of the Motion of Heat. 507 



and the total kinetic energy of such currents per unit volume is 



iMWW+m), ( 33 ) 



N being the number of molecules per unit volume. Calling 

 now M the mass of a molecule, let us consider the flux of the 

 quantity Q = iM(f 2 + 7;"-f f 2 ) : we see that (35) becomes 

 equal to A as defined by (28) ; A therefore represents the 

 total kinetic energy of molecular currents of (ordinary) 

 molecular energy in unit volume, L e. the kinetic energy of 

 the motion of heat-energy in unit volume, and \\\ A dx dy dz 

 represents the same quantity for the total fluid. The idea of 

 " molecular currents " is likely to conserve a definite meaning 

 even when the idea of " molecules " will be found to be 

 superseded. 



5. The energy of motion of the heat-energy is susceptible 

 of several kinds of variation, from various sources, to which 

 the consecutive terms of the right-hand side of (32) refer. 

 The first term represents the loss by convection across the 

 surface ; the second the gain due to viscosity ; the third 

 expresses the reversible effect of the mean pressure doing 

 work. The fourth term relates to the communication of heat 

 through the surface, since \pr x , iP'V; an( i ip r z are the values 

 of the total component fluxes of energy. In order to find the 

 meaning of the fifth term, let us substitute for the differential 

 coefficients values from (12) and two other equations which 

 can be written down from symmetry ; then that term will be 



and represents therefore the source of variation due to inter- 

 action between molecules. This we shall call the "interior" 

 source of variation, whereas the foregoing will be described 

 as "exterior" sources : in fact the "interior" source remains 

 active ' even in a fluid at rest when contained in a surface 

 impermeable to heat. We now see that the direction of the 

 interior variation depends on the nature of the mutual action 

 between molecules. Since the quantities (pr x ) 2 , (pr y ) 2 , and 

 {pr z ) 2 are positive, the energy of the motion of heat-energy 

 will be always decreasing if molecular interaction is such as 

 to tend to diminish the absolute values of pr x , pr y , and pr z ; 

 in the opposite case that energy will be always increasing. 

 That it is the first case only that is realized in all fluids in 

 Nature, as attested by the phenomenon of conduction of heat, 

 cannot be deduced from Kinematical Theory. We have 

 ascertained, as it were, the path of change of the energy of 



