192 Mr. J. C. Maxwell on the Dynamical Theory of Gases. 



Pn Pz> K> K> auc ^ & are quantities the absolute values of which 

 can be deduced from experiment. We have not as yet experi- 

 mental data for determining- M, N, or K. 



We thus find for the rate of change of the various functions 

 of the velocity : — 



(<*) jf=/cA 1 p 2 (u.-u l ) + X; (51) 



(/3) ^■=k 1 Af l { v < + tf-2E*\ 



+{?-%/>} } 



also 



> (52) 



-gP = -SAAfcfcfc + k PtW ^ w (2A -3A 2 )K-«,)( P -^) 



M ' + 1U » 1(53) 



+ M^M j 2A ' (M ^' - M '^ } T«Wf A+U)} J 



(y) As the expressions for the variation of functions of three 

 dimensions in mixed media are complicated, and as we shall not 

 have occasion to use them, I shall give the case of a single 

 medium, 



^(tf+Ztf+U^-zkpAttHW+tm . (54) 



+ X(3? 1 2 + ^+r i 5 )+2Y^ 1 + 2Zf i r i . J 



Theory of a Medium composed of Moving Molecules. 



We shall suppose the position of every moving molecule re- 

 ferred to three rectangular axes, and that the component veloci- 

 ties of any one of them, resolved in the directions of co t y, z, are 



u + %> v + rj, w+X> 



where w, v, w are the components of the mean velocity of all the 

 molecules which are at a given instant in a given element of 

 volume, and f, 77, f are the components of the relative velocity of 

 one of these molecules with respect to the mean velocity. 



The quantities u } v, to may be treated as functions of %, y, z, 



