclopaedia), 440 
 Erskine, Lord, 334 
 Evangelicism, 43 
 Evelyn, John, 66 
 
 ^AIRPLAYS Letter, 472 
 
 JL Fancourt, Samuel, 291 
 
 Faraday, Michael, 482 
 
 Ferguson, James, 261, 262 
 
 Fermat, 451 
 
 Ferrari, Baron (Duodecimal System), 
 
 293, 371 
 Fielding, 113 
 
 Fielding's Miscellanies, 435 
 Fienus, Thomas, 48 
 Fifteens of Bungus, 38, 39 
 
 The Royal Society, 38, 39 
 Filopanti, 310 
 Finleyson, Thomas, 190 
 Finsecus, Orontius, (Cyc.), 35, 68 
 Flamsteed, John, 56, 187, 278, 279, 283, 
 
 451, 452, 453, 454 
 
 Margaret (Valentine), 188 
 Fletcher, Captain J., 282 
 
 Mr., (Mathematical Society,) 233 
 Fludd, Robert, 461 
 
 Folkes, Martin, 16, 81 
 Fontenelle, 81, 121 
 Forbes, President, 140 
 ^Formal Logic, 94, 201, et seq., 297, 298 
 Forman, Captain (A.N.), 178, 185, 
 Forster, Thomas Ignace Maria, 194, 195 
 Foscarini, 67 
 Foster, (Lect. Gresham College,) 456 
 
INDEX. 
 
 505 
 
 FOU 
 
 Fourrier, 292 
 
 Fox, George, 245, 246 
 
 Francis, Philip, 312 
 
 Francceur, L. B., 284 
 
 Franklin, Benjamin, 429 
 
 Free Press, The, 342 
 
 Freher, Andreas (Mys.), 461 
 
 French Lottery, 168, 169 
 
 Frend, William, 117, 118, 119, 123, 124, 
 
 149, 186 
 
 Fresnel, 280, 281 
 From Matter to Spirit, Eeviews of, 378 to 
 
 388 
 
 Fromondus, Libertus, 48, 62 
 Frost, Isaac (Muggletonian), 244, 245 
 Fry, Elizabeth, 133, 134 
 Fulton (Engineer), 88 
 
 n ADBURY, John ( Ast.), 69 
 
 VJ Galbraith, Mr., 499 
 
 Galileo, 4, 5, 24, 26, 40, 49, 53, 60, 61, 
 
 81, 134, 144, 235, 320, 383, 430 
 Galloway, Thomas (Fifteens), 39 
 and James Ivory, 345 
 Garrick, David (couplet), 16 
 Gascoigne (Macclesfield Letters), 450 
 Gassendi, 66 
 Gauss, 187 
 Geber (Arabian), 288 
 Gentleman's Magazine, The, 151, 282 
 General Dictionary, The, 451 
 Geological Society, The, 21 
 Gergonne, 204 
 Ghetaldus, 53 
 .-Gibbon, Edward, 154 
 Gilbert, William, 5, 45, 49 
 Gillott's Steel Pens, 459 
 Gladstone, William Ewart, 353, 407, 
 
 417 
 
 Godwin, Bishop, 135 
 Golius, 65 
 
 Gompertz, Benjamin, 233, 236 
 Gonsales, Domingo, 135 
 Goulburn, Hon. TL, 173, 174, 175 
 Goulden, S. (Zetetic Astronomy), 306, 
 
 307, 308 
 
 Grandamicus, Jacobus, 65 
 Grange, Armand (Cyc.), 316 
 Grant, Professor (Hist. Astronomy), 243. 
 
 337 
 
 ^-Grassini, Signora, 137 
 Graunt, John,' 68, 69 
 Gray's Bard, 434 
 Greene, Robert, 80, 81 
 Gregg, Tresham Dames, 297, et scq. 
 Gregorian Calendar, The, 217, et seq. 
 Gregory, David, 44, 451 
 
 James, 71, 123, 124 
 
 Olinthus, 295 
 
 Pope, 222, 223, 224 
 Grevil, Sir Fulk, 120 
 
 HOB 
 
 Grey, Earl, 191, 416 
 
 Grosart, Alexander, 84, 85, 86, 87 
 
 Grove, Edward (Correlation of Force), 462 
 
 Gruenberger, Christopher, 46 
 
 Grynseus, Thomas, 44 
 
 Guldinus, 53 
 
 Gunning (Reminiscences of Cambridge), 
 
 118, 154 
 Guthrie (Astronomy), 244 
 
 HAILES, J. D., Challenge to Astrono- 
 mical Society, 339, 340 
 Hale, Matthew, 73, 74 
 
 Sir William, 74 
 Hales, Stephen, 74 
 Hall, Basil, 370 
 
 Hallam, Henry, 56, 95, 434, 464, 467 
 
 Halley, 123, 451, 470 
 
 Halliwell, John Orchard, 349, 350, 351, 
 
 449 
 Hamilton, Sir William, 68, 70, 201, et scq., 
 
 284 
 
 Sir W. Rowan, 22, 201, 317, 324, 325, 
 422, 476 
 
 Hampden, John, 206 
 Hardy, Matthew, 179 
 Hardy, Thomas, 106 
 Harriot, 451 
 
 Harmonicon Coeleste, 448 
 Hatto, Bishop, 473 
 Hauff, 136 
 Hawksbee, 93 
 Hawkins, John, 454 
 ^-Hawthorne, Nathaniel, 281 
 Headlong Hall, 475 
 Heath, Douglas D., 49 
 Heinfetter, Herman, 311 
 Herbart, J. F., 150 
 Herigenius, 288 
 Herschel, Sir John, 52, 178, 179, 180, 
 
 181, 185, 197, 237, 238, 239, 242, 307, 
 
 311, 370, 421, 422, 426 
 Herschel, Sir William, 52, 90, 134, 135, 
 
 138, 180, 192, 480 
 Heteropath's Letter, 159, 160, 161 
 Heywood (Analysis of Kant), 282 
 Hicks, J. Power, (Computation,) 292 
 ^.Higgins, Godfrey, 152 
 
 Celtic Druids, 164, 165, 166, 
 Hilary, Pope, 221 
 
 Hill, Sir John, 16, 17, 18 
 
 Rev. Rowland, 114 
 
 Sir Rowland, 98, 137 
 Hind, William, 238 
 Hippocrates, 287 
 
 Historical Society of Science, 449 
 
 Hoar, Mr., Master of the Mint, 4. r 6, 
 
 457 
 Hobbes, Thomas, 65, 66, 67, 85, 83, 
 
 301 
 Hobhouse, John Cam, 334 
 
506 
 
 INDEX. 
 
 HOD 
 
 LIB 
 
 Hoddcr's Arithmetic, 429 
 Hodges, Walter, 140 
 Hodge, C. B., 69 
 Hoffman, 136 
 Holloway, Dr., 140 
 
 Holyoake^ G. J. (TheReasoner), 247, 248 
 Hone, William, 74, 106, et seq. 
 Hooke, 49, 450 
 Hook, Theodore, 425 
 Hopkins, James (Sun Paradox), 276 
 Horace (Sham), 475 
 Home, Bishop, 90, 91, 93, 140 
 George, 92 
 Horner, Leonard, 105 
 Homer's Method, 292, 374, 375 
 Horner's Papers, 351 
 Houlston, William (Cyc.), 354 
 Howard, Edward, 78, 79 
 Howitt, William (History of the Super- 
 natural), 378 
 Howison, William, 151 
 Howley, Archbishop, 43 
 Hudibras (Quotation from), 396 
 Hulls, Jonathan, 88, 254 
 /Hume, Joseph, 216 
 Hussein Effendi, 258 
 Huyghens, 62, 64, 71, 123, 140, 450, 454 
 
 /TNDEX EXPURGATORIUS, 265 
 . JL Inglis, John Bellenden, 283 
 
 Innocent I., Pope, 220 
 / Irving, Rev. Ed., 284 
 
 Ivory, James, 345, 346 
 
 Interminable fraction n, 171, 172, 413 
 
 [ACK, Richard, 88 
 fj Jacobitism, 43 
 Jacotot, 167 
 Jacquard, 27 
 
 Jameson, Anna (Legendary Art), 290 
 Janson (Cyc.), 179 
 Jeffries, Judge, 109 
 ^ Jenner, Dr. (Vaccination), 386 
 Jewish Passover, 217 
 Johnson, Samuel, 15, 266, 417, 433, 447 
 
 Henry Coleman (Cyc., &c.), 214 
 Johnston, W. Harris, 292 
 
 John the Baptist, 43 
 
 Jonchere, M. de la (A.N.), 87 
 
 Jones, Rev. W. (of Nayland), 140, et seq. 
 
 William, 449, et seq. 
 Jonson, Ben, 10 
 Jokeby, 470 
 
 Jopling (Great Pyramid), 312 
 Journal of Education, 173 
 Julian Calendar, 221, et seq. 
 Junius's Letters (Author of), 313 
 
 KANT Immanuel, 153, 154, 282 
 Kater, Captain, 8 
 Karsten (parallels), 136 
 Kastner, 31, 67, 68 
 Keckermann, Claudius, 3 
 Keill (Macclesfield Letters), 251 
 Kepler, 49, 53, 55, 80, 213, 235, 360, 
 
 361 
 
 Kerrigan, Lieut., 186, 216 
 King, Dr., 146 
 Kircher (Adolphe), 64, 136 
 Kirkringius, 74 
 Kittle, Samuel, 140 
 Knight, Charles, 321, 444 
 
 Go wan, 93 
 
 Payne, 434 
 
 Kcenig, S. (Attestation of De Faure), 89 
 
 IACOMME, Joseph (Cyc.), 32, 33, 322 
 J La Condamine (Macclesfield Let- 
 ters), 451 
 
 Lacroix, (Ed. of Montucla's History of 
 Cyclometry), 95, 289 
 
 Lactantius, 25, 58, 60 
 
 Lagrange, 173, 189, 250, 305 
 
 Laing, F. H. (Negative Quantities), 373 
 
 Lamb, Charles, 106, 431 
 
 Lambert, 204, 205, 294, 393 
 
 Lambert, General, 455 
 
 Laplace, 18, 151, 155, 167,170, 172, 198, 
 243, 249, 250, 475 
 
 Lardner, Dionysius, 11, 420 
 
 Nathaniel, 398 
 
 Larriva, Don Juan (Cyc.), 459 
 Latin Numerals (666), 489 
 Lauder, William (A.N.), 179 
 Laurent, Paul (on Atoms). 187 
 Laurie, James (Moon paradox), 251, 
 252 
 
 Sir Peter, 277 
 Lausbergius, Philip (Cyc.), 46 
 
 ^-Law, William (Mys.), 151, 460, 461 
 Lee, Dr. R., 44 
 Lee, Prof. (Orientalist), 78 
 Lee, Weyman, 93, 94 
 Legendre, 1?6, 393, 499 
 Leggatt (martyr), 40 
 Legh, Peter (Ombrology), 293 
 Leibnitz, 4, 6, 40, 279, 308, 470 
 Leisure Hour, The, 312 
 Leland, 136 
 
 Leo X., Pope, 220, 285, 499 
 Lettres sur FAtlantide de Platon, 99 
 Leverrier. 31, 53, 211, 237, 238, 239, 241, 
 
 242, 253, 343, 348, 451 
 Lewis, Sir G. C., 358, et seq. 
 Lexicon Universale, Hofman, 439 
 Libri, Guglielmo, 29, 41, 136, 448 
 Library of Useful Knowledge, 167 
 
INDEX. 
 
 507 
 
 LIL 
 
 Lilly, 451 
 
 Lipenius, 179 
 
 Little, James (On Logarithms"), 128 
 
 Living Authors (Watkins and Shoberl), 
 
 431 
 Locke, John, 85, 86, 305, 326 
 
 Eichard (Cyc.), 87 
 Logan, Eev. Dr. 205 
 
 Logical Doggrel, by Sir W. Hamilton, 208 
 London Society, The, 215 
 Long, St. John, 2, 274, 386, 387 
 
 George, 444, 445 
 
 Longitude, The, discovered (Whiston),87 
 
 Longley, Archbishop, 197 
 
 Longomentanus (Cyc.), 65 
 
 Lotteries, 168 
 
 Louis XVIII., 107 
 ^Louis Napoleon, 77, 289 
 
 Lovett, E. 99 
 
 Lowe, Eobert, (Decimal Coinage), 363 to 
 
 370 
 
 - Lowndes, 249 
 .Lubbock, Sir John, 167, 168, 174, 348 
 
 Lucas, Frederic, 267 
 
 Lunar Motion (Jellinger Symons), 304 
 
 Lunn, J. E. (Calculation), 292 
 
 Luther, Martin, 37, HI, 285, 403 
 
 Lycabettus, Mount, 361 
 
 Lyndhurst, Lord Chancellor, 118 
 
 MACAULAY, Lord, 83, 190, 191, 281, 
 282, 455 
 
 Machine, Steam, (Jonathan Hulls,) 88 
 Macclesfield Letters, 448, et seq. 
 - Earl of, 6, 450, 451 
 Mac Elshender, John (Moon Paradox), 
 
 305, 306 
 Mackey, Eev. John, 214 
 
 Sampson Arnold, 151, 463 
 Macchiavel, 144 
 
 Maclear, Sir Thomas, 370 
 
 Macleod, H. Dunning, 372 
 
 Mac Cook, 214 
 
 Magliabecchi Library, 448 
 
 Magnus, Baveme and Cocker, 30 
 
 Magus, Simon, 33 
 
 Maitland, Eev. Samuel, 43, 97 
 
 Hist, of London, 69 
 Malacarne (Cyc.), 71 
 
 x Manning, Eevd. Henry E., 406 
 Mansel, Eevd. Dr. (Phrontisterion), 358 
 Mansuete, Father, 282 
 Marcelis, Jacob (Cyc.), 77 
 Margarita Philosophica, The, 439 
 Marryat, Captain (Dog Fiend), 306 
 
 Samuel, 283 
 
 Martin, E., M.P. for Gal way, 409 
 
 Old Ben, 91 
 
 Martyrologium Eomanum, 290 
 Mary, Queen, 223 
 
 Maseres, Francis, 117, 121, 122, 123 
 
 MOK 
 
 Mason, Monk, 337 
 Mathematical Society, New, 236 
 - Old, 230, et seq. 
 Mathers, Patrick, 124 
 Maty, Dr., 17, 18 
 
 Maupertius (Macclesfield Letters), 451 
 .-Maurice, Eevd. F. D., 315 
 Maurolycus, 72 
 
 Maximilian. Emperor of Germany, 439 
 Maxwell, Alexander, 63 
 Mecanique Analytique (Lagrange), 189 
 
 Celeste, 250 
 
 Mechanic's Magazine, 213, 344, 347, 350, 
 
 351 
 
 Medical Eeform (Letter on), 159 
 Medici, Cosmo de', 448 
 Melanchthon (or Schwartzerd), 464 
 Mesolabum, The (Slusius), 71 
 Mercator's Planisphere, 309 
 Mersenne, Father, 65, 448, 449 
 Meslier, Jean, 379 
 Messange, Mallemont de, 471 
 Methode Jacotot, (P. Y. de Sepres), 167 
 Metius, Adrian, 62 
 
 Peter, 35, 62 
 
 Meton (Lunar Calendar), 361 
 
 Metonic Cycle, 221 
 (Mill, James, 154 
 I John Stuart. 353, 408 
 
 Miller, S. (A.N.), 100 
 r Joe (Story from), 108 
 
 Milne, Mr., Actuary, 172 
 
 Milner, Dr. Isaac, 148, 149 
 
 Lamp, 149 
 
 Eev. John, 263, 264, 265 
 Milton, John, 113, 465 
 Milward, Ei., 418 
 Minerva Press Novels, 114 
 Modestus, St., 289 
 Mollendorf, Marshal, 250, 474 
 Monthly Magazine, 144 
 Montmort (Macclesfield Letters), 451 
 Montague, Charles (Lord Halifax), 456, 
 
 457 
 Montucla, 30, 31, 32, 37, 43, 44, 57, 67, 
 
 71, 72, 95, 96, 97, 179, 288, 470, 490 
 Mojn-hoax, The, 337 
 Mo n Controversy, India, 262 
 Moon Paradox, 303, 304 
 Moore, Dr., 113 
 More, Hannah, 113, et seq. 
 
 Henry, 73 
 Morgan, Sylvanus, 5 
 
 Lady, 114 
 
 William, 133 
 Morhof, 41 
 Morin Sieu?, 62 
 Morinus, J. B., 89 
 
 Morland (Macclesfield Letters), 450 
 Mormon, The, Newspaper, 294 
 Morning Post, The, 173, 198 
 Morrison, Lieut. (Zadkiel), 277 
 
508 
 
 INDEX. 
 
 MOS 
 
 Moses, 41 
 Mouton, 102, 450 
 M. P.'s, an, Arithmetic, 417 
 Muggleton, Lodovick, 244 
 Muggletonians, The, 244, 245, 246 
 Murhard (Oyc.), 31, 44, 179 
 Murphy, Arthur (Tr. of Tacitus), 454, 
 455 
 
 J. L., 285 
 
 P. (Weather Almanac), 198, 199, 
 246 
 
 Kobert, 214 
 
 Murray, John (Publisher), 111, 346 
 
 Lindley, 466 
 
 Mungo, (Astronomical lecturer), 456 
 Museum Collection, The, 449, tt seq. 
 Musgrave, Abp., 196, 197 
 
 Mydorge, 179 
 
 ^Mystery of Christ (Behmen), 460 
 Mystrom (Tonal System), 370, 371 
 
 X"] 
 
 V. 
 
 "VTAMES of the Beast, 403, et seq. 
 
 i.1 Napier's Bones, 473 
 
 Napier, John, 45, 46, 53, 54, 70 
 
 Napoleon I., 137, 145, 249, 250, 352, 
 427 
 
 Napoleon III., 77 
 
 Nautical Almanac, 180, 181, 182, 347, 
 348, 369, 460, 485 
 
 Nauticus, (Cyc.), 333, 335, 356 
 
 Neal, Archbishop of York, 376 
 
 Neal's History of the Puritans, 61 
 
 Neptune (Planet), 236, et seq., 253, 343 
 
 New. and Full Moon (Table), 227 
 
 New Testament, 23, 386 
 
 Newton, Sir Isaac, 4, 5, 6, 18, 21, 48, 49, 
 50, 53| 54, 56, 66, 78, 81, 82, 83, 85, 
 86, 87, 88, 91, 92, 96, 98, 100, 117, 
 134, 135, 143, 152, 156, 187, 188,213, 
 231, 235, 243, 244, 245, 250, 275,294, 
 305, 3,40, 345, 355, 432, 446, 449, 451, 
 456, 463, 469, 472, 478, 479 
 r Nicene Creed, 228 
 S Council, 220, 228 
 
 Nicholas of Cusa, 33 
 
 Nichols, (Anecdotes) 104, 154 
 
 Dr. 444 
 
 Nicolas, Sir Harris, 217 
 
 Nicollet, 197, 198 
 
 Nieuwentiit, 470 
 
 Notes and Queries, 9, 66, 90, 91, 98, 114, 
 115, 116, 146, 151, 153, -245, 265, 266, 
 268, 418 
 
 Number of the Beast, 401, et seq. 
 
 Nursery Rhymes, 349 
 
 OCCAM, 275 
 Odgers, Nicholas, 376, 377 
 Oldenburgh, 450, 455 
 Oliver Twist, 394 
 
 POE 
 
 Oughtred, 450, 451, 456 
 
 Owenson, Sydney, (Lady Morgan,) 114 
 
 Ozanam, 189 
 
 PAINE, Thomas, 102, 104, 110, 143 
 Paley's Evidences, 402 
 Paley, William, 133, 146 
 Palmer, Charles, 134 
 John (Mail coaches), 419, 420 
 
 Thomas Fysshe, 420 
 Pallieur, 65 
 
 Palmerston, Viscount, 174, 216 
 Panizzi, Antonio, 90, 244 
 Papist and Protestant, 265, et seq. 
 Paracelsus, 403 
 
 Pardies (Macclesfield Letters), 451 
 Paradoxers (Ways of), 3 et seq. 
 Park, Mungo, 309, 337 
 Parsey, Arthur (Cyc.), 176, 177 
 Parr, Dr. Samuel, 103, 104, 105, 109 
 Pasbergius, Manderupius, 235 
 [^Pascal, Blaise, 30, 62, 132, 296, 475 
 Passot (A.N.), 167 
 Passover, Jewish, 226 
 Patrick, St., 331 
 Paucton, 103 
 Paulian, Father, 98 
 Peacock, Dr. (Dean of Ely), 117, 214 
 Peel, Sir Kobert, 155, 215 
 Peel, Yates, 174 
 
 Pell (Macclesfield Letters), 65, 450 
 Pemberton, 81 
 Penny Cyclopaedia, 173, 214, 261, 266 
 
 439, et seq., 460 
 
 Penny Cyclopaedia (Supplement, 60, 61) 
 Pepys, W., 69 
 
 Perigal, Henry, (Moon,) 261, 262 
 Perpetual Motion (Predaval), 213, 285, 
 
 286, 342 
 Perspective, 176 
 Peters, William (Cyc.), 255, 459 
 Petit, Andre, 186 
 Petty, Sir William, 69, 450 
 Philalethes, Eugenius, 151 
 Phillips, Sir Kichard, 143, 144, 145, 152 
 Philo of Gadara, 30 
 Philosophia Sacra, 140, 141 
 Philosophical Transactions, 214, 422, 
 
 436 
 
 Pike, Samuel, 140 
 ^Pilgrim's Progress, 447 
 Pindar, 434, 
 Peter, 433 
 Piozzi, Mrs., 433 
 Pitt, Earl of Chatham, 123 
 Place, Francis, 119, 120 
 Platts, Eev. J., 266 
 Playfair, Professor, 138 
 Pliny, 215, 439 
 Ploucquet, 204, 205 
 >Poe, Edgar, 337 
 
 
INDEX. 
 
 509 
 
 roi 
 
 SAM 
 
 Poisson, 176, 250 
 
 Pons (Comet Finder), 279 
 
 Pope, Alexander, 436 
 
 Porta, J. Baptista, 45, 53 
 
 Porteus, Bishop, 115 
 
 Porus of Nicaea, 30 
 
 Powell, Baden, 430 
 
 Praed, Winthrop Mackworth, 371 
 
 Pratt, Dr. H., 354 
 
 Pratt, Orson (Mormon), 294 
 
 Predaval, Count de, 213 
 
 Prescott, Bartholemew, 161, 167 
 
 Prester John, 47 
 
 Price, Eichard, 133 
 
 Prince Consort, 342, 343 
 
 Princess Alexandra, 243 
 
 Protimalethes, 252 
 
 Pseudochrist and Antichrist, 252 
 
 Pseudomath, Philomath and Graphomath, 
 
 473, et seq. 
 Ptolemy, 425 
 Pujos, M., 179 
 Puseyism, 43 
 
 Pyramids, The, 308, 311, 377 
 Pythagoras, 151, 287, 367 
 
 QUAELES, Philip, 436 
 Quartadecimans, The, 220 
 Quarterly Keview, 346, 385 
 Church of England, 192 
 Q. E. D., 255 
 Quintilian, 439 
 Quotem, Caleb, 246 
 
 T)ABELAIS, 64, 124 
 
 _Lt (Imitation of), 125, et seq. 
 
 Eacovian Catechism, 85 
 
 Ealeigh, Sir Walter, 467 
 
 Eambler, 113 
 
 Eamchundra, 231 
 
 Eamus, Peter, 4 
 
 Eaymarus (Nicolaus), 35 
 
 Eeal Character, Wilkins', 70 
 
 Eeasoner, The (Holyoake), 274, et seq. 
 
 Eecalcati (Cyc.), 389, 458 
 
 Eecherches Curieuses des Mesures, &c., 
 
 46 
 
 Eecorde, Eobert, 467, 468 
 Eeddie, James, 371, 372, 477, 478, 479, 
 
 Kefonn Bill, 191 
 
 Eeisch, Gregory, 439 
 
 Eeligion and Philosophy, 273, 274 
 
 Eeligio Laici (Dryden), 295 
 
 Eeligious Tract Society, 85, 86, 87, 114, 
 
 115, 116, 117, 141 
 1 Eemains ' The (of Bacon), 86, 87 
 Eenatus Franciscus Siusius (Mesola- 
 
 bum), 71 
 Eeuchlin (or Capnio), 464 
 
 Eevilo (Oliver Byrne), 142, 199, 200 
 
 Eeyneau, 45 
 
 Eeynolds, Sir Joshua, 202 
 
 Eheticus, 46 
 
 Eibadeneira, 290 
 
 Eichards, George (Camb. Prize Poet), 
 
 431, 432 
 
 Eichardson, Samuel, 121 
 Eichelieu, Cardinal (Official Eeport), 62 
 Eigaud, John, 450 
 
 Stephen, 83, 450, 452 
 
 Eights of Boys and Girls (Parr), 1Q3, 104 
 
 Man (Paine), 103, 104 
 
 Woman (Wollstonecraft), 103, 104 
 Eingelberg, 439 
 
 Eipley, Sir G. (Ale.), 75 
 
 Eitchie, Eev. W. (Geometry), 177, 178 
 
 Eittershusius, 40 
 
 Eitualism, 43 
 
 Eobertson, Dr. (Hutchinsonian), 140 
 
 Eoberval, 65 
 
 Eobinson, Bryan (on Ether), 88 
 
 Dr. (Armagh), 370 
 
 H. Crabb, 283, 435 
 
 Eobert, 106 
 Eoblin, Justin, 341 
 Eock of Ages, The, 141 
 Eogers, Samuel, 425 
 
 Eoget, P. M. (Thesaurus), 246 
 
 Eokeby, or Eookby, 470 
 
 Eoman Christian, 263 
 
 Eomanus, Adrianus, 67 
 
 Eoss, Capt, 182 
 
 Eosse, Earl of, 20 
 
 Eossi, Gaetano (Cyc.), 137 
 
 Eough, Serjt., 118 
 
 Eowning, 93 
 
 Eoyal Naval Club, 166 
 
 Eoyal Observatory, Berlin, 238 
 
 Eoyal Society, The, 16, 17, 18, 19, 20, 21, 
 22, 38, 39, 66, 69, 80, 97, 98, 122, 167, 
 176, 238, 374, 375, 376, 422,.436, 455, 
 456 J 
 
 Committee of, 449 
 
 (Signatures), 422 
 
 (Library), 83 
 
 (Transactions), 20 
 Eudolf, Chr., 499 
 Eussell (Printer), 110 
 
 Eussia (Meteorology in), 54 j 
 
 Eutherford, W. (Cyc.), 374 
 
 ,^QABBATAEIANISM, 311 
 
 ' k5 Sabellianism, 142 
 
 Sabben, James (Tris.), 255 
 
 Sacrobosco, 221 
 
 Sadler, Dr., 141, 142, 143 
 
 Sadleir, Dr. Francis, 155 
 
 Salmasius, 362 
 
 Salicettus, Th. (Gephyrauder), 43, 44 
 .Sam Slick, 337 
 
510 
 
 INDEX. 
 
 SAN 
 
 Sanchez, Peter, 136 
 
 Sanders, M. A., 124 
 
 Saturday's Moon, A, 195 
 
 Saunderson, 80, 232, 451 
 
 Scaliger, Joseph, 31, 67, 68, 353, 410 
 
 Julius, 68 
 Sara, Kobert, 179 ' 
 Schopp, 41 
 
 Schoolboy's Defence, A, 411 
 
 Schott, Gaspar (Ale.), 43, 44, 291 
 
 Schwal, 137 
 
 Scott, Walter, 15, 20, 34, 35, 78, 114, 
 
 427, 469, 474 
 
 Schumacher, Prof., 65, 66, 449 
 Scriptural Calendar, 256 
 Scripture and Science, 426, 427, 428 
 Selden's Table Talk, 418 
 Senarmont, M., 280 
 Sentinel, The, 297 
 Shaftesbury, Earl of, 370 
 Shakspeare, 10 
 
 Shanks, William (Cyc.), 290, 291 
 Sharpe, Granville, 141 
 Shaw, Peter, 84 
 Sheepshanks, John, 88 
 
 Eichard, 174, 175, 344 
 Shepherd, Attorney General, 74, 107 
 Sheridan, Tom, 104, 105 
 Simpson, Thos., 232, 451 
 
 Simson, Robt. (of Kirktonhill), 117, 120, 
 
 121, 138 
 
 Sinclair, Prof., 124 
 2/cii/5a7T(ros, 268 
 Sloane, Hans, 18 
 Slipslop, Misses, 466 
 Slusius, 450 
 Smith, Ambrose, 170 
 
 James (Rejected Addresses), 336 
 
 Rev. James, 287, 288, 378 
 
 James (Cyc.), 32, 316, et seq. to 
 337 (inc.), 352, 353, 354, 356, 357, 
 389, 390, 391, 408 to 416 (inc.), 460, 
 472 to 477 (inc.), 488, 489 
 
 Sydney, 163 
 
 Thos., 211 
 Smithfield Burnings, 40 
 Smollett, 113 
 
 Smyth, Piazzi, 292 
 
 Snell, Willebrord, 48 
 
 Socinians, The, 85, 447 
 
 Socinus, Faustus, 3, 85 
 
 Socrates, 220 
 
 Sohnke's BibHotheca Mathematica, 337 
 
 Solar Parliament, The, 181, 182, 183, 
 
 184 
 
 Somerville, Mary, 143 
 Somnium Ciceronis, &c. (Home), 90 
 Southcott, Joanna, 287, 313 
 South, Sir Js. 370 
 Spearman, 140 
 Spedding, James, 49, 53, 85 
 
 THI 
 
 Speed, John, 120 
 
 Speke, Captain, 46 
 
 Spencer, Earl (The late), 251 
 
 Spinoza, Benedict, 3, 29 
 
 Spiritualism, 286, 287, 288, 378, et seq. 
 
 Spurius Cassius and Spurius Melius, 476 
 
 Stapulensis, Faber, 31 
 
 Starkie, George, 75 
 
 Statter, Dover, 301 
 
 Steel, James, 293 
 
 Stephens, Henry, 31 
 
 Stevin and Dumortier, 189 
 
 Stephenson, George, 342 
 
 Robert, 342 
 
 Stevinus, Simon, 53, 189, 190, 288 
 
 Stifelius, Michael, 499 
 
 Stiles, John (Camb. Carrier), 453 
 
 St. Martin, Louis Claude, 100, 101 
 
 St. Mesmin (Menut de), 168 
 
 Strafford, Lord, 142 
 
 Stratford, W. S., 180 
 
 Stukeley, Dr., 140 
 
 St. Vincent, Gregory (Cyc.), 67, 70 
 
 Substitute for Declaration of Belief, 424 , 
 
 425 
 
 Suffield, George, 292 
 Sullamar, Henry (Cyc.), 179 
 Sumner, Bishop of Chester, 196 
 
 Bishop of Winchester, 196 
 Sussameus, Hubertus, 35 
 Suvaroff (at Ismail), 305 
 Swedenborg, Emanuel, 151 
 Swedenborgians, The, 287 
 Swift, Dean, 79, 80 
 Sylvester, Professor, 472 
 Symington, (Engineer,) 88 
 Symons, Jellinger, 251, 261, 304 
 Sympathetic Powder, 16, 66 
 
 nHABLEAU Naturel des Rapports, &c. 
 
 1 (St. Martin), 102 
 
 Tablet, The, 266, 267 
 
 Talbot, Sir Gilbert, 16, 66 
 
 Tarporley, 451 
 
 Tartaglia, 288 
 
 Tassius, 65 
 
 Tate, Rev. James, 119 
 
 Tauler, John (Mys.), 463 
 
 Taylor, Brook, 451 
 
 'John (on 666), 216 
 
 John, 311, 312 
 
 Robert, (Devil's Chaplain,) 161, 162, 
 166 
 
 Thomas (Platonist), 112 
 Teissier, Anthony, 68 
 Tenterden, Lord Chief Justice, 108 
 Tetragonismus, 31 
 
 Thales, 288, 303 
 Thelwall, John, 106 
 Theophrastus, 361 
 Thiebault, 250, 474 
 
INDEX. 
 
 511 
 
 THO 
 
 Thompson (Gen. Perronet), 173,210, 3>,2, 
 
 373 
 Thomson, Archbishop, 197 
 
 Dr. (Hist. Royal Soc.), 16 
 Ihom, Rev. David, 402, et seq. 
 
 J. Hamilton, 402 
 Thorndike, Dr., 457, 458 
 
 Thorn, Dr. (666, &c.), 355, 356, 357, 358, 
 
 394 to 408, 489 
 Thrale, Mrs., 143, 433 
 Thurlow, Lord, 133 
 Thyracus, 35 
 Tippoo, 35 
 
 Torriano, Evangelista, 148 
 Towneley, 451 
 Tractarianism, 42, 43 
 Transmigration, 310 
 Trinity, The, (Illustrated by Astronomy,) 
 
 103 
 
 Trinitarianism of Bacon, 86 
 Trochoidal Curves, 261 
 Troughton and Simms, 90 
 Turnor, Mr. (Newton's apple-tree), 81 
 Tycho Brahe, 49, 235, 451, 471 
 
 TTNITARIAN Controversy, 402 
 U Unitarians, The, 266, 268, 447 
 United Service Journal, 258 
 r Magazine, 253 
 University College, 153, 268 
 University of London, 153, 156 
 Upton, W. (Trie.), 256, 257, 258 
 Urban, Pope, 430 
 Useful Knowledge Society, 192, 442, 444, 
 
 447 
 Useful Knowledge, Library of, 167 
 
 TTALENTINE, Basil, (Ale.), 74, 75 
 V Van Schooten, 288 
 Verses on Paradoxers, 484 
 Verses on the Soundness of the Earth, 309 
 Vestiges of Creation, 210, 211 
 Viceroy of Egypt, 290 
 Victorinus of Aquitaine, 221 
 Victoria Toto Ccelo, (J. Keddie, 372) 
 Vieta, 67, 390, 448 
 Village Dialogues, 114 
 Vitruvius, 439 
 
 Vitus, St., 289, 290, 438, 460 
 Vivian, 103 
 Voltaire, 64, 90, 146 
 
 Chretien, 145, et sea. 
 Vogel, A.P., 230 
 
 Von Gumpach, 341 
 
 WALKER, W. E., 459 
 Wallis, 66, 450, 458 
 Wallich, Dr., 257 
 Walpole, Horace, 17, 78 
 Walsh, John, 154, 155, 156, 157, 354 
 Walter, Peter, Usurer, 435 
 Wa,rburton, Henry, 37, 213 
 
 ZYT 
 
 Ward, Seth, 450 
 
 Waring, 133 
 
 Warner, 451, 457, 458 
 
 Warren, Samuel, 475 
 
 Watt, 98, 104, 249 
 
 Weddle, Thomas, 373, 374 
 
 Weld (Hist. Royal Soc.), 16 
 
 Wellington, Duke of, 190 
 
 Wesleyanism, 43 
 
 Westminster Review, 173 
 
 Whately, Archbishop, 145, 146, 196 
 
 Whewell, Rev. Dr., 63, 317, 415, 416, 417, 
 
 430 
 Whiston, John, 87 
 
 William, 79, 87, 93 
 White, Blanco, 146 
 
 Kirk, 432 
 
 Richard (Albius, Cyc.), 9 
 
 R., 66 
 
 White Stone, The, 316 
 
 Whitworth, Professor, 477 
 
 Whizgig, The, 151 
 
 Wightman, G., 40 
 
 Wilkins, Bishop (Real character), 62, 70, 
 
 135, 338, 373 
 William III., 310 
 William IV., 176 
 Williams,Thomas(Weights and Measures), 
 
 102 
 
 Mr. (Sec. Ast. Soc.), 233 
 
 R., Boston, 281 
 Wilson's Euclid, 477 
 
 John (Theorem), 132, 133 
 
 R. (Moon's Rotation), 253 
 Wingate's Arithmetic, 455 
 Wirgman, Thomas, 153, 154 
 Wiseman, Cardinal, 266, 267, 447 
 Wolzogeu, Baron, 65 
 Wollstonecraft, Mary, 103, 104 
 Wood, Anthony, 70 
 
 Wood's Athense Oxonieuses, 461 
 Wood, Jean, 138 
 
 - William, 145 
 
 Woodley, Captain, R.N., 185, 186 
 Wordsworth, William, 435 
 Wright, .Thomas, 90, 91 
 Wronski, Hoene, 148 
 Wrottesley, Lord, 379 
 
 TTOUNG, Brigham, 294 
 1 Dr. Thomas, 18, 22, 148 
 Yvon, Paul, 179 
 
 ZACH, Baron (Solar Spots), 279, 380 
 Zachary, Pope, 24, et seq. 
 Zadkiel's Almanac, 195, 277, 472 
 Zetetic Astronomy, 306. 307, 308 
 Zodiac of Denderah, 341 
 
 - Esne, 341 
 
 Palmyra, 167 
 Zypceus, 101 
 
 Zytphen (A.C.), 471, 472 
 
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