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



The rate of loss of kinetic energy through imperfect elasticity is 

 next considered and it appears that the rate, estimated per unit time 

 and volume, must vary directly as the square of the quasi-pressui e, 

 and inversely as the mean velocity of agitation. Since the kinetic 

 energy lost is taken up in volatilising solid matter, it follows that the 

 heat generated must follow the same law. The mean temperature of 

 the gases generated in any part of the swarm depends on a great 

 variety of circumstances, but it seems probable that its variation 

 would be according to some law of the same kind. Thus, if the spec- 

 troscope enables us to form an idea of the temperature in various parts 

 of a nebula, we shall at the same time obtain some idea of the distri- 

 bution of density. 



It has been assumed that the outer portion of the swarm is in con- 

 vective equilibrium, and therefore there is a definite limit beyond 

 which it cannot extend. Now a medium can only be said to be in 

 convective equilibrium when it obeys the laws of gases, and the 

 applicability of those laws depends on the frequency of collisions. 

 But at the boundary of the adiabatic layer the velocity of agitation 

 vanishes, and collisions become infinitely rare. These two proposi- 

 tions are mutually destructive of one another, and it is impossible to 

 push the conception of convective equilibrium to its logical conclusion. 

 There must, in fact, be some degree of rarity of density and of 

 collisions at which the statistical treatment of the medium breaks 

 down. 



I have sought to obtain some representation of the state of things 

 by supposing that collisions never occur beyond a certain distance from 

 the centre of the swarm. 



Then from every point of the surface of the sphere, which limits 

 the region of collisions, a fountain of meteorites is shot out, in all 

 azimuths and at all inclinations to the vertical, and with velocities 

 grouped about a mean according to the law of error. These 

 meteorites ascend to various heights, without collision, and, in falling 

 back 011 to the limiting sphere, cannonade its surface, so as to counter- 

 balance the hydrostatic pressure at the limiting sphere. 



The distribution in space of the meteorites thus shot out is investi- 

 gated in the paper, and it is found that near the limiting sphere the 

 decrease in density is somewhat more rapid than the decrease corre- 

 sponding to convective equilibrium. 



But at more remote distances the decrease is less rapid, and the 

 density ultimately tends to vary inversely as the square of the dis- 

 tance from the centre. 



It is clear that according to this hypothesis the mass of the system 

 is infinite in a mathematical sense ; for the existence of meteorites 

 with nearly parabolic and hyperbolic orbits necessitates an infinite 

 number, if the loss of the system shall be made good by the supply. 



