Budget of Paradoxes/G

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A Budget of Paradoxes by Augustus De Morgan


The mathematical and philosophical works of the Right Rev. John Wilkins[502].... In two volumes. London, 1802, 8vo.

This work, or at least part of the edition—all for aught I know—is printed on wood; that is, on paper made from wood-pulp. It has a rough surface; and when held before a candle is of very unequal transparency. There is in it a reprint of the works on the earth and moon. The discourse on the possibility of going to the moon, in this and the edition of 1640, is incorporated: but from the account in the [ 227 ] life prefixed, and a mention by D'Israeli, I should suppose that it had originally a separate title-page, and some circulation as a separate tract. Wilkins treats this subject half seriously, half jocosely; he has evidently not quite made up his mind. He is clear that "arts are not yet come to their solstice," and that posterity will bring hidden things to light. As to the difficulty of carrying food, he thinks, scoffing Puritan that he is, the Papists may be trained to fast the voyage, or may find the bread of their Eucharist "serve well enough for their viaticum."[503] He also puts the case that the story of Domingo Gonsales may be realized, namely, that wild geese find their way to the moon. It will be remembered—to use the usual substitute for, It has been forgotten—that the posthumous work of Bishop Francis Godwin[504] of Llandaff was published in 1638, the very year of Wilkins's first edition, in time for him to mention it at the end. Godwin makes Domingo Gonsales get to the moon in a chariot drawn by wild geese, and, as old books would say, discourses fully on that head. It is not a little amusing that Wilkins should have been seriously accused of plagiarizing Godwin, Wilkins writing in earnest, or nearly so, and Godwin writing fiction. It may serve to show philosophers how very near pure speculation comes to fable. From the sublime to the ridiculous is but a step: which is the sublime, and which the ridiculous, every one must settle for himself. With me, good fiction is the sublime, and bad speculation the ridiculous. The number of bishops in my list is small. I might, had I possessed the book, have opened the list of quadrators with an Archbishop of Canterbury, or at least with a divine who was not wholly not archbishop. Thomas Bradwardine[505] (Bragvardinus, Bragadinus) was elected in [ 228 ] 1348; the Pope put in another, who died unconsecrated; and Bradwardine was again elected in 1349, and lived five weeks longer, dying, I suppose, unconfirmed and unconsecrated.[506] Leland says he held the see a year, unus tantum annulus,[507] which seems to be a confusion: the whole business, from the first election, took about a year. He squared the circle, and his performance was printed at Paris in 1494. I have never seen it, nor any work of the author, except a tract on proportion.

As Bradwardine's works are very scarce indeed, I give two titles from one of the Libri catalogues.

"Arithmetic. Brauardini (Thomæ) Arithmetica speculativa revisa et correcta a Petro Sanchez Ciruelo Aragonesi, black letter, elegant woodcut title-page, VERY RARE, folio. Parisiis, per Thomam Anguelast (pro Olivier Senant), s. a. circa 1510.[508]

"This book, by Thomas Bradwardine, Archbishop of Canterbury must be exceedingly scarce as it has escaped the notice of Professor De Morgan, who, in his Arithmetical Books, speaks of a treatise of the same author on proportions,[509] printed at Vienna in 1515, but does not mention the present work.

[ 229 ]

"Bradwardine (Archbp. T.). Brauardini (Thomæ) Geometria speculativa, com Tractato de Quadratura Circuli bene revisa a Petro Sanchez Ciruelo, SCARCE, folio. Parisiis, J. Petit, 1511.[510]

"In this work we find the polygones étoilés,[511] see Chasles (Aperçu, pp. 480, 487, 521, 523, &c.) on the merit of the discoveries of this English mathematician, who was Archbishop of Canterbury in the XIVth Century (tempore Edward III. A.D. 1349); and who applied geometry to theology. M. Chasles says that the present work of Bradwardine contains 'Une théorie nouvelle qui doit faire honneur au XIVe Siècle.'"[512]

The titles do not make it quite sure that Bradwardine is the quadrator; it may be Peter Sanchez after all.[513]



Nouvelle théorie des parallèles. Par Adolphe Kircher[514] [so signed at the end of the appendix]. Paris, 1803, 8vo.

An alleged emendation of Legendre.[515] The author refers [ 230 ] to attempts by Hoffman,[516] 1801, by Hauff,[517] 1799, and to a work of Karsten,[518] or at least a theory of Karsten, contained in "Tentamen novæ parallelarum theoriæ notione situs fundatæ; auctore G. C. Schwal,[519] Stuttgardæ, 1801, en 8 volumes." Surely this is a misprint; eight volumes on the theory of parallels? If there be such a work, I trust I and it may never meet, though ever so far produced.

[ 231 ]


Soluzione ... della quadratura del Circolo. By Gaetano Rossi.[520] London, 1804, 8vo.

The three remarkable points of this book are, that the household of the Prince of Wales took ten copies, Signora Grassini[521] sixteen, and that the circumference is \scriptstyle 3\frac{1}{5} diameters. That is, the appetite of Grassini for quadrature exceeded that of the whole household (loggia) of the Prince of Wales in the ratio in which the semi-circumference exceeds the diameter. And these are the first two in the list of subscribers. Did the author see this theorem?



Britain independent of commerce; or proofs, deduced from an investigation into the true cause of the wealth of nations, that our riches, prosperity, and power are derived from sources inherent in ourselves, and would not be affected, even though our commerce were annihilated. By Wm. Spence.[522] 4th edition, 1808, 8vo.

A patriotic paradox, being in alleviation of the Commerce panic which the measures of Napoleon I.—who felt our Commerce, while Mr. Spence only saw it—had awakened. In this very month (August, 1866), the Pres. Brit. Assoc. has applied a similar salve to the coal panic; it is fit that science, which rubbed the sore, should find a plaster. We ought to have an iron panic and a timber panic; and [ 232 ] a solemn embassy to the Americans, to beg them not to whittle, would be desirable. There was a gold panic beginning, before the new fields were discovered. For myself, I am the unknown and unpitied victim of a chronic gutta-percha panic: I never could get on without it; to me, gutta percha and Rowland Hill are the great discoveries of our day; and not unconnected either, gutta percha being to the submarine post what Rowland Hill is to the superterrene. I should be sorry to lose cow-choke—I gave up trying to spell it many years ago—but if gutta percha go, I go too. I think, that perhaps when, five hundred years hence, the people say to the Brit. Assoc. (if it then exist) "Pray gentlemen, is it not time for the coal to be exhausted?" they will be answered out of Molière (who will certainly then exist): "Cela était autrefois ainsi, mais nous avons changé tout cela."[523] A great many people think that if the coal be used up, it will be announced some unexpected morning by all the yards being shut up and written notice outside, "Coal all gone!" just like the "Please, ma'am, there ain't no more sugar," with which the maid servant damps her mistress just at breakfast-time. But these persons should be informed that there is every reason to think that there will be time, as the city gentleman said, to venienti the occurrite morbo.[524]



An appeal to the republic of letters in behalf of injured science, from the opinions and proceedings of some modern authors of elements of geometry. By George Douglas.[525] Edinburgh, 1810, 8vo.

Mr. Douglas was the author of a very good set of [ 233 ] mathematical tables, and of other works. He criticizes Simson,[526] Playfair,[527] and others,—sometimes, I think, very justly. There is a curious phrase which occurs more than once. When he wants to say that something or other was done before Simson or another was born, he says "before he existed, at least as an author." He seems to reserve the possibility of Simson's pre-existence, but at the same time to assume that he never wrote anything in his previous state. Tell me that Simson pre-existed in any other way than as editor of some pre-existent Euclid? Tell Apella![528]

1810. In this year Jean Wood, Professor of Mathematics in the University of Virginia (Richmond),[529] addressed a printed circular to "Dr. Herschel, Astronomer, Greenwich Observatory." No mistake was more common than the natural one of imagining that the Private Astronomer of the king was the Astronomer Royal. The letter was on the [ 234 ] difference of velocities of the two sides of the earth, arising from the composition of the rotation and the orbital motion. The paradox is a fair one, and deserving of investigation; but, perhaps it would not be easy to deduce from it tides, trade-winds, aerolithes, &c., as Mr. Wood thought he had done in a work from which he gives an extract, and which he describes as published. The composition of rotations, &c., is not for the world at large: the paradox of the non-rotation of the moon about her axis is an instance. How many persons know that when a wheel rolls on the ground, the lowest point is moving upwards, the highest point forwards, and the intermediate points in all degrees of betwixt and between? This is too short an explanation, with some good difficulties.


The Elements of Geometry. In 2 vols. [By the Rev. J. Dobson,[530] B.D.] Cambridge, 1815. 4to.

Of this unpunctuating paradoxer I shall give an account in his own way: he would not stop for any one; why should I stop for him? It is worth while to try how unpunctuated sentences will read.

The reverend J Dobson BD late fellow of saint Johns college Cambridge was rector of Brandesburton in Yorkshire he was seventh wrangler in 1798 and died in 1847 he was of that sort of eccentricity which permits account of his private life if we may not rather say that in such cases private life becomes public there is a tradition that he was called Death Dobson on account of his head and aspect of countenance being not very unlike the ordinary pictures of a human skull his mode of life is reported to have been very singular whenever he visited Cambridge he was never known to go twice to the same inn he never would sleep at the rectory with another person in the house some ancient charwoman used to attend to the house but never slept in it he has been known in the time of coach travelling to have [ 235 ] deferred his return to Yorkshire on account of his disinclination to travel with a lady in the coach he continued his mathematical studies until his death and till his executors sold the type all his tracts to the number of five were kept in type at the university press none of these tracts had any stops except full stops at the end of paragraphs only neither had they capitals except one at the beginning of a paragraph so that a full stop was generally followed by some white as there is not a single proper name in the whole of the book I have I am not able to say whether he would have used capitals before proper names I have inserted them as usual for which I hope his spirit will forgive me if I be wrong he also published the elements of geometry in two volumes quarto Cambridge 1815 this book had also no stops except when a comma was wanted between letters as in the straight lines AB, BC I should also say that though the title is unpunctuated in the author's part it seems the publishers would not stand it in their imprint this imprint is punctuated as usual and Deighton and Sons to prove the completeness of their allegiance have managed that comma semicolon and period shall all appear in it why could they not have contrived interrogation and exclamation this is a good precedent to establish the separate right of the publisher over the imprint it is said that only twenty of the tracts were printed and very few indeed of the book on geometry it is doubtful whether any were sold there is a copy of the geometry in the university library at Cambridge and I have one myself the matter of the geometry differs entirely from Euclid and is so fearfully prolix that I am sure no mortal except the author ever read it the man went on without stops and without stop save for a period at the end of a paragraph this is the unpunctuated account of the unpunctuating geometer suum cuique tribuito[531] Mrs Thrale[532] would have been amused [ 236 ] at a Dobson who managed to come to a full stop without either of the three warnings.

I do not find any difficulty in reading Dobson's geometry; and I have read more of it to try reading without stops than I should have done had it been printed in the usual way. Those who dip into the middle of my paragraph may be surprised for a moment to see "on account of his disinclination to travel with a lady in the coach he continued his mathematical studies until his death and [further, of course] until his executors sold the type." But a person reading straight through would hardly take it so. I should add that, in order to give a fair trial, I did not compose as I wrote, but copied the words of the correspondent who gave me the facts, so far as they went.



Philosophia Sacra, or the principles of natural Philosophy. Extracted from Divine Revelation. By the Rev. Samuel Pike.[533] Edited by the Rev. Samuel Kittle.[534] Edinburgh, 1815, 8vo.

This is a work of modified Hutchinsonianism, which I have seen cited by several. Though rather dark on the subject, it seems not to contradict the motion of the earth, or the doctrine of gravitation. Mr. Kittle gives a list of some Hutchinsonians,—as Bishop Horne;[535] Dr. Stukeley;[536] the Rev. [ 237 ] W. Jones,[537] author of Physiological Disquisitions; Mr. Spearman,[538] author of Letters on the Septuagint and editor of Hutchinson; Mr. Barker,[539] author of Reflexions on Learning; Dr. Catcott,[540] author of a work on the creation, &c.; Dr. Robertson,[541] author of a Treatise on the Hebrew Language; Dr. Holloway,[542] author of Originals, Physical and Theological; Dr. Walter Hodges,[543] author of a work on Elohim; Lord President Forbes (ob. 1747).[544]

The Rev. William Jones, above mentioned (1726-1800), the friend and biographer of Bishop Horne and his stout [ 238 ] defender, is best known as William Jones of Nayland, who (1757)[545] published the Catholic Doctrine of the Trinity; he was also strong for the Hutchinsonian physical trinity of fire, light, and spirit. This well-known work was generally recommended, as the defence of the orthodox system, to those who could not go into the learning of the subject. There is now a work more suited to our time: The Rock of Ages, by the Rev. E. H. Bickersteth,[546] now published by the Religious Tract Society, without date, answered by the Rev. Dr. Sadler,[547] in a work (1859) entitled Gloria Patri, in which, says Mr. Bickersteth, "the author has not even attempted to grapple with my main propositions." I have read largely on the controversy, and I think I know what this means. Moreover, when I see the note "There are two other passages to which Unitarians sometimes refer, but the deduction they draw from them is, in each case, refuted by the context"—I think I see why the two texts are not named. Nevertheless, the author is a little more disposed to yield to criticism than his foregoers; he does not insist on texts and readings which the greatest editors have rejected. And he writes with courtesy, both direct and oblique, towards his antagonists; which, on his side of this subject, is like letting in fresh air. So that I suspect the two books will together make a tolerably good introduction to the subject for those who cannot go deep. Mr. Bickersteth's book is well arranged and indexed, which is a point of superiority to Jones of Nayland. There is a point which I should gravely recommend to writers on the orthodox side. The Unitarians in [ 239 ] England have frequently contended that the method of proving the divinity of Jesus Christ from the New Testament would equally prove the divinity of Moses. I have not fallen in the way of any orthodox answers specially directed at the repeated tracts written by Unitarians in proof of their assertion. If there be any, they should be more known; if there be none, some should be written. Which ever side may be right, the treatment of this point would be indeed coming to close quarters. The heterodox assertion was first supported, it is said, by John Bidle or Biddle (1615-1662) of Magdalen College, Oxford, the earliest of the English Unitarian writers, previously known by a translation of part of Virgil and part of Juvenal.[548] But I cannot find that he wrote on it.[549] It is the subject of "αἱρεσεων ἀναστασις, or a new way of deciding old controversies. By Basanistes. Third edition, enlarged," London, 1815, 8vo.[550] It is the appendix to the amusing, "Six more letters to Granville Sharp, Esq., ... By Gregory Blunt, Esq." London, 8vo., 1803.[551] This much I can confidently say, that the study of these tracts would prevent orthodox writers from some curious slips, which are slips obvious to all sides of opinion. The lower defenders of orthodoxy frequently vex the spirits of the higher ones.

Since writing the above I have procured Dr. Sadler's answer. I thought I knew what the challenger meant when he said the respondent had not grappled with his main [ 240 ] propositions. I should say that he is clung on to from beginning to end. But perhaps Mr. B. has his own meaning of logical terms, such as "proposition": he certainly has his own meaning of "cumulative." He says his evidence is cumulative; not a catena, the strength of which is in its weakest part, but distinct and independent lines, each of which corroborates the other. This is the very opposite of cumulative: it is distributive. When different arguments are each necessary to a conclusion, the evidence is cumulative; when any one will do, even though they strengthen each other, it is distributive. The word "cumulative" is a synonym of the law word "constructive"; a whole which will do made out of parts which separately will not. Lord Strafford [552] opens his defence with the use of both words: "They have invented a kind of accumulated or constructive evidence; by which many actions, either totally innocent in themselves, or criminal in a much inferior degree, shall, when united, amount to treason." The conclusion is, that Mr. B. is a Cambridge man; the Oxford men do not confuse the elementary terms of logic. O dear old Cambridge! when the New Zealander comes let him find among the relics of your later sons some proof of attention to the elementary laws of thought. A little-go of logic, please!

Mr. B., though apparently not a Hutchinsonian, has a nibble at a physical Trinity. "If, as we gaze on the sun shining in the firmament, we see any faint adumbration of the doctrine of the Trinity in the fontal orb, the light ever generated, and the heat proceeding from the sun and its beams—threefold and yet one, the sun, its light, and its [ 241 ] heat,—that luminous globe, and the radiance ever flowing from it, are both evident to the eye; but the vital warmth is felt, not seen, and is only manifested in the life it transfuses through creation. The proof of its real existence is self-demonstrating."

We shall see how Revilo[553] illustrates orthodoxy by mathematics. It was my duty to have found one of the many illustrations from physics; but perhaps I should have forgotten it if this instance had not come in my way. It is very bad physics. The sun, apart from its light, evident to the eye! Heat more self-demonstrating than light, because felt! Heat only manifested by the life it diffuses! Light implied not necessary to life! But the theology is worse than Sabellianism[554]. To adumbrate—i.e., make a picture of—the orthodox doctrine, the sun must be heavenly body, the light heavenly body, the heat heavenly body; and yet, not three heavenly bodies, but one heavenly body. The truth is, that this illustration and many others most strikingly illustrate the Trinity of fundamental doctrine held by the Unitarians, in all its differences from the Trinity of persons held by the Orthodox. Be right which may, the right or wrong of the Unitarians shines out in the comparison. Dr. Sadler confirms me—by which I mean that I wrote the above before I saw what he says—in the following words: "The sun is one object with two properties, and these properties have a parallel not in the second and third persons of the Trinity, but in the attributes of Deity."

The letting light alone, as self-evident, and making heat self-demonstrating, because felt—i.e., perceptible now and then—has the character of the Irishman's astronomy:

[ 242 ]

"Long life to the moon, for a dear noble cratur,
Which serves us for lamplight all night in the dark,
While the sun only shines in the day, which by natur,
Wants no light at all, as ye all may remark."



Sir Richard Phillips[555] (born 1768) was conspicuous in 1793, when he was sentenced to a year's imprisonment[556] for selling Paine's Rights of Man; and again when, in 1807[557], he was knighted as Sheriff of London. As a bookseller, he was able to enforce his opinions in more ways than others. For instance, in James Mitchell's[558] Dictionary of the Mathematical and Physical Sciences, 1823, 12mo, which, though he was not technically a publisher, was printed for him—a book I should recommend to the collector of works of reference—there is a temperate description of his doctrines, which one may almost swear was one of his conditions previous to undertaking the work. Phillips himself was not only an anti-Newtonian, but carried to a fearful excess the notion that statesmen and Newtonians were in league to deceive the world. He saw this plot in Mrs. Airy's[559] pension, and in Mrs. Somerville's[560]. In 1836, he [ 243 ] did me the honor to attempt my conversion. In his first letter he says:

"Sir Richard Phillips has an inveterate abhorrence of all the pretended wisdom of philosophy derived from the monks and doctors of the middle ages, and not less of those of higher name who merely sought to make the monkish philosophy more plausible, or so to disguise it as to mystify the mob of small thinkers."

So little did his writings show any knowledge of antiquity, that I strongly suspect, if required to name one of the monkish doctors, he would have answered—Aristotle. These schoolmen, and the "philosophical trinity of gravitating force, projectile force, and void space," were the bogies of his life.

I think he began to publish speculations in the Monthly Magazine (of which he was editor) in July 1817: these he republished separately in 1818. In the Preface, perhaps judging the feelings of others by his own, he says that he "fully expects to be vilified, reviled, and anathematized, for many years to come." Poor man! he was let alone. He appeals with confidence to the "impartial decision of posterity"; but posterity does not appoint a hearing for one per cent. of the appeals which are made; and it is much to be feared that an article in such a work of reference as this will furnish nearly all her materials fifty years hence. The following, addressed to M. Arago,[561] in 1835, will give posterity as good a notion as she will probably need:

"Even the present year has afforded EVER-MEMORABLE examples, paralleled only by that of the Romish Conclave which persecuted Galileo. Policy has adopted that maxim of Machiavel which teaches that it is more prudent to reward [ 244 ] partisans than to persecute opponents. Hence, a bigotted party had influence enough with the late short-lived administration [I think he is wrong as to the administration] of Wellington, Peel, &c., to confer munificent royal pensions on three writers whose sole distinction was their advocacy of the Newtonian philosophy. A Cambridge professor last year published an elaborate volume in illustration of Gravitation, and on him has been conferred a pension of 300l. per annum. A lady has written a light popular view of the Newtonian Dogmas, and she has been complimented by a pension of 200l. per annum. And another writer, who has recently published a volume to prove that the only true philosophy is that of Moses, has been endowed with a pension of 200l. per annum. Neither of them were needy persons, and the political and ecclesiastical bearing of the whole was indicated by another pension of 300l. bestowed on a political writer, the advocate of all abuses and prejudices. Whether the conduct of the Romish Conclave was more base for visiting with legal penalties the promulgation of the doctrines that the Earth turns on its axis and revolves around the Sun; or that of the British Court, for its craft in conferring pensions on the opponents of the plain corollary, that all the motions of the Earth are 'part and parcel' of these great motions, and those again and all like them consecutive displays of still greater motions in equality of action and reaction, is A QUESTION which must be reserved for the casuists of other generations.... I cannot expect that on a sudden you and your friends will come to my conclusion, that the present philosophy of the Schools and Universities of Europe, based on faith in witchcraft, magic, &c., is a system of execrable nonsense, by which quacks live on the faith of fools; but I desire a free and fair examination of my Aphorisms, and if a few are admitted to be true, merely as courteous concessions to arithmetic, my purpose will be effected, for men will thus be led to think; and if they think, then the fabric [ 245 ] of false assumptions, and degrading superstitions will soon tumble in ruins."

This for posterity. For the present time I ground the fame of Sir R. Phillips on his having squared the circle without knowing it, or intending to do it. In the Protest presently noted he discovered that "the force taken as 1 is equal to the sum of all its fractions ... thus \scriptstyle 1 = \frac{1}{4} + \frac{1}{9} + \frac{1}{16} + \frac{1}{25}, &c., carried to infinity." This the mathematician instantly sees is equivalent to the theorem that the circumference of any circle is double of the diagonal of the cube on its diameter.[562]

I have examined the following works of Sir R. Phillips, and heard of many others:

Essays on the proximate mechanical causes of the general phenomena of the Universe, 1818, 12mo.[563]
Protest against the prevailing principles of natural philosophy, with the development of a common sense system (no date, 8vo, pp. 16).[564]
Four dialogues between an Oxford Tutor and a disciple of the common-sense philosophy, relative to the proximate causes of material phenomena. 8vo, 1824.
A century of original aphorisms on the proximate causes of the phenomena of nature, 1835, 12mo.

Sir Richard Phillips had four valuable qualities; honesty, zeal, ability, and courage. He applied them all to teaching [ 246 ] matters about which he knew nothing; and gained himself an uncomfortable life and a ridiculous memory.


Astronomy made plain; or only way the true perpendicular distance of the Sun, Moon, or Stars, from this earth, can be obtained. By Wm. Wood.[565] Chatham, 1819, 12mo.

If this theory be true, it will follow, of course, that this earth is the only one God made, and that it does not whirl round the sun, but vice versa, the sun round it.



Historic doubts relative to Napoleon Buonaparte. London, 1819, 8vo.

This tract has since been acknowledged by Archbishop Whately[566] and reprinted. It is certainly a paradox: but differs from most of those in my list as being a joke, and a satire upon the reasoning of those who cannot receive narrative, no matter what the evidence, which is to them utterly improbable a priori. But had it been serious earnest, it would not have been so absurd as many of those which I have brought forward. The next on the list is not a joke.

The idea of the satire is not new. Dr. King,[567] in the dispute on the genuineness of Phalaris, proved with humor that Bentley did not write his own dissertation. An attempt has lately been made, for the honor of Moses, to prove, [ 247 ] without humor, that Bishop Colenso did not write his own book. This is intolerable: anybody who tries to use such a weapon without banter, plenty and good, and of form suited to the subject, should get the drubbing which the poor man got in the Oriental tale for striking the dervishes with the wrong hand.

The excellent and distinguished author of this tract has ceased to live. I call him the Paley of our day: with more learning and more purpose than his predecessor; but perhaps they might have changed places if they had changed centuries. The clever satire above named is not the only work which he published without his name. The following was attributed to him, I believe rightly: "Considerations on the Law of Libel, as relating to Publications on the subject of Religion, by John Search." London, 1833, 8vo. This tract excited little attention: for those who should have answered, could not. Moreover, it wanted a prosecution to call attention to it: the fear of calling such attention may have prevented prosecutions. Those who have read it will have seen why.

The theological review elsewhere mentioned attributes the pamphlet of John Search on blasphemous libel to Lord Brougham. This is quite absurd: the writer states points of law on credence where the judge must have spoken with authority. Besides which, a hundred points of style are decisive between the two. I think any one who knows Whately's writing will soon arrive at my conclusion. Lord Brougham himself informs me that he has no knowledge whatever of the pamphlet.

It is stated in Notes and Queries (3 S. xi. 511) that Search was answered by the Bishop of Ferns[568] as S. N., with [ 248 ] a rejoinder by Blanco White.[569] These circumstances increase the probability that Whately was written against and for.



Voltaire Chrétien; preuves tirées de ses ouvrages. Paris, 1820, 12mo.

If Voltaire have not succeeded in proving himself a strong theist and a strong anti-revelationist, who is to succeed in proving himself one thing or the other in any matter whatsoever? By occasional confusion between theism and Christianity; by taking advantage of the formal phrases of adhesion to the Roman Church, which very often occur, and are often the happiest bits of irony in an ironical production; by citations of his morality, which is decidedly Christian, though often attributed to Brahmins; and so on—the author makes a fair case for his paradox, in the eyes of those who know no more than he tells them. If he had said that Voltaire was a better Christian than himself knew of, towards all mankind except men of letters, I for one should have agreed with him.

Christian! the word has degenerated into a synonym of man, in what are called Christian countries. So we have the parrot who "swore for all the world like a Christian," and the two dogs who "hated each other just like Christians." When the Irish duellist of the last century, whose name may be spared in consideration of its historic fame [ 249 ] and the worthy people who bear it, was (June 12, 1786) about to take the consequence of his last brutal murder, the rope broke, and the criminal got up, and exclaimed, "By —— Mr. Sheriff, you ought to be ashamed of yourself! this rope is not strong enough to hang a dog, far less a Christian!" But such things as this are far from the worst depravations. As to a word so defiled by usage, it is well to know that there is a way of escape from it, without renouncing the New Testament. I suppose any one may assume for himself what I have sometimes heard contended for, that no New Testament word is to be used in religion in any sense except that of the New Testament. This granted, the question is settled. The word Christian, which occurs three times, is never recognized as anything but a term of contempt from those without the pale to those within. Thus, Herod Agrippa, who was deep in Jewish literature, and a correspondent of Josephus, says to Paul (Acts xxvi. 28), "Almost thou persuadest me to be (what I and other followers of the state religion despise under the name) a Christian." Again (Acts xi. 26), "The disciples (as they called themselves) were called (by the surrounding heathens) Christians first in Antioch." Thirdly (1 Peter iv. 16), "Let none of you suffer as a murderer.... But if as a Christian (as the heathen call it by whom the suffering comes), let him not be ashamed." That is to say, no disciple ever called himself a Christian, or applied the name, as from himself, to another disciple, from one end of the New Testament to the other; and no disciple need apply that name to himself in our day, if he dislike the associations with which the conduct of Christians has clothed it.



Address of M. Hoene Wronski to the British Board of Longitude, upon the actual state of the mathematics, their reform, [ 250 ] and upon the new celestial mechanics, giving the definitive solution of the problem of longitude.[570] London, 1820, 8vo.

M. Wronski[571] was the author of seven quartos on mathematics, showing very great power of generalization. He was also deep in the transcendental philosophy,[572] and had the Absolute at his fingers' ends. All this knowledge was rendered useless by a persuasion that he had greatly advanced beyond the whole world, with many hints that the Absolute would not be forthcoming, unless prepaid. He was a man of the widest extremes. At one time he desired people to see all possible mathematics in

\operatorname{F}x = A_0\Omega_0 + A_1\Omega_1 + A_2\Omega_2 + A_3\Omega_3 + &c

which he did not explain, though there is meaning to it in the quartos. At another time he was proposing the general solution of the[573] fifth degree by help of 625 independent equations of one form and 125 of another. The first separate memoir from any Transactions that I ever possessed was given to me when at Cambridge; the refutation (1819) of this asserted solution, presented to the Academy of Lisbon by Evangelista Torriano. I cannot say I read it. The tract above is an attack on modern mathematicians in general, and on the Board of Longitude, and Dr. Young.[574]

[ 251 ]



1820. In this year died Dr. Isaac Milner,[575] President of Queens' College, Cambridge, one of the class of rational paradoxers. Under this name I include all who, in private life, and in matters which concern themselves, take their own course, and suit their own notions, no matter what other people may think of them. These men will put things to uses they were never intended for, to the great distress and disgust of their gregarious friends. I am one of the class, and I could write a little book of cases in which I have incurred absolute reproach for not "doing as other people do." I will name two of my atrocities: I took one of those butter-dishes which have for a top a dome with holes in it, which is turned inward, out of reach of accident, when not in use. Turning the dome inwards, I filled the dish with water, and put a sponge in the dome: the holes let it fill with water, and I had a penwiper, always moist, and worth its price five times over. "Why! what do you mean? It was made to hold butter. You are always at some queer thing or other!" I bought a leaden comb, intended to dye the hair, it being supposed that the application of lead will have this effect. I did not try: but I divided the comb into two, separated the part of closed prongs from the other; and thus I had two ruling machines. The lead marks paper, and by drawing the end of one of the machines along a ruler, I could rule twenty lines at a time, quite fit to write on. I thought I should have killed a friend to whom I explained it: he could not for the life of him understand how leaden lines on paper would dye the hair.

But Dr. Milner went beyond me. He wanted a seat suited to his shape, and he defied opinion to a fearful point. [ 252 ] He spread a thick block of putty over a wooden chair and sat in it until it had taken a ceroplast copy of the proper seat. This he gave to a carpenter to be imitated in wood. One of the few now living who knew him—my friend, General Perronet Thompson[576]—answers for the wood, which was shown him by Milner himself; but he does not vouch for the material being putty, which was in the story told me at Cambridge; William Frend[577] also remembered it. Perhaps the Doctor took off his great seal in green wax, like the Crown; but some soft material he certainly adopted; and very comfortable he found the wooden copy.

Budget of Paradoxes Milners lamp.png

The same gentleman vouches for Milner's lamp: but this had visible science in it; the vulgar see no science in the construction of the chair. A hollow semi-cylinder, but not with a circular curve, revolved on pivots. The curve was calculated on the law that, whatever quantity of oil might be in the lamp, the position of equilibrium just brought the oil up to the edge of the cylinder, at which a bit of wick was placed. As the wick exhausted the oil, the cylinder slowly revolved about the pivots so as to keep the oil always touching the wick.

Great discoveries are always laughed at; but it is very often not the laugh of incredulity; it is a mode of distorting the sense of inferiority into a sense of superiority, or a mimicry of superiority interposed between the laugher and his feeling of inferiority. Two persons in conversation [ 253 ] agreed that it was often a nuisance not to be able to lay hands on a bit of paper to mark the place in a book, every bit of paper on the table was sure to contain something not to be spared. I very quietly said that I always had a stock of bookmarkers ready cut, with a proper place for them: my readers owe many of my anecdotes to this absurd practice. My two colloquials burst into a fit of laughter; about what? Incredulity was out of the question; and there could be nothing foolish in my taking measures to avoid what they knew was an inconvenience. I was in this matter obviously their superior, and so they laughed at me. Much more candid was the Royal Duke of the last century, who was noted for slow ideas. "The rain comes into my mouth," said he, while riding. "Had not your Royal Highness better shut your mouth?" said the equerry. The Prince did so, and ought, by rule, to have laughed heartily at his adviser; instead of this, he said quietly, "It doesn't come in now."



De Attentionis mensura causisque primariis. By J. F. Herbart.[578] Kœnigsberg, 1822, 4to.

[ 254 ]

This celebrated philosopher maintained that mathematics ought to be applied to psychology, in a separate tract, published also in 1822: the one above seems, therefore, to be his challenge on the subject. It is on attention, and I think it will hardly support Herbart's thesis. As a specimen of his formula, let t be the time elapsed since the consideration began, \beta the whole perceptive intensity of the individual, \phi the whole of his mental force, and z the force given to a notion by attention during the time t. Then,

z = \phi \left(1 - \epsilon^{-\beta t}\right)

Now for a test. There is a jactura, v, the meaning of which I do not comprehend. If there be anything in it, my mathematical readers ought to interpret it from the formula

v = \frac{\pi\phi\beta}{(1 - \beta)}\epsilon^{-\beta t} + \mathrm{C}\epsilon^{-t}

and to this task I leave them, wishing them better luck than mine. The time may come when other manifestations of mind, besides belief, shall be submitted to calculation: at that time, should it arrive, a final decision may be passed upon Herbart.



The theory of the Whizgig considered; in as much as it mechanically exemplifies the three working properties of nature; which are now set forth under the guise of this toy, for children of all ages. London, 1822, 12mo (pp. 24, B. McMillan, Bow Street, Covent Garden).

The toy called the whizgig will be remembered by many. The writer is a follower of Jacob Behmen,[579] William Law,[580] [ 255 ] Richard Clarke,[581] and Eugenius Philalethes.[582] Jacob Behmen first announced the three working properties of nature, which Newton stole, as described in the Gentleman's Magazine, July, 1782, p. 329. These laws are illustrated in the whizgig. There is the harsh astringent, attractive compression; the bitter compunction, repulsive expansion; and the stinging anguish, duplex motion. The author hints that he has written other works, to which he gives no clue. I have heard that Behmen was pillaged by Newton, and Swedenborg[583] by Laplace,[584] and Pythagoras by Copernicus,[585] and Epicurus by Dalton,[586] &c. I do not think this mention will revive Behmen; but it may the whizgig, a very pretty toy, and philosophical withal, for few of those who used it could explain it.

[ 256 ]



A Grammar of infinite forms; or the mathematical elements of ancient philosophy and mythology. By Wm. Howison.[587] Edinburgh, 1823, 8vo.

A curius combination of geometry and mythology. Perseus, for instance, is treated under the head, "the evolution of diminishing hyperbolic branches."


The Mythological Astronomy of the Ancients; part the second: or the key of Urania, the words of which will unlock all the mysteries of antiquity. Norwich, 1823, 12mo.
A Companion to the Mythological Astronomy, &c., containing remarks on recent publications.... Norwich, 1824, 12mo.
A new Theory of the Earth and of planetary motion; in which it is demonstrated that the Sun is vicegerent of his own system. Norwich, 1825, 12mo.
The analyzation of the writings of the Jews, so far as they are found to have any connection with the sublime science of astronomy. [This is pp. 97-180 of some other work, being all I have seen.]

These works are all by Sampson Arnold Mackey,[588] for whom see Notes and Queries, 1st S. viii. 468, 565, ix. 89, 179. Had it not been for actual quotations given by one correspondent only (1st S. viii. 565), that journal would have handed him down as a man of some real learning. An extraordinary man he certainly was: it is not one illiterate shoemaker in a thousand who could work upon such a singular mass of Sanskrit and Greek words, without showing [ 257 ] evidence of being able to read a line in any language but his own, or to spell that correctly. He was an uneducated Godfrey Higgins.[589] A few extracts will put this in a strong light: one for history of science, one for astronomy, and one for philology:

"Sir Isaac Newton was of opinion that 'the atmosphere of the earth was the sensory of God; by which he was enabled to see quite round the earth:' which proves that Sir Isaac had no idea that God could see through the earth.

"Sir Richard [Phillips] has given the most rational explanation of the cause of the earth's elliptical orbit that I have ever seen in print. It is because the earth presents its watery hemisphere to the sun at one time and that of solid land the other; but why has he made his Oxonian astonished at the coincidence? It is what I taught in my attic twelve years before.

"Again, admitting that the Eloim were powerful and intelligent beings that managed these things, we would accuse them of being the authors of all the sufferings of Chrisna. And as they and the constellation of Leo were below the horizon, and consequently cut off from the end of the zodiac, there were but eleven constellations of the zodiac to be seen; the three at the end were wanted, but those three would be accused of bringing Chrisna into the troubles which at last ended in his death. All this would be expressed in the Eastern language by saying that Chrisna was persecuted by those Judoth Ishcarioth!!!!! [the five notes of exclamation are the author's]. But the astronomy of those distant ages, when the sun was at the south pole in winter, would leave five of those Decans cut off from our view, in the latitude of twenty-eight degrees; hence Chrisna died of [ 258 ] wounds from five Decans, but the whole five may be included in Judoth Ishcarioth! for the phrase means 'the men that are wanted at the extreme parts.' Ishcarioth is a compound of ish, a man, and carat wanted or taken away, and oth the plural termination, more ancient than im...."

I might show at length how Michael is the sun, and the D'-ev-'l in French Di-ob-al, also 'L-evi-ath-an—the evi being the radical part both of 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, "and hence we called our land which is saved from the water by the name of marsh." But it will be of more use to collect the character of S. A. M. from such correspondents of Notes and Queries as have written after superficial examination. Great astronomical and philological attainments, much ability and learning; had evidently read and studied deeply; remarkable for the originality of his views upon the very abstruse subject of mythological astronomy, in which he exhibited great sagacity. Certainly his views were original; but their sagacity, if it be allowable to copy his own mode of etymologizing, is of an ori-gin-ale cast, resembling that of a person who puts to his mouth liquors both distilled and fermented.



Principles of the Kantesian, or transcendental philosophy. By Thomas Wirgman.[590] London, 1824, 8vo.

Mr. Wirgman's mind was somewhat attuned to psychology; but he was cracky and vagarious. He had been a fashionable jeweler in St. James's Street, no doubt the son or grandson of Wirgman at "the well-known toy-shop in [ 259 ] St. James's Street," where Sam Johnson smartened himself with silver buckles. (Boswell, æt. 69). He would not have the ridiculous large ones in fashion; and he would give no more than a guinea a pair; such, says Boswell, in Italics, were the principles of the business: and I think this may be the first place in which the philosophical word was brought down from heaven to mix with men. However this may be, my Wirgman sold snuff-boxes, among other things, and fifty years ago a fashionable snuff-boxer would be under inducement, if not positively obliged, to have a stock with very objectionable pictures. So it happened that Wirgman—by reason of a trifle too much candor—came under the notice of the Suppression Society, and ran considerable risk. Mr. Brougham was his counsel; and managed to get him acquitted. Years and years after this, when Mr. Brougham was deep in the formation of the London University (now University College), Mr. Wirgman called on him. "What now?" said Mr. B. with his most sarcastic look—a very perfect thing of its kind—"you're in a scrape again, I suppose!" "No! indeed!" said W., "my present object is to ask your interest for the chair of Moral Philosophy in the new University!" He had taken up Kant!

Mr. Wirgman, an itinerant paradoxer, called on me in 1831: he came to convert me. "I assure you," said he, "I am nothing but an old brute of a jeweler;" and his eye and manner were of the extreme of jocosity, as good in their way, as the satire of his former counsel. I mention him as one of that class who go away quite satisfied that they have wrought conviction. "Now," said he, "I'll make it clear to you! Suppose a number of gold-fishes in a glass bowl,—you understand? Well! I come with my cigar and go puff, puff, puff, over the bowl, until there is a little cloud of smoke: now, tell me, what will the gold-fishes say to that?" "I should imagine," said I, "That they would not know what to make of it." "By Jove! you're a Kantian;" said he, and with this and the like, he left me, vowing that [ 260 ] it was delightful to talk to so intelligent a person. The greatest compliment Wirgman ever received was from James Mill, who used to say he did not understand Kant. That such a man as Mill should think this worth saying is a feather in the cap of the jocose jeweler.

Some of my readers will stare at my supposing that Boswell may have been the first down-bringer of the word principles into common life; the best answer will be a prior instance of the word as true vernacular; it has never happened to me to notice one. Many words have very common uses which are not old. Take the following from Nichols (Anecd. ix. 263): "Lord Thurlow presents his best respects to Mr. and Mrs. Thicknesse, and assures them that he knows of no cause to complain of any part of Mr. Thicknesse's carriage; least of all the circumstance of sending the head to Ormond Street." Surely Mr. T. had lent Lord T. a satisfactory carriage with a movable head, and the above is a polite answer to inquiries. Not a bit of it! carriage is here conduct, and the head is a bust. The vehicles of the rich, at the time, were coaches, chariots, chaises, etc., never carriages, which were rather carts. Gibbon has the word for baggage-wagons. In Jane Austen's novels the word carriage is established.



John Walsh,[591] of Cork (1786-1847). This discoverer has had the honor of a biography from Professor Boole, who, at my request, collected information about him on the scene of his labors. It is in the Philosophical Magazine for November, 1851, and will, I hope, be transferred to some biographical collection where it may find a larger class of readers. It is the best biography of a single hero of the kind that I know. Mr. Walsh introduced himself to me, [ 261 ] as he did to many others, in the anterowlandian days of the Post-office; his unpaid letters were double, treble, &c. They contained his pamphlets, and cost their weight in silver: all have the name of the author, and all are in octavo or in quarto letter-form: most are in four pages, and all dated from Cork. I have the following by me:

The Geometric Base, 1825.—The theory of plane angles. 1827.—Three Letters to Dr. Francis Sadleir. 1838.—The invention of polar geometry. By Irelandus. 1839.—The theory of partial functions. Letter to Lord Brougham. 1839.—On the invention of polar geometry. 1839.—Letter to the Editor of the Edinburgh Review. 1840.—Irish Manufacture. A new method of tangents. 1841.—The normal diameter in curves. 1843.—Letter to Sir R. Peel. 1845.—[Hints that Government should compel the introduction of Walsh's Geometry into Universities.]—Solution of Equations of the higher orders. 1845.

Besides these, there is a Metalogia, and I know not how many others.

Mr. Boole,[592] who has taken the moral and social features of Walsh's delusions from the commiserating point of view, which makes ridicule out of place, has been obliged to treat Walsh as Scott's Alan Fairford treated his client Peter Peebles; namely, keep the scarecrow out of court while the case was argued. My plan requires me to bring him in: and when he comes in at the door, pity and sympathy fly out at the window. Let the reader remember that he was not an ignoramus in mathematics: he might have won his spurs if he could have first served as an esquire. Though so illiterate that even in Ireland he never picked up anything more Latin than Irelandus, he was a very pretty mathematician spoiled in the making by intense self-opinion.

This is part of a private letter to me at the back of a page of print: I had never addressed a word to him:

[ 262 ]

"There are no limits in mathematics, and those that assert there are, are infinite ruffians, ignorant, lying blackguards. There is no differential calculus, no Taylor's theorem, no calculus of variations, &c. in mathematics. There is no quackery whatever in mathematics; no % equal to anything. What sheer ignorant blackguardism that!

"In mechanics the parallelogram of forces is quackery, and is dangerous; for nothing is at rest, or in uniform, or in rectilinear motion, in the universe. Variable motion is an essential property of matter. Laplace's demonstration of the parallelogram of forces is a begging of the question; and the attempts of them all to show that the difference of twenty minutes between the sidereal and actual revolution of the earth round the sun arises from the tugging of the Sun and Moon at the pot-belly of the earth, without being sure even that the earth has a pot-belly at all, is perfect quackery. The said difference arising from and demonstrating the revolution of the Sun itself round some distant center."

In the letter to Lord Brougham we read as follows:

"I ask the Royal Society of London, I ask the Saxon crew of that crazy hulk, where is the dogma of their philosophic god now?... When the Royal Society of London, and the Academy of Sciences of Paris, shall have read this memorandum, how will they appear? Like two cur dogs in the paws of the noblest beast of the forest.... Just as this note was going to press, a volume lately published by you was put into my hands, wherein you attempt to defend the fluxions and Principia of Newton. Man! what are you about? You come forward now with your special pleading, and fraught with national prejudice, to defend, like the philosopher Grassi,[593] the persecutor of Galileo, principles [ 263 ] and reasoning which, unless you are actually insane, or an ignorant quack in mathematics, you know are mathematically false. What a moral lesson this for the students of the University of London from its head! Man! demonstrate corollary 3, in this note, by the lying dogma of Newton, or turn your thoughts to something you understand.

"Walsh Irelandus."

Mr. Walsh—honor to his memory—once had the consideration to save me postage by addressing a pamphlet under cover to a Member of Parliament, with an explanatory letter. In that letter he gives a candid opinion of himself:

(1838.) "Mr. Walsh takes leave to send the enclosed corrected copy to Mr. Hutton as one of the Council of the University of London, and to save postage for the Professor of Mathematics there. He will find in it geometry more deep and subtle, and at the same time more simple and elegant, than it was ever contemplated human genius could invent."

He then proceeds to set forth that a certain "tomfoolery lemma," with its "tomfoolery" superstructure, "never had existence outside the shallow brains of its inventor," Euclid. He then proceeds thus:

"The same spirit that animated those philosophers who sent Galileo to the Inquisition animates all the philosophers of the present day without exception. If anything can free them from the yoke of error, it is the [Walsh] problem of double tangence. But free them it will, how deeply soever they may be sunk into mental slavery—and God knows that is deeply enough; and they bear it with an admirable grace; for none bear slavery with a better grace than tyrants. The lads must adopt my theory.... It will be a sad reverse for all our great professors to be compelled to become schoolboys in their gray years. But the sore scratch is to be compelled, as they had before been compelled one thousand years ago, to have recourse to Ireland for instruction." [ 264 ]

The following "Impromptu" is no doubt by Walsh himself: he was more of a poet than of an astronomer:

"Through ages unfriended,
With sophistry blended,
Deep science in Chaos had slept;
Its limits were fettered,
Its voters unlettered,
Its students in movements but crept.
Till, despite of great foes,
Great Walsh first arose,
And with logical might did unravel
Those mazes of knowledge,
Ne'er known in a college,
Though sought for with unceasing travail.
With cheers we now hail him,
May success never fail him,
In Polar Geometrical mining;
Till his foes be as tamed
As his works are far-famed
For true philosophic refining."

Walsh's system is, that all mathematics and physics are wrong: there is hardly one proposition in Euclid which is demonstrated. His example ought to warn all who rely on their own evidence to their own success. He was not, properly speaking, insane; he only spoke his mind more freely than many others of his class. The poor fellow died in the Cork union, during the famine. He had lived a happy life, contemplating his own perfections, like Brahma on the lotus-leaf.[594]

[ 265 ]



The year 1825 brings me to about the middle of my Athenæum list: that is, so far as mere number of names mentioned is concerned. Freedom of opinion, beyond a doubt, is gaining ground, for good or for evil, according to what the speaker happens to think: admission of authority is no longer made in the old way. If we take soul-cure and body-cure, divinity and medicine, it is manifest that a change has come over us. Time was when it was enough that dose or dogma should be certified by "Il a été ordonné, Monsieur, il a été ordonné,"[595] as the apothecary said when he wanted to operate upon poor de Porceaugnac. Very much changed: but whether for good or for evil does not now matter; the question is, whether contempt of demonstration such as our paradoxers show has augmented with the rejection of dogmatic authority. It ought to be just the other way: for the worship of reason is the system on which, if we trust them, the deniers of guidance ground their plan of life. The following attempt at an experiment on this point is the best which I can make; and, so far as I know, the first that ever was made.

Say that my list of paradoxers divides in 1825: this of itself proves nothing, because so many of the earlier books are lost, or not likely to be come at. It would be a fearful rate of increase which would make the number of paradoxes since 1825 equal to the whole number before that date. Let us turn now to another collection of mine, arithmetical books, of which I have published a list. The two collections are similarly circumstanced as to new and old books; the paradoxes had no care given to the collection of either; the arithmetical books equal care to both. The list of arithmetical books, published in 1847, divides at 1735; the paradoxes, up to 1863, divide at 1825. If we take the process which is most against the distinction, and allow every year [ 266 ] from 1847 to 1863 to add a year to 1735, we should say that the arithmetical writers divide at 1751. This rough process may serve, with sufficient certainty, to show that the proportion of paradoxes to books of sober demonstration is on the increase; and probably, quite as much as the proportion of heterodoxes to books of orthodox adherence. So that divinity and medicine may say to geometry, Don't you sneer: if rationalism, homœopathy, and their congeners are on the rise among us, your enemies are increasing quite as fast. But geometry replies—Dear friends, content yourselves with the rational inference that the rise of heterodoxy within your pales is not conclusive against you, taken alone; for it rises at the same time within mine. Store within your garners the precious argument that you are not proved wrong by increase of dissent; because there is increase of dissent against exact science. But do not therefore 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 antipharmacopœal drenches, pills, and powders. Who ever heard of my asking the legislature to fine blundering circle-squarers? Remember that the D in dogma is the D in decay; but the D in demonstration is the D in durability.



I have known a medical man—a young one—who was seriously of the opinion that the country ought to be divided into medical parishes, with a practitioner appointed to each, and a penalty for calling in any but the incumbent curer. How should people know how to choose? The hair-dressers once petitioned Parliament for an act to compel people to wear wigs. My own opinion is of the opposite extreme, as in the following letter (Examiner, April 5, 1856); which, to my surprise, I saw reprinted in a medical journal, as a [ 267 ] plan not absolutely to be rejected. I am perfectly satisfied that it would greatly promote true medical orthodoxy, the predominance of well educated thinkers, and the development of their desirable differences.


"Sir. The Medical Bill and the medical question generally is one on which experience would teach, if people would be taught.

"The great soul question took three hundred years to settle: the little body question might be settled in thirty years, if the decisions in the former question were studied.

"Time was when the State believed, as honestly as ever it believed anything, that it might, could, and should find out the true doctrine for the poor ignorant community; to which, like a worthy honest state, it added would. Accordingly, by the assistance of the Church, which undertook the physic, the surgery, and the pharmacy of sound doctrine all by itself, it sent forth its legally qualified teachers into every parish, and woe to the man who called in any other. They burnt that man, they whipped him, they imprisoned him, they did everything but what was Christian to him, all for his soul's health and the amendment of his excesses.

"But men would not submit. To the argument that the State was a father to the ignorant, they replied that it was at best the ignorant father of an ignorant son, and that a blind man could find his way into a ditch without another blind man to help him. And when the State said—But here we have the Church, which knows all about it, the ignorant community declared that it had a right to judge that question, and that it would judge it. It also said that the Church was never one thing long, and that it progressed, on the whole, rather more slowly than the ignorant community.

"The end of it was, in this country, that every one who chose taught all who chose to let him teach, on condition only of an open and true registration. The State was [ 268 ] allowed to patronize one particular Church, so that no one need trouble himself to choose a pastor from the mere necessity of choosing. But every church is allowed its colleges, its studies, its diplomas; and every man is allowed his choice. There is no proof that our souls are worse off than in the sixteenth century; and, judging by fruits, there is much reason to hope they are better off.

"Now the little body question is a perfect parallel to the great soul question in all its circumstances. The only things in which the parallel fails are the following: Every one who believes in a future state sees that the soul question is incomparably more important than the body question, and every one can try the body question by experiment to a larger extent than the soul question. The proverb, which always has a spark of truth at the bottom, says that every man of forty is either a fool or a physician; but did even the proverb maker ever dare to say that every man is at any age either a fool or a fit teacher of religion?

"Common sense points out the following settlement of the medical question: and to this it will come sooner or later.

"Let every man who chooses—subject to one common law of manslaughter for all the crass cases—doctor the bodies of all who choose to trust him, and recover payment according to agreement in the courts of law. Provided always that every person practising should be registered at a moderate fee in a register to be republished every six months.

"Let the register give the name, address, and asserted qualification of each candidate—as licentiate, or doctor, or what not, of this or that college, hall, university, &c., home or foreign. Let it be competent to any man to describe himself as qualified by study in public schools without a diploma, or by private study, or even by intuition or divine inspiration, if he please. But whatever he holds his qualification to be, that let him declare. Let all qualification [ 269 ] which of its own nature admits of proof be proved, as by the diploma or certificate, &c., leaving things which cannot be proved, as asserted private study, intuition, inspiration, &c., to work their own way.

"Let it be highly penal to assert to the patient any qualification which is not in the register, and let the register be sold very cheap. Let the registrar give each registered practitioner a copy of the register in his own case; let any patient have the power to demand a sight of this copy; and let no money for attendance be recoverable in any case in which there has been false representation.

"Let any party in any suit have a right to produce what medical testimony he pleases. Let the medical witness produce his register, and let his evidence be for the jury, as is that of an engineer or a practitioner of any art which is not attested by diplomas.

"Let any man who practises without venturing to put his name on the register be liable to fine and imprisonment.

"The consequence would be that, as now, anybody who pleases might practise; for the medical world is well aware that there is no power of preventing what they call quacks from practising. But very different from what is now, every man who practises would be obliged to tell the whole world what his claim is, and would run a great risk if he dared to tell his patient in private anything different from what he had told the whole world.

"The consequence would be that a real education in anatomy, physiology, chemistry, surgery, and what is known of the thing called medicine, would acquire more importance than it now has.

"It is curious to see how completely the medical man of the nineteenth century squares with the priest of the sixteenth century. The clergy of all sects are now better divines and better men than they ever were. They have lost Bacon's reproach that they took a smaller measure of things than any other educated men; and the physicians are now [ 270 ] in this particular the rearguard of the learned world; though it may be true that the rear in our day is further on in the march than the van of Bacon's day. Nor will they ever recover the lost position until medicine is as free as religion.

"To this it must come. To this the public, which will decide for itself, has determined it shall come. To this the public has, in fact, brought it, but on a plan which it is not desirable to make permanent. We will be as free to take care of our bodies as of our souls and of our goods. This is the profession of all who sign as I do, and the practice of most of those who would not like the name



The motion of the Sun in the Ecliptic, proved to be uniform in a circular orbit ... with preliminary observations on the fallacy of the Solar System. By Bartholomew Prescott,[596] 1825, 8vo.

The author had published, in 1803, a Defence of the Divine System, which I never saw; also, On the inverted scheme of Copernicus. The above work is clever in its satire.



Manifesto of the Christian Evidence Society, established Nov. 12, 1824. Twenty-four plain questions to honest men.

These are two broadsides of August and November, 1826, signed by Robert Taylor,[597] A.B., Orator of the Christian Evidence Society. This gentleman was a clergyman, [ 271 ] and was convicted of blasphemy in 1827, for which he suffered imprisonment, and got the name of the Devil's Chaplain. The following are quotations:

"For the book of Revelation, there was no original Greek at all, but Erasmus wrote it himself in Switzerland, in the year 1516. Bishop Marsh,[598] vol. i. p. 320."—"Is not God the author of your reason? Can he then be the author of anything which is contrary to your reason? If reason be a sufficient guide, why should God give you any other? if it be not a sufficient guide, why has he given you that?"

I remember a votary of the Society being asked to substitute for reason "the right leg," and for guide "support," and to answer the two last questions: he said there must be a quibble, but he did not see what. It is pleasant to reflect that the argumentum à carcere[599] is obsolete. One great defect of it was that it did not go far enough: there should have been laws against subscriptions for blasphemers, against dealing at their shops, and against rich widows marrying them.

Had I taken in theology, I must have entered books against Christianity. I mention the above, and Paine's Age of Reason, simply because they are the only English modern works that ever came in my way without my asking for them. The three parts of the Age of Reason were published in Paris 1793, Paris 1795, and New York 1807. Carlile's[600] edition is of London, 1818, 8vo. It must be republished when the time comes, to show what stuff governments and clergy were afraid of at the beginning of this century. I should never have seen the book, if it [ 272 ] had not been prohibited: a bookseller put it under my nose with a fearful look round him; and I could do no less, in common curiosity, than buy a work which had been so complimented by church and state. And when I had read it, I said in my mind to church and state,—Confound you! you have taken me in worse than any reviewer I ever met with. I forget what I gave for the book, but I ought to have been able to claim compensation somewhere.


502 ^  On Bishop Wilkins see note 171 on page 100.

503 ^  Provision for a journey.

504 ^  See note 179.

505 ^  Thomas Bradwardine (1290-1349), known as Doctor Profundus, proctor and professor of theology at Oxford, and afterwards Chancellor of St. Paul's and confessor to Edward III. The English ascribed their success at Crécy to his prayers.

506 ^  He was consecrated Archbishop of Canterbury by the Pope at Avignon, July 13, 1349, and died of the plague at London in the same year.

507 ^  "One paltry little year."

508 ^  The title is carelessly copied, as is so frequently the case in catalogues, even of the Libri class. It should read: Arithmetica thome brauardini || Olivier Senant || Venum exponuntur ab Oliuiario senant in vico diui Jacobi sub signo beate Barbare sedente. The colophon reads: Explicit arithmetica speculatiua thōe brauardini bñ reuisa et correcta a Petro sanchez Ciruelo aragonensi mathematicas legēte Parisius, īpressa per Thomā anguelart. There were Paris editions of 1495, 1496, 1498, s. a. (c. 1500), 1502, 1504, 1505, s. a. (c. 1510), 1512, 1530, a Valencia edition of 1503, two Wittenberg editions of 1534 and 1536, and doubtless several others. The work is not "very rare," although of course no works of that period are common. See the editor's Rara Arithmetica, page 61.

509 ^  This is his Tractatus de proportionibus, Paris, 1495; Venice, 1505; Vienna, 1515, with other editions.

510 ^  The colophon of the 1495 edition reads: Et sic explicit Geometria Thome brauardini cū tractatulo de quadratura circuli bene reuisa a Petro sanchez ciruelo: operaqz Guidonis mercatoris diligētissime impresse parisiº in cāpo gaillardi. Anno dñi. 1495. die. 20, maij.

This Petro Ciruelo was born in Arragon, and died in 1560 at Salamanca. He studied mathematics and philosophy at Paris, and took the doctor's degree there. He taught at the University of Alcalà and became canon of the Cathedral at Salamanca. Besides his editions of Bradwardine he wrote several works, among them the Liber arithmeticae practicae qui dicitur algorithmus (Paris, 1495) and the Cursus quatuor mathematicarum artium liberalium (Alcalà, 1516).

511 ^  Star polygons, a subject of considerable study in the later Middle Ages. See note 35.

512 ^  "A new theory that adds lustre to the fourteenth century."

513 ^  There is nothing in the edition of 1495 that leads to this conclusion.

514 ^  The full title is: Nouvelle théorie des parallèles, avec un appendice contenant la manière de perfectionner la théorie des parallèles de A. M. Legendre. The author had no standing as a scientist.

515 ^  Adrien Marie Legendre (1752-1833) was one of the great mathematicians of the opening of the nineteenth century. His Eléments de géométrie (1794) had great influence on the geometry of the United States. His Essai sur la théorie des nombres (1798) is one of the classics upon the subject. The work to which Kircher refers is the Nouvelle théorie des parallèles (1803), in which the attempt is made to avoid using Euclid's postulate of parallels, the result being merely the substitution of another assumption that was even more unsatisfactory. The best presentations of the general theory are W. B. Frankland's Theories of Parallelism, Cambridge, 1910, and Engel and Stäckel's Die Theorie der Parallellinien von Euclid bis auf Gauss, Leipsic, 1895. Legendre published a second work on the theory the year of his death, Réflexions sur ... la théorie des parallèles (1833). His other works include the Nouvelles méthodes pour la détermination des orbites des comètes (1805), in which he uses the method of least squares; the Traité des fonctions elliptiques et des intégrales (1827-1832), and the Exercises de calcul intégral (1811, 1816, 1817).

516 ^  Johann Joseph Ignatz von Hoffmann (1777-1866), professor of mathematics at Aschaffenburg, published his Theorie der Parallellinien in 1801. He supplemented this by his Kritik der Parallelen-Theorie in 1807, and his Das eilfte Axiom der Elemente des Euclidis neu bewiesen in 1859. He wrote other works on mathematics, but none of his contributions was of any importance.

517 ^  Johann Karl Friedrich Hauff (1766-1846) was successively professor of mathematics at Marburg, director of the polytechnic school at Augsburg, professor at the Gymnasium at Cologne, and professor of mathematics and physics at Ghent. The work to which Kircher refers is his memoirs on the Euclidean Theorie der Parallelen in Hindenburg's Archiv, vol. III (1799), an article of no merit in the general theory.

518 ^  Wenceslaus Johann Gustav Karsten (1732-1787) was professor of logic at Rostock (1758) and Butzow (1760), and later became professor of mathematics and physics at Halle. His work on parallels is the Versuch einer völlig berichtigten Theorie der Parallellinien (1779). He also wrote a work entitled Anfangsgründe der mathematischen Wissenschaften (1780), but neither of these works was more than mediocre.

519 ^  Johann Christoph Schwab (not Schwal) was born in 1743 and died in 1821. He was professor at the Karlsschule at Stuttgart. De Morgan's wish was met, for the catalogues give "c. fig. 8," so that it evidently had eight illustrations instead of eight volumes. He wrote several other works on the principles of geometry, none of any importance.

520 ^  Gaetano Rossi of Catanzaro. This was the libretto writer (1772-1855), and hence the imperfections of the work can better be condoned. De Morgan should have given a little more of the title: Solusione esatta e regolare ... del ... problema della quadratura del circolo. There was a second edition, London, 1805.

521 ^  This identifies Rossi, for Joséphine Grassini (1773-1850) was a well-known contralto, prima donna at Napoleon's court opera.

522 ^  William Spence (1783-1860) was an entomologist and economist of some standing, a fellow of the Royal Society, and one of the founders of the Entomological Society of London. The work here mentioned was a popular one, the first edition appearing in 1807, and four editions being justified in a single year. He also wrote Agriculture the Source of Britain's Wealth (1808) and Objections against the Corn Bill refuted (1815), besides a work in four volumes on entomology (1815-1826) in collaboration with William Kirby.

523 ^  "That used to be so, but we have changed all that."

524 ^  "Meet the coming disease."

525 ^  George Douglas (or Douglass) was a Scotch writer. He got out an edition of the Elements of Euclid in 1776, with an appendix on trigonometry and a set of tables. His work on Mathematical Tables appeared in 1809, and his Art of Drawing in Perspective, from mathematical principles, in 1810.

526 ^  See note 443.

527 ^  John Playfair (1748-1848) was professor of mathematics (1785) and natural philosophy (1805) at the University of Edinburgh. His Elements of Geometry went through many editions.

528 ^  "Tell Apella" was an expression current in classical Rome to indicate incredulity and to show the contempt in which the Jew was held. Horace says: Credat Judæus Apella, "Let Apella the Jew believe it." Our "Tell it to the marines," is a similar phrase.

529 ^  As De Morgan says two lines later, "No mistake is more common than the natural one of imagining that the"—University of Virginia is at Richmond. The fact is that it is not there, and that it did not exist in 1810. It was not chartered until 1819, and was not opened until 1825, and then at Charlottesville. The act establishing the Central College, from which the University of Virginia developed, was passed in 1816. The Jean Wood to whom De Morgan refers was one John Wood who was born about 1775 in Scotland and who emigrated to the United States in 1800. He published a History of the Administration of J. Adams (New York, 1802) that was suppressed by Aaron Burr. This act called forth two works, a Narrative of the Suppression, by Col. Burr, of the 'History of the Administration of John Adams' (1802), in which Wood was sustained; and the Antidote to John Wood's Poison (1802), in which he was attacked. The work referred to in the "printed circular" may have been the New theory of the diurnal rotation of the earth (Richmond, Va., 1809). Wood spent the last years of his life in Richmond, Va., making county maps. He died there in 1822. A careful search through works relating to the University of Virginia fails to show that Wood had any connection with it.

530 ^  There seems to be nothing to add to Dobson's biography beyond what De Morgan has so deliciously set forth.

531 ^  "Give to each man his due."

532 ^  Hester Lynch Salusbury (1741-1821), the friend of Dr. Johnson, married Henry Thrale (1763), a brewer, who died in 1781. She then married Gabriel Piozzi (1784), an Italian musician. Her Anecdotes of the late Samuel Johnson (1786) and Letters to and from Samuel Johnson (1788) are well known. She also wrote numerous essays and poems.

533 ^  Samuel Pike (c. 1717-1773) was an independent minister, with a chapel in London and a theological school in his house. He later became a disciple of Robert Sandeman and left the Independents for the Sandemanian church (1765). The Philosophia Sacra was first published at London in 1753. De Morgan here cites the second edition.

534 ^  Pike had been dead over forty years when Kittle published this second edition. Kittle had already published a couple of works: King Solomon's portraiture of Old Age (Edinburgh, 1813), and Critical and Practical Lectures on the Apocalyptical Epistles to the Seven Churches of Asia Minor (London, 1814).

535 ^  See note 334.

536 ^  William Stukely (1687-1765) was a fellow of the Royal Society and of the College of Physicians and Surgeons. He afterwards (1729) entered the Church. He was prominent as an antiquary, especially in the study of the Roman and Druidic remains of Great Britain. He was the author of numerous works, chiefly on paleography.

537 ^  William Jones (1726-1800), who should not be confused with his namesake who is mentioned in note 281 on page 135. He was a lifelong friend of Bishop Horne, and his vicarage at Nayland was a meeting place of an influential group of High Churchmen. Besides the Physiological Disquisitions (1781) he wrote The Catholic Doctrine of the Trinity (1756) and The Grand Analogy (1793).

538 ^  Robert Spearman (1703-1761) was a pupil of John Hutchinson, and not only edited his works but wrote his life. He wrote a work against the Newtonian physics, entitled An Enquiry after Philosophy and Theology (Edinburgh, 1755), besides the Letters to a Friend concerning the Septuagint Translation (Edinburgh, 1759) to which De Morgan refers.

539 ^  A writer of no importance, at least in the minds of British biographers.

540 ^  Alexander Catcott (1725-1779), a theologian and geologist, wrote not only a work on the creation (1756) but a Treatise on the Deluge (1761, with a second edition in 1768). Sir Charles Lyell considered the latter work a valuable contribution to geology.

541 ^  James Robertson (1714-1795), professor of Hebrew at the University of Edinburgh. Probably De Morgan refers to his Grammatica Linguae Hebrææ (Edinburgh, 1758; with a second edition in 1783). He also wrote Clavis Pentateuchi (1770).

542 ^  Benjamin Holloway (c. 1691-1759), a geologist and theologian. He translated Woodward's Naturalis Historia Telluris, and was introduced by Woodward to Hutchinson. The work referred to by De Morgan appeared at Oxford in two volumes in 1754.

543 ^  His work was The Christian plan exhibited in the interpretation of Elohim: with observations upon a few other matters relative to the same subject, Oxford, 1752, with a second edition in 1755.

544 ^  Duncan Forbes (1685-1747) studied Oriental languages and Civil law at Leyden. He was Lord President of the Court of Sessions (1737). He wrote a number of theological works.

545 ^  Should be 1756.

546 ^  Edward Henry Bickersteth (1825-1906), bishop of Exeter (1885-1900); published The Rock of Ages; or scripture testimony to the one Eternal Godhead of the Father, and of the Son, and of the Holy Ghost at Hampstead in 1859. A second edition appeared at London in 1860.

547 ^  Thomas Sadler (1822-1891) took his Ph.D. at Erlangen in 1844, and became a Unitarian minister at Hampstead, where Bickersteth's work was published. Besides writing the Gloria Patri (1859), he edited Crabb Robinson's Diaries.

548 ^  This was his Virgil's Bucolics and the two first Satyrs of Juvenal, 1634.

549 ^  Possibly in his Twelve Questions or Arguments drawn out of Scripture, wherein the commonly received Opinion touching the Deity of the Holy Spirit is clearly and fully refuted, 1647. This was his first heretical work, and it was followed by a number of others that were written during the intervals in which the Puritan parliament allowed him out of prison. It was burned by the hangman as blasphemous. Biddle finally died in prison, unrepentant to the last.

550 ^  The first edition of the anonymous Ἁιρεσεων ἀναστασις (by Vicars?) appeared in 1805.

551 ^  Possibly by Thomas Pearne (c. 1753-1827), a fellow of St. Peter's College, Cambridge, and a Unitarian minister.

552 ^  Thomas Wentworth, Earl of Strafford, was borne in London in 1593, and was executed there in 1641. He was privy councilor to Charles I, and was Lord Deputy of Ireland. On account of his repressive measures to uphold the absolute power of the king he was impeached by the Long Parliament and was executed for treason. The essence of his defence is in the sentence quoted by De Morgan, to which Pym replied that taken as a whole, the acts tended to show an intention to change the government, and this was in itself treason.

553 ^  The name assumed by a writer who professed to give a mathematical explanation of the Trinity, see farther on.—S. E. De M.

554 ^  Sabellius (fl. 230 A.D.) was an early Christian of Libyan origin. He taught that Father, Son, and Holy Spirit were different names for the same person.

555 ^  Sir Richard Phillips was born in London in 1767 (not 1768 as stated above), and died there in 1840. He was a bookseller and printer in Leicester, where he also edited a radical newspaper. He went to London to live in 1795 and started the Monthly Magazine there in 1796. Besides the works mentioned by De Morgan he wrote on law and economics.

556 ^  It was really eighteen months.

557 ^  While he was made sheriff in 1807 he was not knighted until the following year.

558 ^  James Mitchell (c. 1786-1844) was a London actuary, or rather a Scotch actuary living a good part of his life in London. Besides the work mentioned he compiled a Dictionary of Chemistry, Mineralogy, and Geology (1823), and wrote On the Plurality of Worlds (1813) and The Elements of Astronomy (1820).

559 ^  Richarda Smith, wife of Sir George Biddell Airy (see note 129) the astronomer. In 1835 Sir Robert Peel offered a pension of £300 a year to Airy, who requested that it be settled on his wife.

560 ^  Mary Fairfax (1780-1872) married as her second husband Dr. William Somerville. In 1826 she presented to the Royal Society a paper on The Magnetic Properties of the Violet Rays of the Solar Spectrum, which attracted much attention. It was for her Mechanism of the Heavens (1831), a popular translation of Laplace's Mécanique Céleste, that she was pensioned.

561 ^  Dominique François Jean Arago (1786-1853) the celebrated French astronomer and physicist.

562 ^  For there is a well-known series

1 + \tfrac{1}{2}^2 + \tfrac{1}{3}^2 + ... = \frac{\pi^2}{6}.

If, therefore, the given series equals 1, we have

2 = \tfrac{1}{6} \pi^2
or \pi^2 = 12\!,
whence \pi = 2 \sqrt{3}.

But c = \pi d\!, and twice the diagonal of a cube on the diameter is 2d \sqrt{3}.

563 ^  There was a second edition in 1821.

564 ^  London, 1830.

565 ^  He was a resident of Chatham, and seems to have published no other works.

566 ^  Richard Whately (1787-1863) was, as a child, a calculating prodigy (see note 132), but lost the power as is usually the case with well-balanced minds. He was a fellow of Oriel College, Oxford, and in 1825 became principal of St. Alban Hall. He was a friend of Newman, Keble, and others who were interested in the religious questions of the day. He became archbishop of Dublin in 1831. He was for a long time known to students through his Logic (1826) and Rhetoric (1828).

567 ^  William King, D.C.L. (1663-1712), student at Christ Church, Oxford, and celebrated as a wit and scholar. His Dialogues of the Dead (1699) is a satirical attack on Bentley.

568 ^  Thomas Ebrington (1760-1835) was a fellow of Trinity College, Dublin, and taught divinity, mathematics, and natural philosophy there. He became provost of the college in 1811, bishop of Limerick in 1820, and bishop of Leighlin and Ferns in 1822. His edition of Euclid was reprinted a dozen times. The Reply to John Search's Considerations on the Law of Libel appeared at Dublin in 1834.

569 ^  Joseph Blanco White (1775-1841) was the son of an Irishman living in Spain. He was born at Seville and studied for orders there, being ordained priest in 1800. He lost his faith in the Roman Catholic Church, and gave up the ministry, escaping to England at the time of the French invasion. At London he edited Español, a patriotic journal extensively circulated in Spain, and for this service he was pensioned after the expulsion of the French. He then studied at Oriel College, Oxford, and became intimate with men like Whately, Newman, and Keble. In 1835 he became a Unitarian. Among his theological writings is his Evidences against Catholicism (1825). The "rejoinder" to which De Morgan refers consisted of two letters: The law of anti-religious Libel reconsidered (Dublin, 1834) and An Answer to some Friendly Remarks on "The Law of Anti-Religious Libel Reconsidered" (Dublin, 1834).

570 ^  The work was translated from the French.

571 ^  J. Hoëné Wronski (1778-1853) served, while yet a mere boy, as an artillery officer in Kosciusko's army (1791-1794). He was imprisoned after the battle of Maciejowice. He afterwards lived in Germany, and (after 1810) in Paris. For the bibliography of his works see S. Dickstein's article in the Bibliotheca Mathematica, vol. VI (2), page 48.

572 ^  Perhaps referring to his Introduction à la philosophie des mathématiques (1811).

573 ^  Read "equation of the."

574 ^  Thomas Young (1773-1829), physician and physicist, sometimes called the founder of physiological optics. He seems to have initiated the theory of color blindness that was later developed by Helmholtz. The attack referred to was because of his connection with the Board of Longitude, he having been made (1818) superintendent of the Nautical Almanac and secretary of the Board. He opposed introducing into the Nautical Almanac anything not immediately useful to navigation, and this antagonized many scientists.

575 ^  Isaac Milner (1750-1820) was professor of natural philosophy at Cambridge (1783) and later became, as De Morgan states, president of Queens' College (1788). In 1791 he became dean of Carlisle, and in 1798 Lucasian professor of mathematics. His chief interest was in chemistry and physics, but he contributed nothing of importance to these sciences or to mathematics.

576 ^  Thomas Perronet Thompson (1783-1869), fellow of Queens' College, Cambridge, saw service in Spain and India, but after 1822 lived in England. He became major general in 1854, and general in 1868. Besides some works on economics and politics he wrote a Geometry without Axioms (1830) that De Morgan includes later on in his Budget. In it Thompson endeavored to prove the parallel postulate.

577 ^  De Morgan's father-in-law. See note 441.

578 ^  Johann Friedrich Herbart (1776-1841), successor of Kant as professor of philosophy at Königsberg (1809-1833), where he established a school of pedagogy. From 1833 until his death he was professor of philosophy at Göttingen. The title of the pamphlet is: De Attentionis mensura causisque primariis. Psychologiae principia statica et mechanica exemplo illustraturus.... Regiomonti,... 1822. The formulas in question are given on pages 15 and 17, and De Morgan has omitted the preliminary steps, which are, for the first one:

\beta (\phi - z) \delta t = \delta z\!
unde \beta t = \frac{\mathrm{Const}}{(\phi - z)}.
Pro t = 0\! etiam z = 0\!; hinc \beta t = \log \frac{\phi} {(\phi - z)}.
z = \phi \left(1 - \epsilon^{-\beta t}\right);
et   \frac{\delta z}{\delta t} = \beta\phi\epsilon^{-\beta t}

These are, however, quite elementary as compared with other portions of the theory.

579 ^  See note 371.

580 ^  William Law (1686-1761) was a clergyman, a fellow of Emanuel College, Cambridge, and in later life a convert to Behmen's philosophy. He was so free in his charities that the village in which he lived became so infested by beggars that he was urged by the citizens to leave. He wrote A serious call to a devout and holy life (1728).

581 ^  He was a curate at Cheshunt, and wrote the Spiritual voice to the Christian Church and to the Jews (London, 1760), A second warning to the world by the Spirit of Prophecy (London, 1760), and Signs of the Times; or a Voice to Babylon (London, 1773).

582 ^  His real name was Thomas Vaughan (1622-1666). He was a fellow of Jesus College, Oxford, taking orders, but was deprived of his living on account of drunkenness. He became a mystic philosopher and gave attention to alchemy. His works had a large circulation, particularly on the continent. He wrote Magia Adamica (London, 1650), Euphrates; or the Waters of the East (London, 1655), and The Chymist's key to shut, and to open; or the True Doctrine of Corruption and Generation (London, 1657).

583 ^  Emanuel Swedenborg, or Svedberg (1688-1772) the mystic. It is not commonly known to mathematicians that he was one of their guild, but he wrote on both mathematics and chemistry. Among his works are the Regelkonst eller algebra (Upsala, 1718) and the Methodus nova inveniendi longitudines locorum, terra marique, ope lunae (Amsterdam, 1721, 1727, and 1766). After 1747 he devoted his attention to mystic philosophy.

584 ^  Pierre Simon Laplace (1749-1827), whose Exposition du système du monde (1796) and Traité de mécanique celeste (1799) are well known.

585 ^  See note 117.

586 ^  John Dalton (1766-1844), who taught mathematics and physics at New College, Manchester (1793-1799) and was the first to state the law of the expansion of gases known by his name and that of Gay-Lussac. His New system of Chemical Philosophy (Vol. I, pt. i, 1808; pt. ii, 1810; vol. II, 1827) sets forth his atomic theory.

587 ^  Howison was a poet and philosopher. He lived in Edinburgh and was a friend of Sir Walter Scott. This work appeared in 1822.

588 ^  He was a shoemaker, born about 1765 at Haddiscoe, and his "astro-historical" lectures at Norwich attracted a good deal of attention at one time. He traced all geologic changes to differences in the inclination of the earth's axis to the plane of its orbit. Of the works mentioned by De Morgan the first appeared at Norwich in 1822-1823, and there was a second edition in 1824. The second appeared in 1824-1825. The fourth was Urania's Key to the Revelation; or the analyzation of the writings of the Jews..., and was first published at Norwich in 1823, there being a second edition at London in 1833. His books were evidently not a financial success, for Mackey died in an almshouse at Norwich.

589 ^  Godfrey Higgins (1773-1833), the archeologist, was interested in the history of religious beliefs and in practical sociology. He wrote Horae Sabbaticae (1826), The Celtic Druids (1827 and 1829), and Anacalypsis, an attempt to draw aside the veil of the Saitic Isis; or an Inquiry into the Origin of Languages, Nations, and Religions (posthumously published, 1836), and other works. See also ON GODFREY HIGGINS.

590 ^  The work also appeared in French. Wirgman wrote, or at least began, two other works: Divarication of the New Testament into Doctrine and History; part I, The Four Gospels (London, 1830), and Mental Philosophy; part I, Grammar of the five senses; being the first step to infant education (London, 1838).

591 ^  He was born at Shandrum, County Limerick, and supported himself by teaching writing and arithmetic. He died in an almshouse at Cork.

592 ^  George Boole (1815-1864), professor of mathematics at Queens' College, Cork. His Laws of Thought (1854) was the first work on the algebra of logic.

593 ^  Oratio Grassi (1582-1654), the Jesuit who became famous for his controversy with Galileo over the theory of comets. Galileo ridiculed him in Il Saggiatore, although according to the modern view Grassi was the more nearly right. It is said that the latter's resentment led to the persecution of Galileo.

594 ^  De Morgan might have found much else for his satire in the letters of Walsh. He sought, in his Theory of Partial Functions, to substitute "partial equations" for the differential calculus. In his diary there is an entry: "Discovered the general solution of numerical equations of the fifth degree at 114 Evergreen Street, at the Cross of Evergreen, Cork, at nine o'clock in the forenoon of July 7th, 1844; exactly twenty-two years after the invention of the Geometry of Partial Equations, and the expulsion of the differential calculus from Mathematical Science."

595 ^  "It has been ordered, sir, it has been ordered."

596 ^  Bartholomew Prescot was a Liverpool accountant. De Morgan gives this correct spelling on page 278. He died after 1849. His Inverted Scheme of Copernicus appeared in Liverpool in 1822.

597 ^  Robert Taylor (1784-1844) had many more ups and downs than De Morgan mentions. He was a priest of the Church of England, but resigned his parish in 1818 after preaching against Christianity. He soon recanted and took another parish, but was dismissed by the Bishop almost immediately on the ground of heresy. As stated in the text, he was convicted of blasphemy in 1827 and was sentenced to a year's imprisonment, and again for two years on the same charge in 1831. He then married a woman who was rich in money and in years, and was thereupon sued for breach of promise by another woman. To escape paying the judgment that was rendered against him he fled to Tours where he took up surgery.

598 ^  Herbert Marsh, Bishop of Peterborough. See note 449.

599 ^  "Argument from the prison."

600 ^  Richard Carlile (1790-1843), one of the leading radicals of his time. He published Hone's parodies (see note 250) after they had been suppressed, and an edition of Thomas Paine (1818). He was repeatedly imprisoned, serving nine years in all. His continued conflict with the authorities proved a good advertisement for his bookshop.