APPENDIX. 
(A.) 
THE FOLLOWING IS A BRIEF NOTICE OF SOME OTHER 
INTERESTING RESULTS OF THE RESEARCHES OF LA- 
PLACE WHICH HAVE NOT BEEN MENTIONED IN THE 
TEXT. 
Method for determining the orbits of comets.—Since comets 
are generally visible only during a few days or weeks at the 
utmost, the determination of their orbits is attended with 
peculiar difficulties. The method devised by Newton for 
effecting this object was in every respect worthy of his 
genius. Its practical value was illustrated by the brilliant 
researches of Halley on cometary orbits. It necessitated, 
however, a long train of tedious calculations, and, in conse- 
quence, was not much used, astronomers generally preferring 
to attain the same end by a tentative process. In the year 
1780, Laplace communicated to the Academy of Sciences an 
analytical method for determining the elements of a comet’s 
orbit. This method has been extensively employed in France. 
Indeed, previously to the appearance of Olber’s method, about 
the close of the last century, it furnished the easiest and most 
expeditious process hitherto devised, for calculating the para- 
bolic elements of a comet’s orbit. 
Invariable plane of the solar system.—In consequence of 
the mutual perturbations of the different bodies of the plan- 
etary system, the planes of the orbits in which they revolve 
