362 Note 2: distribution of an attracting fluid 



ordinary statements of the theory of two fluids, which usually assert that 

 bodies, under all circumstances, contain immense quantities of both fluids. 



In the two-fluid theory, by depriving matter of both fluids, we get an in- 

 active substance which gives us no trouble, but in the one-fluid theory, matter 

 deprived of fluid exerts a strong attraction on the fluid, the consideration of 

 which would considerably complicate the mathematical problem. 



[In connexion with this remark and with Note 3 a quotation from Green's 

 Memoir of 1833 ( 6) is relevant. 



" In order to explain the phenomena which electrified bodies present, 

 Philosophers have found it advantageous either to adopt the hypothesis of 

 two fluids, the vitreous and resinous of Dufay for example, or to suppose with 

 jEpinus and others, that the particles of matter when deprived of their natural 

 quantity of electric fluid, possess a mutual repulsive force. It is easy to per- 

 ceive that the mathematical laws of equilibrium deducible from these two 

 hypotheses ought not to differ, when the quantity of fluid or fluids (according 

 to the hypothesis we choose to adopt) which bodies in their natural state are 

 supposed to contain is so great, that a complete decomposition shall never be 

 effected by any forces to which they may be exposed, but that in every part 

 of them a farther decomposition shall always be possible by the application of 

 still greater forces. In fact the mathematical theory of electricity merely con- 

 sists in determining p the analytical value of the fluid's density, so that the 

 whole of the electrical actions exerted upon any point p, situated at will in the 

 interior of the conducting bodies, may exactly destroy each other, and conse- 

 quently p have no tendency to move in any direction. For the electric fluid 

 itself, the exponent n is equal to 2, and the resulting value of p is always such 

 as not to require that a complete decomposition should take place in the body 

 under consideration; but there are certain values of n for which the resulting 

 values of p will render $pdv greater than any assignable quantity; for some 

 portions of the body it is therefore evident that how great soever the quantity 

 of the fluid or fluids may be, which in a natural state this body is supposed to 

 possess, it will then become impossible strictly to realize the analytical value 

 of p, and therefore some modification at least will be rendered necessary, by the 

 limit fixed to the quantity of fluid or fluids originally contained in the body, 

 and as Dufay's hypothesis appears the more natural of the two, we shall keep 

 this principally in view, when in what follows it may become requisite to 

 introduce either."] 



Infinite plate with plane parallel surfaces. 



The distribution of the fluid in an infinite plate with plane parallel surfaces 

 is given in the general solution which we have obtained for a body bounded 

 by a quadric surface, namely, p - Cp n ~*. 



In the case of the plate we must suppose it bounded by the planes x = + a, 

 and x a, and then p is defined by the equation 



x 2 = a 2 (i - />). 



