In fact, the best chronometers must be corrected from time to time, and the corrections are made by the aid of astronomic observations; arrangements are made so that the sidereal clock marks the same hour when the same star passes the meridian. In other words, it is the sidereal day, that is, the duration of the rotation of the earth, which is the constant unit of time. It is supposed, by a new definition substituted for that based on the beats of the pendulum, that two complete rotations of the earth about its axis have the same duration. However, the astronomers are still not content with this definition. Many of them think that the tides act as a check on our globe, and 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 perfect 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 [alpha] happens, causing as consequence at the end of a certain time the effect [alpha]'. At another place in the world very far away from the first, happens the phenomenon [beta], which causes as consequence the effect [beta]'. The phenomena [alpha] and [beta] are simultaneous, as are also the effects [alpha]' and [beta]'. Later, the phenomenon [alpha] is reproduced under approximately the same conditions as before, and _simultaneously_ the phenomenon [beta] is also reproduced at a very distant place in the world and almost under the same circumstances. The effects [alpha]' and [beta]' also take place. Let us suppose that the effect [alpha]' happens perceptibly before the effect [beta]'.