prove experimentally is that if a hollow vessel A B be charged, there is no force due to this charge acting on a small charge P înside; or there is no field of electrical force inside a hollow, charged, conductor.

B

Faraday constructed a small insulated room. He went inside it with delicate electroscopic apparatus, and then the whole was highly charged. No electric field inside, due to this charge, could be detected.

Now it can be proved mathematically that no possible law of force between the small charge P and the different portions of electricity on the vessel A B, except the law of inverse squares, could account for this resultant zero force on P.

Formula expressing the three laws.-We can express all the three laws by the one formula

Q × Q'

F=

Here we pay proper attention to the 'rule of signs' in the product Q × Q', and consider the force to be repulsive if the product is +, attractive if the product is The force F is in dynes if r is measured in centimètres, and if Q and Q' are measured in the absolute units given in § 12.

§ 14. First Ideas as to Induction.-As stated in § 1, we shall at present use the somewhat unscientific 'two-fluid' language in this first sketch of the main phenomena of electrostatics.

Instruments used.—The gold-leaf electroscope has already been described. The insulated conductors need no comment.

But the proof-plane needs some explanation. It consists of a small metal (or gilt paner) disc at the end of a thin insulating rod. The theory of its use involves the following considerations. We shall see that electric charges reside only on the surfaces of conductors. Consequently, if the small disc of the proof-plane be applied to a conductor so as for the time to form part of its surface, the electricity that was on the portion of the conductor covered by the disc will now be found on the disc. When the proof-plane is removed (care being taken to remove it so that every part of it leaves the conductor at one and the same

moment) the charge that it carries away can be taken as a sample both in sign, and in degree of concentration, of the charge existing on that part of the conductor to which the proof-plane was applied.

The main facts of induction will be understood from the experiments that follow, and the figures represent roughly to the eye the condition of things in each case.

Note.-Insulating stands.—A very good, but somewhat expensive, form of insulating stand is that due to Professor Clifton. It can be obtained at Powell's glass-works, or through electrical instrument makers. Professor S. P. Thompson has devised a simple and very effective form, that can be made in any laboratory. A description of it may be seen in Nature, vol. xxix. page 385.

Well-polished ebonite rods are also good, but in delicate experiments care must be taken to discharge them frequently in a Bunsen's flame. They may be cleaned with paraffin oil, this latter having been rendered anhydrous by means of a few lumps of sodium kept in the bottle.

Experiments.—(i.) A B is a large rod of ebonite excited with catskin and placed in a stand. CD is an insulated cylinder, previously discharged, placed

TI

FIG. i.

B

near A B. It will be found that the state of equilibrium of CD is altered. Whereas it was totally uncharged, we now find on it a distribution somewhat as given below.

Applying the proof-plane to different parts on its surface in succession, and converging the charges so obtained to an electroscope, we can show that the end C opposite to the charged A B is strongly + charged. The charge is feebler as we approach the centre of the cylinder; about the centre there will be a region where no charge is to be detected; while, as we approach

the end D, we find a stronger and stronger

charge. The proof-plane must

be discharged in a Bunsen's flame between each two trials. Note.--When the charge has been conveyed to the gold-leaf electrʊscope by the proof-plane, its strength can be roughly seen by observing the amount of divergence of the leaves, while its sign can be recognised by the approach of an excited ebonite rod.

(ii.) While the conductor C D is in the presence of the charged body A B, let us touch CD at any point. This will connect it with, and so make it form part of, the earth.

We should have expected this, since the portions of the earth near A B would probably, judging from experiment (i.), be +ly charged, while the would go as far away from A B as possible. But still it seems at first a little surprising that the charge should escape as readily if we touch the end C as if we touch the end D. This will be explained in Chapter V. § 6 (d'). Here we may only say that the presence of the at the end C renders it as easy for the to pass to earth by the route near A B as by the other route.

ΠΙ

FIG. iii.

(iii.) The divided cylinders.--We may construct our cylinder of two halves separately insulated.

If we allow the whole, when forming one cylinder, to be acted upon inductively as in fig. i., and then separate the two halves, we shall find the half nearer A B to be +ly charged, the half further from A B to be -ly charged.

(iv.) Charging the gold-leaf electroscope by induction. -The second experi

ment shows us how we may charge a conductor by induction; and this method is almost invariably employed when we desire to charge the gold-leaf electro

scope.

An excited rod is held near the knob of the electroscope. so that the leaves diverge with a charge of a similar sign to that of the rod. We then discharge the electroscope of this repelled' electricity by touching the knob, so that the leaves again collapse. If we remove the hand and then withdraw the excited rod, the leaves will diverge with a charge whose sign is opposite to that of the inducing rod.

$ 15. First Ideas as to Distribution. In considering the distribution of an electric charge on a conductor, we assume that we are dealing with simple continuous conductors, or those in which all the parts are connected by conducting matter. Such cases as that of an insulated ball hung inside a vessel will be considered later under the head of condensers. They are cases of systems of conductors and not of simple conductors.

We shall find the following general facts to hold, it being taken for granted that, unless the contrary is stated, the conductor in question is in the middle of a large room (see § 11, note).

(i.) The charge is on the surface of the body only. In the case of closed, or nearly closed, hollow conductors, the charge will in general be on the outside surface only.

(ii.) The distribution depends upon the shape of the body. The density of charge is greatest on all salient points; all projecting corners, or prominent regions of great curvature, having a far greater density than have the other regions.

We here give some facts with respect to the distribution on bodies of certain forms.

Note.--By density of charge we mean quantity of electricity per unit area. We shall say more concerning this in Chapter X.

On a sphere the distribution is uniform.

On a ellipsoid of revolution the densities of the charges at the extremities of the axes are proportional to the lengths of the

axes.

On a cube Riess found that the density at the middle points of the edges is about two and a half times as great as at the middle of a face, while at the corners it is more than four times as great.

On a circular disc the density is greatest round the edge. As

we move from the edge the density falls off rapidly, and for a considerable region near the centre of either face of the disc the density is nearly uniform.

More exactly, Coulomb found the following distribution on a disc of 10 inches diameter.

On a cylinder of an elongated form the density is much greater at the ends than at the middle.

In the case of a cylinder of circular section whose diameter was 2 inches, length 30 inches, and whose ends were hemispherical, Coulomb obtained the following results.

It is to be noticed that this is somewhat the form given usually to the 'prime-conductors' of electrical machines.

On a cone the density is greatest at the apex.

When the cone is of a very small angle, and the point is very sharp-a common needle is an extreme case of this kind-the density at the point becomes very great indeed. As a consequence of this, though why it is a consequence it is not so easy to explain as would at first sight appear, the air no longer serves to separate the charge residing on the point from the charge induced upon the walls or other surroundings. It is found that a stream of electrified air proceeds from the point towards the induced charge of opposite sign that exists on the walls, &c.; and the conductor is thus discharged. Thus a sharp projecting point will almost completely discharge any conductor to which it is fixed. In a similar manner, but by inductive action, an earth-connected pointed conductor will nearly discharge a charged body, towards which it is presented; for there will proceed from the point to the