A METAPHYSICAL DISCUSSION 229 



standard error, no matter how small this is taken to be. So 

 also with the symbol dt : it is not an infinitesimally small dura- 

 tion, but the limit to a duration which always diminishes. Our 

 falling body, therefore, is at certain points — Sq, Si, S2> etc. — when 

 the time is Iq^ ^i, ^2? etc. The s-points coincide with the i-points, 

 the former being read from a measuring rod, and the latter from 

 a clock. Representing these coincidences graphically, we get the 

 following " one-to-one correspondence " of s-point with ^point. 



Obviously we might remove the origins, or zeros, of the time and 

 space scales further to the left without altering the character of the 

 diagram: t = 1 second might just as well be t = 10, and s -- 100 feet 

 might as obviously be t = 1,000 — the inclinations of the dotted 

 lines showing the coincidences would not be changed. 



Fia. 51. — The Upper Points represent Observed Times, the Lower 

 Ones the Corresponding Space. 



What, then, we obtain from such an analysis is, the relation 

 between s -points (which have no magnitudes) and ^points (which 

 have no duration). In other words, it is a naked relation that we 

 obtain, and nothing else — ^there are no space or time regarded as 

 entities. Space and time are not entities, as we have seen already. 



The relation is the ratio between the differentials ds and dt; 



thus — 7 



ds 



dt = ^'^ 



and this is what we find when we observe the fall of a stone in 

 vacuo. Such differential equations are the " laws of nature." 

 As a rule, however, we try to avoid using the space-time equa- 

 tions in their differential forms, and we express them, when 

 possible, otherwise. Thus the above relation is more easily 

 recognisable in its integral shape — 



^=igt\ 



We have now reached the conclusion to which we have been 

 tending. Nature, as we know it intellectually — ^that is, the Nature 

 of Science — is a system of relations, and nothing more. It is, 

 however, our practice to speak of these more fundamental rela- 

 tions as " matter," " fields of force," " energy," " atoms," 

 " electrons," " radiation," and so on, all these things " occurring " 



