1911 Encyclopædia Britannica/Accumulator

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ACCUMULATOR, the term applied to a number of devices whose function is to store energy in one form or another, as, for example, the hydraulic accumulator of Lord Armstrong (see Hydraulics, sec. 179). In the present article the term is restricted to its use in electro-technology, in which it describes a special type of battery. The ordinary voltaic cell is made by bringing together certain chemicals, whose reaction maintains the electric currents taken from the cell. When exhausted, such cells can be restored by replacing the spent materials, by a fresh “charge” of the original substances. But in some cases it is not necessary to get rid of the spent materials, because they can be brought back to their original state by forcing a reverse current through the cell. The reverse current reverses the chemical action and re-establishes the original conditions, thus enabling the cell to repeat its electrical work. Cells which can thus be “re-charged” by the action of a reverse current are called accumulators because they “accumulate” the chemical work of an electric current. An accumulator is also known as a “reversible battery,” “storage battery” or “secondary battery.” The last name dates from the early days of electrolysis. When a liquid like sulphuric acid was electrolysed for a moment with the aid of platinum electrodes, it was found that the electrodes could themselves produce a current when detached from the primary battery. Such a current was attributed to an “electric polarization” of the electrodes, and was regarded as having a secondary nature, the implication being that the phenomenon was almost equivalent to a storage of electricity. It is now known that the platinum electrodes stored, not electricity, but the products of electro-chemical decomposition. Hence if the two names, secondary and storage cells, are used, they are liable to be misunderstood unless the interpretation now put on them be kept in mind. “Reversible battery” is an excellent name for accumulators.

Sir W. R. Grove first used “polarization” effects in his gas battery, but R. L. G. Planté (1834–1889) laid the foundation of modern methods. That he was clear as to the function of an accumulator is obvious from his declaration that the lead-sulphuric acid cell could retain its charge for a long time, and had the power d’emmagasiner ainsi le travail chimique de la pile voltaique: a phrase whose accuracy could not be excelled. Planté began his work on electrolytic polarization in 1859, his object being to investigate the conditions under which its maximum effects can be produced. He found that the greatest storage and the most useful electric effects were obtained by using lead plates in dilute sulphuric acid. After some “forming” operations described below, he obtained a cell having a high electromotive force, a low resistance, a large capacity and almost perfect freedom from polarization.

The practical value of the lead-peroxide-sulphuric-acid cell arises largely from the fact that not only are the active materials (lead and lead peroxide, PbO2) insoluble in the dilute acid, but that the sulphate of lead formed from them in the course of discharge is also insoluble. Consequently, it remains fixed in the place where it is formed; and on the passage of the charging current, the original PbO2 and lead are reproduced in the places they originally occupied. Thus there is no material change in the distribution of masses of active material. Lastly, the active materials are in a porous, spongy condition, so that the acid is within reach of all parts of them.

Planté carefully studied the changes which occur in the formation, charge and discharge of the cell.Planté’s cell. In forming, he placed two sheets of lead in sulphuric acid, separating them by narrow strips of caoutchouc (fig. 1). When a charging current is sent through the cell, the hydrogen liberated at one plate escapes, a small quantity possibly being spent in reducing the surface film of oxide generally found on lead. Some of the oxygen is always fixed on the other (positive) plate, forming a surface film of peroxide. After a few minutes the current is reversed so that the first plate is peroxidized, and the peroxide previously formed on the second plate is reduced to metallic lead in a spongy state. By repeated reversals, the surface of each plate is alternately peroxidized and reduced to metallic lead. In successive oxidations, the action penetrates farther into the plate, furnishing each time a larger quantity of spongy PbO2 on one plate and of spongy lead on the other. It follows that the duration of the successive charging currents also increases. At the beginning. a few minutes suffice; at the end, many hours are required.

EB1911 Accumulator - Fig 1.png
 Fig. 1.

After the first six or eight cycles, Planté allowed a period of repose before reversing. He claimed that the PbO2 formed by reversal after repose was more strongly adherent, and also more crystalline than if no repose were allowed. The following figures show the relative amounts of oxygen absorbed by a given plate in successive charges (between one charge and the next the plate stood in repose for the time stated, then was reduced, and again charged as anode):—

Separate Periods
of Repose.
Charge. Relative Amount of
Peroxide formed.
. .  First  1.0
18 hours  Second  1.57
2 days  Third  1.71
4 days  Fourth  2.14
2 days  Fifth  2.43

and so on for many days (Gladstone and Tribe, Chemistry of Secondary Batteries). Seeing that each plate is in turn oxidized and then reduced, it is evident that the spongy lead will increase at the same rate on the other plate of the cell. The process of "forming" thus briefly described was not continued indefinitely, but only till a fair proportion of the thickness of the plates was converted into the spongy material, PbO2 and Pb respectively. After this, reversal was not permitted, the cell being put into use and always charged in a given direction. If the process of forming by reversal be continued, the positive plate is ultimately all converted into PbO, and falls to pieces.

Planté made excellent cells by this method, yet three objections were urged against them. They required too much time to "form"; the spongy masses (PbO2 more especially) fell off for want of mechanical support, and the separating strips of caoutchouc were not likely to have a long life. The first advance was made by C. A. Faure (1881), who greatly shortened the time required for "forming" by giving the plates a preliminary coating of red lead, whereby the slow process of biting into the metal was avoided. At the first charging, the red lead on the + electrode is changed to PbO2, while that on the — electrode is reduced to spongy lead. Thus one continuous operation, lasting perhaps sixty hours, takes the place of many reversals, which, with periods of repose, last as much as three months.

EB1911 Accumulator - Fig 2. Tudor positive plate.png
  Fig. 2.—Tudor positive plate.

Faure used felt as a separating membrane, but its use was soon abolished by methods of construction due to E. Volckmar, J. S. Sellon, J. W. Swan and others. These inventors put the paste not on to plates of lead, but into the holes of a grid, which, when carefully designed, affords good mechanical support to the spongy masses, and does away with the necessity for felt, &c. They are more satisfactory, however, as supporters or spongy lead than of the peroxide, since at the point of contact in the latter case the acid gives rise to a local action, which slowly destroys the grid. Disintegration follows sooner or later, though the best makers are able to defer the failure for a fairly long time. Efforts have been made by A. Tribe, D. G. Fitzgerald and others to dispense with a supporting grid for the positive plate, but these attempts have not yet been successful enough to enable them to compete with the other forms.

For many years the battle between the “Planté” type and the Faure or “pasted” type has been one in which the issue was doubtful, but the general tendency is towards a mixed type at the present time. There are many good cells, the value of all resting on the care exercised during the manufacture and also in the choice of pure materials. Increasing emphasis is laid on the purity of the water used to replace that lost by evaporation, distilled water generally being specified. The following descriptions will give a good idea of modern practice.

The “chloride cell” has a Planté positive with a pasted negative.Chloride cell. For the positive a lead casting is made, about 0.4 inch thick pierced by a number of circular holes about half an inch in diameter. Into each of these holes is thrust a roll or rosette of lead ribbon, which has been cut to the right breadth (equal to the thickness of the plate), then ribbed or gimped, and finally coiled into a rosette. The rosettes have sufficient spring to fix themselves in the holes of the lead plate, but are keyed in position by a hydraulic press. The plates are then “formed” by passing a current for a long time. In a later pattern a kind of discontinuous longitudinal rib is put in the ribbon, and increases the capacity and life by strengthening the mass

EB1911 Accumulator - Fig 3. Tudor negative plate.png
 Fig. 3.—Tudor negative plate.

without interfering with the diffusion of acid. The negative plate was formerly obtained by reducing pastilles of lead chloride, but by a later mode of construction it is made by casting a grid with thin vertical ribs, connected horizontally by small bars of triangular section. The bars on the two faces are “staggered,” that is, those on one face are not opposite those on the other. The grid is pasted with a lead oxide paste and afterwards reduced; this is known as the “exide” negative.

EB1911 Accumulator - Figs 4, 5, 6.png
 Fig. 4. Fig. 5. Fig. 6

The larger sizes of negative plate are of a “box” type, formed by riveting together two grids and filling the intervening space with paste. A feature of the “chloride” cells is the use of separators made of thin sheets of specially prepared wood, These prevent short circuits arising from scales of active material or from the formation of “trees” of lead which sometimes grow across in certain forms of battery.

The Tudor cell has positives formed of lead plates cast in one piece with a large surface of thin vertical ribs,Tudor cell. intersected at intervals by horizontal ribs to give the plates strength to withstand buckling in both directions (fig. 2). The thickness of the plates is about 0.4 inch, and the developed surface is about eight times that of a smooth plate of the same size. A thoroughly adherent and homogeneous coating of peroxide of lead is formed on this large surface by an improved Planté process. The negative plate (fig. 3) is composed of two grids riveted together to form a shallow box; the outer surfaces are smooth sheets pierced with many small holes. The space between them is intersected by ribs and pasted (before riveting).

EB1911 Accumulator - Fig 7.png
 Fig. 7.

Many of the E.P.S. cells, made by the Electrical Power Storage Company,E.P.S. cell. are of the Faure or pasted type, but the Planté formation is used for the positives of two kinds of cell. The paste for the positive plates is a mixture of red lead with sulphuric acid; for the negative plates, litharge is substituted for red lead. Figs. 4 and 5 roughly represent the grids employed for the negative and positive plates respectively of a type used for lighting. Fig. 6 is the cross section of the casting used for the Planté positive of the larger cells for rapid discharge. Finer indentations on the side expose a large surface. Fig. 7 shows a complete cell.

The Hart cell, as used for lighting, is a combination of the Planté and Faure (pasted) types.Hart cell. The plates hang by side lugs on glass slats, and are separated by three rows of glass tubes 3/8 inch diameter (fig. 8). The tubes rest in grooved teak wood blocks placed at the bottom of the glass boxes. The blocks also serve as base for a skeleton framework of the same material which surrounds and supports the section. Of course the wood has to be specially treated to withstand the acid. A special non-corrosive terminal is used. A coned bolt draws the lug ends of adjacent cells together, fitting in a corresponding tapered hole in the lugs, and thus increasing the contact area. The positive and negative tapers being different, a cell cannot be connected up in the wrong way.

EB1911 Accumulator - Fig 8. - Hart Accumulator.png
 Fig. 8.—Hart Accumulator.

In America, in addition to some of the cells already described, there are types which are not found in England.Gould cell. Two may be described. The Gould cell is of the Planté type. A special effort is made to reduce local and other deleterious action by starting with perfectly homogeneous plates. They are formed from sheet lead blanks by suitable machines, which gradually raise the surface into a series of ribs and grooves. The sides and middle of the blank are left untouched and amply suffice to distribute the current over the surface of the plate. The grooves are very fine, and when the active material is formed in them by electro-chemical action, they hold it very securely.

The Hatch cell has its positive enclosed in an envelope.Hatch cell. A very shallow porous tray (made of kaolin and silica) is filled with red lead paste, an electrode of rolled sheet lead is placed on its surface, and over this again is placed a second porous tray filled with paste. The whole then looks like a thin earthenware box with the lug of the electrode projecting from one end. The negatives consist of sheet lead covered by active material. Hatch cell. On assembling the plates, each negative is held between two positive “boxes,” the outsides of which have protecting vertical ribs. These press against the active material on the negative plates, and help to keep it in position. At the same time, the clearance between the ribs allows room for acid to circulate freely between the negative plate and the outer face of the positive envelope. Diffusion of the acid through this envelope is easy, as it is very porous and not more than 132 inch thick.

Traction Cells.—Attempts to run tramcars by accumulators have practically all failed, but traction cells are employed for electric broughams and light vehicles for use in towns. There are no large deviations in manufacture except those imposed by limited space, weight and vibration. The plates are generally thinner and placed closer together. The Plante positive is not used so much as in lighting types. The acid is generally a little stronger in order to get a higher electromotive force (e.m.f.). To prevent the active material from being shaken out of the grids, corrugated and perforated ebonite separators are placed between the plates. The "chloride" traction cell uses a special variety of wood separator: the “exide” type of plate is used for both positive and negative. Cells are now made to run 3000 or more miles before becoming useless. The specific output can be made as high as 10 or 11 watt-hours per pound of cell, but this involves a chance of shorter life. The average working requirement for heavy vehicles is about 50 watt-hours per 1000 lb. per mile.

Ignition Cells for motor cars are made on the same lines as traction cells, though of smaller capacity. As a rule two cells are put up in ebonite or celluloid boxes and joined in series so as to give a 4-volt battery, the pressure for which sparking coils are generally designed. The capacity ranges from 20 to 100 ampere-hours, and the current for a single cylinder engine will average one to one and a half amperes during the running intervals.

General Features.—The tendency in stationary cells is to allow plenty of space below the plates, so that any active material which falls from the plates may collect there without risk of short-circuit, &c. More space is allowed between the plates, which means that (a) there is more acid within reach, and (b) a slight buckling is not so dangerous, and indeed is not so likely to occur. The plates are now generally made thicker than formerly, so as to secure greater mechanical rigidity. At the same time, the manufacturers aim at getting the active materials in as porous a state as possible.

The figures with regard to specific output are difficult to classify. It would be most interesting to give the data in the form of watt-hours per pound of active material, and then to compare them with the theoretical values, but such figures are impossible in the nature of the case except in very special instances. For many purposes, long life and trustworthiness are more important than specific output. Except in the case of traction cells, therefore, the makers have not striven to reduce weight to its lowest values. Table I. shows roughly the weight of given types of cells for a given output in ampere hours.

Table I.
Type of Cell. Capacity in ampere-hours if discharged in Weight of Cell.
9 hrs. 6 hrs. 3 hrs. 1 hr.
 Ordinary lighting 200 182 153 101 100 pounds.
{{{1}}}{{{1}}} 420 380 300 210 100 pounds.
{{{1}}}{{{1}}} 1200 1080 880 600 670 pounds.
 Central station and High Rate 3500 3100 2500 1700 2000 pounds.
{{{1}}}{{{1}}} 6000 5400 4400 3000 3200 pounds.
 Traction 220 185 155 125 40 pounds.
Traction . . 440 . . . . 90 pounds.

Influence of Temperature on Capacity.—These figures are true only at ordinary temperatures. In winter the capacity is diminished, in summer it is increased. The differences are due partly to change of liquid resistance but more especially to the difference in the rate at which acid can diffuse into or out of the pores: obviously this is greater at higher temperatures. The increase in capacity on warming is appreciable, and may amount to as much as 3% per degree centigrade (Gladstone and Hibbert, Journ. Inst. Elec. Eng. xxi. 441; Helm, Electrician, Nov. 1901, i. 55; Liagre, L’Éclairage électrique, 1901,xxix. 150). Notwithstanding these results, it is not advisable to warm accumulators appreciably. At higher temperatures, local action is greatly increased and deterioration becomes more rapid. It is well, however, to avoid low winter temperatures.

Working of accumulators.—Whatever the type of cell may be, it is important to attend to the following working requirements—(1) The cells must be fully equal to the maximum demand, both in discharge rate and capacity. (2) All the cells in one series ought to be equal in discharge rate and capacity. This involves similarity of treatment. (3) The cells are erected on strong wooden stands. Where floor space is too expensive, they can be erected in tiers; but, if possible, this should be avoided. They ought to lie in rows, so arranged that it is easy to get to one side (at least) of every cell, for examination and testing, and if need be to detach and remove it or its plates. Where a second tier is placed over the first, sufficient clearance space must be allowed for the plates to be lifted out of the lower boxes. The cells are insulated by supporting them on glass or mushroom-shaped oil insulators. If the containing vessels are made of glass, it it desirable to put them in wooden trays which distribute the weight between the vessel and insulators. To prevent acid spray from filling the air of the room, a glass plate is arranged over each cell. The positive and negative sections are fixed in position with insulating forks or tubes, and the positive terminal of one cell is joined to the negative of the next by burning or bolting. If the latter method is adopted, the surfaces ought to be very clean and well pressed home. The joint ought to be covered by vaseline or varnish. When this has been done, examination ought to be made of each cell to see that the plates are evenly spaced, that the separators (glass tubes or ebonite forks between the plates) are in position and vertical, and that there are no scales or other adventitious matter connecting the plates. The floor of the cell ought to be quite clear; if anything lies there it must be removed. (4) To mix the solution a gentle stream of sulphuric acid must be poured into the water (not the other way, lest too great heating cause an accident). It is necessary to stir the whole as the mixing proceeds and to arrange that the density is about 1190, or according to the recommendation of the maker. About five volumes of water ought to be taken to one volume of acid. After mixing, allow to cool for two or three hours. The strong acid ought to be free from arsenic, copper and other similar impurities. The water ought to be as pure as can be obtained, distilled water being best; rain water is also good. If potable water be employed, it will generally be improved by boiling, which removes some of the lime held in solution. The impurity in ordinary drinking water is very slight; but as all cells lose by evaporation and require additions of water from time to time, there is a tendency for it to increase. The acid must not be put into the cells till everything is ready for charging. (5) A shunt-wound or separately-excited dynamo being ready and running so as to give at will 2.6 or 2.7 volts per cell, the acid is run into the cells. As soon as this is done, the dynamo must be switched on and charging commenced. The positive terminal of the dynamo must be joined to the positive terminal of the battery. If necessary, the + end of the machine must be found by a trial cell made of two plain lead sheets in dilute acid. It is important also to maintain this first charging operation for a long time without a break. Twelve hours is a minimum time, twenty-four not too much. The charging is not even then complete, though a short interval is not so injurious as in the earlier stage. The full charge required varies with the cells, but in all types a full and practically continuous first charge is imperatively necessary. During the early part of this charge the density of the acid may fall; but after a time ought to increase, and finally reach the value desired for permanent working. Towards the end of the “formation” vigilant observation must be exercised. It is important to notice whether any cells are appreciably behind the others in voltage, density or gassing. Such cells may be faulty, and in any case they must be charged and tended till their condition is like that of the others. They ought not to go on the discharge circuit till this is assured. The examination of the cells before passing them as ready for discharge includes:—(a) Density of acid as shown by the hydrometer. (b) Voltage. This may be taken when charging or when idle. In the first case it ought to be from 2.4 to 2.6 volts, according to conditions. In the second ease it ought to be just over 2 volts, provided that the observation is not taken too soon after switching in the charging current. For about half an hour after that is done, the e.m.f. has a transient high value, so that, if it be desired to get the proper e.m.f. of the cell, the observation must be taken thirty minutes after the charging ceases. (c) Eye observations of the plates and the acid between them. The positive plates ought to show a rich dark brown colour, the negatives a dull slate-blue, and the space between ought to be quite clear and free from anything like solid matter. All the positives ought to be alike, and similarly all the negatives. If the cells show similarity in these respects they will probably be in good working order.

As to management, it is important to keep to certain simple rules, of which these are the chief:—(1) Never discharge below a potential difference of 1.85 (or in rapid discharge, 1.8) volt. (2) Never leave the cells discharged, if it be avoidable. (3) Give the cells a special full charging once a month. (4) Make a periodic examination of each cell, determining its e.m.f., density of acid, the condition of its plates and freedom from growth. Any incipient growth, however small, must be carefully watched. (5) If any cell shows signs of weakness, keep it off discharge till it has been brought back to full condition. See that it is free from any connexion between the plates which would cause short-circuiting; the frame or support which carries the plates sometimes gets covered by a conducting layer. To restore the cell, two methods can be adopted. In private installations it may be disconnected and charged by one or two cells reserved for the purpose; or, as is preferable, it may be left in circuit, and a cell in good order put in parallel with it. This acts as a "milking" cell, not only preventing the faulty one from discharging, but keeping it supplied with a charging current till its potential difference (p.d.) is normal. Every battery attendant should be provided with a hydrometer and a voltmeter. The former enables him to determine from time to time the density of the acid in the cells; instruments specially constructed for the purpose are now easily procurable, and it is desirable that one be provided for every 20 or 25 cells. The voltmeter should read up to about 3 volts and be fitted with a suitable connector to enable contacts to be made quickly with any desired cell. A portable glow lamp should also be available, so that a full light can be thrown into any cell; a frosted bulb is rather better than a clear one for this purpose. He must also have some form of wooden scraper to remove any growth from the plates. The scraping must be done gently, with as little other disturbance as possible. By the ordinary operations which go on in the cell, small portions of the plates become detached. It is important that these should fall below the plates, lest they short-circuit the cell, and therefore sufficient space ought to be left between the bottom of the plates and the floor of the cell for these “scalings” to accumulate without touching the plates. It is desirable that they be disturbed as little as possible till their increase seriously encroaches on the free space. It sometimes happens that brass nuts or bolts, &c., are dropped into a cell; these should be removed at once, as their partial solution would greatly endanger the negative plates. The level of the liquid must be kept above the top of the plates. Experience shows the advisability of using distilled water for this purpose. It may sometimes be necessary to replenish the solution with some dilute acid, but strong acid must never be added.

The chief faults are buckling, growth, sulphating and disintegration. Buckling of the plates generally follows excessive discharge, caused by abnormal load or by accidental short-circuiting. At such times asymmetry in the cell is apt to make some part of the plate take much more than its share of the current. That part then expands unduly, as explained later, and curvature is produced. The only remedy is to remove the plate, and press it back into shape as gently as possible. Growth arises generally from scales from one part falling on some other—say, on the negative. In the next charging the scale is reduced to a projecting bit of lead, which grows still further because other particles rest on it. The remedy is, gently to scrape off any incipient growth. Sulphating, the formation of a white hard surface on the active material, is due to neglect or excessive discharge. It often yields if a small quantity of sulphate of soda be added to the liquid in the cell. Disintegration is due to local action, and there is no ultimate remedy. The end can be deferred by care in working, and by avoiding strains and excessive discharge as much as possible.

Table II.
Substance. Colour. Density. Specific Resistance.
 Lead . . . .   slate blue  11.3   0.0000195 ohm
 Peroxide of lead   dark brown   9.28   5.6 to 6.8 ohm
 Sulphuric acid after charge   clear liquid   1.210   1.37 ohm
 Sulphuric acid after discharge   clear liquid   1.170   1.28 ohm
 Sulphuric acid in pores   clear liquid   below
  8.0 ohm
 Sulphate of lead   white   6.3   non-conductor.

Accumulators in Repose.—Accumulators contain only three active substances—spongy lead on the negative plate, spongy lead peroxide on the positive, and dilute sulphuric acid between them. Sulphate of lead is formed on both plates during discharge and brought back to lead and lead peroxide again during charge, and there is a consequent change in the strength of acid during every cycle. The chief properties of these substances are shown in Table II.

The curve in fig. 9 shows the relative conductivity (reciprocal of resistance) of all the strengths of sulphuric acid solutions, and by its aid and the figures in the preceding table, the specific resistance of any given strength can be determined.

EB1911 Accumulator - Fig 9.png
 Fig. 9.

The lead accumulator is subject to three kinds of local action. First and chiefly, local action on the positive plate, because of the contact between lead peroxide and the lead grid which supports it. In carelessly made or roughly handled cells this may be a very serious matter. It would be so, in all circumstances if the lead sulphate formed on the exposed lead grid did not act as a covering for it. It explains why Plante found "repose" a useful help in "forming," and also why positive plates slowly disintegrate; the lead support is gradually eaten through. Secondly, local action on the negative plate when a more electro-negative metal settles on the lead. This often arises when the original paste or acid contains metallic impurities. Similar impurity is also introduced by scraping copper wire, &c., near a battery. Thirdly, local action due to the acid varying in strength in different parts of a plate. This may arise on either plate and is set up because two specimens of either the same lead or the same peroxide give an e.m.f. when placed in acids of different strengths. J. H. Gladstone and W. Hibbert found that the e.m.f. depends on the difference of strength. With two head plates, a maximum of about quarter volt was obtained, the lead in the weaker acid being positive. With two peroxide plates the maximum voltage was about 0.64, the plate in stronger acid being positive to that in weaker. The electromotive force of a cell depends chiefly on the strength of the acid, as may be seen from fig. 10 taken from Gladstone and Hibbert’s paper (Journ. Inst. Elec. Eng., 1892).The observations with very strong acid were difficult to obtain, though even that with 98% acid marked X is believed to be trustworthy. C. Heim (Elek. Zeit, 1889), F. Streintz (Ann. Phys. Chem. xlvi. p. 449) and F. Dolezalek (Theory of Lead Accumulators, p. 55) have also given tables.

EB1911 Accumulator - Fig 10.png
 Fig. 10.

It is only necessary to add to these results the facts illustrated by the following diffusion curves, in order to get a complete clue to the behaviour of an accumulator in active work. Fig. 11 shows the rate of diffusion from plates soaked in 1.175 acid and then placed in distilled water. It is from a paper by L. Duncan and H. Wiegand (Elec. World, N.Y., 1889), who were the first to show the importance of diffusion. About one half the acid diffused out in 30 minutes, a good illustration of the slowness of this process. The rate of diffusion is much the same for both positive and negative plates; but slower for discharged plates than for charged ones. Discharge affects the rate of diffusion on the lead plate more than on the peroxide plate. This is in accordance with the density values given in Table I. For while lead sulphate is formed in the pores of both plates, the consequent expansions (and obstructions) are different; 100 volumes of lead form 290 volumes of sulphate (a threefold expansion), and 100 volumes of peroxide form 186 volumes of sulphate (a twofold expansion). The influence of diffusion on the electromotive force is illustrated by fig. 12. A cell was prepared with 20% acid. It also held a porous pot containing stronger acid, and into this the positive plate was suddenly transferred from the general body of liquid. The e.m.f. rose by diffusion of stronger acid into the pores. Curve I. in fig. 12 shows the rate of rise when the porous pot contained 34% acid; curve II. was obtained with the stronger (58%) acid (Gladstone and Hibbert, Phil. Mag., 1890). Of these two curves the first is more useful, because its conditions are nearer those which occur in practice.

EB1911 Accumulator - Fig 11.png
 Fig. 11.

At the end of a discharge it is a common thing for the plates to be standing in 25% acid, while inside the pores the acid may not exceed 8% or 10%. If the discharge be stopped, we have conditions somewhat like fig. 12, and the e.m.f. begins to rise. In one minute it has gone up by about 0.08 volt, &c.

EB1911 Accumulator - Fig 12.png
 Fig. 12.

Charge and Discharge.—The most important practical questions concerning an accumulator are:—its maximum rate of working; its capacity at various discharge rates; its efficiency; and its length of life. Apart from mechanical injury all these depend primarily on the way the cell is made, and then on the method of charging and discharging. For each type and size of cell there is a normal maximum discharging current. Up to this limit any current may be taken; beyond it, the cell may suffer if discharge be continued for any appreciable time. The most important point to attend to is the voltage at which discharge shall cease. The potential difference at terminals must not fall below 1.80 volt during discharge at ordinary rates (10 hours) or 1.75 to 1.70 volt for 1 or 2 hour rate. The reason underlying the figures is simple. These voltages indicate that the acid in the pores is not being renewed fast enough, and that if the discharge continue the chemical action will change: sulphate will not be formed in situ for want of acid. Any such change in action is fatal to reversibility and therefore to life and constancy in capacity. To illustrate: when at slow discharge rates the voltage is 1.80 volt, the acid in the pores has weakened to a mean value of about 2.5% (see fig. 11), which is quite consistent with some part of the interior being practically pure water. With high discharge rates, something like 0.1 volt may be lost in the cells, by ordinary ohmic fall, so that a voltage reading of 1.73 means an e.m.f. of a little over 1.8 volt, and a very weak density of the acid inside the pores. Guided by these figures, an engineer can determine what ought to be the permissible drop in terminal volts for any given working conditions. Messrs W. E. Ayrton, C. G. Lamb, E. W. Smith and M. W. Woods were the first to trace the working of a cell through varied conditions (Journ. Inst. Elec. Eng., 1890), and a brief résumé of their results is given below.

They began by charging and discharging between the limits of 2.4 and 1.6 volts.

EB1911 Accumulator - Fig 13.png
 Fig. 13.

Fig. 13 shows a typical discharge curve. Noteworthy points are:—(1) At the beginning and at the end there is a rapid fall in p.d.., with an intermediate period of fairly uniform value. (2) When the p.d. reaches 1.6 volt the fall is so rapid that there is no advantage in continuing the action. When the p.d. had fallen to 1.6 volt the cell was automatically switched into a charging circuit, and with a current of 9 amperes yielded the curve in fig. 14. Here again there is a rapid variation in p.d. (in these cases a rise) at the beginning and end of the operation. The cells were now carried through the same cycle several times, giving almost identical values for each cycle. After some days, however, they became more and more difficult to charge, and the return on discharge was proportionately less. It became impossible to charge up to a p.d. of 2.4 volts, and finally the capacity fell away to half its first value. Examination showed that the plates were badly scaled, and that some of the scales had partially connected the plates. These scales were cleared away and the experiments resumed, limiting the fall of p.d. to 1.8 volt. The difficulties then disappeared, showing that discharge to 1.6 volt caused injury that did not arise at a limit of 1.8. Before describing the new results it will be useful to examine these two cases in the light of the theory of e.m.f. already given.

EB1911 Accumulator - Fig 14.png
 Fig. 14.

(a) Fall in e.m.f. at beginning of discharge.—At the moment when previous charging ceases the pores of the positive plate contain strong acid, brought there by the charging current. There is consequently a high e.m.f. But the strong acid begins to diffuse away at once and the e.m.f. falls rapidly. Even if the cell were not discharged this fall would occur, and if it were allowed to rest for thirty minutes or so the discharge would have begun with the dotted line (fig. 13). (b) Final rapid fall.—The pores being clogged by sulphate the plugs cannot get acid by diffusion, and when 5% is reached the fall in e.m.f. is disproportionately large (see fig. 10). If discharge be stopped, there is an almost instantaneous diffusion inwards and a rapid rise in e.m.f. (c) The rise in e.m.f. at beginning and end of the charging is due to acid in the pores being strengthened, partly by diffusion, partly by formation of sulphuric acid from sulphate, and partly by electrolytic carrying of strong acid to the positive plate. The injurious results at 1.6 volt arise because then the pores contain water. The chemical reaction is altered, oxide or hydrate is formed, which will partially dissolve, to be changed to sulphate when the sulphuric acid subsequently diffuses in. But formed in this way it will not appear mixed with the active masses in the electrolytic paths, but more or less alone in the pores. In this position it will more or less block the passage and isolate some of the peroxide. Further, when forming in the narrow passage its disruptive action will tend to force off the outer layers. It is evident that limitation of p.d. to 1.8 volt ought to prevent these injuries, because it prevents exhaustion of acid in the plugs.

EB1911 Accumulator - Fig 15.png
 Fig. 15.

Fig. 15 shows the results obtained by study of successive periods of rest, the observations being taken between the limits of 2.4 and 1.8 volts. Curves A and B show the state and capacity at the beginning. After a 10 days’ rest the capacity was smaller, but repeated cycles of work brought it back to C and D. A second rest (10 days), followed by many cycles, then gave E and F. After a third rest (16 days) and many cycles, G and H were obtained. After a fourth rest (16 days) the first discharge gave I and the first charge J. Repeated cycles brought the cells back to K and L. Curves M and N show first cycle after a fifth rest (16 days); O and P show the final restoration brought about by repeated cycles of work. The numbers given by the integration of some of these curves are stated in Table III.

Table III.
Capacity and Efficiency under Various
Conditions of Working.
Experiment. Discharge. Charge. Efficiency.
Quantity. Energy.
Normal cycle  102  201.7  104.5  230.7  97.2  87.4
 after 1st rest
 100  179  103.8  228.2  96.8  85.8
Ditto, after
 2nd rest
  91  176.7  103.8  228.2  96.8  85.8
 after 3rd rest
  82.6  161.3  86.2  190.5  95.8  84.7
 immediately }
  56.5  110.5  86.2  190.5  65.5  58[1]
 after rest  }   56.5  110.5  71.1  158.3  79.6  69.6
 after 8 cycles
  80  156.9  83.8  184.6  95.5  85

The table shows that the efficiency in a normal cycle may be as high as 87.4%; that during a rest of sixteen days the charged accumulator is so affected that about 30% of its charge is not available, and in subsequent cycles it shows a diminished capacity and efficiency; and that by repeated charges and discharges the capacity may be partially restored and the efficiency more completely so. These changes might be due to—(a) leakage or short-circuit, (b) some of the active material having fallen to the bottom of the cell or (c) some change in the active materials. (a) is excluded by the fact that the subsequent charge is smaller, and (b) by the continued increase of capacity during the cycles that follow the rest. Hence the third hypothesis is the one which must be relied upon. The change in the active materials has already been given. The formation of lead sulphate by local action on the peroxide plate and by direct action of acid on spongy metal on the lead plate explains the loss of energy shown in curve M, fig. 15, while the fact that it is probably formed, not in the path of the regular currents, but on the wall of the grid (remote from the ordinary action), gives a probable explanation of the subsequent slow recovery. The action of the acid on the lead during rest must not be overlooked.

EB1911 Accumulator - Fig 16.png
 Fig. 16.

We have seen that capacity diminishes as the discharge rate increases; that is, the available output increases as the current diminishes. R. E. B. Crompton’s diagram illustrating this fact is given in fig. 16. At the higher rates the consumption of acid is too rapid, diffusion cannot maintain its strength in the pores, and the fall comes so much earlier.

EB1911 Accumulator - Fig 17.png
 Fig. 17.

The resistance varies with the condition of the cell, as shown by the curves in fig. 17. It may be unduly increased by long or narrow lugs, and especially by dirty joints between the lugs. It is interesting to note that it increases at the end of both charge and discharge, and much more for the first than the second. Now the composition of the active materials near the end of charge is almost exactly the same as at the beginning of discharge, and at first sight there seems nothing to account for the great fall in resistance from 0.0115 to 0.004 ohm; that is, to about one-third the value. There is, however, one difference between charging and discharging—namely, that due to the strong acid near the positive, with a corresponding weaker acid near the negative electrode. The curve of conductivity for sulphuric acid shows that both strong and weak acid have much higher resistances than the liquid usually employed in accumulators, and it is therefore reasonable to suppose that local variations in strength of acid cause the changes in resistance. That these are not due to the constitution of the plugs is shown by the fact that, while the plugs are almost identical at end of discharge and beginning of charge, the resistance falls from 0.0055 to 0.0033 ohm.

While a current flows through a cell, heat is produced at the rate of C2R × 0.24 calories (water-gram-degree) per second. As a consequence the temperature tends to rise. But the change of temperature actually observed is much greater during charge, and much less during discharge, than the foregoing expression would suggest; and it is evident that, besdies the heat produced according to Joule's law, there are other actions which warm the cell during charge and cool it during discharge. Duncan and Wiegand (loc. cit.), who first observed the thermal changes, ascribe the chief influence to the electrochemical addition of H2SO4 to the liquid during charge and its removal during discharge. Fig. 18 gives some results obtained by Ayrton, Lamb, &c. This elevation of temperature (due to electrolytic strengthening of acid and local action) is a measure of the energy lost in a cycle, and ought to be minimized as much as possible.

EB1911 Accumulator - Fig 18.png
  Fig. 18.

Chemistry.—The chemical theory adopted in the foregoing pages is very simple. It declares that sulphate of lead is formed on both plates during discharge, the chemical action being reversed in charging. The following equations express the experimental results.

Condition before discharge:—

  + plate   Liquid   — plate
  x. PbO2 +  [   y. H2SO4  ]  + z. Pb
n. H2O

After discharge:—

  + plate  Liquid   — plate
 [  (xp). PbO2  ] + [   (y−2p). H2SO4  ] + [   (zp). Pb ]
 p.PbSO4  (n+2p). H2O  p.PbSO4

During charge, the substances are restored to their original condition: the equation is therefore reversed. An equation of this general nature was published by Gladstone and Tribe in 1882, when Oley first suggested the “sulphate” theory, which was based on very numerous analyses. Confirmation was given by E. Frankland in 1883, E. Reynier 1884, A. P. P. Crova and P. Garbe 1885, C. Heim and W. F. Kohlrausch 1889, W. E. Ayrton, &c., with G. H. Robertson 1890, C. H. J. B. Liebenow 1897, F. Dolezalek 1897, and M. Mugdan 1899. Yet there has been, as Dolezalek says, an incomprehensible unwillingness to accept the theory, though no suggested alternative could offer good verifiable experimental foundation. Those who seek a full discussion will find it in Dolezalek's Theory of the Lead Accumulator. We shall take it that the sulphate theory is proved, and apply it to the conditions of charge and discharge.

EB1911 Accumulator - Fig 19.png
  Fig. 19.

From the chemical theory it will be obvious that the acid in the pores of both plates will be stronger during charge than that outside. During discharge the reverse will be the case. Fig. 19 shows a curve of potential difference during charge, with others showing the concurrent changes in the percentage of PbO2 and the density of acid. These increase almost in proportion to the duration of the current, and indicate the decomposition of sulphate and liberation of sulphuric acid. There are breaks in the p.d. curve at A, B, C, D where the current was stopped to extract samples for analysis, &c. The fall in e.m.f. in this short interval is noteworthy; it arises from the diffusion of stronger acid out of the pores. The final rise of pressure is due to increase in resistance and the effect of stronger acid in the pores, this last arising partly from reduced sulphate and partly from the electrolytic convection of SO4 (see also Dolezalek, Theory, p. 113) . Fig. 20 gives the data for discharge. The percentage of PbO2 and the density here fall almost in proportion to the duration of the current. The special feature is the rapid fall of voltage at the end.

Several suggestions have been made about this phenomenon. The writer holds that it is due to the exhaustion of the acid in the pores. Plante, and afterwards Gladstone and Tribe, found a possible cause in the formation of a film of peroxide on the spongy lead. E. J. Wade has suggested a sudden readjustment of the spongy mass into a complex sulphate. To rebut these hypotheses it is only necessary to say that the fall can be deferred for a long time by pressing fresh acid into the pores hydrostatically (see Liebenow, Zeits. fur Elektrochem., 1897, iv. 61), or by working at a higher temperature. This increases the diffusion inwards of strong acid, and like the increase due to hydrostatic pressure maintains the e.m.f. The other suggested causes of the fall therefore fail. Fig. 20 also shows that when the discharge current was stopped at points A, B, C, D to extract samples, the voltage immediately rose, owing to inward diffusion of stronger acid. The inward diffusion of fresh acid also accounts for the recuperation found after a rest which follows either complete discharge or a partial discharge at a very rapid rate. If the discharge be complete the recuperation refers only to the electromotive force; the pressure falls at once on closed circuit. If discharge has been rapid, a rest will enable the cell to resume work because it brings fresh acid into the active regions.

EB1911 Accumulator - Fig 20.png
  Fig. 20.

As to the effect of repose on a charged cell, Gladstone and Tribe's experiments showed that peroxide of lead lying on its lead supoort suffers from a local action, which reduces one molecule of PbO2 to sulphate at the same time that an atom of the grid below it is 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 + H2SO4 = PbSO4 + 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.

Kelvin and Helmholtz have shown that the e.m.f. of a voltaic cell oan 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

 E = H/46000 + TdE/dT,

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 dE/dT 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 PbO2, 62400; for PbSO4, 216210; for H2SO4, 192920; and for H2O, 68400 calories. Writing the equation in its simplest form for strong acid, and ignoring the temperature coefficient term,

 PbO2 + 2H2SO4 + Pb = 2PbSO4 + 2H2O
 −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 of heat evolved by dilution of the acid, because the chemical action must take the H2SO4 from the diluted liquid. The dotted curve in fig. 10 indicates the calculated e.m.f. at various points when this 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%. Below 5 the position is reversed. The question remains, Can the temperature coefficient be obtained? This is difficult, because the 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
dE/dT.106 140 228 335 285 255 130 73

Unpublished experiments by the writer give dE/dT.106 = 350 for acid of density 1.156. With stronger acid, a true cycle could not be obtained. Taking Streintz’s value, 335 for 25% acid, the second term of the equation is TdE/dT = 290 × .000335 = 0.0971 volt. The first term gives 88800 calories = 1.9304 volt. Adding the second term, 1.9304 + 0.0971 = 2.2075 volts. The observed value is 2.030 volts (see fig. 10), a remarkably good agreement. This calculation and the general relation shown in fig. 10 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%, 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.[2]

Accumulators in Central Stations.—As the efficiency of accumulators is not generally higher than 75%, and machines must be used to charge them, it is not directly economical to use cells alone for public supply. Yet they play an important and an increasing part in public work, because they help to maintain a constant voltage on 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.

EB1911 Accumulator - Fig 21.png
  Fig. 21.

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. Both these plans have proved unsatisfactory, and the battery is now preferably joined across the mains in parallel with the dynamo. The cells take the peaks of the load and thus relieve the dynamo and engine of sudden changes, as shown in fig. 21. Here the line current (shown by the erratic curve) varied spasmodically from 0 to 375 amperes, yet the dynamo current varied from 100 to 150 amperes only (see line A). At the same time the line voltage (535 volts normal) was kept nearly constant. In the late evening the cells became exhausted and the dynamo charged them. Extra voltage was required at the end of a “charge” and was provided by a “booster.” Originally a booster was an auxiliary dynamo worked in series with the chief machine, and driven in any convenient way. It has developed into a machine with two or more exciting coils, and having its armature in series with the cells (see fig. 22). The exciting coils act in opposition; the one carrying the main current sets up an e.m.f. in the same direction as that of the cells, and helps the cells to discharge as the load rises. When the load is small, the voltage on the mains is highest and the shunt exciting current greatest. The booster e.m.f. now acts with the dynamo and against the cells, and causes them to take a full charge. Even this arrangement did not suffice to keep the line voltage as constant as seemed desirable in some cases, as where lighting and traction work were put on the same plant. Fig. 23 is a diagram of a complex booster which gives very good regulation. The booster B has its armature in series with the accumulators A, and is kept running in a given direction at a constant speed by means of a shunt-wound motor (not shown), so that the e.m.f. induced in the armature depends on the excitation. This is made

EB1911 Accumulator - Fig 22.png
  Fig. 22.

to vary in value and in direction by means of four independent enciting coils, C1, C2, C3, C4. The last is not essential, as it merely compensates for the small voltage drop in the armature. It is obvious that the excitation C3 will be proportionate to the difference in voltage between the battery and the mains, and it is arranged that battery volts and booster volts shall equal the volts on the mains. Under this excitation there is no tendency for the battery to charge or discharge. But any additional excitation leads to strong currents one way or the other. Excitation C1 rises with the load on the line, and gives an e.m.f. helping the battery to discharge most when the load is greatest. C2 is dependent on the bus-bar voltage, and is greatest when the generator load is small: it opposes C1 and therefore excites the booster to charge the battery. The exact generator load at which the booster shall reverse its e.m.f. from a charging to a discharging value is adjusted by the resistance R2 in series with C2. A similar resistance R6 allows the excitation of C3 to be adjusted. Very remarkable regulation can be obtained by reversible boosters of this type. In traction and lighting stations it is quite possible to keep the variation of bus-bar pressure within 2% of the normal value, although the load may momentarily vary from a few amperes up to 200 or 300.

J. B. Entz has introduced an auxiliary device which enables him to use a much more simple booster. The Entz booster has no series coil and only one shunt coil, the direction and value of excitation due to this being controlled by a carbon regulator, it having two arms, the resistance of each of which can be varied by pressure due to the magnetizing action of a solenoid. The main current from the generator passes through the solenoid and causes one or other of the two carbon arms to have the less

EB1911 Accumulator - Fig 23.png
  Fig. 23.

resistance. This change in resistance determines the direction of the exciter field current, and therefore the direction of the boost. A photograph of the switchboard at Greenock where this booster is in use shows the voltmeter needle as if it had been held rigid, although the exposure lasted 90 minutes. On the same photograph the ammeter needle does not appear, its incessant and large movements preventing any picture from being formed.

Alkaline Accumulators.—Owing to the high electro-chemical equivalent of lead, a great saving in weight would be secured by using almost any other metal. Unfortunately no other metal and its compounds can resist the acid. Hence inventors have been incited to try alkaline liquids as electrolytes. Many attempts have been made to construct accumulators in this way, though with only moderate success. The Lalande-Chaperon, Desmazures, Waddell-Entz and Edison are the chief cells. T. A. Edison's cell has been most developed, and is intended for traction work. He made the plates of very thin sheets of nickel-plated steel, in each of which 24 rectangular holes were stamped, leaving a mere framework of the metal. Shallow rectangular pockets of perforated nickel-steel were fitted in the holes and then burred over the framework by high pressures. The pockets contained the active material. On the positive plate this consisted of nickel peroxide mixed with flake graphite, and on the negative plate of finely divided iron mixed with graphite. Both kinds of active material were prepared in a special way. The graphite gives greater conductivity. The liquid was a 20% solution of caustic potash. During discharge the iron was oxidized, and the nickel reduced to a lower state of oxidation. This change was reversed during charge. Fig. 24 shows the general features.

EB1911 Accumulator - Fig 24.png
 Fig. 24.—Edison Accumulator.

The chief results obtained by European experts showed that the e.m.f. was 1.33 volt, with a transient higher value following charge. A cell weighing 17.8 lb. had a resistance of 0.0013 ohm, and an output at 60 amperes of 210 watt-hours, or at 120 amperes of 177 watt-hours. Another and improved cell weighing 12.7 lb. gave 14.6 watt-hours per pound of cell at a 20-ampere rate, and 13.5 watt-hours per pound at a 60 ampere rate. The cell could be charged and discharged at almost any rate. A full charge could be given in 1 hour, and it would stand a discharge rate of 200 amperes (Journ. Inst. Elec. Eng., 1904, pp. 1-36).

Subsequently Edison found some degree of falling-off in capacity, due to an enlargement of the positive pockets by pressure of gas. Most of the faults have been overcome by altering the form of the pocket and replacing the graphite by a metallic conductor in the form of flakes.

References.—G. Planté, Recherches sur L’électricité (Paris, 1879); Gladstone and Tribe, Chemistry of Secondary Batteries (London, 1884); Reynier, L’Accumulateur voltaïque (Paris, 1888); Heim, Die Akkumulatoren (Berlin, 1889); Hoppe, Die Akk. fur Elektricität (Berlin, 1892); Schoop, Handbuch für Akk. (Stuttgart, 1898): Sir E. Frankland, "Chemistry of Storage Batteries," Proc. Roy. Soc., 1883; Reynier, Jour. Soc. Franc. de Phys., 1884; Heim, “Ü. d. Einfluss der Säuredichte auf die Kapazität der Akk.,” Elek. Zeits., 1889; Kohlrausch and Heim, “Ergebnisse von Versuchen an Akk. für Stationsbetrieb,” Elek. Zeits., 1889; Darrieus, Bull. Soc. Intern. des Élect., 1892; F. Dolezalek, The Theory of the Lead Accumulator (London, 1906); Sir D. Salomons, Management of Accumulators (London, 1906) E. J. Wade, Secondary Batteries (London, 1901); L. Jumau, Les Accumulateurs électriques (Paris, 1904). (W. Ht.) 

  1. This discharge is here compared with the charge that preceded the rest; in the next line the same discharge is compared with the charge following the rest.
  2. For the discussion of later electrolytic theories as applied to accumulators, see Dolezalek, Theory of the Lead Accumulator.