On Practiced Geodesy. 51 



cos A = Q R. (R. - R.) 



" M, (R, + R.) (R, - R.) 



.*. cos A, = cos A,, = --^ = tan A 2 ■ tan ^,. 



To find the chord k and the angle which it makes with 

 the polar axis, we have — 



7 _ 2 5 • sin J 2 



COS 6 = - — - — • (R, sin I, — R;, sin I,) 



k 



To find the sides of the plane triangle p^ C^ p^^, we have — 



Co p, = R, COS I,; C p,, = R,, cos I,/, 'p;p„ = ^ • sin ^. 



And knowing the three sides of this plane triangle, we can 

 find its angles <^,, <^,^, w. 



Then from the spherical triangles S^PI, S^^PI, we have the 

 following formulae from which to obtain the azimuths — 



We can also find the sides IS^, IS,,, of these spherical tri- 

 angles ; and then we have — 



A =^, — >\>, 



a, = 90° — IS,; a„ = IS, — 90°. 



And as a test of accuracy of the work we have a, + a,, = X 



Example (Problem 1). 



Let l^ = 38°; I, = 37°; « = 1°, 15^, 00"; be the given 

 latitudes and diflference of longitude of the stations. 



First then, to find the values of the normals R^, R,^, drawn 



