PARTICULARLY APPLICABLE TO SOME GEODETICAL PROBLEMS 139 



Find x, y, and s, from these equations 



a? -\- xy ^-y- = &, 



X^ +XZ +z' =i\ 



i/ + yx + s^ =«l 

 Here a, h, c are given numbers. 



These equations become identical with the equations of Art. 10. 

 or 18, if we suppose the angles «, /3, 7 to be all equal, and each 120", 

 because then 2 cos a= - 1. Therefore A, B, C being the angles of a tri- 

 angle whose sides are a, b, c, and 



A' = 120"- J, B' = 120''-B, C' = 120°-c. 



In this case Formula v. becomes 



b 



[a b c] 



sin 60' = -be sin A'. 

 a 



Here a' may be any number, provided we take 



,, sin B' , 



= —. 77 a. 



sm 



C 



sin A 



sin A' 

 As a numerical example, let 



ar^ + .ry + y^ = 193 = c^, 

 x-'-\-xz+%-=2\9 = b\ 

 y' + yz+z' =271 =a\ 



In this case «= 1646208 

 A =14-79865 

 c = 13-89244 

 And by the formula, Art. 32. 



^ = 69°. 56'. 12", A' = 5(f. 3'. 18" 



.6 = 57.36.46, i?' = 62.23.14 



C = 52.26.32, C'=67.33.28 



s2 



rrti. 



Logarithms. 



1-2164846, 

 1-1702226, 

 1-1427786. 



9-8846034, 

 9-9474829, 

 9-9657965. 



