40 
MR. LUBBOCK’S RESEARCHES 
“ Erit angulus GPg (seu inclinationis horarise variatio) ad angulum 
33" 16'" 3"" ut IT X AZ X TG X ad AT cub.” Prop. XXXIV. 
The stability of the system requires that the quantities c and g, which are 
determined by quadratic equations, should be rational. This is the case in 
the Theory of the Moon. 
In the Planetary Theory, by well known theorems, 
d£=(l _Vl- e -)d^+ — (dVjdi 
d to = — an 
dv 
a n 
y sin i \/ 1 — e 9 
Neglecting the terms which are periodical, 
d e 
— d to- 
_ m i 
/ hr,— 
5 a* b 1 
f=* — 
* 7 
m ; a 3 
d t 
P 
1 a* 3 ’° 
4 a* 3>1 J 
4 
y, a* 
d £ 
— d v 
_ m , J 
_ 3 
a ' b ”1 — 
m, a 3 
d t 
P 1 
*a» J ’° 4 
a* 3ll J 
4 ju, a/ 
which evidently coincides with the result given p. 38. 
Considering the parallactic inequality, 
(1 — m)-r l01 
^101 = ^ 
2 ri01 “ 8(1 
_ 3m 1 a^r_2_ 1 _ 
8 pa* 1(1 - m) + 6 ) ~ 
3 m l a 4 1 1 
— m) p/J (1 — m ) 
191. 200 m, a 4 
77 .37 
'‘'•101 
3.5 m t a 4 1 40 
+ ~W uTa} J 37 
which equations give r 101 = — -07521 — ; and if the parallactic inequality = i22"-38 
according to Burg, and a = ^=j or a * = that is, if the moon’s hori- 
zontal parallax = 57', the sun’s parallax, according to the preceding equa- 
tions, is 12"7 ; which however differs widely from the accurate value 8" - 54. 
When the square of the disturbing force is neglected, the variable part of 
the angle t -j- z may be considered the same as that of the angle x, and there- 
3a 
+ 
3.3.5 a 3 
2. 4 
+ &C. 
