370 Dr. L. Silberstein on the 



is straight. There is no defining of " straight " nor of 

 " uniform." All so-called definitions of these terms are but 

 apparent, each of them containing a vicious circle. 



A definition of uniform motion such as Dr. Campbell 

 repeats after the naive little text-books [to wit : " we define 

 uniform motion as that of a body which covers equal distances 

 in equal times," p. 654] would be exactly as bad as : a straight 

 line is that which slopes down or up (relatively to another 

 straight !) by equal heights in equal horizontal distances. 

 It is precisely such a "definition" which prevents most 

 people from seeing the possibility of non-intersecting, 

 Lobatchevskyan straights and the hypothetical nature of 

 Euclid's parallel axiom. And the kinematical correlata of 

 these things are made manifest in my first paper, showing the 

 possibility of a generalized (hyperbolic) system of kinematics. 

 The analogy between "uniform" and "straight" becomes 

 still more manifest if one thinks of the modern relativist's 

 four-world, in which a " straight " stands for a space-straight 

 as well as for uniform motion or propagation. But there is 

 no need to appeal to that famous "union" of space and time 

 to show the fundamental, irreducible character of uniform 

 motion ; this character belongs to it historically, since times 

 immemorial until our days. Both the assumption of uni- 

 formity and the rigid subdivision of the paths or angles are 

 inherent in all the more precise chronometric methods ever 

 devised by man. 



This settles the first and chief point of the present note. 

 It is scarcely necessary to add that in declaring such and 

 such a phenomenon to go on uniformly the physicist's, or 

 the astronomer's, choice is, among other things, based upon 

 reasons of convenience, aiming at a certain kind of simplicity 

 of laws or differential equations, such as I attempted to 

 explain in the introductory chapter of the " Theorj^ of 

 Relativity." 



The second point being already settled at the very beginning, 

 let us pass at once to our third point, concerning that is 

 Dr. Campbell's own views on the question of the measure- 

 ment of time. Dr. Campbell is under the fatal misappre- 

 hension that he requires but " three definitions " in order to 

 set up a system of measurement of time [nay, of any other 

 magnitude]. These are his (1), (2), and (3), p. 653. The 

 second concerns only the equality of two time-intervals 

 whose both the beginning and the ends coincide, and the 

 third fixes only, in the usual way, the meaning of the sum 

 of two adjacent (consecutive and gapless) intervals. They 

 need not detain us any further. The whole burden is loaded 



