510 Mr. Norman Campbell on the 



II. The Consequences of the Principle. 



6. But the chief objections which are raised against the 

 Principle o£ Relativity are urged, not so much against the 

 foundations of the Principle, as against its consequences. 

 Two consequences seem to cause especial difficulty, and these 

 will be considered. 



The first difficulty concerns the u composition of velocities." 



The Principle of Relativity leads to the conclusion that, if an 



observer on a quiet system S measures the velocity of a quiet 



system S' relative to him and finds it u, and if an observer on 



S' finds the velocity relative to him of a third quiet system 



S" to be v, then the observer on S will find the velocity of S" 



relative to him to be 



u-j-v 

 w— , 



and not, as experience with small velocities might lead us* to 

 expect, u + v. (u and v are taken in the same direction.) 



This conclusion seems absurd to many people. Let us 

 inquire into the consequences of rejecting it and substituting 

 the law w = u + v. We must then, of course, reject one of the 

 fundamental propositions (B), (C), or (D) ; the rejection of 

 (A) would not help us, because this proposition is not implied 

 in the conclusion. Now, if an objector proposed to reject (B) 

 or (C) I should have no argument to use against him, for the 

 experimental evidence for these propositions is just as strong 

 and just as weak as that for the proposition iu = u-\-v. All 

 these propositions, as well as (A), can be tested only by com- 

 paring the experiences of different observers, who have been 

 moving relatively to each other with high velocities, when 

 they meet again on a quiet system. Now since no two human 

 beings have ever, within historic times, moved relatively to 

 each other with a uniform velocity of 10 4 cm./sec. and subse- 

 quently compared their experiences, and since, on the other 

 hand, we do not expect to detect divergencies from the laws 

 of a quiet system or from the laws predicted by the Principle 

 of Relativity until the relative velocity reaches at least 10 6 

 cm./sec, the evidence for all these propositions is extremely 

 precarious. Nor does it seem in the least likely to become 

 less precarious : so far as I know, nobody has made the 

 faintest suggestion as to how a relative velocity of more than 

 10 4 between two human beings might be attained in such a 

 way that they could perform delicate measurements. The one 

 proposition among those which are fundamental to the 

 Principle of Relativity which there appears to be some hope 



