of the canal CG to be such that the repulsion of the coatings AB and DF thereon shall be not sensibly less than if it was infinite, and that the thickness of the glass Gg is very small in respect of the distance of R from it, and that the repulsion of R does not sensibly alter the disposition of the fluid in Tt and Ss, and also that the repulsion of R on GC and EM together is not much less than if GM was infinite, and also not much greater than the repulsion of the glass NnvV on CG.

For let the quantity of fluid in Tt and Ss be so much altered that the united repulsion of R and those two coatings on the two canals GC and EM together, and also their repulsion on gP, shall be the same as that of the two coatings alone before the approach of R.

By Prop. II. Cor. 1. the quantity of fluid in Tt will be very little altered thereby, for the repulsion of R on the canal gP is very nearly the same as its repulsion on gC and EM together.

As the repulsion of Tt, Ss and R together on the two canals GC and EM together is the same as before the approach of R, it follows that if their repulsion on gC is less than before, their repulsion on EM will be as much increased.

Let now the quantity of fluid in AB and DF be so much altered that their repulsion on gC shall be as much diminished as that of Kkil and R on the same column is diminished, and that their repulsion on EM shall be as much diminished as that of Kkil and R on the same is increased, it is plain that the fluid in all three canals will be exactly in equilibrio, and by the preceding corollary the quantity of fluid in AB will be very little altered, and therefore the proportion of the redundant fluid in AB and Tt to each other will be very little altered*.

186] COR. VII. By Prop. [XXIV. Art. 86] all which is said in this proposition and corollaries holds good equally whether the canals GC, EM and GP are straight or crooked.

187] Let DE be an uniform canal of incompressible fluid infinitely continued towards E, and let A and B be given points in a right line with D, and let AB be bisected in C, the force with which any particle of fluid repels this canal (supposing the repulsion to be inversely as the square of the distance) is inversely as its distance from the point D, and therefore the sum of the forces with which two equal particles of fluid placed in A and B repels this canal is to the sum of the forces with which they would repel it if both collected in the point C,

188] Let us now examine how far the proportion of the quantity of fluid in the large circle and the two small ones in Experiment v., [Art. 273] Fig. 18, bear to each other will be affected by the circumstances mentioned in [Art. 276], supposing the plates to be connected by canals of incompressible fluid.

First it appears from Cor. [VII. Art. 186], that the quantity of redundant fluid in the large circle, and also in the two small ones, will bear very nearly the same proportion to that in the jar A as it would if it had been placed at an infinite distance from A, for the distance of the plate from the jar was in neither experiment less than 63 inches, and neither the length nor the diameter of the coated part of the jar exceeded four inches, so that the repulsion of the jar on the canal connecting it to the plate could not differ by more than 1 part from what it would be if the canal was infinitely continued, and would most probably differ from it by not more than or part of that quantity*; for the same reason the deficience of fluid in the trial plate will bear very nearly the same proportion to that in the jar, &c. as it would if it had been placed at an infinite distance from it.

* The repulsion of a globe 4 inches diameter on a straight uniform canal of incompressible fluid extending 63 inches from it differs by only part from what it would be if the canal was infinitely continued, but the repulsion of a Leyden vial of that size on the same column differs probably not more than or of that quantity from what it would be if infinitely continued.

It is plain that if the plates had been placed at such a distance from the jar that the quantity of fluid in them had been considerably less than if they had been placed at an infinite distance, still the quantity in the large circle would bear very nearly the same proportion to that in the two small ones as it would if they had been placed at an infinite distance.

189] Secondly, it is plain that in trying the large circle, the repulsion of that circle increases the deficience of fluid in the trial plate, and the attraction of the trial plate increases the redundance in the circle. Now the repulsion of the plate Ee on the canal mMNa, and the attraction of the trial plate T on rRSA (supposing mMNa and rRSA to be infinitely continued beyond a and A) are by [Cor. IV. Art. 183] very nearly the same as if the redundant fluid in Ee and the deficient fluid in T were both collected in the centers of their respective plates, and the quantity of redundant fluid in Ee may be considered as equal to the deficient in T, and consequently the repulsion of Ee on m MNa is very nearly equal to the attraction of T on rRSA. Moreover, the repulsion of Ee on its own canal rRSA must be equal to the attraction of T on mMNa, as the jars with which they communicate are both equally electrified, and therefore, by Cor. [IV.], the quantity of redundant fluid in Ee will be increased in very nearly the same ratio as the deficient in T.

190] In like manner, in trying the two small circles, the quantity of redundant fluid in them is increased in very nearly the same ratio as the deficient in T, for as half the distance of the two circles never bore a greater proportion to em than that of 18 to 72, the repulsion of the two circles on the canal m MNa will be very nearly the same, and the deficience of fluid in 7 will be increased in very nearly the same ratio as if all the redundant fluid in them were collected in e, the middle point between them.

The quantity of redundant fluid in Bb indeed will be increased in a rather greater ratio, and that in Cc in a rather less ratio than if it was placed at e, but the ratio in which the quantity of fluid in Bb is increased must very nearly as much exceed that in which it would be increased if it was placed at eas that in which Cc is increased falls short of it, as the attraction of T on the canal fRSA exceeds that on TRSA by nearly the same quantity as its attraction gRSA falls short of it, and therefore the quantity of redundant fluid in both circles together is increased in very nearly the same proportion as that in a circle placed ine would be, and consequently the redundance in the two circles. is increased in very nearly the same ratio as the deficience in the trial plate*.

* Memorandum relating to the second article.

191] The attraction of the trial plate on the canals fRSA and gRSA and the repulsion of the circles Bb and Cc on the canal mMNa is very nearly the same as if the deficient or redundant fluid in the plates was collected in the centre of their respective plates, and therefore the repulsion of the circles Bb and Cc on the canal mMNn is inversely as the distances of their centres from m, and the increase of the quantity of redundant fluid in the circles Bb and Cc by the attraction of T is in the same proportion.

192] Consequently, in trying either the large circle or the two small ones, the trial plate must be opened to very nearly the same surface to contain the same charge as them as it must be if they were placed at an infinite distance from the trial plate, and consequently no sensible alteration can be produced in the phenomena of the experiment by the repulsion and attraction of the circles and trial plate on each other.

193] Thirdly, for the same reason it appears that as the circles and the trial plate are both at much the same distance from the ground and walls of the room, no sensible alteration can be produced in the experiment by the ground near the circles being rendered undercharged and that near the trial plate overcharged.

It must be observed, indeed, that the distance of the circles and trial plate from the ground is much less than their distance from each other, and consequently the alteration of the charge of the two circles and trial plate produced by this cause will not be so nearly alike as that caused by their attraction and repulsion on each other; but as, on the other hand, the whole alteration of their charge produced by this cause is, I imagine, much less than that produced by the other, I imagine that this cause can hardly have a more sensible effect in the experiment than the preceding.

194] Fourthly, we have not as yet taken notice that the canals by which the jars Aa communicate with the ground are but short, and meet the ground at no great distance from the jars.

But it may be shewn by the same kind of reasoning used in Prop. [II. Art. 178], with the help of the second corollary to the preceding proposition, that the quantity of redundant fluid in the circles will bear very nearly the same proportion to that in the positive side of the jar A, whether the canal by which A communicates with the ground is long or short.

Besides that, if it was possible for this circumstance to make much alteration in the proportion which the redundant fluid in the circles bears to that in A, it would in all probability have very nearly the same effect in trying the two small circles as in trying the large one, so that no sensible alteration can be produced in the experiment from this circumstance.

It appears, therefore, that none of the above-mentioned circumstances can cause any sensible alteration in this experiment*.

Therefore take the point a so that the repulsion of a particle at a on that canal shall be a mean between the repulsions of the same particle thereon when placed at B and C, the charge of T will be increased in the same proportion as it would be by the repulsion of a plate containing as much redundant fluid as the two plates together whose centre was a, and the charge of the two circles together will also be increased in the same proportion as that of the circle whose centre is a would be thereby.

* [Note 17.]

[195

THOUGHTS CONCERNING ELECTRICITY.

195] Electricity seems to be owing to a certain elastic fluid interspersed between the particles of bodies, and perhaps also surrounding the bodies themselves in the form of an atmosphere.

196] This fluid, if it surrounds bodies in the form of an atmosphere, seems to extend only to an imperceptible distance from them*, but the attractive and repulsive power of this fluid extends to very considerable distances.

197] That the attraction and repulsion of electricity extend to considerable distances is evident, as corks are made to repel by an excited tube held out at a great distance from them. That the electric atmospheres themselves cannot extend to any perceptible distance, I think, appears from hence, that if two electric conductors be placed ever so near together so as not to touch, the electric fluid will not pass rapidly from one to the other except by jumping in the form of sparks, whereas if their electric atmospheres extended to such a distance as to be mixed with one another, it should seem as if the electricity might flow quietly from one to the other in like manner as it does through the pores of any conducting matter.

But the following seems a stronger reason for supposing that these atmospheres cannot extend to any perceptible distance from the body they surround, for if they did it should seem that two flat bodies whenever they were laid upon one another should always become electric thereby, for in that case there is no room for

There are several circumstances which shew that two bodies, however smooth and strongly pressed together, do not actually touch each other. I imagine that the distance to which the electric atmospheres, if there are any, extend must be less than the smallest distance within which two bodies can be made to approach.