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 

 1 780, 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 



