190 Theory of a Non-Conservative Gas [CH. vni 



infinitely probable that it will remain on that same stream line throughout 

 its motion. Obviously each stream line in this space represents a family of 

 clusters in the former space. Unfortunately for the simplicity of treatment 

 it is no longer true, as it was in the previous case, that two stream lines 

 cannot intersect. 



The result stated in the last section can now be expressed by the state- 

 ment that when the energy is so small that there is very little dissipation of 

 energy (or, more precisely, when a value of E is reached so small that it is 

 possible for F to remain very small throughout a finite range of values for E}, 

 then the stream lines in the new generalised space tend to combine into 

 a single stream line. And of the gases which have cooled from an unknown 

 higher temperature, all except an infinitesimal fraction, will be represented 

 by points on this stream line. 



The Normal State for a Non-Conservative Gas. 



228. When a gas is represented by a point on the single stream line just 

 found we shall say that the gas is in the normal state. This state is 

 obviously analogous to the normal state previously found for a conservative 

 gas. For as we have just seen, if the conditions for a normal state to be 

 possible are satisfied, it is infinitely probable that a gas selected at random 

 from gases which have cooled from higher temperatures, will be in the 

 normal state, and, in general, gases which are not in the normal state tend 

 towards that state. And the conditions necessary for a normal state to be 

 possible are that it shall be possible for F to remain very small throughout a 

 finite range of E: in other words, that the rate of cooling shall be very slow. 



In nature, this condition is fulfilled in the case of a gas in the ordinary 

 state, which is not radiating energy to a perceptible extent, e.g., in the case 

 of the air of the atmosphere. An investigation of the mechanism by which 

 it comes about that the condition is fulfilled is given in the next chapter. 

 At present we are content with the knowledge that a gas of this kind is in a 

 definite normal state, which is entirely different from the normal state in 

 a conservative gas, in which the energy of each momentoid is the same. 



We conclude this part of the subject by discussing two mechanical 

 illustrations of the theory which has been developed in this chapter. 



I. The example from 206. 



229. In the mechanical illustration suggested in 206, it was pointed 

 out that the mean temperatures in the vessels A and B might be supposed 

 to represent energies of two momentoids, of which the latter was affected by 



