Worcester daily spy. [volume] (Worcester [Mass.]) 1850-1888, 1859-01-07
0Qturtcster 4ailp Spg.
Scientific aob Economical.

HE PROCESSION OF THE EQUINoxEs.-M
Poinsot, the distinguished member of the In
stitute, and celebrated for the discovery of the
theory of couples in mechanics, has recently
solved an important problem, which has baf
fled the ingenuity of mathematicians since the
time of Newton. 1t is well known that the in
tersections of the terrestrial equator with the
ecliptc, called the equinoxes, never occur
twice at the same point, but that every year
they appear to recede by about 50-1S seconds.
This retrograde motion is called the "preces-
sion of the equinoxes."
To explain this motion by the theory of uni
versal gravitation became an important prob
lem at the time when Newton made the great
discovery. He himself attempted an expIana-
ton oft, but the imperfect state of astronomy
at that period deprived him of the advantage of
certain date which were indispensable to arrive
at the desired solution. In l747, Bradley, by
series of laboriOus observations, patiently
continued for the space of twenty years, at
length ascertained that the earth's axis had
peculiar swinging motion, Of which no astrono-
mer before had even suspected the existence;
all this motion he called mutation" He also
proved that this mutation, which causes the
axis of the earth to describe in space a sort of
fluted cone, having base of an elptical form,
but modified by certain minute undulations,
about 400 in number, was closely connected
with the motion of procession. D'Aembert
then took up the problem, and in 1749 publish
ed a solution of it, which, indeed, accounts for
the above motions in a general way but is far
from sufficient to explain the cause of those
singular fluctuations which the pole of the
earth describes.
The delicacy of the question will be easily
understood, from the fact, that within the
compass of the EARTH the axis appears to have
no motion at all, and that the phenomenon of
mutation is only perceptble at an immeasura-
BILE distance in the heavens. We now come to
NJ Poinsots admirable solution, founded on his
well known theory of couples. Negecting all
useless considerations that had embarrassed
his predecessors, he proves by mathematical
calculations, which, considering the difficulty
ofthe problem, have the merit of extraordina-
ry simplicity, that by the law of gravitation,
the earth axis must describe an oscillation of
W seconds i'll virtue of the attraction of the
sun, and 16 seconds in virtue of that of the
moon, or about Is seconds in all, in the course
of nine years and three months, after which
similar oscillation takes place in the contrary
direction.
This quantity of Is seconds all but exactly
comedies with the results of observation; and
his determination of the procession is equally
exact, since he finds it to be 504 seconds. 1t
must be borne in mind that observation al
ways has great advantage over calculation in
astronomy, since it gives facts as they are,
while IN calculation it is often necessary to re-
Ject certain small quantities which stand in the
way of indignation.
NJ. Ponsot also proves a singular fact, viz:
that the procession would be the same if the
earth, instead of being a solid spheroid, were
hollow, or if its mass or volume were changed,
provided its momentum of inertia remain the
same. Thus all d'Alembe1t's complicated
specuations touching the influence of the sea,
the nature of the strata of the earth, &C., turn
out to be useless. M. Poinsot demonstrates
various other curious theorems connected with
the subject, but which are too abtruse to be
mentioned here.-London Times