176 
SECOND REPORT- 1882 . 
cipal perturbations of Jupiter to the sixth order of eccentrici¬ 
ties, &c. In the Mem. Ast. Soc., vol. 2, Plana gave remarks 
on Laplace’s investigations of the perturbations of Jupiter and 
Saturn depending on the second order of the disturbing force. 
As the greater part of Laplace's investigation was suppressed, 
it was ordv possible to compare the results, and to examine the 
correctness of some equations given by Laplace. Plana’s re¬ 
sults differed much from Laplace’s : and a simple equation 
between the perturbations of Jupiter and those of Saturn, given 
by Laplace, appeared to be incorrect. Laplace in answer 
{Conn, des Temps 1829, published 1826,) allowed that his equa¬ 
tion was not perfectly correct, but maintained that Plana’s error 
was much greater. In the Turin Memoirs 1827, Plana in 
reply said that Laplace's answer did not enter sufficiently into 
details. In the Conn, des Temps 1831, Poisson pointed out some 
terms omitted by Plana. In the Turin Memoirs 1830, Plana 
again made some calculations, and still obtained results differ¬ 
ing from Laplace’s. Finally, in a memoir of which an extract 
is printed in the Conn, des Temps 1833, M. Pontecoulant 
stated that he had found errors in the calculations both of La¬ 
place and of Plana, and that on correcting these, both determi¬ 
nations agreed. In the Turin Memoirs 1831, Plana acknow¬ 
ledges that this is true. And thus the discussion of these terms 
appears to be finished, and physical astronomy has gained much 
from this inquiry, prosecuted at first by M. Plana under the 
repulsive circumstances of comparing a final result with La- 
place’s without an intermediate step. An elaborate investiga¬ 
tion of the theory of Jupiter and Saturn by Hansen, on the 
principles which I have described as peculiar to him, has lately 
been received in this country. 
On the theory of satellites, little has been done. In the 
Conn, des Temps 1821, Laplace has investigated the effect of 
the long inequality of Jupiter and Saturn on the other bodies 
of the system, and has shown that they are sensible only in the 
motions of Jupiter’s satellites. In the Ast. Soc. Mem., vol. 2, 
Plana objected to Laplace’s theory, in reference to the seventh 
satellite of Saturn. Laplace, in the Conn, des Temps 1829, 
maintained its correctness, which Plana {Turin Mem. 1827,) has 
again denied. In the Conn, des Temps 1831, Poisson has shown 
that both methods produce the same results: and here, I believe, 
the question rests. In the Ast. Nachr., No. 193, are expres¬ 
sions, by Bessel, for those variations of the elements of Saturn's 
sixth satellite which do not depend on its position in its orbit: 
the permanent variations and variations of long period, in fact, 
analogous to the secular equations of the planets. 
