THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 27 
In the application of the very general formulz care must be taken to note the 
signification of the various terms employed. 
In case of 
3] no 
Ki. . COS [2 (Q.— 9x) — K,,. | 
2 : : si 
A, =" h,..sin [1 (Q—9.) — Kid, 
oe ° O=N0 n s 
n shows the number of divisions of the circumference; and we divide by ; in form- 
ing k,, to save division when forming the coefficients ¢,, S,. 
The index and multiple 7 shows the term in the series 
1p +4 B cos (e’ — Q) +b. cos 2(¢ — Q) + b. cos 3(¢ — @) + ete. 
The double index 7, x shows the term of the series of La Place’s coefficients and 
the particular point in the circumference. 
The index » shows the general term of the series expressing the values of 
(¢) (s) 
ix) When we give to » values from » = 0, to the highest value of » needed in 
in) 
the approximation. 
2 & z . 
In ~.&,., 0(Q. — 9.) — Ki for each value of 7, there are » values of each 
n yk) «9 ? 
quantity. 
© GO CO 2 © 
The next step is to express the n values of PA eAn As As) A>, ete, respec- 
tively in terms of a periodic series. And since these quantities are functions of the 
mean anomaly g, if we designate them generally by Y, of which the special values are 
i Cate a MVS Ma are ee arct NC, 25 > y 
we have 
Y = he, + c cos g + © cos 2g + ete. ) (40) 
+s, sing +s, sin 2g + ete. ) re, 
The values of ¢,, s,, in this series are found from the ~ special values or 3% 
