44 Mr. H. R. Hasse on the Equations of 



The conclusion arrived at is that it is not possible to deduce 

 a unique system of electrodynamical * equations for matter 

 in motion by means of the principle of relativity, the corre- 

 sponding equations for matter at rest being assumed to be 

 known. In other words, the knowledge o£ the electrodyna- 

 mical equations for matter at rest, which we may deduce 

 from experimental evidence and not necessarily from any 

 theory of the constitution of matter, together with the 

 principle of relativity is not sufficient for the deduction of 

 the equations of electrodynamics for matter in motion. 



We can, however, make use of the principle or! relativity 

 in the following form. Having found from certain physical 

 conceptions f the equations of the electromagnetic field for 

 matter in motion, we may apply the transformations of the 

 principle of relativity to deduce the constitutive relations 

 which complete the scheme of electrodynamical equations- 

 Such a deduction is applicable only to such cases of motion 

 as are given by the particular transformation used, always 

 transforming from matter in motion to matter at rest. In 

 the form in which this principle would now be used, it might 

 perhaps be better expressed as the hypothesis of the null 

 influence of the Earth's motion on optical and electrical phe- 

 nomena, in which form it is based directly on experimental 

 evidence. For the equations of the electromagnetic field given 

 by Larmor and Lorentz the problem as above stated was solved 

 independently by the author J for the case of uniform trans- 

 lation, the constitutive relations necessary to complete the 

 scheme of equations being derived by means of the above 

 hypothesis. 



In the general case of a variable velocity we should start 

 from the equations of the field for matter in motion, referred 

 to space-time coordinates x, y, z, f, and apply to them th& 

 necessary transformation to bring a particular point to rest 

 referred to a system of coordinates a? l5 2/ l5 z u t x . The known 

 constitutive relations for matter at rest in this space would 

 then transform back into the required constitutive relations 



* The term " electrodynamical equations " is to be understood to 

 include two groups, viz. " the equations of the electromagnetic field " 

 and the " constitutive relations." 



t E. g., the equations of Larmor and Lorentz, based on the conception 

 of matter made up of discrete electrons ; or Walkers equations based on 

 the conception of polarizations. 



X Proc. Lond. Math. Soc. ser. 2, vol. viii. (1910). Deduced also from 

 Minkowski's work by Miriinanoff, Annalen der Physik, vol. xxviii. (1909). 

 p. 192. 



