﻿652 On the Time Scale. 



useful. "We define our time scale by saying that Newton's 

 laws shall be true, simply because it pleases us to do so ; 

 and it pleases us because we prefer simple to complicated 

 statements of fact, when our choice is free. 



Now all this has reference to ordinary experience where 

 the observers are all relatively at rest or nearly so. But if 

 we drop this restriction, a different definition of the time 

 scale may be more convenient ; if so, we are entirely at 

 liberty to adopt it, if we do not delude ourselves with any 

 nonsense about clocks " running at a constant rate," — 

 the term "a constant rate" being quite meaningless except 

 in connexion with some time scale outside of and independent 

 of the clock itself. 



The notion of time, as defined by reference to Newton's 

 first law and to the measurable quantity length, is so in- 

 grained in us that the symbol " t " in our equations seems to 

 us as if it ought, somehow or other, always to stand for the old 

 familiar mean solar time. In reality it stands for a derived 

 quantity which may be defined by means of true, i. e., 

 measurable, quantities, through the mediation of Newton's laws 

 or Maxwell's equations or any other statement of observed 

 facts which we may happen to be interested in having 

 appear in a particular form. In the past we have paid 

 attention only to Newton's laws, defined the time scale by 

 reference to them, and used the same time scale in all 

 branches of physics. It now turns out that if the usual 

 form of the electromagnetic equations is to be retained when 

 velocities comparable with that of light are in question, the 

 time scale must be defined by those equations, so that the 

 facts of mechanics are no longer expressible by Newton's 

 laws. And since such velocities occur practically only in 

 connexion with electromagnetic experiments, it may quite 

 legitimately be thought better to pay attention to the electro- 

 magnetic than to the mechanical equations when, as for these 

 high velocities, a choice must be made. 



Whether a quantity can be so defined that it may replace 

 our familiar " t" in all the equations of physics, for 

 observations made under all possible circumstances, and 

 without requiring any too serious modifications in the forms 

 of the equations, rercains to be seen. If it can, we may 

 find it well to adopt the new quantity and call it " time." 

 But the task will not be accomplished by shutting one's eyes 

 to the fact that any time scale is merely an arbitrary system 

 of numbering successive events, nor by any use of clocks 

 which run " uniformiter," when uniformiter is defined only 

 by reference to the Latin dictionary. 



Washington. 

 February loth, 1912. 



