(It depends also on the curvature of the knobs, and on the medium between A and B ; but we suppose these conditions to remain constant.)

Hence, if we keep the distance between A and B fixed, the difference of potential between A and B at the moment when the jar discharges itself in a spark across the gap A B will also be fixed. Let us now put the outer coating of the jar to earth, put A at a fixed distance (that we will call 1) from B, and charge the jar by placing the knob D near the prime conductor of a machine; and let us suppose that it takes a difference of potential measured by v, for a spark to pass from A to B.

Then on charging the jar we shall shortly perceive a brilliant discharge to pass from A to B; this discharge leaving the jar uncharged. At the moment of this discharge there was on the inner coating a charge + Q, determined by the relation

There was, on the inner surface of the outer coating, a charge -Q; and there had passed to earth a quantity + Q1.

Hence, every time that the jar discharges itself, the + Q, and the Q1, that are opposed to each other, neutralise each other; while there has passed to earth a quantity + Q1.

If we put A and B at a distance apart twice as great as before, or at a distance 2, then we have Q2 = K. V2= K. 21 = 2 QI

Let us now see how the unit jar is used. We connect the outside coating of our small unit jar with the inside of a large Leyden jar whose outer coating is to earth.

1

If we now work the machine, then each time that the unit jar discharges itself we know that a certain quantity + Q1 of electricity has passed away from the outside of the unit jar into the large jar. And so, by counting the sparks of discharge of the unit jar, we are able to give the large jar a charge represented by Q1, 2 Q1, 3 Q1, &c.

Comments and notes.-(i.) We ought to have the unit jar so small as compared with the jar to be charged, and the knobs A and B at such a distance apart, that a considerable number of discharges of the unit jar may take place by the time that we have given the required charge to the large jar. For we cannot stop charging the moment that a spark passes, and therefore there will always be a fraction of + Q, in excess given to the large jar.

(ii.) We have said that, at each discharge of the unit jar, a quantity + Q has passed into the large jar. This is not accurately true. The outside of the unit jar is a small conductor at a considerable distance from surrounding bodies, and the inside of a large jar is a relatively large conductor having the outer coating of the jar very near it and opposed to it. These two form one conductor at one potential, since they are connected; but the capacity of the first is negligibly small as compared with that of the second. The charge + Q1 distributes itself between these two portions of the conductor in the ratio of their capacities. Hence, we may say that very nearly the whole charge, that would have passed to earth if the outside of the unit jar had been to earth, will have passed into the large jar.

(iii.) It requires a certain difference of potential v for a spark to pass between A and B. If then A is connected with the prime conductor of the machine, and B with the inside of a large jar, we cannot charge this latter up to the full potential of the prime conductor, but to a potential less than this by the amount v.

§ 9. Cascade arrangement of Leyden Jars.-P, Q, and R are three Leyden ars mounted on insulated stands, arranged 'in

R

cascade' as indicated in the figure. These jars must be equal in capacity. To insure this we may take one jar of many that are presumably equal, and then by comparison choose two or more others equal to it. If we give a certain charge to our jar chosen, and measure the potential of the inside (when the outside is to earth), this potential ought to fall to one-half when the knob is connected with that of an uncharged equal jar. This method is employed in Chapter IX. § 4.

But for rough experimental purposes it will be sufficient to choose the jars as follows. Let an electrical machine be worked for some time so that it has got into a constant condition. Then charge the jars in question with a unit jar interposed, as shown in the last section. If the jars refuse further charge after the same number of discharges of the unit jar have taken place, then their capacity will be approximately equal.

Having arranged our three (or more) jars as shown, let us work the machine.

When no more charge will pass, then the inside of the first jar will be at a potential V1; which will be that of the prime conductor, or something less, according as the knob is or is not in contact with the prime conductor. The outside of the first jar and the inside of the second jar (in contact with the former) will be at some lower potential V. The outside of the second jar and the inside of the third will be at a still lower potential V; 3; and the outside of the third will be at zero potential, which we may call Vo of zero-V, as we please.

Now, as shown in the last section, if there be in the first jar a 'bound' charge + Q, then there has passed into the second jar also a quantity + Q, and from the outside of this into the third jar also a quantity + Q, if we neglect the trivial 'free' charges on the outside of the first jar and on the knob of the second jar, and

so on.

That is, in the cascade arrangement we have of necessity equal charges in the jar. But by Chapter VI. § 4 (explained further in Chapter X.) we have

for second jar Q = K. (V2 — V3)

2

for third jar Q=K. (V3 - Vo).

So that, since Q and K are the same for each jar, we see that

V1 − V2 = V2 − V3 = V3 — V0 = 3 (V1 — Vo).

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Hence the total fall of potential that is possible, viz. the fall measured by V1 Vo (or by V1, since we take V。 as our zero), has been broken up into three equal falls.

(This is somewhat like the breaking up of a large waterfall into three smaller ones.)

Now let us consider the charge Q' that is given to one of these jars when its outside coating is to earth and its inside coating is at the potential V, of the prime conductor; ie. its charge, when it has been charged in the usual way. By our formula we shall have

Q' = K. (V1 - Vo).

But by what has preceded we see that this equals 3Q. Hence Q' = 3Q.

We see then that the sum of all the charges given to the jars, when these are arranged in cascade, equals the charge given to a single jar when this is treated in the usual manner.

The above reasoning can readily be extended to any number n jars. For further on the 'cascade arrangement' the reader is referred to Chapter X. § 30.

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§ 10. Nature of the Leyden Jar Charge. It is now time to investigate, as far as we are able, what is meant by the expression 'an electric charge.' All that we have hitherto observed indicates that neither + charges,' nor charges,' can exist by themselves; but that there must always co-exist two equal charges of opposite sign. In fact, it would seem that in all electrostatic phenomena there inust be a + charge and an equal — charge, separated by some insulating medium called a dielectric. It is probable that in the case of two conductors thus separated by a dielectric it is the surfaces of the dielectric in immediate contact with the conductors that are in the condition that we have called '+charged' and '- charged' respectively; though it is usual, and perhaps more convenient, to speak of the conductors them. selves as so charged.

Various experiments tend to show that the dielectric is, under these conditions, subjected to a stress; and to this it yields to a greater or less degree, becoming deformed or strained.

The conductors appear to play somewhat the following part. They mark out the portion of the dielectric that can be converted into an electric field and can be put under a stress; and they allow this stress to be imposed or taken away with rapidity. If the stress be continued for a sufficient time, it is found that all solid dielectrics become strained (or distorted) to an appreciable distance from the conducting surfaces; and that then the strain cannot at once be removed, or the 'condensor' cannot be at once discharged. Some of the stress remains and must be allowed to be relieved gradually. This gives rise to the residual charges' discussed below.

Experiments. (i.) Leyden jar with moveable coatings. —A is a Leyden jar so constructed as to be separable into three portions; B the glass jar, D the inside coating, and C the outside coating.

The jar is put together, charged as usual, and then placed on an insulating stand. The inside is then removed, a small charge coming away with it, and

a small charge being 'set free' on the outside coating. Then the glass is lifted out of its outer coating and set down on the table, and finally the outer coating may be handled and removed. In all this we notice but very slight discharges on touching D and C respectively.

On carefully putting the whole together again (on the insulating stand), a discharging rod (fig. ii.) will show us that the whole charge of the condenser has been (approximately) unaffected by the above process. Hence, since the coatings B and C were separately put to earth by handling, the charge of the condenser must have resided in the glass. We could not, how

ever, discharge the glass by itself; it was necessary to have the metal coatings as distributors.

(ii.) Residual charge.-The penetration of the charge, from the surfaces inwards, is shown by the following.

If a Leyden jar be discharged and then left for a time, a second small discharge can be obtained, and so on.

That the interior of the glass is actually strained or distorted is shown by the fact that its optical properties, when it is under the electrical stress, undergo an alteration similar to or identical with that produced by mechanical stress.

FIG. ii.

When the electrical stress is excessive, the material may give way and a hole may be made; through this a discharge takes place, since the air which then separates the two charges is far weaker to withstand the stress than is glass.

§ 11. Various Effects of the Discharge.-The Leyden jar gives us a means of observing the effects of electrical discharge. There is nothing essentially different between the discharge between the prime conductor and the floor and walls, where was collected the induced charge of opposite sign, and the discharge between the inner and outer coatings of the Leyden jar. Only the latter