Chapter VI: Part 6

Accordingly, * * * was withdrawn, and a discussion took place, for which see the _Athenaeum_, No. 1126, May 26, 1849, p. 544. The _Mechanics' Magazine_ was very sore, but up to this day has never ventured beyond an attack on Airy, private whisperings against Adams--(see _ante_, p. 147),--and the above against myself. In due time, I doubt not my name will appear as one of the _ames damnees_[266] of the _Mechanics' Magazine_.[267]

T. S. DAVIES ON EUCLID.

First, as to Mr. Halliwell. The late Thomas Stephens Davies,[268] excellent in geometry, and most learned in its history, was also a good hand at enmity, though not implacable. He and Mr. Halliwell, who had long before been very much one, were, at this date, very much two. I do not think T. S. Davies wrote this article; and I think that by giving my reasons I shall do service to his memory. It must have been written at the beginning of February; and within three days of that time T. S. Davies was making over to me, by his own free act, to be kept until claimed by the relatives, what all who knew even his writings knew that he considered as the most precious deposit he had ever had in his keeping--Horner's[269] papers. His letter announcing the transmission is dated February 2, 1850. This is a strong point; but there is another quite as strong. Euclid and {152} his writings were matters on which T. S. Davies knew neither fear nor favor: he could not have written lightly about a man who stood high with him as a judge of Euclid. Now in this very letter of Feb. 2, there is a sentence which I highly value, because, as aforesaid, it is on a point on which he would never have yielded anything, to which he had paid life-long attention, and on which he had the bias of having long stood alone. In fact, knowing--and what I shall quote confirms me,--that in the matter of Euclid his hand was against every man, I expected, when I sent him a copy of my 22-column article, "Eucleides" in Smith's _Dictionary_,[270] to have received back a criticism, that would have blown me out of the water: and I thought it not unlikely that a man so well up in the subject might have made me feel demolished on some points. Instead of this, I got the following: "Although on one or two minor points I do not quite accord with your views, yet as a whole and without regard to any minor points, I think you are the first who has succeeded in a delineation of Euclid as a geometer." All this duly considered, it is utterly incredible that T. S. Davies should have written the review in question. And yet Mr. Halliwell is treated just as T. S. Davies would have treated him, as to tone and spirit. The inference in my mind is that we have here a marked instance of the joining of hatreds which takes place in journals supported by voluntary contributions of matter. Should anything ever have revived this article--and no one ever knows what might have been fished up from the forgotten mass of journals--the treatment of Mr. Halliwell would certainly have thrown a suspicion on T. S. Davies, a large and regular contributor to the Magazine. It is good service to his memory to point out what makes it incredible that he should have written so unworthy an article.

The fault is this. There are four extracts: the first {153} three are perfectly well printed. The printing of the _Mechanics' Magazine_ was very good. I was always exceedingly satisfied with the manner in which my articles appeared, without my seeing proof. Most likely these extracts were printed from my printed paper; if not the extractor was a good copier. I know this by a test which has often served me. I use the subjunctive--"if no man _have_ done nothing," an ordinary transcriber, narrating a quotation almost always lets his own habit write _has_. The fourth extract has three alterations, all tending to make me ridiculous. _None_ is altered, in two places, into _nine_, _denial_ into _decimal_, and _comes_ into _aims_; so that "none, the denial of one, comes to be associated with the denial of plurality," reads as "nine, the decimal of one, aims to be associated with the decimal of plurality." This is intentional; had it been a compositor's reading of bad handwriting, these would not have been the only mistakes; to say nothing of the corrector of the press. And both the compositor and reader would have guessed, from the first line being translated into "one is not one," that it must have been "one's none," not "one's nine." But it was not intended that the gem should be recovered from the unfathomed cave, and set in a Budget of Paradoxes.

We have had plenty of slander-paradox. I now give a halfpennyworth of bread to all this sack, an instance of the paradox of benevolence, in which an individual runs counter to all the ideas of his time, and sees his way into the next century. At Amiens, at the end of the last century, an institution was endowed by a M. de Morgan, to whom I hope I am of kin, but I cannot trace it; the name is common at Amiens. It was the first of the kind I ever heard of. It is a Salle d'Asyle for children, who are taught and washed and taken care of during the hours in which their parents must be at work. The founder was a large wholesale grocer and colonial importer, who was made a Baron by Napoleon I for his commercial success and his charities. {154}

JAS. SMITH AGAIN.

1862. Mr. Smith replies to me, still signing himself Nauticus: I give an extract:

"By hypothesis [what, again!] let 14 deg. 24' be the chord of an arc of 15 deg. [but I wont, says 14 deg. 24'], and consequently equal to a side of a regular polygon of 24 sides inscribed in the circle. Then 4 times 14 deg. 24' = 57 deg. 36' = the radius of the circle ..."

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

"Si quem dura manet sententia judicis, olim
Damnatum aerumnis suppliciisque caput,
Hunc neque fabrili lassent ergastula massa,
Nec rigidas vexent fossa metalla manus.
Circus quadrandus: nam--caetera quid moror?--omnes
Poenarum facies hic labor unus habet."[273]

{155}

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

Mr. Smith is determined that half a column shall not do. Not a day without something from him: letter, printed proof, pamphlet. In what is the last at this moment of writing he tells me that part of the title of a work of his will be "Professor De Morgan in the pillory without hope of escape." And where will he be himself? This I detected by an effort of reasoning which I never could have made except by following in his steps. In all matters connected with [pi] the letters l and g are closely related: this appears in the well-known formula for the time of oscillation [pi] [sqrt](l : g). Hence g may be written for l, but only once: do it twice, and you require the time to be [pi] [sqrt](l^2 : g^2). This may be reinforced by observing that if as a datum, or if you dislike that word, by hypothesis, the first l be a g, it is absurd that it should be an l. Write g for the first l, and we have _un fait accompli_. I shall be in pillory; and overhead, in a cloud, will sit Mr. James Smith on one stick laid across two others, under a nimbus of 3-1/8 diameters to {156} the circumference--in [pi]-glory. Oh for a drawing of this scene! Mr. De Morgan presents his compliments to Mr. James Smith, and requests the honor of an exchange of photographs.

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

A FEW SMALL PARADOXERS.

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

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

Considerations respecting the figure of the Earth.... By C. F.
Bakewell.[275] London, 1862, 8vo.

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

On eccentric and centric force: a new theory of projection. By H. F. A.
Pratt, M.D.[276] London, 1862, 8vo.

Dr. Pratt not only upsets Newton, but cuts away the very ground he stands on: for he destroys the first law of motion, and will not have the natural tendency of matter in motion to be rectilinear. This, as we have seen, was John Walsh's[277] notion. In a more recent work "On Orbital Motion," London, 1863, 8vo., Dr. Pratt insists on another of Walsh's notions, namely, that the precession of the equinoxes is caused by the motion of the solar system round a distant central sun. In this last work the author refers to a few notes, which completely destroy the theory of gravitation in terms "perfectly intelligible as well to the unlearned as to the learned": to me they are quite unintelligible, which rather tends to confirm a notion I have long had, that I am neither one thing nor the other. There is an ambiguity of phrase which delights a writer on logic, always on the look-out for specimens of _homonymia_ or _aequivocatio_. The author, as a physician, is accustomed to "appeal from mere formulae": accordingly, he sets at nought the whole of the mathematics, which he does not understand. This equivocation between the formula of the physician and that of the mathematician is as good, though not so perceptible to the world at large, as that made by Mr. Briggs's friend in _Punch's_ picture, which I cut out to paste into my Logic. Mr. Briggs wrote for a couple of _bruisers_, meaning to prepare oats for his horses: his friend sent him the Whitechapel Chicken and the Bayswater Slasher, with the gloves, all ready.

{158}

On matter and ether, and the secret laws of physical change. By T. R.
Birks, M.A.[278] Cambridge, 1862, 8vo.

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

DR. THORN AND MR. BIDEN.

The history of the 'thorn tree and bush' from the earliest to the
present time: in which is clearly and plainly shown the descent of her
most gracious Majesty and her Anglo-Saxon people from the half tribe of
Ephraim, and possibly from the half tribe of Manasseh; and consequently
her right and title to possess, at the present moment, for herself and
for them, a share or shares of the desolate cities and places in the
land of their forefathers! By Theta, M.D.[279] (Private circulation.)
London, 1862, 8vo.

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

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

In one letter I am informed that not a line should I have had, but for my "sneer at 666," which, therefore, I am well pleased to have given. I am also told that my name means the "'garden of death,' that place in which the tree of knowledge was plucked, and so you are like your name 'dead' to the fact that you are an Israelite, like those in Ezekiel 37 ch." Some hints are given that I shall not fare well in the next world, which any one who reads the chapter in Ezekiel will see is quite against his comparison. The reader must not imagine that my prognosticator means _Morgan_ to be a corruption of _Mortjardin_; he proves his point by Hebrew: but any philologist would tell him the true derivation of the name, and how _Glamorgan_ came to get it. It will be of much comfort to those young men who have not got through to know that the tree of knowledge itself was once in the same case. And so good bye to 666 for the present, and the assumption that the enigma is to be solved by the united numeral forces of the letters of a word.

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

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

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

{161}

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

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

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

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

When I was a little boy at school, one of my school-fellows took it into his head to set up a lottery of marbles: the thing took, and he made a stony profit. Soon, one after another, every boy had his lottery, and it was, "I won't put into yours unless you put into mine." This knocked up the scheme. It will be the same with the prophets. Dr. Thorn, Mr. Biden, Mrs. Cottle,[281] etc. will grow imitators, until we are all pointed out in the Bible: but A will not admit B's claim unless B admits his. For myself, as elsewhere shown, I am the first Beast in the Revelations.

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

{162}

SIR G. C. LEWIS.

An historical survey of the Astronomy of the Ancients. By the Rt. Hon.
Sir G. C. Lewis.[282] 8vo. 1862.

There are few men of our day whom I admire more than the late Sir G. Lewis: he was honest, earnest, sagacious, learned, and industrious. He probably sacrificed his life to his conjunction of literature and politics: and he stood high as a minister of state in addition to his character as a man of letters. The work above named is of great value, and will be read for its intrinsic merit, consulted for its crowd of valuable references, quoted for its aid to one side of many a discussion, and opposed for its force against the other. Its author was also a wit and a satirist. I know of three classical satires of our day which are inimitable imitations: Mr. Malden's[283] _Pragmatized Legends_, Mr. Mansel's[284] _Phrontisterion_, and Sir G. Cornewall Lewis's _Inscriptio Antiqua_. In this last, HEYDIDDLEDIDDLETHECATANDTHEFIDDLE etc. is treated as an Oscan inscription, and rendered into Latin by approved methods. As few readers have seen it, I give the result:

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

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

(P. 154). The periodic times of the five planets were stated by Eudoxus,[286] as we learn from Simplicius;[287] the following is his statement, to which the true times are subjoined, for the sake of comparison:

STATEMENT OF EUDOXUS TRUE TIME
Mercury 1 year -- 87d. 23h.
Venus 1 " -- 224d. 16h.
Mars 2 " 1y. 321d. 23h.
Jupiter 12 " 11y. 315d. 14h.
Saturn 30 " 29y. 174d. 1h.

Upon this determination two remarks may be made. First, the error with respect to Mercury and Venus is considerable; with respect to Mercury, it is, in round numbers, 365 instead of 88 days, more than four times too much. Aristotle remarks that Eudoxus distinguishes Mercury and Venus from the other three planets by giving them one sphere each, with the poles in common. The proximity of Mercury to the sun would render its course difficult to observe and to measure, but the cause of the large error with respect to Venus (130 days) is not apparent.

{165}

Sir G. Lewis takes Eudoxus as making the planets move round the sun; he has accordingly compared the _geocentric_ periods of Eudoxus with our _heliocentric_ periods. What greater blunder can be made by a writer on ancient astronomy than giving Eudoxus the Copernican system? If Mercury were a black spot in the middle of the sun it would of course move round the earth in a year, or appear to do so: let it swing a little on one side and the other of the sun, and the average period is still a year, with slight departures both ways. The same for Venus, with larger departures. Say that a person not much accustomed to the distinction might for once write down the mistake; how are we to explain its remaining in the mind in a permanent form, and being made a ground for such speculation as that of the difficulty of observing Mercury leading to a period four times what it ought to be, corrected in proof and published by an industrious and thoughtful person? Only in one way: the writer was quite out of his depth. This one case is conclusive; be it said with all respect for the real staple of the work and of the author. He knew well the difference of the systems, but not the effect of the difference: he is another instance of what I have had to illustrate by help of a very different person, that it is difficult to reason well upon matter which is not familiar.

(P. 254). Copernicus, in fact, supposed the axis of the earth to be always turned towards the Sun.^{(169)} [(169). See Delambre, _Hist. Astr. Mod._, Vol. I, p. 96]. It was reserved to Kepler to propound the hypothesis of the constant parallelism of the earth's axis to itself.

If there be one thing more prominent than another in the work of Copernicus himself, in the popular explanations of it, and in the page of Delambre[288] cited, it is that the _parallelism of the earth's axis_ is a glaring part of the {166} theory of Copernicus. What Kepler[289] did was to throw away, as unnecessary, the method by which Copernicus, _per fas et nefas_,[290] secured it. Copernicus, thinking of the earth's orbital revolution as those would think who were accustomed to the _solid orbs_--and much as the stoppers of the moon's rotation do now: why do they not strengthen themselves with Copernicus?--thought that the earth's axis would always incline the same end towards the sun, unless measures were taken to prevent it. He _did_ take measures: he invented a _compensating_ conical motion of the axis to preserve the parallelism; and, which is one of the most remarkable points of his system, he obtained the precession of the equinoxes by giving the necessary trifle more than compensation. What stares us in the face at the beginning of the paragraph to which the author refers?

"C'est donc pour arriver a ce parallelisme, ou pour le conserver, que Copernic a cru devoir recourir a ce mouvement egal et oppose qui detruit l'effet qu'il attribue si gratuitement au premier, de deranger le parallelisme."[291]

Parallelism at any price, is the motto of Copernicus: you need not pay so dear, is the remark of Kepler.

The opinions given by Sir G. Lewis about the effects of modern astronomy, which he does not understand and singularly undervalues, will now be seen to be of no authority. He fancies that--to give an instance--for the determination of a ship's place, the invention of chronometers has been far more important than any improvement in astronomical theory (p. 254). Not to speak of latitude,--though the omission is not without importance,--he ought to have known that longitude is found by the difference between what o'clock it is at Greenwich and at the ship's place, at {167} one absolute moment of time. Now if a chronometer were quite perfect--which no chronometer is, be it said--and would truly tell Greenwich mean time all over the world, it ought to have been clear that just as good a watch is wanted for the time at _the place of observation_, before the longitude of that place with respect to Greenwich can be found. There is no such watch, except the starry heaven itself: and that watch can only be read by astronomical observation, aided by the best knowledge of the heavenly motions.

I think I have done Sir G. Lewis's very excellent book more good than all the reviewers put together.

I will give an old instance in which literature got into confusion about astronomy. Theophrastus,[292] who is either the culprit or his historian, attributes to Meton,[293] the contriver of the lunar calendar of nineteen years, which lasts to this day, that his solstices were determined for him by a certain Phaeinus of Elis on Mount Lycabettus. Nobody else mentions this astronomer: though it is pretty certain that Meton himself made more than one appointment with him for the purpose of observing solstices; and we may be sure that if either were behind his time, it was Meton. For _Phaeinus Helius_ is the shining sun himself; and in the astronomical poet Aratus[294] we read about the nineteen years of the shining sun:

[Greek: Enneakaideka kukla phaeinou eelioio].[295]

Some man of letters must have turned Apollo into Phaeinus of Elis; and there he is in the histories of astronomy to {168} this day. Salmasius[296] will have Aratus to have meant him, and proposes to read [Greek: eleioio]: he did not observe that Phaeinus is a very common adjective of Aratus, and that, if his conjecture were right, this Phaeinus would be the only non-mythical man in the poems of Aratus.

[When I read Sir George Lewis's book, the points which I have criticized struck me as not to be wondered at, but I did not remember why at the time. A Chancellor of the Exchequer and a writer on ancient astronomy are birds of such different trees that the second did not recall the first. In 1855 I was one of a deputation of about twenty persons who waited on Sir G. Lewis, as Chancellor of the Exchequer, on the subject of a decimal coinage. The deputation was one of much force: Mr. Airy, with myself and others, represented mathematics; William Brown,[297] whose dealings with the United States were reckoned by yearly millions, counted duodecimally in England and decimally in America, was the best, but not the only, representative of commerce. There were bullionists, accountants, retailers, etc. Sir G. L. walked into the room, took his seat, and without waiting one moment, began to read the deputation a smart lecture on the evils of a decimal coinage; it would require alteration of all the tables, it would impede calculation, etc. etc. Of those arguments against it which weighed with many of better knowledge than his, he obviously knew nothing. The members of the deputation began to make their statements, and met with curious denials. He interrupted me with "Surely there is no doubt that the calculations of our books of arithmetic are easier {169} than those in the French books." He was not aware that the _universally admitted_ superiority of decimal _calculation_ made many of those who prefer our system for the market and the counter cast a longing and lingering look towards decimals. My answer and the smiles which he saw around, made him give a queer puzzled look, which seemed to say, "I may be out of my depth here!" His manner changed, and he listened. I saw both the slap-dash mode in which he dealt with subjects on which he had not thought, and the temperament which admitted suspicion when the means of knowledge came in his way. Having seen his two phases, I wonder neither at his more than usual exhibition of shallowness when shallow, nor at the intensity of the contrast when he had greater depth.]

DECIMAL COINAGE.

Among the paradoxers are the political paradoxers who care not how far they go in debate, their only object being to carry the House with them for the current evening. What I have said of editors I repeat of them. The preservation of a very marked instance, the association of political recklessness with cyclometrical and Apocalyptic absurdity, may have a tendency to warn, not indeed any hardened public-man and sinner, but some young minds which have yearnings towards politics, and are in formation of habits.

In the debate on decimal coinage of July 12, 1855, Mr. Lowe,[298] then member for Kidderminster, an effective speaker and a smart man, exhibited himself in a speech on which I wrote a comment for the Decimal Association. I have seldom seen a more wretched attempt to distort the points of a public question than the whole of this speech. Looking at the intelligence shown by the speaker on other occasions, {170} it is clear that if charity, instead of believing all things, believed only all things but one, he might tremble for his political character; for the honesty of his intention on this occasion might be the incredible exception. I give a few paragraphs with comments:

"In commenting on the humorous, but still argumentative speech of Mr. Lowe, the member for Kidderminster, we may observe, in general, that it consists of points which have been several times set forth, and several times answered. Mr. Lowe has seen these answers, but does not allude to them, far less attempt to meet them. There are, no doubt, individuals, who show in their public speaking the outward and visible signs of a greater degree of acuteness than they can summon to guide their private thinking. If Mr. Lowe be not one of these, if the power of his mind in the closet be at all comparable to the power of his tongue in the House, it may be suspected that his reserve with respect to what has been put forward by the very parties against whom he was contending, arises from one or both of two things--a high opinion of the arguments which he ignored--a low opinion of the generality of the persons whom he addressed. [Both, I doubt not].

"Did they calculate in florins In the name of common sense, ?" how can it be objected to a system that people do not use it before it is introduced? Let the decimal system be completed, and calculation shall be made in florins; that is, florins shall take their proper place. If florins were introduced _now_, there must be a column for the odd shilling. "He was glad that some hon. If the hon. gentleman make gentleman had derived benefit this assertion of himself, it from the issue of florins. His is not for us to gainsay it. only experience of their It only proves that he is one convenience was, that when he of that class of {171} men who ought to have received are described in the old song, half-a-crown, he had generally of which one couplet runs received a florin, and when he thus: ought to have paid a florin, he had generally paid I sold my cow to buy me a half-a-crown." (Hear, hear, calf; and laughter.) I never make a bargain but I lose half, With a etc. etc. etc.

But he cannot mean that Englishmen in general are so easily managed. And as to Jonathan, who is but John lengthened out a little, he would see creation whittled into chips before he would even split what may henceforth be called the Kidderminster difference. The House, not unmoved--for it laughed--with sly humor decided that the introduction of the florin had been "eminently successful and satisfactory."

The truth is that Mr. Lowe here attacks nothing except the coexistence of the florin and half-crown. We are endeavoring to abolish the half-crown. Let Mr. Lowe join us; and he will, if we succeed, be relieved from the pressure on his pocket which must arise from having the turn of the market always against him.

"From a florin they get to 2 Note the sophism of expressing
2-5ths of a penny, but who our coin in terms of the
ever bought anything, who ever penny, which we abandon,
reckoned or wished to reckon instead of the florin, which
in such a coin as that?" we retain. Remember that this
(Hear, hear.) 2 2-5ths is the hundredth part
of the pound, which is called,
as yet, a _cent_. Nobody buys
anything at a cent, because
the cent is not yet
introduced. Nobody reckons in
cents for the same reason.
Everybody wishes to reckon in
cents, who wishes to combine
the advantage of decimal
reckoning with the
preservation of the pound as
{172} the highest unit of
account; amongst others, a
majority of the House of
Commons, the Bank of England,
the majority of London
bankers, the Chambers of
Commerce in various places,
etc. etc. etc.
"Such a coin could never come Does 2-1/2d. never pass from
into general circulation hand to hand? And is 2-1/2d.
because it represents nothing so precisely the modulus of
which corresponds with any of popular wants, that an
the wants of the people." alteration of 4 per cent.
would make it useless? Of all
the values which 2-1/2d.
measures, from three pounds of
potatoes down to certain
arguments used in the House of
Commons, there is not one for
which a cent would not do just
as well. Mr. Lowe has fallen
into the misconception of the
person who admired the
dispensation of Providence by
which large rivers are made to
run through cities so great
and towns so many. If the cent
were to be introduced
to-morrow, straightway the
buns and cakes, the soda-water
bottles, the short omnibus
fares, the bunches of
radishes, etc. etc. etc.,
would adapt themselves to the
coin.
"If the proposed system were The confusion of ideas here
adopted, they would all be exhibited is most instructive.
compelled to live in decimals The speaker is under the
for ever; if a man dined at a impression that _we_ are
public house he would have to introducing fractions: the
pay for his dinner in decimal truth is, that we only want to
fractions. (Hear, hear.) He abandon the _more difficult_
objected to that, for he fractions which we _have got_,
thought that a man ought to be and to introduce _easier
able to pay for his dinner in fractions_. Does he deny this?
integers." (Hear, hear, and a Let us trace his denial to its
laugh.) legitimate consequences. A man
ought to pay for his dinner in
integers.

{173}

Now, if Mr. Lowe insists on it that our integer is the pound, he is bound to admit that the present integer is the pound, of which a shilling, etc., are fractions. The next time he has a chop and a pint of stout in the city, the waiter should say--"A pound, sir, to you," and should add, "Please to remember the waiter in integers." Mr. Lowe fancies that when he pays one and sixpence, he pays in integers, and so he does, if his integer be a penny or a sixpence. Let him bring his mind to contemplate a mil as the integer, the lowest integer, and the seven cents five mils which he would pay under the new system would be payment in integers also. But, as it happens with some others, he looks _up_ the present system, with Cocker,[299] and Walkingame,[300] and always looks _down_ the proposed system. The word _decimal_ is obstinately associated with _fractions_, for which there is no need. Hence it becomes so much of a bugbear, that, to parody the lines of Pope, which probably suggested one of Mr. Lowe's phrases--

"Dinner he finds too painful an endeavor,
Condemned to pay in decimals for ever."

"The present system, however, A pleasant sum even for an
had not yet been changed into accomplished mathematician.
decimal system. That change What does divided by the
might appear very easy to decimal of a pound mean?
accomplished mathematicians Perhaps it means _reduced_ to
and men of science, but it was the decimal of a pound! Mr.
one which it would be very Lowe supposes, as many others
difficult to carry out. (Hear, do, that, after the change,
hear). What would have to be all calculations will be
done? Every sum would have to _proposed in old money_, and
be reduced into a vulgar then _converted into new_. He
fraction of a pound, and then cannot hit the {174} idea that
divided by the decimal of a the new coins will take the
pound--a pleasant sum for an place of the old. This lack of
old applewoman to work out!" apprehension will presently
(Hear, hear, and laughter.) appear further.
"It would not be an agreeable Let the members be assured
task, even for some members of that nine half-pence will be,
that House, to reduce 4-1/2d., for every practical purpose,
or nine half-pence, to mils." 18 mils. But now to the fact
(Hear, hear.) asserted. Davies Gilbert[301]
used to maintain that during
the long period he sat in the
House, he never knew more than
three men in it, at one time,
who had a tolerable notion of
fractions. [I heard him give
the names of three at the time
when he spoke: they were
Warburton,[302] Pollock,[303]
and Hume.[304] He himself was
then out of Parliament.]
Joseph Hume affirmed that he
had never met with more than
ten members who were
arithmeticians. But both these
gentlemen had a high standard.
Mr. Lowe has given a much more
damaging opinion. He evidently
means that the general run of
members could not do his
question. It is done as
follows: Since farthings gain
on mils, at the rate of a
whole mil in 24 farthings (24
farthings being 25 mils), it
is clear that 18 farthings
being three-quarters of 24
farthings, will gain
three-quarters of a mil; that
is, 18 farthings are eighteen
{175} mils and three-quarters
of a mil. Any number of
farthings is as many mils and
as many twenty-fourths of a
mil. To a certain extent, we
feel able to protest against
the manner in which
Kidderminster has treated the
other constituencies. We do
not hold it impossible to give
the Members of the House in
general a sufficient knowledge
of the meaning and
consequences of the _decimal_
succession of units, tens,
hundreds, thousands, etc.; and
we believe that there are in
the House itself competent
men, in number enough to teach
all the rest. All that is
wanted is the power of
starting from the known to
arrive at the unknown. Now
there is one kind of decimals
with which every member is
acquainted--the _Chiltern
Hundreds_. If public opinion
would enable the competent
minority to start from this in
their teaching, not as a
basis, but as an alternative,
in three weeks the
fundamentals would be
acquired, and members in
general would be as fit to
turn 4-1/2d. into mils, as any
boys on the lower forms of a
commercial school.

For a long period of years, allusion to the general ignorance of arithmetic, has been a standing mode of argument, and has always been well received: whenever one member describes others as _knownothings_, those others cry _Hear_ to the country in a transport of delight. In the meanwhile the country is gradually arriving at the conclusion that a true joke is no joke. "The main objection was, if Fine words, wrongly used. The they went below 6d., that the new coins are commensurable new scale of coins would not with, and in a finite ratio be commensurate in any finite to, the old ones. The farthing ratio with anything in this is to the mil as 25 to 24. The new currency of mils." speaker has something here in the bud, which we shall presently meet with in the flower; and fallacies are more easily nipped in flower than in bud. {176} "No less than five of our This dreadful change of value present coins must be called consists in sixpence farthing in, or else--which would be going to the half-shilling worse--new values must be instead of sixpence. Whether given to them." the new farthings be called mils or not is of no consequence. "If a poor man put a penny in Mr. Lowe, who cannot pass a his pocket, it would come out half-crown for more than a a coin of different value, florin, or get in a florin at which he would not understand. less than half-a-crown, has Suppose he owed another man a such a high faith in the penny, how was he to pay him ? sterner stuff of his fellow Was he to pay him in mils? countrymen, that he believes Four mils would be too little, any two of them would go to and five mils would be too fisty cuffs for the 25th part much. The hon. gentlemen said of a farthing. He reasons there would be only a mil thus: He has often heard in between them. That was exactly the streets, "I'd fight you it. He believed there would be for the fiftieth part of a a 'mill' between them." (Much farden:" and having (that is, laughter.) for a Member) a notion both of fractions and logic, he infers that those who would fight for the 50th of a farthing would, _a fortiori_, fight for a 25th. His mistake arises from his not knowing that when a person offers to fight another for 1/200d., he really means to fight for love; and that the stake is merely a matter of form, a feigned issue, a _pro forma_ report of progress. Do the Members of the House think they have all the forms to themselves? "What would be the present We should hardly believe all expression for four-pence? this to be uttered in earnest, Why, 0.166 (a laugh); for if we had not known {177} that threepence? .0125; for a several persons who have not penny? .004166, and so on _ad Mr. Lowe's humor, nevertheless infinitum_ (a laugh); for a have his impressions on this half-penny? .002083 _ad point. It must therefore be infinitum_. (A laugh). What answered; but how is this to would be the present be done seriously? expression for a farthing? Why, .0010416 _ad infinitum_. _Dialogue between a member of (A laugh). And this was the Parliament and an orange-boy, system which was to cause such three days after the a saving in figures, and these introduction of the complete were the quantities into which decimal system. The member, the poor would have to reduce going down to the House, wants the current coin of the realm. oranges to sustain his voice (Cheers). With every respect in a two hours' speech on for decimal fractions, of moving that 100000l. be placed which he boasted no profound at the disposal of Her knowledge, he doubted whether Majesty, to supply the poor the poor were equal to mental with ready-reckoners._ arithmetic of this kind, (hear, hear) and he hoped the _Boy._ Fine oranges! two a adoption of the system would penny! two a penny! {178} be deferred until there were some proof that they would be _Member._ Here boy, two! Now, able to understand it; for, how am I to pay you? after all, this was the question of the poor, and the _Boy._ Give you change, your whole weight of the change honor. would fall upon them. Let the rich by all means have _Member._ Ah! but how? Where's permission to perplex your ready-reckoner? themselves by any division of a pound they pleased; but do _Boy._ I sells a better sort not let them, by any nor them. Mine's real Cheyny. experiment like this, impose difficulties upon the poor and _Member._ But you see a compel men to carry farthing is now .0014166666 ready-reckoners in their _ad infinitum_, and if we pocket to give them all these multiply this by 4---- fractional quantities." (Hear, hear.) _Boy._ Hold hard, Guv'ner; I sees what you're arter. Now what'll you stand if I puts you up to it? which Bill Smith he put me up in two minutes, cause he goes to the Ragged School.

_Member._ You don't mean that
you do without a book!

_Boy._ Book be blowed. Come
now, old un, here's summut for
both on us. I got a florin,
you gives me a half-a-crown
for it, and I larns you the
new money, gives you your
oranges, and calls you a brick
into the bargain.

_Member_ (_to himself_). Never
had such a chance of getting
off half-a-crown for value
since that ---- fellow Bowring
carried his crochet.
(_Aloud._) Well, boy, it's a
bargain. Now!

_Boy._ Why, look 'e here, my
trump, its a farden more to
the tizzy--that's what it is.

_Member_. What's that?

_Boy._ Why, you knows a
sixpence when you sees it.
(_Aside_). Blest if I think he
does! Well, its six browns and
a farden now. A lady buys two
oranges, and forks {179} out a
sixpence; well in coorse, I
hands over fippence farden
astead of fippence. I always
gives a farden more change,
and takes according.

_Member_ (_in utter surprise,
lets his oranges tumble into
the gutter_). Never mind! They
won't be wanted now. (_Walks
off one way. Boy makes a pass
of naso-digital mesmerism, and
walks off the other way_).

To the poor, who keep no books, the whole secret is "Sixpence farthing to the half shilling, twelve pence halfpenny to the shilling." The _new twopence halfpenny_, or cent, will be at once five to the shilling.

In conclusion, we remark that three very common misconceptions run through the hon. Member's argument; and, combined in different proportions, give variety to his patterns.

First, he will have it that we design to bring the uneducated into contact with _decimal fractions_. If it be so, it will only be as M. Jourdain was brought into contact with prose. In fact, _Quoi! quand je dis, Nicole, apportez-moi mes pantoufles, c'est de la prose?_[305] may be rendered: "What! do you mean that _ten to the florin is a cent a piece_ must be called decimal reckoning?" If we had to comfort a poor man, horror-struck by the threat of _decimals_, we should tell him what manner of fractions had been inflicted upon him hitherto; nothing less awful than _quarto-duodecimo-vicesimals_, we should assure him.

Secondly, he assumes that the penny, such as it now is, will remain, as a coin of estimation, after it has ceased to be a coin of exchange; and that the mass of the people will continue to think of prices in old pence, and to calculate them in new ones, or else in new mils. No answer is required to this, beyond the mere statement of the nature of the assumption and denial.

{180}

Thirdly, he attributes to the uneducated community a want of perception and of operative power which really does not belong to them. The evidence offered to the Committee of the House shows that no fear is entertained on this point by those who come most in contact with farthing purchasers. And this would seem to be a rule,--that is, fear of the intelligence of the lower orders in the minds of those who are not in daily communication with them, no fear at all in the minds of those who are.