331, 332] Maxwell's Equations of Transfer 279 



or, again, if we write 



D d 9 9 9 



ru = :TI+' M oo- + Vo3- + Wo5-, 



Dt at dx dy dz 



so that j- denotes differentiation following an element of gas in its motion, 

 the equation becomes 



AQ ........... (652). 



As before if we put Q = u in this equation, we have AQ = 0. Also 

 Q = u , so that 



9g = 1 



du 



8Q = 9Q =0 



dv dw 



and also 



= u (U + w ) = u, 



vQ = v (u + MO) = uv, etc. 

 Hence the equation becomes 



Du 9 d , , 9 , v 



,-v \f \J V I r\ \V \J / I *-- IOOOK 



x/t, uuu dy oz m 



an equation of motion which is identical with our previous equation (360). 



There are of course two similar equations obtained from the general 

 equation by putting Q=v and Q=w respectively. When these equations 

 were obtained before in 173, they were regarded as expressing the motion 

 of the gas in terms of the forces acting upon the gas. On the present 

 occasion it is convenient to regard them as equations expressing X, Y and Z 

 in terms of the motion of the gas. 



From these three equations and equation (652) we can obtain an equation 

 which does not contain X, Y or Z, and which is therefore true for a gas 

 independently of the action of external forces. Effecting the elimination 

 of X, Y and Z, this equation is found to be 



or, arranging the terms in a form more convenient for use, 

 'DQ dQDu dQDv dQ 



v 



___ 



Dt du Dt dv Dt dw Dt 



|g(,u) + l(,Uv) + ^(,uw)}] +A<2 ...(654). 



