1888.] Conditions of a Sivarm of Meteorite*, $c. J3 



But if we consider the subject from a physical point of view, this 

 conclusion appears unobjectionable.* The ejection of molecules with 

 exceptionally high velocities from the surface of a liquid is called 

 evaporation, and the absorption of others is called condensation. The 

 general history of a swarm, as sketched at the beginniDg, may then be 

 put in different words, for we may say that at first a swarm gains by 

 condensation, that condensation and evaporation balance, and finally 

 that evaporation gains the day. 



If the hypothesis of convective equilibrium be pushed to its logical 

 conclusion, we reach a definite limit to the swarm, whereas if collisions 

 be entirely annulled the density goes on decreasing inversely as the 

 square of the distance. The truth must clearly lie between these two 

 hypotheses. It is thus certain that even the small amount of evapora- 

 tion, shown by the formulae derived from the hypothesis of no colli- 

 sion, must be in excess of the truth ; and it may be that there are 

 enough waifs and strays in space ejected from other systems to make 

 good loss. Whether or not the compensation is perfect, a swarm of 

 meteorites would pursue its evolution without being sensibly affected 

 by a slow evaporation. 



Up to this point the meteorites have been considered as of uniform 

 size, bub it will be well to examine the more truthful hypothesis that 

 they are of all sizes, grouped about a mean according to a law of 

 error. 



It appears, from the investigation in the paper, that the larger 

 stones move slower, the smaller ones faster, and the law is that the 

 mean kinetic energy is the same for all sizes. It is proved that the 

 mean path between collisions is shorter in the proportion of 7 to 11, 

 and the mean frequency of collision greater in the proportion of 4 to 3, 

 than if the meteorites were of uniform mass equal to the mean. Hence 

 the numerical results found for meteorites of uniform size are applic- 

 able to non-uniform meteorites of a mean mass about a quarter greater 

 than the uniform mass; for example, the results for uniform meteo- 

 rites of 3J tonnes apply to non-uniform ones of mean mass a little 

 over 4 tonnes. 



The means here spoken of refer to all sizes grouped together, but 

 there is a separate mean free path and mean frequency appropriate to 

 each size. These are investigated in the paper, and their values 

 illustrated in a figure. It appears that collisions become infinitely 

 frequent for the infinitely small ones, because of their infinite velocity, 

 and again infinitely frequent for the infinitely large ones, because of 

 their infinite size. There is a minimum frequency of collision for a 



* [It must be borne in mind that the very high velocities which occur occasionally 

 in a medium with perfectly elastic molecules, must happen with great rarity among.st 

 meteorites. An impact of such violence that it ought to generate a hyperbolic velo- 

 city will probably merely cause fracture. Added November 23, 1388.] 



