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34 with that here dealt with, and there is no positive evidence that they will do what is required by the theory. The only known change which has been shown to be competent to affect the e.m. f. to this degree is the change which may locally and temporarily occur in the strength of the acid.1

(3) There are two explanations of the rapid fall at the end of discharge. The one already given ascribes the fall to a weakening of the acid in the spongy masses. This has already been considered and need not be further elaborated. The other explanation was first given by Plante, and adopted by Gladstone and Tribe, and afterwards by Robertson. All these workers observed that, at the end of a discharge, patches or small films of peroxide of lead were formed on the surface of the lead plate. Such films speedily tend to annul the e.m.f. and bring the current to zero. Which of these two hypotheses (both representing actual facts and both competent to produce the change under consideration) contributes most to the result is a difficult question. But if a careful comparison be made of the time at which peroxide appears on the negative, with the fall of e.m.f., it will be seen that the fall begins before the films can be detected with certainty. Thus (in Fig. 32) Robertson could not be sure of peroxide on the negative at the point C, although the fall had fairly begun at that time.

(4) The explanation of the rapid recuperation after discharge is that the cause of the rapid fall has ceased and that the conditions existing before it are now re-established. If the discharge fall be ascribed to peroxide films on the negative, then on stopping the discharge the films are destroyed by local action, and the e.m.f. is restored. If the fall be due to exhaustion of acid, then stopping the current allows acid to diffuse into the pores almost instantly, and so restores the E.M.F. If the discharge has not been carried too far, this is most- probably the true cause. If the potential difference is below l 8 volt, both actions take place.

(5) As to the effect of repose on a charged cell, Gladstone and Tribe’s experiments showed that peroxide of lead lying on its lead support suffered from a local action, which reduced one molecule of Pb02 to sulphate at the same time that an atom of the grid below it was also changed to sulphate. There is thus not only a loss of the available peroxide, but a corrosion of the grid or plate. It is through this action that the supports gradually give way. On the negative plate an action arises between the finely divided lead and the sulphuric acid, with the result that hydrogen is set free.

Pb + H2S04=PbS04 + H2.

This involves a diminution of available spongy lead, or loss of capacity, occasionally with serious consequences. The capacity of the lead plate is reduced absolutely, of course, but its relative value is more seriously affected. In the discharge it gets sulphated too much, because the better positive keeps up the e.m.f. too long. In the succeeding charge, the positive is fully charged before the negative, and the differences between them tend to increase in each cycle.

(6) Kelvin and Helmholtz have shown that the e.m.f. of a voltaic cell can be calculated from the energy developed by the chemical action. For a dyad gram equivalent ( = 2 grams of hydrogen, 207 grams of lead, &c.), the equation connecting them is

value is so small and it is not easy to secure a good cycle of observations. Streintz has given the following values :—

E 1-9223 1-9828 2-0031 2-0084 2-0105 2-078 2-2070 335 285 255 130 228 73 g-10* 140 hi

-f=AL + t— 46000 cZT

where E is the e.m.f. in volts, H is the heat developed by a dyad equivalent of the reacting substances, T is the absolute temperature, and -r^ is the temperature coefficient of the e.m.f. If the E. m. f. does not change with temperature, the second term is zero. The thermal values for the various substances formed and decomposed are:—For Pb02, 62400 ; for PbS04, 216210 ; for II2S04, 192920 ; and for H20, 68400 calories. Writing the equation in its simplest form for strong acid, and ignoring the temperature coefficient term,

Pb02 + 2H2S04 + Pb = 2PbS04 + 2H20 -62440-385840 +432420 + 136720

leaving a balance of 120860 calories. Dividing by 46000 gives 2'627 volts. The experimental value in strong acid, according to Gladstone and Hibbert, is 2-607 volts, a very close approximation. For other strengths of acid, the energy will be less by the quantity evolved when the acid is diluted. The dotted curve in Fig. 11 indicates the calculated e.m.f. at various points when tins is taken into account. The difference between it and the continuous curve must, if the chemical theory be correct, depend on the second term in the equation. The figure shows that the observed e.m.f. is above the theoretical for all strengths from 100 down to 5 per cent. Below 5 the position is reversed. The question remains, Can the temperature coefficient be obtained ? This is difficult, because the

These figures illustrate the difficulty of getting good determinations ; it is quite improbable that cells so nearly alike as those giving 2"003 and 2 "008 volts should have temperature coefficients differing by 16 per cent. Unpublished experiments by the writer cZE give ^-rj+106 = 350 for acid of density 1-156. With stronger acid, a true cycle could not be obtained. Taking Streintz’s value, 335 for dE 25 per cent, acid, the second term of the equation is T^ = 290x •000335 = 0-0971 volt. The first term gives 88800 calories = 1-9304 volt. Adding the second term, 1 "9304 + 0-0971 = 2-0275 volts. The observed value is 2-030 volts (see Fig. 11 and table 2), a remarkably good agreement. This calculation and the general relation shown in Fig. 11 render it highly probable that, if the temperature coefficient were known for all strengths of acid, the result would be equally good. It is worth observing that the reversal of relationship between the observed and calculated curves, which takes place at 5 or 6 per cent., suggests that the chemistry must be on the point of altering as the acid gets weak, a conclusion which has been already arrived at on purely chemical grounds.

The thermodynamical relations are thus seen to confirm very strongly the chemical and physical analyses.As the efficiency of accumulators is not generally higher than 75 per cent., and machines must be used to charge them, it is not directly economical to use Accumucells alone for public supply. Yet they play an lators ia important and an increasing part in public work, central because they help to maintain a constant voltage stat:onson the mains, and can be used to distribute the load on the running machinery over a much greater fraction of the day. Used in parallel with the dynamo, they quickly yield current when the load increases, and immediately begin to charge when the load diminishes, thus largely reducing the fluctuating stress on dynamo and engine for sudden variations in load. Their use is advantageous if they can be charged and discharged at a time when the steam plant would otherwise be working at an uneconomical load. Regulation of the potential difference is managed in various ways. More cells may be thrown in as the discharge proceeds, and taken out during charge; but this method often leads to trouble, as some cells get unduly discharged, and the unity of the battery is disturbed. Sometimes the number of cells is kept fixed for supply, but the p.d. they put on the mains is reduced during charge by employing regulating cells in opposition. The working cells are then all kept in similar condition. But these methods are now being discarded. The number of cells is now fixed and the battery joined to the mains. The heaviest part of the load is shared by battery and dynamo, and after the evening’s discharge the dynamo may charge the cells. But they must be charged to a higher potential difference than that kept on the mains, otherwise they cannot be said to be brought back to good condition. This may be done by disconnecting the battery and charging from a dynamo which gives the requisite higher e.m.f.; or it may be done (and this is usual) by taking the current from the mains to the battery through a “ booster,” that is, a dynamo arranged so that its e.m.f. is added to that of the mains. The power requisite for driving its armature may be obtained from any convenient source, but it is most usual to couple the armature to the shaft of a motor driven from the mains. There are certain disadvantages in carrying accumulators

1 Gladstone and Hibbert, Phil. Mag. 1890 ; Jour. Inst. Elec. Eng. 1892. Dolezalek, Ann. Phys. Chem. 1898. Mugdan, Elekt. Zeitschrift, 1899.

2 For the discussion of later electrolytic theories as applied to accumulators, see Electro-chemistry by Le Blanc ; also an article by Hoppe, Elektrotech. Runds. 1898.