THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 125 
(c) (s) 
Again, since A;,, A;, are given in the forms 
(c) (s) 
A,, = >C,,cosvg + >C,,sinvg 
(c) Om 
A, = 2S,,cosyg + >S,,sin vg, 
(c) _ (8) (ce) 
we have the following equations to find the values of the coefficients C,,, C,,, Si, 
(s) 
i,ve 
(O38 )= 4% Xs (2) = Yo— ¥, 
dona 7.8% (i) Sie 
GIO) =e Ke Aj = B=, 
(AUS) Ss Ee G)=V%— Vs 
(0.4) = (0.8 ) + (4.12) 
(1.5) = (19 ) + (5.13) 
(2.6) = (2.10) + (6.14) (0.2) = (04) + (26) 
(3.7) = (3.11) + (7.15) (1.3) = (1.5) + (3.7) 
4 (Gy + 2e,) = (0.2) 
A(G—2o) = Gs) 
AGE @) = ©@8)=Ge) 
4(e— o) = §[ (1.9) — (5.13) | — (0) —@aB)]/ cos 45° 
4(s + 8) = $[ (1.9) —(5.13) | + [ (8.11) — (7.15) |{ cos 45° 
(Ge) — (210) (G14) 
8c, = (0.4) — (2.6) 
8s, = (1.5) — (3.7) 
