ARISING FROM INEQUALITIES OF TEMPERATURE. 701 



(15) Final Equations of Motion. 



We are now prepared to complete the equations of motion by inserting in 

 (42) the values of the quantities a\ a/3, ay, and we find for the equation in x 



du dj^ fd?u d'u d*u\ 1 d Idu dv dw\ 

 9 u? d fd'd d-0 d 



If we write 



1 Idu dv dw 9 0*6 d*9 d' 



Updt" 



or, if the pressure p is constant, so that pd0 + 0dp = 



10 u. W 



then the equation (55) may be written 



du dp' (d*u d'u d*u 



- 



If there are no external forces such as gravity, then one solution of the 

 equations is 



u = v = w = Q, p' = constant, 



and if the boundary conditions are such that this solution is consistent with 

 them, it will become the actual solution as soon as the initial motions, if any 

 exist, have subsided. This will be the case if no slipping is possible between 

 the gas and solid bodies in contact with it. 



But if such slipping is possible, then wherever in the above solution there 

 is a tangential stress in the gas at the surface of a solid or liquid, there 

 cannot be equilibrium, but the gas will begin to slide over the surface till 

 the velocity of sliding has produced a frictional resistance equal and opposite 

 to the tangential stress. When this is the case the motion may become steady. 



