154 Physical Properties [CH. vn 



Combining this contribution to 2X with that already found (expression 

 (361)), we find as the whole value of 



i-* fd^xx d&vx dtff zx \\ 777 



= mva - -~ - - v - - ~- zx dscdyde. 



[_ V dx dy dz J J 



and there are, of course, similar equations giving the values of 2 Y and 2Z. 



Hence equation (360), on dividing throughout by dxdydz and replacing 

 mv by p, becomes 



d d d d 



dz 

 175. Let us write 





p. (363) _ 



Pyx = yx + pUV, etc. 



then equation (362) may be written 



9 9 



-r. o^- ^ ^ 0t - ~~ ~-~ ~- 

 dt ox dy dz/ ex dy dz 



This equation is identical in form with the hydrodynamical equation of a 

 fluid of density p moving with a velocity u , v , w , the body forces being 

 E, H, Z per unit mass, and the pressures being the system 



Pxx, Pyx, Pzx, Pxy ...... etc ...................... (365). 



We may, therefore, speak of this system of pressures as the total pressure at 

 the point x, y, z. As is clear from equation (363), the pressures arise partly 

 from the intermolecular forces and partly from the molecular agitation in 

 the gas. 



If we multiply equation (352) throughout by m, it becomes 



which is formally the same as the hydrodynamical equation of continuity, and 

 the hydrodynamical analogy is now complete. 



We have, therefore, seen that we may regard a gas as a continuous 

 fluid, of which the motion is subject to hydrodynamical equations of motion 

 and continuity of the usual type. This is the justification, in discussing 

 the mass-motion of gases the propagation of sound, for instance, for 

 treating the gas as if it was a continuous fluid of the kind contemplated 

 in hydrodynamics. 



