G2S Mr. Norman Campbell on Relativity 



even the argument which they used would s^em to show that 

 it is not valid for collisions in the line of relative motion. 

 That they omitted to note that it is only valid for small values 

 o£ u seems to be due to a neglect to observe that, when a 

 body appears to B to be moving in a direction making an 

 angle 6 with the direction of relative motion, the same angle 

 does not in general appear as 6 to A. 



On these grounds, then, the application of the result which 

 Dr. Tolman has made in his last paper appears quite un- 

 justifiable. But the error which I wish to discuss is much 

 more interesting and deep-seated. 



4. It must be remembered that, if (A) is to state the 

 foundation of Newtonian mechanics, the quantities u a , Vb, 

 etc. must be measured relative to axes which have no 

 absolute acceleration. Now I have pointed out in another 

 paper * that no amount of experiment can determine whether 

 a body is or is not absolutely accelerated : any conclusion 

 which Ave reach on the point is determined wholly by the 

 assumptions which we make as to the nature of the circum- 

 stances which determine acceleration. We can take any body 

 we please as absolutely unaccelerated, so long as the further 

 assumptions we thus bind ourselves to make are accepted as 

 soon as the necessity for them arises. Prof. Lewis and 

 Dr. Tolman in their argument are dealing with a state of 

 affairs of which we have no experience whatsoever ; we have 

 not observed, and are not likely to observe, a collision 

 between two bodies projected from two systems, moving 

 with a relative velocity approaching that of light, and each 

 containing an observer who can afterwards tell us the value 

 he found for m. Accordingly they can make any assump- 

 tions they like, happy in the confidence that they will never 

 have to make any more, unless they want to do so, because 

 their theory cannot possibly come within the range of 

 experiment. In general, then, there is not the smallest 

 objection to their taking the systems A and B to be 

 absolutely unaccelerated, and applying (A) to values of the 

 velocities determined relative to those systems. 



5. But there is one system which cannot be taken as 

 absolutely unaccelerated and on which the axes to which the 

 velocities mentioned in (A) are referred must not be placed. 

 This system is either of those which are taking part in the 

 reaction. For (A) involves the change of velocity for each 

 of the bodies : if velocities are measured relative to one of 

 the bodies, change of velocity relative to that body means 

 the change of velocity of a body relative to itself, an expression 



* Phil. Mag. [6] xix. p. 168 (1910). 



