THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 69 
Putting 
— = . cos @ sin J cos II, = a sin J sin, 
© @ 0) (2) 
a= oh a oy) a, Se Oh 
(1) (8) (0) (2 
ye eos | Beer Bs cer 
ete. GUC, 
we have 
(Ly = — 3 be. po 
+ l. 9.6, sing +- L,. Po. 71 COSY 
+1.p,.d.smn( g— g') 4 h.pieyicos( g— yg’) 
—l.,.6,.sin(—g— 9’) +1.—:% cos(—g— g’) 
— 2lep, cos ( — g') (4) 
+l.p..6, sn( g—29') +h.—.y, cos( g—2g9’) 
—l.p,.6, sin(—g—29') + 1.2.7, cos (—g— 29’) 
— 2he.p. cos ( — 29’) 
+ ete. + ete. 
For (7 )” we have the expression 
Ci) Econ te( Se 
Putting 
pope = cos J, and using the p; coefficients as for (Z)’, 
we have 
(Dy = © 4 1. pcos (—g’) + hy. pr c0s(—29') + ete. (5) 
To obtain an expression for the factor [G)— = a | it is only necessary to 
a 
have that for (Ne 
