1888.] Conditions of a Swarm of Meteorites, <$-c. 11 



with meteorites of 3J kilos., the collisions are sufficiently frequent 

 even beyond the orbit of Neptune to allow the kinetic theory to be 

 applicable in the sense explained. But if the meteorites weigh 

 #J tonnes, the criterion ceases to be very small at about distance 24, 

 and if they weigh 3125 tonnes they cease to be very small at about 

 the orbit of Jupiter. It may be concluded then that, as far as 

 frequency of collision is concerned, the hydrodynamical treatment of 

 a swarm of meteorites is justifiable. 



Although the numerical results are necessarily affected by the con- 

 jectural values of the mass and density of the meteorites, yet it was 

 impossible to arrive at any conclusion whatever as to the validity of 

 the theory without numerical values, and such a discussion as the 

 above was therefore necessary. 



I now pass on to consider some results of this view of a swarm 

 of meteorites, and to consider the justifiability of the assumption of 

 an isothermal-adiabatic arrangement of density. 



With regard to the uniformity of distribution of kinetic energy in 

 the isothermal sphere, it is important to ask whether or not sufficient 

 time can have elapsed in the history of the system, to allow of the 

 equalisation by diffusion. 



It is shown therefore in the paper that in the case of the numerical 

 example primitive inequalities of kinetic energy would, in a few 

 thousand years, be sensibly equalised over a distance some ten times 

 as great as our distance from the sun. This result then goes to show 

 that we are justified in assuming an isothermal sphere as the centre 

 of the swarm. As, however, the swarm contracts the rate of diffusion 

 diminishes as the inverse f power of its linear dimensions, whilst the 

 rate of generation of inequalities of distribution of kinetic energy, 

 through the imperfect elasticity of the meteorites, increases. Hence, 

 in a late stage of the swarm, inequalities of kinetic energy would be 

 set up, there would be a tendency to the production of convective 

 currents, and thus the whole swarm would probably settle down to 

 the condition of convective equilibrium throughout. 



It may be conjectured then that the best hypothesis in the early stages 

 of the swarm is the isothermal-adiabatic arrangement, and later an 

 adiabatic sphere. It has not seemed worthwhile to discuss this latter 

 hypothesis in detail at present. 



The same investigation also gives the coefficient of viscosity of the 

 quasi-gas, and shows that it is so great that the meteor-swarm 

 must, if rotating, revolve nearly without relative motion of its parts, 

 other than the motion of agitation. But as the viscosity diminishes 

 when the swarm contracts, this would probably not be true in the 

 later stages of its history, and the central portion would probably 

 rotate more rapidly than the outside. It forms, however, no part of 

 the scope of this paper to consider the rotation of the system. 



