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 LV. On the Time Scale. By E. Buckingham *. 



IN the examination of our notion of time which is 

 necessitated by recent speculalions, one point hardly 

 seems to receive the attention it merits. This is the evident 

 fact that in the nature of things time is not a measurable 

 quantity ; that times can be numbered in accordance with 

 any system we please which does not introduce ambiguity 

 into the meanings of "before/' "after," and "at the same 

 time" ; and that no system has any more justification than 

 another, a priori. 



We have a simple criterion by which we may decide 

 whether two temperatures are the same or which is the 

 higher. When we go farther and express temperatures or 

 intervals of temperature by numbers, we do so by adopting 

 an arbitrary convention for numbering temperature, in other 

 words, a scale. With regard td time, the case is analogous. 

 W T e can say that two events are simultaneous, or that one 

 occurs later than the other, and all other observers will 

 agree with us if they are situated as we are With relation to 

 the two events. But when we go farther and say lioiv much 

 later one event is than the other, we adopt a scale fof 

 numbering time : we do not measure it in any proper sense, 

 for a past interval of time cannot be superposed upon nor 

 substituted for one now elapsing or to come, so that the 

 fundamental operation which lies at the basis of all trtie 

 measurement is not Only absent but in the nature of things 

 impossible. Tomorrow differs qualitatively from today, as the 

 warmth of summer does from the chill of winter. As with tem- 

 perature, our choice of a scale has been and always will be 

 dictated solely by convenience and subject to arbitrary change 

 whenever we change our minds as to what is most convenient. 



Why is it that we use mean solar time instead of sun- 

 dial time ? Because if we use mean solar time a body not 

 acted on by any push or pull that we can detect moves 

 " uniformiter in directum." We can use Newton's first law 

 if we adopt this mode of numbering time, but not if we 

 adopt an essentially different one. Newton's laws are the 

 simplest and most perspicuous summary of the facts of pure 

 dynamics, and for this reason and this only, we adopt a time 

 scale which shall make them a correct representation of the 

 observed facts. In effect, we use the first law to fix our 

 time scale. It would be an utter absurdity to say that we 

 "assume" that time "really" does progress in this wav. 

 An assumption is a proposition of which the truth or falsity 

 can be decided by reference to some independent criterion ! 

 a definition is neither true nor false, it is only useful or not 

 * Communicated bj the Author. 



