CHAPTER IX.

ELECTRICAL MACHINES.

85. Electric Machines in General.—Any contrivance which serves for the continuous generation of electrical energy may be called an electrical machine. Such contrivances are frequently spoken of as sources of electricity, although no process is known which can be properly described as the production or generation of electricity. All that can be done by any electrical process is to transfer electricity in such a way that the quantity which enters any closed space across one part of the bounding surface is equal to the quantity which simultaneously leaves the same space across some other part of the surface. Or, if we prefer to speak of two different kinds of electricity, we must say that whenever a given quantity of positive electricity is transferred in one direction across a given surface, an equal quantity of negative is simultaneously transferred in the opposite direction across the same surface. It is thus impossible either to increase or decrease the absolute quantity of electricity within a given space.

The energy of an electric field (§ 55), namely Q (V – V'), being proportional jointly to the charge and to the difference of potentials, is increased when either of these factors separately, or their product, is increased. In the various kinds of electrical machines, the mechanical energy expended is partly expended in overcoming the ordinary friction of the moving parts, but in addition to this there is always an expenditure of energy in maintaining motion in opposition to electric force, and the electric energy generated by the machine is equal to the mechanical energy thus expended.

Electrical machines may be divided into two classes, namely, those in which the friction of heterogeneous substances plays an essential part in the electrical action, and those whose action depends on electrical induction. Machines of the former class

are called friction machines, those of the latter class are called induction machines.

86. General Mode of Action.-In either case an electric field is established, one boundary of which is formed by a moving part of the machine, which may be called the carrier, and the other boundary usually by the surface of the room. The motion of the machine brings the carrier into a position in which either the whole of it at once, or the various parts of it in succession, are more or less completely surrounded by an insulated conductor, the collector of the machine. Consequently, the field of force extending between the carrier and the room is cut into two parts, one extending from the carrier to the collector, and the other from the collector to the room. If the carrier is formed of conducting material and comes into connection with the collector as it passes, or if, being a non-conductor, its surface comes sufficiently near to a number of fine points projecting inwards from the inner surface of the collector, the first mentioned part of the field is abolished, the carrier passing away unelectrified and ready to be electrified afresh by friction or by induction. The result is thus to set up an electric field between the collector of the machine and the room. The charge, and therewith the difference of potentials of this field, increases with the continued action of the machine. By appropriate connections a greater or less portion of the charge and energy of the field may be transferred to a field bounded by any given conducting surfaces. In this way a Leyden jar or any other condenser may be charged.

87. Law of Increase of Charge.—In general, in a friction machine, each portion of the surface of the carrier is in the same electrical condition every time it comes under the influence of the collector, and consequently it increases the charge of the field established by the machine by the same amount every time; in other words, the charge of the field, and the difference of potentials which is proportional to the charge, increase in arithmetical progression. In other cases, however, particularly with induction machines, the charge frequently varies as the terms of a geometrical progression. Consider, for example, the following arrangement, which may be taken as a type of all inductive machines. Two metal jars, A and B, are placed on insulating stands, the potential of A exceeding that of the room by some small amount, and the potential of B exceeding that of the room by V. A metal ball is hung by an insulating thread inside

each jar, and while there is connected for a moment with the room. Each jar thus becomes one boundary of an electric field, the second boundary of which is formed partly by the ball hanging inside the corresponding jar, and partly by the surface of the room. If c is the capacity of the part of the field extending between the inner surface of a jar and its ball, and C the capacity of the part of the field extending between the outer surface of a jar and the room, the total capacity of each field is C + c, and the electrification of the ball in the jar A is - CV, and that of the other ball is -CV. Now transfer each ball to the other jar, letting it first go down to the bottom and then raising it a little by the insulating thread. The balls thus give up their electrification completely to the jars, which therefore acquire the potentials V respectively, or, more C + c

Vi

с

+ V and V; = V"'

C + c

=

с

shortly, VV, mV and V = V mV This gives, for the difference of potentials

Next let both balls be again connected for a moment with the room and then retransferred to the jars they were in before, allowed to touch the bottom and raised. The potentials of the jars thus become V2 = V1 – mV; and V1 = V1⁄2 – mV1 respectively, and the difference becomes

V1⁄2 − V1⁄2 = (1 + m) (V1 − V1) = (1 + m)2 (V, − V').

If the same series of operations be repeated over and over again, the difference of potentials becomes progressively greater and greater, being, after ʼn times,—

88. Frictional Machine.-This consists of a glass plate, P, movable about a horizontal axis (Fig. 81); of two pairs of cushions, C, placed at the ends of a vertical diameter; and of two U-shaped insulated conductors, s and s', provided with points on the side towards the plate. These conductors are called combs. Electrification results from friction of the glass against the cushions, and as each part of the electrified glass comes between the arms of the combs, the electrification is transferred to the latter, and the plate passes on almost unelectrified; accordingly a quantity of electricity,

equal to that which the plate has brought, is communicated to the insulated prime conductor, DD', connected with the combs.

Glass is the best material for the plate, but as there is considerable variation in the quality of glass, some care is needed in selecting it; that which is least hydroscopic is the best. All parts of the machine should be kept thoroughly dry.

The cushions are ordinarily of leather stuffed with horse hair, and are kept pressed against the plate by springs. If the pressure is sufficient to bring, the rubbers into good contact with the glass, further pressure does not increase the electrification. The surface of the rubber should be covered with a conductor such as that variety of sulphide of tin known as aurum musivum, or, still better,

with Kienmayer's amalgam, which is composed of zinc, tin, and mercury; this is reduced to powder, and a little lard having been applied to the cushion, some of the powder is spread evenly over it.

The contact between the glass and the rubber sets up a fixed difference of potentials between them, the glass becoming positively electrified, and the rubber negative. This difference of potentials is at first very small, since the equal oppositely electrified surfaces are very close together. But as each portion of the glass moves away from the rubber, its potential acquires a very high value, and, in order to prevent loss, quadrant-shaped pieces of oiled silk, not shown in the figure, are often fixed to the rubbers so as to enclose on both sides the parts of the plate between the rubbers and the combs. These are kept in contact with the plate by the electrical attraction.

The rubbers are usually put in connection with the earth by strips of tin-foil which pass down the support; the conductor of the machine thus gives positive electricity. But machines are also constructed in which the cushions are supported by glass legs, and connected with a second system of conductors. Either positive or negative electricity may thus be obtained at will. Whether the rubbers are insulated or not, the yield of the machine is the same for the same atmospheric conditions, as is also the difference of potentials between the rubbers and the conductors. It is only the absolute value of the potential which changes.

In order to take sparks from either the positive or the negative conductor, the experimenter must be electrically connected with the other conductor. If this is not insulated the table and floor generally serve as a sufficient connection.

Similarly, to charge a Leyden jar or battery, the rubbers of the machine must be connected with one coating and the prime conductor with the other. Here, again, if the rubber is uninsulated, the table generally forms a sufficient connection between it and the outer coating. But if either the rubber or the outer surface of the jar is insulated, some conducting connection must be provided.

In order to estimate the potential of the conductor, a small electroscope known as Henley's electrometer (R, Fig. 81) is used. This is a small pendulum formed of a thread with a pith-ball at the end, movable about an axis in front of a scale. The diver