461 



APPENDIX VI 

 CONDUCTION OF HEAT 



55*. Transference of Energy 



As interpreted in our theory, viscosity and heat-conduction are 

 closely allied phenomena. Viscosity consists in the transference 

 of the forward momentum of the molecules from layer to layer; 

 heat-conduction is the transference of the kinetic energy of the 

 molecular motions from place to place. 



The calculation of the heat-conduction is thus to be begun and 

 carried out quite analogously to that of viscosity in 47*. The 

 only difference consists in this : that in place of the ^/-directed 

 momentum nno sin s cos <f>, is to be substituted the total kinetic 

 energy, which is Jmw 2 if we here neglect atomic motions and 

 consider those of the molecules only. If, then, we assume the 

 gaseous medium to be practically at rest so far as the exterior is 

 concerned, we obtain the formula 



Q = JfJ^{ "ds sin s cos s| Q drN(fan/*)*l Q d< u*Ke-* rl<a e- kmto \ 



which denotes the kinetic energy or heat carried across unit area 

 of a surface in unit time in the direction of increasing x. 



Maxwell's law, which the formula assumes, is of course 

 strictly applicable only to the case of a gas in a perfectly uniform 

 state throughout, and not for one in which the mass and motion 

 are unequally distributed. But, just as for viscosity and diffusion, 

 the application of Maxwell's law to the case of heat-conduction 

 also is justifiable as a sufficient approximation to the truth, if only 

 the change in the values of the variable magnitudes with place 

 occurs everywhere sufficiently slowly, so that a constant state may 

 be assumed to exist in a tolerably large region. 



For the problem of heat-conduction the most important of the 

 magnitudes which vary with place is the mean value of the mole- 

 cular energy which, by a formula developed before in 19*, p. 388, 



