upper plate is made in two parts, a central disc and a surrounding ring. The disc is suspended from one arm of a balance and hangs so that its lower surface is exactly flush with that of the ring, which is separately supported, though the two are in conducting communication.

The plate B is connected with the earth, while A, which is insulated by hard rubber or glass at r, is connected with the charged conductor whose potential is to be determined. There is a charge on A and an opposite induced charge on B and consequently an attraction between them. balance the force with which the disc is attracted is exactly measured.

By means of the

The difference of potential V between the plates A and B may then be found in electrostatic units by the formula

where d is the distance between the plates in cms., F is the force of attraction in dynes, and S is the area of the disc in square centimeters.

The instrument is called an absolute electrometer, because its determinations depend directly on measurements of length and force and it may be used to standardize other instruments.

The guard ring, as it is called, which surrounds the attracted disc was introduced by Lord Kelvin to cause a uniform distribution over the central disc, without which the difference of potential could not be calculated by the above simple formula. For in case of two parallel plates the distribution is denser toward the edges, but is extremely uniform near the center if the plates are not too far apart.

The balance must be enclosed in a metal case, as shown by the dotted lines, to screen it from all outside disturbing electrical attractions.

559. Quadrant Electrometer. The quadrant electrometer, also designed by Lord Kelvin, is shown in figure 309. A small round brass box is cut into four quadrants which are slightly separated from each other, and mounted on insulating supports as shown in the figure. The needle consists of a thin flat plate of aluminum, broad at the two ends as shown in the plan, and

mounted on a light vertical wire of aluminum which passes through its center and carries on its upper end a small mirror by which the motions of the needle are observed.

The flat needle is suspended by a fine quartz fiber or by two parallel fine fibers of silk constituting a bifilar suspension, so that it hangs horizontally in the middle of the box formed by the four quadrants and in the position shown.

H

B

The diagonally opposite quadrants A A are connected by wire conductors to the pole P', while the quadrants BB are connected to the pole P. The needle is given a positive charge so that if the A quadrants are connected with a positively charged body while the B quadrants are joined to earth, it will turn toward the B quadrants; while if the A quadrants are negative it will turn toward them. The deflection of the needle is read by the motion of a narrow beam of light, reflected from the attached mirror upon a graduated scale, and is nearly proportional to the difference of potential between the A and B quadrants. instrument may be many times greater than that of the gold-leaf electroscope. To secure the greatest sensitiveness a very light paper needle is used, hung by an exceedingly fine quartz fiber.

FIG. 309.-Quadrant electrometer.

The sensitiveness of this

Another method of using the instrument is to connect the B quadrants to the body to be tested, while the needle and A quadrants are connected together and to the earth. In this case the needle will turn toward the B quadrants whether the charged body is positive or negative, and the deflection is nearly proportional to the square of the difference of potential measured.

DISPLACEMENT THEORY

560. Theories of Electricity.-The early investigators thought of electrified bodies as containing something which they called an imponderable fluid, because it could flow from one body to another and yet did not seem to possess weight or inertia.

Symmer conceived two such fluids, positive and negative electricities, which neutralized each other when mingled.

Franklin, however, advocated the view that there was but a single electricity and that for every body there was a normal amount when it showed no electrification; if there was an excess it showed one kind of electrification, while if there was a deficiency of the electric fluid the body was electrified in the opposite way.

The strong points of this theory are that it explains how opposite charges neutralize each other and how it is impossible to develop a positive charge anywhere without at the same time. causing an equal negative charge to appear somewhere else.

But Franklin's theory assumed that each portion of the electric fluid repelled every other portion.

561. Faraday's Theory.-Faraday, however, conceived that electrical forces were communicated by the insulating medium between electrified bodies and showed that, while the force between two charged conductors does not depend on the kind of metal used for the conductors or whether they are solid or hollow, it does depend on the kind of insulating medium that separates them.

562. Displacement Theory.-One of the clearest developments of Faraday's theory is that due to Maxwell, which may be called the displacement theory. All space, conductors and insulators alike, are thought of as pervaded and filled with an absolutely incompressible fluid, electricity. This fluid flows through conductors somewhat as water flows through some quite porous material-it experiences more or less frictional resistance. In insulators or dielectrics, on the other hand, the electric fluid cannot flow, but is held by an elastic resistance, much as water is held in jelly. Particles of electricity in a conductor may be compared with shot in a mass of molasses,they experience a resistance to their motion, but there is no tendency to spring back when the displacing force is removed.

In the dielectric or insulator, on the other hand, particles of electricity are thought of as held in elastic equilibrium like shot in a mass of rubber,-if force is applied there is a certain yielding or displacement; if the force is increased the particles are displaced more, but there is no continuous flow, and as soon as the force is removed they spring back to their original positions. There is an active restitution force in the dielectric by which it tends to return to the original unstrained condition.

Now suppose that the act of charging A and B by an electrical machine consists in causing some electricity to flow out

FIG. 310.

B

of B into A. In consequence of its incompressibility, electricity cannot be forced into A without causing an outward displacement of the electricity in the dielectric around A, at the same time there will be an inward displacement toward B and all the lines of displacement must run from A to B in the direction of the lines of force. Thus at every point of the dielectric there will be a displacement of electricity in the direction of the arrows. The total displacement across any surface surrounding A, such as that shown by the dotted line, will be equal to the charge that was forced into A. This is a consequence of the assumption that electricity fills all space and is absolutely incompressible.

But all the displaced electricity in the dielectric is urged back toward its unstrained condition by the elastic restitution force in the dielectric, it therefore produces a pressure back on the electricity in A and a negative pressure in B, so that if A and B are now connected by a wire there will be a flow from A to B, until the displaced medium has sprung back to the original state. The electric discharge is thus conceived of as forced from A to B by the springing back of the dielectric and not as due to any attraction between electricities in A and B.

This difference in pressure between A and B due to the reaction of the displaced dielectric is the difference between their potentials. Suppose that after A and B are charged they are moved nearer together. The strain will now take place through

a less thickness of dielectric and the difference in pressure between A and B will accordingly be less. The work required to produce a given charge will therefore be less when they are nearer together; that is, the energy of the charge will be less. They will therefore tend to move together; that is, there is an attraction between A and B. For if they are moved apart they will have more energy, but they can only get this additional energy from the work done in separating them; therefore there must be a force opposing the separation or a force of attraction.

563. Tubes of Force.-The electric field may be conceived as divided up into tubes by means of surfaces in the direction of the lines of force. (Compare $502). These tubes of force will always have at one end a positive charge and at the other an equal negative charge.

In the displacement theory they are tubes of equal displacement and the amount displaced inward at one end of such a tube must of course be equal to the amount displaced outward at the other end if the medium is incompressible.

564. Induction as Explained by Displacement Theory.— Suppose A and B are conductors near each other (Fig. 311) and having no charge at first. Let a positive charge be given to A.

The tubes of displacement will extend out from A in every direction toward the walls of the room. But since B is a conductor there is no force resisting electric displacement through it, whereas in every other direction there is the active elastic reaction of the dielectric to be overcome. Displacement can therefore take place more readily on the side of A toward B than in other directions and a number of tubes of displacement will terminate on B. On the farther side of B there must be an equal displacement away from B. These constitute equal negative and positive charges respectively.