28 PROFESSOa G. H. DARWIN ON THE MECHANICAL CONDITIONS OF 
In the isothei’mal part it is clearly In the adiabatic part it is half the 
element of mass into the square of velocity of agitation integrated through the layer, 
that is to say, ^. M~, dx X 'o^, and, since z = — , we have 
1 Ml) 2 
for the total internal kinetic energy of agitation. This is rigorously onedialf of the 
energy lost in concentration. 
Hence, if a meteor swarm concentrates into this arrangement of density, one half of 
the original energy is occupied in vaporising and heating parts of the meteorites on 
imjDact, and the other half is retained as kinetic energy of agitation. 
I find by quadrature that —^dx= '64:3. Hence, the potential energy lost in 
J -359 * 
concentration is (1‘643), and that part of it which is retained as energy of 
agitation is \Mvq {\'643). The whole mass of the system is 2T767 M, and we may, 
therefore, write these 
■7548 (2-1767 M) V and \ X '7548 (2-1767 M) 
It is clear then tliat the average mean square of velocity of agitation of the tvhole 
system is -7548 Vq.'‘' Or, shortly, the average temperature is very nearly f of the 
temperature of the isothermal nucleus. 
It follows from this whole investigation that for any given mass of matter, arranged 
in an isothermal-adiabatic sphere of given dimensions, the actual velocities of agitation 
are determinable throughout. 
§ 8. On the “ Sj^here of Action.” 
When two meteorites pass near to one another, each will be deflected from its 
straight path by the atti'action of the other. The question arises as to whether the 
amount of such deflection can be so great that the passage of two meteorites near to 
one another ought to be estimated as an encounter in the kinetic theory. 
We shall now, therefore, find the deflection of two meteorites, moving with the 
mean relative velocity, when they pass so close as just to graze one another. 
The mean square of relative velocity in the isothermal portion is 2 v^q, and this may 
be taken as the square of the velocity at infinity in the relative hyperbola described 
The angle between the asymptotes of the hyperbola is the deflection due to this sort 
of encounter. 
Let a, e be the semi-axis and eccentricity of the hyperbola. Then, if e be large, the 
* M. Ritter gives '741 in place of '755, but, as already remarked, be uses a different value for the 
ratio of tlie specific beats. 
