1888.] Conditions of a Swarm of Meteorites, #c. 7 



a condition of wide dispersion, and form a swarm in which collisions 

 are frequent. 



For the sake of simplicity, the bodies are treated as spherical, and 

 in the first instance as being of uniform size. 



Tt is assumed provisionally that the kinetic theory of gases may be 

 applied for the determination of the distribution of the meteorites in 

 space. No account being taken of the rotation of the system, the 

 meteorites will be arranged in concentric spherical layers of equal 

 density of distribution, and the quasi-gas, whose molecules are 

 meteorites, being compressible, the density will be greater towards 

 the centre of the swarm. The elasticity of a gas depends on the 

 kinetic energy of agitation of its molecules, and therefore in order to 

 determine the law of density in the swarm we must know the dis- 

 tribution of kinetic energy of agitation. 



It is assumed that when the system comes under our notice, 

 uniformity of distribution of energy has been attained throughout 

 a central sphere, which is surrounded by a layer of meteorites with 

 that distribution of kinetic energy which, in a gas, corresponds to 

 convective equilibrium, and with continuity of density and velocity of 

 agitation at the sphere of separation. Since in a gas in convective 

 equilibrium the law connecting pressure and density is that which 

 holds when the gas is contained in a vessel impermeable to heat, such 

 an arrangement of gas has been called by M. Bitter* an isothermal- 

 adiabatic sphere, and the same term is adopted here as applicable to a 

 swarm of meteorites. The justifiability of these assumptions will be 

 considered later. 



The first problem which presents itself then is the equilibrium of 

 an isothermal sphere of gas under its own gravitation. The law of 

 density is determined in the paper, 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 iso- 

 thermal 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 | 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 or 

 atmosphere in convective equilibrium. The law of density in the 

 adiabatic layer is determined in the paper, 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 

 * ' Annalen der Physik und Cheraie,' vol. 16 (1882;, p. 166. 



