74 A NEW METHOD OF DETERMINING 
and hence 
In the same way we derive the partial differential coefficients with respect to 
y and 2. 
The equations (1) then become 
d2 
dx 
“2 4 eA+m)2 =P +m) 
“4A +m)4 =e (1+ m) | (2) 
= + (1 +m), =k (1+m) = 
a 
Let X, Y, Z, be the disturbing forces represented by the second members of 
equations (2), 
R, the disturbing force in the direction of the disturbed radius-vector, 
S, the disturbing force, in the plane of the orbit, perpendicular to the disturbed 
radius-vector, and positive in the direction of the motion. 
If f be the angle between the line of apsides and the radius-vector, the angle be- 
tween this line and the direction of S will be 90° -+ f. We then have 
Ka—Ssnj, v= S cos j- 
In case of 2, we have 
R= xX ee, 
and for S, 
From these we find 
