Electrodynamics for Moving Ponderable Media. 45 



in the .r, y, z, t space. The method of course depends on a 

 knowledge o£ the transformation*. 



A different method has been used by Cunningham f. He 

 obtains the constitutive relations for matter in motion 

 with a uniform velocity by an averaging process, using 

 the Larmor-Lorentz transformation when dealing with the 

 electrons themselves. There is no essential difference in 

 the two methods as they both depend on a knowledge of the 

 transformation required to reduce a particular point in motion 

 to a point at rest. 



The particular point which is to be emphasized is that the 

 principle of relativity can in no way supersede any theory 

 of the constitution of matter. The well-known transformation 

 of Larmor and Lorentz is, as Minkowski remarked, essentially 

 a mathematical deduction from the differential equation 



for the propagation of waves with the velocity of light, and 

 quite independent of any theory of the propagation. 



On the other hand, the principle of relativity can be used in 

 order to obtain the constitutive relations necessary to com- 

 plete the scheme of electrodynamical equations, the equations 

 of the electromagnetic field for matter in motion having been 

 previously deduced from some theory of the constitution of 

 matter J, such constitutive relations being limited in their 

 application by the transformation used. 



Minkowski's method depends on the following three 

 axioms §. 



1. If a single point of the matter is momentarily at rest, 

 so that the vector w for that point is null — the surrounding 



* The general form of the transformation for the simplest case of 

 accelerated motion so far investigated is given in a recent paper by the 

 author, " The Equations of the Theory of Electrons transformed relative 

 to a system in accelerated motion," Proc. Lond. Math. Soc. ser. 2, vol. xii. 

 (1913). 



t E. Cunningham, " The Application of the Mathematical Theory of 

 Relativity to the Electron Theory of Matter," Proc. Lond. Math. Soc. 

 ser. 2, vol. x. (1911). 



J It is much more difficult to obtain the constitutive relations for 

 matter in motion than to obtain the equations of the electromagnetic 

 field. Cf. Larmor, ' JEther and Matter,' p. 113, where the constitutive 

 relations given are stated only to be correct to the first order of the 

 ratio of the velocity of the matter to that of light. 



§ Loc. cit. § 8, p. 489. 



