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



medium moving in any manner whatever, — then for that 

 particular point at the particular instant the relations between 

 the various vectors are given by Maxwell's electrodynamical 

 equations for matter at rest. 



2. The velocity of matter is always less than that of 

 light. 



3. The general equations of the electromagnetic field are 

 of such a nature that, for any " Lorentz-Transformation " of 

 the space and time coordinates, the resulting equations 

 contain the transformed vectors in the same manner as the 

 original equations contain the original vectors, the different 

 sets of vectors being related to each other in a certain definite 

 manner *. 



This last axiom is called the principle of relativity. 



Since Minkowski only applies his axioms to the case of 

 media in uniform motion, the first axiom can be replaced 

 by the following : — For media at rest the equations of the 

 electromagnetic field are the ordinary Maxwellian differential 

 equations, and further, the equations connecting the different 

 vectors are the constitutive relations of the ordinary type. 

 In this form the axiom needs no comment, nor does the 

 second axiom. As to the third axiom, we must notice (1) 

 that the " Lorentz-Transformation " only applies to the case 

 of uniform motion in a straight line so that Minkowski's 

 resulting equations only hold for this case t, and (2) that 

 the definite manner in which the different sets of vectors are 

 related depends on the above transformation; and therefore 

 the connexion between them is only defined for the case of a 

 constant velocity when the transformation is linear J. 



We shall follow Minkowski's method of deriving his 

 equations, and to this end we consider a space x, ?/, z in 

 which matter is in motion at time t with a constant velocity 

 w parallel to the axis of x. W e may then apply the trans- 

 formation 



x=e(x 1 + wt 1 ), y=!/i, ~=~i, t = e(t l + wx l ), . (1) 



where e 2 = (l — w 2 ) -1 , the velocity of light being unity, to 

 obtain a point x v y l9 z l at rest in the second space corre- 

 sponding to the moving point a?, y, z in the first space. 



Since the matter is at rest in the x^ y l9 z u t 1 space the 

 electrodynamical equations are, according to the first axiom, 



* Loc. cit. § o, p. 483, Definition of " Eaum-Zeit-Vektor I. und II. 

 Art." 



t This obvious limitation does not seem to be sufficiently recognized, 

 since Minkowski's equations have been freely applied in the case of a 

 variable velocity. See note at the end of the paper. 



t Loc. cit. p. 484. 



