circuit, as well as on their E.M.F. The E.M.F. of a cell is independent of its size, and is determined solely by the materials chosen and their condition. The resistance depends on the size of the cell, the conducting qualities of the liquid, the thickness of the liquid which the current must traverse, etc.

The definition of the strength of a current is as follows: The strength of a current is the quantity of electricity which flows past any point of the circuit in one second.* Suppose that at the end of 10 seconds 25 coulombs of electricity to have passed through a circuit, then the average current during that time has been 21 coulombs per second, or 21 amperes. The usual strength of currents used in telegraphing over main lines is only from five to ten thousandths of an ampere.

If in t seconds a quantity of electricity Q has flowed through the circuit, then the current C during that time is represented by the equation

=

This should be compared with Art. 162.

The laws which determine the strength or quantity of a current in a circuit were first enunciated by Dr. G. S. Ohm, who stated them in the following law :

191. Ohm's Law. The current varies directly as the electromotive-force, and inversely as the resistance of the circuit; or, in other words, anything that makes the

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*The terms "strength of current," "intensity of current," are oldfashioned, and mean no more than "current" means that is to say, the number of amperes that are flowing. The terms "strong," "great," and "intense," as applied to currents, mean precisely the same thing. Formerly, before Ohm's Law was properly understood, electricians used to talk about "quantity currents" and "intensity currents," meaning by the former term a current flowing through a circuit in which there is very small resistance inside the battery or out; and by the latter expression they designated a current due to a high electromotive force. The terms were convenient, but should be avoided as misleading.

E.M.F. of the cell greater will increase the current, while anything that increases the resistance (either the internal resistance in the cells themselves or the resistance of the external wires of the circuit) will diminish the current. In symbols this becomes

where E is the number of volts, R the number of ohms of the circuit, and C the number of amperes of current.

Example. To find the current that can be sent through a resistance of 5 ohms by an E.M.F. of 20 volts. 20÷ 5 = 4 amperes.

(See further concerning Ohm's Law in Lesson XXXIII.) Ohm's Law says nothing about the energy or power couveyed by a current. The power of a current is proportional both to the current and to the electromotive-force which drives it (see Art. 435).

The inter

192. Resistance and Grouping of Cells. nal resistances of the cells we have named differ very greatly, and differ with their size. Roughly speaking, we may say that the resistance in a Daniell's cell is about five times that in a Grove's cell of equal size. The Grove's cell has indeed both a higher E.M.F. and less internal resistance. It would in fact send a current about eight times as strong as the Daniell's cell of equal size through a short stout wire.

We may then increase the strength of a battery in two ways:

(1) By increasing its E.M.F.

(2) By diminishing its internal resistance.

The electromotive-force of a cell being determined by the materials of which it is made, the only way to increase the total E.M.F. of a battery of given materials is to increase the number of cells joined "in series." It

is frequent in the telegraph service to link thus together two or three hundred of the flat Daniell's cells; and they are usually made up in trough-like boxes, containing a series of 10 cells, as shown in Fig. 106.

To diminish the internal resistance of a cell the following expedients may be resorted to:

(1) The plates may be brought nearer together, so that the current shall not have to traverse so thick a stratum of liquid.

(2) The size of the plates may be increased, as this

affords the current, as it were, a greater number of possible paths through the stratum of liquid.

(3) The zincs of several cells may be joined together, to form, as it were, one large zinc plate, the coppers being also joined to form one large copper plate. Suppose four similar cells thus joined "in parallel," the current has four times the available number of paths by which it can traverse the liquid from zinc to copper; hence the internal resistance of the whole will be only of that of a single cell. But the E.M.F. of them will be no greater thus than that of one cell.

It is most important for the student to remember that the current is also affected by the resistances of the wires of the external circuit; and if the external resistance be

N

already great, as in telegraphing through a long line, it is little use to diminish the internal resistance if this is already much smaller than the resistance of the line wire. It is, on the contrary, advantageous to increase the number of cells in series, though every cell adds a little to the total resistance.

Example. If the line has a resistance of 1000 ohms, and five cells are used each of which has an E.M.F. of 1·1 volt and an internal resistance of 3 ohms. By Ohm's Law the current will be 55 1015; or 0.0054 ampere. If now eight cells are used, though the total resistance is thereby increased from 1015 to 1040 ohms, yet the E.M.F. is increased from 5.5 to 88 volts, and the current to 0.0085 ampere.

The E.M.F. of the single-fluid cells of Volta and Smee is marked in the table as doubtful, for the opposing E.M.F. of polarization sets in almost before the true E.M.F. of the cell can be measured. The different values assigned to other cells are accounted for by the different degrees of concentration of the liquids. Thus in the Daniell's cells used in telegraphy, water only is supplied at first in the cells containing the zincs; and the E.M.F. of these is less than if acid or sulphate of zinc were added to the water.

193. Other Batteries. Numerous other forms of battery have been suggested by different electricians. There are three, of theoretical interest only, in which, instead of using two metals in one liquid which attacks them unequally, two liquids are used having unequal chemical action on the metal. In these there is no contact of dissimilar metals. The first of these was invented by the Emperor Napoleon III. Both plates were of copper dipping respectively into solutions of dilute sulphuric acid and of cyanide of potassium, separated by a porous cell. The second of these combinations, due to Wöhler, employs plates of aluminium only, dipping respectively into strong nitric acid and a solution of caustic soda. In

the third, invented by Dr. Fleming, the two liquids do not even touch one another, being joined together by a second metal. In this case the liquids chosen are sodium persulphide and nitric acid, and the two metals copper and lead. A similar battery might be made with copper and zinc, using solutions of ordinary sodium sulphide, and dilute sulphuric acid in alternate cells, a bent zinc plate dipping into the first and second cells, a bent copper plate dipping into second and third, and so on; for the electromotive-force of a copper-sodium-sulphide-zinc combination is in the reverse direction to that of a copper-sulphuric acid-zinc combination.

Upward proposed a chlorine battery, having slabs of zinc immersed in chloride of zinc and kathodes of carbon surrounded by crushed carbon in a porous pot, gaseous chlorine being pumped into the cells, and dissolving into the liquids to act as a depolarizer. It has an E.M.F. of 2 volts.

Bennett described a cheap and most efficient battery, in which old meat-canisters packed with iron filings answer for the positive element, and serve to contain the exciting liquid, a strong solution of caustic soda. Scrap zine thrown into mercury in a shallow inner cup of porcelain forms the anode.

Marié Davy employed a cell in which the zinc dipped into sulphate of zinc, while a carbon plate dipped into a pasty solution of mercurous sulphate. When the cell is in action mercury is deposited on the surface of the carbon, so that the cell is virtually a zinc-mercury cell. It was largely used for telegraphy in France before the introduction of the Leclanché cell.

Obach's dry cell has an outer cylinder of zinc which serves as a case, lined with plaster of Paris soaked in salammoniac; with a central carbon kathode surrounded with binoxide of manganese mixed with graphite.

The Fitch cell, used in the United States, is a zinccarbon cell with an excitant composed of salammoniac