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of the cylinder will be increased. The capacity of the cylinder in presence of a conducting plane at distance c, is

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Thus in Cavendish's experiment he used a brass wire 72 inches long and 0.185 in diameter. The capacity of this wire at a great distance from any other body would be 5.668 inches. Cavendish placed it horizontally 50 inches from the floor. The inductive action of the floor would increase its capacity to 5.994 inches; Cavendish, by comparison with his globe, makes it 5.844.

To compare with this he had two wires each 36 inches long and 0.1 inch diameter.

The capacity of one of these at a distance from any other body would be 2.8697 inches, or the two together would be 5·7394 inches.

The two wires were placed parallel and horizontal at 50 inches from the floor. Each wire was therefore influenced by the other wire, and also by the negative images of itself and the other wire.

The denominator of the fraction expressing the capacity is therefore

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The numerator of the fraction which expresses the capacity of both wires together is 36, so that the capacity of the two is

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If we suppose the plate AB to be overcharged and the plate DF to be equally undercharged, the redundant fluid in any element of AB being numerically equal to the deficient fluid in the corresponding element of DF, then what Cavendish calls the repulsion on the column CE in opposite directions becomes in modern language the excess of the potential at Cover that at E. Hence the object of the Lemma is to determine approximately the difference of the potentials of two curved plates when their equal and opposite charges are given, and to deduce their charges when the difference of their potentials is given.

NOTE 15, Art. 169.

On the Theory of Dielectrics.

Cavendish explains the fact discovered by him, that the charge of a coated glass plate is much greater than that of a plate of air of the same dimensions, by supposing that in certain portions of the glass the electric fluid is free to move, while in the rest of the glass it is fixed.

Probably for the sake of being able to apply his mathematical theorems, he takes the case in which the conducting parts of the glass are in the form of strata parallel to the surfaces of the glass. He is perfectly aware that this is not a true physical theory, for if such conducting strata existed in a plate of glass, they would make it a good conductor for an electric current parallel to its surfaces. As this is not the case, Cavendish is obliged to stipulate, as in this proposition, that the conducting strata conduct freely perpendicularly to their surfaces, but do not conduct in directions parallel to their surfaces.

The idea of some peculiar structure in plates of glass was not peculiar to Cavendish. Franklin had shewn that the surface of glass plates could be charged with a large quantity of electricity, and therefore supposed that the electric fluid was able to penetrate to a certain depth into the glass, though it was not able to get through to the other side, or to effect a junction with the negative charge on the other side of the plate.

The most obvious explanation of this was by supposing that there was a stratum of a certain thickness on each side of the plate into which electricity can penetrate, but that in the middle of the plate there was a stratum impervious to electricity. Franklin endeavoured to test this hypothesis by grinding away five-sixths of the thickness of the glass from the side of one of his vials, but he found that the remaining sixth was just as impervious to electricity as the rest of the glass*.

It was probably for reasons of this kind, as well as to ensure that his thin plates were of the same material as his thick ones, that Cavendish prepared his thin plate of crown glass by grinding equal portions off both sides of a thicker plate. [Art. 378.]

It appears, however, from the experiments, that the proportion of the thickness of the conducting to the non-conducting strata is the same for the thin plates as the thick ones, so that the operation of grinding must have removed non-conducting portions as well as conducting ones, and we cannot suppose the plate to consist of one non-conducting stratum with a conducting stratum on each side, but must suppose that the conducting portions of the glass are very small, but so numerous that they form a considerable part of the whole

* Franklin's Works, 2nd Edition, Vol. 1. p. 301, Letter to Dr Lining, March 18, 1755.

volume of the glass. If we suppose the conducting portions to be of small dimensions in every direction, and to be completely separated from each other by non-conducting matter, we can explain the phenomena without introducing the possibility of conduction through finite portions of glass.

It was probably because Cavendish had made out the mathematical theory of stratified condensers, but did not see his way to a complete mathematical theory of insulating media, in which small conducting portions are disseminated, that he here expounds the theory of strata which conduct electricity perpendicularly to their surfaces but not parallel to them.

In forming a theory of the magnetization of iron, Poisson was led to the hypothesis that the magnetic fluids are free to move within certain small portions of the iron, which he calls magnetic molecules, but that they cannot pass from one molecule to another, and he calculates the result on the supposition that these molecules are spherical, and that their distances from each other are large compared with their radii.

When Faraday had afterwards rediscovered the properties of dielectrics, Mossotti, noticing the analogy between these properties and those of magnetic substances, constructed a mathematical theory of dielectrics, by taking Poisson's memoir and substituting electrical terms for magnetic, and Italian for French, throughout.

A theory of this kind is capable of accounting for the specific inductive capacity being greater than unity, without introducing conductivity through portions of the substance of sensible size.

Another phenomenon which we have to account for is that of the residual charge of condensers, and what Faraday called electric absorption. The only notice which Cavendish has left us of a phenomenon of this kind is that recorded in Arts. 522, 523, in which it appeared "that a Florence flask contained more electricity when it continued charged a good while than when charged and discharged immediately."

To illustrate this phenomenon, I gave in "Electricity and Magnetism," Art. 328, a theory of a dielectric composed of strata of different dielectric and conducting properties.

Professor Rowland has since shown* that phenomena of the same kind would be observed if the medium consisted of small portions of different kinds well mingled together, though the individual portions may be too small to be observed separately.

It follows from the property of electric absorption that in experiments to determine the specific inductive capacity of a substance, the result depends on the time during which the substance is electrified. Hence most of those who have attempted to determine the value of this quantity for glass have obtained results so inconsistent with

* American Journal of Mathematics, No. I. 1878, p. 53.

each other as to be of no use.
with glass, to perform the experiment as quickly as possible.

It is absolutely necessary, in working

Cavendish does not give the exact duration of one of his "trials,” but each trial probably took less than two or three seconds. His results are therefore comparable with those recently obtained by Hopkinson*, who effected the different operations by hand.

The results obtained by Gordont, who employed a break which gave 1200 interruptions per second, and those obtained by Schiller‡ by measuring the period of electric oscillations, which were at the rate of about 14000 per second, are much smaller than those obtained by Cavendish and by Hopkinson.

Hopkinson finds that the quotient of the specific inductive capacity divided by the specific gravity does not vary much in different kinds of flint glass. As Cavendish always gives the specific gravity, I have compared his results with those of Hopkinson for glass of corresponding specific gravity.

Electrostatic capacity of glass.

Specific Caven- Hop- Wüllner. Gordon. Schiller. gravity. dish. kinson.

Flint-glass

3.279 7.93

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To find the effect on the capacity of a condenser arising from the presence of another condenser at a distance which is large compared with the dimensions of either condenser.

Let A and B be the electrodes of the first condenser, let L and N be the capacities of A and B respectively, and M their coefficient of mutual induction, then if the potential of A is 1 and that of B is 0, the charge of A will be L and that of B will be M, and if both A and B are at potential 1 the charge of the whole will be L+ 2M + N,

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p. 17.

Proceedings of the Royal Society, June 14, 1877; Phil. Trans., 1878, Part I., ↑ Proc. R. S. Dec. 12, 1878. Pogg. Ann. 152 (1874), p. 535.

and this cannot be greater than half the greatest diameter of the condenser.

Let a and b be the electrodes of the second condenser, let its coefficients be l, m, n, and let its distance from their first condenser be R.

Let us first take the condenser AB by itself, and let us suppose that the potentials of A and B are x and y respectively, then their charges will be Lx+ My and Mx + Ny respectively.

At a distance R from the condenser the potential arising from these charges will be

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and if the second condenser, whose capacity when its electrodes are in contact is 1+ 2m+n, is placed at a distance R from the first and connected to earth, its charge will be

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This charge of the second condenser will produce a potential QR-1 at a distance R, and will therefore alter the potentials of A and B by this quantity, so that the potentials of A and B will be + QR1 and y+QR respectively.

To find the capacity of A as altered by the presence of the second condenser, we must make the potential of A= 1 and that of B = 0, which gives

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and the capacity of A is Lx + My or L+ (L+M) y, or

[AA] = L +

(L+M)3 (l + 2m+ n)
R-(L+2M+N) (l + 2m+ n)'

The charge of B is Mx + Ny or M+(M+N) y, or

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The charges of a and b are (l + m) P and − (m + n) P respectively, or

[Aa] =

R(L+M) (l+m)
R-(L+2M+N) (1+2m+n)
R(L+M) (m + n)

[Ab] = − R2 − (L + 2M+N)(l+2m+n)

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