ELECTRICITY. 



fluid, with ii much force as lour grains of lead attract 

 it, and one grain of electric fluid will repel one grain of 

 clcitric fluid, with a> much force as four grains of lead 

 wfll re|>el four grains of It-ad. 



All bodies in tlu-ir n.itural stile, w itli regard to elec- 

 tricity, contain such n quantity of i-lcctric fluid, intt r- 

 9j>er*cd bctwicn their particles. that the attraction of 

 tfi< electric fluid, in any small part of the body, on a 

 given particle of matter, shall he equal to the repulsion 

 of the matter, in the snnie small part on the same par- 

 ticle. When a body is in this suite. Mr Cavendish calls 

 it taturated mi h clfctucjluid ; when the Ixxly contains 

 more than this quantity of electric fluid, he calls itourr 

 charged, and when it contains less, he calls it under. 

 charged. 



I.erain* I. Lemma 1. Let EA r (Plate CCLI. Fig. 1.) repre- 

 sent a cone continued infinitely ; let A be the vertex, 

 and B b and D d planes parallel to the base ; and let the 

 cone be filled with uniform matter, whose particles repel 

 each other with a force inversely as the n power of 

 the distance. If n is greater than 3, the force with 

 which a particle at A is repelled by EBAe, or all that 



part of the cone beyond B b is as _ ) . For sup- 



posing AB to flow, the fluxion of EB 6 e is proportion- 

 al to AB X AB 1 , and the fluxion of its repulsion on 



A is proportional to ^-ft ( ^- ; the fluent of which is 

 ' wn ' cn wnen AB is infinite is equal to 



fCI.I. 



r. i. 



nothing ; consequently the repulsion of EB b e is pro- 

 portional to - or to . 



Carol. If AB is infinitely small, _ ^ is infinitely 



great ; therefore the repulsion of that part of the cone 

 between A and B b, on A, is infinitely greater than 

 the repulsion of all that beyond it. 



- : 3. I.nnma 2. By the same method of reasoning it ap- 

 pears, that if n is equal to 3, the repulsion of the mat- 

 ter between B b and D d on a particle at A, is pro- 



AD 



portional to the logarithm of - =- ; consequently, the 



An 



repulsion of that part is infinitely small in respect of 

 that between A and B b, and also infinitely small in 

 respect of that beyond D d. 



I'ura 3. Lemma 3. In like manner, if n is less than 3, the 

 repulsion of the part between A and B 6 on A is pro- 

 portional to AB' "; consequently, the repulsion of the 

 matter between A and B b on A, is infinitely small in 

 respect of that beyond it. 



Dejiiiiliun. If the electric fluid in any body is by any 

 means confined in such a manner that it cannot move 

 from one part of the body to the other, it is called 

 immoveable : if it is able to move readily from one 

 part to another, it is called moveaUc. 



r*or. 1. Prop. 1. A body overcharged with electric fluid at- 

 tracts or repels a particle of matter or fluid, and is at- 

 tracted or repelled by it, with exactly the same force 

 a* it would, if the matter in it, together with so much 

 of the fluid as is sufficient to saturate it, was taken away, 

 or as if the body consisted only of the redundant fluid 

 in it. In like manner an undercharged body attracts 



(.'i|{ 1. 



or repels with the same force, as if it consisted only Theoretical 

 of the redundant matter; the electric lluiil, together I'-Kftricity. 

 with so much of the matter a- i- -ullicient to s.-ilurate 

 it, being taken away. Tlii- is c\idcnt from the dc- 

 Jinitioii of saturation. 



/'/<//). II. Two over or undercharged bodies attract p Eop 

 or repel each other with jiM the same force that they 

 would, if each body consisted only of the- redundant 

 fluid in it, if overcharged, or of the redundant mat- 

 ter in it, if undercharged. For, let the two bodies be 

 called A and 15: by the last proposition, the rt iliindatit 

 substance in B impcU each particle of fluid and matter 

 in A, and con.-c<|iici:tly ini|>els the whole body A, with 

 the same force that the whole Inxlv 1! hii|>els it : for the 

 same reason, the redundant substance in A impels the 

 redundant substance in 15, with the same force that the 

 whole body A impels it. It is shown, therefore, that 

 the whole body B impels the whole body A, with the 

 same force that the redundant uli-tance in 15 impels 

 the whole body A, or with which the whole body A 

 impels the redundant substance in 1! ; and that the 

 whole body A impels the redundant substance in B 

 with the same force that the redundant substance in A 

 impels the redundant substance in B. Therefore the 

 whole body B impels the whole body A, with the 

 same force with which the redundant substance in A 

 impels the redundant substance in B, or with which 

 the redundant substance in B impels the redundant 

 substance in A. 



( 'oral. Let the matter in all the rest of space, except 

 in two given bodies, be saturated with immoveable fluid; 

 and let the fluid in those two bodies be also immoveable. 

 Then, if one of the bodies is saturated, and the other 

 either over or under charged, they will not at all attract 

 or repel each other. If the bodies are both overchar- 

 ged, they will repel each other. If they are both un- 

 dercharged, they will also repel each other. If one is 

 o\crchargcd and the other undercharged, they will at- 

 tract each other. 



N. n. In this corollary it is understood that a body 

 overcharged is overcharged in all parts, or at least no 

 where undercharged ; in like manner, that a body un- 

 dercharged is undercharged in all parts, or at least no 

 where overcharged. 



Prop. III. If all the bodies in the universe are satu- PS.OP. 3, 

 rated with electric fluid, it is plain that no part of the 

 fluid can have any tendency to move. 



Prop. IV. If the quantity of electric fluid in the uni- PHOP. 4 

 verse is exactly sufficient to saturate the matter there- 

 in, but unequally dispersed, so that some Ixxlies are 

 overcharged and others undercharged ; then, if the elec- 

 tric fluid is not confined, it will immediately move till 

 all the bodies in the universe are saturated. For, sup- 

 posing 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 undercharged, a particle at its surface 

 will be attracted towards the body by the redundant 

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



Lemma !. Let BDE, bile, and ,3 2 1, (Fig. 2.) be con- Lemma &. 

 centric spherical surfaces, whose centre is C; if the 

 space * lii is filled with uniform matter, whose particles F '8- * 

 repel with a force inversely as the square of the distance; 

 a particle placed any where within the space C6, as at 

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



By the ipace Bi or B/Si is meant ihc space comprehended between the 'poetical surface* BDE and 

 and /iJt > bjr the pace C* or C/3, to meant the spheres We or /93t< 



or between BDE 



