56 On Practical Geodesy. 



sin V = 9-8965321441 sin I" = 9-9023486165 



sin (0 = 8 -3387529285 sin w = 83387529285 



18-2352850726 18-2411015450 



sin A,, = 9-8447496921 sin A, = 9-8505661645 



.'. sin V = 8-3905353805 .-. sin v = 8-3905353805 



.-. V = 1°,, 24',, 29" • 956648 



To find the portions v,„ v„ into which v is divided by the 

 point 0. 



From the spherical triangles S„OE,„ S,OE,, we have — 

 sin v„ - sin = sin a,,; sin v, * sin = sin a/, 

 and from these — 



sin V,, 



sin a,, 



R, 



sin V, 



sin a, 



^, 



and .-. (see formulae 27, 33, 34) — 



log R, = 7-3212526296 tan J v = 2-0895709833 



log R,, = 7-3212277292 tan (a;— 45°) = 5-4573930282 



.-. tan 03 = 10-0000249004 .-. tan J (i/, — v,) = 7-5469640115 

 .-. X = 45°,, 00',, 05"-91314 .-. J (v„— v,) = 0°„ 00',, 00" -072776 



But i (v„+v,) = 0°„ 42',, 14"-978324 



.-. v„ = 0°„ 42',, 15"-051100 



V, = 0°,, 42',, 14"-905548 



To find the angles 0„ 0,„ which a plane parallel to the 

 two normals makes with the normal chordal planes — 



O, = A, — A, = 0°„ 07',, 22"-50377 

 a„ = A„ — A,, = 0°„ 07',, 22"-o0377 



.*. we have in actual practice (as has been already demon- 

 strated) Q, = 12,, ; and we may write O to represent their 

 common value. 



To find the angles a„ a„, of depression of the chord below 

 the tangent planes at the stations S^, S^^, we have — 



tan a, = tan v, ' cos O tan a,, = tan v„ ' cos O 



tan V, = 8-0895585138 tan v„ = 8-0895834524 



cos a = 9-9999990005 cos O = 9-9999990005 



.-. tana, - 8-0895575143 .-. tana,, = 8-0895824529 



.-. a, = 0°„ 42',, 14"-899714 ' .-. a„ - 0°,, 42',, 15"-045266 



.-. :S = a, + a„ = 1°„ 24',, 29"-94498 



