106 Mr EARNSHAW, ON THE NATURE 



15. It appears then that at the most, the equilibrium can only be 

 stable in one plane; and that the medium may be so constituted that 

 the equilibrium shall be stable only in one line. The character of in- 

 stability, which in the preceding articles we have shewn necessarily 

 attaches to a medium constituted of particles placed at finite intervals, 



and attracting each other with forces varying as -=p, cannot be removed 



by supposing the particles to repel each other with forces varying ac- 

 cording to the same law. The equation d} V + d*K+ d\ V = 0, frOm 

 which the instability arises, holds equally for attraction and repulsion. 



It may be observed also that the instability cannot be removed by 

 arrangement; for though the values of d)V, d^V, d\V depend upon the 

 arrangement of the particles, the fact that one at least must be posi- 

 tive and one negative depends only upon the equation d}V+d\V + dlf r =0, 

 which is true for every arrangement. And consequently, whether the 

 particles be arranged in cubical forms, or in any other manner, there 

 will always exist a direction of instability. 



It is therefore certain, that the medium in which luminiferous waves 

 are transmitted to our eyes is not constituted of such particles. The 

 coincidence of numerical results, derived from the hypothesis of a 

 medium of such particles, with experiment, only shews that numeri- 

 cal results are no certain test of theory, when limited to a few cases 

 only. 



16. It has been noticed, that the instability of a system depends 

 upon the equation d) V + d% V + d\ V = 0. With the ordinary law of 

 attraction it always holds good. If, however, the force of molecular 



attraction be assumed to vary as -j^, and we write 



V for 2 l!-4 , 

 n — 1 



we shall find 



d}V+ d)V + dlV= (n - 2) 2 (A) (i). 



