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 s = ( l - V1 — e°-) d ns + 
2 a°-n 
d v 
. (i*) a < 
p. sin (v 1 — e- \ Q < / 
Neglecting - the terms which are periodical. 
d s — d ns _ 7n j f a 3 , 5 a 2 
d t p 1 a ( 3 ' ,0 4 a~ 
d s — d v _ in, f a 3 ^ _ 3 a- ^ 
d t p la/ 3,0 4 af 3,1 
b 
3,1 
} 
} 
m, a 3 
4 p. a 3 
* 7 vi, a 5 
4 p, a 3 
which evidently coincides with the result given p. 38. 
Considering the parallactic inequality, 
(1 _ 7n) -r 101 — r 101 
3771, a 4 f 2 
8 p-a, 4 L (1 — m) 
7-101 — 
3 m, a 4 1 1 
8(1 —m) j u-a 4 J (1 — m) 
191 . 200 777, a 4 
77.37 pa, 4 
A 
ioi — 
+ 
3.5 77i, a 4 1 40 
37 u.a 4 j37 
which equations give r l0l = — -07521 — ; and if the parallactic inequality = l22"-38 
according to Burg, and a = ~ or a i = that is, if the moon’s hori¬ 
zontal parallax = 5/', 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 -f- z may be considered the same as that of the angle x, and there- 
3 . 3.5 
2.4 
•6 ) ,° = 2{ l +(i)\7’ + * C -} 
7 3a. 
6 j,i — — + 
°/ 
