508 Dr. L. Natanson on the Kinetic Energy 



the motion of heat-energy, but we are unable to say why one 

 of the two possible directions of change is invariably selected. 

 6. It may be well to point out that the problem here dis- 

 cussed bears distinct analogy to the problem of our former 

 paper, where the Dissipation Function F represented what 

 may now be called the " interior " variation of molar fluid- 

 energy and was seen to depend on the effect of molecular 

 interaction on the values of 



q x =pP—p and s x =prj£ .... (37) 



and similar quantities, in analogy to the present proposition 

 concerning the fifth term of (3*2), right-hand side. Put 



^=-^ ; ^ = ~57' .... (38) 



8t St 



and let p, y , /u, z , j/y, v z be defined by similar equations. Suppose 

 the Kmematical Theory of the Viscosity-problem to be given; 

 then what we have to do in order to complete the solution is 

 simply to prove that the /-t's and the v's have constant and 

 equal values : the results indeed given at the end of § 2 of 

 the former paper, and likewise the well-known equations of 

 motion of viscous fluids, can then be easily deduced. The 

 common value of the /a's and the v's is the coefficient of 

 viscosity and is positive if the mutual action between mole- 

 cules is such as to tend always to dissipate the disturbances 

 q and s. Again, put 



/.,= - 5 -|^ 5 (39) 



8 



r, 



8t 

 and let h y and k z be defined by similar equations. It follows 

 from (12) and (39) that 



p*=~j ^(F+^ 2 +r). • • • (40) 



From (17) therefore we obtain, calling i(f 2 +V 2 + P) = 0, 



v* ♦ **- (£('-rD + 1 (*£)+&«£>) - «"» 



the equation of conduction, as usually given, following from 

 this for a fluid at rest, if it is conceded that 6 means the 

 temperature at (osyz) . The value of the last term of equation 

 (32) is now 



;~tfW!0 a ± ^(|) 2+ *(&*}**¥ • (42) 



