58 GEODESIC INVESTIGATIONS. 



For the approximate radii of curvatm'e of arc cl at its extremities. 



p'=-r-. ' , 



R sm- A -\- R COS" A 

 I 



R" X R 



p"=: 



R" sin^ A!' + R cos^ A!' approx. 



For the circular measure of arc d ; the number of seconds contained in the 

 circvilar measure of arc d \ and the length of the chord of the arc. 



2d 



2 = 



P' + P" 



2 X 206264"-80624 



2(^ sin^ 



Flane Triangle. 

 For the angle C which the chord e subtends at the earth's centn 

 (*-/) {s—r") 



Sini C 



A 



r r 

 in which s :=■ h. {r'-\-r"-\-c) 



First Spherical Triangle. 

 For the angles A, i', a' respectively. 



tan i {A + i') = "°^ \ ^/r'l cot i V 

 ' cos 2 (7 + y ) 



tan 1(^-0 = '!"!,^^;"";! cot i V 

 ' sm t (y + ;' ) 



sin i {A + i') 



cot I a' = .' tan \ {y'—v') 



sin \ A — i') 



in which 7' = 90°+ i 2 

 and ^ F= 90°- ^ A' 



