3 i2 POPULAR SCIENCE MONTHLY 



that the rotation of the earth is becoming slower and slower. Thus 

 would be explained the apparent acceleration of the motion of the 

 moon, which would seem to be going more rapidly than theory permits 

 because our watch, which is the earth, is going slow. 



IV. 



All this is unimportant, one will say; doubtless our instruments of 

 measurement are imperfect, but it suffices that we can conceive a per- 

 fect instrument. This ideal can not be reached, but it is enough to 

 have conceived it and so to have put rigor into the definition of the 

 unit of time. 



The trouble is that there is no rigor in the definition. When we 

 use the pendulum to measure time, what postulate do we implicitly 

 admit? It is that the duration of two identical phenomena is the 

 same; or, if you prefer, that the same causes take the same time to 

 produce the same effects. 



And at first blush, this is a good definition of the equality of two 

 durations. But take care. Is it impossible that experiment may some 

 day contradict our postulate? 



Let me explain myself. I suppose that at a certain place in the 

 world the phenomenon a happens, causing as consequence at the end 

 of a certain time the effect a'. At another place in the world very 

 far away from the first, happens the phenomenon /?, which causes as 

 consequence the effect /?'. The phenomena a and /3 are simultaneous, 

 as are also the effects a and /?'. 



Later, the phenomenon a is reproduced under approximately the 

 same conditions as before, and simultaneously the phenomenon /3 is 

 also reproduced at a very distant place in the world and almost under 

 the same circumstances. The effects a and /3' also take place. Let us 

 suppose that the effect a happens perceptibly before the effect /3'. 



If experience made us witness such a sight, our postulate would be 

 contradicted. For experience would tell us that the first duration aa 

 is equal to the first duration /?£' and that the second duration aa is 

 less than the second duration /?/?'. On the other hand, our postulate 

 would require that the two durations aa' should be equal to each other, 

 as likewise the two durations /?/?'. The equality and the inequality 

 deduced from experience would be incompatible with the two equalities 

 deduced from the postulate. 



Now can we affirm that the hypotheses I have just made are absurd ? 

 They are in no wise contrary to the principle of contradiction. Doubt- 

 less they could not happen without the principle of sufficient reason 

 seeming violated. But to justify a definition so fundamental I should 

 prefer some other guarantee. 



