106 A NEW METHOD OF DETERMINING 
Putting 
p=sin?i sin (oc — Q)) , g =sin 7 cos (o — Q)) — sin %, 
we find 
s= qsin(v—Q)) — p cos (v—Q)). 
Instead of s, let us use 
and we have 
n= 7gsn(@—Q,)— £ pars (=): 
Q FE: a ; 
Introducing 7 and calling #& the new function taking the place of u, we have, 
putting © + 7 for v, 2 being the longitude of the perihelion, 
a@E dgp . dp p 
=a 7, 22 (© =F %)—= Qy) = =F @, COS (@ + 7 — Qo). 
d dp : : i s 
To find and = we will employ the method given by Watson in the eighth 
chapter of his Theoretical Astronomy. 
Thus « and (@ being direction cosines we have 
A SO =— B O3 
also 
2 = rsin? sin (v—o). 
But 
T = 7 COS ¥, and ¥ = Tr sin v. 
Hence 
2 = —xsin? sins + y sin? cos o, 
