A Budget of Paradoxes Volume II Part 14

That is, four times the chord of an arc is the chord of four times the arc: and the sum of four sides of a certain pentagon is equal to the fifth. This is the capital of the column, the crown of the arch, the apex of the pyramid, the watershed of the elevation. Oh! J. S.! J. S.! groans Geometry--_Summum J. S. summa injuria_![271] The other J. S., Joseph Scaliger,[272] as already mentioned, had his own way of denying that a straight line is always the shortest distance between two points. A parallel might be inst.i.tuted, but not in half a column. And J. S. the _second_ has been so tightly handled that he may now be dismissed, with an inscription for his circular shield, obtained by changing _Lexica contexat_ into _Circus quadrandus_ in an epigram of J. S. the _first_:

"Si quem dura manet sententia judicis, olim d.a.m.natum aerumnis suppliciisque caput, Hunc neque fabrili la.s.sent ergastula ma.s.sa, Nec rigidas vexent fossa metalla ma.n.u.s.

Circus quadrandus: nam--caetera quid moror?--omnes Poenarum facies hic labor unus habet."[273]

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I had written as far as _d.a.m.natum_ when in came the letter of Nauticus as a printed slip, with a request that I would consider the slip as a 'revised copy.' Not a word of alteration in the part I have quoted! And in the evening came a letter desiring that I would alter a gross error; but not the one above: this is revising without revision! If there were cyclometers enough of this stamp, they would, as cultivation progresses--and really, with John Stuart Mill in for Westminster, it seems on the move, even though, as I learn while correcting the proof, Gladstone be out from Oxford; for Oxford is no worse than in 1829, while Westminster is far above what she ever has been: election time excuses even such a parenthesis as this--be engaged to amuse those who can afford it with paralogism at their meals, after the manner of the other jokers who wore the caps and bells.

The rich would then order their dinners with _panem et Circenses_,--up with the victuals and the circle-games--as the poor did in the days of old.

Mr. Smith is determined that half a column shall not do. Not a day without something from him: letter, printed proof, pamphlet. In what is the last at this moment of writing he tells me that part of the t.i.tle of a work of his will be "Professor De Morgan in the pillory without hope of escape." And where will he be himself? This I detected by an effort of reasoning which I never could have made except by following in his steps. In all matters connected with [pi] the letters l and g are closely related: this appears in the well-known formula for the time of oscillation [pi] [sqrt](l : g).

Hence g may be written for l, but only once: do it twice, and you require the time to be [pi] [sqrt](l^2 : g^2). This may be reinforced by observing that if as a datum, or if you dislike that word, by hypothesis, the first l be a g, it is absurd that it should be an l. Write g for the first l, and we have _un fait accompli_. I shall be in pillory; and overhead, in a cloud, will sit Mr. James Smith on one stick laid across two others, under a nimbus of 3-1/8 diameters to {156} the circ.u.mference--in [pi]-glory. Oh for a drawing of this scene! Mr. De Morgan presents his compliments to Mr.

James Smith, and requests the honor of an exchange of photographs.

_July 26._--Another printed letter.--Mr. James Smith begs for a distinct answer to the following plain question: "Have I not in this communication brought under your notice _truths_ that were never before dreamed of in your geometrical and mathematical philosophy?" To which, he having taken the precaution to print the word _truths_ in italics, I can conscientiously answer, Yes, you have. And now I shall take no more notice of these _truths_, until I receive something which surpa.s.ses all that has yet been done.

A FEW SMALL PARADOXERS.

The Circle secerned from the Square; and its area gauged in terms of a triangle common to both. By Wm. Houlston,[274] Esq. London and Jersey, 1862, 4to.

Mr. Houlston squares at about four poetical quotations in a page, and brings out [pi] = 3.14213.... His frontispiece is a variegated diagram, having parts designated Inigo and Outigo. All which relieves the subject, but does not remove the error.

Considerations respecting the figure of the Earth.... By C. F.

Bakewell.[275] London, 1862, 8vo.

Newton and others think that in a revolving sphere the {157} loose surface matter will tend to the equator: Mr. Bakewell thinks it will tend to the poles.

On eccentric and centric force: a new theory of projection. By H. F. A.

Pratt, M.D.[276] London, 1862, 8vo.

Dr. Pratt not only upsets Newton, but cuts away the very ground he stands on: for he destroys the first law of motion, and will not have the natural tendency of matter in motion to be rectilinear. This, as we have seen, was John Walsh's[277] notion. In a more recent work "On Orbital Motion,"

London, 1863, 8vo., Dr. Pratt insists on another of Walsh's notions, namely, that the precession of the equinoxes is caused by the motion of the solar system round a distant central sun. In this last work the author refers to a few notes, which completely destroy the theory of gravitation in terms "perfectly intelligible as well to the unlearned as to the learned": to me they are quite unintelligible, which rather tends to confirm a notion I have long had, that I am neither one thing nor the other. There is an ambiguity of phrase which delights a writer on logic, always on the look-out for specimens of _h.o.m.onymia_ or _aequivocatio_. The author, as a physician, is accustomed to "appeal from mere formulae": accordingly, he sets at nought the whole of the mathematics, which he does not understand. This equivocation between the formula of the physician and that of the mathematician is as good, though not so perceptible to the world at large, as that made by Mr. Briggs's friend in _Punch's_ picture, which I cut out to paste into my Logic. Mr. Briggs wrote for a couple of _bruisers_, meaning to prepare oats for his horses: his friend sent him the Whitechapel Chicken and the Bayswater Slasher, with the gloves, all ready.

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On matter and ether, and the secret laws of physical change. By T. R.

Birks, M.A.[278] Cambridge, 1862, 8vo.

Bold efforts are made at molecular theories, and the one before me is ably aimed. When the Newton of this subject shall be seated in his place, books like the present will be sharply looked into, to see what amount of antic.i.p.ation they have made.

DR. THORN AND MR. BIDEN.

The history of the 'thorn tree and bush' from the earliest to the present time: in which is clearly and plainly shown the descent of her most gracious Majesty and her Anglo-Saxon people from the half tribe of Ephraim, and possibly from the half tribe of Mana.s.seh; and consequently her right and t.i.tle to possess, at the present moment, for herself and for them, a share or shares of the desolate cities and places in the land of their forefathers! By Theta, M.D.[279] (Private circulation.) London, 1862, 8vo.

This is much about _Thorn_, and its connected words, Thor, Thoth, Theta, etc. It is a very mysterious vagary. The author of it is the person whom I have described elsewhere as having for his device the round man in the three-cornered hole, the writer of the little heap of satirical anonymous letters about the Beast and 666. By accident I discovered the writer: so that if there be any more thorns to crackle under the pot, they need not be anonymous.

Nor will they be anonymous. Since I wrote the above, I have received _onymous_ letters, as _ominous_ as the rest. The writer, William Thorn, M.D., is obliged to reveal {159} himself, since it is his object to prove that he himself is one 666. By using W for double Vau (or 12) he cooks the number out of his own name. But he says it is the number not of a beast but of a man, and adds, "Thereby hangs a tale!" which sounds like contradiction. He informs me that he will talk the matter over with me: but I shall certainly have nothing to say to a gentleman of his number; it is best to keep on the safe side.

In one letter I am informed that not a line should I have had, but for my "sneer at 666," which, therefore, I am well pleased to have given. I am also told that my name means the "'garden of death,' that place in which the tree of knowledge was plucked, and so you are like your name 'dead' to the fact that you are an Israelite, like those in Ezekiel 37 ch." Some hints are given that I shall not fare well in the next world, which any one who reads the chapter in Ezekiel will see is quite against his comparison.

The reader must not imagine that my prognosticator means _Morgan_ to be a corruption of _Mortjardin_; he proves his point by Hebrew: but any philologist would tell him the true derivation of the name, and how _Glamorgan_ came to get it. It will be of much comfort to those young men who have not got through to know that the tree of knowledge itself was once in the same case. And so good bye to 666 for the present, and the a.s.sumption that the enigma is to be solved by the united numeral forces of the letters of a word.

It is worthy of note that, as soon as my Budget commenced, two guardian spirits started up, fellow men as to the flesh, both totally unknown to me: they have stuck to me from first to last. James Smith, Esq., finally Nauticus, watches over my character in this world, and would fain preserve me from ignorance, folly, and dishonesty, by inclosing me in a magic circle of 3-1/8 diameters in circ.u.mference. The round man in the three-cornered hole, finally William Thorn, M.D., takes charge of my future destiny, {160} and tries to bring me to the truth by unfolding a score of meanings--all right--of 666. He hints that I, and my wife, are servants of Satan: at least he desires us both to remember that we cannot serve G.o.d and Satan; and he can hardly mean that we are serving the first, and that he would have us serve the second. As becomes an interpreter of the Apocalypse, he uses seven different seals; but not more than one to one letter. If his seals be all signet-rings, he must be what Aristophanes calls a sphragidonychargocometical fellow. But--and many thanks to him for the same--though an M.D., he has not sent me a single vial. And so much for my tree of secular knowledge and my tree of spiritual life: I dismiss them with thanks from myself and thanks from my reader. The dual of the Pythagorean system was Isis and Diana; of the Jewish law, Moses and Aaron; and of the City of London, Gog and Magog; of the Paradoxiad, James Smith, Esq., and William Thorn, M.D.

_September, 1866._ Mr. James Biden[280] has favored me with some of his publications. He is a rival of Dr. Thorn; a prophet by name-right and crest-right. He is of royal descent through the De Biduns. He is the _watchman_ of Ezekiel: G.o.d has told him so. He is the author of _The True Church_, a phrase which seems to have a book-meaning and a mission-meaning.

He shall speak for himself:

"A crest of the Bidens has significance. It is a lion rampant between wings--wings in Scripture denote the flight of time. Thus the beasts or living creatures of the Revelations have each six wings, intimating a condition of mankind up to and towards the close of six thousand years of Bible teaching. The two wings of the crest would thus intimate power towards the expiration of 2000 years, as time is marked in the history of Great Britain.

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"In a recent publication, _The Pestilence, Why Inflicted_, are given many reasons why the writer thinks himself to be the appointed watchman foretold by Ezekiel, chapters iii. and x.x.xiii. Among the reasons are many prophecies fulfilled in him. Of these it is now needful to note two as bearing especially on the subject of the reign of Darius.

"1.--In Daniel it is said, 'Darius the Median took the kingdom, being about threescore and two years old.'--Daniel v. 31.

"When 'Belshazzar' the king of the Chaldeans is found wanting, Darius takes the kingdom. It is not given him by the popular voice; he a.s.serts his right, and this is not denied. He takes it when about sixty-two years of age. The language of Daniel is prophetic, and Darius has in another an ant.i.type. The writer was born July 18th, 1803; and the claim was a.s.serted at the close of 1865, when he was about sixty-two years of age.

"The claims which have been a.s.serted demand a settled faith, and which could only be reached through a long course of divine teaching."

When I was a little boy at school, one of my school-fellows took it into his head to set up a lottery of marbles: the thing took, and he made a stony profit. Soon, one after another, every boy had his lottery, and it was, "I won't put into yours unless you put into mine." This knocked up the scheme. It will be the same with the prophets. Dr. Thorn, Mr. Biden, Mrs.

Cottle,[281] etc. will grow imitators, until we are all pointed out in the Bible: but A will not admit B's claim unless B admits his. For myself, as elsewhere shown, I am the first Beast in the Revelations.

Every contraband prophet gets a few followers: it is a great point to make these sequacious people into Buridan's a.s.ses, which they will become when prophets are so numerous that there is no choosing.

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SIR G. C. LEWIS.

An historical survey of the Astronomy of the Ancients. By the Rt. Hon.

Sir G. C. Lewis.[282] 8vo. 1862.

There are few men of our day whom I admire more than the late Sir G. Lewis: he was honest, earnest, sagacious, learned, and industrious. He probably sacrificed his life to his conjunction of literature and politics: and he stood high as a minister of state in addition to his character as a man of letters. The work above named is of great value, and will be read for its intrinsic merit, consulted for its crowd of valuable references, quoted for its aid to one side of many a discussion, and opposed for its force against the other. Its author was also a wit and a satirist. I know of three cla.s.sical satires of our day which are inimitable imitations: Mr.

Malden's[283] _Pragmatized Legends_, Mr. Mansel's[284] _Phrontisterion_, and Sir G. Cornewall Lewis's _Inscriptio Antiqua_. In this last, HEYDIDDLEDIDDLETHECATANDTHEFIDDLE etc. is treated as an Oscan inscription, and rendered into Latin by approved methods. As few readers have seen it, I give the result:

"Hejus dedit libenter, dedit libenter. Deus propitius [est], deus [donatori] libenter favet. Deus in viarum {163} junctura ovorum dape [colitur], deus mundi. Deus in litatione voluit, benigno animo, haedum, taurum intra fines [loci sacri] portandos. Deus, bis l.u.s.tratus, beat fossam sacrae libationis."[285]

How then comes the history of astronomy among the paradoxes? Simply because the author, so admirably when writing about what he knew, did not know what he did not know, and blundered like a circle-squarer. And why should the faults of so good a writer be recorded in such a list as the present? For three reasons: First, and foremost, because if the exposure be not made by some one, the errors will gradually ooze out, and the work will get the character of inaccurate. Nothing hurts a book of which few can fathom the depths so much as a plain blunder or two on the surface. Secondly, because the reviews either pa.s.sed over these errors or treated them too gently, rather implying their existence than exposing them. Thirdly, because they strongly ill.u.s.trate the melancholy truth, that no one knows enough to write about what he does not know. The distinctness of the errors is a merit; it proceeds from the clear-headedness of the author. The suppression in the journals may be due partly to admiration of the talent and energy which lived two difficult lives at once, partly to respect for high position in public affairs, partly to some of the critics being themselves men of learning only, unable to detect the errors. But we know that action and reaction are equal and contrary. If our generation take no notice of defects, and allow them to go down undetected among merits, the next generation will discover them, will perhaps believe us incapable of detecting them, at least will p.r.o.nounce our judgment good for nothing, and will form an {164} opinion in which the merits will be underrated: so it has been, is, and will be. The best thing that can be done for the memory of the author is to remove the unsound part that the remainder may thrive.

The errors do not affect the work; they occur in pa.s.sages which might very well have been omitted: and I consider that, in making them conspicuous, I am but cutting away a deleterious fungus from a n.o.ble tree.