38 
MR. LUBBOCK’S RESEARCHES 
f . m. a* , ] 
cn = n< 1 — — : — b, , > 
l 4 pa* 3>1 J 
= n {' -47 7 } nearl y- 
This coincides with the first term of the expression, Math. Tracts, p. 59. 
f , 2 m, a’ 1 
a = a < 1 — i- — > 
l 3p a?) 
j m, 
1 + r 0 _ 
3 p a 
-fil 
2 a, 3 
14 - El°± 
6 p a , 3 
The equation for determining- z gives 
+ £1 + (*F\ = 0 
d P r 3 ^ \ dz J 
If s = 7 sin (g n t + e — v) 
-g*+l+ 3 r 0 + ^-b 3iO = 0 
2 p a, 3 
ni. fa 3 , a* , 1 
r °“7T 12 0,8 is>0 2V 
g* =1 + ^(l£i 30 _l5! * 31 + J!L4 30 \ = o 
S /u, 1 2 a, 3 3,0 2 a, 2 3,1 2a, 3 3,0 / 
g = 1 + 
{ fi! 63 - A fi! b . 3 , ) 
la, 3 3,0 4 a/ 2 3,1 J 
73 = n {1 — 2r 0 } 
gw = n4 1 + 
V- 
= n ( 1 + p f! & 3 , ) 
= n ji + Vh. | nearly. 
This also coincides with the first term of the expression. Math. Tracts, p. 59; 
and it appears that when the square of the disturbing force is neglected, the 
mean motion of the perihelium of a planet is retrograde and equal to the mean 
motion of its node taken with a contrary sign. 
The equations 
dv + 
r' 1 sin (A' — v ) 
h* tan i 
