Attractions of Charged Spheres 37 



I think there can be no doubt, but what this proposition must hold good 

 in general. 



18] LEMMA IV. Let BDE, bde, and /JSe (Fig. 2), be concentric spherical 

 surfaces, whose center is C : if the space * Bb is filled 

 with uniform matter, whose particles repel with a 

 force inversely as the square of the distance, a 

 particle placed anywhere within the space Cb, as 

 at P, will be repelled with as much force in one 

 direction as another, or it will not be impelled in 

 any direction. This is demonstrated in Newton, 

 Princip. Lib. I, Prop. 70. It follows also from his 

 demonstration, that if the repulsion is inversely as 

 some higher power of the distance than the square, 

 the particle P will be impelled towards the center ; and if the repulsion is 

 inversely as some lower power than the square, it will be impelled from 

 the center f. 



19] LEMMA V. If the repulsion is inversely as the square of the 

 distance, a particle placed anywhere without the sphere BDE, is repelled 

 by that sphere, and also by the space Bb, with the same force that it would 

 if all the matter therein was collected in the center of the sphere ; provided 

 the density of the matter therein is everywhere the same at the same 

 distance from the center. This is easily deduced from Prop. 71, of the same 

 book, and has been demonstrated by other authors. 



20] PROP. V. PROBLEM i. Let the sphere BDE be filled with uniform 

 solid matter, overcharged with electric fluid: let the fluid therein be 

 moveable, but unable to escape from it: let the fluid in the rest of infinite 

 space be moveable, and sufficient to saturate the matter therein ; and let 

 the matter in the whole of infinite space, or at least in the space Bfi, 

 whose dimensions will be given below, be uniform and solid; and let the 

 law of the electric attraction and repulsion be inversely as the square of 

 the distance : it is required to determine in what manner the fluid will be 

 disposed both within and without the globe. 



Take the space Bb such, that the interstices between the particles of 

 matter therein shall be just sufficient to hold a quantity of electric fluid, 

 whose particles are pressed close together, so as to touch each other, equal 

 to the whole redundant fluid in the globe, besides the quantity requisite 

 to saturate the matter in Bb ; and take the space Bfi such, that the matter 

 therein shall be just able to saturate the redundant fluid in the globe: 



* By the space Bb or Bfi, 1 mean the space comprehended between the spherical 

 surfaces BDE and bde, or between BDE and /38: by the space Cb or C|3, I mean 

 the spheres bde or flfif. 



{f Hence the only law according to a power of the distances which permits 

 absence of force inside a charged shell is the inverse square.} 



