where I represents the intensity of the current, E the electromotive force or difference of potential at the two extremities of the circuit, R the electric resistance of the circuit.

This formula expresses: The intensity of a current in an electric circuit is in direct proportion to the electro-motive force, and in inverse proportion to the resistance.

We shall have to refer to this law on many occasions in examining the sources of electricity and its applications.

Electrical Units.-We know that a current which traverses an electric circuit of a certain resistance possesses a certain electro-motive force, and a fixed intensity. To have an exact idea of this current, we must measure its elements: difference of potential, intensity, and resistance. The measuring of electric elements is a very delicate and difficult task, and is beyond our province, but we must say a few words about the units which have been fixed upon after continued research, and have now been universally adopted.

In 1863, the British Association appointed a committee, composed of the most eminent electricians of Great Britain, to fix upon a standard for electric measurement. After eight years of work, the committee published a very detailed report, and fixed upon the electrical units, guided by considerations upon which we cannot enter here.

The units adopted by the English Commission were founded on the centimetre, the gramme, and the second. They are all derived from one another by definitions which are sometimes of a very complicated nature, but which present the advantage of clearly establishing these units, and allow of their being fixed anew, in case it should be necessary.

But these units possess a still greater advantage over the empirical units which were formerly in use. They require no other coefficient of reduction but multiples of

ELECTRIC BATTERIES.

ten. The introduction of these coefficients of reduction arises from the fact that the original units, to which the committee has given the name of absolute units, were rather too small for practice, which necessitated the use of large numbers in calculation; decimal multiples of these units have been substituted for them, and these multiples have been named after men celebrated in electric science.

The unit of resistance adopted by the committee is the Ohm. It corresponds to the resistance of an iron wire of four millimetres diameter and about a hundred metres in length. In France, it was the custom—a custom which is gradually disappearing-to count the electrical resistance in kilometres of telegraph wire. The kilometre of wire is equivalent to about ten ohms. In Germany, the Siemens unit is used, represented by the resistance of a column of purified mercury, one metre long and one millimetre square in section: it is nearly equal to the ohm.

The unit of electro-motive force takes the name of Volt. It corresponds very nearly to the electro-motive force generated by one Daniell element whose exact value in volts is 1.079. The thermo-electric unit of Gaugain is occasionally used, whose electro-motive force is 1826 of a volt, and of the Daniell element.

This is the electro-motive force developed by a thermoelectric couple of copper and bismuth, one of the solderings of which is kept at 0° and the other at 100° C.

This unit, now almost obsolete, has the advantage, from a scientific point of view, of being very constant, and of allowing at all times of a practical determination without any difficulty. The use of the volt, however, although not representing a real standard, is preferred on account of the simplicity which it introduces into calculation.

Unit of intensity. It is defined by Ohm's formula—

E

I =

R

and takes the name of Ampère. It used formerly to be called Weber, and is the intensity of current which traverses a conductor, whose resistance is one ohm, and whose electromotive force is one volt.

Unit of quantity. It takes the name of Coulomb, and represents the quantity of electricity which traverses, during one second, a conductor of one ohm resistance and a difference of potential of one volt.

This enables us at once to establish the relation between the intensity of a current and the quantity of electricity. A current with an intensity of one ampère yields per second a quantity of electricity equal to one coulomb. A current with an intensity of ampère will yield a quantity of electricity equal to one coulomb in 100 seconds, etc.

The currents employed in telegraphy vary between five and ten milliampères; those which serve for the electric light vary between one and fifty ampères; finally, in certain electro-chemical operations, the intensity of the current reaches 1000 ampères. It is most essential to employ very powerful currents for these operations, because the quantity of metal deposited is proportional to the intensity of the current, that is to say, to the quantity of electricity which passes during unit of time.

Joule's Law. The law discovered by the celebrated physicist Joule is expressed by the formula

W = I2Rt.

The quantity of heat or of work W developed by an electric circuit is proportional to the square of the intensity

of the current I, to the resistance of the circuit R, and to

the time t.

This formula gives, on replacing R by its value taken from Ohm's formula

W = IE.t

The work is proportional to the intensity of the current and to the electro-motive force. We find here again the analogy with the flow of water, where the work is proportional to the volume and to the pressure or height of the fall.

Unit of capacity. It takes the name of Farad, and represents the capacity of a condenser which contains one coulomb of electricity when charged to the potential of one volt. The quantity of electricity contained in a condenser is proportional to the electro-motive force, as in a reservoir of compressed air the weight of the enclosed air is proportional to the pressure, always supposing that the air follows Mariotte's law.

In practice, the farad is too large a quantity, and the unit adopted is the microfarad, which equals 1000000 farad.

We have, therefore, five electrical quantities and five corresponding units: (1) electro-motive force, expressed in volts; (2) resistance of the conductors, in ohms; (3) intensity of the current, in ampères; (4) quantity of electricity, in coulombs; (5) capacity of a condenser, in microfarads.

We can now enter upon an account of the electric batteries, confining ourselves to the newest systems which are most extensively used.

Classification of Batteries.-The batteries can be divided into several perfectly distinct groups, although there exists no absolutely rational and methodical classification—

1. From the nature of the soluble electrode; in practice, however, this character has no importance, for in almost all batteries zinc is used as the soluble electrode.

2. From the nature of the acting agent, which is sometimes an acid, generally sulphuric acid; acetic acid in Pulvermacher's battery; sometimes a salt like common salt, sal ammoniac, mercuric sulphate, lead sulphate, etc.

3. From the nature of the depolarizing agent, which can be copper sulphate, nitric acid, peroxide of lead, peroxide of manganese; in some cases the depolarizing and the acting agent form one single solution in the same liquid, as for instance in Poggendorf's battery, where zinc and carbon are immersed in a solution of potassic bichromate and sulphuric acid.

We shall therefore examine these batteries in groups. of like nature, following the excellent classification of M. Alfred Niaudet, in his Traité Élémentaire de la Pile Électrique.

SINGLE-LIQUID BATTERIES.

Since Volta's piles, a great number of single-liquid batteries have been constructed: the crown of cups or couronne de tasses, Cruikshank's battery, Wollaston's battery, the spiral battery, Muncke's battery, are only modifications of the fertile principle discovered by the Italian physicist.

These apparatus are very little used now in practice, on account of the rapid polarization of the elements. They are described in almost all treatises on physics.

In certain single-liquid batteries copper has been replaced by electrodes of other substances.