280 Free Path Phenomena [OH. xv 



Since Q is in general a function of ^t , v , w and the mean values 

 U~2, uv, etc., etc., the bracket on the left-hand side is seen to be the differential 

 coefficient of Q with respect to the time, regarding the mean values as 

 functions of the time, but u , v 0> w as constants. 



Special Forms assumed by Equation of Transfer. 



333. The equation just found is the general equation expressing the 

 transfer of Q. Further progress is only possible by calculating AQ, the 

 term which arises from collisions, directly from the dynamics of a collision. 

 This, however, is only possible when the value of Q is known, and when we 

 have made a special assumption as to the law of force between molecules. 



Maxwell uses the same equation (654) for the investigation of the three 

 phenomena of viscosity, conduction of heat and diffusion, regarding viscosity 

 as a transfer of momentum, conduction of heat as a transfer of energy, and 

 diffusion as a transfer of mass. 



Before calculating the form assumed by AQ on giving the requisite forms 

 to Q and making special assumptions as to the law of force, we shall find it 

 convenient to examine the simplifications introduced into equation (654) on 

 giving these forms to Q. 



334. Let us first put 

 Q = u? + v 2 + w* 



= w 2 + v<? + w * + u 2 + v 2 + w 2 + 

 Thus Q = w 2 + v 2 + y fl 2 + U 2 + v~2 -1- w, 



uQ = u (u 2 + v 2 + w 2 ) + 2w u 2 + 2v uv + 2w uw. 



We are going to assume the molecules to be point centres of force, 

 so that their only kinetic energy is energy of translation. Hence, by the 

 conservation of energy, we may take AQ = 0. The equation now becomes 



T) 



*-* / A n n\ _ V f V 



L W Ox/ 



[<i _ 

 - ^- fi>u (u 2 + V 2 + w 2 ) 

 ex l 



- 2, u -f uv + uw 



doc l \ ox cy oz 



