506 Mr. Norman Campbell on the 



a quiet system, the known laws for quiet systems would state 

 a relation between the time and the coordinates of the various 

 parts of the system on the one hand, and some quantities P, 

 Q, R, representing the physical state of the system on the 

 other (forces, for example). Let this relation be represented 



by 



/(*,y,*,t,P,Q,R...)=0. 



It is shown, as a consequence of the Principle of Relativity, 

 that the analogous relation for the disturbed system is 

 obtained by substituting for each set of coordinates x, y, z, t, 

 belonging to a particle of B, the quantities x r , y', z , t' 3 where 



0\ y\ z', f) =(/8(« - vt). y, z, fi{t- ™) )• 



It must be noted that the quantities P, Q, R, . . . will often 

 involve implicitly the coordinates and the time, that is to say 

 the values of P, Q, R, . . ., will be determined by certain 

 measurements of %,y, z, t for certain identified particles. In 

 fact there will be a relation of the form 



<KP,Q,R...,*,y,M) = 0. 



In this case the substitution of x 1 , y\ z', t 1 for x, y, z, t must be 

 carried out consistently, and for P, Q, R, . . . must be sub- 

 stituted P', Q', R', . . ., where these latter quantities are given 

 by 



</>(P', Q', R' . . ., x\ y\ z\ f)=4>(?, Q, R . . ., x, y, z, t). 

 In this manner the relation is obtained 



giving directly the relationship which holds for the disturbed 

 system between x 3 y, z, t on the one hand, and P, Q, R, . . . 

 on the other, all measurements being still made by the 

 observer on A with the measuring instruments which form 

 part of his quiet system. This relation is that which we set 

 out to seek, the law for the disturbed system as observed by 

 an observer who forms part of it *. 



So far surely nobody can find any difficulty : anything 

 mere beautifully straightforward it would be hard to conceive. 

 Not only is the result magnificently simple, but it furnishes 

 us with a mathematical instrument of extraordinary power. 

 In place of the elaborate calculations which have hitherto 

 been necessary in dealing with moving systems, all that we 



* The best examples of the process are, of course, those worked out 

 by Einstein in the paper referred to. 



