VOL. LXI.3 PHILOSOPHICAL TRANSACTIONS. 227 



dercharged; in like manner, when he calls it undercharged, he means that it is 

 undercharged in all parts, or at least no where overcharged. 



Prop. 3. — If all the bodies in the universe are saturated with electric fluid, it 

 is plain that no part of the fluid can have any tendency to move. 



Prop. 4. — If the quantity of electric fluid in the universe is exactly sufficient 

 to saturate the matter therein, but unequally dispersed, so that some bodies are 

 overcharged and others undercharged ; then, if the electric fluid is not confined, 

 it will immediately move till all the bodies in the universe are saturated. — For, 

 supposing that any body is overcharged, and the bodies near it are not, a particle 

 at the surface of that body will be repelled from it by the redundant fluid within; 

 consequently some fluid will run out of that body ; but if the body is under- 

 charged, a particle at its surface will be attracted towards the body by the redun- 

 dant matter within, so that some fluid will run into the body. 



N. B. In prob. 4, case 3, there will be shown an exception to this proposition: 

 there may perhaps be some other exceptions to it: but he thinks there can be 

 no doubt that this proposition must hold good in general. 



Lemma 4. — Let bde, bde, and ^h (fig. 2) be concentric spherical surfaces, 

 whose centre is c : if the space* bZ> is filled with uniform matter, whose particles 

 repel with a force inversely as the square of the distance; a particle placed any 

 where within the space ch, 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 demon- 

 strated in Newt. Princip. lib. 1 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 centre; and if the repulsion 

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

 centre. 



Lemma 5. — If the repulsion is inversely as the square of the distance, a par- 

 ticle placed any where without the sphere bde, is repelled by that sphere, and 

 also by the space sb, with the same force that it would if all the matter therein 

 was collected in the centre of the sphere; provided the density of the matter in 

 it is every where the same at the same distance from the centre. This is easily 

 deduced from prop. 7 ] of the same book, and has been demonstrated by other 

 authors. 



Prop. 5, prob. I. — Let the sphere bde be filled with uniform solid matter, 

 overcharged with electric fluid; let the fluid in it be moveable, but unable to 

 escape from it: let the fluid in the rest of infinite space be moveable, and suffi- 

 cient to saturate the matter in it; and let the matter in the whole of infinite 



* By the space b6 or B/S, Mr. C. means the space comprehended between the spherical surfaces 

 BDE and bde, or between bde and /S^i: by the space c6 or C/8, he means the spheres bde or /3^'. 

 — Orig. 



GG 2 



