L. Page — Fundamental Relations of Electrodynamics. 57 



Akt. VI. — A Derivation of the Fundamental Relations of 

 Electrodynamics from those of Electrostatics / by Leigh 

 Page. 



Maxwell's electrodynamic equations are based upon three 

 experimental laws : (1) the inverse square law for the electric 

 force between two point charges relatively at rest ; (2) 

 Ampere's law for the force between current elements, or its 

 equivalent; (3) Faraday's law of current induction. Helm- 

 holtz gave a derivation of Faraday's law from Ampere's law 

 by means of the principle of conservation of energy, which, 

 however, has been shown to be erroneous.* Indeed, it has 

 been impossible by any of the methods heretofore used to 

 derive the electrodynamic equations without making use of all 

 three of these experimental laws. 



The object of this paper is to show, that if the principle of 

 relativity had been enunciated before the date of Oersted's 

 discovery, the fundamental relations of electrodynamics could 

 have been predicted on theoretical grounds as a direct conse- 

 quence of the fundamental laws of electrostatics, extended so 

 as to apply to charges relatively in motion as well as to charges 

 relatively at rest. Of course, only that part of the theory 

 derived from the principle of relativity that is independent of 

 any a priori knowledge of the electrodynamic equations, will 

 be made use of. That is to say, we will use only the kine- 

 matics of relativity : — to use the dynamics of relativity, which 

 is derived from the electrodynamic equations, would be to 

 reason in a circle. 



A material system is defined as an aggregate of material 

 bodies having no relative motion, and showing no linear accel- 

 eration or angular velocity as a whole. Suppose now that we 

 have any number of these systems moving in various directions 

 and with various velocities relative to one another. The 

 principle of relativity states that there are no experimental 

 methods, practical or ideal, of distinguishing one such system 

 as being marked out as different from all the others. In other 

 words, if there is an ether, there exist no experimental 

 methods by which we can find out which of these various sys- 

 tems is at rest relative to the ether. 



One of the most obvious consequences of this principle is 

 that the velocity of light, as measured in any one system, must 

 be the same as measured in any other system. Otherwise 

 there would be accessible to us an experimental method of 

 locating the luminiferous ether, which is in contradiction to 



* Maxwell's " Electricity and Magnetism," 3d edition, vol. ii, p. 192. 



