• Common Sense of Relativity. 511 



of establishing definitely is (D) : we have the source of light 

 relative to which we are moving with a velocity of b* x 10 6 

 always available in the stars, and it is not too much to hope 

 that some day experimental ingenuity will succeed in 

 measuring the velocity of the light from it with an accuracy 

 of one part in ten thousand. It seems to me incredible that 

 anyone, who understands what he is doing, vail really propose 

 to reject definitely a proposition which he may hope to prove 

 in the near future in favour of one for which there is never 

 likely to be the smallest direct experimental evidence. 



But I think these people do not understand what they are 

 doing : they have been confused by the most fruitful caus9 

 of confusion, the habit of using one word to denote two quite 

 different ideas. " Velocity " is commonly used to mean 

 either " mathematical velocity " or u physical velocity." 

 Mathematical velocity is defined as the ratio of a certain 

 variable x to a certain variable t. From the definition of a 

 variable and a ratio, it follows that 



£l . lT 2 _ ^1 + ^2 . 

 t + t ~~ t 



this is a perfectly purely logical conclusion, and to deny it 

 would be absurd. On the other hand, " physical velocity " in 

 its simplest meaning is a number equal to the ratio of two 

 numbers — one representing the groups of metre rods that have 

 to be placed together in order that their ends may coincide 

 with certain points, and the other expressing the occurrence 

 of certain events in an instrument called a clock. From the 

 definition nothing whatsoever can be predicted as to the 

 relations of u, v, and w, but experiment shows us that, for all 

 values of u and v which can be attained practically in this 



. „ X x X 2 X x + #2 mi • 



way, il m=-, v——, then m — — - — . Ihis experi- 

 it t 



mental proposition has become so familiar, and the association 



of the experimental u and v with the mathematical — and 



'— so habitual, that people who do not think very deeply 



about these things have come to believe that a means the 



same thing as — -; and that, therefore, since it would be 



absurd to deny that ~+ — = — — — , it is absurd to deny 

 J tit 



that u + v — w. There is no more absurdity in being forced 



to deny this assertion in the face of fresh evidence than there 



was in the necessity for Mill's Central African philosopher 



