42 On Practical Geodesy. 



To find fi, % and the angle a , we have — 



tan i 2 = tan J v cos Q, ov % = v ' cos O 

 A = 2 • O • sin J :S, or A = O • :S • sin 1" 



To find the length h of the geodesic chord between the 

 stations — 



7 _ H, sin V sin w _ R,, sin I" sin w 

 sin A,, cos ^ S sin A^ cos J ^ 

 Then to find s, we have — 



= ^ • ^'^ • sin r^ 

 "A • sin J ]S 



And to find the angles a^^, a^, of depression of the chord k 

 below the tangent planes to the earth at the stations S^^, S^, 

 we have — ■ 



tan 2/ = ^ 



(a, - a,) = {y — 45°) • 2 • sin 1" 

 (a, + a,) = X 



Problem 2. 



Given the latitude l^, the azimuth A^, and the length s 

 and circular measure 2 of the geodesic arc between the 

 stations ; to find the latitude l^^, the azimuth A^^, the differ- 

 ence of longitude w, &c. 



First Method. 

 To find the angle <j>„ we have, from the spherical triangle 

 PS^I— 



tanH^. + ^.)=- -|;;;-|^j 'taniA. 



tani(^.-/^.)- :;::ig;;l| -taniA. 



^p" It may be proper to observe that I 2 is used in these 

 formulas instead of the angle a^ of depression of the chord; 

 but as the difference of these will in all actual cases be less 

 than yL of a second, and that the numerators vary as the 

 denominators when i ^ varies in value, and that any varia- 

 tion in J 5 which increases or decreases ^ (</>, + P) will 

 decrease or increase J (<^^ — p) ; .-., as respects the value of 



