178 
SECOND REPORT — 1832 . 
1833, and of two years from 1833 to the time of its reappear¬ 
ance, 1887. In the Ast. Nadir. Nos. 210 and 211, Encke 
has described the method by which he calculated the varia¬ 
tion of elements of the periodical comet bearing his name, 
undoubtedly the most troublesome of all. Using the same 
general methods, the perturbations produced by Mercury were 
computed for every four days ; those of the Earth and Venus 
for every twelve days ; and those of Mars, Jupiter and Saturn, 
for every thirty-six days. These calculations were carried 
on till the comet reached a certain distance from the planets, 
and then its place was referred to the centre of gravity of the 
sun and planets. For some details Encke refers to Arge- 
lander’s treatise on the comet of 1811, a work which I have 
not been able to procure. For Encke’s comet the effect of 
a resisting medium, whose density is inversely as the square 
of the distance from the sun, was calculated by the same 
method. This had been done analytically for several laws of 
density by Plana, in Zach’s Correspondance, vol. 13; it is 
also noticed by Mosotti, Mem . Ast. Soc. vol. 2. In the Conn. 
des Temps 1832, Damoiseau has described his own method. 
He refers the co-ordinates to the original plane of the comet’s 
orbit, (taking its original axis-major for the axis of one ordinate,) 
and resolves the disturbing forces in these directions, and finds 
the variation of elements in terms of these forces, which he in¬ 
tegrates by quadratures. As the ordinates of the comet are 
conveniently calculated by means of the eccentric anomaly, he 
calculates the variations for given intervals of that angle. This 
is the method that he has adopted in the Turin Memoirs 
1817-1818, for Halley’s comet, varying the eccentric anomaly by 
1° each time for the perturbations of Jupiter, by 2° for those 
of Saturn, and by 6° for those of Uranus. He has also used it in 
the calculations for the comets of short period, Conn, des Temps 
1827 and 1830, and Memoires 1826. In the Conn, des Temps 
1833, is an extract from Pontecoulant’s Memoir on the same 
comet; he refers generally to Lagrange’s method, and states 
that having with the first elements computed by quadratures 
the perturbations of the elements through 30° (of eccentric 
anomaly, I suppose), he has then used the elements so cor¬ 
rected in the calculations for the next 80°, when he has again 
changed the elements from the result of these calculations ; and 
so on for each successive 30°. 
The following additions have been made to the theories con¬ 
nected with the figure of the’ earth, &c. In the Phil. Trans. 
1809, is a paper by Mr. Ivory, of which the most important 
part is the very beautiful theorem for finding the attraction of a 
