CHAPTER VIII. 



THE THEORY OF A NON^CONSERVATIVE GAS. 



GENERAL DYNAMICS OF NON-CONSERVATIVE SYSTEMS. 



207. IT is proper to begin the study of the dynamics of a non-conserva- 

 tive gas by attempting to repeat, mutatis mutandis, the investigation which 

 was carried out in Chapter V. for a conservative gas. In fact Chapter V. may 

 be regarded as a study of the general equations of the dynamics of a con- 

 servative system, when the simplifying supposition is made that the dynamical 

 system is an aggregate of a very great number of similar systems. 



It might be thought at first sight that it would be an easy matter to 

 repeat the former investigation, taking into account the dissipation of energy 

 represented by an unknown general dissipation function. Unfortunately this 

 is uot so. In the former case the ultimate result happened to be entirely 

 independent of the constitution of the molecules of the gas. In the present 

 more general case in which the gas is not supposed to satisfy the conservation 

 of energy, no ultimate general result of this kind can be obtained. It will 

 therefore be found that no progress is possible which is at all comparable 

 with that accomplished in the former case, but the fact that the possible 

 progress is small would be no reason for neglecting the investigation. 



The Dissipation Function. 



208. As a preliminary to the general dynamical theory, it must be 

 explained how it is that a gas in nature is adequately represented by a system 

 of similar molecules and a dissipation function, and we must investigate the 

 appropriate form for this dissipation function. 



We shall assume that the complete dynamical system consists of the 

 molecules of the gas and the ether by which these molecules are surrounded, 

 and we shall therefore suppose that all energy lost to the molecules is energy 

 gained to the ether. But in estimating this quantity there is a difficulty, for 

 we do not know sufficient about the line of demarcation between ether and 

 matter to be able to say at what stage precisely the energy is transferred 

 from the one to the other. 



