Adams. — On Natural Sines. 411 



^-4^ (7m 6 + 21m 5 Am + 35m 4 Am 2 + 35m 3 Am 3 

 n? +4o.) 



_l_ il^L (9m 8 + 36m 7 Am + 84m 6 Am 2 + &c.) 



- ^r- ( llml ° + 55m 9 Am + &c.) 



+ t^L (13m 12 + &c.) - &c. (AQ) 



" Nous trouverons de meine en faisant Am constant 



. . m ir b • Am 2 



A'- sin — • y = - — ^ — ( 6m + 6 ^m) 



+ ^p- (20m 3 + 60m 2 Am + 70mAm 2 + 30Am s ) 



_ d ■ Am' ^ 2m6 + 2l0m 4 A??i + 490m 3 Am 2 + 

 " 630m 2 Am 3 + 434m ■ Am 4 + 126Am 5 ) 



+ 11^ (72m 7 + 504m 6 Am + 1764m 8 Am 2 

 w + 3780m 4 Am 3 + &c.) 



_ Zi^!L 2 (iiOm 9 + 990m 8 Am + 4620m 7 Am 2 



■ Am -+- aozum iii 



+ &C.) 



+ 0_Jp! (156m 11 + 1716m 10 Am + &c.) 



h ■ Am 2 



n l 



■(210??i 13 + &c.) + &c. (A 2 Q) 



A 3 sin- • - = - 6b ' AmS + ° ' AmS (60m 2 + 180mAm + 150Am 2 ) 



n 2 n 3 ' n b x 



- d ' A . wt8 (210m 4 + 1260m 8 Am + 3150m 2 Am 2 + 

 n 3780mAm s + 1806 Am 4 ) 



• + e ' A 9 w3 (504m 6 + 4536m 5 Am + 18900m 4 Am 2 + 

 n 45360m 3 Am 3 + &c.) 



_ /-Am3 (gg0;;i8 + nQSOm^vi + 69300m 6 Am 2 + 

 nU Ac.) 

 g ' *"* (1716m 10 + 25740m 9 Am + 193050 m 8 Am 2 



+ &C.) 



_ ^!!i 3 (2730m 12 + 49140m u Am + &c.) + &c. (A 8 Q) 



A < sin -L » = i_^! (120m + 240Am) 



_ ^-^-* (840m 3 + 5040m 2 Am + 10920mAm 2 + 

 8400Am 3 ) 



(3024??i 5 + 30240m 4 Am + 131040?re 3 Am 2 

 + &c.) 



+ 



e • Am 4 



IV 3 



