129 



5 . A a .A 



4 cs,*A w/A «,*A 



• « 



I . , A o 4a j-,A 2?2<z . J A 



2. n x/. = 1 2b/. 



16 cs,*A fj/A «,'A «,'A a,'A 



3 -^ A 



-\- - njl. &c. &c. 



a a,«A 



A ^, A 2x, A 



The^. = V 



cs,*A ys,^A 3a, A 



A s, A 4J,A 4. 2^ A 



cs^A 5«,^A ^.ys^A f.jWjA 



A X, A 6j, A 6. 4/, A 6.4.2^A 



cs,^A 7",'' A 7.5w,5A 7. 5.3^3 A 7.5.3a,A 

 Whence, from the above equations we readily deduce 2a (the anomaly in 



. .. /,A , , t,A 



theellipfe) = 2A+2Xfl+a= 2A-\ X4-3«, A-6cs, AX«+ 



10 28poa,'A 



X 4o8-i6oa/A-iiooa,''A-425«°AH-252«'°Ax n'. It maybe ob- 

 ferved, that if the axis major of the ellipfe be unity, and the exccntricity 

 =e, n= i-e the perihelion diftance. The co-efficient of « is precifely the 

 fame as that found by Laplace,* by a very different method. Q^ E. I. 



* Mecanique Cclefte Tom. i. p- 186 

 Vol. IX. R What 



