several materials it may be removed from equilibrium as regards their relative quantities, and so be suitable for producing electromotive force. Instances of this are difficult to find in practice, as in reactions between salts very often equilibrium is only reached when the amount of some constituent becomes immeasurably small. Thus, if metallic copper be put into a solution of a silver salt, silver will be deposited: a reaction that may be written

Cu + 2Ag Cu" + 2Ag

This is, presumably, a reversible reaction; i.e. deposition of silver will cease when the concentration of the silver ions is sufficiently reduced, and that of copper ions sufficiently increased. · But the difference in free energy between the two metals (measured by difference in electro-affinity, p. 159) is so great that it will only be compensated by concentration difference when the ratio of copper to silver is to be reckoned by millions, and the residue of silver in solution has fallen below the possibilities of chemical analysis.

A case in which the connection between E.M.F. and concentration could be followed experimentally has been exhaustively worked out by Ogg.' Silver and mercury are near together on the scale of electro-affinity; hence, if one of these metals be allowed to act on a salt of the other, we have a reaction that is undoubtedly reversible, viz.—

2Ag + Hg2 ̈2Hg + 2Ag'

Here the mercurous ions are written Hg2", not 2Hg, as Ogg showed, by several lines of reasoning, that mercury always forms divalent ions. This state of equilibrium was measured chemically by shaking up mercury with silver nitrate solution, or silver amalgam with mercurous nitrate solution, and analysing the resulting solution: both silver and mercury were found dissolved in appreciable quantity. Again, the equilibrium was established electro-chemically, by setting up a cell of the pattern Ag (amalgam): AgNO, HgNO, Hg

by varying the strengths of solution, either Ag or Hg could be Zeitschr. phys. Chem., 22. 535 (1897); 27. 285-311 (1898).

1

made positive. Both classes of experiment were carried out quantitatively and shown to yield the same results as to the relative affinities of the two metals. These experiments will be more fully dealt with in the second volume.

§ 8. METHODS OF MEASUREMENT.

In measurements of electromotive force and electrode potential, the requirements are chiefly (i.) a source of current; (ii.) a standard of comparison; (iii.) an instrument to compare the electromotive force with the standard.

A. MEASUREMENT OF ELECTROMOTIVE FORCE.

(i.) As source of current, a battery of accumulators is by far the most useful.1 Full details as to the treatment of accumulators are to be found in various technical hand-books, but the manipulation is so easy that it will be sufficient to mention a few practical points only. Accumulators are usually made up with acid of 1'18 to 1'20 density; when charged they have an E.M.F. on open circuit of about 2'05 volts ; but for charging 2.5 volts each should be allowed, hence only 44 cells can be charged from mains at 110 volts. A battery of a few cells such as is required for measuring and for electrolysis, should be joined up in series with an adequate resistance and charged off the mains till the cells gas freely. Once a week is enough to keep a battery in good order. the cells have to be left for long they should be fully charged first.

If

As the water in the acid evaporates, distilled water should be added from time to time, so as to make it up without accumulation of chlorides: the liquid should be kept at least a centimetre above the top of the plates. Good insulation of the leads is important, as it allows the cells to retain their charge better, and keep a steady electromotive force. Glass

1 In places where no means exist for charging accumulators, recourse must be had to primary cells. The " cupron' " cell has been highly recommended for this purpose.

T. P. C.

Q

cells are the best in this respect, and may be paraffined to keep the acid from creeping.

Accumulators should not be discharged so that their voltage falls below 18. The maximum discharge rate is usually reckoned at o'or ampere per square centimetre of positive plate. The smallest size of ordinary cell, with one positive and two negative plates, designed to give two to three amperes is quite sufficient for most measuring purposes, especially for potentiometers; and if only used to give two or three centi-amperes, will maintain a practically unvarying voltage for a day. Traces of foreign metals (except mercury) are highly deleterious to the lead accumulator, and must be carefully avoided.

The public electric supply, when not alternating, can be used for many purposes, but not for potential measurements of any accuracy, as it constantly fluctuates within small limits (1 or 2 per cent.). Lamps serve satisfactorily as resistances to regulate current by, and are often inserted to avoid the risk of excessive currents.

For measurements in which currents neither large nor very constant are required, Leclanché cells-most conveniently "dry cells "-serve excellently. The voltage is about 1'4; cells of moderate size have a resistance of 0.5 to 5 ohms, and will give small currents (one or two centi-amperes) with good constancy. Dry cells will last for months without attention.

For some purposes it is necessary to have a source of current the potential difference of which will remain practically constant, independently of the current taken from it (within limits). When the required potential difference is that of one or more cells, there is, of course, no difficulty; but to obtain a steady potential difference of adjustable magnitude, the device

+

A

C

B

shown in Fig. 43 is used. Current from a battery (or the public supply if not alternating) is passed through a resistance AB, and wires from the ends of a part AC of this resistance are led away to the apparatus to be supplied. By adjusting the length AC the potential can be varied. It is necessary that the

FIG. 43.

current to be taken through the experimental circuit should be a good deal smaller than that flowing through AB. For use with a battery of a few volts AB may be a wire of a few ohms wound on a drum, with a sliding contact at C. If a high voltage supply is used, AC may be an adjustable resistance, and CB a lamp. A voltmeter may conveniently be put across the wires leading from AC to the experimental circuit.

(ii.) As standards of electromotive force, either the Clark or cadmium cell is nearly always used. These are described in full below (§ 9). The E.M.F. at temperature t is, according to Jaeger,' for the Clark

1'4328 000119 (t

15) — 0000007 († — 15)2

for the cadmium cell with saturated solution

1*01860'000038 (t—20) — 0'00000065 (t-20)2

for the Weston form of cadmium cell

I'0190 constantly.

Cadmium cells have the great advantage of being nearly independent of temperature, and so are rapidly replacing the Clark as practical standards.

(iii.) Instruments or arrangements of instruments for comparing voltages may be divided into direct reading and null; the former usually require some current to work them, and are used for approximate measurements; the latter in the form of the potentiometer measure electromotive forces on open circuit, and are capable of a high degree of accuracy.

Direct-reading voltmeters, designed for technical use, are to be had, of range from volt upwards. One of the most useful patterns is the "cell-tester" intended for use with accumulators, and reading to 3 volts as a maximum. Voltmeters are based upon the magnetic effects of electric currents, and usually contain either magnets or soft iron, which makes them liable to change with age. It is therefore well to recalibrate them from time to time. The readings of the instrument should be accurate to one per cent.; and a voltmeter cannot be regarded as satisfactory that takes more than about

1 See also tables, p. 260.

ampere when showing its maximum reading. Thus the celltester mentioned above should have a resistance of at least 300 ohms; instruments for high voltage are made by putting extra resistance coils in series with the working parts.

The terminals of a voltmeter are connected directly to the two points between which the potential difference is to be measured. Thus they may be applied to the positive and negative poles of an accumulator (whether an open circuit, charging or discharging); but attention must be paid to the internal resistance of the cell, etc., to be tested. Thus, if a voltmeter has a resistance of 300 ohms, and is connected to an accumulator of one-tenth ohm, only 3000 of the total resistance of the circuit is external to the instrument; but the electromotive force in the circuit is distributed in proportion to the resistance to be overcome; nearly all of it will be spent on the voltmeter (2999, to be exact), and the reading will be practically correct. But if the same instrument were used to test a cadmium cell of 200 ohms, no less than two-fifths of the resistance would be in the cell; only three-fifths of the electromotive force would be spent on the voltmeter, the readings of which would therefore be entirely wrong.

If, then, the internal resistance of the cell or other object to be measured is at all large, the voltmeter must be replaced by a more delicate instrument, requiring less current to work it.

Such an instrument is the D'Arsonval galvanometer; having a large fixed magnet it is practically independent of outside influences, and can be relied upon for constancy to the same extent as a good voltmeter. Galvanometers of 100 ohms (an average resistance) can be had, with pointer, to give their maximum deflexion for o'ooo1 ampere, and to indicate to o'ooooo ampere; when used with telescope and scale they may be made a hundred times more sensitive. Thus, by putting large resistances in series with such instruments, they can be used to measure the electromotive force of voltaic combinations that are not adapted to give more than infinitesimal currents; but the percentage accuracy is not much greater than that of direct reading voltmeters.