THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 167 
The constants of integration are now to be so determined as to make the pertur- 
bations zero for the Epoch. The following equations fulfill this condition : 
C+ k,sing— k,cosg + 47% k, sin 2g — $y” kh, cos 2g + ete. + (ndz)y = Yo 
us (ndz), = 0 
k + k,cosg+ ksng-+ 7k, cos2g + 7°) k, sin 2g + ete ai 
ole 
NN — $k, cosg — 3k, sin g — 37 ky, cos 2g — dy k, sin 2g — ete. + (v)o = 
Smale 
+ hk, sin g — 3k, cosg + 7K, sin 2g — x7 ky cos 2g + ete 
d+ %sing + 4 cosg + 7 1, sn 2g 4- 4%, cos 2g + ete. + (a) = 0. 
Ll, cosg — l,sin g + 7” 1, cos 2g — 7° 1, sin 2g + ete. 4 ( = .)) = 0 
To find %, and k, we have 
k, [cos g — e + 7°) cos 2g + 7 cos 3g + ete.] + ky [sin g + 7 sin 2g + ete. | 
— 84, + 6 (r)) + 4-5 (nbz) = 0 
k, [sin g + 27° sin 2g + 37° sin 3g + ete.] — k,[cos g + 27” cos 2g + ete. ] 
d aa 
ar Dae (ro == 
where 
N= —2k—ja4—44%4, 4 = — 82".7162, 
6 
ky being found from 
hey = chy + 3%, — 3 (nd2)) — 6 (0) 
We have also 
1 = — él, 
The symbols (ndz),, (v)o, etc., represent the values of néz, v, etc., at the Epoch. 
