of Trigonometrical Quantities from one another. 167 



By the second formula, 



Tan (a- A *) = 11-70537923 

 tan x (89 2') =11-77280468 



A log tan. r = -00742545 



sin 2 .* Isi 1 19-9998764 cos x 8-2271335 



A log tan. r 3-8707229 A log tan x 3-8707229 



3.8705993 4-0978564 



sin* x( A log .7') = -0074233 4 sin* a- (A log tana-) = -0037116 



A log tan x = ' -00012635 4-1015680 



tan k x (44 3V) = 9'99267245 



tan \(x x) - 9-99254610 



By either formula, the result is obtained true to eight places o* 

 decimals ; if x were a less angle, the accuracy would be greater ; 

 we may therefore safely employ the formula? with MUTTON'S or 

 SHERWIN'S Tables : with VLACQ'S Trigonometria Artificialis, the 

 tangent of half the angle may be found true to ten decimal 

 places. 



THE short paper which follows this was originally intended 

 to have formed a part of it ; as, however, their objects are differ- 



ent, they are given separate from one another. 



' 



'W O'K 



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 : A :: (fl -K A)- 1, irie : ( 



