A SWARM OF METEORITES, AND ON THEORIES OF COSMOGONY. 
G1 
sphere of gas under its own gravitation. The law of density is determined in § 4 ; 
but it will here suffice to remark that, if a given mass be enclosed in an envelope of 
given radius, there is a minimum temperature (or energy of agitation) at which 
isothermal equilibrium is possible. The minimum energy of agitation is found 
to be such that the mean square of velocity of the meteorites is almost exactly f 
(viz. 1T917) of the square of the velocity of a satellite grazing the surface of the 
sphere in a circular orbit. 
As indicated above, it is supposed that in the meteor-swarm the rigid envelope 
bounding the isothermal sphere is replaced by a layer of meteorites in convective 
equilibrium. The law of density in the adiabatic layer is determined in § .G, and it 
appears that, when the isothermal sphere has minimum temperature, the mass of the 
adiabatic atmosphere is a minimum relatively to that of the isothermal sphere. 
Numerical calculation shows, in fact, that the isothermal sphere cannot amount in 
mass to more than 46 per cent, of the mass of the whole isothermal-adiabatic sphere, 
and that the limit of the adiabatic atmosphere is at a distance equal to 2’786 times 
the radius of the isothermal sphere.A table of various cpiantities in such a system, 
at various distances from the centre, is given in Table III., § 6. 
It is next proved, in § 7, that the total energy, existing in the form of energy of 
agitation in an isothermal-adiabatic sphere, is exactly one-half of the potential energy 
lost in the concentration of the matter from a condition of infinite dispersion. This 
result is brought about by a continual transfer of energy from a molar to a molecular 
form, for a portion of the kinetic energy of a meteorite is constantly being transferred 
into the form of thermal energy in the volatilised gases generated on collision. The 
thermal energy is then lost by radiation. 
It is impossible as yet to sum up all the considerations which go to justify the 
assumption of the isothermal-adiabatic arrangement; but it is clear that uniformity 
of kinetic energy of agitation in the isothermal S 2 :)here must be j^rincipally brought 
about by a process of difiusion. It is, therefore, interesting to consider what amount 
of inequality in the kinetic energy would have to be smoothed away. 
The arrangement of density in the isothermal-adiabatic sphere being given, it is 
easy to compute what the kinetic energy would be at any part of the swarm, if each 
meteorite fell from infinity to the neighbourhood where we find it, and there retained 
all the velocity due to such fall. The variation of the square of this velocity gives an 
indication of the amount of inequality of kinetic energy which has to be degraded by 
conversion into heat and redistributed by diffusion in the attainment of uniformity. 
This may be called “ the theoretical value of the kinetic energy ; it is tabulated in 
Table III., on the line called “square of velocity of satellite.” It rises from zero at 
the centre of the sphere to a maximum, which is attained nearly half way through 
the adiabatic layer, and then falls again. If the radius of the isothermal sj^here be 
unity, then from to 2 the variations of this theoretical value of the kinetic energy 
* These results had been previously discovered by M. Rittek. 
