508 Mr. Norman Campbell on the 



is found to be the same by all relatively unaccelerated 

 observers ; the second is that this velocity has been measured; 

 the third is that it is the velocity of light. Only the first 

 proposition is implicated in the result stated in the last 

 paragraph : the quantity c is this universal veloeit}-, whatever 

 it may turn out to be. The second and third propositions 

 are not introduced until the result is applied to the deduction 

 of the optical and electrical laws for a disturbed system from 

 those for a quiet system. 



The first proposition is that which is really characteristic 

 of the Principle of Relativity, and is the feature which 

 distinguishes it from all other theories. It seems at first 

 sight rather startling, but perhaps it may be made to appear 

 more plausible, if it is pointed out that it means some velocity 

 must be " physically infinite" — that is to say, it must be such 

 that the addition to it or subtraction from it of finite velocities 

 do not change its magnitude. If its magnitude had turned out 

 to be represented on the scale of measurement of velocities 

 ordinarily adopted by a mathematically infinite number, no 

 difficulty would have been felt with regard to it : it is the fact 

 that the second part of the Second Postulate proposes to repre- 

 sent the physically infinite velocitv by a mathematically finite 

 number which causes surprise. There is, however, nothing- 

 more difficult in such a representation than there is in the 

 representation of the physically infinite low temperature by 

 the mathematically infinitesimal number zero ; both repre- 

 sentations are merely consequences of the definitions of 

 velocity and temperature adopted, and physical and mathe- 

 matical infinity could be easily brought into agreement by a 

 change of definition *. 



But if the first and second parts of the Second Postulate 

 be accepted, there can be no doubt about the third, for if we 

 are going to identify the physically infinite velocity with anv 

 velocity which has ever been observed, there is, on general 

 grounds, no doubt as to its identification with the velocity of 

 light. For this velocity clearly cannot be less than any 

 velocity which has been measured : to suppose that it could 

 would be self-contradictory. Hence if we are to identify the 

 physically infinite velocity with any velocity which has been 

 measured, it must be with the greatest velocity which has 

 been measured, the velocity of light in vacuo. The agree- 

 ment of the propositions deduced from the Principle of 

 Relativity with the aid of this identification with the 

 experimental work of Bucherer is strong evidence for the 

 second part of the postulate — that is, for the view that 



* This line of thought will be developed in a later paper. 



