68 L. Page — Fundamental Relations of Electrodynamics. 



If — is small, this reduces to 

 c 



,, di sin 6 , 



E ; = — - ds 



dt r 



which is the expression for the induced electromotive force in 

 one wire due to a variation of the current in another. 



Conclusions. 



Our ohject was to deduce the fundamental laws of electro- 

 dynamics,- — the law for the force between currents, and the 

 law governing current induction, — from those of electrostatics. 

 We assumed that part of the theory derived from the principle 

 of relativity which depends only upon the fact that the velocity 

 of light must be the same as measured in different systems, 

 and which depends in no way upon the electrodynamic equa- 

 tions. Then we extended the following conceptions of electro- 

 statics to moving charges : 



(1) To an observer at rest relative to a charge, the charge 

 can be replaced by a field of lines of force radiating from the 

 charge in such a way that equal solid angles contain equal 

 numbers of lines of force. 



(2) To an observer relative to whom the charge is in motion, 

 as well as to an observer at rest relative to the charge, the 

 electric intensity due to the charge is proportional to the 

 instantaneous density of the lines of the force at the point 

 considered. 



By the means of these extensions of electrostatic concep- 

 tions to moving charges, we were able to deduce (a) the 

 expression for the electric intensity due to a charge moving 

 relative to the observer ; (h) Ampere's law, or its equivalent ; 

 (c) Faraday's law, or its equivalent. 



Viewed from another standpoint, the fact that we have been 

 able, by means of the principle of relativity, to deduce the 

 fundamental relations of electrodynamics from those of electro- 

 statics, may be considered as some confirmation of the principle 

 of relativity. 



I want to express my thanks to Professor PI. A. Bumstead 

 for several valuable suggestions, and to Dr. H. M. Dadourian 

 for his help and encouragement. 



Sheffield Scientific School, March 7th, 1912. 



