210 GRAVITATION [APR a 



It is clear that if gravitation is in any sense of electric 

 origin it must be a second order disturbance, or some 

 higher even order, superposed upon the main electric effect, 

 and be independent of sign. It would, in fact, depend 

 upon e*. For the gravitative force between two electrons 

 at distance r would be 



- _ 



r i-7 T z- 



The electric force between the same two electrons at the 

 same distance is 



&m 



F 2 = 2 - 



KT 2 



Therefore the ratio of the gravitative to the electric force 

 at any distance is constant and equal to 



where F is the electric force between two spherical 

 electrons in contact, and v is the velocity of light. 

 Numerically this ratio of the two forces is 



FI _ /m\ 2 _ 1 / _1_\ 2 _ -, _ 42 



F 2 ~ Kfy \eJ ~9xl0 20 xl-5xl0 7 \10V " 



so the electric force exceeds the gravitative as much as the 

 globe of the earth exceeds in bulk an ultra-microscopic 

 object. 



When there is an agglomeration of electrons of opposite 

 sign, their electric influence at a distance disappears, but 

 their gravitative potential will be proportional to the sum 

 of the squares of the charges. So with 10 21 mixed electrons 

 in each of two bodies, at any distance apart, the gravitative 

 force between them will equal the electric force between 

 two single electrons at the same distance. 



In my 1885 Report to the British Association on Electro- 

 lysis, page 745, the following statement is made : If the 



