104 CONDUCTION OF HEAT 281 



through unit area of such a horizontal plane under the given 

 circumstances. 



If we now go back to the consideration respecting the 

 current of diffusion which was w r orked out in 95, we have 

 merely to change the meaning of the symbol n which occurs 

 in it in order to apply it to the flow of heat. There n 

 denoted the difference of the values which the number of 

 molecules per unit volume of one of the two diffusing gases 

 has in two different layers separated by unit length. We 

 may take over this signification to the present problem in 

 so far as we can refer it to the number of warmer or colder 

 particles which meet each other ; we understand therefore by n 

 the difference of the values of the number of the, for instance, 

 warmer particles in two different layers which are separated 

 by unit of length. Then it follows that the number of 

 particles which in unit time carry heat over unit area may 

 be expressed by the product 



nD, 



where D denotes the coefficient of diffusion. 



We have, however, yet another alteration to consider ; 

 for we have no longer to do with the number of particles 

 that pass across, but, as we have already said, with the 

 energy carried over by them. Instead, therefore, of the 

 number n, we must introduce the difference of the heat- 

 energy per unit volume at two layers which are distant from 

 each other by unit length. 



We have taken the difference of temperature corre- 

 sponding to this distance to be 1 degree ; hence the 

 difference in the thermal energy of a molecule in two layers 

 separated by unit length is me calories, if c denotes the 

 specific heat at constant volume and m the mass of a mole- 

 cule. It thus follows that the difference of the energies per 

 unit volume for which we are looking is 



Nmc 



in thermal units, if N denotes, as before, the number of 

 molecules in unit volume, and the expression 



! = NmcD 



