MECHANICAL EQUIVALENT OF PRESSURE MARGULES 515 



In equation (I) substitute 

 P 



Jf-o 



dfi = F (ft) -F (ft Q ) 



then with the equation 



I ft dk — I /i dk 



which expresses the constancy of the mass of the gas enclosed within 

 the volume k we obtain the following: 



JdF p 

 ft F (ft) dk = Constant ; 



dfj. ft 2 

 dt J dt\ ft! 



The equation of continuity of a mass of gas 



d/i djjiu) d (jiv) d (jiw) = Q 

 dt dx dy dz 



combined with the preceding gives us 



dA _ r p dp 

 dt J ft dt 



n^dk-'[F 



J u dt J 



6 (ft u) d {ft v) d (ft w) 



— + + 



dx dy dz 



dk. 



By well-known transformation, the second integral on the right 

 hand becomes 



— { ft( u + v — + iv -)dk — C ftF (u cos TV* + v cos Ny 



J \ dx dy dz I J 



+ w cos Nz) dO 



where O is the surface of the volume k and ./V is the normal to that 

 surface directed inward. 



The last portion of this expression vanishes when no gas passes 

 inward or "outward through O. 



