108 Sir J. W. Lubbock on some Methods of developing 



15 3 

 B 3 is multiplied by cos 6 — cos 9 = 2 sin — sin 



B A 



B, 



2 2 



cos 8 — cos 1 2 = 2 sin 10 sin 2 



25 . 5 

 cos 10 — cos 15 = 2 sin— sin - 



— ' — 



sin6 — sin 9= —2 cos— sin - 



sin 8 — sin 12=— 2 cos 10 sin 2 



25 . 5 

 sin 10 — sin 15 = — 2 cos — sin-. 



The following Table exhibits the indices of the arguments which 

 are introduced when the difference of the sines and cosines are re- 

 placed by products. 



Table III.— Indices of variable factor. 



Let 



2nd Operation. Elimination of B x and A x 



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

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

 (l)3+(l) 5 -2(l)4Cosl = (2) 3 



