FOECE 675 



by force, instead of supposing that its velocity is unchanged we may 

 suppose that its position or its acceleration is unchanged. 



Let us for a moment suppose that one of these two laws is a law 

 of nature, and substitute it for a law of inertia: what will be the 

 natural generalization? A moment's reflection will show us. In 

 the first case, we may suppose that the velocity of a body depends only 

 on its position and that of neighboring bodies; in the. second case, 

 that the variation of the acceleration of a body depends only on the 

 position of the body and of neighboring bodies, on their velocities 

 and accelerations; or, in mathematical terms, the differential equations 

 of the motion would be of the first order in the first case and of the 

 third order in the second. 



Let us now modify our supposition a little. Suppose a world ana- 

 logous to our solar system, but one in which by a singular chance the 

 orbits of all the planets have neither eccentricity nor inclination; 

 and further, suppose that the masses of the planets are too small 

 for their mutual perturbations to be sensible. Astronomers living 

 in one of these planets would not hesitate to conclude that the orbit 

 of a star can only be circular and parallel to a certain plane ; the posi- 

 tion of a star at a given moment would then be sufficient to determine 

 its velocity and path. The law of inertia which they would adopt 

 would be the former of the two hypothetical laws I have mentioned. 



Now, imagine this system to be some day crossed by a body of vast 

 mass and immense velocity coming from distant constellations. All 

 the orbits would be profoundly disturbed. Our astronomers would not 

 be greatly astonished. They would guess that this new star is in 

 itself quite capable of doing all the mischief; but, they would say, as 

 soon as it has passed by. order will again be established. No doubt 

 the distances of the planets from the sun will not be the same as 

 before the cataclysm, but the orbits will become circular again as soon 

 as the disturbing cause has disappeared. It would be only when \he 

 perturbing body is remote, and when the orbits, instead of being 

 circular are found to be elliptical, that the astronomers would find 

 out their mistake, and discover the necessity of reconstructing their 

 mechanics. 



I have dwelt on these hypotheses, for it seems to me that we can 

 clearly understand our generalized law of inertia only by opposing it 

 to a contrary hypothesis. 



Has this generalized law of inertia been verified by experiment, and 

 can it be so verified ? When Newton wrote the Principia, he certainly 

 regarded this truth as experimentally acquired and demonstrated. 

 It was so in his eyes, not only from the anthropomorphic conception 

 to which I shall later refer, but also because of the work of Galileo. It 

 was so proved by the laws of Kepler. According to those laws, in fact, 

 the path of a planet is entirely determined by its initial position and 



