514 PROCEEDINGS OF THE AMERICAN ACADEMY. 



negative electricity p, (always negative). The electric forces due to 



all the positive and all the negative electricity we may call £ and E, 



+ - 



and the magnetic forces H and H, while the velocities of the charges 



may be represented in terms of P and P, their ratios to the velocity of 

 light. 



These quantities may be supposed to satisfy the following set of 



which determine the positive forces in terms of the positions and 

 velocities of the positive charges, and the negative forces in terms 

 of those of the negative charges. But in addition to these equations 

 we have the following pair, 



(9) E + pxH + k — 6' (E+pxH) = 0, 



(10) E+pxH+k = 0, 



which must hold at every point of every electron, positive or negative, 



+ - 



and in which K and K are forces per unit charge due to the internal 



stresses of the electron, while G is a very small number Avhose presence 



in equation (9) accounts for the phenomena of gravitation.^ 



+ - 



The laws governing the vectors K and K ma^^ be deduced from the 



fact that the deformation of the electron when its velocity is very 



great is the same as that of a perfectly flexible and compressible, 



charged, conducting shell, with no internal stresses, subject to a 



constant external hydrostatic pressure or internal hydrostatic ten- 



+ - 



sion.^ Therefore, we may assume that K and K are forces such as 

 would result from such a tension, and that they are transmitted by 



1 For further details on this point see D. L. Webster, "On an Electromag- 

 netic Theory of Gravitation," These Proceedings, 47, 1-4 (1912). The rea- 

 soning and conclusions are changed but little if we introduce a similar term in 

 equation (10). and thereby gain in symmetry in our theory. 



2 Poincare, Comptes Rendus, 140, 1504-8. 



