_Redit labor actus in orbem._[584] Among the matters which have come to me
since the Budget opened, there is a pamphlet of quadrature of two pages and
a half from Professor Recalcati,[585] already mentioned. It ends with
"Quelque objection qu'on fasse touchant les raisonnements ci-dessus on
tombera toujours dans l'absurde."[586] A civil engineer--so he says--has
made the quadrature "no longer a problem, but an axiom." As follows: "Take
the quadrant of a circle whose circumference is given, square the quadrant
which gives the true square of the circle. Because 30 / 4 = 7.5 x 7.5 =
56.25 = the positive square of a circle whose circumference is 30."
Brevity, the soul of wit, is the "wings of mighty-winds" to quadrature, and
sends it "flying all abroad." A _surbodhicary_--something like M.A. or
LL.D., I understand--at Calcutta, published in 1863 the division of an
{315} angle into any odd number of parts, demonstration and all in--when
the diagram is omitted--one page, good-sized, well-leaded type, small
duodecimo. But in the Preface he acknowledges "sheer inability" to execute
his task. Mr. William Dean, of Todmorden, in 1863, announced 3-9/64 as
proved both practically and geometrically: he has been already mentioned
anonymously. Next I have the tract of Don Juan Larriva, published at Leiria
in 1856, and dedicated to Queen Victoria. Mr. W. Peters,[587] already
mentioned, who has for some months been circulating diagrams on a card,
publishes (August, 1865) _The Circle Squared_. He agrees with the
Archpriest of St. Vitus. He hints that a larger publication will depend
partly on the support he receives, and partly on the castigation, for which
last, of course, he looks to me. Cyclometers have their several styles of
wit; so have anticyclometers too, for that matter. Mr. Peters will not
allow me any extra-journal being: I am essentially a quotation from the
_Athenaeum_; "A. De Morgan" _et praeterea nihil_.[588] If he had to pay for
keeping me set up, he would find out his mistake, and would be glad to
compound handsomely for a stereotype. Next comes a magnificent sheet of
pasteboard, printed on both sides. Having glanced at it and detected
quadrature, I began methodically at the beginning--"By Royal Command," with
the lion and unicorn, and all that comes between. Mercy on us! thought I to
myself: has Her Majesty referred the question to the Judicial Committee of
the Privy Council, where all the great difficulties go now-a-days, and is
this proclamation the result? On reading further I was relieved by finding
that the first side is entirely an advertisement of Joseph Gillott's[589]
steel pens, with engraving of his {316} premises, and notice of novel
application of his unrivalled machinery. The second side begins with "the
circle rectified" by W. E. Walker,[590] who finds [pi] =
3.141594789624155.... This is an off-shoot from an accurate geometrical
rectification, on which is to be presumed Mr. Gillott's new machinery is
founded. I have no doubt that Mr. Walker's error, which is only in the
sixth place of decimals, will not hurt the pens, unless it be by the
slightest possible increase of the tendency to open at the points. This
arises from Mr. Walker having rectified above proof by .000002136034362....
Lastly, I, even I myself, who have long felt that I was a quadrature below
par, have solved the problem by means which, in the present state of the
law of libel, I dare not divulge. But the result is permitted; and it goes
far to explain all the discordances. The ratio of the circumference to the
diameter is not always the same! Not that it varies with the radius; the
geometers are right enough on that point: but it varies with the time, in a
manner depending upon the difference of the true longitudes of the Sun and
Moon. A friend of mine--at least until he misbehaved--insisted on the mean
right ascensions: but I served him as Abraham served his guest in
Franklin's parable. The true formula is, A and a being the Sun's and Moon's
longitudes,
[pi] = 3-13/80 + 3/80 cos(A - a).
Mr. James Smith obtained his quadrature at full moon; the Archpriest of St.
Vitus and some others at new moon. Until I can venture to publish the
demonstration, I recommend the reader to do as I do, which is to adopt
3.14159..., and to think of the matter only at the two points of the lunar
month at which it is correct. The _Nautical Almanac_ will no doubt give
these points in a short time: I am in correspondence with the Admiralty,
with nothing {317} to get over except what I must call a perverse notion on
the part of the Superintendent of the _Almanac_, who suspects one
correction depending on the Moon's latitude; and the Astronomer Royal leans
towards another depending on the date of the Queen's accession. I have no
patience with these men: what can the Moon's node of the Queen's reign
possibly have to do with the ratio in question? But this is the way with
all the regular men of science; Newton is to them etc. etc. etc. etc.
The following method of finding the circumference of a circle (taken from a
paper by Mr. S. Drach[591] in the _Phil. Mag._, Jan. 1863, Suppl.) is as
accurate as the use of 3.14159265. From three diameters deduct
8-thousandths and 7-millionths of a diameter; to the result add five per
cent. We have then not quite enough; but the shortcoming is at the rate of
about an inch and a sixtieth of an inch in 14,000 miles.