Mr green, on THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 33 



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 consequently 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 fpdv 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. 



7. The foregoing general observations being premised, we will proceed 

 in the present article to determine mathematically the law of the density 

 p, when the equilibrium has established itself in the interior of a con- 

 ducting sphere A, supposing it free from the actions of exterior bodies, 

 and that the particles of fluid contained therein repel each other with 

 forces which vary inversely as the w"" power of the distance. For this 

 purpose it may be remarked, that the formula (1), Art. 1, immediately 

 gives the values of the forces acting on any particle p, in virtue of 

 the repulsion exerted by the whole of the fluid contained in A. In 

 this way we get 



1 dV 

 - _ .-jr = the force directed parallel to the axis X, 



1 dV 



- ■ _ . y— = the force directed parallel to the axis Y, 



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. 



Vol. V. Paet I. E 



