674 SCIENCE AND HYPOTHESIS 



We might endeavor to enunciate the fundamental law of mechanics 

 in a language independent of all these conventions; and no doubt we 

 should in this way get a clearer idea of those laws in themselves. This 

 is what M. Andrade has tried to do, to some extent at any rate, in his 

 Lemons de Mecanique physique. Of course the enunciation of these 

 laws would become much more complicated, because all these con- 

 ventions have been adopted for the very purpose of abbreviating and 

 simplifying the enunciation. As far as we are concerned, I shall 

 ignore all these difficulties; not because I disregard them, far from it; 

 but because they have received sufficient attention in the first two 

 parts of the book. Provisionally, then, we shall admit absolute time 

 and Euclidean geometry. 



The Principle of Inertia. A body under the action of no force can 

 only move uniformly in a straight line. Is this a truth imposed on 

 the mind a priori ? If this be so, how is it that the Greeks ignored it ? 

 How could they have believed that motion ceases with the cause of 

 motion? or, again, that every body, if there is nothing to prevent it, 

 will move in a circle, the noblest of all forms of motion ? 



If it be said that the velocity of a body cannot change, if there is 

 no reason for it to change, may we not just as legitimately maintain 

 that the position of a body cannot change, or that the curvature of its 

 path cannot change, without the agency of an external cause? Is, 

 then, the principle of inertia, which is not an a priori truth, an exper- 

 imental fact? Have there ever been experiments on bodies acted on 

 by no forces ? and, if so, how did we know that no forces were acting ? 

 The usual instance is that of a ball rolling for a very long time on a 

 marble table ; but why do we say it is under the action of no force ? 

 Is it because it is too remote from all other bodies to experience any 

 sensible action? It is not further from the earth than if it were 

 thrown freely into the air; and we all know that in that case it 

 would be subject to the attraction of the earth. Teachers of mechan- 

 ics usually pass rapidly over the example of the ball, but they add that 

 the principle of inertia is verified indirectly by its consequences. This 

 is very badly expressed; they evidently mean that various conse- 

 quences may be verified by a more general principle, of which the 

 principle of inertia is only a particular case. I shall propose for 

 this general principle the following enunciation: The acceleration 

 of a body depends only on its position and that of neighboring bodies, 

 and on their velocities. Mathematicians would say that the move- 

 ments of all the material molecules of the universe depend on 

 differential equations of the second order. To make it clear that this 

 is really a generalization of the law of inertia we may again have 

 recourse to our imagination. The law of inertia, as I have said above, 

 is not imposed on us a priori; other laws would be just as compatible 

 with the principle of sufficient reason. If a body is not acted upon 



