wire. Between a and P, f and Q, there should be wire of the same thickness and length respectively. In fig. ii., m is a small plane mirror revolving on a horizontal axis that lies parallel to the line of the three sparks a b, c d, and ef.

Above it is a horizontal screen of ground glass, marked out in degrees in a manner indicated later on.

The mirror can be made to revolve rapidly, its rate of revolution being indicated by clockwork or by the musical note produced by its striking a fine metal wire.

If the discharges take place very rapidly, then a person looking down from above will see some of the sparks reflected in the mirror as it passes through the position proper for reflection of the sparks to the eye; others of the sparks will not be seen, owing to the mirror being unsuitably situated at the moment of their

Occurrence.

The rotation of the mirror will of course distort, by 'drawing out' in the direction of the motion any spark that lasts an appreciable time; i.e. that lasts while the mirror has moved appreciably.

Now it is found that, for moderate rates of revolution of the mirror, we see on the screen X Y merely three points of light,

lying parallel to the sparks of which they are the images, as represented in fig. iii.

But when the mirror revolves with sufficient rapidity, we see these points drawn out' into three lines of equal length, covering a number of degrees on the glass screen that is definite for each definite rate of revolution of the mirror, as indicated in fig. iv.

Further, we see that the bright lines answering to the sparks

H

ab and ef have their ends lying in a direction parallel to the line of sparks, while the bright line answering to the spark cd is displaced as shown.

This shows (i.) that the duration of the spark is such that the mirror turns through an appreciable angle while it is reflecting; and (ii.) that, whereas the sparks ab and eƒ occur simultaneously, the spark cd occurs later than either.

The fact that the spark has duration was perhaps obvious beforehand; we cannot conceive of 'no duration.' But this apparatus gives us a measure of the duration of a spark under any particular conditions of distance between a and b, and nature of the intervening gas.

But the fact that the lines answering to the sparks ab and ef are still similarly situate shows that these occur simultaneously, and that the discharge is of the dual nature indicated before, and that when we speak of its 'passing from one coating of the jar to the other' we are but using a convenient convention.

§14. The Condensing Electroscope.-Before concluding this chapter on condensers, we must describe the 'condensing electroscope,' a piece of apparatus in which the principle of experiment (v.) of § 2 in this chapter is made use of. If the reader will turn to the figure to Chapter XI. § 3, he will there see the apparatus in question represented.

On the plate N of a gold-leaf electroscope is placed another plate M, separated from the first by a thin insulating film of shellac.

When M is put to earth, the plate N considered by itself will have a capacity very large as compared with its capacity when 'isolated.' Hence, if it and the gold leaves are raised to a very low potential when M is to earth, the charge that it has received will suffice to raise it to a potential many times greater when M is removed. Thus the leaves, which did not stir when at some small difference v from zero, may diverge widely when this has been multiplied to (say) 500 v.

We can, in fact, multiply any potential v by the fraction,
capacity of N, when M is on it, and is to earth
capacity of N when isolated

§ 15. Various Forms of Electrical Discharge.-We have many times alluded to the passage of a 'spark' or 'disruptive electrical

discharge.' It may not be out of place to enumerate a few of the forms in which this discharge may take place.

I. The ordinary spark.-When we approach the finger, or any other conductor, to the prime conductor of a machine, or to any other conductor that is of a high potential but has not a very great capacity, the discharge usually takes place in the form of a jagged spark of no very great luminosity. If the opposed surfaces be of very gentle curvature, as e.g. two spheres of large radius, the spark will be straighter and more brilliant. In both cases there will be heard a sharp crack or other report. II. The Leyden jar discharge.-In the Leyden jar we have stored up a quantity of electricity that is very great as compared with that stored on any ordinary isolated conductor. In Leyden jar discharges the spark is usually very brilliant and dense in appearance, and much straighter than in case (i.) above. Moreover, the sound is very strident.

III. The brush discharge.-If any projecting part of the prime conductor of a machine be of very sharp curvature, or still more if it be pointed, the discharge from this part will be in the form of a beautiful faintly luminous brush, and this discharge will be nearly or quite silent.

IV. Discharge in vacuo.'-When the discharge takes place through a tube or other vessel in which the air or other gas is very rare, the whole tube is filled with a faint luminosity, and there is no sound.

CHAPTER VII.

INDUCTION MACHINES.

§ 1. Some further Propositions in the Theory of Potential.— Still pursuing our system of introducing more and more of the theory of potential as we require it, we shall here discuss certain points that we must make clear before we can rightly understand the theory of induction machines.

By induction machines we mean those pieces of apparatus by means of which we can obtain continuous supplies of + and electricity without any friction or chemical action; the essentials being (1) an initial supply of electricity that can act inductively on conductors placed near to it, and (2) mechanical work to effect such movements of the parts of the apparatus as shall give us continuous action. The common electrophorus is the simplest form of such a machine; and the reader can see how it differs in principle from a frictional machine, though in both cases mechanical work is the source of energy.

(i.) There is no field of force inside a simple closed conductor.— If we have a simple closed conductor, that is, a closed vessel containing no insulated charged bodies, it can be shown experimentally that there is no field of force inside it, or that it, and all the space inside it, are at one potential.

(ii.) Concerning partially closed vessels.-If we experiment with a partially closed vessel, such as a tin pail whose height is greater than the diameter of the mouth, and if it be placed so that those external objects which are opposite to the opening are relatively remote, then we shall find that there is no appreciable field of force in the inside of the vessel.

(iii.) Insulated uncharged conductors inside a vessel.—If into the inside of a charged vessel there be introduced an uncharged conductor, there is nothing to alter the fact of the potential being the

same throughout. The insulated conductor is in a region of no field of force, and hence there is no inductive action between it and the charged vessel. The conductor is at the same potential

as this vessel and the space inside it.

(iv.) An insulated uncharged conductor partially inside a vessel. -Let A be an insulated vessel charged +, and let B be an insulated uncharged conductor partly inside and partly outside the vessel.

The conductor B must be at one potential; and yet the one end is more remote from the vessel than is the other end.

B +

1

FIG. i.

As in Chapter IV. § 14 (i.), and in Chapter VI. § 2 (i.), there will be a redistribution of electricity a on B, there being a charge on the end inside A, and the complementary + charge on the end outside the whole of B being at a potential below that of A but above that of the earth. There will be also inside A a portion of its + charge equal to the charge induced on the lower end of B. All this can be shown experimentally. It is what we should expect from Chapter VI. § 2 (i.).

A;

(v.) An earth-connected body inside a vessel.—If the body B be put to earth, it will be at zero potential. As in Chapter VI. § 2 (ii.), we shall find that it now has a charge greater in amount than the charge in the last case.

(vi.) Two vessels at different potentials; a conductor inside each of them.-If we have two vessels A and B at potentials + V and — V, there being an insulated conductor (initially uncharged) inside each of thein, and if these conductors be joined by a conducting wire, it is not difficult to predict what will take place.

The conductor C will, before joining, be at + V, and D will

be at

A

FIG. ii.

B

FIG. iii.

V. Hence, when they are brought to the same potential by joining, there will be a discharge between C and D ; C will become charged -ly, and D will become charged +ly.

Further, if we now disconnect C and D and lift them still insulated from the vessels, and drop C into B and I into A, they