218 Mr. Bowditch’s estimate of the height Sc. 
SOLUTION. 
This figure is to be marked like the first, then on SM (continued 
if necessary) let fall the perpendicular AW. Suppose a plane drawn 
through w, perpendicular to Cw, to cut the line sm in &. Join Cd 
cutting SM in B, and let CA continued cut sm in a. Find in the tri- 
angle PSW, the angles PWS, PSW, WSM (or ASW), and the side 
SW as in the last problem. Then in the right-angled spheric trian- 
gle SAW are given SW and the angle ASW, to find by spherics SA, 
AW, and the angle SWA. The angle Csm, or its supplement, is 
equal to the angle Csa, the angle sCa =arch SA, and the angle Cas= 
180°—Csa—sCa. 
Sine Cas : Sine Csa :: Cs : Ca 
Tene AWB=: mee (1— <<. Cosine AW) 
The affection of the angle AWB may be determined by the fig- 
ure and the data of the problem.* 
Sine MWB = = x Cotang. Cwm x Tang. Cas x Cos. AWB. 
MWA=AWB+ MWB, 
The sign to be made use of is easily discovered by the figure, observ- 
ing that the point B falls between M and S. 
Cotang. mCw (=Cotang. MW) = Cosine MWA x Cotang. AW. 
* This angle may also be found in the following manner. Having in the plane 
triangle aCw, the sides Ca, Cw, and the angle aCw (=arch AW) the angles Caw; 
Cwa, may be found by plane trigonometry, and AWB by this formula 
Tang. AWB = ©°: Cwaxtang. Cas 
Sine Caw 
