352 D. Trowbridge on the Nebular Hypothesis. 
3 
eet ate FP ee ea a eee 
This value of T in (2) gives 
sr Ge OF 
lo 
18. To find the value of &,, we may consider the ratio of the 
radius of gyration of the sun to his radius the same as the 
ratio of the similar quantities in the earth, without material 
error. If we take, for the present, a for the equatorial radius of 
the earth, and « for the ellipticity of the surface; then if the 
earth be homogeneous, the moment of inertia with respect to 
the axis of rotation will be 
8 
rind bei be —é), 
in which ¢ is the density; and if the earth be heterogeneous, the 
moment of inertia will be 
Mirae fy Ba fa'h(t a \]da's 5 ae 
0 
in which ¢’, a’ and «’ apply to any stratum below the surface. 
Since the earth is a solid of equilibrium, we easily find the value 
of the integral of the second member of (5), by the methods 
oii in works on the Figure of the Earth.” In that way we 
n 
ise yee ee. 
The time of rotation of the sun is approximately 25434, and 
his radius, 441,000 miles. The time of revolution of the earth 
around the sun is 3654256. With these numbers and the co- 
efficient of a? in (6), we easily find the logarithm of the coéfli- 
cient of a* in (4) to be 8:000845, 10 being added to render the 
index positive. By enclosing the logarithm in brackets, (4) 
becomes 
| k=[s000ss5]a®# . .... - (7). 
By means of (7) we can easily compute the value of & for each 
of the planets, 
19, Let a, represent the mean distance of Mercury from the 
sun, a, that of Venus, and so on to a, for Neptune, a, being 
the mean distance of all the asteroids; then we have 
 _ ® See Pratt’s Figure of the Earth, pp. 72-74. It would have been sufficient 
for our purpose to consider the sun ‘oe alia but for the fact that I afterwards 
of density in the solar spheroid. 
