THE EQUILIBRIUM OP FLUIDS. 151 



2 2.4 



n 4 . n 2 . n 

 2.4.6 



from which we may immediately deduce fj (i} and thence suc- 

 cessively 



f(x', y', ) -/">+/' +/'< 2 > + &c... +/"", 



"i /.a /2 '2 '2\ *> _/? / / ' '\ 



and p = (1 cc y & ) f (m ? V & ) 



Application of the general Methods exposed in the preceding 

 Articles to Spherical conducting Bodies. 



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 ^Epinus and others, 

 that the particles of matter when deprived of their natural quan- 

 tity 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 quan- 

 tity 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 determin- 

 ing p* the analytical value of the fluid's density, so % that the 



* 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 which we choose to consider as positive over that of 

 the fluid of opposite name in any element dv of the volume of the body is expressed 

 by pdv, whereas on the other hypothesis pdv serves to measure the excess of the 

 quantity of fluid in the element dv over what it would possess in a natural state. 



