284 



it is changed to 



NEW SERIES for the 



i -f cof 2 a . 2 

 i — cof 2^ 3 



?=■-< 



( 



I I — coftf , I I — cof ^ « . I I 



cof 7 tf 



41+ cof a 4 a 1 + cof ~ a 4 3 1 + cof 7 a 



+ ~ 



1 — - cof i a 



4* 1 -j- c °f 



8 U / 



or, putting - a inflead of a, and - a inftead of - a. and fo on, 

 2 4 2 



in order that the formula may contain only the cofines of the 

 arch and its fub-multiples, and dividing the whole expreflion 

 By 4> 



r 1 1 -f- cof a , 1 

 4 1 — cof a 6 



a 



=H 



( I * — c °f 2 * 1 i_ 1 — cof 7 a , £ 1 — cof fa 

 V 1 + cofi^ r 4^1 + cof^a 4 4 1 + cofi-tf 



r¥h*l 



cof 



TK 



a 



+, &c.) 



4' 1 -f- cof-^a 



and this is the fecond feries which I propofed to inveftigate, 

 reduced to its moft convenient form. 



18. We may determine two limits to the rate of convergen- 

 cy of the feries juft now found, in the fame manner as we have 

 found the limits of that of our firft feries ; and, indeed, the rea- 

 foning employed in the one cafe is immediately applicable to 

 the other. For if the firft feries, which is 



a 



-1— + I tan - a -f - tan - a -f I tan \ a -h, &c. 

 tan« 224488 



be 



