VOL. Lxi.] Philosophical transactions. 225 



repel 1 grain of electric fluid with as much force as n grains of lead repel n grains 

 of lead. 



All bodies in their natural state, with regard to electricity, contain such a 

 quantity of electric fluid interspersed between their particles, that the attraction 

 of the electric fluid in any small part of the body, on a given particle of matter, 

 shall be equal to the repulsion of the matter in the same small part on the same 

 particle. A body in this state Mr. C. calls saturated with electric fluid; if the 

 body contains more than this quantity of electric fluid, he calls it overcharged: 

 if less, he calls it undercharged. This is the hypothesis; he now proceeds to 

 examine the consequences which will flow from it. 



Lemma 1. — Let EAe (pi. 6, fig. 1) represent a cone continued infinitely; let a 

 be the vertex, and b6 and nrf planes parallel to the base; and let the cone be 

 filled with uniform matter, whose particles repel each other with a force in- 

 versely as the n power of the distance. If n is greater than 3, the force with 

 which a particle at a is repelled by Esbe, or all that part of the cone beyond b^, 



is as — TTT- For supposing ah to flow, the fluxion of Esbe is proportional to 



— AB X AB*, and the fluxion of its repulsion on a is proportional to 



~ "*" : the fluent of which is ■ ; which when ab is infinite is 



^b"- 2 n - 3 X ab"" i 



equal to nothing; consequently the repulsion of EB^-e is proportional to 



or to 



u-SxAB'-J AB'-J 



Carol. If ab is infinitely small, — ;:tr^ is infinitely great; therefore the repul- 

 sion of that part of the cone between a and b^, on A, is infinitely greater than 

 the repulsion of all that beyond it. 



Lemma 1. — By the same method of reasoning it appears, that if n is equal to 

 3, the repulsion of the matter between -rI and xid on a particle at a, is propor- 

 tional to the logarithm of — ; consequently, the repulsion of that part is infi- 

 nitely small in respect of that between a and b^, and also infinitely small in 

 respect of that beyond nrf. 



Lemma 3. — In like manner, if n is less than 3, the repulsion of the part be- 

 tween A and ^h on a is proportional to abJ - " : consequently the repulsion of the 

 matter between a and b6 on a, is infinitely small in respect of that beyond it. 



Carol. It is easy to see, from these 3 lemmata, that if the electric attraction 

 and repulsion had been supposed to be inversely as some higher power of the 

 distance than the cube ; a particle could not have been sensibly affected by the 

 repulsion of any fluid, except what was placed close to it. If the repulsion was 

 inversely as the cube of the distance, a particle could not be sensibly affected by 

 the repulsion of any finite quantity of fluid, except what was close to it. But 



VOL. XXII. G G 



