Commentary continued; second volume.—Discussion between
the English and French mathematicians; Dr. Bowditch’s
criticisms.—Errors in La Place in regard to the earth,
&c.—Third volume; motions of the moon.—Fourth volume; many
errors discovered in it.—Halley’s Comet.—Curious phenomena of
capillary attraction.
[Sidenote: CRITIC OF IVORY AND POISSON.]
[Sidenote: “I HAVE GOT IT!”]
In the second volume of the Commentary, Dr. Bowditch makes very copious
notes, in which he shows a perfect knowledge of the works of the chief
mathematicians of Europe. He stands as critic between two of the eminent
men of science of that day—Messrs. Ivory and Poisson, the former an
Englishman, the latter a Frenchman; and in reference, likewise, to a
difficult subject, namely, the revolution or the turning of a fluid mass
upon its own axis, as our earth does. He not merely agrees with Mr.
Poisson, but, by a very simple illustration, proves the total inaccuracy
of Mr. Ivory’s views. I well remember the earnestness with which he
studied this subject. Day after day, he returned to the task of finding
out some “simple case,” with which to prove to the satisfaction of others
the truth of his own view. At length, when he did discover it, he jumped
up in ecstasy, and, rubbing his hands and forehead with delight, walked
about the library-room, crying out, “I have got it!”
Dr. Bowditch in this volume points out five errors or omissions made by
La Place, some of which are very important. One refers to the form of
our earth, and had been previously communicated to the Academy. There is
another of some moment, relative to the time occupied in the revolution
of one of Saturn’s rings, La Place having made it longer than was true.
Finally, on the subject of the motion of the earth about its centre of
gravity, he points out an error, in which La Place gives to two numbers
only one third of their true value.
[Sidenote: OLBERS AND GAUSS.]
In the third volume, occupied as it is with the motions of the planets
and of the moon, and with all the phenomena accompanying these, Dr.
Bowditch shows much learning, and his power of bringing modern science
to the thorough study of any topic. As in the previous volume, he labors
without fear upon subjects treated of with much earnestness by La Place,
Poisson, and Pontecoulant, in France, and Plana in Italy.
On the theory of the motions of the moon,—a very difficult and
interesting subject,—Dr. Bowditch makes very copious notes; and the
volume terminates with an appendix of more than two hundred and fifty
pages, in which he gives the history of modern astronomy, in reference
to the calculations of the movements of planets and comets. In this he
speaks of Olbers and Gauss. The former, from having discovered three
planets since the beginning of this century, was called “The fortunate
Columbus of the Heavens.” The latter was one of the most remarkable men
in the world for the rapidity with which he was able to perform the most
tedious and troublesome calculations.[13]
[Sidenote: ERRORS IN LA PLACE.]
We come now to the last volume, in printing the thousandth page of which
he died. It was the most difficult to him of the whole, and probably
will raise him higher, in the estimation of the scientific world, than
either of the others. In the first place, I would remark, that either
from the difficulty of the subject, or from the inattention of La Place,
an unusual number of errors was discovered. No less than twenty-four
errors or omissions are pointed out. Many of these seem insignificant,
but often, as may be supposed, they materially affect the calculation.
Most of them refer to the derangements and the motions of Jupiter’s
satellites—a subject which occupies three hundred and fourteen pages of
the volume. The keenness of Dr. Bowditch’s criticism is again perceived
while treating upon a subject in dispute between Plana and La Place. Dr.
Bowditch points out one mistake, and Poisson another, whereby Plana’s
views are proved to coincide entirely with La Place’s, instead of being
opposed to them.
[Sidenote: NOTE ON HALLEY’S COMET.]
I find a note upon Halley’s comet, to which I alluded as presenting
a grand spectacle in our western sky a few years since, and I cannot
forbear mentioning the coincidence. Dr. Bowditch, when making his notes
upon the subject of the motions and revolutions of comets, speaks of
Halley’s comet, and mentions all that is known about it, and its probable
appearance. This note was prepared some time before it was printed. It
terminates thus: “Since writing the preceding part of this note the comet
has again appeared, and, _at the time of printing this page, is visible
in the heavens_, not far distant from the place corresponding to the
elements of Mr. Pontecoulant.”
[Sidenote: CAPILLARY ATTRACTION.]
[Sidenote: LA PLACE AND POISSON.]
The work, so far as Dr. Bowditch is concerned, finishes with the most
curious and difficult subject of capillary attraction, or that power
whereby a liquid rises in narrow tubes beyond the level of the fluid
outside, as we see familiarly in sponges, and cloths, and in very minute
glass tubes. You may think this subject of little moment; yet La Place
thought it more curious than almost any other, and he earnestly calls
the attention of mathematicians to it. It is a subject so difficult
of investigation, that it requires the keenest efforts of the best
intellects to rightly understand it. After La Place’s investigations
were published, Gauss considered the subject, and arrived at results
similar to those presented by La Place. But in 1831, Poisson, the first
mathematician then living, of whom we have already spoken, put forth
a work in which he announced many new views. This he thought himself
justified in doing, after taking into consideration certain particulars
which La Place had neglected. Dr. Bowditch received the work while
engaged in printing this volume. He ceased printing, and devoted six
months or more to a thorough perusal of the new French work. The result
was, that he proved that without an exception, unless where an evident
error was made by La Place, the principles of this mathematician, when
fairly carried out, would produce all the results which Poisson had given
as new in his work. By this labor Dr. Bowditch proved that Poisson’s
so-called new theory of capillary attraction was founded in error. This
is decidedly the most important work of the translator. It places him
much higher than before in the scale of mathematical rank.
I would willingly give a further analysis, but I forbear, because it
would not be interesting to you. It was in correcting this, his noblest
task, in the full strength of his intellect, that he was destined to die.