THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 
For 2. cos 0, write x + = and then we have 
[1 + a — 2a cos 6] ° — [1 4 @—a (e+ ye 
= [1—ae|~ [a—“]- 
Expanding we have 
1G So ee ee a a’a? + ete 
online: Ss a ss) Ia? s stl s+2 @ s stl s+2 
[1 al Sea aoa gee ee ae ae 3 
s 19 (aes ! 5 
+* a a ae aie 
Peep eae 
a (2 ae ee Sa eee] (w +‘) 
el ee Ge) ae! 
s stl st2\2s+3 s+4 (¢ Ve =) 
sees Be aa . Be + ete. wr 
s s 1 s+2 03 ei Size 2 Sap 2 S=- 8 6 
ee ge a) Se a 
Ag + ete. | (2° +.) 
| 
i 
5 
But « + ~ = 2cos6, a? + = 2.c0s 20, a + ©, = 2.cos36, etc., 
