Common Sensjs of Relativity. 505 



ns how to change from the form suitable for a quiet system 

 to that suitable for a disturbed system not only the laws 

 which it is the special business of the theory to investigate, 

 but any laws whatsoever. Instead of working out, as 

 heretofore, the transformation necessary for each special law, 

 we shall arrive at a transformation which is valid for all 

 laws. 



The three chief * propositions necessary for this purpose 

 are as follows : — 



(B.) "Space is homogeneous and three-dimensional : time 

 is homogeneous and one-dimensional. " Mathematically this 

 means that the transformation of the space and time co- 

 ordinates is to be linear. It would take us too far afield 

 to inquire what it means in terms of observations, and since 

 no difficulty appears to have been felt in connexion with it, 

 it is unimportant for our present purpose. 



(0.) "If the velocity of a system 8' relative to S is 

 determined by an observer on S to be v, then the velocity of 

 8 relative to S' determined by an observer on S' is v " f. The 

 necessity for introducing this proposition is generally over- 

 looked. But it is a proposition which can be reasonably 

 doubted and of which the truth can be tested by experiment 

 only. Of course, all the evidence that there is is favourable : 

 if it were not, we should not speak of " relative velocity ." 



(D.) " The velocity of light determined by all observers 

 who are not accelerated relatively to each other is the same, 

 whatever may be the relative velocities of the observers." 

 This proposition is known as the Second Postulate of 

 Relativity and more will be said about it hereafter. 



4. The result which represents the attainment of the 

 primary object of the Principle of Relativity is deduced from 

 these fundamental propositions by purely mathematical 

 argument. It may be stated as follows : — 



Suppose that the disturbed system consists of two parts, A 

 and B, each of which, regarded as a complete system, is quiet : 

 let A be the part which contains the observer and his 

 instruments for measuring #, y, z, t, and let the relative 

 velocity of A and B be v. Then if A and B formed together 



* The other propositions are those which are implied in all physical 

 measurement and in all theories. The propositions given are not those 

 given by Einstein explicitly, but those which seem to be implied by his 

 argument. 



f The sign attributed to v is a matter of pure convention ; so long- as 

 each observer adheres to his own convention throughout, it does not 

 signify whether the same or contrary signs are attributed to the relative 

 velocity by the two observers. 



Phil. Mag. S. 6. Vol. 21. No. 124. April 1911. 2 L 



