﻿Electron Theory of Matter. 21 



system, the hydrodynamic attraction between the two systems 



is 



, 4i7riia 2 a' 2 aa' 

 T i 



The electromagnetic masses of the systems are given by 



M = nm, M' = nm\ 



where m, m are the masses of the electrons. 



Hence the attraction is — 5- — 7 . 



r z mm 



This is the law of gravitation. The last factor is the 

 gravitation constant. In order to account for gravitation 

 quantitatively it must have the value 6' 7 x 10 -8 . 



§ 9. When the electrons are in motion the values of m, m! 

 and those of a, a depend on the velocity. This makes the 

 gravitation constant depend on the velocity. To avoid the 

 difficulty several ways can be suggested : 



(1) The mass m of the electron, and the pressure at its 

 surface, differ from their values when the electron is at rest 

 by quantities of the order /3 2 ; when the velocity of the 

 electron is not a large fraction of the velocity of light, the 

 difference is very small. 



(2) An atom, if built up out of electrons, probably contains 

 electrons moving with very different velocities ; the gravita- 

 tional attraction between two atoms is therefore an average 

 taken for electrons with very different velocities. The table 

 of values of /3 for rings of electrons given in § 4 shows that 

 for rings of considerable numbers of electrons the value of 

 /3 does not alter much with the number of electrons in the 

 ring, and for these rings the values of (3 are large ; the 

 gravitational attraction diminishes as ft approaches the value 

 unity, because the pressure at the surface of the electron 

 diminishes and because the mass of the electron increases. 

 Hence rings of few electrons, which move slowly, produce 

 an effect which is practically the same as that for electrons at 

 rest ; rings of many electrons, which move quickly, produce 

 a smaller effect, but the difference is very slight for a con- 

 siderable difference in the number of electrons in the ring. 

 The mean gravitation constant for the whole atom need not 

 differ very much for atoms containing very different numbers 

 of electrons, and therefore of very different atomic weights. 



Whether this be the reason why the gravitation constant is 

 the same for all kinds of atoms or not, the same difficulty 

 arises in Lorentz's theory of gravitation. Lorentz supposes 



