LAWS OF DECREMENT. 391 



Having thus found the plane angles d f e, dfg, 

 which may be regarded as the sides of a spherical 

 triangle, we may from these and the angle / deduce 

 the values of the angles subtended by these sides. 



Let us call the angle subtended by the side dfg, 

 / 6 , and that subtended by dfe, I 7 . 



We have y dfg + V d f e ^ ^ 59"+23 54' 52" 



56 20' 51" 

 v dfg \/dfe3^ a 25' 59" 23 54' 52" 



= 8 31' 7" 



and \ 56 20' 51" = 28 10' 25" 

 \ 8 SI 1 7"= 4 15' 33" 

 \ I, = 52 32' 30". 



Having thus two of the sides and an angle, of a 

 spherical triangle, whose other angles are I 6 and J 7 , 

 we may find | the sum, and | the difference, of the 

 angles J 6 and/ 7 , and thence the value of each, in 

 the following manner. 



1. Tofnd \ their sum. 



T . cot. 52 32' 30" cos.4 15' 33' 

 tang. i(/ 6 +/ 7 ) = ______ 



log. cot. 52 32' 30" = 9-8843264 

 log. cos. 4 15' 32 9-9987989 



19-8831253 x 

 W. cos. 28 10' 25" = 9 9452316 



log. tang. \ (/ 6 +/ 7 = 9-9378937 

 Therefore \ (/ 6 +/ 7 ) = 40 55' 2". 



