Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/480

 number added to the group by collisions in the same interval is. Then we have

and therefore

Now, the law of distribution of velocities which Maxwell postulated for the molecules of a perfect gas at rest is expressed by the equation

where denotes the number of moving corpuscles in unit volume,  denotes the resultant velocity of a corpuscle (so that, and  denotes a constant which specifies the average intensity of agitation, and consequently the temperature. It is assumed that the law of distribution of velocities among the electrons in a metal is nearly of this form; but a term must be added in order to represent the general drifting of the electrons parallel to the axis of . The simplest assumption that can be made regarding this term is that it is of the form

we shall, therefore, write

The value of may now be determined from the equation

for on the left-hand side, the Maxwellian term

would give a zero result, since is equal to  in Maxwell's system; thus  must depend solely on the term ; and