_December 31, 1867_
Many thanks for the present of Mr. James Smith's letters {338} of Sept. 28
and of Oct. 10 and 12. He asks where you will be if you read and digest his
letters: you probably will be somewhere first. He afterwards asks what the
WE of the _Athenaeum_ will be if, finding it impossible to controvert, it
should refuse to print. I answer for you, that We-We of the _Athenaeum_, not
being Wa-Wa the wild goose, so conspicuous in "Hiawatha," will leave what
controverts itself to print itself, if it please.
_Philomath_ is a good old word, easier to write and speak than
_mathematician_. It wants the words between which I have placed it. They
are not well formed: _pseudomathete_ and _graphomathete_ would be better:
but they will do. I give an instance of each.
The _pseudomath_ is a person who handles mathematics as the monkey handled
the razor. The creature tried to shave himself as he had seen his master
do; but, not having any notion of the angle at which the razor was to be
held, he cut his own throat. He never tried a second time, poor animal! but
the pseudomath keeps on at his work, proclaims himself clean-shaved, and
all the rest of the world hairy. So great is the difference between moral
and physical phenomena! Mr. James Smith is, beyond doubt, the great
pseudomath of our time. His 3-1/8 is the least of a wonderful chain of
discoveries. His books, like Whitbread's barrels, will one day reach from
Simpkin & Marshall's to Kew, placed upright, or to Windsor laid
length-ways. The Queen will run away on their near approach, as Bishop
Hatto did from the rats: but Mr. James Smith will follow her were it to
John o' Groats.
The _philomath_, for my present purpose, must be exhibited as giving a
lesson to presumption. The following anecdote is found in Thiebault's[631]
_Souvenirs de vingt ans de sejours a Berlin_, published in 1804. The book
itself got a high character for truth. In 1807 Marshal Mollendorff[632]
{339} answered an inquiry of the Duc de Bassano,[633] by saying that it was
the most veracious of books, written by the most honest of men. Thiebault
does not claim personal knowledge of the anecdote, but he vouches for its
being received as true all over the north of Europe.[634]
Diderot[635] paid a visit to Russia at the invitation of Catherine the
Second. At that time he was an atheist, or at least talked atheism: it
would be easy to prove him either one thing or the other from his writings.
His lively sallies on this subject much amused the Empress, and all the
younger part of her Court. But some of the older courtiers suggested that
it was hardly prudent to allow such unreserved exhibitions. The Empress
thought so too, but did not like to muzzle her guest by an express
prohibition: so a plot was contrived. The scorner was informed that an
eminent mathematician had an algebraical proof of the existence of God,
which he would communicate before the whole Court, if agreeable. Diderot
gladly consented. The mathematician, who is not named, was Euler.[636] He
came to Diderot with the gravest air, and in a tone of perfect conviction
said, "_Monsieur!_
(a + b^n)/n = x
_donc Dieu existe; repondez!_"[637] Diderot, to whom algebra was Hebrew,
though this is expressed in a very roundabout way by Thiebault--and whom we
may suppose to have expected some verbal argument of alleged algebraical
closeness, was disconcerted; while peals of laughter sounded on all sides.
Next day he asked permission to return to France, which was granted. An
algebraist would have {340} turned the tables completely, by saying,
"Monsieur! vous savez bien que votre raisonnement demande le developpement
de x suivant les puissances entieres de n".[638] Goldsmith could not have
seen the anecdote, or he might have been supposed to have drawn from it a
hint as to the way in which the Squire demolished poor Moses.
The _graphomath_ is a person who, having no mathematics, attempts to
describe a mathematician. Novelists perform in this way: even Walter Scott
now and then burns his fingers. His dreaming calculator, Davy Ramsay,
swears "by the bones of the immortal Napier." Scott thought that the the
philomaths worshiped relics: so they do, in one sense. Look into
Hutton's[639] Dictionary for _Napier's Bones_, and you shall learn all
about the little knick-knacks by which he did multiplication and division.
But never a bone of his own did he contribute; he preferred elephants'
tusks. The author of _Headlong Hall_[640] makes a grand error, which is
quite high science: he says that Laplace proved the precession of the
equinoxes to be a periodical inequality. He should have said the variation
of the obliquity. But the finest instance is the following: Mr.
Warren,[641] in his well-wrought tale of the martyr-philosopher, was
incautious enough to invent the symbols by which his _savant_ satisfied
himself Laplace[642] was right on a doubtful point. And this is what he put
together--
[sqrt]-3a^2, [rectangle]y^2 / z^2 + 9 - n = 9, n x log e.
Now, to Diderot and the mass of mankind this might be Laplace all over:
and, in a forged note of Pascal, would {341} prove him quite up to
gravitation. But I know of nothing like it, except in the lately received
story of the American orator, who was called on for some Latin, and
perorated thus: "Committing the destiny of the country to your hands,
Gentlemen, I may without fear declare, in the language of the noble Roman
poet,
E pluribus unum,
Multum in parvo,
Ultima Thule,
Sine qua non."[643]
But the American got nearer to Horace than the martyr-philosopher to
Laplace. For all the words are in Horace, except _Thule_, which might have
been there. But [rectangle] is not a symbol wanted by Laplace; nor can we
see how it could have been; in fact, it is not recognized in algebra. As to
the junctions, etc., Laplace and Horace are about equally well imitated.
Further thanks for Mr. Smith's letters to you of Oct. 15, 18, 19, 28, and
Nov. 4, 15. The last of these letters has two curious discoveries. First,
Mr. Smith declares that he has _seen_ the editor of the _Athenaeum_: in
several previous letters he mentions a name. If he knew a little of
journalism he would be aware that editors are a peculiar race, obtained by
natural selection. They are never seen, even by their officials; only heard
down a pipe. Secondly, "an ellipse or oval" is composed of four arcs of
circles. Mr. Smith has got hold of the construction I was taught, when a
boy, for a pretty four-arc oval. But my teachers knew better than to call
it an ellipse: Mr. Smith does not; but he produces from it such
confirmation of 3-1/8 as would convince any _honest_ editor.
Surely the cyclometer is a Darwinite development of a spider, who is always
at circles, and always begins again when his web is brushed away. He
informs you that he {342} has been privileged to discover truths unknown to
the scientific world. This we know; but he proceeds to show that he is
equally fortunate in art. He goes on to say that he will make use of you to
bring those truths to light, "just as an artist makes use of a dummy for
the purpose of arranging his drapery." The painter's lay-figure is for
flowing robes; the hairdresser's dummy is for curly locks. Mr. James Smith
should read Sam Weller's pathetic story of the "four wax dummies." As to
_his_ use of a dummy, it is quite correct. When I was at University
College, I walked one day into a room in which my Latin colleague was
examining. One of the questions was, "Give the lives and fates of Sp.
Maelius,[644] and Sp. Cassius."[645] Umph! said I, surely all know that
Spurius Maelius was whipped for adulterating flour, and that Spurius Cassius
was hanged for passing bad money. Now, a robe arranged on a dummy would
look just like the toga of Cassius on the gallows. Accordingly, Mr. Smith
is right in the drapery-hanger which he has chosen: he has been detected in
the attempt to pass bad circles. He complains bitterly that his geometry,
instead of being read and understood by you, is handed over to me to be
treated after my scurrilous fashion. It is clear enough that he would
rather be handled in this way than not handled at all, or why does he go on
writing? He must know by this time that it is a part of the institution
that his "untruthful and absurd trash" shall be distilled into mine at the
rate of about 3-1/8 pages of the first to one column of the second. Your
readers will never know how much they gain by the process, until Mr. James
Smith publishes it all in a big book, or until they get hold of what he has
already published. I have six pounds avoirdupois of pamphlets and letters;
and there is more than half a pound of letters {343} written to you in the
last two months. Your compositor must feel aggrieved by the rejection of
these clearly written documents, without erasures, and on one side only.
Your correspondent has all the makings of a good contributor, except the
knowledge of his subject and the sense to get it. He is, in fact, only a
mask: of whom the fox
"O quanta species, inquit, cerebrum non habet."[646]
I do not despair of Mr. Smith on any question which does not involve that
unfortunate two-stick wicket at which he persists in bowling. He has
published many papers; he has forwarded them to mathematicians: and he
cannot get answers; perhaps not even readers. Does he think that he would
get more notice if you were to print him in your journal? Who would study
his columns? Not the mathematician, we know; and he knows. Would others?
His balls are aimed too wide to be blocked by any one who is near the
wicket. He has long ceased to be worth the answer which a new invader may
get. Rowan Hamilton,[647] years ago, completely knocked him over; and he
has never attempted to point out any error in the short and easy method by
which that powerful investigator condescended to show that, be right who
may, he must be wrong. There are some persons who feel inclined to think
that Mr. Smith should be argued with: let those persons understand that he
has been argued with, refuted, and has never attempted to stick a pen into
the refutation. He stated that it was a remarkable paradox, easily
explicable; and that is all. After this evasion, Mr. James Smith is below
the necessity of being told that he is unworthy of answer. His friends
complain that I do nothing but _chaff_ him. Absurd! I winnow him; and if
nothing but chaff results, whose fault is that? I am usefully employed: for
he is the type of a class which ought to be known, and which I have done
much to make known.
{344}
Nothing came of this until July 1869, when I received a reprint of the
above letter, with a comment, described as Appendix D of a work in course
of publication on the geometry of the circle. The _Athenaeum_ journal
received the same: but the Editor, in his private capacity, received the
whole work, being _The Geometry of the Circle and Mathematics as applied to
Geometry by Mathematicians, shown to be a mockery, delusion, and a snare_,
Liverpool, 8vo, 1869. Mr. J. S. here appears in deep fight with Professor
Whitworth,[648] and Mr. Wilson,[649] the author of the alleged amendment of
Euclid. How these accomplished mathematicians could be inveigled into
continued discussion is inexplicable. Mr. Whitworth began by complaining of
Mr. Smith's attacks upon mathematicians, continued to correspond after he
was convinced that J. S. proved an arc and its chord to be equal, and only
retreated when J. S. charged him with believing in 3-1/8, and refusing
acknowledgment. Mr. Wilson was introduced to J. S. by a volunteer defense
of his geometry from the assaults of the _Athenaeum_. This the editor would
not publish; so J. S. sent a copy to Mr. Wilson himself. Some
correspondence ensued, but Mr. Wilson soon found out his man, and withdrew.
There is a little derision of the _Athenaeum_ and a merited punishment for
"that unscrupulous critic and contemptible mathematical twaddler, De
Morgan."