100 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
tion referred to the ecliptic, « the obliquity of the equator, and w 
the distance from the ecliptic to the equator coynted on the orbit, 
we have the following equations for finding J, N, and w. These 
equations come from the triangle between the equator, the ecliptic, 
and the orbit of the satellite. They are similar to those given in 
the Theoria Mot., Art. 55, 
in Beh w— N nm , &+s 
sin cos = ¢c0s > Sin 
2 2 2 
A _ w—N pe ij 4 
sin 4 J sin 5} = sin > sin —> 
w+ N n e+iz 
cos 2 J cos ——g— = cos 7 C08 —G 
‘ _ wt Nv BF gee) ag 
cos + J sin —9 = sy OG 
For the inverse problem of finding 7, NV, and w from J, N, and 
e, we have from the same triangle 
: n-— w N fife 3 
cos ¢ 2 COs 5) = C08 F COS —Z 
eee Se) , No. Paes 
cos #2 sin 5} = siN 5 C08 —p 
‘ ; n w NN’, J—e 
sin + 2% cos —7 = cos 5 sin —F5 
; sud» Mb erate etal ky era 
sin $7 sin 5} = sin 5 sin 5) 
POSITION OF A SATELLITE. 
