ELECTRICITY. 



541 



iTieoretical 

 Klectncity. 



Pr ATE 

 CCL1. 

 Fig. 19. 



Electrical 

 attraction 

 and repul- 

 on. 



g. 19. 



notice of the effect which the body A will have in al- 

 tering the quantity and disposition of the fluid in B ; 

 but in reality this will make the bodies attract each 

 other with more force than they would otherwise do ; 

 for in each of these cases the body A attracts the fluid 

 in B ; which will cause some fluid to flow from the far- 

 ther parts of B to the nearer, and will also cause some 

 fluid to flow into it, if it is not insulated, and will con- 

 sequently cause B to act upon A with more force than 

 it would otherwise do. 



Cote 4. Let us now suppose that B is negatively 

 electrified ; and let A be insulated, and contain just 

 fluid enough to saturate it, they will attract each other; 

 for B will' be undercharged; it will therefore attract 

 the fluid in A, and will cause some fluid to flow from 

 the farthest part of A, where it is attracted with less 

 force, to the nearest part, where it is attracted with 

 more force ; so that B will attract the fluid in A with 

 more force than it repels the matter. 



Case 5. and 6. If A is now supposed to be not insu- 

 lated and not electrified, B being still negatively elec- 

 trified ; it is plain that they will attract with more force 

 than in the last case : and if A is positively electrified, 

 they will attract with still more force. 



!n these last tliree cases also, the effect which A has 

 in altering the quantity and disposition of the fluid in 

 B, tends to increase the force with which the two bo- 

 dies attract. 



Case 7- It is plain, that a non-conducting body satu- 

 rated with fluid, is not at all attracted or repelled by an 

 over or tinder charged body, until, by the action of the 

 electrified body on it, it has either acquired some addi- 

 tional fluid from the air, or had some driven out of it, 

 or till some fluid is driven from one part of the body to 

 the other. 



Cate 8. Let us no\r suppose that the two bodies A 

 and B are both positively electrified in the same de- 

 gree. It is plain, that were it not for the action of one 

 body on the other, they would both be overcharged, 

 and would repel each other. But it may perhaps be 

 said, that one of them, as A, may, by the action of the 

 other on it, be either rendered undercharged on the 

 whole, or at least may be rendered undercharged in 

 that part nearest to B ; and that the attraction of this 

 undercharged part on a particle of the fluid in B, may 

 be greater than the repulsion of the more distant over- 

 charged part : so that on the whole the body A may at- 

 tract a particle of fluid in B. If so, it must be affirm- 

 ed, that the body B repels the fluid in A ; for other- 

 wise, that part of A which is nearest to B could not be 

 rendered undercharged. Therefore, to obviate this ob- 

 jection, let the bodies be joined by the straight canal 

 DC of incompressible fluid (Fig. 19.) The body B will 

 repel the fluid in all parts of this canal ; for as A is 

 upposed to attract the fluid in B, B will not only be 

 more overcharged than it would otherwise be, but it 

 will also be more overcharged in that part nearest to 

 A, than in the opposite part. Moreover, as the near 

 undercharged part of A is supposed to attract a particle 

 of fluid in B, with^ more force than the more distant 

 overcharged part repels it ; it must, a fortiori, attract a 

 particle in the canal with more force than the other re- 

 pels it; therefore the body A must attract the fluid in 

 the canal ; and consequently some fluid must flow from 

 B to A, which is impossible ; for as A and B are both 

 electrified in the same degree, they contain the same 

 quantity of fluid as if they both communicated with a 

 third body at an infinite distance, by canals of incom- 

 pressible fluid ; and therefore by the cor. to Prop. 22, 

 if a communication is made between them by a canal 



of incompressible fluid, the fluid would have no dispo- 

 sition to flow from one to the other. 



Case 9. But if one of the bodies, as A, is positive, 

 ly electrified in a less degree than B, then it is possi- 

 ble for the bodies to attract each other ; for in this case 

 the force with which B repels the fluid in A may be so 

 great, as to make the body A either entirely under- 

 charged, or at least to make the nearest part of it so 

 much undercharged, that A shall on the whole attract 

 a particle of fluid in B. It may be worth remarking, 

 with regard to this case, that when two bodies, both 

 electrified positively but unequally, attract each other, 

 you may, by removing them to a greater distance from, 

 each other, cause them to repel ; for as the stronger 

 electrified body repels the fluid in the weaker with less 

 force when removed to a greater distance, it will not be 

 able to drive so much fluid out of it, or from the nearer 

 to the farther part, as when placed at a less distance. 



Cate 10. and 11. By the same reasoning it appears, 

 that if the two bodies are both negatively electrified in 

 the same degree, they must repel each other : but if 

 they are both negatively electrified in different degrees, 

 it is possible for them to attract each other. 



All these cases are conformable to experiment. 



Case 12. Let two cork balls be suspended by con- 

 ducting threads, from the same positively electrified 

 body, in such a manner, that if they did not repel, they 

 would hang close together : they will both be equally 

 electrified, and will repel each other : let now an over- 

 charged body, more strongly electrified than them, be 

 brought under them ; they will become less overchar- 

 ged, and will separate less than before: on bringing 

 the body still nearer, they will become not at all over- 

 charged, and will not separate at all : and on bringing 

 the body still nearer, they will become undercharged, 

 and will separate again. 



Case 13. Let all the air of a room be overcharged ; 

 and let two cork balls be suspended close to each other 

 by conducting threads communicating with the wall. 

 By Prop. 13, it is highly probable that the balls will be un- 

 dercharged ; and therefore they should repel each other. 



These last two cases are experiments of Mr Canton's, 

 and are described in Phil. Trail*. 1753, p. 350, where 

 are other experiments of the same kind, all readily ex- 

 plicable by the preceding theory. 



3. On the cases in which bodies receive electricity 

 from or part with it to the air. 



Lemma 1. Let the body A, Fig. 6, either stand near 

 some over or under charged body, or at a distance from 

 any. It seems highly probable, that if any part of its 

 surface, as M N, is overcharged, the fluid will endea- 

 vour to run out through that part, provided the air ad- 

 jacent to it is not overcharged. 



For let G l>e any point in that surface, and P a point 

 within the body, extremely near to it ; it is plain that a 

 p.-irticle of fluid at P must be repelled with as much 

 force in one direction as another (otherwise it could not 

 be at rest), unless all the fluid between P and G is 

 i t'd close together ; in which case it may be repel- 

 led with more force towards G, than it is in the contra- 

 ry direction : now, a particle at G is repelled in the di- 

 rection PG, i. e. from P to G, by all the redundant fluid 

 between I' and G ; and a particle at P is repelled by 

 the same fluid in the contrary direction ; so that, as the 

 particle at P is repelled with not less force in the di- 

 rection PG than in the contrary, MrC. does not see how 

 a particle at G can help being repelled with more force 

 in that direction than the contrary, unless the air on 

 the outside of the surface MX was more overcharged 

 than the space between P and G. 



Theoretical 

 Electricity. 



On cases 

 in which 

 bodies re- 

 ceive elec- 

 tricity from 

 or part 

 with it to 

 the air. 



Lemma 1. 



PLATE 

 CCLI. 

 Fig. 6. 



