110 Mr EARNSHAW, ON THE NATURE 



Then as in (16), we have 



d}V + dlV+dlV= - (n - 2) 2 (J^) ; 



equations which do not contain the quantity /d. 



I think it therefore not improbable, that each particle of the lumi- 

 niferous ether exerts two forces, one attractive . and varying reciprocally 

 as the square of the distance; and the other repulsive and varying 

 inversely in a higher ratio than the square; at any rate this supposi- 

 tion does away with the necessity of the envelope mentioned at the 

 beginning of this article. 



21. Let us now generalize the problem, and inquire for what laws 

 of molecular force vibration is possible in the particles of ether. 



Let tyr be the law of molecular force; and assume V = — 2 {mf r <f>r) ; 



.-. d)V+dlV+dlV=--2 L(^ + 0V)}, 

 (p'r for brevity denoting d r (pr. 



Now one condition to be fulfilled is, that d)V+djV+ d\ V= a nega- 

 tive quantity, and consequently the law of force must be such that 



2 d>r 



— *— + <p'r = a positive quantity ; 



for all values of r from r = the distance between two neighbouring 

 particles, to r = oo ; let ^r be any function of r which is positive be- 

 tween these limits, then 



-f- +<pr = ^r; 



.'. %r<pr + r*<p'r = r^-^r, 



.-. r*<pr = C+ t(f*+r), 



