24 - Examination of Kirkwood’s Analogy. + 
For instance, we may compute the distance p; from the cone 
at which any planet must have received its projectile force, in 
order to produce at the same time its double movement of trans- — 
lation and rotation. Now let v= the planet’s preseht angular 
rotatory velocity. The en, K=pmv, will be a-constant quane 
denoting its momentum of rotation. 
If the planet, in a more primitive _ existed i in the form obs: 
a ring revolving round the sun, having its present orbit for that 
of the centre of gravity of the ring, the momentum K of rota- 
ae must, by virtue of pen principle " — of move- 
ent, have existed in so orm in the . It is easy to per- 
send that this crapeanea °K: is precisely ihe amount which must 
be distributed among the particles of the ring, in order to preserve 
to all the condition of dynamical equilibrium, while those of 
each generating surface of the ring were wheeling round with 
the same angular velocity. It is also clear that this mean angu- 
lar velocity must be that of the primary planet in its orbit, and 
accenting the quantities p and v for the case of the ring, we ‘have 
the equations, 
=pmv=p' mv’ 
ee 
7. Fes 
ee 
p=7-D -p 
But on the hypothesis that the law of decrease of density from — 
centre to surface in the primitive shape was the same as at present, 
Let r= the present radius of the planet; 
A= that of the generating figure of the primitive ring; 
Then, ee: 
P r 
x 3 
And, R=;.D*.r 
The value of R from this formula, comes out a very small 
fraction of D for the small planets, and near! y equal to D in the j 
case of Jupiter, Uranus, and Saturn. If any inference can be _ 
drawn from this result, it is unfavorable to the hypothesis that — 
the — law of decrease of density was the same as the ~ 
at If ae planets have really passed from the shape of a revolving — 
ring to their present state, the prevalence of Kirkwood’s analogy 
ows a nice adaptation of parts in every stage of the transition. _ 
ei the primitive quantity of caloric (free and latent) had un- 
rgone a very great change beyond that now indicated in the 
cooling of their crusts; if the primitive quantity of movement of 
