THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 89 
or 
kh an cos % 
ly COO Cie, 
If we put 
he 
Y cos @,’ 
we have 
h re an 
~ ¢os g 
These values of h and h, being substituted in the expressions for WW, - is found 
expressed in terms of the elements and of », in a very simple form. To find the rela- 
: dz 0 
tion between a and v, we use the equation 
2. B ° 
(1 + v) —— A*(1-+0)! Z 
e e h 
and as this is also equal to eee 
“dt 
we find 
ie tk 1 
dt sh (A+)? 
(22) 
For the purpose of keeping the formulz simple and compact, HANSEN makes use 
of the device of designating the time, and the functions of the time other than the 
elements, by different letters. 
Thus for é, r, «, f, 2, v, & Y, we write, 
T, 0, Ny @, 6, B, & v, respectively. 
Whenever we integrate, these new symbols are to be treated as constants, noting 
that the original symbols are used after integration. 
Ao TE: SATO, SAD, Th. 
