296 Free Path Phenomena [OH. xv 



In calculations in which we ignored deviations from the normal state, 

 we took (equation (662)), 



q = U 2 = V 2 = W 2 . 

 Hence we may now, to the same order of approximation, take 



P 



q p- 



Introducing 77, defined by equation (709), we can write equations (704) 

 and (705) in the form 



............ (711), 



t]v\ ox 3 



. ...(712). 



Hence IP = (D* + v* + w*) ( v* + w~ 2 2 IT 2 ) 



_P <1 ( 9 3u 2 fdu dv dw \\ 



~ I * o o I o -- ^5 -- ~^T~ 1 

 p rjv \ ox 6\ox oy 02 J j 



so that P xx = iji 



= __ 

 r)v\ ox 3 



Similarly 



Now in a viscous fluid of coefficient of viscosity K, the system of pressures 

 is given by equations of the form * 



p du y (d u d v d w \ 



ox \ox oy oz j 



p /dv du\ 



\da; dyj ' 



These pressures agree exactly with those found for the gas, if we take 



* = ^- (716). 



TJP 



Putting p = ^vmC*, this reduces to 



1 mC* RT 



"=3 



so that K is found to be independent of the density, and directly proportional 

 to the temperature, in accordance with the results already obtained. 



* See, for instance, Lamb's Hydrodynamics, p. 512. 



