Theory of Molecular Action according to Newton's Law. 127 

 commence to move in the direction of a normal. But on ac- 

 count of the existing relation, the three quantities -^ , 



. u -, -tto-j cannot all have the same sign. The surface is 

 dg z an 1 



consequently an hyperboloid, and thus " there are in general 

 only three directions in which a particle can be displaced, so 

 that the force called into play may act in the direction of the 

 displacement." It appears then that " the constitution of a 

 medium, composed of detached attractive particles, can never 

 be such that the force of restitution called into play by a dis- 

 turbance in any direction shall act in the line of displacement. 

 Hence those media which are distinguished as uncrystallized 

 cannot consist of detached particles which either attract or re- 

 pel each other, with forces varying inversely as the square of 

 the distance; because it is assumed as a characteristic of such 

 media, that the forces of restitution act always in the direc- 

 tion of displacement." (Art. 10.) 



To this argument there are two objections: — 



a. That the excepted case embodies the real state of things ; 



b. That even were it otherwise, nothing is established against 

 the molecular theorv. 



d?X d?V 



dp -°> dg* 



• yi = is excepted ; indeed the author expressly points 



out this circumstance in Art. 8. We proceed to show that 

 this is the very case to be considered, in a medium of sym- 

 metry. But this phrase will perhaps itself raise an objec- 

 tion to our arguments. We hope to be excused then if we 

 make a short digression hereupon. A medium of perfect 

 symmetry, it has been argued, " has never been shown to 

 exist in nature, nor is it proved even that it can exist." We 

 reply that, most assuredly, a medium of perfect symmetry 

 amongst detached particles cannot exist in nature. It is quite 

 inconceivable. Those who have adopted it, have done so " fo; 

 the sake of simplifying their equations." (Earnshaw, Phil. 

 Mag., S. 3. vol.xx. May 1842, p. 37Q). Nor have they regarded 

 themselves as proceeding without reasons as valid and as well 

 founded as those on which any one process in mathematical 

 physics is based. If it be true from experiment that it is per- 

 fectly indifferent in what direction light passes through certain 

 media, then is it of necessity equally true that the sensible 

 forces are .altogether uninfluenced by direction. And more- 

 over if it is quite the same thing whether motion takes place 

 from right to left or from left to right, it is inconceivable that 



a. It is evident that the case in which -j-^ — 0, , * = 0, 



