and the success of the whole process often depends on the fulfilment of the requirement that the metal shall be obtained in coherent plates of sufficient thickness, which shall not require to be melted or otherwise treated subsequently. Whenever possible, the area of the anode is made to exceed that of the cathode ; then, the cathode-surface remaining constant, the difference of potential in the bath may be reduced to any fixed limit by increasing the anode area. The current-density at the anode will thus be lower than that at the cathode. In the electrolysis of fused substances this condition cannot always be observed, especially if the containing vessel itself be employed as cathode; but the substances deposited at the anode are in these cases nearly always gaseous (chlorine, oxygen, or carbonic oxide), so that they rapidly rise to the surface and escape. No general

rule can be laid down for the selection of a suitable currentdensity. But the electromotive force necessary for any given electrolytic process should be calculated, and then the metal should be deposited by a current of which the potential does not vary greatly from this amount. The current-density at the cathode determined by this electromotive force will always be correct, provided that the metal deposited has the desired properties.

Calculation of Potential.-For full details of calculations to determine the electromotive force required in an electrolytic process, reference should be made to the text-books named above. For use in metallurgical practice, and in the research laboratories connected with works, the formulæ hitherto employed are not in all cases suitable since, as Nernst himself points out, only those circuits in which liquids alone are employed to the exclusion of metals have at present been studied in full detail. For the electro-deposition of metals such calculations are rarely made, the chief desideratum being the extraction of the required metal in a directly utilisable form. This difficulty has caused the failure of many theoretically good processes; and even the most accurate calculation can only afford values which approximate the real requirements. But these are imperfections inseparable from the comparatively crude methods of work required in practice; and they will in no wise detract from the services of Nernst, who has given so clear an insight into the phenomena of electrolysis.

Formulæ for the calculation of approximate values have been determined as follows:-One coulomb (ampere-second) deposits 0.010359 multiplied by a milligramme-equivalent (or 0.000010359 times a gramme-equivalent) of any substance. A gramme-equivalent of any ion carries, therefore, a charge of 96,537 coulombs. If the ion should be set in motion by an electromotive force, E (in volts), an expenditure of work equivalent to 96,537 × E joules is effected. Since the work of 1 joule (= 1 volt-coulomb) is equal to the energy which an acceleration of 1 metre in a

1

9.81

second is able to impart to a mass of 1 kilogramme (and is therefore equivalent to = 0·102 kilogramme-metre), it corresponds to 0.00024 kilogramme-calorie, or 0.24 gramme-calorie, 425 kilogramme-metres being equivalent of 1 kilogramme-calorie. The heat of decomposition (H) of a gramme-equivalent of various substances would, therefore, correspond to a heat quantity of 0.24 0.96537 x E gramme-calorie. From this equation H = 0·24 × 0.96537 × E is obtained

If the usual heat of formation of a compound be taken, this number may be substituted for H; but then the fraction must be divided by the number (n) representing the valency of the ions. contained in the solution; therefore

The heat evolved by a current of 1 ampere in traversing a resistance of 1 ohm amounts to 0.24 gramme-calorie per second; and to produce a current of 1 ampere in a resistance of 1 ohm, a fall of potential of 1 volt is necessary. The heat-equivalent of 1 watt (1 volt-ampere) is therefore 0.24 gramme-calorie, so that an electric horse-power (746 volt-amperes) affords 0.179 kilogramme-calorie per second. Given, then, a known power (I.H.P.) in horse-power, the heat obtainable from it, H (in kilogramme-calories), in the external electric circuit is

H 0.179 × I.H. P. × ε × ε × Ea

=

if the efficiencies of the motor, of transmission, and of the dynamo, respectively be represented by the symbols, E., and Ed

With a given current strength, C (in amperes), and a known resistance, R (in ohms), the heat h (in gramme-calories) obtainable in t seconds can be determined by the following formula of Joule's :

From the numbers so obtained, and from the weight and the specific heat of the substance which affords the resistance, the approximate temperature obtainable may be determined with ease, especially if the duration of the electric heating be short. The materials for further calculation are to be found in electro-technical hand-books and publications, incorporated in numerous tables of the electrical properties of the more important materials.

The heating effect of the electric current has become, in electrometallurgy, of scarcely less importance than the chemical; and in effecting the more difficult reactions, the advantages of the electrical heating process, as compared with those utilising the heat of combustion, must be manifest.

The limit of temperature that may be reached by electrothermic processes is at least 2,000° C. above the highest attainable by combustion, and may be taken at about 4,000° C. To reach this temperature, only the purest carbon blocks may be used as conductors and resistances for the current, and even these begin to be converted into vapour at about 4,000°.

The desired temperature is produced by the conversion of electric energy into heat either within the substance to be heated, or in other substances placed in immediate contact with

it.

For this purpose, if the material to be treated be a conductor, it is introduced as a resistance into the electric circuit; otherwise it is placed in intimate contact with a suitable resistance. Substances fusible or reducible with difficulty may be thus treated even in vessels made of a non-refractory material, or of one which, if raised to the full temperature of the furnace, would exert a prejudicial influence upon the chemical reactions taking place within. By heating-methods of this character, the author has succeeded in proving that every oxide is capable of being reduced by means of carbon.

A further great advantage in the use of electric furnaces is the possibility of a rapid and almost instantaneous heating to the required temperature, and of an equally rapid regulation of the heat applied. Finally, it may be noted that the electric heating of a substance may readily be conducted in vacuo, or in any required atmosphere, so that the chemical action of particular gases may be excluded or applied at will.

[The Cost of Electro-metallurgical Work.-This is obviously one of the points upon which it is most difficult to generalise. It is characteristic of "applied science" that apparatus and methods must be modified to suit local conditions; and there must be an elasticity of detail in an industrial process, that is often under-estimated by those who have never come into touch with practical work. But if the process itself be subject to variation, the cost is even more so; for this depends partly upon the special modification of the process that is adopted (which is, of course, governed to a large extent by the same local conditions that influence the cost); partly upon the charges for supervision, and for labour, skilled and otherwise; partly upon the situation of the works, their proximity to the raw material and to sources of power, and the expense of transport both for plant, materials, and finished product; partly upon the nature of the power used, and upon the way in which it is applied; and partly upon the size of

If

the installation, and the continuity with which it is run. steam-power be used, the local cost of the fuel per heat unit, and other minor considerations connected with the behaviour of the fuel during combustion, must be known; and if water power be available, the cost of damming, diverting, controlling, and utilising the water must be taken into account, together with the rental of the fall, and the possibility of climatic interruptions to the continuity of the process. All these conditions are so variable under different circumstances that it is impossible to give any generally applicable estimate of cost.

In generating electricity by steam-power, it has been found that in electric-lighting stations, a Board of Trade unit of electricity (that is, 1,000 watt-hours or 1 kilowatt-hour) may be produced with good triple-expansion engines for 1d. This sum is equal to 1d. per electrical H.P., and includes such indirect charges as management, interest, and depreciation, &c. In very large lighting installations the cost has been reduced considerably below this figure; and there is no doubt that with continuous working it should be very far below it. It must be remembered that in electric light stations the work is very intermittent, and the average proportion of the capacity of the plant actually used is rarely in excess of 20 per cent., even when calculated upon the whole year, and that these conditions are most unfavourable to economy. The annual cost of each H.P., if calculated on the basis of 11d. per E.H.P.-hour for 365 × 24 hours would amount to a little over £41. A very small plant, even if worked continuously, might, it is true, give an equally unfavourable result, but with a large plant run continuously, such as would be used in electro-metallurgical installations, it should not exceed one-third, and under favourable circumstances it may be less than one-fourth, this amount.

Emery has estimated as follows the cost of running a 250H.P. compound condensing engine, requiring 18 lbs. of water per I.H.P., assuming an evaporation of 8 lbs. of water per lb. of coal, with coal at 12s. 6d. per ton :—

Total cost per net H. P.

* Electrician, 1896, vol. xxxviii., p. 9.

The original estimate is given

in dollars and cents; for purposes of calculation, these have been reckoned

at 4s. 2d. and d. respectively.

This charge is based on observation.

This estimate is apparently made out, however, upon the basis of a 3,080-hour year (or 10 hours a day for 308 days); if run continuously the above cost works out to

=

(365 x 24 x 0.407)d. £14, 17s.,

as the cost of each H.P. per annum. In the latter case all the items would be smaller than those given in the estimate, and the annual cost of each H.P. should therefore fall proportionately below £14, 17s. With a triple-expansion engine of 500 H.P., using every care, the cost of a net H.P. hour is estimated at 0.35d. per hour, or (less than) £12, 15s. per annum on continuous running. It will thus be seen that continuous work and the use of a high percentage of the load for which the generators were designed are most favourable to economy, and hence to the application of power to electro-metallurgical work.

The cost of water-power is very variable. Emery (loc. cit.) states that it has been developed in America for from £1, 13s. to £2, 10s. per H. P.-year; but that in a plant on the Merrimac, mainly owing to high rent-charges, it has cost £6, 5s. per annum. The cost at Schaffhausen is taken at £2, 10s. per H.P.-year. It is a somewhat common fallacy to assert that water-power may be had for nothing, but the capital outlay upon an installation for utilising it may be very considerable, and in some cases might be almost prohibitive; and, as Swinburne has pointed out, it is probable that in the course of a few years the commercial value of waterfalls will become better known, higher rents will be demanded, and the balance in favour of water as compared with steam-power will then be reduced almost to a vanishing point.

There are to be seen in America electro-metallurgical works using steam in successful competition with others run by water-power. Hence, although streams and falls will naturally be utilised as fully as possible, there is little doubt that steam will be more than able to hold its own in this field, more especially, if advantage be taken of the waste power that is superabundantly available in many districts. The outlook for electro-metallurgy is therefore bright. Very many electric smelting and refining processes have already displaced the older and more costly and cumbrous metallurgical methods, as the following pages will show, and every year brings fresh victories in the same field.-TRANSLATOR.]