512 Mr. Norman Campbell on the 



having to deny in the face of fresh evidence his previously 

 undoubted proposition that "all men are black." 



7. But the greatest difficulties in connexion with the 

 Principle of Relativity appear to concern certain propositions 

 about length and time. In what follows I shall, for brevity, 

 discuss only time : everything I say will apply, mutatis 

 mutandis, to length. 



The Principle of Relativity leads to the following conclu- 

 sion. Suppose I examine a number of clocks which, with me 

 and my instruments, form a quiet system, and I find that they 

 all go n times as fast as my standard clock. That is to say, 

 for the quiet system, the " law " of these clocks is that they 



return to some standard state when t = — , where P is anv 



n 



integer. Now one of these clocks is transferred to a system 

 moving relatively to me with a velocity v. Let us suppose 

 that, at the moment when t = 0, this clock is just passing me, 

 so that x = 0. Then the Principle of Relativity states that 

 the <; law " for the disturbed system of myself and the clock 



p 

 is that the clock returns to a standard position when t' = — 



or when Bit V ) = — , 



\ c J n 1 



p 

 or ; since x=vt, when P=/3— . 



That is to say, the clock now agrees, not with the clocks with 

 which it formerly agreed on the quiet system, but with one 



on the quiet wdrich goes -5 as fast as those clocks. 



There is nothing new in the form of this conclusion. The 

 crudest arguments based on the oldest theory of light lead to 

 the conclusion that the rate of a clock as obsei ved by a certain 

 observer must change with the relative motion of clock and 

 observer. For, it will be argued, the observer does not see 

 the clock " as it really is at the moment," but " as it was a 

 time T earlier, where T is the time taken for light to reach 

 the observer." And on these lines it is easy to show that the 

 apparent rate of a clock moving away from the observer with 



a velocity v is U — -J times the rate of the same clocks 



observed at rest. It is only the magnitude of the change 

 concerning which the two theories differ. 



" Yes/' says our objector, "that is all very well : of course 

 the apparent rate of the clock changes with motion, but does 



