THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 93 
We then have 
GUY GN WwW, 1 dW, . 
dg a 3 dz: 206 SP Sa ie 06 + ete. 
Retaining only terms of the second order, the equations (25) and (26), replacing 6¢ 
by dz, give 
MZ = MtE+ 9+ to f [Wot . de + | dt 
yaaa f(s 2M sda 
The equation (26) has been put in simpler form by Hix. For this purpose from (21) 
and (22) we have 
(29) 
Mt) ere=$—a4m 
Hence 
Developing the second member and adding JW, we have 
M2 = Mt + Go + NH f Se dt. (30) 
The next step is to express sale and = in terms of the disturbing force. From (19) 
we find 
i) 
TY 
| 
~~ e082, C08 (% = 7%) — COS", 
4 = ——.sin (y— m). 
