OF ARTS AND SCIENCES. 



287 



'■'■ S V = the perturbation of Neptune's true longitude = 



-f 174.37 sin. (^ — J^) 



— 8.63 sin. 2 (i[ — f ) 



— 1.70 sin. 3(i[ — f ) 



— 0.54 sin. 4 (^ — :^) 



— 0.21 sin. 5{w — '^) 



— 0.09 sin. 6(it — f ) 



— 0.04 sin. 7(ii — f ) 



— 0.02 sin. 8(1^—1^) 



— 0.01 sin. 9(i[ — :^) 



— 0.01 sin. 10(it — f) 



= (l+i"^)< 



+ (1 + F^)<i 



+ (l + i"ig)<i 



+ 1.93 sin. (^ — ^■^) 



— 105.20 sin. (2 ^ — i[ — n^) 



— 0.09 sin. (2 ^ — ]^ — 71]^) 

 + 14.71 sin. (2^ -3f + 77^) 



— 0.01 sin. (3 ]j[ —2^ — 71^) 



— 0.39 sin. (3 ¥ — 4f + 7ijg;) 



— 0.09 sin. (4 i[ — 5 ^ 4- 71^) 



— 0.03 sifl. (5^—6^ + 71^) 



— 0.01 sin. (6^— 7f + 71;^) 



— 0.004340 t COS. (^ — Txj^) 



-f- 0.23 sin. (i^ — TTj^N 



+ 166S.30 sin. (2f — ii — 71^^^) 



+ O'.lGsin. (2^ — f — 7rj^) 



— 58.87 sin. (2 n — 3 f + ttj^j) 



— 0.03sin. (3i[— 2f — Tij^) 

 + l.SOsin. (3^— 4|: + 7ij^) 



— 0.02sin. (4 II— 3f — 7Tjj[) 

 + 0.28sin. (4^—5^4-713^) 



— 0.01 sin. (5^ — 4|: — TTj^) 

 + 0.10 sin. (5 n —6:^4- 7rj^) 



— 0.01 sin. (6 IT -5:^ — 71 jjj) 

 4- 0.05sin. (6 II — 7f 4-7rjj[) 

 -H 0.03sin. (7 n— 8f 4-7Tj^) 

 4- O.Olsin. (8ii— 9f 4-71^^) 



1^ 4- 0.018461 t COS. (^ — TT^) 



