FORCE 685 



nothing paradoxical in the relative motion of two bodies being dis- 

 turbed when the motion of one or the other is modified by an external 

 cause. NOT need I dwell on the case of relative motion referring to 

 axes which rotate uniformly. If the sky were forever covered with 

 clouds, and if we had no means of observing the stars, we might, 

 nevertheless, conclude that the earth turns round. We should be 

 warned of this fact by the flattening at the poles, or by the experiment 

 of Foucault's pendulum. And yet, would there in this case be any 

 meaning in saying that the earth turns round? If there is no abso- 

 lute space, can a thing turn without turning with respect to some- 

 thing; and, on the other hand, how can we admit Newton's conclu- 

 sion and believe in absolute space? But it is not sufficient to state 

 that all possible solutions are equally unpleasant to us. We must 

 analyze in each case the reason of our dislike, in order to make our 

 choice with the knowledge of the cause. The long discussion which 

 follows must, therefore, be excused. 



Let us resume our imaginary story. Thick clouds hide the stars 

 from men who cannot observe them, and even are ignorant of their 

 existence. How will those men know that the earth turns round ? No 

 doubt, for a longer period than did our ancestors, they will regard the 

 soil on which they stand as fixed and immovable. They will wait a 

 much longer time than we did for the coming of a Copernicus; but 

 this Copernicus will come at last. How will he come? In the first 

 place, the mechanical school of this world would not run their heads 

 against an absolute contradiction. In the theory of relative motion we 

 observe, besides real forces, two imaginary forces, which we call ordi- 

 nary centrifugal force and compounded centrifugal force. Our imag- 

 inary scientists can thus explain everything by looking upon these two 

 forces as real, and they would not see in this a contradiction of the 

 generalized principle of inertia, for these forces would depend, the one 

 on the relative positions of the different parts of the system, such as 

 real attraction?, and the other on their relative velocities, as in the 

 case of real frictions. Many difficulties, however, would before long 

 awaken their attention. If they succeeded in realizing an isolated 

 system, the centre of gravity of this system would not have an ap- 

 proximately rectilinear path. They could invoke, to explain this fact, 

 the centrifugal forces which they would regard as real, and which, 

 no doubt, they would attribute to the mutual actions of the bodies 

 only they would not see these forces vanish at great distances that is 

 to say, in proportion as the isolation is better realized. Far from it. 

 Centrifugal force increases indefinitely with distance. Already this 

 difficulty would seem to them sufficiently serious, but it would not 

 detain them for long. They would soon imagine some very subtle 

 medium analogous to our ether, in which all bodies would be bathed, 

 and which would exercise on them a repulsive action. But that is not 



