of the Motion of Heat. 509 



In order to complete our solution we have to prove that the 

 k's have constant and equal values. It will be observed that 

 the role of the expression 



in Conduction is much the same as that played by Lord 

 Rayleigh's Dissipation Function F in Viscosity ; and we 

 therefore propose to call this expression u the Dissipation 

 Function of Conduction." 



In his great paper " On the Dynamical Theory of Gases," 

 Maxwell practically confined himself to the case of a force 

 between molecules varying inversely as the fifth power of 

 their distance. It may, we think, be legitimately assumed 

 that the Theory of Matter will progress in the future without 

 the aid of any such hypothesis. Whatever may be the law 

 of molecular force, whatever may even be the opinion we 

 hold as to the existence of molecules, we shall be justified in 

 seeking to find a general law of subsidence of disturbances 

 in fluids or possibly in all bodies — a general Laiv of Relaxation 

 in Maxwell's sense of the term. Let a, /3, 7 denote constants, 

 being the reciprocals of time-periods ; we have 



8q x 8sx 8r x Q /i.v 



hi = ~ a ^' w = -i s * ; w = ~P r *'' ■ ' (44) 



and it does not seem unlikely that these equations should 

 be special and no doubt approximate expressions of some 

 general relation. 



The subsidence of disturbances, to which we alluded, forms 

 a characteristic feature of phenomena which are going on in 

 matter, as contrasted with those of which the aether is the 

 seat. Now this property of gradually calming every kind of 

 disturbance (which seems to be a fundamental property of 

 matter) is in formal contrast with another property attributed 

 to matter, i.e. with inertia. It seems therefore legitimate to 

 suppose that it is with the properties of the aether that we are 

 ultimately concerned in ordinary dynamics ; and if we adopt 

 the well-known doctrine which asserts that matter may consist 

 in some kind of disturbance in the aether, we shall find nothing 

 to surprise us in such an assumption. 



Phil. Mag. S. 5. Vol. 39. No. 241. June 1895. 2 M 



