676 SCIENCE AND HYPOTHESIS 



initial velocity; this, indeed, is what our generalized law of inertia 

 requires. 



For this principle to be only true in appearance lest we should 

 fear that some day it must be replaced by one of the analogous prin- 

 ciples which I opposed to it just now we must have been led astray 

 by some amazing chance such as that which had led into error our 

 imaginary astronomers. Such an hypothesis is so unlikely that it need 

 not delay us. No one will believe that there can be such chances; no 

 doubt the probability that two eccentricities are both exactly zero is 

 not smaller than the probability that one is 0.1 and the other 0.2. 

 The probability of a simple event is not smaller than that of a 

 complex one. If, however, the former does occur, we shall not attri- 

 bute its occurrence to chance; we shall not be inclined to believe that 

 nature has done it deliberately to deceive us. The hypothesis of an 

 error of this kind being discarded, we may admit that so far as astro- 

 nomy is concerned our law has been verified by experiment. 



But Astronomy is not the whole of Physics. May we not fear that 

 some day a new. experiment will falsify the law in some domain of 

 physics? An experimental law is always subject to revision; we may 

 always expect to see it replaced by some other and more exact law. But 

 no one seriously thinks that the law of which we speak will ever be 

 abandoned or amended. Why? Precisely because it will never be 

 submitted to a decisive test. 



In the first place, for this test to be complete, all the bodies of the 

 universe must return with their initial velocities to their initial posi- 

 tions after a certain time. We ought then to find that they would re- 

 sume their original paths. But this test is impossible; it can be 

 only partially applied, and even when it is applied there will still be 

 some bodies which will not return to their original positions. Thus 

 there will be a ready explanation of any breaking down of the law. 



Yet this is not all. In Astronomy we see, the bodies whose motion 

 we are studying, and in most cases we grant that they are not subject 

 to the action of other invisible bodies. Under these conditions, our 

 law must certainly be either verified or not. But it is not so in 

 Physics. If physical phenomena are due to motion, it is to the motion 

 of molecules which we cannot see. If, then, the acceleration of bodies 

 we cannot see depends on something else than the positions or veloci- 

 ties of other visible bodies or of invisible molecules, the existence of 

 which we have been led previously to admit, there is nothing to 

 prevent us from supposing that this something else is the position or 

 velocity of other molecules of which we have not so far suspected 

 the existence. The law will be safeguarded. Let me express the same 

 thought in another form in mathematical language. Suppose we are 

 observing n molecules, and find that their 3n co-ordinates satisfy a 

 system of 3n differential equations of the fourth order (and not of 



