96 A NEW METHOD OF DETERMINING. 
we have 
d 
Wy — f 2h’ rr dQ 
Te = hy {2 cos (f—0) —1 + , [eos (Fa) —1]} (#2) 
(30) 
+ 2h sin (f— 0) » (47) 
: P dW. See : 
This expression for 7, is the one used by Hansen in his Awseinandersetzung. 
It is given in a much simpler form in his posthumous memoir, and as the latter is the 
form in which we will employ it, we will now give the process employed by HansEn 
to effect the transformation. 
Substituting first the value of h, omitting the dash placed over certain quantities, 
noting that in the posthumous memoir ¢ takes the place of o, and remembering that 
we are here concerned only with terms of the first order with respect to the mass, we 
have 
Ss | 22 cos Go) 1+ a [cos (f —o)—1] ew 
VA 1—é? 
an Po 7k e dQ 
te ass oa (f o) (4) 
From the relation 
p = al —e’)—ep cosa 
we have 
Pp von ep COS w 
a(1—e*) a(1—e*) © 
. : dw 5 : — 
An inspection of the value of “q_ Shows that its expression consists of three 
parts, one independent of 7, the other two multiplied by p cos o, and p sin a, re- 
spectively. 
