272.]

THE VOLTAMETER.

545

advantage is obtained by increasing the number of cells in the battery.

It is particularly worthy of remark, that in every cross section of any voltaic circuit at a given instant, the quantity of electricity which traverses it is uniform: consequently, the same quantity of hydrogen makes its appearance upon the plate, b, of the cell B, which contains the liquid for decomposition, as is disengaged and collected during the same interval from each plate in the battery itself. If each zinc plate of the battery be weighed before the experiment is begun and after it is concluded, it will be found that each plate has lost weight to an equal extent. The interposition of the liquid at в may occasion a great reduction in the amount of electricity which is thrown into circulation: but at every transverse section of the battery, the electricity that does circulate is uniform in quantity; and the measurement of the chemical action, whether it be estimated by the quantity of gas which is evolved at any one point, or by the quantity of zinc which is dissolved, may be employed as a sure indication of the quantity of electricity in circulation: in other words, retardation of the current by the liquid conductor is necessarily attended with an equal retardation in the conducting wire, and in each cell of the battery itself.

(272) The Voltameter.-The foregoing important law was discovered by Faraday. As one of its consequences he was enabled to employ a decomposing cell, such as is shown at в, fig. 226, as a measure of the voltaic power of any circuit such an instrument is called a Voltameter. For each 65 milligrammes of zinc dissolved in any one cell of the battery, 18 milligrammes of water are decomposed in the voltameter; whilst 22:32 cubic centimetres or 2 milligrammes of hydrogen, and 11'16 cubic centimetres or 16 milligrammes of oxygen, at o° C. and 760mm. Bar., are evolved upon its plates; at the same time 22:38 cubic centimetres of hydrogen are evolved

from every platinum plate in the cells of the battery. A more convenient form of . voltameter is shown in fig. 227. It consists of an upright glass cell, to the neck of which a bent tube, c, for the conveyance of

FIG. 227.

546

THE VOLTAMETER.

[272. the disengaged gases, is fitted by grinding; the vessel is filled with diluted sulphuric acid; a, b, are the two platinum plates, each of which is connected by a wire which passes through the foot of the instrument, to a mercury cup, by means of which communication can be made with the wires which convey the current from the battery: oxygen and hydrogen are liberated by the action of the current upon the acidulated water, both gases then rise to the surface of the liquid, and are conveyed by the bent tube, c, to the graduated jar, d, which stands in a small pneumatic trough.*

It is to be observed that the action of a simple zinc and platinum battery is not steady; it gradually declines, and before the acid has become saturated with zinc, the current almost ceases. On breaking the contact of the conducting wire with the two ends of the battery, and allowing it to remain disconnected for a few minutes, the action is partially restored; but it again gradually declines after the circuit has been completed. These effects were traced by Daniell to the action of the current upon the zincic sulphate, which is formed in each cell of the battery during the operation; the zinc salt is decomposed in the manner shown in the subjoined diagram, in which ZnSO, represents the zincic sulphate, and Pt and Zn the platinum and zinc plates of the cell. The brackets placed above the symbols indicate the arrangement of the particles before the current passes; those below show the change produced by the voltaic action:—

Pt Zn SO, Zn SO, Zn

In this manner metallic zinc becomes reduced or deposited upon each platinum plate, and the power of the battery is arrested when the two surfaces which are opposed become virtually zinc and zinc instead of platinum and zinc. This evil may be obviated by interposing a porous diaphragm between the two plates, as in the batteries of Daniell and of Grove (265, 266); in these cases a sufficient communication between the zinc and the copper or the platinum plates, is still kept up by means of liquid through the pores of the diaphragm, but the zincic sulphate is prevented from mixing with the liquid which is in contact with the copper or the platinum.

* At low temperatures the proportion of oxygen evolved is always a little below the calculated quantity, owing to the retention of a small quantity by the acid liquid in the voltameter, in the form of hydric peroxide (H,O,); the larger the positive electrode employed, the greater is the diminution of the oxygen.

273.1

n E n R+ r

=

FURTHER APPLICATION OF OHM'S THEORY.

547

(273) Further Application of Ohm's Theory.-All the phenomena of compound circuits admit of ready calculation by the application of Ohm's law; for instance, if n represent the number of the plates, the expression for any compound series, the cells of which are similar in nature and equal in size, becomes A; since in each cell not only is a new electro-motive force introduced, but at the same time a new resistance. Provided that the exterior resistance is such as would be offered by a metallic wire which may be even many miles in length, it is possible exactly to double the current by doubling the number of cells, if at the same time the size of the plates be doubled; for But if, when the number of cells is doubled and the surface of the plates also is doubled, a voltameter be employed to measure the current, instead of introducing a wire as the exterior resistance, the current measured by the voltameter is not found to be doubled, as might naturally have been expected this difference arises from the counter current which is produced in the voltameter itself, by the accumulation of the oxygen and hydrogen upon its plates. Call this counter current e, and the formula becomes n R+r

2nE

2n R = 2

+

2n E n R+r

n E-e

This

The values both of e, (the counter current offered by the voltameter,) and r, which, if short thick conducting wires be used, is virtually the resistance of the voltameter itself, may be very simply estimated in the way proposed by Wheatstone. method consists in comparing two experiments in which the resistances remaining the same, the electro-motive forces alone vary. Upon the supposition that the voltameter merely offers an increased resistance without introducing any counteracting electromotive force, five single cells should produce a result equal to half that obtained by the use of ten cells of double size; but by experiment, the effects as measured by the voltameter are as 6 20. Comparing these effects with the arrangements which produce them, we obtain the following proportion, from which the value of e is deduced in terms of E:

The resistance r of the voltameter may be calculated with equal ease; for taking two similar batteries, each composed of ten cells, but in one of which the plates are exactly double the size of those in the other, the electro-motive forces will continue the same. while the resistance alone will vary. Under these circumstances the experimental results, furnished by the voltameter in equal

fore r=3 R. By substituting in the formula the values for e and r thus obtained by experiment, the results for any given number of cells may be calculated; and on comparing the values obtained by such calculation with the numbers furnished by actual experiment, Daniell (Phil. Trans. 1842, 146) obtained the following results:

Any alteration in the size of the plates of the voltameter necessarily alters the resistance which it offers to the current, and the influence of this change in the voltameter is most perceptible when a battery consisting of a few plates which expose a large surface is employed.

The preceding considerations will render it evident that no general answer can be given to the question, 'What number of cells should a battery contain in order that it may produce the greatest current?" The electro-motive force, E, varies in amount with the kind of battery which is used; the values for R and r will also vary with the varying circumstances of the experiment. It is found that every different arrangement requires the employment of a distinct number of cells in order to obtain from it the maximum effect with the least expenditure of zinc. This number will vary even with the same form of battery, according to the size of the battery plates, the length of wire in the circuit, and the nature of the liquid conductor in the decomposing cell. It may be stated, however, as a general principle, that the most advan tageous effect is obtained when the value of A, in the formula n E-e +A, most nearly approaches o5, E and R each being=1: in other words, the advantage is greatest when the exterior resistances-viz., those of the conducting wire and voltameter togetherare equal to the sum of the resistances due to the battery itself; it may therefore be concluded that when the exterior resistance is trifling, as usually occurs when the circuit is metallic and not of very great length, little or nothing is gained by employing a large number of cells; two or three plates of large surface being the best under such circumstances; but that where a considerable chemical resistance is to be overcome, power is gained by employing a series numerous in proportion to the resistance so intro

n r

=

274.]

duced.

WHEATSTONE'S RHEOSTAT.

549

In no case, however, is it possible by the use of a series of plates of uniform dimensions, even if of unlimited number, to produce in any transverse section, such as an included voltameter, a chemical action greater in amount than that which would occur in a single cell of the arrangement in which the circuit was completed by a stout metallic wire.

(274) Wheatstone's Rheostat and Resistance Coils.-Guided by the principles which have just been explained, Wheatstone (Phil. Trans. 1843, 303) contrived an apparatus termed the Rheostat, by which measured amounts of resistance may be introduced into the voltaic circuit: if the effect which such added resistance has upon the amount of the current in circulation be measured, the different values of E, R, and r in different arrangements, may be deduced by a simple calculation.

The rheostat is represented in fig. 228: g is a cylinder of well-baked wood, 1 inch (4 centimetres) in diameter and 6 inches (15 centimetres) in length; it turns easily upon a horizontal axis: on this cylinder a spiral groove is cut, the thread of which contains 40 turns to the inch. This groove runs from one end of the cylinder to the other, and in it is coiled a brass wire 16 inch (0.25mm.)

in diameter; h is a brass cylinder, placed parallel to g, and equal to it in diameter; the thin wire upon g is connected at the end i with a brass ring, and at the other extremity is attached to the cylinder h; at i is a metallic spring, one end of which is connected with a binding screw, and the other end of which rests against the brass ring, and effects the communication with one wire of the battery: m is a movable key, by which the wire can be wound upon the brass cylinder, or by transferring the key to the axis of g, it can be unwound from 4, and returned to the wooden cylinder, g. In consequence of the non-conducting quality of dry wood, the coils of wire on the wooden cylinder are insulated from each other, so that the current traverses the whole length of the wire coiled upon this cylinder, but the coils not being insulated from each other on the brass cylinder, the current immediately passes from the point of contact to the brass spring at k, which is in communication with the other wire from the battery.