32 Mr green, ON THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 

 But it is evident we may satisfy the last equation by making 



/«=(l-e)''^C7-«. 



Expanding now and replacing e?7„'''; e^UJ^^, &c. by these values UJIi, 

 U^%, &c. we get 



from which we may immediately deduce ^'® and thence successively 



/'« = r" (/„'« +/'« r'^ +/;« r" +//« r'» + &c.) 

 fW, !/, 85') =/'<"' +/'«+/'<^' + &c +/'« 



and > = (1 - X'"- - y" - z'"-y^.f(x', y , %), 



Application of the general Methods exposed in the preceding Articles 

 to Spherical conducting Sodies. 



(6) 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 perceive 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 consists in determining p* the analytical value of 



* It may not be Improper to remark that p is always supposed to represent the density 

 of the free fluid, or that which manifests itself by its repulsive force; and therefore, when 

 the hypothesis of two fluids is employed, the measure of the excess of the quantity of either 



fluid 



