each other as to be of no use.

It is absolutely necessary, in working

with glass, to perform the experiment as quickly as possible.

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

Do., a thinner piece 3.284 7.65

Light flint

3.2

Dense flint......

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,

* Proceedings of the Royal Society, June 14, 1877; Phil. Trans., 1878, Part I., p. 17. † 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

and if the second condenser, whose capacity when its electrodes are in contact is 7+ 2m+n, is placed at a distance R from the first and connected to earth, its charge will be

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 + QR-1 and y+QR respectively.

1

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

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

The charges of a and b are (l+m) P and (m+n) P respect

ively, or

R(L+M) (l+m)

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

R(L+M) (m + n)

R2 − (L + 2M + N)(l + 2m+ n) *

In these expressions we must remember that M is a negative quantity, that L+M and M+ N can neither of them be negative, and that their sum L+ 2M+N cannot be greater than the largest semidiameter of the condenser. Hence if R is large compared with the dimensions of the condensers, the second term of the values of [AA] and [AB] will be quite insensible, and even if the condensers are placed very near together these terms will be small compared with L, M, or N.

If a, instead of being part of a condenser, is a conductor at a considerable distance from any other conductor, we may put m = n = 0, and if A is also a simple conductor, M=N=0, and we find

by which the capacities and mutual induction of two simple conductors at a distance R can be calculated when we know their capacities when at a great distance from other conductors. Note 24.

See

NOTE 17, ART. 194.

Theory of the Experiment with the Trial Plate.

Let A and B be the inner, a and b the outer coatings of the Leyden jars.

Let C be the body tried and D the trial plate, M the wire connecting A with C, and N the wire connecting b with D.

Let E be the electrometer with its connecting wires.

Let the coefficients of induction be expressed by pairs of symbols within square brackets, thus, let [(4+ C) (C + D)] denote the sum of the charges of A and C when C and D are both raised to potential 1 and all the other conductors are at potential 0.

First Operation.-The insides of the two jars are charged to potential P, the outsides and all other bodies being at potential 0.

The charge of A is [4 (A + B)]P, and that of b is [b (A + B)] P。.

Second Operation.-The outside coating of b is insulated, the charg ing wire is removed, and the inside of B is connected to earth. The charges of A and of b remain as before.

Third Operation.-A is connected to C by the wire M, and b is connected to D by the wire N.

The charge of A

is communicated to A, C, and M, and the potential of this system is P, and the charge of b is communicated to b, D and N, and the potential of this system is P..

1

Hence we have the following equations to determine P, and P, in terms of P.,

[(A + C + M) (A + C + M)] P1 + [(A + C + M ) (b + D + N)] P2

=

· [A (A + B)] P。,

(1)

[(A + C + M) (b + D + N )] P2 + [(b + D + N ) (b + D + N)] P2

Fourth Operation. The wires M and N are disconnected from C and D respectively, and the jars A and b are discharged and kept connected to earth.

The charges of C and D remain the same as before.

Fifth Operation.-The bodies C and D are connected with each other and with the electrometer E, and the final potential of the system CDE is observed by the electrometer to be P

Equating the final charge of the system CDE to that of the system CD at the end of the fourth equation,

[(C + D + E) (C + D + E )] P2 = [(C + D) (A + C + M)] P1

+ [(C + D) (b + D + N)] P2. Eliminating P, and P, from equations (1), (2) and (3), P2 [(C + D + E)2] {[(A + C + M)3] [(b + D + N)3]

= P。

J[4 (4 + 1

(3)

− [(A + C + M) (b + D + N)]2}

[A (A + B)] {[(C + D) (A + C + M )] [(b + D + N)3]
− [(C + D) (b + D + N)][(A + C + M) (b + D + N)]}
+ [b(A + B)] {[(C + D) (b + D + N )][(A + C + M)2]
− [(C + D) (A + C + M )] [(A + C + M ) (b + D + N)]}

(4)

By means of his gauge electrometer, Art. 249, Cavendish made the value of P, the same in every trial, and altered the capacity of D, the trial plate, so that P, in one trial had a particular positive value, and in another an equal negative value. He then wrote down the difference of the two values of D as an indication to guide him in the choice of trial plates, and the sum of the two values, by means of which he compared the charges of different bodies.

He then substituted for C a body, C', of nearly equal capacity, and repeated the same operations, and finally deduced the ratio of C to C' from the equation

C : C' :: D1 + D ̧ : D'' + D ̧'.

1

2

The capacities of the two jars were very much greater than any of the other capacities or coefficients of induction in the experiment, and of these [b (B+b)] was less than half the greatest diameter of the second

jar, and may therefore be neglected in respect of [b2] or [Bb]. We may therefore put [Bb] = - [b3], and in equation (4) neglect all terms except those containing the factors [4] [b] or [42] [Bb].

We thus reduce equation (4) to the form

P ̧[(C + D + E)2] = P。 {[(C + D) (A + C + M )] − [(C + D) (b + D + N)]} = P, {[C2] + [C' (A + M)] − [C (b + N)] -[D]-[D(b+N)] + [D (A + M)]}

(5)

The bodies to be compared were either simple conductors, such as spheres, disks, squares and cylinders, and those trial plates which consisted of two conducting plates sliding on one another, or else coated plates or condensers.

Now the coefficient of induction between a coated plate and a simple conductor is much less than that between two simple conductors of the same capacity at the same distance, and the coefficient of induction between two coated plates is still smaller. See Note 16.

Hence if both the bodies tried are coated plates, the equation (5) is reduced to the form

P ̧([C'3] + [D2] + [E']) = P. ([C2] - [D3]),

(6)

so that the experiment is really a comparison of the capacities of the two bodies C and D.

But if either of them is a simple conductor, we must add to its capacity its coefficient of induction on the wire and jar with which it is connected, and subtract from it its coefficient of induction on the other wire and jar. These two coefficients of induction are both negative, but that belonging to its own wire and jar is probably greater than the other, so that the correction on the whole is negative.

Hence in Cavendish's trials the capacity deduced from the experiment will be less for a simple conductor than for a coated plate of equal real capacity.

This appears to be the reason why the capacities of the plates of air when expressed in "globular inches," that is, when compared with the capacity of the globe, are about a tenth part greater than their computed values. See Art. 347.

It would have been an improvement if Cavendish, instead of charging the inside of both jars positively and then discharging the outside of B, had charged the inside of A and the outside of B from the same conductor, and then connected the outside of both to earth, using the inside of B instead of the outside, to charge the trial plate negatively. In this way the excess of the negative electricity over the positive in B would have been much less than when the outside was negative.

With a heterostatic electrometer, such as those of Bohnenberger or Thomson, in which opposite deflections are produced by positive and negative electrification, the determination of the zero electrification may