definition. Instead of saying: ‘The same causes take the same time to produce the same effects,’ we should say: ‘Causes almost identical take almost the same time to produce almost the same effects.’
Our definition therefore is no longer anything but approximate. Besides, as M. Calinon very justly remarks in a recent memoir:[1]
One of the circumstances of any phenomenon is the velocity of the earth’s rotation; if this velocity of rotation varies, it constitutes in the reproduction of this phenomenon a circumstance which no longer remains the same. But to suppose this velocity of rotation constant is to suppose that we know how to measure time.
Our definition is therefore not yet satisfactory; it is certainly not that which the astronomers of whom I spoke above implicitly adopt, when they affirm that the terrestrial rotation is slowing down.
What meaning according to them has this affirmation? We can only understand it by analyzing the proofs they give of their proposition. They say first that the friction of the tides producing heat must destroy vis viva. They invoke therefore the principle of vis viva, or of the conservation of energy.
They say next that the secular acceleration of the moon, calculated according to Newton’s law, would be less than that deduced from observations unless the correction relative to the slowing down of the terrestrial rotation were made. They invoke therefore Newton’s law. In other words, they define duration in the following way: time should be so defined that Newton’s law and that of vis viva may be verified. Newton’s law is an experimental truth; as such it is only approximate, which shows that we still have only a definition by approximation.
If now it be supposed that another way of measuring time is adopted, the experiments on which Newton’s law is founded would none the less have the same meaning. Only the enunciation of the law would be different, because it would be translated into another language; it would evidently be much less simple. So that the definition implicitly adopted by the astronomers may be summed up thus: Time should be so defined that
- ↑ Etude sur les diverses grandeurs, Paris, Gauthier-Villars, 1897.
