325 
of a sphere of radins a; suppose the charge e to be uniformly distri¬ 
buted over the surface of the sphere. Then m, if purely electro¬ 
magnetic in its origin, is 
= 2e 2 /3ac 2 (11) 
and F takes the simple form 
F = 2jia. (12) 
If we suppose the charge e to be uniformly distributed over the 
volume of the sphere we find 
i 7 — I na. (13) 
It follows that F ought to be of order 10“ 12 cm. and to have the 
same value for all substances to which Planck's Theory can be 
supposed to apply. 
§ 10. In his Theory of Extinction, Lorentz supposes that a vibra¬ 
ting electron is not at all subject to forces tending to damp its 
vibration; accordingly, in writing down the solution of the equation 
of motion he does not confine himself to the forced vibration; he 
considers the general solution which includes of course the natural 
vibration. Now the effect of the encounters between the molecules, 
say of a gaseous body, will be that the vibration of the electron 
will (many times in a second) be profoundly disturbed and will be 
transformed into a motion of a wholly different kind. Let t 0 repre¬ 
sent the moment of the last impact which an electron has under¬ 
gone; the arbitrary constants of the natural vibration are then de¬ 
termined from the condition that 2£ 0 and 2£ 0 are zero; and if 
d'= t — t 0 represents the period of time which has elapsed since the 
last impact, £ for a given & can be evaluated. 
From Maxwell's law of distribution of molecular velocities it 
appears that the number of molecules (in unit volume) for which 
the time & lies between given limits, say & and & -j- d&. is expressed 
(at any instant) by 
4d& r°° 
( 1 ) 
a 3 j /Ji Jo w v 
a being the modulus of velocity (that is, the most probable speed) and 
dd'Biy) 
