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



adiabatic atmosphere is at a distance equal to 2' 786 times the radius 

 of the isothermal sphere.* 



It is also proved that the total energy, existing in the form of 

 energy of agitation, is exactly one-half of the potential energy lost in 

 the concentration of the matter from a condition of infinite dispersion. 

 This result is brought about by a continual transfer of energy from a 

 molar to a molecular form, for a portion of the kinetic energy of a 

 meteorite is constantly being transferred into the form of thermal 

 energy in the volatilised gases generated on collision. The thermal 

 energy is then lost by radiation. 



It is impossible as yet to sum up all the considerations which go to 

 justify the assumption of the isothermal-adiabatic arrangement, but it 

 is clear that uniformity of kinetic energy must be principally brought 

 about by a process of diffusion. It is therefore interesting to consider 

 what amount of inequality in the kinetic energy would have to be 

 smoothed away. 



The arrangement of density in the isothermal-adiabatic sphere 

 being given, it is easy to compute what the kinetic energy would be 

 at any part of the swarm, if each meteorite fell from infinity to the 

 neighbourhood where we find it, and there retained all the velocity 

 due to such fall. The variation of the square of this velocity gives 

 an indication of the amount of kinetic energy which has to be 

 degraded by conversion into heat and distributed by diffusion, in the 

 attainment of uniformity. This may be called " the theoretical value 

 of the kinetic energy." It appears that in the swarm, this square of 

 velocity rises from zero at the centre of the swarm to a maximum, 

 which is attained nearly half-way through the adiabatic layer, and 

 then diminishes. It is found that the variations of this theoretical 

 value are inconsiderable throughout the greater part of the range. 

 Since this " theoretical value of the kinetic energy " is zero at the 

 centre, there must be diffusion of kinetic energy from without 

 inwards, and considerations of the same kind show that when a 

 planet consolidates there must be a cooling of the middle strata both 

 outwards and inwards. 



We must now consider the nature of the criterion which determines 

 whether the hydrostatic treatment of a meteor-swarm is permissible. 



The hydrodynamical treatment of an ideal plenum of gas leads to 

 the same result as the kinetic theory with regard to any phenomenon 

 involving purely a mass, when that mass is a large multiple of the 

 mass of a molecule ; to any phenomenon involving purely a length, 

 when the cube of that length contains a large number of molecules ; 

 and to any phenomenon involving purely a time, when that time is a 

 large multiple of the mean interval between collisions. Again, any 



* This is one of the results established by M. Ritter in a series of papers in the 

 ' Annalen der Physik und Cliemie ' from 1878 onwards. 



