IN THE INTERIOR OP TRANSPARENT BODIES. 413 



which forces are evidently zero, if the law of molecular force be such 

 as make C zero in all cases. 



If the law of molecular force be the inverse square of the distance 

 it is easy to see that C must be zero, no matter whether the force be 

 attractive or repulsive. 



For suppose that the molecular force (i. e mrfir)) equals ± — , then 



„, ri $*»+v+&p) 



-*2«.{p ;Z j. 



Since Zmf{r)§a? = ^mf{r)ly* = 2mJ\r)8* 

 in consequence of the symmetry : and this last expression 



= + ~2m 



\p ^J . 



which is zero (observing that r does not become oo for any particle under 

 the sign 2, since the displaced particle is not included under the sign 2). 



Hence C is zero if the molecular force be an attractive or repulsive 

 force varying inversely as the square of the distance ; and this is evidently 

 true no matter how many different kinds of particles compose the system. 

 Hence it is not likely that the molecular force is an attractive or repul- 

 sive force, varying inversely as the square of the distance. 



There is therefore good reason for supposing that C is not zero in 

 the equations (D), and we shall accordingly proceed upon that sup- 

 position. 



§ 17. I now proceed to prove two remarkable and very general 

 theorems respecting transverse and normal vibrations, by the help of which 

 the equations (Z)) may be reduced to very simple forms. I believe 

 that these theorems, at least the first of them, is capable of very important 

 applications. 



Vol. VII. Paet III. 3 A 



