quantities of electricity pass through the two metallic arcs, and equal volumes of hydrogen gas are evolved on the two copper plates. If the chemical action in one cell becomes stronger than that in the other, the excess takes the purely chemical form, and the superabundant hydrogen is all evolved upon the zinc.

The current which passes from o to p in a two pair circuit is not greater in quantity than that which traverses the connecting wire of a simple circuit; provided that the quantity of zinc dissolved off the zinc plate of the latter in a given time is equal to that dissolved from each zinc plate of the two-pair circuit, and that no purely chemical action takes place in either case (as when amalgamated zinc is used); or else that in both cases the quantity of purely chemical action bears the same proportion to that of the electro-chemical action. For the negative electricity which in the two-pair battery runs through op, proceeds, not from both zinc plates, but only from Ž1; and if no more of this plate be oxidized in a given time than of the zinc plate of a single pair, the quantity of negative electricity developed in the former case will likewise not be greater than that developed in the latter. The negative electricity evolved from Z2 merely passes through the arc gi, and is absorbed at C1 by the hydrogen. Similarly, with batteries consisting of several pairs;— so many pairs, so many separate currents.

If the circuit be opened at gi while it remains closed at op, C' and Z2 become the poles. If, therefore, in a battery consisting of several pairs, and having its ends metallically connected, any zinc plate be separated from the copper plate with which it is associated, those two plates become the poles.

The quantity of electricity in the current may however be increased by augmenting the number of pairs, if the electro-chemical action in the individual pairs is accompanied by purely chemical action. For, the greater tension or velocity of the current produced by several pairs causes the purely chemical action to diminish and the electro-chemical action to increase. But this increase of quantity can only rise to the maximum at which the action becomes wholly electro-chemical-and consequently, all the negative electricity of the zinc passes to the hydrogen through the other metal.

It appears then that the union of several pairs in a battery increases the tension of the electric current in direct proportion to the number of pairs, and likewise augments the quantity to a certain extent in those cases in which a considerable quantity of the negative electricity of the zinc in the simple circuit is withdrawn from the current by purely chemical action.

We may conclude then that the Quantity of the electric current of a galvanic battery depends: 1. On the strength of the electro-chemical action in the individual simple circuits of which the battery is composed― principally therefore on the circumstances considered (pp. 376....381.) 2. On the number of pairs-because as that number is increased, pure chemical action is more and more prevented.

The Tension depends: 1. On the tension of a simple circuit: and 2. On the number of simple circuits conjoined.

According to the view just laid down, a galvanic battery of zinc and copper with fluid, should be constructed in the following order: ZfC, ZfC, ZfC, &c.; and accordingly, the zinc pole is negative and the copper positive, as in the simple circuit. But according to the contact theory, which regards the contact of the two metals as the principal source of the

electricity, the battery should be arranged as follows, CZf, CZƒ, CZƒ, &c. In this arrangement, the copper pole on the left is negative and the zinc pole on the right positive. Hence, the expressions, copper pole instead of negative pole-and zinc pole instead of positive pole, are of frequent occurrence. But according to the chemical theory, the outermost copper on the left and the outermost zinc on the right are altogether without influence on the force of the battery; and if these two external members are removed, the first mentioned arrangement remains behind.]

Ohm's Formula, relating to the Quantity of the Electric Current.

1. For a conductor into whose extremities the two electricities flow with a given tension:

Let A be the electrical tension; K the conducting power of the wire or other conductor; w the surface of its transverse section; L its length; Q the quantity of the current, then

Hence the quantity of the entering electricities which pass through the wire in a given time, varies directly as the tension of the electricities, the conducting power and thickness of the conductor,-and inversely as its length. Hence also, the quantity of the current in two conductors is the same, when, with equal electrical tension and conducting power, the ratio of the transverse section to the length is the same in both; or, with equal tension and equal transverse section, the ratio of the conducting power to the length is the same; or, with equal conducting power and equal transverse section, the ratio of the tension to the length is the

same.

2. For a simple Galvanic circuit.

Let A be the electromotive power of the circuit (or the tension ?), R the resistance which the current meets with in the circuit itself. This is the resultant of the following individual resistances:-a. Resistance of the two metallic plates which the current has to traverse; b. Resistance of the liquid through which, according to the ordinary view, the current passes, [according to p. 343, f, this is the resistance which the liquid opposes to the transposition of atoms]. To this, Fechner and Poggendorff add c): the resistance of transition,-i. e. the resistance which exists to the passage of the electric current from the metal to the liquid, and conversely.

Also, let be the resistance of the conductor which unites the two metals, and Q the quantity of the electric current which enters it; then

When the resistance r of the conductor which closes the circuit is

inconsiderable in comparison with the resistance R in the individual circuits, it nearly vanishes in the formula, and there remains

that is to say: the quantity of the current is the same, whether it proceeds from one pair or from several.

But if the resistance of the conductor which closes the circuit is considerable-e. g., from the interposition of water, &c.—then, Q increases

A

considerably with the number of pairs—because then R+ gives a much

The development of this subject may be found in Ohm's Memoirs already cited on page 307; likewise in Ohm's Galvanische Kette, Berlin, 1827; Fechner, Maassbestimmungen der galvanischen Kette, Leipzig, 1831; Pouillet (Pogg. 42, 281); Henrici (Pogg. 53, 277).

Quantity of the Electric Current of a Galvanic Battery.

With amalgamated zinc and platinum in dilute sulphuric acid, the quantity of the current is not increased by augmenting the number of pairs. One pair, by the oxidation of one atom of zinc-provided the connecting wire be thick enough to transmit the feeble current without diminution supplies as much electricity in the form of a current, as 1000 pairs would supply by the oxidation of 1000 atoms of zinc. In all the cells, equal quantities of water are decomposed and equivalent quantities of zinc dissolved, viz. 32.5 parts (1 At.) of zinc, to 1 part (1 At.) of hydrogen gas evolved. (Faraday.)

A number of pairs does not produce a stronger deflection of the galvanometer than a single pair; one pair acts more, another less strongly. The sum of the effects [quantities] of the single pairs divided by the number of pairs gives the effect [quantity] of the pile: hence, a larger pair added to a number of smaller pairs increases the action,-a smaller pair diminishes it. (Marianini.)

Even though the several pairs, from differences in extent of surface or in the nature of the liquid, should individually produce different quantities of electricity,-still, all the currents which pass from the electronegative to the electro-positive metals of the several pairs, after the union of these pairs, are mathematically equal. The quantity of electricity in the current of a battery is greater than that of the weakest pair taken singly, because, when this pair is joined to the battery, no more pure chemical action takes place in it. A very feeble pair is to be regarded only as an interposed plate (vid. seq.) which weakens the current; and the quantity of the current remains the same, even when the weak pair is introduced in the reverse order. (De la Rive.)

The quantity of the current of a pile charged with dilute sulphuric acid is very much diminished, when this pile is united in the proper order with another containing only water. (Schönbein.)

If 10 pairs of amalgamated zinc plates and platinum plates are separately immersed in dilute sulphuric acid, different quantities of hydrogen gas are evolved in a given time on the surfaces of the several platinum plates, the variation amounting to about of the whole. But when all the 10 pairs are united into a battery, the quantity of gas evolved on

each platinum plate is the same, and equal to that which was before evolved on the platinum plate of the weakest pair. If the rings of all the zinc and platinum plates are immersed in a vessel filled with mercury, the development of gas on the platinum plates again becomes as unequal as in the first case. If every two zinc plates be connected with every two platinum plates, and the 5 double pairs united into a battery, the evolution of gas is the same in all the cells. When 8 pairs are left simple, and connected with one double pair to form a battery, the quantity of gas evolved on the two platinum plates of the double pair taken together, is not greater than that evolved on each platinum plate of the single pairs. When each of the 10 zinc plates is placed between two platinum plates, the evolution of gas on each double plate is increased nearly twofold; and part of the gas likewise escapes on that surface of the platinum which is turned away from the zinc. When unamalgamated zinc is used, a great deal of hydrogen gas is evolved upon its surface; but the quantity evolved on the platinum is the same as when the zinc is amalgamated; hence the local pure chemical] action does not interfere with the force of the current. (Daniell.)

If several pairs of amalgamated zinc and platinum in dilute sulphuric acid are united into a battery, and the polar wires dipped into dilute sulphuric acid, the quantity of hydrogen gas evolved in each exciting cell of the battery is exactly the same as that set free in the decomposing cell. When the circuit is imperfectly closed by the interposition of a long thin wire or a liquid conductor, the quantity of gas evolved in all the cells is diminished, but is the same in all; the greater the number of pairs, the less does this diminution in the quantity of hydrogen gas amount to. (Matteucci.)

Twenty pairs of zinc and copper give the same deflection of 20° as one pair, when the circuit is closed by a wire of sufficient thickness. But when the current is conducted from the poles through a stratum of water, the deflection with one pair amounts to 10°, with 5 pairs to 15.3°, and with 20 pairs to 19°. (Buff.)

One pair of plates gives the same deflection, whether the metals are separated by one or five pieces of cloth saturated with liquid; but when several pairs are united, the deflection diminishes as the thickness of the cloth is increased. The diminution is less however in proportion as the liquid conducts better [i. e., exerts chemical action]. Marianini.

The following experiments by Binks were made with amalgamated zinc plates and platinum plates of equal size in dilute sulphuric acid.

The quantity of zinc dissolved in a given time diminishes as the number of plates is increased, in the following proportion-the first number denoting the number of pairs of plates, the second the loss of zinc: 157,-2:3·9;-4:38,-8:38,-16:34,-32:36,-40:38,

48:2.7.

A similar diminution takes place in the quantity of hydrogen gas evolved, when two pairs of unequal surface are united: a denotes the surface of each of the pairs of the plates, b the quantity of hydrogen gas which each would have developed by itself, c the quantity evolved after their union:

It is remarkable that when the surfaces of the two pairs of plates are very unequal, the quantity of hydrogen evolved on the copper of the larger pair is greater than that evolved on the copper of the smaller. (Binks.)

The electric current of a battery ceases when the whole is cooled to - 18° [in consequence of the freezing of the liquid?]; it increases with the temperature, but ceases again at 100°, and recommences with violence on subsequent cooling. It is however considerably increased by heating only half of the battery to 100° (Dessaignes, Ann. Chim. Phys. 24, 203), -[this deserves verification].-A battery which at 15° gives a current, capable, when conducted through a watery liquid, of disengaging 22 measures of hydrogen gas in a given time, yields 39 measures in the same time, when heated to 52°. (Despretz, Gilb. 72, 310.)

When the current of a trough-battery has diminished, it may be increased almost double by stirring the acid liquid between the zinc and copper plates with a feather. (Faraday.)

Electrical Tension of the Battery.

The tension of the unclosed circuit, as determined by the electrometer, increases directly as the number of pairs. (Volta, Bohnenberger (Gilb. 57, 346), Singer, Marianini.) It increases as the square of the number of pairs. (Delezennes, J. Phys. 82, 269). In the unclosed circuit, it increases as the square of the number of pairs, and in the closed circuit directly as the number; for the statical effects of a given quantity of electricity, as shown in the open circuit by the electrometer, are to the dynamical effects which the galvanometer exhibits in the closed circuit, in the ratio of the square to the simple number. (Peltier.)

The tension, as shown by the electrometer in the unclosed circuit is not affected by the size of the plates, but only by their number. When one, pole is connected with the ground, the maximum of tension is the same, whether the battery be charged with river-water, solution of sulphuret of soda, or water acidulated with nitric acid; but in the last case, the maximum tension is instantly attained, more slowly in the second, and most slowly of all in the first. When the battery is insulated, the tension is altogether weaker,-strongest however when the charge is made with river-water, weakest when water acidulated with nitric acid is used: in the latter case, it often vanishes altogether. (De la Rive.) In the unclosed circuit, the nitric acid exerts an oxidizing action, not only on the zinc, but likewise on the copper, thereby giving rise to an opposite current; but when the circut is closed, the oxidation of the copper ceases. (Buff.)

The middle pair of an unclosed circuit of twenty pairs of zinc and copper does not act more strongly on an electrometer furnished with a condenser, than one single pair would. The greater the number of pairs included in the circuit by touching one of them with the condenser and the other with the finger, the stronger is the divergence of the gold leaves. Likewise, when the circuit is closed, but in such a manner that the current is obliged to pass through water-not decomposing it perceptibly-a certain degree of tension is manifest, increasing towards the poles. Even when dilute sulphuric acid is used instead of water, tension is still apparent, although the liquid is decomposed; but not when the circuit is completely closed by a metallic conductor. Whenever, therefore, an obstacle, such as water, is to be overcome, electricity accumulates in the poles till it acquires sufficient tension to overcome the resistance. (Buff.)

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