of the Dissipation Function. 457 



we obtain 

 p'^(u 2 + v 2 + w 2 + F + y 2 + ?) 



-^ 



-r ^- (2upr)t; + 2vp7) 2 -+ 2wpr)t;+ pr)^ 2 + prj* + pr)^ 1 ) 



+ ^(2upl$+2vp& + 2wpF +pl%* + pW+P?) 



= 2p (uX + vY + wZ) -f p t (u 2 + v 2 + v? + f + v 2 + f). (10) 

 By (8) this equation is reduced to 



= ip|^ 2 + ^ + iy 2 + f + ^+?) (11) 



All these equations are quite independent of any view we 

 may entertain as to the intimate nature of molecules and as 

 to the law of force between them ; accordingly they may be 

 said to belong to the Kinematical Part of the Theory of 

 constitution of fluids. 



2. If we suppose that the molecules of the fluid do not 

 contain any internal energy (or that they contain such energy 

 in absolutely constant amount) the energy of a molecule will 

 be only that which depends on the velocity of its centre of 

 inertia. Assuming this equation (11) may be transformed. 

 Pat for brevity, 



"du "dv "die no 



^-=a; ^-=o; ^- =c ; . . . . (12) 

 0# oy oz 



"dv 'div . "dw dw -p "du "dv n , Q 

 ^z dy ^>% ^z dy d>v 



and let us add to the left-hand side 



i(F+?+?)f +ip(¥-rv 2 +?)0, . . (U) 



where d— a + b + c. Multiplying by dx dy dz and integrating 



