THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 17 
of m. The former system may be regarded as the particular values’ which these 
elements have at the instant ¢ = 0. 
In Elliptic motion we have 
nt + go= e—esine 
r cos f = acose—ae 
rsin f = acos¢sine - 
Dan 
an? = k’ (1 + m) 
Now let mz be the mean anomaly which by means of the constant elements gives 
the same value for the true longitude that is given by the system of variable elements. 
Further, let the quantities depending on mz be designated by a superposed dash, and 
let the true disturbed value of r be given by the relation r= r (1+ 7). 
We have then ; 
Ne = E€—eQ sine 
r COS f = A COS E — AE 
r sin f = a cos oy sine 
Ve vi + 1 
ayny = kh? (1+ m). 
We will now first give BkRuNNow’s method of finding expressions for the pertur- 
bation of the time, and of the radius vector. 
Neglecting the mass m, multiplying the first of equations (1) by y, the second 
by x, we have 
ye = {( Ya— Xy) d+ © 
C being the constant of integration. 
Introducing 
_ x cS a 
cos f = *, and sin f = = 
