6 
PROFESSOR G. PI. DARWIN ON THE MECHAPIICAL CONDITIONS OF 
If jjL be the attractional constant, the lost energy of condensation is well known to 
be But on the hypothesis that there is no loss of energy at each encounter, 
this must be equal to the sum of the kinetic energies of all the meteorites. If, there¬ 
fore, be the mean square of velocity of a meteorite, we must have ^ MqV^ = 
so that ^ IX MJa. 
But homogeneity of density and uniformity of kinetic energy of agitation are 
impossible ; for the meteor-swarm must be much condensed towards its centre, so that 
we have largely underestimated the lost potential energy of the system. Also, the 
velocity of agitation must decrease towards the outside, or else the swarm would 
extend to infinity. Besides this, the partial conversion of molar into molecular energy, 
which must take place on each encounter, has been neglected. 
We shall see below reason for believing that throughout a large central volume the 
mean square of velocity of agitation is nearly uniform, and that outside of this region 
it falls off. 
Suppose, then, that M is the mass and a the radius of that portion of the swarm 
in which the square of velocity of agitation is uniforiu; letiq® be that square of velocity, 
and let it be defined by reference to the potential of M at distance a, so that 
^ 
O 
3f 
( 1 ) 
where /3 is a coefficient for which a numerical value will be found below. 
The square of velocity of agitation outside of the radius a is to be denoted by 
and srdDsequent investigation will be necessary to evaluate v'^ in terms of rqh 
If we denote by cIq the Earth’s distance from the Sun, and by u^^ the Earth’s 
velocity in its orbit, we have 
Whence, 
Vq = /Buq 
«0 
.(2) 
iM^aj 
.(3) 
If in-any distribution of meteorites w is the sum of the masses of all the meteorites 
in unit volume, or the density of the swarm at any point, and if X be that distance 
which is called in the kinetic theory of gases “ the mean distance between neighbouring 
molecules,” we have 
to 
i-i) 
Now, the mean density of that part of the swarm in which the kinetic enei’gy of 
agitation is constant being p, we have 
P = 
and 
4:7ra'^ 
X3= 4 
77 . 
])i ^ 
m' to 
(5) 
((5) 
