GEODESIC IjSTVESTIGATIOXS. 165 



ProWem 3. 



Given the latitudes I', I", and the azimuth A' ; to find the azimuth A" . 

 the difference of longitude a> of the stations, and all the other entities deter- 

 mined in the preceding problem. 



We can at once find the azimuth A" from either formulae (10), (12), which 



give— 



J,/ ■ ,, H, cos V 

 sm A =: sm A 



*sin- A" =. sin" A' 



? sin- A"z=. sin- A' 



Or we can proceed otherwise. Thus : — 

 Find the arc P-D„ or L,, by means of 



' R„ cos t 





tan^ V' 



' + 



o2 



tan^ V 



+ 





tan- I" 



+ : 



1-00671945 



tan^ I' + 1-00671945 



cot L,, ■=. (1 — e-) tan- I" + e- 



Then from the triangle S, P D„ we have — 



cos I' . sin A' 



R, . sin I' 

 R„ . cos I" 



sin D„ = 



sin jL„ 



cot i ^ = COS ^ {L, + ^.) _ ^^^ i (^. ^ _p ) _ 

 cos i {L„ — I,) 

 And to find A" 



tan 1 (^' + ^'0 = ""' f i^' ~ ^!2 • cot i a, . 

 sm I (?' + i ) 



The other entities can now be found as in Problem 1. 



I^g" When we tnow the latitudes V, I", and azimuths A', A", of two 

 mutually visible stations on the earth from actual observations, we can find 



an approximate value of— from the equation. 



tan- V — tan2 I" f^i^'") "^ 



a^ ^sm A / 



p — / sin A" \ '^__^ 



Vsin A"/ 



Using this value of , we should omit each one of the four measured 



entities V , I" , A' , A" , in tiirn, and compute new values of the same, and 

 the four corresponding values of u by means of problems 2 and 3. 



Then taking the means as the most accurate values of I', I", and w, we 

 should employ them as in problem 1, and find the corresponding values for 

 A , A , 22 , 2:2 



* "When either the sine, cosine or tangent of an angle is equated to a knoivn quantity /, 

 we can express theother elementary fuQctions by means of /; and .•. always find the angle 

 with precision from the tables. — (See Todhunter's Trig., pages 165, 166.) 



M 



