64 Lieut.-Generai Stracliey. On the 



Since A» = p 1 cos nl5° -f 2i sm w'15°, 



A = J?!, and A 6 = q lt 



and putting [A x , A n ~\ for the sum of the series of quantities A t to A w , 

 and [cos 75, cos 15] for the sum of cos 75 + cos 60 + cos 45 + cos 15, it 

 follows that 



[A 1? A 3 ] = Pl [cos 75°, cos 15°] + 3l [sin 15°, sin 75°], 

 [A 7 , A u ] = -^[coslS , cos75°]+^[sin 75°, sin 15°], 



and 



A +[A 1? A 5 ]-[A 7 , A n ] = Pl {l + 2[sinl5°, sin 75°]} = 7-5956^, 

 A 6 + [A 15 A 5 ] + [A 7 , A n ] = ffl {l + 2[sinl5°, sin 75°]} = 7-5956 2l . 

 In like manner, 



Bo+CBx + BJ-^ + BJ =jp 2 {l + 2[sin.30 + sin60]} = 3732p 2 , 

 Bs+^ + BJ + ^ + Bg] = 22 {l + 2[sin30 + sin60]} = 3732 2s , 

 Co+Ci-Og == p 3 {l + 2 sin 45°} = 2-4142^3, 

 Ci + C 2 + C 3 = 2s { 1 + 2 sin 45°} = 2-414223, 

 D + D 1 — D 2 =p 4 {l + 2 sin 30} = 2p 4 , 

 D x + D 2 = 2 4 . 2 sin 60 = 17321g 4 . 



Substituting for A, B, 0, D, their values in terms of d, A, d, &c, 

 we have — 



7-5956?! 





7-5956 2l 





3732pj 



= i{2o+[2 1 + 2 2 ]-[2 4 +2 5 ]}, 



3732 28 



= i{2 3 + E2 1 -fS 2 ] + [2 4 + S]}, 



2-4142p 3 



= i{^o+^i-^} = i«, 



2-414223 









1-732124 





And 



