458 Dr. L. Natanson on the Kinetic Interpretation 

 throughout the volume occupied by the medium, we have then 



^^[pfa + PV 2 b + pl 2 c + P ^A + p^B + P f]C]dj;d^dz^0; (15) 



here the direction-cosines of the normal to ihe element dB of 

 the surface are denoted by I, m, n. If the medium cannot 

 flow across the surface, the second term on the left-hand side 

 may be omitted. Assuming this and calculating "dK/^t from 

 equations (8) in a similar way we find 



^ -$$[pPa+ ■P? i + P&c+pv$A+ptjjB+pY n G]dvdydz 



= $p(uX + vY+wZ)da:dyda:; . . (16) 



hence 



^ = - § + SH uX + " Y + "' z ) <fe d v d *> • • ( 17 ) 



i. e. molar energy is subject to change from two sources, the 

 first being the influence of external forces, the second being 

 the possible transformation of molecular energy E into molar 

 energy K or vice versa. Let us denote the rate of change of 

 K due to the second source of variation by "ft 1 K fat ; we have 



^ = - ^ = - WlpPa + PV*b + rf*c + pv£ A + p&B + pJnO]da! dy dz.(\8) 



Let us put 



dp=p&+pi?+pg*. (19) 



F = ( P - P f*)a + (2y-pv*)b+(p-p?)c-pvSA-pgB- P f v C 



=(p-pT*K<*-¥)+(p-p&)(i>-W+(p-p?)(e-i0) 



> (20) 



-prttk-pm-pfrlO- 



Equation (18) may then be written 



g = -^=jjj(F-p^,^rf,; . . (21) 



the molecular energy E is therefore subject to change from 

 two sources : first, the work of the ordinary average pressure, 

 and second, the effect of a disturbance giving rise to tangential 

 pressures and to inequality of the normal ones, F being the 

 rate (per unit of volume and time) at which molecular energy 

 is generated by the effect of the disturbance. 

 Put in (7) 



Q=(^+?) 2 ; Q=(v+V)(w+S)'> • • (22) 



