30 ; On Kirkwood’s Analogy: ' 
Here all the quantities on one side are known, and we'use the 
mass of the new planet thus obtained for the solution of the 
problem. This being substituted in either of ane fae 238 equa- 
tions, will give us the mean regs of the plan s 
Or, if for convenience we make BY gn = = 
—A-+( a +B) C 
14+C 
w the only question is as to the value to be sopted 1 for Mr. 
Walker’ s constant, which it seems to me should be deduced from 
observation only. 
n computing the value of k, I obtain for 
we shall have— a= 
Venus, . 19374 
Earth, 9) ia er 
arama, . ws a se oe ee 
The mean of this, . . . “1.939 
is the quantity assumed for 4, in Shain tie results of which I 
shall speak ; these three planets being the only ones to which the 
- formula can be applied. It will be seen that the values obtained 
are most con temhaeag'e of Mr. Walker’s results. Unless we suppose 
the nebular matter to have been equally distributed through the 
solar system, we could not expect to find & absolutely constant, ‘ 
even if it were an approximation to the number 2. 
alker here remarked that the constant used by Dr. 
Gould answered better than the constant 2. 
Dr. Gould continued,—We do not know the extent of Mercury’s | 
influence inside its orbit, and hence cannot know the diameter of — 
its sphere of attraction. Nor can we apply the formula to Mars or | 
to Jupiter, for we do not know what planet may have been be- — 
tween them. We cannot apply it to Uranus, for we do not know — 
its period of rotation. ‘There remain but the three planets men- — 
tioned above 
iy Calculating, from the equations thus developed, the m 
distance which: would belong to a planet between Mars and Jupi- > 
ter, and thence, by Kirkwood’s analogy, the corresponding time 
; of rotation, we do not find it so great, that, by mere centrifugal 
Pe force, the planet could _ been exploded, and its mass scattered 
in the form of asteroi 
From a very rough sciiouastite of the place and size of the 
ypothetical planet, I obtain a mean distance 3. 12, a 
z'saz- _ This mass is very much smaller than the mass of our — 
h, and would agree with the supposition of a small planet, 
smaller even than Venus, but would be at least equal in size t0 — 
twelve or fifteen Asteroids. 
a a aa aol lil Ree ni an in fig rh sae ee MPPs a Akg 
eee ee 
