312 



NEW SERIES for the 



Inftead of S, we now fubftitute in this expreffion s, - j, - s, -- s, 



248 



&c. fuccefiively, and multiply the remits by the terms of the 



feries 1,* -, -g, — p &c. fo as to form the following feries of 

 4 4 4 



equations, the number of which is n. 



1 



tan s 



1 

 2 2 tan 2 i- s 



1 

 4 2 tan 2 ^j 



a ',, +- 1 tan 2 i ^ + £ 

 2 2 tan 7/ 4 22 



,. T a , + - a tan 2 1 s -f — 

 4 tan £ j 4* 4 ^ 2.4 



77* r-7— + — tan 2 — j -4- — 



8 2 tan 2 i* 43 8 ^ 2.4" 



8' tan 2 i s ~ i6 2 tan 2 T V J + 4 ^ tan2 l6" f + £#> 

 &c. 



From thefe, by proceeding in all refpedts as in the article 

 above quoted, that is, by adding, and rejecting what is common 

 to each fide of the fum, we get 



1 __ 



i S 



,2« tan — 



' 2 n 



tan ~ s 



<! +^tan 2 ^ + -itan 2 ls+ i, tan* * .r . . . -f .1 tan 2 1 j 

 4 2 4* 4 4^ 8 4a 



2 n 



1* ~* ~r* 1" 2 • • • » ~f— . 



2 2.4 2.4 2.4"— 1 



Now, 



