60 GEODESIC IXYESTIGATIOXS. 



For testing the correctness of the calculations we have — 



a' + a" + C = 180° 



1^^ They are angles of one plane triangle, but obtained from two spherical 

 triangles and one plane triangle. 



Example. 



Given :— « = 20992639 ; h = 20852899 ; d = 316800 ; 

 I' = 48° 50' 48"-590 ; A' =. 46° 15' S6"-y70 



To find : — 2 , c , C , A, , A„ , A'" , w , i , i" , A 

 a' , A." , I" , v' , v" 



We find :— log a = 7-3206164 ; log 5 — 7-3191664 

 log a2= 14-6412329 ; log J^ = 14-6383328 



log £2 = 3-82317107 



To arire at approximate values of I" , ai , and A" we have — 



ili" =: 1 + e'^ cos^ r (!) 



log e'2 = 3 • 823117107 



log cos= r = 1 • 63654980 .-. e- cos^ I' = 0-002882178 



3 • 45972087 l + e- cos- I' = 1002882178 = M 



.-. log ilf = 0-0012499 



k =. log sin 1" = 6-6855749 (2) 



a 

 i?, = K (3) 



I 1 — e- sin- /' I 



log e2 = 3-8231710 



log sin2 /' = 1-7535358 .'. e- sin^ I' = 0-0037732 



3-5767068 1— e^ sin^ I' = 0-9962268 



log« =7-3206164 

 i _ 



log (1 — e- sin'^ 1') = 1-9991791 .-. log E] - 7-3214373 



.-. log K, =. 7 3214373 



