985 
Physics. — “On the Energy and the Radius of the Electron’. 
By. J. D. van Der Waats Jr. (Communicated by Prof. J. D. 
VAN DER WAALS). 
(Communicated in the meeting of February 24, 1917). 
It is well known that the contracting electron (the so called 
Lorentz-electron) has its electric energy U and its magnetic energy 
T, but has moreover still a quantity of energy of another kind. 
Poincaré *) has calculated the amount of this energy, which we 
will indicate by £. He has found’): 
e 4 
E— FE = kt 3k. e ° ° . 
ae ar X aoe ae : (1) 
E, represents an integration constant, a the radius of the electron, 
w 
e its charge, c the velocity of light, £ = \/1—8?, 8 =-—, and w the 
C 
velocity of the electron. The energy therefore can be interpreted as 
a 
the work done by an internal constant negative pressure a 
Ta 
when the volume of the electron changes. If we calculate the mass 
of the electron from its electromagnetic momentum © in the usual 
way followed by Lorentz, then it appears that this mass satisties 
the equation 
1 
m= (T+U+H-.......- @ 
provided we put #,—O. At least this equation is satisfied for the 
electron with surface charge, to which case I will confine myself. 
If ZE, =0, the energy £ is the work required to increase the volume 
of the electron from the value O to the actual value. According to 
equation (2) we do not ascribe to the electron any other mass than 
that which follows from its energy according to the wellknown 
principle. 
I will here consider the calculation of £ a little more closely. In 
calculating this quantity Poincaré took as basis the condition that 
the contracted form of the electron will be its equilibrium-form, and 
that E therefore is the work of a force which is in equilibrium 
with the electromagnetic forces. He has not brought it in connection 
with the dynamics of the electron in an accurate way. For he writes: 
0 
Ge Oe ee 
dw 
which equation however is uot satisfied. 
1) H. Poincaré, Rend. del cire. mat. di Palermo. Tomo XXI, Ad. d. 23 Luglio 1905. 
2) The here used notation is another than that of PorscarÉ, 
