OF MOLECULAR FORCES. 107 



By an investigation precisely similar to that in Art. 11, we find 

 F' = d}V.x + .. 



G' = d* g V.y + ... 



H'-dlF % + .. 



Now, since 2 [-^r,] is necessarily positive, one at least of the quan- 

 tities, d}V, d 2 g V t d%V, in equation (1) is necessai-ily positive for all 

 values of n equal to or greater than 2 ; and consequently, one at 

 least of the equations (2) must necessarily denote translation. And 

 this is true whatever be the arrangement of the particles. 



But when n is less than 2 the right-hand member of (1) is 

 negative, in which case it is possible that all the equations (2) may 

 denote vibration. 



Hence, if the luminiferous ether consist of detached particles which 



attract each other with forces varying as yr , n must be less than 2. 



In a similar manner it may be shewn, that if the ether consist 

 of repulsive particles, n must be greater than 2. 



It must be remarked, however, that although these conditions with 

 regard to the value of n should be satisfied by the law of attraction 

 of the particles, yet their arrangement must be such as shall make 

 dyV, d\V, d\V all negative for every particle in the system, other- 

 wise it will be unstable and incapable of transmitting light. 



17. If the medium be of the kind denominated uncrystallized, the 

 vibration of a particle in any direction must be completed in the same 

 time, in which case the arrangement must be such as simultaneously 

 to satisfy the equations, 



d}V=dlV=dlV=^ s(2!L) f 

 n being less than 2. 



o2 



