of a Spherical Mass of Gas. 4(37 



Hence we see that 



1 

 1 



Now there are two cases to consider. 



Case 1. 07 >. 4. 



Then, ?z being less than unity, 



n < ^ ; 



that is, the whole sphere contracts uniformly in consequence 

 of loss of heat. 



Case 2. 07 -< 4. 



Now 1\ >. r ; 



that is, the sphere expands uniformly in consequence of loss 

 of heat. 



In both cases 



r x 6 x = rO. 



In the first case, therefore, as the gas loses heat the sphere 

 contracts and the temperature rises ; whereas, in the second 

 case, with loss of heat the sphere expands and the temperature 

 falls. 



It is clear that, since a gas for which 7 (the ratio of the 

 specific heats) is less than 1J, loses energy as it expands, it 

 must be supplied with energy from outside in order to con- 

 tract. Also it follows that in any given state of convective 

 equilibrium such a gas has more internal energy than it could 

 have obtained by contraction from a state of infinite diffusion. 

 This conclusion agrees with Perry's theorem as stated by 

 Lord Kelvin on page 368 of ' Nature' for February 14, 1907. 



If, however, the gas has been supplied by some means 

 with the heat necessary for a state of convective equilibrium, 

 the gradual inevitable loss of heat will only drive the particles 

 further and further apart until the outer portions come within 

 the sphere of attraction of some other body, after which 

 this body will gradually suck in the whole of the gas. 



But a gas for which 7 is greater than 14- w T ill condense as 

 it loses heat until a liquid nucleus is formed at its centre. 

 After that stage is reached the results obtained for a wholly 

 gaseous mass will no longer apply. 



2 K 2 



