Such a list is here given; it is taken from Ganot.

Note. It is sometimes not easy to obtain signs of electrification on bodies, as flannel, gun-cotton, &c., which are not good insulators. In such cases we

may fasten them to the ends of thin ebonite rods. Thus, if we so fasten a piece of gun-cotton and of cotton-wool to the ends of two ebonite rods, and then rub them together, we shall find them to be strongly excited with opposite electrifications; but if we hold the two in the hand and then rub them, we shall get little or no such signs.

§ 9. Equal quantities of the opposite Electrifications are always produced simultaneously. This is a fact of great and fundamental significance; and is indissolubly bound up with the essentially dual nature of electrostatic phenomena.

In every case of electrical excitement there is a separation of a state of equilibrium into what may be expressively, though perhaps not very exactly, termed an overbalance and an underbalance respectively.

What and electrifications' mean we do not yet know. But one thing at least is certain; that the total electrifications produced in any way from a state of neutrality will, if collected together on one conductor, give zero electrification. Or, we never have any + or electrification produced without an equal quantity of or electrification (respectively) being simultaneously produced. The sense in which the word 'equal' is used has just been explained.

Experiments. (i.) The following experiment is well-known.

A flannel cap is made, so as to fit on to the end of an ebonite rod, and the whole is carefully discharged in a Bunsen's flame. Then, by means of a long and dry silk thread attached to the cap, this latter is twisted round upon the rod.

Still it will be found that the whole has no effect upon the leaves of an electroscope.

But if the cap be drawn off the rod, still insulated by means of the silk thread, it will be found that the two are oppositely excited.

Here then we have opposite electrifications produced, whose equality was shown by the fact that the whole system had zero action on the electroscope.

(ii.) In § 16 we shall see that when a charged conductor is lowered into a hollow vessel such as A, one that is nearly closed and is open only towards the comparatively remote ceiling, the effect upon this vessel will be the same as if it had received the entire charge of the body. This will be the case whether the charged body be a good or a bad conductor, whether it touch the vessel or hang insulated within it.

In the figure we have such an insulated vessel A, and with it is connected an electroscope E. Hence, in all cases of electrical excitement we may

CO+

+

E

introduce the rubber and rubbed into the vessel A simultaneously. If this be done with the rod and cap of the last experiment, it will be found that they give together a zero action, while separately they cause the leaves to diverge equally with opposite electrification.

Notes.-(i.) On discharging bodies. All bodies may be readily discharged by passing them through the flame of a Bunsen's burner. The completeness of discharge should be tested by their having zero action on an electroscope.

(ii.) On testing the charge for sign.' When the leaves are divergent with any charge, a rod of ebonite excited

with flannel may be approached. If the leaves diverge still more, their charge was similar to that of the rod, or negative; but if they fall together, their charge was positive. The reason for this will be explained later; that it is the case can easily be proved experimentally by the student.

§ 10. The Fluid' Theories of Electricity. The mobility of electrification (or electricity), its ready passage along conductors, and certain other characteristics early suggested the name electric fluid. But the absence of weight, the attractions and repulsions of the two sorts of electrification, and other phenomena, such as the extraordinary speed of movement, arguing absence of mass, all show us that if we are to hold previous ideas associated with the word fluid we must regard the term 'electric fluid' merely as a rough analogy, if indeed it should be used at all.

Believing that too little is known as to the nature of electrification, and of the phenomena of electric strains and movements, to make any term at present in the language really a good one, we

shall, for lack of better terms, speak of ' + and or electricities.'

The expressions +' and '-' retain their algebraic meaning. Equal and opposite electrifications, when imparted to the same conductor, give zero electrification; while, if the quantities be unequal, we have left simply the balance of the one or the other as the case may be.

When it is assumed that there are two fluids possessing, in a sense that has been made clear, 'opposite' properties, we are said to be employing the two-fluid theory of electricity.

+

When it is assumed that there is but one fluid of which an excess in one place and a defect in another give rise to the phenomena of and electrical charges respectively, we are said to employ the one-fluid theory. The reader is again warned that in the present state of knowledge it is unadvisable to lay much stress upon either view.

§ 11. The Three Laws of Electrostatics.—With respect to the attractions and repulsions of electrified conductors, it is found that three main laws hold. These are as follows.

Law 1. Like electricities repel, and unlike attract, one another. This means that if two bodies are charged with electrifications of like or of unlike sign respectively, there will be observed between them 'repulsion' or 'attraction' respectively. (We here use the usual terms without asserting that they are accurate.)

§ 12. Law II. The Force varies as Q × Q'.---This means that if we have two quantities of electricity, Q and Q' respectively, on two conductors, and if the conditions as to distance remain constant, then the force in dynes that exists between the conductors is proportional to QxQ', being repulsive if the algebraic product be +, attractive if the product be

We must here suppose the bodies to be in the middle of a very 'large' room; and the conductors should be two 'small' spheres, so that we may consider the distance between Q and Q' to be the distance between the centres of these spheres.

Note.-The word large means very great compared with the distance between the spheres; the word small means very small compared with the

same.

Measurement of Quantity; unit Quantity.-It was said that in magnetism (see Chapter III. § 4) we had no independent law

E

that force varied as up', since we measured the product μ' by the force, and would be arguing in a circle if we made of this an independent law.

In electricity the case is somewhat different. We do indeed define unit quantity as that which at unit distance from an exactly similar quantity repels it with unit force, thus measuring our unit by force. But we can find multiples or submultiples of this unit without reference to force.

Thus we can empty a series of bodies, each carrying unit charge, into an insulated hollow body; the charge will go wholly to the outside surface, thus charging one and the same surface with any number of units desired.

Or again, we can charge a sphere with unit quantity, and then, hanging it in the middle of a large room, bring into contact with it one, two, three, &c., exactly similar spheres.

Theory and experiment will show that the unit is subdivided • into,,, &c., provided that the spheres are arranged with perfect symmetry.

(i) Proof of Law II. by torsion balance.--Referring to the figure of the torsion balance we have to imagine only the following modifications.

270

BD 180°

+90°

Instead of the needle we have a light arm of straw, A B, carrying a small gilt sphere at each end.

When the straw arm is at zero each of these equal spheres rests against another equal sphere at C and D, these latter being connected with each other, but otherwise insulated. This arrangement of two spheres &c. is to insure its being a true couple that acts on the needle. A like arrangement would have been desirable in magnetism, but we could not have found two exactly equal poles to act on the two poles of the needle, whereas we can readily get equal quantities of electricity on the gilt balls. If C is now charged, the charge will be shared by all four balls alike if they have been made accurately equal spheres, and the arm A B will be deflected. We bring it back by torsion to some conveniently small angle, and measure the total angie of

torsion (see Chapter III. § 2), and so the torsion couple. We may suppose that we have a sphere S charged, so large that the quantity on it is not appreciably altered by several times charging the torsion balance from it. Let us charge the balls of the torsion balance from the sphere S1, and measure the torsion as above. Then discharge the whole.

Next make S, share its charge with an equal sphere S2, and charge the balls again from either S, or S.

A little thought, and reference to the assumption as to the size of S, made above, will show us that each ball now has one-half the charge that it had before. We shall now find that for the same deflexion the torsion couple required to balance the electric couple is one-quarter what it was before; that is, the force between the balls is one-quarter the former force.

Now since the quantity on each ball is one-half what it was, this result confirms the law that 'the force varies as Q × Q'.

§ 13. Law III.

1 The Force varies as -The meaning of 72

this law has been already explained in Chapter III.

In order to test this law by direct experiment it is clear that we must deal with charged spheres of very small size as compared with the distance between them.

a distinct meaning to the distance electricity.

Otherwise, we could not assign

between the two quantities of

All direct experiment is only approximate, and serves to confirm a law for which there is much indirect evidence.

The law theoretically refers to quantities of electricity collected at points, just as do the corresponding laws in magnetism and in gravitation. This gives a definite meaning to r.

Assuming that our methods or experiment and of reasoning have proved the law, the integral calculus enables us to deal with the action on each other of conductors on which there is a known distribution.

(i.) Torsion balance method.—If the student will read Chapter III. § 5, and has learnt the modifications in the torsion balance required for electricity as given in the last section, he will need no further explanation of this method.

(ii) Indirect, but exact, proof.—One of the casicst matters to