any Function of Sines and Cosines. 

 The following table exhibits the entire factor. 



Table VII. 



115 



of which the law is evident. 



The table reads thus : the coefficient of B s in (3)! 

 = 2 6 sin 2 sin 3 sin 4 sin 5 sin 6 sin 28, 

 the coefficient of A 8 in (3), 



= — 2 6 sin 2 sin 3 sin 4 sin 5 sin 6 cos 28. 



Let 



2nd Category, uneven indices. 

 1st Operation. Elimination of i^ and A v 



(i) 1 =»\=h(*i--R\) 



(sD,*«j^(«; T A) 



The indices are given in the alternate columns of Table I. 

 (l) 1 + (l) 3 -2(l) 2 cosl = (2) 1 

 (1) 2 + (1)4-2(1)3 cos 1 = (2) 2 

 (l) 3 4(l) 5 -2(l) 4 cosl=(2) 3 



12 



