Volume I (part 2)

We shall see how Revilo 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. 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:

"Long life to the moon, for a dear noble cratur,

Which serves us for lamplight all night in the dark,

While the sun only shines in the day, which by natur,

Wants no light at all, as ye all may remark."

SIR RICHARD PHILLIPS.

Sir Richard Phillips (born 1768) was conspicuous in 1793, when he was sentenced to a year's imprisonment for selling Paine's Rights of Man; and again when, in 1807, 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 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 pension, and in Mrs. Somerville's. In 1836, he 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, in 1835, will give posterity as good a notion as she will probably need:

"Even the present year has afforded EVER-MEMORABLE examples, paralleled only by that of the Romish Conclave which persecuted Galileo. Policy has adopted that maxim of Machiavel which teaches that it is more prudent to reward partisans than to persecute opponents. Hence, a 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 of false assumptions, and degrading superstitions will soon tumble in ruins."

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

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.

Protest against the prevailing principles of natural philosophy, with the development of a common sense system (no date, 8vo, pp. 16).

Four dialogues between an Oxford Tutor and a disciple of the common-sense philosophy, relative to the proximate causes of material phenomena. 8vo, 1824.

A century of original aphorisms on the proximate causes of the phenomena of nature, 1835, 12mo.

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

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

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

WHATELY'S FAMOUS PARADOX.

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

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

The idea of the satire is not new. Dr. King, in the dispute on the genuineness of Phalaris, proved with humor that Bentley did not write his own dissertation. An attempt has lately been made, for the honor of Moses, to prove, 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 as S. N., with a rejoinder by Blanco White. These circumstances increase the probability that Whately was written against and for.

VOLTAIRE A CHRISTIAN.

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

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

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

WRONSKI ON THE LONGITUDE PROBLEM.

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

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

Fx = A0Ω0 + A1Ω1 + A2Ω2 + A3Ω3 + &c.

which he did not explain, though there is meaning to it in the quartos. At another time he was proposing the general solution of the fifth degree by help of 625 independent equations of one form and 125 of another. The first separate memoir from any Transactions that 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.

DR. MILNER'S PARADOXES.

1820. In this year died Dr. Isaac Milner, President of Queens' College, Cambridge, one of the class of rational paradoxers. Under this name I include all who, in private life, and in matters which concern themselves, take their own course, and suit their own notions, no matter what other people may think of them. These men will put things to uses they were never intended for, to the great distress and disgust of their gregarious friends. I am one of the class, and I could write a little book of cases in which I have incurred absolute reproach for not "doing as other people do." I will name two of my atrocities: I took one of those butter-dishes which have for a top a dome with holes in it, which is turned inward, out of reach of accident, when not in use. Turning the dome inwards, I filled the dish with water, and put a sponge in the dome: the holes let it fill with water, and I had a penwiper, always moist, and worth its price five times over. "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. He spread a thick block of putty over a wooden chair and sat in it until it had taken a ceroplast copy of the proper seat. This he gave to a carpenter to be imitated in wood. One of the few now living who knew him—my friend, General Perronet Thompson—answers for the wood, which was shown him by Milner himself; but he does not vouch for the material being putty, which was in the story told me at Cambridge; William Frend also 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.

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

HERBART'S MATHEMATICAL PSYCHOLOGY.

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

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

z = φ (1 - ε-βt)

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 = πφβ/(1 - β)ε-βt + Cε-t

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

ON THE WHIZGIG.

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

The toy called the whizgig will be remembered by many. The writer is a follower of Jacob Behmen, William Law, Richard Clarke, and Eugenius Philalethes. 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 by Laplace, and Pythagoras by Copernicus, and Epicurus by Dalton, &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.

SOME MYTHOLOGICAL PARADOXES.

A Grammar of infinite forms; or the mathematical elements of ancient philosophy and mythology. By Wm. Howison. 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, 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 evidence of being able to read a line in any language but his own, or to spell that correctly. He was an uneducated Godfrey Higgins. A few extracts will put this in a strong light: one for history of science, one for astronomy, and one for 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 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.

A KANTESIAN JEWELER.

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

Mr. Wirgman's mind was somewhat attuned to psychology; but he was cracky and vagarious. He had been a fashionable jeweler in St. James's Street, no doubt the son or grandson of Wirgman at "the well-known toy-shop in St. James's Street," where Sam Johnson smartened himself with silver buckles. (Boswell, 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 it was delightful to talk to so intelligent a person. The greatest compliment Wirgman ever received was from James Mill, who used to say he did not understand Kant. That such a man as Mill should think this worth saying is a feather in the cap of the jocose jeweler.

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

WALSH'S DELUSIONS.

John Walsh, 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, 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, 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:

"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, the persecutor of Galileo, principles 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."

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.

GROWTH OF FREEDOM OF OPINION.

The year 1825 brings me to about the middle of my Athenæum list: that is, so far as mere number of names mentioned is concerned. Freedom of opinion, beyond a doubt, is gaining ground, for good or for evil, according to what the speaker happens to think: admission of authority is no longer made in the old way. If we take soul-cure and body-cure, divinity and medicine, it is manifest that a change has come over us. Time was when it was enough that dose or dogma should be certified by "Il a été ordonné, Monsieur, il a été ordonné," 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 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.

THE STATUS OF MEDICINE.

I have known a medical man—a young one—who was seriously of the opinion that the country ought to be divided into medical parishes, with a practitioner appointed to each, and a penalty for calling in any but the incumbent curer. How should people know how to choose? The hair-dressers once petitioned Parliament for an act to compel people to wear wigs. My own opinion is of the opposite extreme, as in the following letter (Examiner, April 5, 1856); which, to my surprise, I saw reprinted in a medical journal, as a 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 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 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 in this particular the rearguard of the learned world; though it may be true that the rear in our day is further on in the march than the van of Bacon's day. Nor will they ever recover the lost position until medicine is as free as religion.

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

"Heteropath."

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

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

THE CHRISTIAN EVIDENCE SOCIETY.

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

These are two broadsides of August and November, 1826, signed by Robert Taylor, A.B., Orator of the Christian Evidence Society. This gentleman was a clergyman, 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, 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 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 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 had not been prohibited: a bookseller put it under my nose with a fearful look round him; and I could do no less, in common curiosity, than buy a work which had been so complimented by church and state. And when I had read it, I said in my mind to church and state,—Confound you! you have taken me in worse than any reviewer I ever met with. I forget what I gave for the book, but I ought to have been able to claim compensation somewhere.

THE CABBALA.

Cabbala Algebraica. Auctore Gul. Lud. Christmann. Stuttgard, 1827, 4to.

Eighty closely printed pages of an attempt to solve equations of every degree, which has a process called by the author cabbala. An anonymous correspondent spells cabbala as follows, χαββαλλ, and makes 666 out of its letters. This gentleman has sent me since my Budget commenced, a little heap of satirical communications, each having a 666 or two; for instance, alluding to my remarks on the spelling of chemistry, he finds the fated number in χιμεια. With these are challenges to explain them, and hints about the end of the world. All these letters have different fantastic seals; one of them with the legend "keep your temper,"—another bearing "bank token five pence." The only signature is a triangle with a little circle in it, which I interpret to mean that the writer confesses himself to be the round man stuck in the three-cornered hole, to be explained as in Sydney Smith's joke.

There is a kind of Cabbala Alphabetica which the investigators of the numerals in words would do well to take up: it is the formation of sentences which contain all the letters of the alphabet, and each only once. No one has done it with v and j treated as consonants; but you and I can do it. Dr. Whewell and I amused ourselves, some years ago, with attempts. He could not make sense, though he joined words: he gave me

Phiz, styx, wrong, buck, flame, quid.

I gave him the following, which he agreed was "admirable sense": I certainly think the words would never have come together except in this way:

I, quartz pyx, who fling muck beds.

I long thought that no human being could say this under any circumstances. At last I happened to be reading a religious writer—as he thought himself—who threw aspersions on his opponents thick and threefold. Heyday! came into my head, this fellow flings muck beds; he must be a quartz pyx. And then I remembered that a pyx is a sacred vessel, and quartz is a hard stone, as hard as the heart of a religious foe-curser. So that the line is the motto of the ferocious sectarian, who turns his religious vessels into mudholders, for the benefit of those who will not see what he sees.

I can find no circumstances for the following, which I received from another:

Fritz! quick! land! hew gypsum box.

From other quarters I have the following:

Dumpy quiz! whirl back fogs next.

This might be said in time of haze to the queer little figure in the Dutch weather-toy, which comes out or goes in with the change in the atmosphere. Again,

Export my fund! Quiz black whigs.

This Squire Western might have said, who was always afraid of the whigs sending the sinking-fund over to Hanover. But the following is the best: it is good advice to a young man, very well expressed under the circumstances:

Get nymph; quiz sad brow; fix luck.

Which in more sober English would be, Marry; be cheerful; watch your business. There is more edification, more religion in this than in all the 666-interpretations put together.

Such things would make excellent writing copies, for they secure attention to every letter; v and j might be placed at the end.

ON GODFREY HIGGINS.

The Celtic Druids. By Godfrey Higgins, Esq. of Skellow Grange, near Doncaster. London, 1827, 4to.

Anacalypsis, or an attempt to draw aside the veil of the Saitic Isis: or an inquiry into the origin of languages, nations, and religions. By Godfrey Higgins, &c..., London, 1836, 2 vols. 4to.

The first work had an additional preface and a new index in 1829. Possibly, in future time, will be found bound up with copies of the second work two sheets which Mr. Higgins circulated among his friends in 1831: the first a "Recapitulation," the second "Book vi. ch. 1."

The system of these works is that—

"The Buddhists of Upper India (of whom the Phenician Canaanite, Melchizedek, was a priest), who built the Pyramids, Stonehenge, Carnac, &c. will be shown to have founded all the ancient mythologies of the world, which, however varied and corrupted in recent times, were originally one, and that one founded on principles sublime, beautiful, and true."

These works contain an immense quantity of learning, very honestly put together. I presume the enormous number of facts, and the goodness of the index, to be the reasons why the Anacalypsis found a permanent place in the old reading-room of the British Museum, even before the change which greatly increased the number of books left free to the reader in that room.

Mr. Higgins, whom I knew well in the last six years of his life, and respected as a good, learned, and (in his own way) pious man, was thoroughly and completely the man of a system. He had that sort of mental connection with his theory that made his statements of his authorities trustworthy: for, besides perfect integrity, he had no bias towards alteration of facts: he saw his system in the way the fact was presented to him by his authority, be that what it might.

He was very sure of a fact which he got from any of his authorities: nothing could shake him. Imagine a conversation between him and an Indian officer who had paid long attention to Hindoo antiquities and their remains: a third person was present, ego qui scribo. G. H. "You know that in the temples of I-forget-who the Ceres is always sculptured precisely as in Greece." Col. ——, "I really do not remember it, and I have seen most of these temples." G. H. "It is so, I assure you, especially at I-forget-where." Col. ——, "Well, I am sure! I was encamped for six weeks at the gate of that very temple, and, except a little shooting, had nothing to do but to examine its details, which I did, day after day, and I found nothing of the kind." It was of no use at all.

Godfrey Higgins began life by exposing and conquering, at the expense of two years of his studies, some shocking abuses which existed in the York Lunatic Asylum. This was a proceeding which called much attention to the treatment of the insane, and produced much good effect. He was very resolute and energetic. The magistracy of his time had such scruples about using the severity of law to people of such station as well-to-do farmers, &c.: they would allow a great deal of resistance, and endeavor to mollify the rebels into obedience. A young farmer flatly refused to pay under an order of affiliation made upon him by Godfrey Higgins. He was duly warned; and persisted: he shortly found himself in gaol. He went there sure to conquer the Justice, and the first thing he did was to demand to see his lawyer. He was told, to his horror, that as soon as he had been cropped and prison-dressed, he might see as many lawyers as he pleased, to be looked at, laughed at, and advised that there was but one way out of the scrape. Higgins was, in his speculations, a regular counterpart of Bailly; but the celebrated Mayor of Paris had not his nerve. It was impossible to say, if their characters had been changed, whether the unfortunate crisis in which Bailly was not equal to the occasion would have led to very different results if Higgins had been in his place: but assuredly constitutional liberty would have had one chance more. There are two works of his by which he was known, apart from his paradoxes. First, An apology for the life and character of the celebrated prophet of Arabia, called Mohamed, or the Illustrious. London, 8vo. 1829. The reader will look at this writing of our English Buddhist with suspicious eye, but he will not be able to avoid confessing that the Arabian prophet has some reparation to demand at the hands of Christians. Next, Horæ Sabaticæ; or an attempt to correct certain superstitions and vulgar errors respecting the Sabbath. Second edition, with a large appendix. London, 12mo. 1833. This book was very heterodox at the time, but it has furnished material for some of the clergy of our day.

I never could quite make out whether Godfrey Higgins took that system which he traced to the Buddhists to have a Divine origin, or to be the result of good men's meditations. Himself a strong theist, and believer in a future state, one would suppose that he would refer a universal religion, spread in different forms over the whole earth from one source, directly to the universal Parent. And this I suspect he did, whether he knew it or not. The external evidence is balanced. In his preface he says:

"I cannot help smiling when I consider that the priests have objected to admit my former book, The Celtic Druids, into libraries, because it was antichristian; and it has been attacked by Deists, because it was superfluously religious. The learned Deist, the Rev. R. Taylor [already mentioned], has designated me as the religious Mr. Higgins."

The time will come when some profound historian of literature will make himself much clearer on the point than I am.

ON POPE'S DIPPING NEEDLE.

The triumphal Chariot of Friction: or a familiar elucidation of the origin of magnetic attraction, &c. &c. By William Pope. London, 1829, 4to.

Part of this work is on a dipping-needle of the author's construction. It must have been under the impression that a book of naval magnetism was proposed, that a great many officers, the Royal Naval Club, etc. lent their names to the subscription list. How must they have been surprised to find, right opposite to the list of subscribers, the plate presenting "the three emphatic letters, J. A. O." And how much more when they saw it set forth that if a square be inscribed in a circle, a circle within that, then a square again, &c., it is impossible to have more than fourteen circles, let the first circle be as large as you please. From this the seven attributes of God are unfolded; and further, that all matter was moral, until Lucifer churned it into physical "as far as the third circle in Deity": this Lucifer, called Leviathan in Job, being thus the moving cause of chaos. I shall say no more, except that the friction of the air is the cause of magnetism.

Remarks on the Architecture, Sculpture, and Zodiac of Palmyra; with a Key to the Inscriptions. By B. Prescot. London, 1830, 8vo.

Mr. Prescot gives the signs of the zodiac a Hebrew origin.

THE JACOTOT METHOD.

Epitomé de mathématiques. Par F. Jacotot, Avocat. 3ième edition, Paris, 1830, 8vo. (pp. 18).

Méthode Jacotot. Choix de propositions mathématiques. Par P. Y. Séprés. 2nde édition. Paris, 1830, 8vo. (pp. 82).

Of Jacotot's method, which had some vogue in Paris, the principle was Tout est dans tout, and the process Apprendre quelque chose, et à y rapporter tout le reste. The first tract has a proposition in conic sections and its preliminaries: the second has twenty exercises, of which the first is finding the greatest common measure of two numbers, and the last is the motion of a point on a surface, acted on by given forces. This is topped up with the problem of sound in a tube, and a slice of Laplace's theory of the tides. All to be studied until known by heart, and all the rest will come, or at least join on easily when it comes. There is much truth in the assertion that new knowledge hooks on easily to a little of the old, thoroughly mastered. The day is coming when it will be found out that crammed erudition, got up for examinations, does not cast out any hooks for more.

Lettre à MM. les Membres de l'Académie Royale des Sciences, contenant un développement de la réfutation du système de la gravitation universelle, qui leur a été présentée le 30 août, 1830. Par Félix Passot. Paris, 1830, 8vo.

Works of this sort are less common in France than in England. In France there is only the Academy of Sciences to go to: in England there is a reading public out of the Royal Society, &c.

A DISCOURSE ON PROBABILITY.

About 1830 was published, in the Library of Useful Knowledge, the tract on Probability, the joint work of the late Sir John Lubbock and Mr. Drinkwater (Bethune). It is one of the best elementary openings of the subject. A binder put my name on the outside (the work was anonymous) and the consequence was that nothing could drive out of people's heads that it was written by me. I do not know how many denials I have made, from a passage in one of my own works to a letter in the Times: and I am not sure that I have succeeded in establishing the truth, even now. I accordingly note the fact once more. But as a book has no right here unless it contain a paradox—or thing counter to general opinion or practice—I will produce two small ones. Sir John Lubbock, with whom lay the executive arrangement, had a strong objection to the last word in "Theory of Probabilities," he maintained that the singular probability, should be used; and I hold him quite right.

The second case was this: My friend Sir J. L., with a large cluster of intellectual qualities, and another of social qualities, had one point of character which I will not call bad and cannot call good; he never used a slang expression. To such a length did he carry his dislike, that he could not bear head and tail, even in a work on games of chance: so he used obverse and reverse. I stared when I first saw this: but, to my delight, I found that the force of circumstances beat him at last. He was obliged to take an example from the race-course, and the name of one of the horses was Bessy Bedlam! And he did not put her down as Elizabeth Bethlehem, but forced himself to follow the jockeys.

[Almanach Romain sur la Loterie Royale de France, ou les Etrennes nécessaires aux Actionnaires et Receveurs de la dite Loterie. Par M. Menut de St.-Mesmin. Paris, 1830. 12mo.

This book contains all the drawings of the French lottery (two or three, each month) from 1758 to 1830. It is intended for those who thought they could predict the future drawings from the past: and various sets of sympathetic numbers are given to help them. The principle is, that anything which has not happened for a long time must be soon to come. At rouge et noir, for example, when the red has won five times running, sagacious gamblers stake on the black, for they think the turn which must come at last is nearer than it was. So it is: but observation would have shown that if a large number of those cases had been registered which show a run of five for the red, the next game would just as often have made the run into six as have turned in favor of the black. But the gambling reasoner is incorrigible: if he would but take to squaring the circle, what a load of misery would be saved. A writer of 1823, who appeared to be thoroughly acquainted with the gambling of Paris and London, says that the gamesters by profession are haunted by a secret foreboding of their future destruction, and seem as if they said to the banker at the table, as the gladiators said to the emperor, Morituri te salutant.

In the French lottery, five numbers out of ninety were drawn at a time. Any person, in any part of the country, might stake any sum upon any event he pleased, as that 27 should be drawn; that 42 and 81 should be drawn; that 42 and 81 should be drawn, and 42 first; and so on up to a quine déterminé, if he chose, which is betting on five given numbers in a given order. Thus, in July, 1821, one of the drawings was

8 46 16 64 13.

A gambler had actually predicted the five numbers (but not their order), and won 131,350 francs on a trifling stake. M. Menut seems to insinuate that the hint what numbers to choose was given at his own office. Another won 20,852 francs on the quaterne, 8, 16, 46, 64, in this very drawing. These gains, of course, were widely advertised: of the multitudes who lost nothing was said. The enormous number of those who played is proved to all who have studied chances arithmetically by the numbers of simple quaternes which were gained: in 1822, fourteen; in 1823, six; in 1824, sixteen; in 1825, nine, &c.

The paradoxes of what is called chance, or hazard, might themselves make a small volume. All the world understands that there is a long run, a general average; but great part of the world is surprised that this general average should be computed and predicted. There are many remarkable cases of verification; and one of them relates to the quadrature of the circle. I give some account of this and another. Throw a penny time after time until head arrives, which it will do before long: let this be called a set. Accordingly, H is the smallest set, TH the next smallest, then TTH, &c. For abbreviation, let a set in which seven tails occur before head turns up be TH. In an immense number of trials of sets, about half will be H; about a quarter TH; about an eighth, TH. Buffon tried 2,048 sets; and several have followed him. It will tend to illustrate the principle if I give all the results; namely, that many trials will with moral certainty show an approach—and the greater the greater the number of trials—to that average which sober reasoning predicts. In the first column is the most likely number of the theory: the next column gives Buffon's result; the three next are results obtained from trial by correspondents of mine. In each case the number of trials is 2,048.

H 1,024 1,061 1,048 1,017 1,039

TH 512 494 507 547 480

TH 256 232 248 235 267

TH 128 137 99 118 126

TH 64 56 71 72 67

TH 32 29 38 32 33

TH 16 25 17 10 19

TH 8 8 9 9 10

TH 4 6 5 3 3

TH 2 3 2 4

TH 1 1 1

TH 0 1

TH 0 0

TH 1 1 0

TH 0 0

TH 1 1

&c. 0 0

2,048 2,048 2,048 2,048 2,048

In very many trials, then, we may depend upon something like the predicted average. Conversely, from many trials we may form a guess at what the average will be. Thus, in Buffon's experiment the 2,048 first throws of the sets gave head in 1,061 cases: we have a right to infer that in the long run something like 1,061 out of 2,048 is the proportion of heads, even before we know the reasons for the equality of chance, which tell us that 1,024 out of 2,048 is the real truth. I now come to the way in which such considerations have led to a mode in which mere pitch-and-toss has given a more accurate approach to the quadrature of the circle than has been reached by some of my paradoxers. What would my friend in No. 14 have said to this? The method is as follows: Suppose a planked floor of the usual kind, with thin visible seams between the planks. Let there be a thin straight rod, or wire, not so long as the breadth of the plank. This rod, being tossed up at hazard, will either fall quite clear of the seams, or will lay across one seam. Now Buffon, and after him Laplace, proved the following: That in the long run the fraction of the whole number of trials in which a seam is intersected will be the fraction which twice the length of the rod is of the circumference of the circle having the breadth of a plank for its diameter. In 1855 Mr. Ambrose Smith, of Aberdeen, made 3,204 trials with a rod three-fifths of the distance between the planks: there were 1,213 clear intersections, and 11 contacts on which it was difficult to decide. Divide these contacts equally, and we have 1,218½ to 3,204 for the ratio of 6 to 5π, presuming that the greatness of the number of trials gives something near to the final average, or result in the long run: this gives π = 3.1553. If all the 11 contacts had been treated as intersections, the result would have been π = 3.1412, exceedingly near. A pupil of mine made 600 trials with a rod of the length between the seams, and got π = 3.137.

This method will hardly be believed until it has been repeated so often that "there never could have been any doubt about it."

The first experiment strongly illustrates a truth of the theory, well confirmed by practice: whatever can happen will happen if we make trials enough. Who would undertake to throw tail eight times running? Nevertheless, in the 8,192 sets tail 8 times running occurred 17 times; 9 times running, 9 times; 10 times running, twice; 11 times and 13 times, each once; and 15 times twice.]

ON CURIOSITIES OF π.

1830. The celebrated interminable fraction 3.14159..., which the mathematician calls π, is the ratio of the circumference to the diameter. But it is thousands of things besides. It is constantly turning up in mathematics: and if arithmetic and algebra had been studied without geometry, π must have come in somehow, though at what stage or under what name must have depended upon the casualties of algebraical invention. This will readily be seen when it is stated that π is nothing but four times the series

1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...

ad infinitum. It would be wonderful if so simple a series had but one kind of occurrence. As it is, our trigonometry being founded on the circle, π first appears as the ratio stated. If, for instance, a deep study of probable fluctuation from average had preceded, π might have emerged as a number perfectly indispensable in such problems as: What is the chance of the number of aces lying between a million + x and a million - x, when six million of throws are made with a die? I have not gone into any detail of all those cases in which the paradoxer finds out, by his unassisted acumen, that results of mathematical investigation cannot be: in fact, this discovery is only an accompaniment, though a necessary one, of his paradoxical statement of that which must be. Logicians are beginning to see that the notion of horse is inseparably connected with that of non-horse: that the first without the second would be no notion at all. And it is clear that the positive affirmation of that which contradicts mathematical demonstration cannot but be accompanied by a declaration, mostly overtly made, that demonstration is false. If the mathematician were interested in punishing this indiscretion, he could make his denier ridiculous by inventing asserted results which would completely take him in.

More than thirty years ago I had a friend, now long gone, who was a mathematician, but not of the higher branches: he was, inter alia, thoroughly up in all that relates to mortality, life assurance, &c. One day, explaining to him how it should be ascertained what the chance is of the survivors of a large number of persons now alive lying between given limits of number at the end of a certain time, I came, of course upon the introduction of π, which I could only describe as the ratio of the circumference of a circle to its diameter. "Oh, my dear friend! that must be a delusion; what can the circle have to do with the numbers alive at the end of a given time?"—"I cannot demonstrate it to you; but it is demonstrated."—"Oh! stuff! I think you can prove anything with your differential calculus: figment, depend upon it." I said no more; but, a few days afterwards, I went to him and very gravely told him that I had discovered the law of human mortality in the Carlisle Table, of which he thought very highly. I told him that the law was involved in this circumstance. Take the table of expectation of life, choose any age, take its expectation and make the nearest integer a new age, do the same with that, and so on; begin at what age you like, you are sure to end at the place where the age past is equal, or most nearly equal, to the expectation to come. "You don't mean that this always happens?"—"Try it." He did try, again and again; and found it as I said. "This is, indeed, a curious thing; this is a discovery." I might have sent him about trumpeting the law of life: but I contented myself with informing him that the same thing would happen with any table whatsoever in which the first column goes up and the second goes down; and that if a proficient in the higher mathematics chose to palm a figment upon him, he could do without the circle: à corsaire, corsaire et demi, the French proverb says. "Oh!" it was remarked, "I see, this was Milne!" It was not Milne: I remember well showing the formula to him some time afterwards. He raised no difficulty about π; he knew the forms of Laplace's results, and he was much interested. Besides, Milne never said stuff! and figment! And he would not have been taken in: he would have quietly tried it with the Northampton and all the other tables, and would have got at the truth.

EUCLID WITHOUT AXIOMS.

The first book of Euclid's Elements. With alterations and familiar notes. Being an attempt to get rid of axioms altogether; and to establish the theory of parallel lines, without the introduction of any principle not common to other parts of the elements. By a member of the University of Cambridge. Third edition. In usum serenissimæ filiolæ. London, 1830.

The author was Lieut. Col. (now General) Perronet Thompson, the author of the "Catechism on the Corn Laws." I reviewed the fourth edition—which had the name of "Geometry without Axioms," 1833—in the quarterly Journal of Education for January, 1834. Col. Thompson, who then was a contributor to—if not editor of—the Westminster Review, replied in an article the authorship of which could not be mistaken.

Some more attempts upon the problem, by the same author, will be found in the sequel. They are all of acute and legitimate speculation; but they do not conquer the difficulty in the manner demanded by the conditions of the problem. The paradox of parallels does not contribute much to my pages: its cases are to be found for the most part in geometrical systems, or in notes to them. Most of them consist in the proposal of additional postulates; some are attempts to do without any new postulate. Gen. Perronet Thompson, whose paradoxes are always constructed on much study of previous writers, has collected in the work above named, a budget of attempts, the heads of which are in the Penny and English Cyclopædias, at "Parallels." He has given thirty instances, selected from what he had found.

Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty. He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him which he had not observed: he muttered Il faut que j'y songe encore, and put the paper in his pocket.

THE LUNAR CAUSTIC JOKE.

The following paragraph appeared in the Morning Post, May 4, 1831:

"We understand that although, owing to circumstances with which the public are not concerned, Mr. Goulburn declined becoming a candidate for University honors, that his scientific attainments are far from inconsiderable. He is well known to be the author of an essay in the Philosophical Transactions on the accurate rectification of a circular arc, and of an investigation of the equation of a lunar caustic—a problem likely to become of great use in nautical astronomy."

This hoax—which would probably have succeeded with any journal—was palmed upon the Morning Post, which supported Mr. Goulburn, by some Cambridge wags who supported Mr. Lubbock, the other candidate for the University of Cambridge. Putting on the usual concealment, I may say that I always suspected Dr-nkw-t-r B-th-n- of having a share in the matter. The skill of the hoax lies in avoiding the words "quadrature of the circle," which all know, and speaking of "the accurate rectification of a circular arc," which all do not know for its synonyme. The Morning Post next day gave a reproof to hoaxers in general, without referring to any particular case. It must be added, that although there are caustics in mathematics, there is no lunar caustic.

So far as Mr. Goulburn was concerned, the above was poetic justice. He was the minister who, in old time, told a deputation from the Astronomical Society that the Government "did not care twopence for all the science in the country." There may be some still alive who remember this: I heard it from more than one of those who were present, and are now gone. Matters are much changed. I was thirty years in office at the Astronomical Society; and, to my certain knowledge, every Government of that period, Whig and Tory, showed itself ready to help with influence when wanted, and with money whenever there was an answer for the House of Commons. The following correction subsequently appeared. Referring to the hoax about Mr. Goulburn, Messrs. C. H. and Thompson Cooper have corrected an error, by stating that the election which gave rise to the hoax was that in which Messrs. Goulburn and Yates Peel defeated Lord Palmerston and Mr. Cavendish. They add that Mr. Gunning, the well-known Esquire Bedell of the University, attributed the hoax to the late Rev. R. Sheepshanks, to whom, they state, are also attributed certain clever fictitious biographies—of public men, as I understand it—which were palmed upon the editor of the Cambridge Chronicle, who never suspected their genuineness to the day of his death. Being in most confidential intercourse with Mr. Sheepshanks, both at the time and all the rest of his life (twenty-five years), and never heard him allude to any such things—which were not in his line, though he had satirical power of quite another kind—I feel satisfied he had nothing to do with them. I may add that others, his nearest friends, and also members of his family, never heard him allude to these hoaxes as their author, and disbelieve his authorship as much as I do myself. I say this not as imputing any blame to the true author, such hoaxes being fair election jokes in all time, but merely to put the saddle off the wrong horse, and to give one more instance of the insecurity of imputed authorship. Had Mr. Sheepshanks ever told me that he had perpetrated the hoax, I should have had no hesitation in giving it to him. I consider all clever election squibs, free from bitterness and personal imputation, as giving the multitude good channels for the vent of feelings which but for them would certainly find bad ones.

[But I now suspect that Mr. Babbage had some hand in the hoax. He gives it in his "Passages, &c." and is evidently writing from memory, for he gives the wrong year. But he has given the paragraph, though not accurately, yet with such a recollection of the points as brings suspicion of the authorship upon him, perhaps in conjunction with D. B. Both were on Cavendish's committee. Mr. Babbage adds, that "late one evening a cab drove up in hot haste to the office of the Morning Post, delivered the copy as coming from Mr. Goulburn's committee, and at the same time ordered fifty extra copies of the Post to be sent next morning to their committee-room." I think the man—the only one I ever heard of—who knew all about the cab and the extra copies must have known more.]

ON M. DEMONVILLE.

Demonville.—A Frenchman's Christian name is his own secret, unless there be two of the surname. M. Demonville is a very good instance of the difference between a French and English discoverer. In England there is a public to listen to discoveries in mathematical subjects made without mathematics: a public which will hear, and wonder, and think it possible that the pretensions of the discoverer have some foundation. The unnoticed man may possibly be right: and the old country-town reputation which I once heard of, attaching to a man who "had written a book about the signs of the zodiac which all the philosophers in London could not answer," is fame as far as it goes. Accordingly, we have plenty of discoverers who, even in astronomy, pronounce the learned in error because of mathematics. In France, beyond the sphere of influence of the Academy of Sciences, there is no one to cast a thought upon the matter: all who take the least interest repose entire faith in the Institute. Hence the French discoverer turns all his thoughts to the Institute, and looks for his only hearing in that quarter. He therefore throws no slur upon the means of knowledge, but would say, with M. Demonville: "A l'égard de M. Poisson, j'envie loyalement la millième partie de ses connaissances mathématiques, pour prouver mon systême d'astronomie aux plus incrédules." This system is that the only bodies of our system are the earth, the sun, and the moon; all the others being illusions, caused by reflection of the sun and moon from the ice of the polar regions. In mathematics, addition and subtraction are for men; multiplication and division, which are in truth creation and destruction, are prerogatives of deity. But nothing multiplied by nothing is one. M. Demonville obtained an introduction to William the Fourth, who desired the opinion of the Royal Society upon his system: the answer was very brief. The King was quite right; so was the Society: the fault lay with those who advised His Majesty on a matter they knew nothing about. The writings of M. Demonville in my possession are as follows. The dates—which were only on covers torn off in binding—were about 1831-34:

Petit cours d'astronomie followed by Sur l'unité mathématique.—Principes de la physique de la création implicitement admis dans la notice sur le tonnerre par M. Arago.—Question de longitude sur mer.—Vrai système du monde (pp. 92). Same title, four pages, small type. Same title, four pages, addressed to the British Association. Same title, four pages, addressed to M. Mathieu. Same title, four pages, on M. Bouvard's report.—Résumé de la physique de la création; troisième partie du vrai système du monde.

PARSEY'S PARADOX.

The quadrature of the circle discovered, by Arthur Parsey, author of the 'art of miniature painting.' Submitted to the consideration of the Royal Society, on whose protection the author humbly throws himself. London, 1832, 8vo.

Mr. Parsey was an artist, who also made himself conspicuous by a new view of perspective. Seeing that the sides of a tower, for instance, would appear to meet in a point if the tower were high enough, he thought that these sides ought to slope to one another in the picture. On this theory he published a small work, of which I have not the title, with a Grecian temple in the frontispiece, stated, if I remember rightly, to be the first picture which had ever been drawn in true perspective. Of course the building looked very Egyptian, with its sloping sides. The answer to his notion is easy enough. What is called the picture is not the picture from which the mind takes its perception; that picture is on the retina. The intermediate picture, as it may be called—the human artist's work—is itself seen perspectively. If the tower were so high that the sides, though parallel, appeared to meet in a point, the picture must also be so high that the picture-sides, though parallel, would appear to meet in a point. I never saw this answer given, though I have seen and heard the remarks of artists on Mr. Parsey's work. I am inclined to think it is commonly supposed that the artist's picture is the representation which comes before the mind: this is not true; we might as well say the same of the object itself. In July 1831, reading an article on squaring the circle, and finding that there was a difficulty, he set to work, got a light denied to all mathematicians in—some would say through—a crack, and advertised in the Times that he had done the trick. He then prepared this work, in which, those who read it will see how, he showed that 3.14159... should be 3.0625. He might have found out his error by stepping a draughtsman's circle with the compasses.

Perspective has not had many paradoxes. The only other one I remember is that of a writer on perspective, whose name I forget, and whose four pages I do not possess. He circulated remarks on my notes on the subject, published in the Athenæum, in which he denies that the stereographic projection is a case of perspective, the reason being that the whole hemisphere makes too large a picture for the eye conveniently to grasp at once. That is to say, it is no perspective because there is too much perspective.

ON A COUPLE OF GEOMETRIES.

Principles of Geometry familiarly illustrated. By the Rev. W. Ritchie, LL.D. London, 1833, 12mo.

A new Exposition of the system of Euclid's Elements, being an attempt to establish his work on a different basis. By Alfred Day, LL.D. London, 1839, 12mo.

These works belong to a small class which have the peculiarity of insisting that in the general propositions of geometry a proposition gives its converse: that "Every B is A" follows from "Every A is B." Dr. Ritchie says, "If it be proved that the equality of two of the angles of a triangle depends essentially upon the equality of the opposite sides, it follows that the equality of opposite sides depends essentially on the equality of the angles." Dr. Day puts it as follows:

"That the converses of Euclid, so called, where no particular limitation is specified or implied in the leading proposition, more than in the converse, must be necessarily true; for as by the nature of the reasoning the leading proposition must be universally true, should the converse be not so, it cannot be so universally, but has at least all the exceptions conveyed in the leading proposition, and the case is therefore unadapted to geometric reasoning; or, what is the same thing, by the very nature of geometric reasoning, the particular exceptions to the extended converse must be identical with some one or other of the cases under the universal affirmative proposition with which we set forth, which is absurd."

On this I cannot help transferring to my reader the words of the Pacha when he orders the bastinado,—May it do you good! A rational study of logic is much wanted to show many mathematicians, of all degrees of proficiency, that there is nothing in the reasoning of mathematics which differs from other reasoning. Dr. Day repeated his argument in A Treatise on Proportion, London, 1840, 8vo. Dr. Ritchie was a very clear-headed man. He published, in 1818, a work on arithmetic, with rational explanations. This was too early for such an improvement, and nearly the whole of his excellent work was sold as waste paper. His elementary introduction to the Differential Calculus was drawn up while he was learning the subject late in life. Books of this sort are often very effective on points of difficulty.

NEWTON AGAIN OBLITERATED.

Letter to the Royal Astronomical Society in refutation of Mistaken Notions held in common, by the Society, and by all the Newtonian philosophers. By Capt. Forman, R.N. Shepton-Mallet, 1833, 8vo.

Capt. Forman wrote against the whole system of gravitation, and got no notice. He then wrote to Lord Brougham, Sir J. Herschel, and others I suppose, desiring them to procure notice of his books in the reviews: this not being acceded to, he wrote (in print) to Lord John Russell to complain of their "dishonest" conduct. He then sent a manuscript letter to the Astronomical Society, inviting controversy: he was answered by a recommendation to study dynamics. The above pamphlet was the consequence, in which, calling the Council of the Society "craven dunghill cocks," he set them right about their doctrines. From all I can learn, the life of a worthy man and a creditable officer was completely embittered by his want of power to see that no person is bound in reason to enter into controversy with every one who chooses to invite him to the field. This mistake is not peculiar to philosophers, whether of orthodoxy or paradoxy; a majority of educated persons imply, by their modes of proceeding, that no one has a right to any opinion which he is not prepared to defend against all comers.

David and Goliath, or an attempt to prove that the Newtonian system of Astronomy is directly opposed to the Scriptures. By Wm. Lauder, Sen., Mere, Wilts. Mere, 1833, 12mo.

Newton is Goliath; Mr. Lauder is David. David took five pebbles; Mr. Lauder takes five arguments. He expects opposition; for Paul and Jesus both met with it.

Mr. Lauder, in his comparison, seems to put himself in the divinely inspired class. This would not be a fair inference in every case; but we know not what to think when we remember that a tolerable number of cyclometers have attributed their knowledge to direct revelation. The works of this class are very scarce; I can only mention one or two from Montucla. Alphonso Cano de Molina, in the last century, upset all Euclid, and squared the circle upon the ruins; he found a follower, Janson, who translated him from Spanish into Latin. He declared that he believed in Euclid, until God, who humbles the proud, taught him better. One Paul Yvon, called from his estate de la Leu, a merchant at Rochelle, supported by his book-keeper, M. Pujos, and a Scotchman, John Dunbar, solved the problem by divine grace, in a manner which was to convert all Jews, Infidels, etc. There seem to have been editions of his work in 1619 and 1628, and a controversial "Examen" in 1630, by Robert Sara. There was a noted discussion, in which Mydorge, Hardy, and others took part against de la Leu. I cannot find this name either in Lipenius or Murhard, and I should not have known the dates if it had not been for one of the keenest bibliographers of any time, my friend Prince Balthasar Boncompagni, who is trying to find copies of the works, and has managed to find copies of the titles. In 1750, Henry Sullamar, an Englishman, squared the circle by the number of the Beast: he published a pamphlet every two or three years; but I cannot find any mention of him in English works. In France, in 1753, M. de Causans, of the Guards, cut a circular piece of turf, squared it, and deduced original sin and the Trinity. He found out that the circle was equal to the square in which it is inscribed; and he offered a reward for detection of any error, and actually deposited 10,000 francs as earnest of 300,000. But the courts would not allow any one to recover.

SIR JOHN HERSCHEL.

1834. In this year Sir John Herschel set up his telescope at Feldhausen, Cape of Good Hope. He did much for astronomy, but not much for the Budget of Paradoxes. He gives me, however, the following story. He showed a resident a remarkable blood-red star, and some little time after he heard of a sermon preached in those parts in which it was asserted that the statements of the Bible must be true, for that Sir J. H. had seen in his telescope "the very place where wicked people go."

But red is not always the color. Sir J. Herschel has in his possession a letter written to his father, Sir W. H., dated April 3, 1787, and signed "Eliza Cumyns," begging to know if any of the stars be indigo in color, "because, if there be, I think it may be deemed a strong conjectural illustration of the expression, so often used by our Saviour in the Holy Gospels, that 'the disobedient shall be cast into outer darkness'; for as the Almighty Being can doubtless confine any of his creatures, whether corporeal or spiritual, to what part of his creation He pleases, if therefore any of the stars (which are beyond all doubt so many suns to other systems) be of so dark a color as that above mentioned, they may be calculated to give the most insufferable heat to those dolorous systems dependent upon them (and to reprobate spirits placed there), without one ray of cheerful light; and may therefore be the scenes of future punishments." This letter is addressed to Dr. Heirschel at Slow. Some have placed the infernal regions inside the earth, but others have filled this internal cavity—for cavity they will have—with refulgent light, and made it the abode of the blessed. It is difficult to build without knowing the number to be provided for. A friend of mine heard the following (part) dialogue between two strong Scotch Calvinists: "Noo! hoo manny d'ye thank there are of the alact on the arth at this moment?—Eh! mabbee a doozen—Hoot! mon! nae so mony as thot!"

THE NAUTICAL ALMANAC.

1834. From 1769 to 1834 the Nautical Almanac was published on a plan which gradually fell behind what was wanted. In 1834 the new series began, under a new superintendent (Lieut. W. S. Stratford). There had been a long scientific controversy, which would not be generally intelligible. To set some of the points before the reader, I reprint a cutting which I have by me. It is from the Nautical Magazine, but I did hear that some had an idea that it was in the Nautical Almanac itself. It certainly was not, and I feel satisfied the Lords of the Admiralty would not have permitted the insertion; they are never in advance of their age. The Almanac for 1834 was published in July 1833.

The New Nautical Almanac—Extract from the 'Primum Mobile,' and 'Milky Way Gazette.' Communicated by Aerolith.

A meeting of the different bodies composing the Solar System was this day held at the Dragon's Tail, for the purpose of taking into consideration the alterations and amendments introduced into the New Nautical Almanac. The honorable luminaries had been individually summoned by fast-sailing comets, and there was a remarkably full attendance. Among the visitors we observed several nebulæ, and almost all the stars whose proper motions would admit of their being present.

The Sun was unanimously called to the focus. The small planets took the oaths, and their places, after a short discussion, in which it was decided that the places should be those of the Almanac itself, with leave reserved to move for corrections.

Petitions were presented from α and δ Ursæ Minoris, complaining of being put on daily duty, and praying for an increase of salary.—Laid on the plane of the ecliptic.

The trustees of the eccentricity and inclination funds reported a balance of .00001 in the former, and a deficit of 0".009 in the latter. This announcement caused considerable surprise, and a committee was moved for, to ascertain which of the bodies had more or less than his share. After some discussion, in which the small planets offered to consent to a reduction, if necessary, the motion was carried.

The Focal Body then rose to address the meeting. He remarked that the subject on which they were assembled was one of great importance to the routes and revolutions of the heavenly bodies. For himself, though a private arrangement between two of his honourable neighbours (here he looked hard at the Earth and Venus) had prevented his hitherto paying that close attention to the predictions of the Nautical Almanac which he declared he always had wished to do; yet he felt consoled by knowing that the conductors of that work had every disposition to take his peculiar circumstances into consideration. He declared that he had never passed the wires of a transit without deeply feeling his inability to adapt himself to the present state of his theory; a feeling which he was afraid had sometimes caused a slight tremor in his limb. Before he sat down, he expressed a hope that honourable luminaries would refrain as much as possible from eclipsing each other, or causing mutual perturbations. Indeed, he should be very sorry to see any interruption of the harmony of the spheres. (Applause.)

The several articles of the New Nautical Almanac were then read over without any comment; only we observed that Saturn shook his ring at every novelty, and Jupiter gave his belt a hitch, and winked at the satellites at page 21 of each month.

The Moon rose to propose a resolution. No one, he said, would be surprised at his bringing this matter forward in the way he did, when it was considered in how complete and satisfactory a manner his motions were now represented. He must own he had trembled when the Lords of the Admiralty dissolved the Board of Longitude, but his tranquillity was more than reestablished by the adoption of the new system. He did not know but that any little assistance he could give in Nautical Astronomy was becoming of less and less value every day, owing to the improvement of chronometers. But there was one thing, of which nothing could deprive him—he meant the regulation of the tides. And, perhaps, when his attention was not occupied by more than the latter, he should be able to introduce a little more regularity into the phenomena. (Here the honourable luminary gave a sort of modest libration, which convulsed the meeting with laughter.) They might laugh at his natural infirmity if they pleased, but he could assure them it arose only from the necessity he was under, when young, of watching the motions of his worthy primary. He then moved a resolution highly laudatory of the alterations which appeared in the New Nautical Almanac.

The Earth rose, to second the motion. His honourable satellite had fully expressed his opinions on the subject. He joined his honourable friend in the focus in wishing to pay every attention to the Nautical Almanac, but, really, when so important an alteration had taken place in his magnetic pole (hear) and there might, for aught he knew, be a successful attempt to reach his pole of rotation, he thought he could not answer for the preservation of the precession in its present state. (Here the hon. luminary, scratching his side, exclaimed, as he sat down, "More steamboats—confound 'em!")

An honourable satellite (whose name we could not learn) proposed that the resolution should be immediately despatched, corrected for refraction, when he was called to order by the Focal Body, who reminded him that it was contrary to the moving orders of the system to take cognizance of what passed inside the atmosphere of any planet.

Saturn and Pallas rose together. (Cries of "New member!" and the former gave way.) The latter, in a long and eloquent speech, praised the liberality with which he and his colleagues had at length been relieved from astronomical disqualifications. He thought that it was contrary to the spirit of the laws of gravitation to exclude any planet from office on account of the eccentricity or inclination of his orbit. Honourable luminaries need not talk of the want of convergency of his series. What had they to do with any private arrangements between him and the general equations of the system? (Murmurs from the opposition.) So long as he obeyed the laws of motion, to which he had that day taken a solemn oath, he would ask, were old planets, which were now so well known that nobody trusted them, to....

The Focal Body said he was sorry to break the continuity of the proceedings, but he thought that remarks upon character, with a negative sign, would introduce differences of too high an order. The honourable luminary must eliminate the expression which he had brought out, in finite terms, and use smaller inequalities in future. (Hear, hear.)

Pallas explained, that he was far from meaning to reflect upon the orbital character of any planet present. He only meant to protest against being judged by any laws but those of gravitation, and the differential calculus: he thought it most unjust that astronomers should prevent the small planets from being observed, and then reproach them with the imperfections of the tables, which were the result of their own narrow-minded policy. (Cheers.)

Saturn thought that, as an old planet, he had not been treated with due respect. (Hear, from his satellites.) He had long foretold the wreck of the system from the friends of innovation. Why, he might ask, were his satellites to be excluded, when small planets, trumpery comets, which could not keep their mean distances (cries of oh! oh!), double stars, with graphical approximations, and such obscure riff-raff of the heavens (great uproar) found room enough. So help him Arithmetic, nothing could come of it, but a stoppage of all revolution. His hon. friend in the focus might smile, for he would be a gainer by such an event; but as for him (Saturn), he had something to lose, and hon. luminaries well knew that, whatever they might think under an atmosphere, above it continual revolution was the only way of preventing perpetual anarchy. As to the hon. luminary who had risen before him, he was not surprised at his remarks, for he had invariably observed that he and his colleagues allowed themselves too much latitude. The stability of the system required that they should be brought down, and he, for one, would exert all his powers of attraction to accomplish that end. If other bodies would cordially unite with him, particularly his noble friend next him, than whom no luminary possessed greater weight—

Jupiter rose to order. He conceived his noble friend had no right to allude to him in that manner, and was much surprised at his proposal, considering the matters which remained in dispute between them. In the present state of affairs, he would take care never to be in conjunction with his hon. neighbour one moment longer than he could help. (Cries of "Order, order, no long inequalities," during which he sat down.)

Saturn proceeded to say, that he did not know till then that a planet with a ring could affront one who had only a belt, by proposing mutual co-operation. He would now come to the subject under discussion. He should think meanly of his hon. colleagues if they consented to bestow their approbation upon a mere astronomical production. Had they forgotten that they once were considered the arbiters of fate, and the prognosticators of man's destiny? What had lost them that proud position? Was it not the infernal march of intellect, which, after having turned the earth topsy-turvy, was now disturbing the very universe? For himself (others might do as they pleased), but he stuck to the venerable Partridge, and the Stationers' Company, and trusted that they would outlive infidels and anarchists, whether of Astronomical or Diffusion of Knowledge Societies. (Cries of oh! oh!)

Mars said he had been told, for he must confess he had not seen the work, that the places of the planets were given for Sundays. This, he must be allowed to say, was an indecorum he had not expected; and he was convinced the Lords of the Admiralty had given no orders to that effect. He hoped this point would be considered in the measure which had been introduced in another place, and that some one would move that the prohibition against travelling on Sundays extend to the heavenly as well as earthly bodies.

Several of the stars here declared, that they had been much annoyed by being observed on Sunday evenings, during the hours of divine service.

The room was then cleared for a division, but we are unable to state what took place. Several comets-at-arms were sent for, and we heard rumors of a personal collision having taken place between two luminaries in opposition. We were afterwards told that the resolution was carried by a majority, and the luminaries elongated at 2 h. 15 m. 33,41 s. sidereal time.

* * * It is reported, but we hope without foundation, that Saturn, and several other discontented planets, have accepted an invitation from Sirius to join his system, on the most liberal appointments. We believe the report to have originated in nothing more than the discovery of the annual parallax of Sirius from the orbit of Saturn; but we may safely assure our readers that no steps have as yet been taken to open any communication.

We are also happy to state, that there is no truth in the rumor of the laws of gravitation being about to be repealed. We have traced this report, and find it originated with a gentleman living near Bath (Captain Forman, R.N), whose name we forbear to mention.

A great excitement has been observed among the nebulæ, visible to the earth's southern hemisphere, particularly among those which have not yet been discovered from thence. We are at a loss to conjecture the cause, but we shall not fail to report to our readers the news of any movement which may take place. (Sir J. Herschel's visit. He could just see this before he went out.)

WOODLEY'S DIVINE SYSTEM.

A Treatise on the Divine System of the Universe, by Captain Woodley, R.N., and as demonstrated by his Universal Time-piece, and universal method of determining a ship's longitude by the apparent true place of the moon; with an introduction refuting the solar system of Copernicus, the Newtonian philosophy, and mathematics. 1834. 8vo.

Description of the Universal Time-piece. (4pp. 12mo.)

I think this divine system was published several years before, and was republished with an introduction in 1834. Capt. Woodley was very sure that the earth does not move: he pointed out to me, in a conversation I had with him, something—I forget what—in the motion of the Great Bear, visible to any eye, which could not possibly be if the earth moved. He was exceedingly ignorant, as the following quotation from his account of the usual opinion will show:

"The north pole of the Earth's axis deserts, they say, the north star or pole of the Heavens, at the rate of 1° in 71¾ years.... The fact is, nothing can be more certain than that the Stars have not changed their latitudes or declinations one degree in the last 71¾ years."

This is a strong specimen of a class of men by whom all accessible persons who have made any name in science are hunted. It is a pity that they cannot be admitted into scientific societies, and allowed fairly to state their cases, and stand quiet cross-examination, being kept in their answers very close to the questions, and the answers written down. I am perfectly satisfied that if one meeting in the year were devoted to the hearing of those who chose to come forward on such conditions, much good would be done. But I strongly suspect few would come forward at first, and none in a little while: and I have had some experience of the method I recommend, privately tried. Capt. Woodley was proposed, a little after 1834, as a Fellow of the Astronomical Society; and, not caring whether he moved the sun or the earth, or both—I could not have stood neither—I signed the proposal. I always had a sneaking kindness for paradoxers, such a one, perhaps, as Petit André had for his lambs, as he called them. There was so little feeling against his opinions, that he only failed by a fraction of a ball. Had I myself voted, he would have been elected; but being engaged in conversation, and not having heard the slightest objection to him, I did not think it worth while to cross the room for the purpose. I regretted this at the time, but had I known how ignorant he was I should not have supported him. Probably those who voted against him knew more of his book than I did.

I remember no other instance of exclusion from a scientific society on the ground of opinion, even if this be one; of which it may be that ignorance had more to do with it than paradoxy. Mr. Frend, a strong anti-Newtonian, was a Fellow of the Astronomical Society, and for some years in the Council. Lieut. Kerigan was elected to the Royal Society at a time when his proposers must have known that his immediate object was to put F.R.S. on the title-page of a work against the tides. To give all I know, I may add that the editor of some very ignorant bombast about the "forehead of the solar sky," who did not know the difference between Bailly and Baily, received hints which induced him to withdraw his proposal for election into the Astronomical Society. But this was an act of kindness; for if he had seen Mr. Baily in the chair, with his head on, he might have been political historian enough to faint away.

De la formation des Corps. Par Paul Laurent. Nancy, 1834, 8vo.

Atoms, and ether, and ovules or eggs, which are planets, and their eggs, which are satellites. These speculators can create worlds, in which they cannot be refuted; but none of them dare attack the problem of a grain of wheat, and its passage from a seed to a plant, bearing scores of seeds like what it was itself.

ON JOHN FLAMSTEED.

An account of the Rev. John Flamsteed, the First Astronomer-Royal.... By Francis Baily, Esq. London, 1835, 4to. Supplement, London, 1837, 4to.

My friend Francis Baily was a paradoxer: he brought forward things counter to universal opinion. That Newton was impeccable in every point was the national creed; and failings of temper and conduct would have been utterly disbelieved, if the paradox had not come supported by very unusual evidence. Anybody who impeached Newton on existing evidence might as well have been squaring the circle, for any attention he would have got. About this book I will tell a story. It was published by the Admiralty for distribution; and the distribution was entrusted to Mr. Baily. On the eve of its appearance, rumors of its extraordinary revelations got about, and persons of influence applied to the Admiralty for copies. The Lords were in a difficulty: but on looking at the list they saw names, as they thought, which were so obscure that they had a right to assume Mr. Baily had included persons who had no claim to such a compliment as presentation from the Admiralty. The Secretary requested Mr. Baily to call upon him. "Mr. Baily, my Lords are inclined to think that some of the persons in this list are perhaps not of that note which would justify their Lordships in presenting this work."—"To whom does your observation apply, Mr. Secretary?"—"Well, now, let us examine the list; let me see; now,—now,—now,—come!—here's Gauss—who's Gauss?"—"Gauss, Mr. Secretary, is the oldest mathematician now living, and is generally thought to be the greatest."—"O-o-oh! Well, Mr. Baily, we will see about it, and I will write you a letter." The letter expressed their Lordships' perfect satisfaction with the list.

There was a controversy about the revelations made in this work; but as the eccentric anomalies took no part in it, there is nothing for my purpose. The following valentine from Mrs. Flamsteed, which I found among Baily's papers, illustrates some of the points:

"3 Astronomers' Row, Paradise: February 14, 1836.

"Dear Sir,—I suppose you hardly expected to receive a letter from me, dated from this place; but the truth is, a gentleman from our street was appointed guardian angel to the American Treaty, in which there is some astronomical question about boundaries. He has got leave to go back to fetch some instruments which he left behind, and I take this opportunity of making your acquaintance. That America has become a wonderful place since I was down among you; you have no idea how grand the fire at New York looked up here. Poor dear Mr. Flamsteed does not know I am writing a letter to a gentleman on Valentine's day; he is walked out with Sir Isaac Newton (they are pretty good friends now, though they do squabble a little sometimes) and Sir William Herschel, to see a new nebula. Sir Isaac says he can't make out at all how it is managed; and I am sure I cannot help him. I never bothered my head about those things down below, and I don't intend to begin here.

"I have just received the news of your having written a book about my poor dear man. It's a chance that I heard it at all; for the truth is, the scientific gentlemen are somehow or other become so wicked, and go so little to church, that very few of them are considered fit company for this place. If it had not been for Dr. Brinkley, who came here of course, I should not have heard about it. He seems a nice man, but is not yet used to our ways. As to Mr. Halley, he is of course not here; which is lucky for him, for Mr. Flamsteed swore the moment he caught him in a place where there are no magistrates, he would make a sacrifice of him to heavenly truth. It was very generous in Mr. F. not appearing against Sir Isaac when he came up, for I am told that if he had, Sir Isaac would not have been allowed to come in at all. I should have been sorry for that, for he is a companionable man enough, only holds his head rather higher than he should do. I met him the other day walking with Mr. Whiston, and disputing about the deluge. 'Well, Mrs. Flamsteed,' says he, 'does old Poke-the-Stars understand gravitation yet?' Now you must know that is rather a sore point with poor dear Mr. Flamsteed. He says that Sir Isaac is as crochetty about the moon as ever; and as to what some people say about what has been done since his time, he says he should like to see somebody who knows something about it of himself. For it is very singular that none of the people who have carried on Sir Isaac's notions have been allowed to come here.

"I hope you have not forgotten to tell how badly Sir Isaac used Mr. Flamsteed about that book. I have never quite forgiven him; as for Mr. Flamsteed, he says that as long as he does not come for observations, he does not care about it, and that he will never trust him with any papers again as long as he lives. I shall never forget what a rage he came home in when Sir Isaac had called him a puppy. He struck the stairs all the way up with his crutch, and said puppy at every step, and all the evening, as soon as ever a star appeared in the telescope, he called it puppy. I could not think what was the matter, and when I asked, he only called me puppy.

"I shall be very glad to see you if you come our way. Pray keep up some appearances, and go to church a little. St. Peter is always uncommonly civil to astronomers, and indeed to all scientific persons, and never bothers them with many questions. If they can make anything out of the case, he is sure to let them in. Indeed, he says, it is perfectly out of the question expecting a mathematician to be as religious as an apostle, but that it is as much as his place is worth to let in the greater number of those who come. So try if you cannot manage it, for I am very curious to know whether you found all the letters. I remain, dear sir, your faithful servant,

"Margaret Flamsteed.

Francis Baily, Esq.

"P.S. Mr. Flamsteed has come in, and says he left Sir Isaac riding cockhorse upon the nebula, and poring over it as if it were a book. He has brought in his old acquaintance Ozanam, who says that it was always his maxim on earth, that 'il appartient aux docteurs de Sorbonne de disputer, au Pape de prononcer, et au mathématicien d'aller en Paradis en ligne perpendiculaire.'"

ON STEVIN.

The Secretary of the Admiralty was completely extinguished. I can recall but two instances of demolition as complete, though no doubt there are many others. The first is in

Simon Stevin and M. Dumortier. Nieuport, 1845, 12mo.

M. Dumortier was a member of the Academy of Brussels: there was a discussion, I believe, about a national Pantheon for Belgium. The name of Stevinus suggested itself as naturally as that of Newton to an Englishman; probably no Belgian is better known to foreigners as illustrious in science. Stevinus is great in the Mécanique Analytique of Lagrange; Stevinus is great in the Tristram Shandy of Sterne. M. Dumortier, who believed that not one Belgian in a thousand knew Stevinus, and who confesses with ironical shame that he was not the odd man, protested against placing the statue of an obscure man in the Pantheon, to give foreigners the notion that Belgium could show nothing greater. The work above named is a slashing retort: any one who knows the history of science ever so little may imagine what a dressing was given, by mere extract from foreign writers. The tract is a letter signed J. du Fan, but this is a pseudonym of Mr. Van de Weyer. The Academician says Stevinus was a man who was not without merit for the time at which he lived: Sir! is the answer, he was as much before his own time as you are behind yours. How came a man who had never heard of Stevinus to be a member of the Brussels Academy?

The second story was told me by Mr. Crabb Robinson, who was long connected with the Times, and intimately acquainted with Mr. W***. When W*** was an undergraduate at Cambridge, taking a walk, he came to a stile, on which sat a bumpkin who did not make way for him: the gown in that day looked down on the town. "Why do you not make way for a gentleman?"—"Eh?"—"Yes, why do you not move? You deserve a good hiding, and you shall get it if you don't take care!" The bumpkin raised his muscular figure on its feet, patted his menacer on the head, and said, very quietly,—"Young man! I'm Cribb." W*** seized the great pugilist's hand, and shook it warmly, got him to his own rooms in college, collected some friends, and had a symposium which lasted until the large end of the small hours.

FINLEYSON AS A PARADOXER.

God's Creation of the Universe as it is, in support of the Scriptures. By Mr. Finleyson. Sixth Edition, 1835, 8vo.

This writer, by his own account, succeeded in delivering the famous Lieut. Richard Brothers from the lunatic asylum, and tending him, not as a keeper but as a disciple, till he died. Brothers was, by his own account, the nephew of the Almighty, and Finleyson ought to have been the nephew of Brothers. For Napoleon came to him in a vision, with a broken sword and an arrow in his side, beseeching help: Finleyson pulled out the arrow, but refused to give a new sword; whereby poor Napoleon, though he got off with life, lost the battle of Waterloo. This story was written to the Duke of Wellington, ending with "I pulled out the arrow, but left the broken sword. Your Grace can supply the rest, and what followed is amply recorded in history." The book contains a long account of applications to Government to do three things: to pay 2,000l. for care taken of Brothers, to pay 10,000l. for discovery of the longitude, and to prohibit the teaching of the Newtonian system, which makes God a liar. The successive administrations were threatened that they would have to turn out if they refused, which, it is remarked, came to pass in every case. I have heard of a joke of Lord Macaulay, that the House of Commons must be the Beast of the Revelations, since 658 members, with the officers necessary for the action of the House, make 666. Macaulay read most things, and the greater part of the rest: so that he might be suspected of having appropriated as a joke one of Finleyson's serious points—"I wrote Earl Grey upon the 13th of July, 1831, informing him that his Reform Bill could not be carried, as it reduced the members below the present amount of 658, which, with the eight principal clerks or officers of the House, make the number 666." But a witness has informed me that Macaulay's joke was made in his hearing a great many years before the Reform Bill was proposed; in fact, when both were students at Cambridge. Earl Grey was, according to Finleyson, a descendant of Uriah the Hittite. For a specimen of Lieut. Brothers, this book would be worth picking up. Perhaps a specimen of the Lieutenant's poetry may be acceptable: Brothers loquitur, remember:

"Jerusalem ! Jerusalem! shall be built again!

More rich, more grand then ever;

And through it shall Jordan flow!(!)

My people's favourite river.

There I'll erect a splendid throne,

And build on the wasted place;

To fulfil my ancient covenant

To King David and his race.

"Euphrates' stream shall flow with ships,

And also my wedded Nile;

And on my coast shall cities rise,

Each one distant but a mile.

"My friends the Russians on the north

With Persees and Arabs round,

Do show the limits of my land,

Here! Here! then I mark the ground."

ON THEOLOGICAL PARADOXERS.

Among the paradoxers are some of the theologians who in their own organs of the press venture to criticise science. These may hold their ground when they confine themselves to the geology of long past periods and to general cosmogony: for it is the tug of Greek against Greek; and both sides deal much in what is grand when called hypothesis, petty when called supposition. And very often they are not conspicuous when they venture upon things within knowledge; wrong, but not quite wrong enough for a Budget of Paradoxes. One case, however, is destined to live, as an instance of a school which finds writers, editors, and readers. The double stars have been seen from the seventeenth century, and diligently observed by many from the time of Wm. Herschel, who first devoted continuous attention to them. The year 1836 was that of a remarkable triumph of astronomical prediction. The theory of gravitation had been applied to the motion of binary stars about each other, in elliptic orbits, and in that year the two stars of γ Virginis, as had been predicted should happen within a few years of that time—for years are small quantities in such long revolutions—the two stars came to their nearest: in fact, they appeared to be one as much with the telescope as without it. This remarkable turning-point of the history of a long and widely-known branch of astronomy was followed by an article in the Church of England Quarterly Review for April 1837, written against the Useful Knowledge Society. The notion that there are any such things as double stars is (p. 460) implied to be imposture or delusion, as in the following extract. I suspect that I myself am the Sidrophel, and that my companion to the maps of the stars, written for the Society and published in 1836, is the work to which the writer refers:

"We have forgotten the name of that Sidrophel who lately discovered that the fixed stars were not single stars, but appear in the heavens like soles at Billingsgate, in pairs; while a second astronomer, under the influence of that competition in trade which the political economists tell us is so advantageous to the public, professes to show us, through his superior telescope, that the apparently single stars are really three. Before such wondrous mandarins of science, how continually must homunculi like ourselves keep in the background, lest we come between the wind and their nobility."

If the homunculus who wrote this be still above ground, how devoutly must he hope he may be able to keep in the background! But the chief blame falls on the editor. The title of the article is:

"The new school of superficial pantology; a speech intended to be delivered before a defunct Mechanics' Institute. By Swallow Swift, late M.P. for the Borough of Cockney-Cloud, Witsbury: reprinted Balloon Island, Bubble year, month Ventose. Long live Charlatan!"

As a rule, orthodox theologians should avoid humor, a weapon which all history shows to be very difficult to employ in favor of establishment, and which, nine times out of ten, leaves its wielder fighting on the side of heterodoxy. Theological argument, when not enlivened by bigotry, is seldom worse than narcotic: but theological fun, when not covert heresy, is almost always sialagogue. The article in question is a craze, which no editor should have admitted, except after severe inspection by qualified persons. The author of this wit committed a mistake which occurs now and then in old satire, the confusion between himself and the party aimed at. He ought to be reviewing this fictitious book, but every now and then the article becomes the book itself; not by quotation, but by the writer forgetting that he is not Mr. Swallow Swift, but his reviewer. In fact he and Mr. S. Swift had each had a dose of the Devil's Elixir. A novel so called, published about forty years ago, proceeds upon a legend of this kind. If two parties both drink of the elixir, their identities get curiously intermingled; each turns up in the character of the other throughout the three volumes, without having his ideas clear as to whether he be himself or the other. There is a similar confusion in the answer made to the famous Epistolæ Obscurorum Virorum: it is headed Lamentationes Obscurorum Virorum. This is not a retort of the writer, throwing back the imputation: the obscure men who had been satirized are themselves made, by name, to wince under the disapprobation which the Pope had expressed at the satire upon themselves.

Of course the book here reviewed is a transparent forgery. But I do not know how often it may have happened that the book, in the journals which always put a title at the head, may have been written after the review. About the year 1830 a friend showed me the proof of an article of his on the malt tax, for the next number of the Edinburgh Review. Nothing was wanting except the title of the book reviewed; I asked what it was. He sat down, and wrote as follows at the head, "The Maltster's Guide (pp. 124)," and said that would do as well as anything.

But I myself, it will be remarked, have employed such humor as I can command "in favor of establishment." What it is worth I am not to judge; as usual in such cases, those who are of my cabal pronounce it good, but cyclometers and other paradoxers either call it very poor, or commend it as sheer buffoonery. Be it one or the other, I observe that all the effective ridicule is, in this subject, on the side of establishment. This is partly due to the difficulty of quizzing plain and sober demonstration; but so much, if not more, to the ignorance of the paradoxers. For that which cannot be ridiculed, can be turned into ridicule by those who know how. But by the time a person is deep enough in negative quantities, and impossible quantities, to be able to satirize them, he is caught, and being inclined to become a user, shrinks from being an abuser. Imagine a person with a gift of ridicule, and knowledge enough, trying his hand on the junction of the assertions which he will find in various books of algebra. First, that a negative quantity has no logarithm; secondly, that a negative quantity has no square root; thirdly, that the first non-existent is to the second as the circumference of a circle to its diameter. One great reason of the allowance of such unsound modes of expression is the confidence felt by the writers that √-1 and log(-1) will make their way, however inaccurately described. I heartily wish that the cyclometers had knowledge enough to attack the weak points of algebraical diction: they would soon work a beneficial change.

AN EARLY METEOROLOGIST.

Recueil de ma vie, mes ouvrages et mes pensées. Par Thomas Ignace Marie Forster. Brussels, 1836, 12mo.

Mr. Forster, an Englishman settled at Bruges, was an observer in many subjects, but especially in meteorology. He communicated to the Astronomical Society, in 1848, the information that, in the registers kept by his grandfather, his father, and himself, beginning in 1767, new moon on Saturday was followed, nineteen times out of twenty, by twenty days of rain and wind. This statement being published in the Athenæum, a cluster of correspondents averred that the belief is common among seamen, in all parts of the world, and among landsmen too. Some one quoted a distich:

"Saturday's moon and Sunday's full

Never were fine and never wull."

Another brought forward:

"If a Saturday's moon

Comes once in seven years it comes too soon."

Mr. Forster did not say he was aware of the proverbial character of the phenomenon. He was a very eccentric man. He treated his dogs as friends, and buried them with ceremony. He quarrelled with the curé of his parish, who remarked that he could not take his dogs to heaven with him. I will go nowhere, said he, where I cannot take my dog. He was a sincere Catholic: but there is a point beyond which even churches have no influence.

The following is some account of the announcement of 1849. The Athenæum (Feb. 17), giving an account of the meeting of the Astronomical Society in December, 1858, says:

"Dr. Forster of Bruges, who is well known as a meteorologist, made a communication at which our readers will stare: he declares that by journals of the weather kept by his grandfather, father, and himself, ever since 1767, to the present time, whenever the new moon has fallen on a Saturday, the following twenty days have been wet and windy, in nineteen cases out of twenty. In spite of our friend Zadkiel and the others who declare that we would smother every truth that does not happen to agree with us, we are glad to see that the Society had the sense to publish this communication, coming, as it does, from a veteran observer, and one whose love of truth is undoubted. It must be that the fact is so set down in the journals, because Dr. Forster says it: and whether it be only a fact of the journals, or one of the heavens, can soon be tried. The new moon of March next, falls on Saturday the 24th, at 2 in the afternoon. We shall certainly look out."

The following appeared in the number of March 31:

"The first Saturday Moon since Dr. Forster's announcement came off a week ago. We had previously received a number of letters from different correspondents—all to the effect that the notion of new moon on Saturday bringing wet weather is one of widely extended currency. One correspondent (who gives his name) states that he has constantly heard it at sea, and among the farmers and peasantry in Scotland, Ireland, and the North of England. He proceeds thus: 'Since 1826, nineteen years of the time I have spent in a seafaring life. I have constantly observed, though unable to account for, the phenomenon. I have also heard the stormy qualities of a Saturday's moon remarked by American, French, and Spanish seamen; and, still more distant, a Chinese pilot, who was once doing duty on board my vessel seemed to be perfectly cognizant of the fact.' So that it seems we have, in giving currency to what we only knew as a very curious communication from an earnest meteorologist, been repeating what is common enough among sailors and farmers. Another correspondent affirms that the thing is most devoutly believed in by seamen; who would as soon sail on a Friday as be in the Channel after a Saturday moon.—After a tolerable course of dry weather, there was some snow, accompanied by wind on Saturday last, here in London; there were also heavy louring clouds. Sunday was cloudy and cold, with a little rain; Monday was louring, Tuesday unsettled; Wednesday quite overclouded, with rain in the morning. The present occasion shows only a general change of weather with a tendency towards rain. If Dr. Forster's theory be true, it is decidedly one of the minor instances, as far as London weather is concerned.—It will take a good deal of evidence to make us believe in the omen of a Saturday Moon. But, as we have said of the Poughkeepsie Seer, the thing is very curious whether true or false. Whence comes this universal proverb—and a hundred others—while the meteorological observer cannot, when he puts down a long series of results, detect any weather cycles at all? One of our correspondents wrote us something of a lecture for encouraging, he said, the notion that names could influence the weather. He mistakes the question. If there be any weather cycles depending on the moon, it is possible that one of them may be so related to the week cycle of seven days, as to show recurrences which are of the kind stated, or any other. For example, we know that if the new moon of March fall on a Saturday in this year, it will most probably fall on a Saturday nineteen years hence. This is not connected with the spelling of Saturday—but with the connection between the motions of the sun and moon. Nothing but the Moon can settle the question—and we are willing to wait on her for further information. If the adage be true, then the philosopher has missed what lies before his eyes; if false, then the world can be led by the nose in spite of the eyes. Both these things happen sometimes; and we are willing to take whichever of the two solutions is borne out by future facts. In the mean time, we announce the next Saturday Moon for the 18th of August."

How many coincidences are required to establish a law of connection? It depends on the way in which the mind views the matter in question. Many of the paradoxers are quite set up by a very few instances. I will now tell a story about myself, and then ask them a question.

So far as instances can prove a law, the following is proved: no failure has occurred. Let a clergyman be known to me, whether by personal acquaintance or correspondence, or by being frequently brought before me by those with whom I am connected in private life: that clergyman does not, except in few cases, become a bishop; but if he become a bishop, he is sure, first or last, to become an arch-bishop. This has happened in every case. As follows:

1. My last schoolmaster, a former Fellow of Oriel, was a very intimate college friend of Richard Whately, a younger man. Struck by his friend's talents, he used to talk of him perpetually, and predict his future eminence. Before I was sixteen, and before Whately had even given his Bampton Lectures, I was very familiar with his name, and some of his sayings. I need not say that he became Archbishop of Dublin.

2. When I was a child, a first cousin of John Bird Sumner married a sister of my mother. I cannot remember the time when I first heard his name, but it was made very familiar to me. In time he became Bishop of Chester, and then, Archbishop of Canterbury. My reader may say that Dr. C. R. Sumner, Bishop of Winchester, has just as good a claim: but it is not so: those connected with me had more knowledge of Dr. J. B. Sumner; and said nothing, or next to nothing, of the other. Rumor says that the Bishop of Winchester has declined an Archbishopric: if so, my rule is a rule of gradations.

3. Thomas Musgrave, Fellow of Trinity College, Cambridge, was Dean of the college when I was an undergraduate: this brought me into connection with him, he giving impositions for not going to chapel, I writing them out according. We had also friendly intercourse in after life; I forgiving, he probably forgetting. Honest Tom Musgrave, as he used to be called, became Bishop of Hereford, and Archbishop of York.

4. About the time when I went to Cambridge, I heard a great deal about Mr. C. T. Longley, of Christchurch, from a cousin of my own of the same college, long since deceased, who spoke of him much, and most affectionately. Dr. Longley passed from Durham to York, and thence to Canterbury. I cannot quite make out the two Archbishoprics; I do not remember any other private channel through which the name came to me: perhaps Dr. Longley, having two strings to his bow, would have been one archbishop if I had never heard of him.

5. When Dr. Wm. Thomson was appointed to the see of Gloucester in 1861, he and I had been correspondents on the subject of logic—on which we had both written—for about fourteen years. On his elevation I wrote to him, giving the preceding instances, and informing him that he would certainly be an Archbishop. The case was a strong one, and the law acted rapidly; for Dr. Thomson's elevation to the see of York took place in 1862.

Here are five cases; and there is no opposing instance. I have searched the almanacs since 1828, and can find no instance of a Bishop not finally Archbishop of whom I had known through private sources, direct or indirect. Now what do my paradoxers say? Is this a pre-established harmony, or a chain of coincidences? And how many instances will it require to establish a law?

THE HERSCHEL HOAX.

Some account of the great astronomical discoveries lately made by Sir John Herschel at the Cape of Good Hope. Second Edition. London, 12mo. 1836.

This is a curious hoax, evidently written by a person versed in astronomy and clever at introducing probable circumstances and undesigned coincidences. It first appeared in a newspaper. It makes Sir J. Herschel discover men, animals, etc. in the moon, of which much detail is given. There seems to have been a French edition, the original, and English editions in America, whence the work came into Britain: but whether the French was published in America or at Paris I do not know. There is no doubt that it was produced in the United States, by M. Nicollet, an astronomer, once of Paris, and a fugitive of some kind. About him I have heard two stories. First that he fled to America with funds not his own, and that this book was a mere device to raise the wind. Secondly, that he was a protégé of Laplace, and of the Polignac party, and also an outspoken man. That after the revolution he was so obnoxious to the republican party that he judged it prudent to quit France; which he did in debt, leaving money for his creditors, but not enough, with M. Bouvard. In America he connected himself with an assurance office. The moon-story was written, and sent to France, chiefly with the intention of entrapping M. Arago, Nicollet's especial foe, into the belief of it. And those who narrate this version of the story wind up by saying that M. Arago was entrapped, and circulated the wonders through Paris, until a letter from Nicollet to M. Bouvard explained the hoax. I have no personal knowledge of either story: but as the poor man had to endure the first, it is but right that the second should be told with it.

SOME MORE METEOROLOGY.

The Weather Almanac for the Year 1838. By P. Murphy, Esq., M.N.S.

By M. N. S. is meant member of no society.. This almanac bears on the title-page two recommendations. The Morning Post calls it one of the most important-if-true publications of our generation. The Times says: "If the basis of his theory prove sound, and its principles be sanctioned by a more extended experience, it is not too much to say that the importance of the discovery is equal to that of the longitude." Cautious journalist! Three times that of the longitude would have been too little to say. That the landsman might predict the weather of all the year, at its beginning, Jack would cheerfully give up astronomical longitude—the problem—altogether, and fall back on chronometers with the older Ls, lead, latitude, and look-out, applied to dead-reckoning. Mr. Murphy attempted to give the weather day by day: thus the first seven days of March bore Changeable; Rain; Rain; Rain-wind; Changeable; Fair; Changeable. To aim at such precision as to put a fair day between two changeable ones by weather theory was going very near the wind and weather too. Murphy opened the year with cold and frost; and the weather did the same. But Murphy, opposite to Saturday, January 20, put down "Fair, Probable lowest degree of winter temperature." When this Saturday came, it was not merely the probably coldest of 1838, but certainly the coldest of many consecutive years. Without knowing anything of Murphy, I felt it prudent to cover my nose with my glove as I walked the street at eight in the morning. The fortune of the Almanac was made. Nobody waited to see whether the future would dement the prophecy: the shop was beset in a manner which brought the police to keep order; and it was said that the Almanac for 1838 was a gain of 5,000l. to the owners. It very soon appeared that this was only a lucky hit: the weather-prophet had a modified reputation for a few years; and is now no more heard of. A work of his will presently appear in the list.

THE GREAT PYRAMIDS.

Letter from Alexandria on the evidence of the practical application of the quadrature of the circle in the great pyramids of Gizeh. By H. C. Agnew, Esq. London, 1838, 4to.

Mr. Agnew detects proportions which he thinks were suggested by those of the circumference and diameter of a circle.

THE MATHEMATICS OF A CREED.

The creed of St. Athanasius proved by a mathematical parallel. Before you censure, condemn, or approve; read, examine, and understand. E. B. Revilo. London, 1839, 8vo.

This author really believed himself, and was in earnest. He is not the only person who has written nonsense by confounding the mathematical infinite (of quantity) with what speculators now more correctly express by the unlimited, the unconditioned, or the absolute. This tract is worth preserving, as the extreme case of a particular kind. The following is a specimen. Infinity being represented by ∞, as usual, and f, s, g, being finite integers, the three Persons are denoted by ∞f, (m ∞)s, ∞g, the finite fraction m representing human nature, as opposed to ∞. The clauses of the Creed are then given with their mathematical parallels. I extract a couple:

"But the Godhead of the Father, of the Son, and of the Holy Ghost, is all one: the glory equal, the Majesty co-eternal. "It has been shown that ∞f, ∞g, and (m ∞)s, together, are but ∞, and that each is ∞, and any magnitude in existence represented by ∞ always was and always will be: for it cannot be made, or destroyed, and yet exists.

"Equal to the Father, as touching his Godhead: and inferior to the Father, touching his Manhood." "(m ∞)s is equal to ∞f as touching ∞, but inferior to ∞f as touching m: because m is not infinite."

I might have passed this over, as beneath even my present subject, but for the way in which I became acquainted with it. A bookseller, not the publisher, handed it to me over his counter: one who had published mathematical works. He said, with an air of important communication, Have you seen this, Sir! In reply, I recommended him to show it to my friend Mr.——, for whom he had published mathematics. Educated men, used to books and to the converse of learned men, look with mysterious wonder on such productions as this: for which reason I have made a quotation which many will judge had better have been omitted. But it would have been an imposition on the public if I were, omitting this and some other uses of the Bible and Common Prayer, to pretend that I had given a true picture of my school.

[Since the publication of the above, it has been stated that the author is Mr. Oliver Byrne, the author of the Dual Arithmetic mentioned further on: E. B. Revilo seems to be obviously a reversal.]

LOGIC HAS NO PARADOXERS.

Old and new logic contrasted: being an attempt to elucidate, for ordinary comprehension, how Lord Bacon delivered the human mind from its 2,000 years' enslavement under Aristotle. By Justin Brenan. London, 1839, 12mo.

Logic, though the other exact science, has not had the sort of assailants who have clustered about mathematics. There is a sect which disputes the utility of logic, but there are no special points, like the quadrature of the circle, which excite dispute among those who admit other things. The old story about Aristotle having one logic to trammel us, and Bacon another to set us free,—always laughed at by those who really knew either Aristotle or Bacon,—now begins to be understood by a large section of the educated world. The author of this tract connects the old logic with the indecencies of the classical writers, and the new with moral purity: he appeals to women, who, "when they see plainly the demoralizing tendency of syllogistic logic, they will no doubt exert their powerful influence against it, and support the Baconian method." This is the only work against logic which I can introduce, but it is a rare one, I mean in contents. I quote the author's idea of a syllogism:

"The basis of this system is the syllogism. This is a form of couching the substance of your argument or investigation into one short line or sentence—then corroborating or supporting it in another, and drawing your conclusion or proof in a third."

On this definition he gives an example, as follows: "Every sin deserves death," the substance of the "argument or investigation." Then comes, "Every unlawful wish is a sin," which "corroborates or supports" the preceding: and, lastly, "therefore every unlawful wish deserves death," which is the "conclusion or proof." We learn, also, that "sometimes the first is called the premises (sic), and sometimes the first premiss"; as also that "the first is sometimes called the proposition, or subject, or affirmative, and the next the predicate, and sometimes the middle term." To which is added, with a mark of exclamation at the end, "but in analyzing the syllogism, there is a middle term, and a predicate too, in each of the lines!" It is clear that Aristotle never enslaved this mind.

I have said that logic has no paradoxers, but I was speaking of old time. This science has slept until our own day: Hamilton says there has been "no progress made in the general development of the syllogism since the time of Aristotle; and in regard to the few partial improvements, the professed historians seem altogether ignorant." But in our time, the paradoxer, the opponent of common opinion, has appeared in this field. I do not refer to Prof. Boole, who is not a paradoxer, but a discoverer: his system could neither oppose nor support common opinion, for its grounds were not in the conception of any one. I speak especially of two others, who fought like cat and dog: one was dogmatical, the other categorical. The first was Hamilton himself—Sir William Hamilton of Edinburgh, the metaphysician, not Sir William Rowan Hamilton of Dublin, the mathematician, a combination of peculiar genius with unprecedented learning, erudite in all he could want except mathematics, for which he had no turn, and in which he had not even a schoolboy's knowledge, thanks to the Oxford of his younger day. The other was the author of this work, so fully described in Hamilton's writings that there is no occasion to describe him here. I shall try to say a few words in common language about the paradoxers.

Hamilton's great paradox was the quantification of the predicate; a fearful phrase, easily explained. We all know that when we say "Men are animals," a form wholly unquantified in phrase, we speak of all men, but not of all animals: it is some or all, some may be all for aught the proposition says. This some-may-be-all-for-aught-we-say, or not-none, is the logician's some. One would suppose that "all men are some animals," would have been the logical phrase in all time: but the predicate never was quantified. The few who alluded to the possibility of such a thing found reasons for not adopting it over and above the great reason, that Aristotle did not adopt it. For Aristotle never ruled in physics or metaphysics in the old time with near so much of absolute sway as he has ruled in logic down to our own time. The logicians knew that in the proposition "all men are animals" the "animal" is not universal, but particular yet no one dared to say that all men are some animals, and to invent the phrase, "some animals are all men" until Hamilton leaped the ditch, and not only completed a system of enunciation, but applied it to syllogism.

My own case is as peculiar as his: I have proposed to introduce mathematical thought into logic to an extent which makes the old stagers cry:

"St. Aristotle! what wild notions!

Serve a ne exeat regno on him!"

Hard upon twenty years ago, a friend and opponent who stands high in these matters, and who is not nearly such a sectary of Aristotle and establishment as most, wrote to me as follows: "It is said that next to the man who forms the taste of the nation, the greatest genius is the man who corrupts it. I mean therefore no disrespect, but very much the reverse, when I say that I have hitherto always considered you as a great logical heresiarch." Coleridge says he thinks that it was Sir Joshua Reynolds who made the remark: which, to copy a bull I once heard, I cannot deny, because I was not there when he said it. My friend did not call me to repentance and reconciliation with the church: I think he had a guess that I was a reprobate sinner. My offences at that time were but small: I went on spinning syllogism systems, all alien from the common logic, until I had six, the initial letters of which, put together, from the names I gave before I saw what they would make, bar all repentance by the words

RUE NOT!

leaving to the followers of the old school the comfortable option of placing the letters thus:

TRUE? NO!

It should however be stated that the question is not about absolute truth or falsehood. No one denies that anything I call an inference is an inference: they say that my alterations are extra-logical; that they are material, not formal; and that logic is a formal science.

The distinction between material and formal is easily made, where the usual perversions are not required. A form is an empty machine, such as "Every X is Y"; it may be supplied with matter, as in "Every man is animal." The logicians will not see that their formal proposition, "Every X is Y," is material in three points, the degree of assertion, the quantity of the proposition, and the copula. The purely formal proposition is "There is the probability α that X stands in the relation L to Y." The time will come when it will be regretted that logic went without paradoxers for two thousand years: and when much that has been said on the distinction of form and matter will breed jokes.

I give one instance of one mood of each of the systems, in the order of the letters first written above.

Relative.—In this system the formal relation is taken, that is, the copula may be any whatever. As a material instance, in which the relations are those of consanguinity (of men understood), take the following: X is the brother of Y; X is not the uncle of Z; therefore, Z is not the child of Y. The discussion of relation, and of the objections to the extension, is in the Cambridge Transactions, Vol. X, Part 2; a crabbed conglomerate.

Undecided.—In this system one premise, and want of power over another, infer want of power over a conclusion. As "Some men are not capable of tracing consequences; we cannot be sure that there are beings responsible for consequences who are incapable of tracing consequences; therefore, we cannot be sure that all men are responsible for the consequences of their actions."

Exemplar.—This, long after it suggested itself to me as a means of correcting a defect in Hamilton's system, I saw to be the very system of Aristotle himself, though his followers have drifted into another. It makes its subject and predicate examples, thus: Any one man is an animal; any one animal is a mortal; therefore, any one man is a mortal.

Numerical.—Suppose 100 Ys to exist: then if 70 Xs be Ys, and 40 Zs be Ys, it follows that 10 Xs (at least) are Zs. Hamilton, whose mind could not generalize on symbols, saw that the word most would come under this system, and admitted, as valid, such a syllogism as "most Ys are Xs; most Ys are Zs; therefore, some Xs are Zs."

Onymatic.—This is the ordinary system much enlarged in propositional forms. It is fully discussed in my Syllabus of Logic.

Transposed.—In this syllogism the quantity in one premise is transposed into the other. As, some Xs are not Ys; for every X there is a Y which is Z; therefore, some Zs are not Xs.

Sir William Hamilton of Edinburgh was one of the best friends and allies I ever had. When I first began to publish speculation on this subject, he introduced me to the logical world as having plagiarized from him. This drew their attention: a mathematician might have written about logic under forms which had something of mathematical look long enough before the Aristotelians would have troubled themselves with him: as was done by John Bernoulli, James Bernoulli, Lambert, and Gergonne; who, when our discussion began, were not known even to omnilegent Hamilton. He retracted his accusation of wilful theft in a manly way when he found it untenable; but on this point he wavered a little, and was convinced to the last that I had taken his principle unconsciously. He thought I had done the same with Ploucquet and Lambert. It was his pet notion that I did not understand the commonest principles of logic, that I did not always know the difference between the middle term of a syllogism and its conclusion. It went against his grain to imagine that a mathematician could be a logician. So long as he took me to be riding my own hobby, he laughed consumedly: but when he thought he could make out that I was mounted behind Ploucquet or Lambert, the current ran thus: "It would indeed have been little short of a miracle had he, ignorant even of the common principles of logic, been able of himself to rise to generalization so lofty and so accurate as are supposed in the peculiar doctrines of both the rival logicians, Lambert and Ploucquet—how useless soever these may in practice prove to be." All this has been sufficiently discussed elsewhere: "but, masters, remember that I am an ass."

I know that I never saw Lambert's work until after all Hamilton supposed me to have taken was written: he himself, who read almost everything, knew nothing about it until after I did. I cannot prove what I say about my knowledge of Lambert: but the means of doing it may turn up. For, by the casual turning up of an old letter, I have found the means of clearing myself as to Ploucquet. Hamilton assumed that (unconsciously) I took from Ploucquet the notion of a logical notation in which the symbol of the conclusion is seen in the joint symbols of the premises. For example, in my own fashion I write down ( . ) ( . ), two symbols of premises. By these symbols I see that there is a valid conclusion, and that it may be written in symbol by striking out the two middle parentheses, which gives ( . . ) and reading the two negative dots as an affirmative. And so I see in ( . ) ( . ) that is the conclusion. This, in full, is the perception that "all are either Xs or Ys" and "all are either Ys or Zs" necessitates "some Xs are Zs." Now in Ploucquet's book of 1763, is found, "Deleatur in præmissis medius; id quod restat indicat conclusionem." In the paper in which I explain my symbols—which are altogether different from Ploucquet's—there is found "Erase the symbols of the middle term; the remaining symbols show the inference." There is very great likeness: and I would have excused Hamilton for his notion if he had fairly given reference to the part of the book in which his quotation was found. For I had shown in my Formal Logic what part of Ploucquet's book I had used: and a fair disputant would either have strengthened his point by showing that I had been at his part of the book, or allowed me the advantage of it being apparent that I had not given evidence of having seen that part of the book. My good friend, though an honest man, was sometimes unwilling to allow due advantage to controversial opponents.

But to my point. The only work of Ploucquet I ever saw was lent me by my friend Dr. Logan, with whom I have often corresponded on logic, etc. I chanced (in 1865) to turn up the letter which he sent me (Sept. 12, 1847) with the book. Part of it runs thus: "I congratulate you on your success in your logical researches [that is, in asking for the book, I had described some results]. Since the reading of your first paper I have been satisfied as to the possibility of inventing a logical notation in which the rationale of the inference is contained in the symbol, though I never attempted to verify it [what I communicated, then, satisfied the writer that I had done and communicated what he, from my previous paper, suspected to be practicable]. I send you Ploucquet's dissertation....'

It now being manifest that I cannot be souring grapes which have been taken from me, I will say what I never said in print before. There is not the slightest merit in making the symbols of the premises yield that of the conclusion by erasure: the thing must do itself in every system which symbolises quantities. For in every syllogism (except the inverted Bramantip of the Aristotelians) the conclusion is manifest in this way without symbols. This Bramantip destroys system in the Aristotelian lot: and circumstances which I have pointed out destroy it in Hamilton's own collection. But in that enlargement of the reputed Aristotelian system which I have called onymatic, and in that correction of Hamilton's system which I have called exemplar, the rule of erasure is universal, and may be seen without symbols.

Our first controversy was in 1846. In 1847, in my Formal Logic, I gave him back a little satire for satire, just to show, as I stated, that I could employ ridicule if I pleased. He was so offended with the appendix in which this was contained, that he would not accept the copy of the book I sent him, but returned it. Copies of controversial works, sent from opponent to opponent, are not presents, in the usual sense: it was a marked success to make him angry enough to forget this. It had some effect however: during the rest of his life I wished to avoid provocation; for I could not feel sure that excitement might not produce consequences. I allowed his slashing account of me in the Discussions to pass unanswered: and before that, when he proposed to open a controversy in the Athenæum upon my second Cambridge paper, I merely deferred the dispute until the next edition of my Formal Logic. I cannot expect the account in the Discussions to amuse an unconcerned reader as much as it amused myself: but for a cut-and-thrust, might-and-main, tooth-and-nail, hammer-and-tongs assault, I can particularly recommend it. I never knew, until I read it, how much I should enjoy a thundering onslought on myself, done with racy insolence by a master hand, to whom my good genius had whispered Ita feri ut se sentiat emori. Since that time I have, as the Irishman said, become "dry moulded for want of a bating." Some of my paradoxers have done their best: but theirs is mere twopenny—"small swipes," as Peter Peebles said. Brandy for heroes! I hope a reviewer or two will have mercy on me, and will give me as good discipline as Strafford would have given Hampden and his set: "much beholden," said he, "should they be to any one that should thoroughly take pains with them in that kind"—meaning objective flagellation. And I shall be the same to any one who will serve me so—but in a literary and periodical sense: my corporeal cuticle is as thin as my neighbors'.

Sir W. H. was suffering under local paralysis before our controversy commenced: and though his mind was quite unaffected, a retort of as downright a character as the attack might have produced serious effect upon a person who had shown himself sensible of ridicule. Had a second attack of his disorder followed an answer from me, I should have been held to have caused it: though, looking at Hamilton's genial love of combat, I strongly suspected that a retort in kind

"Would cheer his heart, and warm his blood,

And make him fight, and do him good."

But I could not venture to risk it. So all I did, in reply to the article in the Discussions, was to write to him the following note: which, as illustrating an etiquette of controversy, I insert.

"I beg to acknowledge and thank you for.... It is necessary that I should say a word on my retention of this work, with reference to your return of the copy of my Formal Logic, which I presented to you on its publication: a return made on the ground of your disapproval of the account of our controversy which that work contained. According to my view of the subject, any one whose dealing with the author of a book is specially attacked in it, has a right to expect from the author that part of the book in which the attack is made, together with so much of the remaining part as is fairly context. And I hold that the acceptance by the party assailed of such work or part of a work does not imply any amount of approval of the contents, or of want of disapproval. On this principle (though I am not prepared to add the word alone) I forwarded to you the whole of my work on Formal Logic and my second Cambridge Memoir. And on this principle I should have held you wanting in due regard to my literary rights if you had not forwarded to me your asterisked pages, with all else that was necessary to a full understanding of their scope and meaning, so far as the contents of the book would furnish it. For the remaining portion, which it would be a hundred pities to separate from the pages in which I am directly concerned, I am your debtor on another principle; and shall be glad to remain so if you will allow me to make a feint of balancing the account by the offer of two small works on subjects as little connected with our discussion as the Epistolæ Obscurorum Virorum, or the Lutheran dispute. I trust that by accepting my Opuscula you will enable me to avoid the use of the knife, and leave me to cut you up with the pen as occasion shall serve, I remain, etc. (April 21, 1852)."

I received polite thanks, but not a word about the body of the letter: my argument, I suppose, was admitted.

SOME DOGGEREL AND COUNTER DOGGEREL.

I find among my miscellaneous papers the following jeu d'esprit, or jeu de bêtise, whichever the reader pleases—I care not—intended, before I saw ground for abstaining, to have, as the phrase is, come in somehow. I think I could manage to bring anything into anything: certainly into a Budget of Paradoxes. Sir W. H. rather piqued himself upon some caniculars, or doggerel verses, which he had put together in memoriam [technicam] of the way in which A E I O are used in logic: he added U, Y, for the addition of meet, etc., to the system. I took the liberty of concocting some counter-doggerel, just to show that a mathematician may have architectonic power as well as a metaphysician.

DOGGEREL.
BY SIR W. HAMILTON.

A it affirms of this, these, all,

Whilst E denies of any;

I it affirms (whilst O denies)

Of some (or few, or many).

Thus A affirms, as E denies,

And definitely either;

Thus I affirms, as O denies,

And definitely neither.

A half, left semidefinite,

Is worthy of its score;

U, then, affirms, as Y denies,

This, neither less nor more.

Indefinito-definites,

I, UI, YO, last we come;

And this affirms, as that denies

Of more, most (half, plus, some).

COUNTER DOGGEREL.
BY PROF. DE MORGAN.
(1847.)

Great A affirms of all;

Sir William does so too:

When the subject is "my suspicion,"

And the predicate "must be true."

Great E denies of all;

Sir William of all but one:

When he speaks about this present time,

And of those who in logic have done.

Great I takes up but some;

Sir William! my dear soul!

Why then in all your writings,

Does "Great I" fill the whole!

Great O says some are not;

Sir William's readers catch,

That some (modern) Athens is not without

An Aristotle to match.

"A half, left semi-definite,

Is worthy of its score:"

This looked very much like balderdash,

And neither less nor more.

It puzzled me like anything;

In fact, it puzzled me worse:

Isn't schoolman's logic hard enough,

Without being in Sibyl's verse?

At last, thinks I, 'tis German;

And I'll try it with some beer!

The landlord asked what bothered me so,

And at once he made it clear.

It's half-and-half, the gentleman means;

Don't you see he talks of score?

That's the bit of memorandum

That we chalk behind the door.

Semi-definite's outlandish;

But I see, in half a squint,

That he speaks of the lubbers who call for a quart,

When they can't manage more than a pint.

Now I'll read it into English,

And then you'll answer me this:

If it isn't good logic all the world round,

I should like to know what is?

When you call for a pot of half-and-half,

If you're lost to sense of shame,

You may leave it semi-definite,

But you pay for it all just the same.

I am unspeakably comforted when I look over the above in remembering that the question is not whether it be Pindaric or Horatian, but whether the copy be as good as the original. And I say it is: and will take no denial.

Long live—long will live—the glad memory of William Hamilton, Good, Learned, Acute, and Disputatious! He fought upon principle: the motto of his book is:

"Truth, like a torch, the more it's shook it shines."

There is something in this; but metaphors, like puddings, quarrels, rivers, and arguments, always have two sides to them. For instance,

"Truth, like a torch, the more it's shook it shines;

But those who want to use it, hold it steady.

They shake the flame who like a glare to gaze at,

They keep it still who want a light to see by."

ANOTHER THEORY OF PARALLELS.

Theory of Parallels. The proof of Euclid's axiom looked for in the properties of the Equiangular Spiral. By Lieut-Col. G. Perronet Thompson. The same, second edition, revised and corrected. The same, third edition, shortened, and freed from dependence on the theory of limits. The same, fourth edition, ditto, ditto. All London, 1840, 8vo.

To explain these editions it should be noted that General Thompson rapidly modified his notions, and republished his tracts accordingly.

SOME PRIMITIVE DARWINISM.

Vestiges of the Natural History of Creation. London, 1840, 12mo.

This is the first edition of this celebrated work. Its form is a case of the theory: the book is an undeniable duodecimo, but the size of its paper gives it the look of not the smallest of octavos. Does not this illustrate the law of development, the gradation of families, the transference of species, and so on? If so, I claim the discovery of this esoteric testimony of the book to its own contents; I defy any one to point out the reviewer who has mentioned it. The work itself is described by its author as "the first attempt to connect the natural sciences into a history of creation." The attempt was commenced, and has been carried on, both with marked talent, and will be continued. Great advantage will result: at the worst we are but in the alchemy of some new chemistry, or the astrology of some new astronomy. Perhaps it would be as well not to be too sure on the matter, until we have an antidote to possible consequences as exhibited under another theory, on which it is as reasonable to speculate as on that of the Vestiges. I met long ago with a splendid player on the guitar, who assured me, and was confirmed by his friends, that he never practised, except in thought, and did not possess an instrument: he kept his fingers acting in his mind, until they got their habits; and thus he learnt the most difficult novelties of execution. Now what if this should be a minor segment of a higher law? What if, by constantly thinking of ourselves as descended from primeval monkeys, we should—if it be true—actually get our tails again? What if the first man who was detected with such an appendage should be obliged to confess himself the author of the Vestiges—a person yet unknown—who would naturally get the start of his species by having had the earliest habit of thinking on the matter? I confess I never hear a man of note talk fluently about it without a curious glance at his proportions, to see whether there may be ground to conjecture that he may have more of "mortal coil" than others, in anaxyridical concealment. I do not feel sure that even a paternal love for his theory would induce him, in the case I am supposing, to exhibit himself at the British Association,

With a hole behind which his tail peeped through.

The first sentence of this book (1840) is a cast of the log, which shows our rate of progress. "It is familiar knowledge that the earth which we inhabit is a globe of somewhat less than 8,000 miles in diameter, being one of a series of eleven which revolve at different distances around the sun." The eleven! Not to mention the Iscariot which Le Verrier and Adams calculated into existence, there is more than a septuagint of new planetoids.

ON RELIGIOUS INSURANCE.

The Constitution and Rules of the Ancient and Universal 'Benefit Society' established by Jesus Christ, exhibited, and its advantages and claims maintained, against all Modern and merely Human Institutions of the kind: A Letter very respectfully addressed to the Rev. James Everett, and occasioned by certain remarks made by him, in a speech to the Members of the 'Wesleyan Centenary Institute' Benefit Society. Dated York, Dec. 7, 1840. By Thomas Smith. 12mo, (pp. 8.)

The Wesleyan minister addressed had advocated provision against old age, etc.: the writer declares all private provision un-Christian. After decent maintenance and relief of family claims of indigence, he holds that all the rest is to go to the "Benefit Society," of which he draws up the rules, in technical form, with chapters of "Officers," "Contributors" etc., from the Acts of the Apostles, etc., and some of the early Fathers. He holds that a Christian may not "make a private provision against the contingencies of the future": and that the great "Benefit Society" is the divinely-ordained recipient of all the surplus of his income; capital, beyond what is necessary for business, he is to have none. A real good speculator shuts his eyes by instinct, when opening them would not serve the purpose: he has the vizor of the Irish fairy tale, which fell of itself over the eyes of the wearer the moment he turned them upon the enchanted light which would have destroyed him if he had caught sight of it. "Whiles it remained, was it not thine own? and after it was sold, was it (the purchase-money) not in thine own power?" would have been awkward to quote, and accordingly nothing is stated except the well-known result, which is rule 3, cap. 5, "Prevention of Abuses." By putting his principles together, the author can be made, logically, to mean that the successors of the apostles should put to death all contributors who are detected in not paying their full premiums.

I have known one or two cases in which policy-holders have surrendered their policies through having arrived at a conviction that direct provision is unlawful. So far as I could make it out, these parties did not think it unlawful to lay by out of income, except when this was done in a manner which involved calculation of death-chances. It is singular they did not see that the entrance of chance of death was the entrance of the very principle of the benefit society described in the Acts of the Apostles. The family of the one who died young received more in proportion to premiums paid than the family of one who died old. Every one who understands life assurance sees that—bonus apart—the difference between an assurance office and a savings bank consists in the adoption, pro tanto, of the principle of community of goods. In the original constitution of the oldest assurance office, the Amicable Society, the plan with which they started was nothing but this: persons of all ages under forty-five paid one common premium, and the proceeds were divided among the representatives of those who died within the year.

THE TWO OLD PARADOXES AGAIN.

[I omitted from its proper place a manuscript quadrature (3.1416 exactly) addressed to an eminent mathematician, dated in 1842 from the debtor's ward of a country gaol. The unfortunate speculator says, "I have labored many years to find the precise ratio." I have heard of several cases in which squaring the circle has produced an inability to square accounts. I remind those who feel a kind of inspiration to employ native genius upon difficulties, without gradual progression from elements, that the call is one which becomes stronger and stronger, and may lead, as it has led, to abandonment of the duties of life, and all the consequences.]

1842. Provisional Prospectus of the Double Acting Rotary Engine Company. Also Mechanic's Magazine, March 26, 1842.

Perpetual motion by a drum with one vertical half in mercury, the other in a vacuum: the drum, I suppose, working round forever to find an easy position. Steam to be superseded: steam and electricity convulsions of nature never intended by Providence for the use of man. The price of the present engines, as old iron, will buy new engines that will work without fuel and at no expense. Guaranteed by the Count de Predaval, the discoverer. I was to have been a Director, but my name got no further than ink, and not so far as official notification of the honor, partly owing to my having communicated to the Mechanic's Magazine information privately given to me, which gave premature publicity, and knocked up the plan.

An Exposition of the Nature, Force, Action, and other properties of Gravitation on the Planets. London, 1842, 12mo.

An Investigation of the principles of the Rules for determining the Measures of the Areas and Circumferences of Circular Plane Surfaces ... London, 1844, 8vo.

These are anonymous; but the author (whom I believe to be Mr. Denison, presently noted) is described as author of a new system of mathematics, and also of mechanics. He had need have both, for he shows that the line which has a square equal to a given circle, has a cube equal to the sphere on the same diameter: that is, in old mathematics, the diameter is to the circumference as 9 to 16! Again, admitting that the velocities of planets in circular orbits are inversely as the square roots of their distances, that is, admitting Kepler's law, he manages to prove that gravitation is inversely as the square root of the distance: and suspects magnetism of doing the difference between this and Newton's law. Magnetism and electricity are, in physics, the member of parliament and the cabman—at every man's bidding, as Henry Warburton said.

The above is an outrageous quadrature. In the preceding year, 1841, was published what I suppose at first to be a Maori quadrature, by Maccook. But I get it from a cutting out of some French periodical, and I incline to think that it must be by a Mr. McCook. He makes π to be 2 + 2√(8√2 - 11).

THE DUPLICATION PROBLEM.

Refutation of a Pamphlet written by the Rev. John Mackey, R.C.P., entitled "A method of making a cube double of a cube, founded on the principles of elementary geometry," wherein his principles are proved erroneous, and the required solution not yet obtained. By Robert Murphy. Mallow, 1824, 12mo.

This refutation was the production of an Irish boy of eighteen years old, self-educated in mathematics, the son of a shoemaker at Mallow. He died in 1843, leaving a name which is well known among mathematicians. His works on the theory of equations and on electricity, and his papers in the Cambridge Transactions, are all of high genius. The only account of him which I know of is that which I wrote for the Supplement of the Penny Cyclopædia. He was thrown by his talents into a good income at Cambridge, with no social training except penury, and very little intellectual training except mathematics. He fell into dissipation, and his scientific career was almost arrested: but he had great good in him, to my knowledge. A sentence in a letter from the late Dean Peacock to me—giving some advice about the means of serving Murphy—sets out the old case: "Murphy is a man whose special education is in advance of his general; and such men are almost always difficult subjects to manage." This article having been omitted in its proper place, I put it at 1843, the date of Murphy's death.

A NEW VALUE OF π.

The Invisible Universe disclosed; or, the real Plan and Government of the Universe. By Henry Coleman Johnson, Esq. London, 1843, 8vo.

The book opens abruptly with:

"First demonstration. Concerning the centre: showing that, because the centre is an innermost point at an equal distance between two extreme points of a right line, and from every two relative and opposite intermediate points, it is composed of the two extreme internal points of each half of the line; each extreme internal point attracting towards itself all parts of that half to which it belongs...."

Of course the circle is squared: and the circumference is 3-1/21 diameters.

SOME MODERN ASTROLOGY.

Combination of the Zodiacal and Cometical Systems. Printed for the London Society, Exeter Hall. Price Sixpence. (n. d. 1843.)

What this London Society was, or the "combination," did not appear. There was a remarkable comet in 1843, the tail of which was at first confounded with what is called the zodiacal light. This nicely-printed little tract, evidently got up with less care for expense than is usual in such works, brings together all the announcements of the astronomers, and adds a short head and tail piece, which I shall quote entire. As the announcements are very ordinary astronomy, the reader will be able to detect, if detection be possible, what is the meaning and force of the "Combination of the Zodiacal and Cometical Systems":

"Premonition. It has pleased the Author of Creation to cause (to His human and reasoning Creatures of this generation, by a 'combined' appearance in His Zodiacal and Cometical system) a 'warning Crisis' of universal concernment to this our Globe. It is this 'Crisis' that has so generally 'ROUSED' at this moment the 'nations throughout the Earth' that no equal interest has ever before been excited by Man; unless it be in that caused by the 'Pagan-Temple in Rome,' which is recorded by the elder Pliny, 'Nat. Hist.' i. 23. iii. 3. Hardouin."

After the accounts given by the unperceiving astronomers, comes what follows:

"Such has been (hitherto) the only object discerned by the 'Wise of this World,' in this twofold union of the 'Zodiacal' and 'Cometical' systems: yet it is nevertheless a most 'Thrilling Warning,' to all the inhabitants of this precarious and transitory Earth. We have no authorized intimation or reasonable prospective contemplation, of 'current time' beyond a year 1860, of the present century; or rather, except 'the interval which may now remain from the present year 1843, to a year 1860' (ἡμέρας ἙΞΗΚΟΝΤΑ—'threescore or sixty days'—'I have appointed each "Day" for a "Year,"' Ezek. iv. 6): and we know, from our 'common experience,' how speedily such a measure of time will pass away.

"No words can be 'more explicit' than these of our blessed Lord: viz. 'This Gospel of the Kingdom shall be preached in ALL the Earth, for a Witness to all Nations; and then, shall the End come.' The 'next 18 years' must therefore supply the interval of the 'special Episcopal forerunners.'

(Matt. xxiv. 14.)

"See the 'Jewish Intelligencer' of the present month (April), p. 153, for the 'Debates in Parliament,' respecting the Bishop of Jerusalem, viz. Dr. Bowring, Mr. Hume, Sir R. Inglis, Sir R. Peel, Viscount Palmerston."

I have quoted this at length, to show the awful threats which were published at a time of some little excitement about the phenomenon, under the name of the London Society. The assumption of a corporate appearance is a very unfair trick: and there are junctures at which harm might be done by it.

THE NUMBER OF THE BEAST.

Wealth the name and number of the Beast, 666, in the Book of Revelation. [by John Taylor.] London, 1844, 8vo.

Whether Junius or the Beast be the more difficult to identify, must be referred to Mr. Taylor, the only person who has attempted both. His cogent argument on the political secret is not unworthily matched in his treatment of the theological riddle. He sees the solution in εὐπορία, which occurs in the Acts of the Apostles as the word for wealth in one of its most disgusting forms, and makes 666 in the most straightforward way. This explanation has as good a chance as any other. The work contains a general attempt at explanation of the Apocalypse, and some history of opinion on the subject. It has not the prolixity which is so common a fault of apocalyptic commentators.

A practical Treatise on Eclipses ... with remarks on the anomalies of the present Theory of the Tides. By T. Kerigan, F.R.S. 1844, 8vo.

Containing also a refutation of the theory of the tides, and afterwards increased by a supplement, "Additional facts and arguments against the theory of the tides," in answer to a short notice in the Athenæum journal. Mr. Kerigan was a lieutenant in the Navy: he obtained admission to the Royal Society just before the publication of his book.

A new theory of Gravitation. By Joseph Denison, Esq. London, 1844, 12mo.

Commentaries on the Principia. By the author of 'A new theory of Gravitation.' London, 1846, 8vo.

Honor to the speculator who can be put in his proper place by one sentence, be that place where it may.

"But we have shown that the velocities are inversely as the square roots of the mean distances from the sun; wherefore, by equality of ratios, the forces of the sun's gravitation upon them are also inversely as the square roots of their distances from the sun."

EASTER DAY PARADOXERS.

In the years 1818 and 1845 the full moon fell on Easter Day, having been particularly directed to fall before it in the act for the change of style and in the English missals and prayer-books of all time: perhaps it would be more correct to say that Easter Day was directed to fall after the full moon; "but the principle is the same." No explanation was given in 1818, but Easter was kept by the tables, in defiance of the rule, and of several protests. A chronological panic was beginning in December 1844, which was stopped by the Times newspaper printing extracts from an article of mine in the Companion to the Almanac for 1845, which had then just appeared. No one had guessed the true reason, which is that the thing called the moon in the Gregorian Calendar is not the moon of the heavens, but a fictitious imitation put wrong on purpose, as will presently appear, partly to keep Easter out of the way of the Jews' Passover, partly for convenience of calculation. The apparent error happens but rarely; and all the work will perhaps have to be gone over next time. I now give two bits of paradox.

Some theologians were angry at this explanation. A review called the Christian Observer (of which Christianity I do not know) got up a crushing article against me. I did not look at it, feeling sure that an article on such a subject which appeared on January 1, 1845, against a publication made in December 1844, must be a second-hand job. But some years afterwards (Sept. 10, 1850), the reviews, etc. having been just placed at the disposal of readers in the old reading-room of the Museum, I made a tour of inspection, came upon my critic on his perch, and took a look at him. I was very glad to remember this, for, though expecting only second-hand, yet even of this there is good and bad; and I expected to find some hints in the good second-hand of a respectable clerical publication. I read on, therefore, attentively, but not long: I soon came to the information that some additions to Delambre's statement of the rule for finding Easter, belonging to distant years, had been made by Sir Harris Nicolas! Now as I myself furnished my friend Sir H. N. with Delambre's digest of Clavius's rule, which I translated out of algebra into common language for the purpose, I was pretty sure this was the ignorant reading of a person to whom Sir H. N. was the highest arithmetical authority on the subject. A person pretending to chronology, without being able to distinguish the historical points—so clearly as they stand out—in which Sir H. N. speaks with authority, from the arithmetical points of pure reckoning on which he does not pretend to do more than directly repeat others, must be as fit to talk about the construction of Easter Tables as the Spanish are to talk French. I need hardly say that the additions for distant years are as much from Clavius as the rest: my reviewer was not deep enough in his subject to know that Clavius made and published, from his rules, the full table up to A.D. 5000, for all the movable feasts of every year! I gave only a glance at the rest: I found I was either knave or fool, with a leaning to the second opinion; and I came away satisfied that my critic was either ignoramus or novice, with a leaning to the first. I afterwards found an ambiguity of expression in Sir H. N.'s account—whether his or mine I could not tell—which might mislead a novice or content an ignoramus, but would have been properly read or further inquired into by a competent person.

The second case is this. Shortly after the publication of my article, a gentleman called at my house, and, finding I was not at home, sent up his card—with a stylish west-end club on it—to my wife, begging for a few words on pressing business. With many well-expressed apologies, he stated that he had been alarmed by hearing that Prof. De M. had an intention of altering Easter next year. Mrs. De M. kept her countenance, and assured him that I had no such intention, and further, that she greatly doubted my having the power to do it. Was she quite sure? his authority was very good: fresh assurances given. He was greatly relieved, for he had some horses training for after Easter, which would not be ready to run if it were altered the wrong way. A doubt comes over him: would Mrs. De M., in the event of her being mistaken, give him the very earliest information? Promise given; profusion of thanks; more apologies; and departure.

Now, candid reader!—or uncandid either!—which most deserves to be laughed at? A public instructor, who undertakes to settle for the world whether a reader of Clavius, the constructor of the Gregorian Calendar, is fool or knave, upon information derived from a compiler—in this matter—of his own day; or a gentleman of horse and dog associations, who, misapprehending something which he heard about a current topic, infers that the reader of Clavius had the ear of the Government on a proposed alteration. I suppose the querist had heard some one say, perhaps, that the day ought to be set right, and some one else remark that I might be consulted, as the only person who had discussed the matter from the original source of the Calendar.

To give a better chance of the explanation being at once produced, next time the real full moon and Easter Day shall fall together, I insert here a summary which was printed in the Irish Prayer-book of the Ecclesiastical Society. If the amusement given by paradoxers should prevent a useless discussion some years hence, I and the paradoxers shall have done a little good between us—at any rate, I have done my best to keep the heavy weight afloat by tying bladders to it. I think the next occurrence will be in 1875.

EASTER DAY.

In the years 1818 and 1845, Easter Day, as given by the rules in 24 Geo. II cap. 23. (known as the act for the change of style) contradicted the precept given in the preliminary explanations. The precept is as follows:

"Easter Day, on which the rest" of the moveable feasts "depend, is always the First Sunday after the Full Moon, which happens upon or next after the Twenty-first Day of March; and if the Full Moon happens upon a Sunday, Easter Day is the Sunday after."

But in 1818 and 1845, the full moon fell on a Sunday, and yet the rules gave that same Sunday for Easter Day. Much discussion was produced by this circumstance in 1818: but a repetition of it in 1845 was nearly altogether prevented by a timely reference to the intention of those who conducted the Gregorian reformation of the Calendar. Nevertheless, seeing that the apparent error of the Calendar is due to the precept in the Act of Parliament, which is both erroneous and insufficient, and that the difficulty will recur so often as Easter Day falls on the day of full moon, it may be advisable to select from the two articles cited in the note such of their conclusions and rules, without proof or controversy, as will enable the reader to understand the main points of the Easter question, and, should he desire it, to calculate for himself the Easter of the old or new style, for any given year.

1. In the very earliest age of Christianity, a controversy arose as to the mode of keeping Easter, some desiring to perpetuate the Passover, others to keep the festival of the Resurrection. The first afterwards obtained the name of Quartadecimans, from their Easter being always kept on the fourteenth day of the moon (Exod. xii. 18, Levit. xxiii. 5.). But though it is unquestionable that a Judaizing party existed, it is also likely that many dissented on chronological grounds. It is clear that no perfect anniversary can take place, except when the fourteenth of the moon, and with it the passover, falls on a Friday. Suppose, for instance, it falls on a Tuesday: one of three things must be done. Either (which seems never to have been proposed) the crucifixion and resurrection must be celebrated on Tuesday and Sunday, with a wrong interval; or the former on Tuesday, the latter on Thursday, abandoning the first day of the week; or the former on Friday, and the latter on Sunday, abandoning the paschal commemoration of the crucifixion.

The last mode has been, as every one knows, finally adopted. The disputes of the first three centuries did not turn on any calendar questions. The Easter question was merely the symbol of the struggle between what we may call the Jewish and Gentile sects of Christians: and it nearly divided the Christian world, the Easterns, for the most part, being Quartadecimans. It is very important to note that there is no recorded dispute about a method of predicting the new moon, that is, no general dispute leading to formation of sects: there may have been difficulties, and discussions about them. The Metonic cycle, presently mentioned, must have been used by many, perhaps most, churches.

2. The question came before the Nicene Council (A.D. 325) not as an astronomical, but as a doctrinal, question: it was, in fact, this, Shall the passover be treated as a part of Christianity? The Council resolved this question in the negative, and the only information on its premises and conclusion, or either, which comes from itself, is contained in the following sentence of the synodical epistle, which epistle is preserved by Socrates and Theodoret. "We also send you the good news concerning the unanimous consent of all in reference to the celebration of the most solemn feast of Easter, for this difference also has been made up by the assistance of your prayers: so that all the brethren in the East, who formerly celebrated this festival at the same time as the Jews, will in future conform to the Romans and to us, and to all who have of old observed our manner of celebrating Easter." This is all that can be found on the subject: none of the stories about the Council ordaining the astronomical mode of finding Easter, and introducing the Metonic cycle into ecclesiastical reckoning, have any contemporary evidence: the canons which purport to be those of the Nicene Council do not contain a word about Easter; and this is evidence, whether we suppose those canons to be genuine or spurious.

3. The astronomical dispute about a lunar cycle for the prediction of Easter either commenced, or became prominent, by the extinction of greater ones, soon after the time of the Nicene Council. Pope Innocent I met with difficulty in 414. S. Leo, in 454, ordained that Easter of 455 should be April 24; which is right. It is useless to record details of these disputes in a summary: the result was, that in the year 463, Pope Hilarius employed Victorinus of Aquitaine to correct the Calendar, and Victorinus formed a rule which lasted until the sixteenth century. He combined the Metonic cycle and the solar cycle presently described. But this cycle bears the name of Dionysius Exiguus, a Scythian settled at Rome, about A.D. 530, who adapted it to his new yearly reckoning, when he abandoned the era of Diocletian as a commencement, and constructed that which is now in common use.

4. With Dionysius, if not before, terminated all difference as to the mode of keeping Easter which is of historical note: the increasing defects of the Easter Cycle produced in time the remonstrance of persons versed in astronomy, among whom may be mentioned Roger Bacon, Sacrobosco, Cardinal Cusa, Regiomontanus, etc. From the middle of the sixth to that of the sixteenth century, one rule was observed.

5. The mode of applying astronomy to chronology has always involved these two principles. First, the actual position of the heavenly body is not the object of consideration, but what astronomers call its mean place, which may be described thus. Let a fictitious sun or moon move in the heavens, in such manner as to revolve among the fixed stars at an average rate, avoiding the alternate accelerations and retardations which take place in every planetary motion. Thus the fictitious (say mean) sun and moon are always very near to the real sun and moon. The ordinary clocks show time by the mean, not the real, sun: and it was always laid down that Easter depends on the opposition (or full moon) of the mean sun and moon, not of the real ones. Thus we see that, were the Calendar ever so correct as to the mean moon, it would be occasionally false as to the true one: if, for instance, the opposition of the mean sun and moon took place at one second before midnight, and that of the real bodies only two seconds afterwards, the calendar day of full moon would be one day before that of the common almanacs. Here is a way in which the discussions of 1818 and 1845 might have arisen: the British legislature has defined the moon as the regulator of the paschal calendar. But this was only a part of the mistake.

6. Secondly, in the absence of perfectly accurate knowledge of the solar and lunar motion (and for convenience, even if such knowledge existed), cycles are, and always have been taken, which serve to represent those motions nearly. The famous Metonic cycle, which is introduced into ecclesiastical chronology under the name of the cycle of the golden numbers, is a period of 19 Julian years. This period, in the old Calendar, was taken to contain exactly 235 lunations, or intervals between new moons, of the mean moon. Now the state of the case is:

19 average Julian years make 6939 days 18 hours.

235 average lunations make 6939 days 16 hours 31 minutes.

So that successive cycles of golden numbers, supposing the first to start right, amount to making the new moons fall too late, gradually, so that the mean moon of this cycle gains 1 hour 29 minutes in 19 years upon the mean moon of the heavens, or about a day in 300 years. When the Calendar was reformed, the calendar new moons were four days in advance of the mean moon of the heavens: so that, for instance, calendar full moon on the 18th usually meant real full moon on the 14th.

7. If the difference above had not existed, the moon of the heavens (the mean moon at least), would have returned permanently to the same days of the month in 19 years; with an occasional slip arising from the unequal distribution of the leap years, of which a period contains sometimes five and sometimes four. As a general rule, the days of new and full moon in any one year would have been also the days of new and full moon of a year having 19 more units in its date. Again, if there had been no leap years, the days of the month would have returned to the same days of the week every seven years. The introduction of occasional 29ths of February disturbs this, and makes the permanent return of month days to week days occur only after 28 years. If all had been true, the lapse of 28 times 19, or 532 years, would have restored the year in every point: that is, A.D. 1, for instance, and A.D. 533, would have had the same almanac in every matter relating to week days, month days, sun, and moon (mean sun and moon at least). And on the supposition of its truth, the old system of Dionysius was framed. Its errors, are, first, that the moments of mean new moon advance too much by 1 h. 29 m. in 19 average Julian years; secondly, that the average Julian year of 365¼ days is too long by 11 m. 10 s.

8. The Council of Trent, moved by the representations made on the state of the Calendar, referred the consideration of it to the Pope. In 1577, Gregory XIII submitted to the Roman Catholic Princes and Universities a plan presented to him by the representatives of Aloysius Lilius, then deceased. This plan being approved of, the Pope nominated a commission to consider its details, the working member of which was the Jesuit Clavius. A short work was prepared by Clavius, descriptive of the new Calendar: this was published in 1582, with the Pope's bull (dated February 24, 1581) prefixed. A larger work was prepared by Clavius, containing fuller explanation, and entitled Romani Calendarii a Gregorio XIII. Pontifice Maximo restituti Explicatio. This was published at Rome in 1603, and again in the collection of the works of Clavius in 1612.

9. The following extracts from Clavius settle the question of the meaning of the term moon, as used in the Calendar:

"Who, except a few who think they are very sharp-sighted in this matter, is so blind as not to see that the 14th of the moon and the full moon are not the same things in the Church of God?... Although the Church, in finding the new moon, and from it the 14th day, uses neither the true nor the mean motion of the moon, but measures only according to the order of a cycle, it is nevertheless undeniable that the mean full moons found from astronomical tables are of the greatest use in determining the cycle which is to be preferred ... the new moons of which cycle, in order to the due celebration of Easter, should be so arranged that the 14th days of those moons, reckoning from the day of new moon inclusive, should not fall two or more days before the mean full moon, but only one day, or else on the very day itself, or not long after. And even thus far the Church need not take very great pains ... for it is sufficient that all should reckon by the 14th day of the moon in the cycle, even though sometimes it should be more than one day before or after the mean full moon.... We have taken pains that in our cycle the new moons should follow the real new moons, so that the 14th of the moon should fall either the day before the mean full moon, or on that day, or not long after; and this was done on purpose, for if the new moon of the cycle fell on the same day as the mean new moon of the astronomers, it might chance that we should celebrate Easter on the same day as the Jews or the Quartadeciman heretics, which would be absurd, or else before them, which would be still more absurd."

From this it appears that Clavius continued the Calendar of his predecessors in the choice of the fourteenth day of the moon. Our legislature lays down the day of the full moon: and this mistake appears to be rather English than Protestant; for it occurs in missals published in the reign of Queen Mary. The calendar lunation being 29½ days, the middle day is the fifteenth day, and this is and was reckoned as the day of the full moon. There is every right to presume that the original passover was a feast of the real full moon: but it is most probable that the moons were then reckoned, not from the astronomical conjunction with the sun, which nobody sees except at an eclipse, but from the day of first visibility of the new moon. In fine climates this would be the day or two days after conjunction; and the fourteenth day from that of first visibility inclusive, would very often be the day of full moon. The following is then the proper correction of the precept in the Act of Parliament:

Easter Day, on which the rest depend, is always the First Sunday after the fourteenth day of the calendar moon which happens upon or next after the Twenty-first day of March, according to the rules laid down for the construction of the Calendar; and if the fourteenth day happens upon a Sunday, Easter Day is the Sunday after.

10. Further, it appears that Clavius valued the celebration of the festival after the Jews, etc., more than astronomical correctness. He gives comparison tables which would startle a believer in the astronomical intention of his Calendar: they are to show that a calendar in which the moon is always made a day older than by him, represents the heavens better than he has done, or meant to do. But it must be observed that this diminution of the real moon's age has a tendency to make the English explanation often practically accordant with the Calendar. For the fourteenth day of Clavius is generally the fifteenth day of the mean moon of the heavens, and therefore most often that of the real moon. But for this, 1818 and 1845 would not have been the only instances of our day in which the English precept would have contradicted the Calendar.

11. In the construction of the Calendar, Clavius adopted the ancient cycle of 532 years, but, we may say, without ever allowing it to run out. At certain periods, a shift is made from one part of the cycle into another. This is done whenever what should be Julian leap year is made a common year, as in 1700, 1800, 1900, 2100, etc. It is also done at certain times to correct the error of 1 h. 19 m., before referred to, in each cycle of golden numbers: Clavius, to meet his view of the amount of that error, put forward the moon's age a day 8 times in 2,500 years. As we cannot enter at full length into the explanation, we must content ourselves with giving a set of rules, independent of tables, by which the reader may find Easter for himself in any year, either by the old Calendar or the new. Any one who has much occasion to find Easters and movable feasts should procure Francœur's tables.

12. Rule for determining Easter Day of the Gregorian Calendar in any year of the new style. To the several parts of the rule are annexed, by way of example, the results for the year 1849.

I. Add 1 to the given year. (1850).

II. Take the quotient of the given year divided by 4, neglecting the remainder. (462).

III. Take 16 from the centurial figures of the given year, if it can be done, and take the remainder. (2).

IV. Take the quotient of III. divided by 4, neglecting the remainder. (0).

V. From the sum of I, II, and IV., subtract III. (2310).

VI. Find the remainder of V. divided by 7. (0).

VII. Subtract VI. from 7; this is the number of the dominical letter

1 2 3 4 5 6 7 (7; dominical letter G).

A B C D E F G

VIII. Divide I. by 19, the remainder (or 19, if no remainder) is the golden number. (7).

IX. From the centurial figures of the year subtract 17, divide by 25, and keep the quotient. (0).

X. Subtract IX. and 15 from the centurial figures, divide by 3, and keep the quotient. (1).

XI. To VIII. add ten times the next less number, divide by 30, and keep the remainder. (7).

XII. To XI. add X. and IV., and take away III., throwing out thirties, if any. If this give 24, change it into 25. If 25, change it into 26, whenever the golden number is greater than 11. If 0, change it into 30. Thus we have the epact, or age of the Calendar moon at the beginning of the year. (6).

When the Epact is 23, or less.

XIII. Subtract XII., the epact, from 45. (39).

XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7, if there be no remainder. (7)

When the Epact is greater than 23.

XIII. Subtract XII., the epact, from 75.

XIV. Subtract the epact from 57, divide by 7, and keep the remainder, or 7, if there be no remainder.

XV. To XIII. add VII., the dominical number, (and 7 besides, if XIV. be greater than VII.,) and subtract XIV., the result is the day of March, or if more than 31, subtract 31, and the result is the day of April, on which Easter Sunday falls. (39; Easter Day is April 8).

In the following examples, the several results leading to the final conclusion are tabulated.

Given Year 1592 1637 1723 1853 2018 4686

I. 1593 1638 1724 1854 2019 4687

II. 398 409 430 463 504 1171

III. — 0 1 2 4 30

IV. — 0 0 0 1 7

V. 1991 2047 2153 2315 2520 5835

VI. 3 3 4 5 0 4

VII. 4 4 3 2 7 3

VIII. 16 4 14 11 5 13

IX. — — 0 0 0 1

X. 0 0 0 1 1 10

XI. 16 4 24 21 15 13

XII. 16 4 23 20 13 0 say 30

XIII. 29 41 22 25 32 45

XIV. 4 2 4 7 7 6

XV. 29 43 28 27 32 49

Easter Day Mar.29 Apr.12 Mar.28 Mar.27 Apr.1 Apr.18

13. Rule for determining Easter Day of the Antegregorian Calendar in any year of the old style. To the several parts of the rule are annexed, by way of example, the results for the year 1287. The steps are numbered to correspond with the steps of the Gregorian rule, so that it can be seen what augmentations the latter requires.

I. Set down the given year. (1287).

II. Take the quotient of the given year divided by 4, neglecting the remainder (321).

V. Take 4 more than the sum of I. and II. (1612).

VI. Find the remainder of V. divided by 7. (2).

VII. Subtract VI. from 7; this is the number of the dominical letter

1 2 3 4 5 6 7 (5; dominical letter E).

A B C D E F G

VIII. Divide one more than the given year by 19, the remainder (or 19 if no remainder) is the golden number. (15).

XII. Divide 3 less than 11 times VIII. by 30; the remainder (or 30 if there be no remainder) is the epact. (12).

When the Epact is 23, or less.

XIII. Subtract XII., the epact, from 45. (33).

XIV. Subtract the epact from 27, divide by 7, and keep the remainder, or 7, if there be no remainder, (1).

When the Epact is greater than 23.

XIII. Subtract XII., the epact, from 75.

XIV. Subtract the epact from 57, divide by 7, and keep the remainder, or 7, if there be no remainder.

XV. To XIII. add VII., the dominical number, (and 7 besides if XIV. be greater than VII.,) and subtract XIV., the result is the day of March, or if more than 31, subtract 31, and the result is the day of April, on which Easter Sunday (old style) falls. (37; Easter Day is April 6).

These rules completely represent the old and new Calendars, so far as Easter is concerned. For further explanation we must refer to the articles cited at the commencement.

The annexed is the table of new and full moons of the Gregorian Calendar, cleared of the errors made for the purpose of preventing Easter from coinciding with the Jewish Passover.

The second table (page ) contains epacts, or ages of the moon at the beginning of the year: thus in 1913, the epact is 22, in 1868 it is 6. This table goes from 1850 to 1999: should the New Zealander not have arrived by that time, and should the churches of England and Rome then survive, the epact table may be continued from their liturgy-books. The way of using the table is as follows: Take the epact of the required year, and find it in the first or last column of the first table, in line with it are seen the calendar days of new and full moon. Thus, when the epact is 17, the new and full moons of March fall on the 13th and 28th. The result is, for the most part, correct: but in a minority of cases there is an error of a day. When this happens, the error is almost always a fraction of a day much less than twelve hours. Thus, when the table gives full moon on the 27th, and the real truth is the 28th, we may be sure it is early on the 28th.

Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec.

1 29 27 29 27 27 25 25 23 22 21 20 19 1

14 13 14 13 12 11 10 9 7 7 5 5

2 28 26 28 26 26 24 24 22 21 20 19 18 2

13 12 13 12 11 10 9 8 6 6 4 4

3 27 25 27 25 25 23 23 21 20 19 18 17 3

12 11 12 11 10 9 8 7 5 5 3 3

4 26 24 26 24 24 22 22 20 19 18 17 16 4

11 10 11 10 9 8 7 6 4 4 2 2,31

5 25 23 25 23 23 21 21 19 18 17 16 15 5

10 9 10 9 8 7 6 5 3 3 1 1,30

6 24 22 24 22 22 20 20 18 17 16 15 14 6

9 8 9 8 7 6 5 4 2 2,31 30 29

7 23 21 23 21 21 19 19 17 16 15 14 13 7

8 7 8 7 6 5 4 3 1 1,30 29 28

8 22 20 22 20 20 18 18 16 15 14 13 12 8

7 6 7 6 5 4 3 2,31 30 29 28 27

9 21 19 21 19 19 17 17 15 14 13 12 11 9

6 5 6 5 4 3 2 1,30 29 28 27 26

10 20 18 20 18 18 16 16 14 13 12 11 10 10

5 4 5 4 3 2 1,31 29 28 27 26 25

11 19 17 19 17 17 15 15 13 12 11 10 9 11

4 3 4 3 2 1,30 30 28 27 26 25 24

12 18 16 18 16 16 14 14 12 11 10 9 8 12

3 2 3 2 1,31 29 29 27 26 25 24 23

13 17 15 17 15 15 13 13 11 10 9 8 7 13

2 1 2 1,30 30 28 28 26 25 24 23 22

14 16 14 16 14 14 12 12 10 9 8 7 6 14

1,31 — 1,31 29 29 27 27 25 24 23 22 21

15 15 13 15 13 13 11 11 9 8 7 6 5 15

30 28 30 28 28 26 26 24 23 22 21 20

16 14 12 14 12 12 10 10 8 7 6 5 4 16

29 27 29 27 27 25 25 23 22 21 20 19

17 13 11 13 11 11 9 9 7 6 5 4 3 17

28 26 28 26 26 24 24 22 21 20 19 18

18 12 10 12 10 10 8 8 6 5 4 3 2 18

27 25 27 25 25 23 23 21 20 19 18 17

19 11 9 11 9 9 7 7 5 4 3 2 1,31 19

26 24 26 24 24 22 22 20 19 18 17 16

20 10 8 10 8 8 6 6 4 3 2 1,31 30 20

25 23 25 23 23 21 21 19 18 17 16 15

21 9 7 9 7 7 5 5 3 2 1,31 29 29 21

24 22 24 22 22 20 20 18 17 16 15 14

22 8 6 8 6 6 4 4 2 1,30 30 28 28 22

23 21 23 21 21 19 19 17 16 15 14 13

23 7 5 7 5 5 3 3 1,31 29 29 27 27 23

22 20 22 20 20 18 18 16 15 14 13 12

24 6 5 6 5 4 3 2 1,30 29 28 27 26 24

21 19 21 19 19 17 17 15 14 13 12 11

25 5 4 5 4 3 2 1,31 29 28 27 26 25 25

20 19 20 19 18 17 16 15 13 13 11 11

26 4 3 4 3 2 1,30 30 28 27 26 25 24 26

19 18 19 18 17 16 15 14 12 12 10 10

27 3 2 3 2 1,31 29 29 27 26 25 24 23 27

18 17 18 17 16 15 14 13 11 11 9 9

28 2 1 2 1,30 30 28 28 26 25 24 23 22 28

17 16 17 16 15 14 13 12 10 10 8 8

29 1,31 — 1,31 29 29 27 27 25 24 23 22 21 29

16 15 16 15 14 13 12 11 9 9 7 7

30 30 28 30 28 28 26 26 24 23 22 21 20 30

15 14 15 14 13 12 11 10 8 8 6 6

Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec.

0 1 2 3 4 5 6 7 8 9

185 17 28 9 20 2 12 23 4 15 26

186 7 18 30 11 22 3 14 25 6 17

187 28 9 20 1 12 23 4 15 26 7

188 18 30 11 22 3 14 25 6 17 28

189 9 21 1 12 23 4 15 26 7 18

190 29 10 21 2 13 24 5 16 27 8

191 19 30 11 22 3 14 26 6 17 29

192 10 21 2 13 24 5 16 27 8 19

193 30 11 22 3 14 26 6 17 29 10

194 21 2 13 24 5 16 27 8 19 30

195 11 22 3 14 26 6 17 29 10 21

196 2 13 24 5 16 27 8 19 30 11

197 22 3 14 26 6 17 29 10 21 2

198 13 24 5 16 27 8 19 30 11 22

199 3 14 26 6 17 29 10 21 2 13

For example, the year 1867. The epact is 25, and we find in the table:

J. F. M. AP. M. JU. JL. AU. S. O. N. D.

New 5+ 4 5+ 4 3+ 2 1,31 29 28- 27 26 25

Full 20 19- 20 19- 18 17 16 15 13- 13 11+ 11

When the truth is the day after + is written after the date; when the day before, -. Thus, the new moon of March is on the 6th; the full moon of April is on the 18th.

I now introduce a small paradox of my own; and as I am not able to prove it, I am compelled to declare that any one who shall dissent must be either very foolish or very dishonest, and will make me quite uncomfortable about the state of his soul. This being settled once for all, I proceed to say that the necessity of arriving at the truth about the assertions that the Nicene Council laid down astronomical tests led me to look at Fathers, Church histories, etc. to an extent which I never dreamed of before. One conclusion which I arrived at was, that the Nicene Fathers had a knack of sticking to the question which many later councils could not acquire. In our own day, it is not permitted to Convocation seriously to discuss any one of the points which are bearing so hard upon their resources of defence—the cursing clauses of the Athanasian Creed, for example. And it may be collected that the prohibition arises partly from fear that there is no saying where a beginning, if allowed, would end. There seems to be a suspicion that debate, once let loose, would play up old Trent with the liturgy, and bring the whole book to book. But if any one will examine the real Nicene Creed, without the augmentation, he will admire the way in which the framers stuck to the point, and settled what they had to decide, according to their view of it. With such a presumption of good sense in their favor, it becomes easier to believe in any claim which may be made on their behalf to tact or sagacity in settling any other matter. And I strongly suspect such a claim may be made for them on the Easter question.

I collect from many little indications, both before and after the Council, that the division of the Christian world into Judaical and Gentile, though not giving rise to a sectarian distinction expressed by names, was of far greater force and meaning than historians prominently admit. I took note of many indications of this, but not notes, as it was not to my purpose. If it were so, we must admire the discretion of the Council. The Easter question was the fighting ground of the struggle: the Eastern or Judaical Christians, with some varieties of usage and meaning, would have the Passover itself to be the great feast, but taken in a Christian sense; the Western or Gentile Christians, would have the commemoration of the Resurrection, connected with the Passover only by chronology. To shift the Passover in time, under its name, Pascha, without allusion to any of the force of the change, was gently cutting away the ground from under the feet of the Conservatives. And it was done in a very quiet way: no allusion to the precise character of the change; no hint that the question was about two different festivals: "all the brethren in the East, who formerly celebrated this festival at the same time as the Jews, will in future conform to the Romans and to us." The Judaizers meant to be keeping the Passover as a Christian feast: they are gently assumed to be keeping, not the Passover, but a Christian feast; and a doctrinal decision is quietly, but efficiently, announced under the form of a chronological ordinance. Had the Council issued theses of doctrine, and excommunicated all dissentients, the rupture of the East and West would have taken place earlier by centuries than it did. The only place in which I ever saw any part of my paradox advanced, was in an article in the Examiner newspaper, towards the end of 1866, after the above was written.

A story about Christopher Clavius, the workman of the new Calendar. I chanced to pick up "Albertus Pighius Campensis de æquinoctiorum solsticiorumque inventione... Ejusdem de ratione Paschalis celebrationis, De que Restitutione ecclesiastici Kalendarii," Paris, 1520, folio. On the title-page were decayed words followed by "..hristophor.. C..ii, 1556 (or 8)," the last blank not entirely erased by time, but showing the lower halves of an l and of an a, and rather too much room for a v. It looked very like E Libris Christophori Clavii 1556. By the courtesy of some members of the Jesuit body in London, I procured a tracing of the signature of Clavius from Rome, and the shapes of the letters, and the modes of junction and disjunction, put the matter beyond question. Even the extra space was explained; he wrote himself Clauius. Now in 1556, Clavius was nineteen years old: it thus appears probable that the framer of the Gregorian Calendar was selected, not merely as a learned astronomer, but as one who had attended to the calendar, and to works on its reformation, from early youth. When on the subject I found reason to think that Clavius had really read this work, and taken from it a phrase or two and a notion or two. Observe the advantage of writing the baptismal name at full length.

A COUPLE OF MINOR PARADOXES.

The discovery of a general resolution of all superior finite equations, of every numerical both algebraick and transcendent form. By A. P. Vogel, mathematician at Leipzick. Leipzick and London, 1845, 8vo.

This work is written in the English of a German who has not mastered the idiom: but it is always intelligible. It professes to solve equations of every degree "in a more extent sense, and till to every degree of exactness." The general solution of equations of all degrees is a vexed question, which cannot have the mysterious interest of the circle problem, and is of a comparatively modern date. Mr. Vogel announces a forthcoming treatise in which are resolved the "last impossibilities of pure mathematics."

Elective Polarity the Universal Agent. By Frances Barbara Burton, authoress of 'Astronomy familiarized,' 'Physical Astronomy,' &c. London, 1845, 8vo.

The title gives a notion of the theory. The first sentence states, that 12,500 years ago α Lyræ was the pole-star, and attributes the immense magnitude of the now fossil animals to a star of such "polaric intensity as Vega pouring its magnetic streams through our planet." Miss Burton was a lady of property, and of very respectable acquirements, especially in Hebrew; she was eccentric in all things.

1867.—Miss Burton is revived by the writer of a book on meteorology which makes use of the planets: she is one of his leading minds.

SPECULATIVE THOUGHT IN ENGLAND.

In the year 1845 the old Mathematical Society was merged in the Astronomical Society. The circle-squarers, etc., thrive more in England than in any other country: there are most weeds where there is the largest crop. Speculation, though not encouraged by our Government so much as by those of the Continent, has had, not indeed such forcing, but much wider diffusion: few tanks, but many rivulets. On this point I quote from the preface to the reprint of the work of Ramchundra, which I superintended for the late Court of Directors of the East India Company.

"That sound judgment which gives men well to know what is best for them, as well as that faculty of invention which leads to development of resources and to the increase of wealth and comfort, are both materially advanced, perhaps cannot rapidly be advanced without, a great taste for pure speculation among the general mass of the people, down to the lowest of those who can read and write. England is a marked example. Many persons will be surprised at this assertion. They imagine that our country is the great instance of the refusal of all unpractical knowledge in favor of what is useful. I affirm, on the contrary, that there is no country in Europe in which there has been so wide a diffusion of speculation, theory, or what other unpractical word the reader pleases. In our country, the scientific society is always formed and maintained by the people; in every other, the scientific academy—most aptly named—has been the creation of the government, of which it has never ceased to be the nursling. In all the parts of England in which manufacturing pursuits have given the artisan some command of time, the cultivation of mathematics and other speculative studies has been, as is well known, a very frequent occupation. In no other country has the weaver at his loom bent over the Principia of Newton; in no other country has the man of weekly wages maintained his own scientific periodical. With us, since the beginning of the last century, scores upon scores—perhaps hundreds, for I am far from knowing all—of annuals have run, some their ten years, some their half-century, some their century and a half, containing questions to be answered, from which many of our examiners in the universities have culled materials for the academical contests. And these questions have always been answered, and in cases without number by the lower order of purchasers, the mechanics, the weavers, and the printers' workmen. I cannot here digress to point out the manner in which the concentration of manufactures, and the general diffusion of education, have affected the state of things; I speak of the time during which the present system took its rise, and of the circumstances under which many of its most effective promoters were trained. In all this there is nothing which stands out, like the state-nourished academy, with its few great names and brilliant single achievements. This country has differed from all others in the wide diffusion of the disposition to speculate, which disposition has found its place among the ordinary habits of life, moderate in its action, healthy in its amount."

THE OLD MATHEMATICAL SOCIETY.

Among the most remarkable proofs of the diffusion of speculation was the Mathematical Society, which flourished from 1717 to 1845. Its habitat was Spitalfields, and I think most of its existence was passed in Crispin Street. It was originally a plain society, belonging to the studious artisan. The members met for discussion once a week; and I believe I am correct in saying that each man had his pipe, his pot, and his problem. One of their old rules was that, "If any member shall so far forget himself and the respect due to the Society as in the warmth of debate to threaten or offer personal violence to any other member, he shall be liable to immediate expulsion, or to pay such fine as the majority of the members present shall decide." But their great rule, printed large on the back of the title page of their last book of regulations, was "By the constitution of the Society, it is the duty of every member, if he be asked any mathematical or philosophical question by another member, to instruct him in the plainest and easiest manner he is able." We shall presently see that, in old time, the rule had a more homely form.

I have been told that De Moivre was a member of this Society. This I cannot verify: circumstances render it unlikely; even though the French refugees clustered in Spitalfields; many of them were of the Society, which there is some reason to think was founded by them. But Dolland, Thomas Simpson, Saunderson, Crossley, and others of known name, were certainly members. The Society gradually declined, and in 1845 was reduced to nineteen members. An arrangement was made by which sixteen of these members, who where not already in the Astronomical Society became Fellows without contribution, all the books and other property of the old Society being transferred to the new one. I was one of the committee which made the preliminary inquiries, and the reason of the decline was soon manifest. The only question which could arise was whether the members of the society of working men—for this repute still continued—were of that class of educated men who could associate with the Fellows of the Astronomical Society on terms agreeable to all parties. We found that the artisan element had been extinct for many years; there was not a man but might, as to education, manners, and position, have become a Fellow in the usual way. The fact was that life in Spitalfields had become harder: and the weaver could only live from hand to mouth, and not up to the brain. The material of the old Society no longer existed.

In 1798, experimental lectures were given, a small charge for admission being taken at the door: by this hangs a tale—and a song. Many years ago, I found among papers of a deceased friend, who certainly never had anything to do with the Society, and who passed all his life far from London, a song, headed "Song sung by the Mathematical Society in London, at a dinner given Mr. Fletcher, a solicitor, who had defended the Society gratis." Mr. Williams, the Assistant Secretary of the Astronomical Society, formerly Secretary of the Mathematical Society, remembered that the Society had had a solicitor named Fletcher among the members. Some years elapsed before it struck me that my old friend Benjamin Gompertz, who had long been a member, might have some recollection of the matter. The following is an extract of a letter from him (July 9, 1861):

"As to the Mathematical Society, of which I was a member when only 18 years of age, [Mr. G. was born in 1779], having been, contrary to the rules, elected under the age of 21. How I came to be a member of that Society—and continued so until it joined the Astronomical Society, and was then the President—was: I happened to pass a bookseller's small shop, of second-hand books, kept by a poor taylor, but a good mathematician, John Griffiths. I was very pleased to meet a mathematician, and I asked him if he would give me some lessons; and his reply was that I was more capable to teach him, but he belonged to a society of mathematicians, and he would introduce me. I accepted the offer, and I was elected, and had many scholars then to teach, as one of the rules was, if a member asked for information, and applied to any one who could give it, he was obliged to give it, or fine one penny. Though I might say much with respect to the Society which would be interesting, I will for the present reply only to your question. I well knew Mr. Fletcher, who was a very clever and very scientific person. He did, as solicitor, defend an action brought by an informer against the Society—I think for 5,000l.—for giving lectures to the public in philosophical subjects [i.e., for unlicensed public exhibition with money taken at the doors]. I think the price for admission was one shilling, and we used to have, if I rightly recollect, from two to three hundred visitors. Mr. Fletcher was successful in his defence, and we got out of our trouble. There was a collection made to reward his services, but he did not accept of any reward: and I think we gave him a dinner, as you state, and enjoyed ourselves; no doubt with astronomical songs and other songs; but my recollection does not enable me to say if the astronomical song was a drinking song. I think the anxiety caused by that action was the cause of some of the members' death. [They had, no doubt, broken the law in ignorance; and by the sum named, the informer must have been present, and sued for a penalty on every shilling he could prove to have been taken]."

I by no means guarantee that the whole song I proceed to give is what was sung at the dinner: I suspect, by the completeness of the chain, that augmentations have been made. My deceased friend was just the man to add some verses, or the addition may have been made before it came into his hands, or since his decease, for the scraps containing the verses passed through several hands before they came into mine. We may, however, be pretty sure that the original is substantially contained in what is given, and that the character is therefore preserved. I have had myself to repair damages every now and then, in the way of conjectural restoration of defects caused by ill-usage.

THE ASTRONOMER'S DRINKING SONG.

"Whoe'er would search the starry sky,

Its secrets to divine, sir,

Should take his glass—I mean, should try

A glass or two of wine, sir!

True virtue lies in golden mean,

And man must wet his clay, sir;

Join these two maxims, and 'tis seen

He should drink his bottle a day, sir!

"Old Archimedes, reverend sage!

By trump of fame renowned, sir,

Deep problems solved in every page,

And the sphere's curved surface found, sir:

Himself he would have far outshone,

And borne a wider sway, sir,

Had he our modern secret known,

And drank a bottle a day, sir!

"When Ptolemy, now long ago,

Believed the earth stood still, sir,

He never would have blundered so,

Had he but drunk his fill, sir:

He'd then have felt it circulate,

And would have learnt to say, sir,

The true way to investigate

Is to drink your bottle a day, sir!

"Copernicus, that learned wight,

The glory of his nation,

With draughts of wine refreshed his sight,

And saw the earth's rotation;

Each planet then its orb described,

The moon got under way, sir;

These truths from nature he imbibed

For he drank his bottle a day, sir!

"The noble Tycho placed the stars,

Each in its due location;

He lost his nose by spite of Mars,

But that was no privation:

Had he but lost his mouth, I grant

He would have felt dismay, sir,

Bless you! he knew what he should want

To drink his bottle a day, sir!

"Cold water makes no lucky hits;

On mysteries the head runs:

Small drink let Kepler time his wits

On the regular polyhedrons:

He took to wine, and it changed the chime,

His genius swept away, sir,

Through area varying as the time

At the rate of a bottle a day, sir!

"Poor Galileo, forced to rat

Before the Inquisition,

E pur si muove was the pat

He gave them in addition:

He meant, whate'er you think you prove,

The earth must go its way, sirs;

Spite of your teeth I'll make it move,

For I'll drink my bottle a day, sirs!

"Great Newton, who was never beat

Whatever fools may think, sir;

Though sometimes he forgot to eat,

He never forgot to drink, sir:

Descartes took nought but lemonade,

To conquer him was play, sir;

The first advance that Newton made

Was to drink his bottle a day, sir!

"D'Alembert, Euler, and Clairaut,

Though they increased our store, sir,

Much further had been seen to go

Had they tippled a little more, sir!

Lagrange gets mellow with Laplace,

And both are wont to say, sir,

The philosophe who's not an ass

Will drink his bottle a day, sir!

"Astronomers! what can avail

Those who calumniate us;

Experiment can never fail

With such an apparatus:

Let him who'd have his merits known

Remember what I say, sir;

Fair science shines on him alone

Who drinks his bottle a day, sir!

"How light we reck of those who mock

By this we'll make to appear, sir,

We'll dine by the sidereal clock

For one more bottle a year, sir:

But choose which pendulum you will,

You'll never make your way, sir,

Unless you drink—and drink your fill,—

At least a bottle a day, sir!"

Old times are changed, old manners gone!

There is a new Mathematical Society, and I am, at this present writing (1866), its first President. We are very high in the newest developments, and bid fair to take a place among the scientific establishments. Benjamin Gompertz, who was President of the old Society when it expired, was the link between the old and new body: he was a member of ours at his death. But not a drop of liquor is seen at our meetings, except a decanter of water: all our heavy is a fermentation of symbols; and we do not draw it mild. There is no penny fine for reticence or occult science; and as to a song! not the ghost of a chance.

1826. The time may have come when the original documents connected with the discovery of Neptune may be worth revising. The following are extracts from the Athenæum of October 3 and October 17:

LE VERRIER'S PLANET.

We have received, at the last moment before making up for press, the following letter from Sir John Herschel, in reference to the matter referred to in the communication from Mr. Hind given below:

"Collingwood, Oct. 1.

"In my address to the British Association assembled at Southampton, on the occasion of my resigning the chair to Sir R. Murchison, I stated, among the remarkable astronomical events of the last twelvemonth, that it had added a new planet to our list,—adding, 'it has done more,—it has given us the probable prospect of the discovery of another. We see it as Columbus saw America from the shores of Spain. Its movements have been felt, trembling along the far-reaching line of our analysis, with a certainty hardly inferior to that of ocular demonstration.'—These expressions are not reported in any of the papers which profess to give an account of the proceedings, but I appeal to all present whether they were not used.

"Give me leave to state my reasons for this confidence; and, in so doing, to call attention to some facts which deserve to be put on record in the history of this noble discovery. On July 12, 1842, the late illustrious astronomer, Bessel, honored me with a visit at my present residence. On the evening of that day, conversing on the great work of the planetary reductions undertaken by the Astronomer Royal—then in progress, and since published,—M. Bessel remarked that the motions of Uranus, as he had satisfied himself by careful examination of the recorded observations, could not be accounted for by the perturbations of the known planets; and that the deviations far exceeded any possible limits of error of observation. In reply to the question, Whether the deviations in question might not be due to the action of an unknown planet?—he stated that he considered it highly probable that such was the case,—being systematic, and such as might be produced by an exterior planet. I then inquired whether he had attempted, from the indications afforded by these perturbations, to discover the position of the unknown body,—in order that 'a hue and cry' might be raised for it. From his reply, the words of which I do not call to mind, I collected that he had not then gone into that inquiry; but proposed to do so, having now completed certain works which had occupied too much of his time. And, accordingly, in a letter which I received from him after his return to Königsberg, dated November 14, 1842, he says,—'In reference to our conversation at Collingwood, I announce to you (melde ich Ihnen) that Uranus is not forgotten.' Doubtless, therefore, among his papers will be found some researches on the subject.

"The remarkable calculations of M. Le Verrier—which have pointed out, as now appears, nearly the true situation of the new planet, by resolving the inverse problem of the perturbations—if uncorroborated by repetition of the numerical calculations by another hand, or by independent investigation from another quarter, would hardly justify so strong an assurance as that conveyed by my expressions above alluded to. But it was known to me, at that time, (I will take the liberty to cite the Astronomer Royal as my authority) that a similar investigation had been independently entered into, and a conclusion as to the situation of the new planet very nearly coincident with M. Le Verrier's arrived at (in entire ignorance of his conclusions), by a young Cambridge mathematician, Mr. Adams;—who will, I hope, pardon this mention of his name (the matter being one of great historical moment),—and who will, doubtless, in his own good time and manner, place his calculations before the public.

"J. F. W. HERSCHEL."

Discovery of Le Verrier's Planet.

Mr. Hind announces to the Times that he has received a letter from Dr. Brünnow, of the Royal Observatory at Berlin, giving the very important information that Le Verrier's planet was found by M. Galle, on the night of September 23. "In announcing this grand discovery," he says, "I think it better to copy Dr. Brünnow's letter."

"Berlin, Sept. 25.

"My dear Sir—M. Le Verrier's planet was discovered here the 23d of September, by M. Galle. It is a star of the 8th magnitude, but with a diameter of two or three seconds. Here are its places:

h. m. s. R. A. Declination.

Sept. 23, 12 0 14.6 M.T. 328° 19' 16.0" -13° 24' 8.2"

Sept. 24, 8 54 40.9 M.T. 328° 18' 14.3" -13° 24' 29.7"

The planet is now retrograde, its motion amounting daily to four seconds of time.

"Yours most respectfully, Brünnow."

"This discovery," Mr. Hind says, "may be justly considered one of the greatest triumphs of theoretical astronomy;" and he adds, in a postscript, that the planet was observed at Mr. Bishop's Observatory, in the Regent's Park, on Wednesday night, notwithstanding the moonlight and hazy sky. "It appears bright," he says, "and with a power of 320 I can see the disc. The following position is the result of instrumental comparisons with 33 Aquarii:

Sept. 30, at 8h. 16m. 21s. Greenwich mean time—

Right ascension of planet 21h. 52m. 47.15s.

South declination 13° 27' 20"."

THE NEW PLANET.

"Cambridge Observatory, Oct. 15.

"The allusion made by Sir John Herschel, in his letter contained in the Athenæum of October 3, to the theoretical researches of Mr. Adams, respecting the newly-discovered planet, has induced me to request that you would make the following communication public. It is right that I should first say that I have Mr. Adams's permission to make the statements that follow, so far as they relate to his labors. I do not propose to enter into a detail of the steps by which Mr. Adams was led, by his spontaneous and independent researches, to a conclusion that a planet must exist more distant than Uranus. The matter is of too great historical moment not to receive a more formal record than it would be proper to give here. My immediate object is to show, while the attention of the scientific public is more particularly directed to the subject, that, with respect to this remarkable discovery, English astronomers may lay claim to some merit.

"Mr. Adams formed the resolution of trying, by calculation, to account for the anomalies in the motion of Uranus on the hypothesis of a more distant planet, when he was an undergraduate in this university, and when his exertions for the academical distinction, which he obtained in January 1843, left him no time for pursuing the research. In the course of that year, he arrived at an approximation to the position of the supposed planet; which, however, he did not consider to be worthy of confidence, on account of his not having employed a sufficient number of observations of Uranus. Accordingly, he requested my intervention to obtain for him the early Greenwich observations, then in course of reduction;—which the Astronomer Royal immediately supplied, in the kindest possible manner. This was in February, 1844. In September, 1845, Mr. Adams communicated to me values which he had obtained for the heliocentric longitude, excentricity of orbit, longitude of perihelion, and mass, of an assumed exterior planet,—deduced entirely from unaccounted-for perturbations of Uranus. The same results, somewhat corrected, he communicated, in October, to the Astronomer Royal. M. Le Verrier, in an investigation which was published in June of 1846, assigned very nearly the same heliocentric longitude for the probable position of the planet as Mr. Adams had arrived at, but gave no results respecting its mass and the form of its orbit. The coincidence as to position from two entirely independent investigations naturally inspired confidence; and the Astronomer Royal shortly after suggested the employing of the Northumberland telescope of this observatory in a systematic search after the hypothetical planet; recommending, at the same time, a definite plan of operations. I undertook to make the search,—and commenced observing on July 29. The observations were directed, in the first instance, to the part of the heavens which theory had pointed out as the most probable place of the planet; in selecting which I was guided by a paper drawn up for me by Mr. Adams. Not having hour xxi. of the Berlin star-maps—of the publication of which I was not aware—I had to proceed on the principle of comparison of observations made at intervals. On July 30, I went over a zone 9' broad, in such a manner as to include all stars to the eleventh magnitude. On August 4, I took a broader zone and recorded a place of the planet. My next observations were on August 12; when I met with a star of the eighth magnitude in the zone which I had gone over on July 30,—and which did not then contain this star. Of course, this was the planet;—the place of which was, thus, recorded a second time in four days of observing. A comparison of the observations of July 30 and August 12 would, according to the principle of search which I employed, have shown me the planet. I did not make the comparison till after the detection of it at Berlin—partly because I had an impression that a much more extensive search was required to give any probability of discovery—and partly from the press of other occupation. The planet, however, was secured, and two positions of it recorded six weeks earlier here than in any other observatory,—and in a systematic search expressly undertaken for that purpose. I give now the positions of the planet on August 4 and August 12.

Greenwich mean time.

Aug. 4, 13h. 36m. 25s. ... R.A. 21h. 58m. 14.70s.

N.P.D. 102° 57' 32.2"

Aug. 12, 13h. 3m. 26s. ... R.A. 21h. 57m. 26.13s.

N.P.D. 103° 2' 0.2"

"From these places compared with recent observations Mr. Adams has obtained the following results:

Distance of the planet from the sun ... 30.05

Inclination of the orbit ... 1° 45'

Longitude of the descending node ... 309° 43'

Heliocentric longitude, Aug. 4 ... 326° 39'

"The present distance from the sun is, therefore, thirty times the earth's mean distance;—which is somewhat less than the theory had indicated. The other elements of the orbit cannot be approximated to till the observations shall have been continued for a longer period.

"The part taken by Mr. Adams in the theoretical search after this planet will, perhaps, be considered to justify the suggesting of a name. With his consent, I mention Oceanus as one which may possibly receive the votes of astronomers.—I have authority to state that Mr. Adams's investigations will in a short time, be published in detail.

"J. Challis."

ASTRONOMICAL POLICE REPORT.

"An ill-looking kind of a body, who declined to give any name, was brought before the Academy of Sciences, charged with having assaulted a gentleman of the name of Uranus in the public highway. The prosecutor was a youngish looking person, wrapped up in two or three great coats; and looked chillier than anything imaginable, except the prisoner,—whose teeth absolutely shook, all the time.

Policeman Le Verrier stated that he saw the prosecutor walking along the pavement,—and sometimes turning sideways, and sometimes running up to the railings and jerking about in a strange way. Calculated that somebody must be pulling his coat, or otherwise assaulting him. It was so dark that he could not see; but thought, if he watched the direction in which the next odd move was made, he might find out something. When the time came, he set Brünnow, a constable in another division of the same force, to watch where he told him; and Brünnow caught the prisoner lurking about in the very spot,—trying to look as if he was minding his own business. Had suspected for a long time that somebody was lurking about in the neighborhood. Brünnow was then called, and deposed to his catching the prisoner as described.

M. Arago.—Was the prosecutor sober?

Le Verrier.—Lord, yes, your worship; no man who had a drop in him ever looks so cold as he did.

M. Arago.—Did you see the assault?

Le Verrier.—I can't say I did; but I told Brünnow exactly how he'd be crouched down;—just as he was.

M. Arago (to Brünnow).—Did you see the assault?

Brünnow.—No, your worship; but I caught the prisoner.

M. Arago.—How did you know there was any assault at all?

Le Verrier.—I reckoned it couldn't be otherwise, when I saw the prosecutor making those odd turns on the pavement.

M. Arago.—You reckon and you calculate! Why, you'll tell me, next, that you policemen may sit at home and find out all that's going on in the streets by arithmetic. Did you ever bring a case of this kind before me till now?

Le Verrier.—Why, you see, your worship, the police are growing cleverer and cleverer every day. We can't help it:—it grows upon us.

M. Arago.—You're getting too clever for me. What does the prosecutor know about the matter?

The prosecutor said, all he knew was that he was pulled behind by somebody several times. On being further examined, he said that he had seen the prisoner often, but did not know his name, nor how he got his living; but had understood he was called Neptune. He himself had paid rates and taxes a good many years now. Had a family of six,—two of whom got their own living.

The prisoner being called on for his defence, said that it was a quarrel. He had pushed the prosecutor—and the prosecutor had pushed him. They had known each other a long time, and were always quarreling;—he did not know why. It was their nature, he supposed. He further said, that the prosecutor had given a false account of himself;—that he went about under different names. Sometimes he was called Uranus, sometimes Herschel, and sometimes Georgium Sidus; and he had no character for regularity in the neighborhood. Indeed, he was sometimes not to be seen for a long time at once.

The prosecutor, on being asked, admitted, after a little hesitation, that he had pushed and pulled the prisoner too. In the altercation which followed, it was found very difficult to make out which began:—and the worthy magistrate seemed to think they must have begun together.

M. Arago.—Prisoner, have you any family?

The prisoner declined answering that question at present. He said he thought the police might as well reckon it out whether he had or not.

M. Arago said he didn't much differ from that opinion.—He then addressed both prosecutor and prisoner; and told them that if they couldn't settle their differences without quarreling in the streets, he should certainly commit them both next time. In the meantime, he called upon both to enter into their own recognizances; and directed the police to have an eye upon both,—observing that the prisoner would be likely to want it a long time, and the prosecutor would be not a hair the worse for it."

This quib was written by a person who was among the astronomers: and it illustrates the fact that Le Verrier had sole possession of the field until Mr. Challis's letter appeared. Sir John Herschel's previous communication should have paved the way: but the wonder of the discovery drove it out of many heads. There is an excellent account of the whole matter in Professor Grant's History of Physical Astronomy. The squib scandalized some grave people, who wrote severe admonitions to the editor. There are formalists who spend much time in writing propriety to journals, to which they serve as foolometers. In a letter to the Athenæum, speaking of the way in which people hawk fine terms for common things, I said that these people ought to have a new translation of the Bible, which should contain the verse "gentleman and lady, created He them." The editor was handsomely fired and brimstoned!

A NEW THEORY OF TIDES.

A new theory of the tides: in which the errors of the usual theory are demonstrated; and proof shewn that the full moon is not the cause of a concomitant spring tide, but actually the cause of the neaps.... By Commr. Debenham, R.N. London, 1846, 8vo.

The author replied to a criticism in the Athenæum, and I remember how, in a very few words, he showed that he had read nothing on the subject. The reviewer spoke of the forces of the planets (i.e., the Sun and Moon) on the ocean, on which the author remarks, "But N.B. the Sun is no planet, Mr. Critic." Had he read any of the actual investigations on the usual theory, he would have known that to this day the sun and moon continue to be called planets—though the phrase is disappearing—in speaking of the tides; the sense, of course, being the old one, wandering bodies.

A large class of the paradoxers, when they meet with something which taken in their sense is absurd, do not take the trouble to find out the intended meaning, but walk off with the words laden with their own first construction. Such men are hardly fit to walk the streets without an interpreter. I was startled for a moment, at the time when a recent happy—and more recently happier—marriage occupied the public thoughts, by seeing in a haberdasher's window, in staring large letters, an unpunctuated sentence which read itself to me as "Princess Alexandra! collar and cuff!" It immediately occurred to me that had I been any one of some scores of my paradoxers, I should, no doubt, have proceeded to raise the mob against the unscrupulous person who dared to hint to a young bride such maleficent—or at least immellificent—conduct towards her new lord. But, as it was, certain material contexts in the shop window suggested a less savage explanation. A paradoxer should not stop at reading the advertisements of Newton or Laplace; he should learn to look at the stock of goods.

I think I must have an eye for double readings, when presented: though I never guess riddles. On the day on which I first walked into the Panizzi reading room—as it ought to be called—at the Museum, I began my circuit of the wall-shelves at the ladies' end: and perfectly coincided in the propriety of the Bibles and theological works being placed there. But the very first book I looked on the back of had, in flaming gold letters, the following inscription—"Blast the Antinomians!" If a line had been drawn below the first word, Dr. Blast's history of the Antinomians would not have been so fearfully misinterpreted. It seems that neither the binder nor the arranger of the room had caught my reading. The book was removed before the catalogue of books of reference was printed.

AN ASTRONOMICAL PARADOXER.

Two systems of astronomy: first, the Newtonian system, showing the rise and progress thereof, with a short historical account; the general theory with a variety of remarks thereon: second, the system in accordance with the Holy Scriptures, showing the rise and progress from Enoch, the seventh from Adam, the prophets, Moses, and others, in the first Testament; our Lord Jesus Christ, and his apostles, in the new or second Testament; Reeve and Muggleton, in the third and last Testament; with a variety of remarks thereon. By Isaac Frost. London, 1846, 4to.

A very handsomely printed volume, with beautiful plates. Many readers who have heard of Muggletonians have never had any distinct idea of Lodowick Muggleton, the inspired tailor, (1608-1698) who about 1650 received his commission from heaven, wrote a Testament, founded a sect, and descended to posterity. Of Reeve less is usually said; according to Mr. Frost, he and Muggleton are the two "witnesses." I shall content myself with one specimen of Mr. Frost's science:

"I was once invited to hear read over 'Guthrie on Astronomy,' and when the reading was concluded I was asked my opinion thereon; when I said, 'Doctor, it appears to me that Sir I. Newton has only given two proofs in support of his theory of the earth revolving round the sun: all the rest is assertion without any proofs.'—'What are they?' inquired the Doctor.—'Well,' I said, 'they are, first, the power of attraction to keep the earth to the sun; the second is the power of repulsion, by virtue of the centrifugal motion of the earth: all the rest appears to me assertion without proof.' The Doctor considered a short time and then said, 'It certainly did appear so.' I said, 'Sir Isaac has certainly obtained the credit of completing the system, but really he has only half done his work.'—'How is that,' inquired my friend the Doctor. My reply was this: 'You will observe his system shows the earth traverses round the sun on an inclined plane; the consequence is, there are four powers required to make his system complete:

1st. The power of attraction.

2ndly. The power of repulsion.

3rdly. The power of ascending the inclined plane.

4thly. The power of descending the inclined plane.

You will thus easily see the four powers required, and Newton has only accounted for two; the work is therefore only half done.' Upon due reflection the Doctor said, 'It certainly was necessary to have these four points cleared up before the system could be said to be complete.'"

I have no doubt that Mr. Frost, and many others on my list, have really encountered doctors who could be puzzled by such stuff as this, or nearly as bad, among the votaries of existing systems, and have been encouraged thereby to print their objections. But justice requires me to say that from the words "power of repulsion by virtue of the centrifugal motion of the earth," Mr. Frost may be suspected of having something more like a notion of the much-mistaken term "centrifugal force" than many paradoxers of greater fame. The Muggletonian sect is not altogether friendless: over and above this handsome volume, the works of Reeve and Muggleton were printed, in 1832, in three quarto volumes. See Notes and Queries, 1st Series, v, 80; 3d Series, iii, 303.

[The system laid down by Mr. Frost, though intended to be substantially that of Lodowick Muggleton, is not so vagarious. It is worthy of note how very different have been the fates of two contemporary paradoxers, Muggleton and George Fox. They were friends and associates, and commenced their careers about the same time, 1647-1650. The followers of Fox have made their sect an institution, and deserve to be called the pioneers of philanthropy. But though there must still be Muggletonians, since expensive books are published by men who take the name, no sect of that name is known to the world. Nevertheless, Fox and Muggleton are men of one type, developed by the same circumstances: it is for those who investigate such men to point out why their teachings have had fates so different. Macaulay says it was because Fox found followers of more sense than himself. True enough: but why did Fox find such followers and not Muggleton? The two were equally crazy, to all appearance: and the difference required must be sought in the doctrines themselves.

Fox was not a rational man: but the success of his sect and doctrines entitles him to a letter of alteration of the phrase which I am surprised has not become current. When Conduitt, the husband of Newton's half-niece, wrote a circular to Newton's friends, just after his death, inviting them to bear their parts in a proper biography, he said, "As Sir I. Newton was a national man, I think every one ought to contribute to a work intended to do him justice." Here is the very phrase which is often wanted to signify that celebrity which puts its mark, good or bad, on the national history, in a manner which cannot be asserted of many notorious or famous historical characters. Thus George Fox and Newton are both national men. Dr. Roget's Thesaurus gives more than fifty synonyms—colleagues would be the better word—of "celebrated," any one of which might be applied, either in prose or poetry, to Newton or to his works, no one of which comes near to the meaning which Conduitt's adjective immediately suggests.

The truth is, that we are too monarchical to be national. We have the Queen's army, the Queen's navy, the Queen's highway, the Queen's English, etc.; nothing is national except the debt. That this remark is not new is an addition to its force; it has hardly been repeated since it was first made. It is some excuse that nation is not vernacular English: the country is our word, and country man is appropriated.]

Astronomical Aphorisms, or Theory of Nature; founded on the immutable basis of Meteoric Action. By P. Murphy, Esq. London, 1847, 12mo.

This is by the framer of the Weather Almanac, who appeals to that work as corroborative of his theory of planetary temperature, years after all the world knew by experience that this meteorological theory was just as good as the others.

The conspiracy of the Bullionists as it affects the present system of the money laws. By Caleb Quotem. Birmingham, 1847, 8vo. (pp. 16).

This pamphlet is one of a class of which I know very little, in which the effects of the laws relating to this or that political bone of contention are imputed to deliberate conspiracy of one class to rob another of what the one knew ought to belong to the other. The success of such writers in believing what they have a bias to believe, would, if they knew themselves, make them think it equally likely that the inculpated classes might really believe what it is their interest to believe. The idea of a guilty understanding existing among fundholders, or landholders, or any holders, all the country over, and never detected except by bouncing pamphleteers, is a theory which should have been left for Cobbett to propose, and for Apella to believe.

[August, 1866. A pamphlet shows how to pay the National Debt. Advance paper to railways, etc., receivable in payment of taxes. The railways pay interest and principal in money, with which you pay your national debt, and redeem your notes. Twenty-five years of interest redeems the notes, and then the principal pays the debt. Notes to be kept up to value by penalties.]

THEISM INDEPENDENT OF REVELATION.

The Reasoner. No. 45. Edited by G.J. Holyoake. Price 2d. Is there sufficient proof of the existence of God? 8vo. 1847.

This acorn of the holy oak was forwarded to me with a manuscript note, signed by the editor, on the part of the "London Society of Theological Utilitarians," who say, "they trust you may be induced to give this momentous subject your consideration." The supposition that a middle-aged person, known as a student of thought on more subjects than one, had that particular subject yet to begin, is a specimen of what I will call the assumption-trick of controversy, a habit which pervades all sides of all subjects. The tract is a proof of the good policy of letting opinions find their level, without any assistance from the Court of Queen's Bench. Twenty years earlier the thesis would have been positive, "There is sufficient proof of the non-existence of God," and bitter in its tone. As it stands, we have a moderate and respectful treatment—wrong only in making the opponent argue absurdly, as usually happens when one side invents the other—of a question in which a great many Christians have agreed with the atheist: that question being—Can the existence of God be proved independently of revelation? Many very religious persons answer this question in the negative, as well as Mr. Holyoake. And, this point being settled, all who agree in the negative separate into those who can endure scepticism, and those who cannot: the second class find their way to Christianity. This very number of The Reasoner announces the secession of one of its correspondents, and his adoption of the Christian faith. This would not have happened twenty years before: nor, had it happened, would it have been respectfully announced.

There are people who are very unfortunate in the expression of their meaning. Mr. Holyoake, in the name of the "London Society" etc., forwarded a pamphlet on the existence of God, and said that the Society trusted I "may be induced to give" the subject my "consideration." How could I know the Society was one person, who supposed I had arrived at a conclusion and wanted a "guiding word"? But so it seems it was: Mr. Holyoake, in the English Leader of October 15, 1864, and in a private letter to me, writes as follows:

"The gentleman who was the author of the argument, and who asked me to send it to Mr. De Morgan, never assumed that that gentleman had 'that particular subject to begin'—on the contrary, he supposed that one whom we all knew to be eminent as a thinker had come to a conclusion upon it, and would perhaps vouchsafe a guiding word to one who was, as yet, seeking the solution of the Great Problem of Theology. I told my friend that 'Mr. De Morgan was doubtless preoccupied, and that he must be content to wait. On some day of courtesy and leisure he might have the kindness to write.' Nor was I wrong—the answer appears in your pages at the lapse of seventeen years."

I suppose Mr. Holyoake's way of putting his request was the stylus curiæ of the Society. A worthy Quaker who was sued for debt in the King's Bench was horrified to find himself charged in the declaration with detaining his creditor's money by force and arms, contrary to the peace of our Lord the King, etc. It's only the stylus curiæ, said a friend: I don't know curiæ, said the Quaker, but he shouldn't style us peace-breakers.

The notion that the non-existence of God can be proved, has died out under the light of discussion: had the only lights shone from the pulpit and the prison, so great a step would never have been made. The question now is as above. The dictum that Christianity is "part and parcel of the law of the land" is also abrogated: at the same time, and the coincidence is not an accident, it is becoming somewhat nearer the truth that the law of the land is part and parcel of Christianity. It must also be noticed that Christianity was part and parcel of the articles of war; and so was duelling. Any officer speaking against religion was to be cashiered; and any officer receiving an affront without, in the last resort, attempting to kill his opponent, was also to be cashiered. Though somewhat of a book-hunter, I have never been able to ascertain the date of the collected remonstrances of the prelates in the House of Lords against this overt inculcation of murder, under the soft name of satisfaction: it is neither in Watt, nor in Lowndes, nor in any edition of Brunet; and there is no copy in the British Museum. Was the collected edition really published?

[The publication of the above in the Athenæum has not produced reference to a single copy. The collected edition seems to be doubted. I have even met one or two persons who doubt the fact of the Bishops having remonstrated at all: but their doubt was founded on an absurd supposition, namely, that it was no business of theirs; that it was not the business of the prelates of the church in union with the state to remonstrate against the Crown commanding murder! Some say that the edition was published, but under an irrelevant title, which prevented people from knowing what it was about. Such things have happened: for example, arranged extracts from Wellington's general orders, which would have attracted attention, fell dead under the title of "Principles of War." It is surmised that the book I am looking for also contains the protests of the Reverend bench against other things besides the Thou-shalt-do-murder of the Articles (of war), and is called "First Elements of Religion" or some similar title. Time clears up all things.]