72 A NEW METHOD OF DETERMINING 
CHAPTER TY. 
Derwation of the Equations for Determining the Perturbations of the Mean Anomaly, 
the Radius Vector, and the Latitude, together with Equations for Finding 
the Values of the Arbitrary Constants of Integration. 
HLANSEN’s expressions for the general perturbations are 
dW, 9 
_ dz + ¥* |dt 
Megs = at + Jo + mo f | Wo + 
= ae Ae: 
dt 
dk, — if = dQ 
her’ sin (@ AF 7) C08 
aM ah} 2 (0) G0) Se [cos (f —o) —1] ‘4 
+ 2h, ©. sin (f— 0) r(=). 
In this chapter we will show how these expressions are derived from the equations 
of motion, and from quantities already known. 
The equations for the undisturbed motion of m around the Sun are 
iF 9 Xx 
= PUM) = =0 
“1 +e 1+m)4=0 
<_+#d+m)5=0 
