REPORT ON ASTRONOMY. 
179 
spheroid generally, on a point without it, from the attraction of a 
spheroid on a point within it. In the Memorie della Societa Itali- 
ana, 1810, and the Gottingen Transactions 1811-1813, Plana and 
Gauss have given theorems founded on the same kind of inte¬ 
gration, and adding little to our knowledge of the subject. In 
th o Journal de IF cole Polyteclinique , tom. 8, is a paper by La¬ 
grange on a difficulty in Laplace’s general theory ; and in the 
Pliil. Trans. 1812 and 1822, Mr. Ivory has pursued this objection, 
and given a method of his own, of very great analytical elegance. 
In the Cambridge Transactions , vol. 2, the author of this Re¬ 
port supported Laplace’s correctness with respect to the point 
objected {as Laplace had done himself in the fifth volume of the 
Mec. Cel.), and pointed out what he considered to be another 
defect in Laplace’s reasoning. In a discussion on the figure of 
the earth, Phil. Trans. 1826, I gave a theorem analogous to 
Clairaut's, admitting of extension to all powers of the ellip- 
ticity. In the Conn, des Temps 1829, Poisson gave a very able 
memoir on the attraction of spheroids. In the Phil. Trans. 
1824, and in a later volume, Mr. Ivory introduced a new equa¬ 
tion in the consideration of the equilibrium of fluids of which the 
particles mutually attract each other ; the necessity for this has 
not been generally allowed, and was explicitly denied by Poisson 
in a paper (treating also on other points,) in the Conn, des 
Temps 1831. In the French Memoirs 1817 and 1818, La¬ 
place has applied his general method to the case of an irregular 
nucleus covered by a fluid ; the most general case that can be 
conceived, and the case that comes nearest to the state of the 
earth, but which analysis has not yet completely mastered. 
In the Conn, des Temps 1821, he gave as a consequence of 
this theory, that the gravity on a continent reduced to the level 
of the sea by the factor depending only on the distance from 
the earth's centre, follows the same law as at the surface of 
the sea. In the Journal de VEcole Polyteclinique , tom. 8, 
Poisson investigated the motion of the earth's axis of rotation 
within the earth itself (considering the motion of the axis in 
space as completely treated in the Mec. Cel. liv. 5.) He found 
that neither the place of the axis nor the velocity of rotation is 
permanently altered. In the Mthnoires, 1824, he has treated 
of the earth’s motion about its centre generally (by variation 
of constants), and has compared his numerical results for the 
obliquity, &c., with observation. In the Conn, des Temps 
1827, Laplace has alluded to the combined effect of change in 
the plane of the ecliptic and precessional motion of the earth’s 
axis ; and has shown that in consequence of the latter, the 
limits of the diminution of obliquity are very much contracted. 
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