horizontally below the needle without touching it or one another. Opposite quadrants are joined with fine wires. If quadrants 1 and 3 are ever so little + as compared with quadrants 2 and 4, the needle will turn away from the former to a position more nearly over the latter.

If there is the slightest difference of potential between the pairs of quadrants, the needle, which is held in its zero position by the elasticity of the

wire, will turn, and so indicate the difference of potential. When these deflexions are small, the scale readings will be very nearly proportional to the difference of potential. The instrument is sufficiently delicate to show a difference of potential between the quadrants as small as the of that of the Daniell's cell. If V, be the potential of one pair of quadrants, V, that of the other pair, and V, the potential of the needle, the force tending to turn will be proportional to V1-V, and will also be proportional to the difference between V, and the average of V, and V. Or, in symbols,

3

1

Fig. 151.

where a is a constant depending on the construction of the particular instrument.

Fig. 152 shows a very simple form of the Quadrant Electrometer, as arranged for qualitative experiments. The four quadrants are enclosed within a glass case, and the needle, which carries a light mirror M below it, is suspended from a torsion head C by a very thin metallic wire F. It is electrified to a certain potential by being connected, through a wire attached to C, with a charged Leyden jar or other condenser. In order to observe the minutest motions of the needle, a reading-telescope and scale are so placed that the observer looking through the

T

telescope sees an image of the zero of the scale reflected in the little mirror. The wires connecting quadrants 1 and 3, 2 and 4, are seen above the top of the case.

For very exact measurements many additional refinements are introduced into the instrument. Two sets of quadrants are employed, an upper and a lower, having the needle between them. The torsion wire is replaced

by a delicate bifilar suspension (Art. 130). To keep up the charge of the Leyden jar a "replenisher" is added; and an "attracteddisk," like that of the Absolute Electrometer, is employed in order to act as a gauge to indicate when the jar is charged to the right potential. In these forms the jar consists of a glass vessel placed below the quadrants, coated externally with strips of tinfoil, and containing strong sulphuric acid, which serves the double function of

Fig. 152.

keeping the apparatus dry by absorbing the moisture and of acting as an internal coating for the jar. It is also more usual to throw a spot of light from a lamp upon a scale by means of the little mirror (as described in the case of the Mirror Galvanometer, in Art. 215), than to adopt the subjective method with the telescope, which only one person at a time can use. When the instrument is provided with replenisher and gauge, the measurements

can be made in terms of absolute units, provided the "constant" of the particular instrument (depending on the suspension of the needle, size and position of needle and quadrants, potential of the gauge, etc.) is once ascertained.

289. Use of Quadrant Electrometer. - An example will illustrate the mode of using the instrument. It is known that when the two ends of a thin wire are kept at two different potentials a current flows through the wire, and that if the potential is measured at different points along the wire, it is found to fall off in a perfectly uniform manner from the end that is at a high potential down to that at the low potential. At a point one quarter along the potential will have fallen off one quarter of the whole difference. This could be proved by joining the two ends of the wire through which the current was flowing to the terminals of the Quadrant Electrometer, when one pair of quadrants would be at the high potential and the other at the low potential. The needle would turn and indicate a certain deflexion. Now, disconnect one of the pairs of quadrants from the low potential end of the wire, and place them in communication with a point one quarter along the wire from the high potential end. The needle will at once indicate that the difference of potential is but one quarter of what it was before.

Often the Quadrant Electrometer is employed simply as a very delicate electroscope in systems of measurement in which a difference of electric potential is measured by being balanced against an equal and opposite difference of potential, exact balance being indicated by there being no deflexion of the Electrometer needle. Such methods of experimenting are known as Null Methods, or Zero Methods.

290. Electrostatic Voltmeter. We have seen that in the quadrant electrometer it is necessary to give the needle a high initial charge, the reason being that if there did not exist between the quadrants and the needle a much greater difference of potential than the small voltage we are measuring, the force tending to turn the needle would be too small to be conveniently observed. Where, however, we are dealing with high differences of potential a separately-charged needle is not requisite; we may simply join one conductor to the needle and the other to a set of quadrants, and the force of

attraction, which, other things being equal, increases as the square of the difference of potential, is sufficiently great to give reliable readings. This

is known as the idiostatic method of using the instrument.

A front view of the instrument as commonly used to measure differences of potential of 1000 volts or more, is shown in Fig. 153. The needle NN is a paddle-shaped plate of aluminium supported by knife edges at its centre; its position is controlled by gravity, little weights being hung on a projection at its lower end. The quadrants Q are both behind and in front of it, and so placed that when a difference of potential exists between the needle and them the needle is deflected from its normal position and moves its pointer over a graduated scale.

Fig. 158.

It will be seen that it does not matter whether the needle is positively charged and the quadrants negatively charged or vice versâ; an attraction between the two will always take place, so a deflexion will be given even when the difference of potential is rapidly alternating. This property of the instrument makes it exceedingly useful for the measurement of voltage when alternating currents are used.

Another advantage of this instrument over the high-resistance galvanometers that are used as voltmeters is, that it does not take any current, and consequently it does not waste any power.

Fig. 154.

In order to make the electrostatic voltmeter sufficiently delicate to measure down to 100 volts or so, a number of

needles is placed horizontally one above the other on a vertical aluminium wire, and attracted by a tier of quadrants symmetrically placed on each side; this instrument is Lord Kelvin's multicellular voltmeter. It is shown in elevation and plan in Fig. 154.

291. Dry-Pile Electrometer. - The principle of symmetry observed in the Quadrant Electrometer was previously employed in the Electroscope of Bohnenberger - a much less accurate instrument -in which the charge to be examined was imparted to a single gold leaf, placed symmetrically between the poles of a dry-pile (Art. 193) toward one or other pole of which the leaf was attracted. Fechner modified the instrument by connecting the + pole of the dry-pile with a gold leaf hanging between two metal disks, from the more + of which it was repelled. The inconstancy of dry-piles as sources of electrification led Hankel to substitute a battery of a very large number of small Daniell's cells.

292. Capillary Electrometers. - The Capillary Electrometer of Lippmann, as modified by Dewar, was described in Art. 253.

LESSON XXIII.- Dielectric Capacity, etc.

293. A Leyden jar or other condenser may be regarded as a conductor, in which (owing to the particular device of bringing near together the two oppositelycharged surfaces) the conducting surface can be made to hold a very large charge without its potential (whether + or -) rising very high. The capacity of a condenser, like that of a simple conductor, will be measured (see Art. 271) by the quantity of electricity required to produce unit rise of potential.

294. Theory of Spherical Condenser. - Suppose a Leyden jar made of two concentric metal spheres, one inside the other, the space between them being filled