250 Mb KELLAND, ON THE MOTION OF 



M. Biot carries with it the greatest weight, yet it is far from decisive, 

 and the subject appears to be still open to investigation. 



If, indeed, experimental enquiries had completely set this point at 

 rest, it would remain for us to determine whether the hypothesis 

 which we have adopted was applicable to sound. We should have, 

 if we did not entirely reject it, to introduce a modification, the effect 

 of which would be to cause the second term in the expansion of the 

 velocity to vanish. The same modification would probably apply to 

 the motion of light in vacuo. 



17. Regarding this part of our subject then as probably not 

 opposed to facts, although not deducible from them, let us recur to 

 our equations. 



We have seen that vibrations in the direction of transmission are 

 possible for any law of force, which can be expressed in terms of 

 powers of the reciprocal of the distance, greater than the first (4). 



Now if we suppose n some large quantity, since ^^ enters as the 



coefficient of the square of the velocity, P must be excessively small, 

 for the velocity itself is not large, and, in fact, bears a very small 

 ratio to that of light, which is expressed in an analogous form. 



We are then limited in the choice of our power on both sides — 

 first, n must be positive, secondly, not large, and we shall see pre- 

 sently it cannot be equal to unity. 



Suppose the particles acted on in such a manner that the moving 

 force of one on another is a quantity bearing a given finite ratio to 

 the velocity of transmission : this gives 



P P P 



but -—^ varies as (velocity)" = C, hence — ;p oc -|^; 



.•. - = M — 1 or n = 2. 



2 



