THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 125 
To find the value of C, . we put 
(1 + a— 2a cos (Z’ — Q))~ ve +, “cos( B—Q)+ cos 2( #—Q)-+ ete. | 
) 
2 
(1+ 6 — 26 cos (H’ + Q)? =[t2. nes cos (4 + + Q+ By cos 2 (#’ + Q) 
ls oO 
Hm 
“bE ete. | 
For finding the values of the coéfficients in these expressions we use RUNKLE’S 
Tables for Determining the Values of the Coefficients in the Perturbative Function of 
Planetary Motion, published by the Smithsonian Institution. With the sixteen values 
of a as arguments we enter these tables and find at once the corresponding values of 
q@) (2) (3) 
(0) by br by Ge - (O) GP .Gb) Gea «@)) ae 
b 1 , then those of A OOD etc., ete. 5 Ae bs > bs ae bs , ete., ete., where 6" is found 
a* 
from the sixteen values of 0? = eaae 
Since 6 in (1 — 26 cos (’ + @)) is very small it will suflice to put 
| 
Ou 
a 
Nilo 
Then from 
iz) 
I| 
n (i) 
zN B,,cos271Q 
z 
ro) 
n (i) 
NM Be sina 
2 
5 a 
we have, in case of u (), 
(1) 
= il ee SS Va )- 
La, iN, nO = — qe NV bcos2 Q, 3 o4% = cd bsin2Q; 
