250 Mr. L. A, Pars on 



inevitableness lies deeper, in some limitation imposed upon 

 the form of our knowledge. 



According to the hypothesis of relativity the transforma- 

 tions relating to different pairs of observers must form a 

 group ; that is to say, they must be consistent among them- 

 selves, so that the trans formation from the space and time of 

 observer A to that of observer B followed by the transfor- 

 mation from B to C must be equivalent to the direct trans- 

 formation from A to C *. 



No further assumption about the physical world is neces- 

 sary ; but we have to introduce two conditions defining the 

 particular problem to which the Lorentz transformation 

 applies. 



(1) Space and time are isotropic, and the equations of 

 transformation are linear. We know from the general 

 theory of relativity that space and time are not always 

 isotropic, and that a general non-linear transformation is 

 permissible when regard i<= paid to gravitational fields. The 

 Lorertz transformation does not apply in the more general 

 case ; it is the solution of a special problem, and we can- 

 not dispense with the above conditions which define that 

 problem. 



(2) Two observers agree as to the measure of their rela- 

 tive velocity. It is clear that we must introduce some 

 convention in order to coordinate the two systems of 

 measurement — there would be no significance in the exist- 

 ence of an invariant velocity for observers whose systems 

 of measurement were entirely independent. The conven- 

 tion w r e choose is that they assign the same numerical 

 measure to their relative velocity, It will be remarked 

 that to establish the Lorentz transformation no further co- 

 ordination of the measures is needed. 



If every pair of observers agree as to their relative velocity 

 the measure of velocity for each observer becomes definite 

 s > soon as the measure of one velocity for one observer is 

 prescribed. At least that is the case unless the convention 

 we have adopted is self-contradictory. So far as Ave know 

 at present, it might happen that the convention itself in- 

 volves some inherent inconsistency. One observer measures 

 the velocities of two others f, and in virtue of the con- 



* In a non-relativity theory one observer A " at rest in the aether " 

 would be regarded as fundamental, and it would not be necessary that 

 the transformation from B to C should follow the same law as the 

 transformation from the fundamental observer A to C. 



f The second and third observers are supposed moving in the same 

 direction relative to the first. 



