+ 
i. On Kirkwood’s Analogy. 29 
Apis Waka act S : , 
upon the. one side, as is the case with the earth, may be a planet 
comparatively near, and upon the other a smaller planet at a 
_ greater distance; whence it is evident that the extent of the 
sphere of attraction will be much less upon the former side than 
~ upon the latier. 
In Mr. Walker’s theory he assumes «, in the equation 
2 
Qn § 
O=— ‘Wen to be a constant and equal to a+ asETsTaTE the term 
n ; (k) 
«ke being nearly 2. In the following formulas [I shall denote the 
3 quantities which refer to the Earth by a single accent, those re- 
ferring to Mars by two, to Jupiter by four, and to Saturn by five, 
reserving three accents for the hypothetical planet between Mars 
and Jupiter. I make use of Mr. Walker’s formula for the sphere 
: _ of attraction as follows:—D being the diameter of the sphere, a 
— being the mean distance of the planet, and m being its mass. 
| For Jupiter we have 
Dv= Jf/miv ( * 
So for Mars ; 
aiv—q/’ aY— aiv 
mitt ml * Smet Jem 
if convenience, 
Din | 
avy — aiv 
¥ mv + f/m 
De — (Fearn) VB 
and then we have, : 
i Nie an"! ; 3 
—— aga see kaart ~A, . # 
wee es aiv—a’’—(A+B) i 
Sm” = 
eee? 
B 
vans tani! 
