Ooi Practical Geodes^y. 39 



in which Aj, A„, are the angles which the true " geodesic " 

 joining the stations makes with the meridian traces through 

 the stations, &c. 



^p° The theorem expressed by formula 10, maybe ex-, 

 pressed as follows : — 



The plane perpendicular to any chord of a quadric, of 

 revolution through its middle point, bisects the portion of 

 the axis intercepted by the normals drawn through the 

 extremities of the chord ; and the straight line joining the 

 middle of the chord to the point in which the plane cuts the 

 axis is divided by the equatorial plane of the surface into 

 portions whose ratio is the same as those into which it 

 divides either normal terminating in the axis. 

 . From this we at once perceive that — 



The perpendicular bisecting any chord of a conic bisects 

 the portions of the axes intercepted by the normals drawn 

 through the extremities of the chord ; and that the ratio of 

 the portions of the perpendicular measured from the middle 

 point of the chord to its intersections with the axes, is the 

 same as the ratio of the segments of either of the normals 

 measured from the curve to the axes. 



Problem 1. 



Given the latitudes l^, l^^, of two stations S^, S^^ (on the 

 earth's spheroidal surface), and their difference of longitude 

 (0 j to find the azimuths A^, \/, the circular measure 5 and 

 lengiih s of the geodesic arc between the stations ; the angles 

 a , a^^y of depression of the chord, &c. 



First Method. 

 To find the arcs L', U\ and the azimuths A^, A^^, we have — • 



cot -L' = e^' '^' ^'"^ \' 4- (1 — a tan I, 

 R, cos ^, ^ ' 



cot L" = e^ 



cot A, = 

 cot A„ = 



E,, sin I, 



E,,^ cos l„ 



1 



\^ 





J --. 





cotL' 



cos 



I. 



— sin 



h 



cos 



CO 







sin (0 









cot L' 



cos 



i„ 



— sin 



i„ 



cos 



0) 



or having found the arcs U, Ij\ as above indicated, we can 



