current will, as we have seen, be produced in the coil. We may add, that if the motion of the coil be very rapid this electric current will be very powerful. In Clarke's machine two coils connected with one another, and having a core of soft iron in their centres, are made to rotate backwards and forwards before the poles of a powerful horse-shoe magnet. As this coil with its soft iron core approaches one of the poles, an electric current is induced in the coil, the intensity of which is heightened by the soft iron core, which becomes a magnet by induction, and which on this account heightens the current induced by the permanent magnet in the coil.

Now this secondary current will be in one direction when it passes the one pole, and in the opposite direction when it passes the other pole.

There is, however, a commutator, the object of which is to make the alternate currents of the coils pass from these coils through a set of wires always in the same direction, and not having their direction reversed as in the coils. The arrangement of the commutator is such that when the current is reversed in one of the coils it is passed in the opposite direction through the wires intended to convey it, and thus the current traverses the wire always in the same direction.

Powerful machines on this principle, if not of this very kind, form a very convenient arrangement for obtaining current electricity, and the electric light (Art. 415) can be produced by them in very great perfection. Of late years very powerful magneto-electric machines have been constructed and applied to a variety of useful purposes.

399. Ruhmkorff's Coil.-In Ruhmkorff's coil the ordinary current is changed by induction into one which possesses very great tension. We have in the centre of this coil a core of soft iron, and a current from two or three pairs of a Daniell or Grove's battery is made to pass round this core in such a manner as to transform it when the current passes into a powerful electro-magnet.

This arrangement forms the interior of the interior is inclosed in a thick cylinder of glass.

coil, and this

Outside of

A A

this glass cylinder, and insulated by it from the primary current, we have the induction coil, consisting of a large quantity of fine wire well insulated, and coiled round the glass cylinder; sometimes 40 or 50 miles of wire are used for this purpose.

In such machines there is generally a self-acting arrangement, by which the primary current is alternately introduced and shut off, and the soft iron core is thus rapidly magnetized and demagnetized.

When the primary current is started the exterior coil is, as it were, rapidly brought into the presence of a strong current, and also of a strong magnet, and a powerful induced current is therefore generated in the exterior coil, the direction of the induced current being the reverse of that of the primary current.

But

Again, when the primary current is cut off there will be an induced current in the exterior coil, the direction of which will now be the same as that of the primary current. the secondary current produced when the primary current is broken has more tension than that produced when the primary current is started, so that when the induced current is forced to overcome a great resistance, such for instance as passing through a space of air, it is only the direct secondary currents, those produced when the primary current is interrupted, that are able to pass; and we have therefore virtually, in a Ruhmkorff's coil, a powerful secondary current always in the same direction as the primary current.

The spark of a Ruhmkorff's machine may be made to pass through more than two fect of air.

LESSON XLV.-DISTRIBUTION AND MOVEMENT OF ELECTRICITY IN A VOLTAIC BATTERY.

400. This subject was first studied by Ohm, a German philosopher, who developed from theory the laws regulating the motion and distribution of electricity in a battery. These laws have since been abundantly verified by experiment, and may therefore be received as at least a near approximation

to the truth. In a voltaic battery there are three objects of study: first of all we have the electro-motive force, or the effort put forth to establish a current of electricity; secondly, we have the resistance to be overcome before such a current can be produced; and lastly, we have the intensity of the current which is produced.

401. Electro-motive Force.-Taking these in their order, we have first the electro-motive force. Whatever may be its cause, there is without doubt an electric tension at the poles of a battery, and this may be regarded as the measure of the electro-motive force, inasmuch as it represents the tendency to form a current.

In the first place, this tension is independent of the size of the plates of the battery but depends upon the nature of the materials used; in fact, it mainly depends upon the distance of the two metals from one another in the electro-motive series of Art. 375.

Again, the electro-motive force of six cells of Daniell's battery in line will be six times as great as that of a single cell; and, in like manner, the electro-motive force of four cells of Grove's battery will be four times as great as that of a single cell of the same, so that the electro-motive force varies as the number of cells.

402. Electrical Resistance.-When we discussed thermal conductivity (Art. 219) we imagined a wall one metre in thickness, one side of which was kept at a given temperature, while the other side was one degree Centigrade hotter, and we measured the conductivity by the quantity of heat which flowed in one minute across a square metre of the wall.

We might in a similar manner measure electrical conducttivity; for we might imagine one side of the wall kept uniformly at a given electric tension, and the other side at an electric tension somewhat different, and measure the quantity of electricity that would in consequence flow in one minute across the wall, and this we might term its electric conductivity. But in the science of electricity it is more convenient to conceive of electric resistance, a quality which is the reciprocal of conductivity, so that the quantity of

electricity flowing through a conductor in unit of time, in consequence of an electric difference of tension, will be directly proportional to the conductivity, but will be reciprocally proportional to the electric resistance. In other words, if we denote by intensity the quantity of electricity which passes in unit of time, then we shall have

Intensity of current

=

electro-motive force.

resistance

Or if E be used to denote the electro-motive force of a current, and if R denote the resistance of the circuit, while i

denotes the intensity of the current, we shall have, i this is how Ohm expresed his law.

=

E

R

and

Thus if we double the electro-motive force without altering the resistance, the intensity of the current will be doubled; and again, if we double the resistance without altering the electro-motive force, the intensity will be reduced to one-half. 403. We have now to ascertain how we may estimate the electric resistance of substances. This is found to depend

on three things.

Ist. The electric resistance of a conductor depends upon the nature of its substance.

2nd. Its resistance varies inversely at its cross section; that is to say, a wire with a large cross section offers much less resistance to the passage of a current than one with a small section.

3rd. Its resistance is proportional to its length; that is to say, if a current has to pass through two miles of wire it will be twice as much resisted as if it had to pass through one mile.

404. A battery is generally composed of two parts: Ist, the internal or other liquid conductors which are essential to its action; 2nd, the outer and metallic conductors. The resistance offered by the former may be called the internal resistance, and that offered by the latter, the external resistance of the battery.

Now let us denote by E the electro-motive force of one cell, and by R the essential or internal resistance of one cell of a battery, while r denotes the external resistance, which

may be increased or diminished at will. Then we shall have by Ohm's law for a single cell in this circuit

Next let there be 10 cells, then we shall have the electromotive force and the internal resistance both increased

405. These formulæ will enable us to determine the intensity of the current obtained by any arrangement of a voltaic battery.

Thus let the external resistance sensibly vanish, then the intensity will be the same in both the cases mentioned above; for although in the one case the electro-motive force is increased ten times, the resistance is also unavoidably increased in the same proportion, and hence both numerator and denominator of the fraction representing intensity are multiplied by the same number. If therefore the external resistance be very small, we do not gain much by increasing the number of cells. But suppose that while the essential resistance, or R, is equal to 10, the external resistance is equal to 100, then we shall have, for one cell, i

i

E

=

and for 10 cells,

ΠΙΟ

=

=

IO E E 200

20

; if therefore

the external resistance be great compared to the internal or essential resistance, a considerable increase in the intensity of the current is obtained by increasing the number of cells. Thus, in producing the electric light, it is necessary that the discharge should pass between charcoal points with an airspace between. This implies a great resistance, and it is therefore necessary that there should be a large number of cells.

Again, the thermo-electric current is one in which the external resistance is generally much greater than the internal or essential resistance. For in this case, the whole arrangement being metallic without any interposed fluids, the essential resistance is extremely small; but in order to make use of the current, it is generally necessary to have a coil of wire constituting an external resistance much