D. Trowbridge on the Nebular Hypothesis. 351 
further with our theory, however, it will be advisable to 
enquire into the nature of the constitution of the primitive 
spheroid. For that purpose let us suppose the spheroid already 
separated into rings by the processes of Nature. That being 
done we have the means of arriving, approximately, at the prin- 
cipal radii of gyration of the primitive spheroid at the time the 
several planetary rings were abandoned. To do this we shall 
proceed as follows :— 
The principle of the Conservation of Areas,” teaches us that 
if rotate on an axis, every point of which has the same 
angular velocity, the angular velocity multiplied by the moment 
of inertia with respect to the axis of rotation, will give a product 
that is constant for the same body. Let 
M = the mass of the primitive spheroid ; 
k& = principal radius of gyration ; 
= time of rotation; 
A = a constant; 
m == 314159, &e. 
Then QeMh* ce AT Oe IB 
So long as M remains the same, A will, also; but if M vary, so 
) will A. Hence, as soon as the solar spheroid has thrown off a 
. Ting, the spheroidal mass, M, will be changed, and therefore A 
| willbe no longer the same quantity as before the separation. 
But, according to Dr. Galle, the mass of the sun is 788 times as 
ye as the mass of all the other bodies of the system together.” 
ets; that is, T, its period of revolution, being the same as that 
the ring at the time the fa, Obes abandoned by the solar 
k? oT . 
Cc ees Loti Bee ee ee 
p Mite ae sik 
_ Let the mean distance of the earth from the sun be 1, and the 
_ Mean distance of any other planet be a; then by Kepler’s third 
_ law we have 
’* The reader will find this principle demonstrated in 
treatises on analytic me- 
chanics 7 Cosmos, vol. iv, p. 362. 
