FIG. 223. W [269. so that all the plates of zinc, z, shall be united by conducting wires, and all the platinum plates in a similar way by other wires; or they can with equal readiness be united so that the zinc of one cell shall be connected with the platinum of the following cell. Suppose, for instance, two plates (z and P, fig. 223), one of zinc, the other of platinum, each six inches square, be im P mersed in a vessel of sulphuric acid, at a distance of an inch apart. A current of a certain intensity will be obtained on connecting the two plates by means of a wire, w; and in five minutes a certain quantity of zinc will be dissolved, whilst a corresponding quantity of hydrogen gas will escape from the platinum. Now if the zinc and the platinum be each cut into strips of an inch broad and six inches long, and the several pairs of zinc and platinum strips be immersed in separate vessels of diluted sulphuric acid at the distance of one inch from each other, and if, as in fig. 224, all the zinc strips, z, z, be connected by wires, and all the platinum strips, P, P, be similarly united,-on connecting them together by a wire, as shown at w, the same current will traverse the wire as in the first combination, and the quantity of zinc dissolved in the six plates taken together will in five minutes be the same as that which was dissolved from the single zinc surface in the first arrangement; whilst the quantity of hydrogen gas which will rise from all the six plates of platinum together will be equal to that obtained from a single plate in the former experiment (fig. 223). Such a combination, in whichever of the forms just described it be employed, may be regarded as a single pair of plates, and it constitutes a simple voltaic circuit. By acting upon extensive surfaces arranged in simple circuits, the quantity of electricity which can be thrown into circulation is very large, though its intensity, that is to say, its power of overcoming resistance, is comparatively small. 269.] SIMPLE AND COMPOUND CIRCUITS. 541 The results would, however, be altered if, instead of connecting the divided plates together in the manner represented in fig. 224, they were connected as in fig. 225, in which the zinc in each FIG. 225. cell is supposed to be connected with the platinum plate of the adjacent cell in regular order through the series. When the extreme plates are connected by a thick wire w, the current which traverses this wire in a given time is equal to one-sixth only of the current which was thrown into circulation in the former instances; but the quantity of zinc dissolved in the six cells taken together is the same as before: and if the hydrogen be collected from the six platinum plates, the quantity will be still equal to that disengaged in the experiments shown in figs. 223 and 224. The current has now to traverse each cell of the liquid in succession, and thus has to encounter a great additional resistance. Yet now the current starts from six separate points of origin, and each of these separate points adds its energy in driving forward the current. The electro-motive force is increased sixfold, whilst the resistance of the liquid is increased still more; in the first place it is increased sixfold from the circumstance that the length of the column of liquid which must be traversed, is six times as great, and it is next further increased sixfold by a proportionate diminution in the breadth of the column. In the arrangement of fig. 224 there was a column of liquid six inches wide and one inch thick to be traversed; whilst in the arrangement of fig. 225 there is a liquid column six inches thick and only one inch wide to be traversed. When the plates are arranged in separate compartments, and are connected together alternately, as in fig. 225, they constitute a compound voltaic circuit. Volta's pile (fig. 210) and his crown of cups (fig. 211) are therefore compound circuits, and it is this form of combination which enabled him to obtain results so much superior to those of any previous experimenter. The electricity in this case is not greater in quantity than that obtainable from a simple circuit; nay, it is often much less; but it has a much higher intensity, and its power of overcoming resistances is very much greater, as a further examination will show. If, for example, 50 or 100 miles of wire, such as is used 542 OHM'S THEORY. [269. for telegraph purposes, be introduced in a combination arranged, as in fig. 224, as a simple circuit, the effect obtained would be very materially less than if the same plates were arranged in the form of a compound circuit, as shown in fig. 225. (270) Ohm's Theory.-These considerations may be much simplified, by representing the mutual action of the electro-motive forces and the resistances of any circuit, simple or compound, in the form of a fraction, in the way proposed by Ohm. It has been found by experiment that the quantity of electricity produced by any combination is directly proportioned to the electro-motive force, or chemical energy between the active metal and one of the elements of the liquid upon which it acts; and inversely proportioned to the resistances to be overcome. The numerator of the fraction will therefore be represented by E, the electro-motive force, and the denominator by R+r; where R represents the resistance in the cell or the battery (due chiefly to the attraction between the elements of the liquid for each other), and r all resistances exterior to the cell or the battery, such as the connecting wire thus the expression, would represent the effect of any combination where A indicates the quantity actually in circulation, whether measured by its heating or by its magnetic effects. If the connecting wire be very thick, so as to offer little or no resistance to the current, r becomes evanescent, and the fraction assumes the form of A; the current under these circumstances is proportional to the surface of the plates exposed to the action of the liquid. : = E Let it be assumed, for example, that E=1, and that R=1, when a pair of zinc and platinum plates an inch broad and six inches long is immersed in diluted acid at the distance of one inch asunder, so that under these circumstances, ==1. If a pair of plates six inches broad and six inches long, also at a distance of one inch apart, be immersed in the same acid, since the resistance is inversely as the surface of the plates immersed, the fraction becomes R or E 6 1 6 1 =6; or the current is increased six fold as compared with the former. If the plates be each cut into six similar strips, and be then arranged in pairs, as represented in fig. 224, the same fraction still represents the result, since the relative size and distance of the plates remain unchanged: but if the plates be arranged in succession, so as to produce a compound circuit, as in fig. 225, the fraction becomes == 1; the electromotive force is increased sixfold, but the resistance is increased also in exactly the same proportion. The quantity which under 6 E 6 R 271.] OHM'S THEORY-CHEMICAL DECOMPOSITION. 543 these circumstances circulates through the connecting wire is not greater than if a single cell only, containing a pair of plates one inch broad and six inches long were employed. But suppose now that several miles of wire, such as are employed in telegraphic communication, be introduced into the two combinations severally represented in figs. 224 and 225; r now acquires importance; let this resistance r be twentyfold greater than that of the liquid in each cell. In the first case (with the simple circuit), the fraction becomes R 6 E 1 = 1 6 6 E 6 +r +200049; in the second (the compound circuit), the fraction is 6 R+r 6+20=0'23: so that although in both cases the resistance introduced most materially diminishes the current which enters into circulation, the quantity in the compound circuit is now five times as great as that which emanates under these circumstances from the simple circuit. Indeed, in all cases where great resistances external to the battery have to be overcome, a compound battery has a great advantage over the simple circuit.* (271) Chemical Decomposition.-It is important to remember that the current which circulates through each cell in a compound circuit is not increased by the arrangement, if the connexion between its extremities be made by means of a good conductor ; if, for example, 50 similar and equal cells be connected in succession, and be united by a stout short wire, the quantity of zinc which would be dissolved in a given time in each of these cells would not be greater than that which would be consumed in a single cell of the same size in the same time, if the plates which compose it were connected by a short thick wire. The power of a compound circuit is shown in a striking manner when some liquid such as diluted sulphuric acid is interposed in the course of the conducting wire. The experiments * Let n = the number of the plates in a compound circuit, The fraction which represents the action of a compound battery when its extremities are connected by means of a metallic wire of uniform diameter is nE D the following: D ī A. In this expression is substituted for R, (the re + = sistance in each cell of the battery) to which it is equivalent; since R is directly as the distance between the plates, and inversely as their area, or surface, while represents r. 544 DISSECTED BATTERY. [271. which elucidate this point may be instructively performed by means of the dissected battery. If a pair of platinum plates, a, b, fig. 226, be immersed in the acid conducting-liquid at B, and connected with the wires proceeding from the compound circuit in the manner represented in the figure, the liquid will be decomposed, oxygen will be given off from one plate, a, and will rise in the tube o; whilst hydrogen will be given off from the other plate, b, and may be collected in the tube, H; but if the same cells be arranged as a simple circuit, fig. 224, no such effect is produced. By the introduction of the liquid conductor at B, the resistance is very greatly increased, such a resistance being more considerable than that of many miles of wire. But this is not all: besides this resistance, a new counteracting electro-motive force shows itself, which gives rise to a current operating in a direction the reverse of that in the battery. This force is due to the oxygen and hydrogen which are separated upon the platinum plates, and which, as has been explained when speaking of the gas battery (264), is very considerable. Experiment shows that it is between two and three times as powerful as the electro-motive force of a pair of zinc and platinum plates excited by diluted sulphuric acid. When, therefore, the endeavour is made to decompose the diluted acid by a single pair of zinc and platinum plates, however large a surface they may present to the action of the exciting liquid, no visible action in the cell, B, ensues; a momentary decomposition, too small in amount to be perceived by the eye, produces a development of oxygen and hydrogen upon the two platinum plates, a, b, sufficient to oppose an effectual barrier to the transmission of the current. Even when two pairs of zinc and platinum plates are used, the energy of the current is insufficient to effect any visible decomposition; with three pairs a few bubbles of gas show themselves; and with a more numerous series, the effects increase, rapidly, till at length a point is gained, beyond which no |