THE VALUE OF SCIENCE 313 



V. 



But that is not all. In physical reality one cause does not pro- 

 duce a given effect, but a multitude of distinct causes contribute to 

 produce it, without our having any means of discriminating the part 

 of each of them. 



Physicists seek to make this distinction; but they make it only 

 approximately, and, however they progress, they never will make it 

 except approximately. It is approximately true that the motion of the 

 pendulum is due solely to the earth's attraction; but in all rigor every 

 attraction, even of Sirius, acts on the pendulum. 



Under these conditions, it is clear that the causes which have pro- 

 duced a certain effect will never be reproduced except approximately. 

 Then we should modify our postulate and our 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: 2 



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 proposi- 

 tion. 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 



2 'Etude sur les diverges grandeurs,' Paris, Gauthier-Villars, 1897. 



