112 Mb EARNSHAW, ON MOLECULAR FORCES. 



d}V + d g V + d\V = - il* {££ + 0>)} 



= — 2(/»\J/-r), 



and every one of the quantities d}V, d\V, d\V is negative, whether 

 the particle of ether (the state of which we are investigating) be within 

 a crystallized body, or in vacuo, or in an uncrystallized body. 



In order that V may be a maximum, we must have fulfilled the 

 following conditions, viz. 



d f V=0, d g V=0, d>V=0 (1), 



d}V, d g V, d\V all negative (2), 



and 



d}V.d g V>(d s d g vy 

 div.d\v>(d g d h vy 

 d}V.d\v>(d f d K vy 



(3). 



The three conditions marked (1) are fulfilled, because the particle 

 is in equilibrium by hypothesis ; we have shewn above that the three 

 conditions (2) are fulfilled, otherwise the medium could not be lumini- 

 ferous, i. e. its particles could not vibrate in any direction ; and the 

 last three conditions marked (3) are fulfilled, because the directions of 

 the co-ordinate axes have been taken, such that d f d g V =■ 0, d g d h V = 0, 

 and d f d h V = 0. Consequently V is a maximum. 



S. EARNSHAW. 



