WEBSTER. — PROPERTIES OF THE ETHER. 515 



tlu> iiiatrrial of the electron. Tliis tension is, of course, constant 

 tiiroufihoiit its voluiue only if all the ehai*f,'e of the electron is on its 

 surface, otherwise, it increases as we go nearer the centre of the 

 electron. 



Abraham has raised the objection to this theory, that it involves an 

 instability of the shape of the electron,'^ that would soon destroy 

 all such bodies. IJut this oI)jection is based on the interpretation of 

 the above vectors as mechanical forces per unit charge, tending to 

 accelerate the parts of the electrons invohed, and on the idea that a 

 part of the charge may in some way be displaced from the position in 

 which all these forces exactly balance. Such displacements would 

 result in a rapid disruption of the electron, a process in which equa- 

 tions (9) or (10) could not hold indefinitely. But if we take them as 

 expressions of a fundamental law, which would be violated by such 

 a process, we have a reason why this process cannot occur, nor even 

 start to occur, and the problem of stability of shape of the election is 

 solved. 



To determine the motion of a whole electron from these equations 



(9) and (10) we are aided by the fact that the resultant of the internal 



+ - + 

 forces is zero, but we have to remember that the vectors E, E, H, and 



H, that occur in these equations, include not only the contributions 

 from external sources, but internal as well. Therefore, the eciuations 

 demand motion with constant velocity when the external forces are 

 zero, and the resultant of the actions of different parts of the electron 

 on each other must be zero also. But if the external forces are not 

 zero, each part of the electron must be accelerated in such a manner 

 that the resultant of all the forces, radiated or otherwise, from all 

 other parts, will just balance the resultant of the external forces. 

 Thus we have a reason for the apparent inertia of every electron, and 

 of bodies composed of electrons, so that the laws of motion of matter 

 may be proved to be consequences of the laws of electromagnetic 

 forces. 



Simplification of the Laws. Hamilton's Principle. 



We may, howe\er, simplify these laws still further, by remembering 

 the fact that there is one dynamical principle that applies to all 

 motions of matter and also to all the phenomena of slow changes 

 of positions of electric charges and of the positions and magnitudes 



3 See Lorentz, Theory of Electrons; Chap. V, 1905. 



