276 
Gt ee 
From the right spherical triangles PBY and PAX we have the following 
fundamental relations: 
, 
tan £ tan ¢ tan 7’ tan 7’ 
(tan £ = Sten, = 
sinBY COS 7 sinAX cos & 
2. Kquation of the Spheric Line LM in Terms of its Intercepts. 
The are of a great circle we will call a spheric straight line. Let the inter- 
cepts be OL = a, OM = 8B, and the angle OLM = 4, Fig. 3. Then from the 
right triangles MOL and PAL we have 
tan tan 7’ tan 7’ 
tan ¢ = ——,, and tan ¢ = = = 
sin @ sinAL sin(a — &) 
Kquating these values of tan ¢,and substituting the value of tan 7’ from (1), 
tan 6 tan 7 cos & tan 7 
sina sinacosé — cosasiné sIna — cosa tan£é 
Expressing each function in terms of tangents and reducing, we find the equa- 
tion of the spherie line in the intercept form: 
tan & tan 7 
(2) — RE I 
tan a tan 
