14 Prof. G. H. Darwin. On the Mechanical [Nov. 15, 



certain size, a little less in radius than the mean radius, and consider- 

 ably less in mass than the mean mass. 



For infinitely small meteorites the mean free path reaches a finite 

 limit, equal to about four times the grand mean free path ; and for 

 infinitely large ones, the mean free path becomes infinitely short. It 

 must be borne in mind that there are infinitely few of the infinitely 

 large and infinitely small meteorites. Variety of size does not then, 

 so far, materially affect the results. 



Bat a difference arises when we come to consider the different parts 

 of the swarm. The larger meteorites, moving with smaller velocities, 

 form a quasi-gas of less elasticity than do the smaller ones. Hence 

 the larger meteorites are more condensed towards the centre than are 

 the smaller ones, or the large ones have a tendency to fall down, 

 whilst the small ones have a tendency to rise. Accordingly, the 

 various kinds are to some extent sorted according to size. 



An investigation is made in the paper of the mean mass of meteo- 

 rites at various distances from the centre, both inside and outside of 

 the isothermal sphere, and a figure illustrates the law of diminution 

 of mean mass. 



It is also clear that the loss of the system through evaporation must 

 fall more heavily on the small meteorites than on the large ones. 



After the foregoing summary, it will be well to briefly recapitulate the 

 principal physical conclusions which seem to be legitimately deducible 

 from the whole investigation ; in this recapitulation qualifications 

 must necessarily be omitted or stated with great brevity. 



When two meteorites are in collision, they are virtually highly 

 elastic, although ordinary elasticity must bo nearly inoperative. 



A swarm of meteorites is analogous with a gas, and the laws 

 governing gases may be applied to the discussion of its mechanical 

 properties. This is true of the swarm, from which the sun was 

 formed, when it extended beyond the orbit of the planet Neptune. 



When the swarm was very widely dispersed the arrangement of 

 density and of velocity of agitation of the meteorites was that of an 

 isothermal-adiabatic sphere. Later in its history, when the swarm 

 had contracted, it was probably throughout in convective equilibrium. 



The actual mean velocity of the meteorites is determiuable in a 

 swarm of given mass, when expanded to a given extent. 



The total energy of agitation in an isothermal-adiabatic sphere is 

 half the potential energy lost in the concentration from a condition of 

 infinite dispersion. 



The half of the potential energy lost, which does not reappear as 

 kinetic energy of agitation, is expended in volatilising solid matter, 

 and heating the gases produced on the impact of meteorites. The 

 heat so generated is gradually lost by radiation. 



The amount of heat generated per unit time and volume varies as 



