THE GENERAL PERTURBATIONS OF THE MINOR PLANETS. 83 
as constant if we designate all magnitudes in these factors dependent on ¢ by a Greek 
Jetter. 
We thus obtain 
( = 1 aa 9 at te A 
eS t) — reais fa + a =) Sr dt — A J (26, DG 2) ali 
we ee tea) thee (16) 
- =| (2S i ee 
dt ke y/ por dt dz ke 1/ Po © dz? 
These equations include terms of the second order with respect to the mass. If 
we put 
vs ae (ere ve pond ce Wee sre jr 
we get 
ngz = net + gy tm | W + +r dev] at 
f (17) 
v= N—43( [9% 4+ 0 be] at 
In equations (17) g is the mean anomaly for £=0; JV is the constant of inte- 
gration in the value of ». 
From the value of JV given above, we have 
IW 1 Pi 2 es ae 
i ae (Lae ‘) Sr — —=(X,.v— Y,.8). 
dt hy/ po VP hy/ po ° 
Now since 
X = cos foe — — gin Joa ~ 
¢ 
) 2 
= oes d 
; ar < if 
df 
12 
a 
dr 
Si 1 dQ 
