VIII, A New Series for the Rectification of the Ellipsis ; 

 together with fome Observations on the Evolution 

 of the Formula [aP- -\- ¥ — lab co{<py. By James 

 lyORr, A. M. Communicated by JOHN FhATFAlR^ Pro- 

 fejfor of Mathematics in the Univerfity of Edinburgh, 



[Read Nov. 7. 1796.] 



Dear Sir, 



HAVING, as you know, beftowed a good deal of time and 

 attention on the ftudy of that part of phyfical aftronomy 

 which relates to the mutual difturbances of the planets, I have, 

 naturally, been led to confider the various methods of refolving 

 the formula (<3^ -{■b'^ — 2ab cofip)' into infinite feries of the 

 form A + B cof (p + C cof 2(p + &c. In the courfe of thefe in- 

 veftigations, a feries for the redification of the ellipfis occurred 

 to me, remarkable for its fimplicity, as well as its rapid conver- 

 gency. As I believe it to be new, 1 fend it you, inclofed, to- 

 gether with fome remarks on the evolution of the formula juft 

 mentioned, which, if you think proper, you may fubmit to the 

 confideration of the Royal Society. 



I am. Dear Sir, 



Your's, &c. 



DouGLASTOWN, near Forfar,-) JaMES IVORY. 



20th October 1796. 3 ■' 



To Mr John Playfair, Pro- 

 fejfor of Mathematics, ISc, 



Vol. IV. y Let 



