MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 



63 



Each /S '; was multiplied by sine and cosine i (F — e) for each of its sixteen special values, the 

 products fi "> sin i (F — e) and /?<?' cos i (F — e) then being developed in series proceeding accord- 

 ing to sines and cosines of multiples of f. 



From these followed immediately j D — /cos (s'—F)\ -5 developed in series proceeding according 

 to sines and cosines of is — i't', and by the following formulas, the desired negative odd powers of 

 the distance between the planets. 



5) 



SD-/cos It' 



( 



a v< = 1 



AJ JD-/cos (f'-F)j 



\ y 2 «os 2 e' 



)D-/cos (e'-F)ji 



% y-i cos 2 e' 

 jD-/cos (£'-F)j* 



S. Doc. 139- 



