# Elementary Text-book of Physics/Ch. IV Part IV

Elementary Text-book of Physics  (1897)

Magnetism and Electricity, Chapter IV. Chemical Relations of the Current

CHAPTER IV.

CHEMICAL RELATIONS OF THE CURRENT.

279. Electrolysis.—It has been already mentioned that, in certain cases, the existence of an electrical current in a circuit is accompanied by the decomposition into their constituents of chemical compounds forming part of the circuit. This process, called electrolysis, must now be considered more fully. It is one of those treated generally in § 277, in which work other than heating the circuit is done by the current. That work is done by the decomposition of a body the constituents of which, if left to themselves, tend to recombine, is evident from the fact that, if they be allowed to recombine, the combination is always attended with the evolution of heat or the appearance of some other form of energy. The amount of heat developed, or the energy gained, is, of course, the measure of the energy lost by combination or necessary to decomposition.

Those bodies which exhibit electrolysis are always such as have considerable freedom of motion among their molecules. Ordinarily, they are liquids or solids in solution or fused. The discharge through gases is also probably accompanied by electrolysis. Bodies which can be decomposed were called by Faraday, to whom the nomenclature of this subject is due, electrolytes. The current is usually introduced into the electrolyte by solid terminals called electrodes. The one at the higher potential is called the positive electrode or anode; the other, the negative electrode, or cathode. The two constituents into which the electrolyte is decomposed are called ions. One of them appears at the anode and is called the anion, the other at the cathode and is called the cation.

For the sake of clearness we will describe some typical cases of electrolysis. The original observation of the evolution of gas when the current was passed through a drop of water, made by Nicholson and Carlisle, was soon modified by Carlisle in a way which is still generally in use. Two platinum electrodes are immersed in water slightly acidulated with sulphuric acid, and tubes are arranged above them so that the gases evolved can be collected separately. When the current is passing, bubbles of gas appear on the electrodes. When they are collected and examined, the gas which appears at the anode is found to be oxygen, and that which appears at the cathode to be hydrogen. The quantities evolved are in the proportion to form water. This appears to be a simple decomposition of water into its constituents, but it is probable that the acid in the water is first decomposed, and that the constituents of water are evolved by a secondary chemical reaction.

An experiment performed by Davy, by which he discovered the elements potassium and sodium, is a good example of simple electrolysis. He fused caustic potash in a platinum dish, which was made the anode, and immersed in the fused mass a platinum wire as cathode. Oxygen was then evolved at the anode, and the metal potassium was deposited on the cathode. This is the type of a large number of decompositions.

If, in a solution of zinc sulphate, a plate of copper be made the anode and a plate of zinc the cathode, there will be zinc deposited on the cathode and copper taken from the anode, so that, after the process has continued for a time, the solution will contain a quantity of cupric sulphate. This is a case similar to the electrolysis of acidulated water, in which the simple decomposition of the electrolyte is modified by secondary chemical reactions.

If two copper electrodes be immersed in a solution of cupric sulphate, copper will be removed from the anode and deposited on the cathode, without any important change occuring in the character or concentration of the electrolyte. This is an example of the special case in which the secondary reactions in the electrolyte exactly balance the work done by the current in decomposition, so that on the whole no chemical work is done.

280. Faraday's Laws.—The researches of Faraday in electrolysis developed two laws, which are of great importance in the theory of chemistry as well as in electricity:

(1) The amount of an electrolyte decomposed is directly proportional to the quantity of electricity which passes through it; or, the rate at which a body is electrolyzed is proportional to the current strength.

(2) If the same current be passed through different electrolytes, the quantity of each ion evolved is proportional to its chemical equivalent. The chemical equivalent is the weight of the radical of the ion in terms of the weight of the atom of hydrogen, divided by its valency.

If we define an electro-chemical equivalent as the quantity of any ion which is evolved by unit current in unit time, then the two laws may be summed up by saying:

The number of electro-chemical equivalents evolved in a given time by the passage of any current through any electrolyte is equal to the number of units of electricity which pass through the electrolyte in the given time.

The electro-chemical equivalents of different ions are proportional to their chemical equivalents. Thus, if zinc sulphate, cupric sulphate, and argentic chloride be electrolyzed by the same current, zinc is deposited on the cathode in the first case, copper in the second, and silver in the third. The amounts by weight deposited are in proportion to the chemical equivalents, 32.6 parts of zinc, 31.7 parts of copper, and 108 parts of silver.

Faraday's laws may also be stated in another form, in which the word "ion" has a different meaning. The process of electrolysis consists in the separation of each molecule of the electrolyte into its constituent radicals. Each of these radicals is called an ion. If the valency of the radical be 1, the ion is called a univalent ion; if it be n, the ion is either called an n-valent ion or nunivalent ions. To illustrate, we know that when hydrogen is evolved from hydrochloric acid, HCl, its ion is univalent. Now when it is evolved from water, H2O, we may either consider the H2 as a bivalent ion or as two univalent ions. Similarly we may consider the O as a bivalent ion or as two univalent ions, though it can never be actually broken up into two such ions. We may consider a molecule, then, as made up either of two n-valent ions or of 2n univalent ions. The weight of each of the n-valent ions may be measured in terms of the weight of the hydrogen atom taken as a unit, and is the molecular weight of the ion. This weight divided by the valency n is the weight of the univalent ion. It may be called the ionic weight.

Now the passage of a current through different electrolytes evolves their constituents in amounts proportional to their molecular weights divided by their valencies. It therefore evolves the ions in proportion to their ionic weights, or it evolves the same number of univalent ions in each electrolyte. Faraday's two laws may therefore be summed up in the statement that the number of univalent ions evolved by a current in any electrolyte is proportional to the quantity of current.

By this mode of considering electrolysis, we are led to the conclusion that each pair of univalent ions liberated during electrolysis is associated with a pair of charges numerically equal and of opposite sign. These charges are called ionic charges. An n-valent ion is associated with n ionic charges. If we use the conception of tubes of force, each positive univalent ion may be considered as the origin of a tube of force which terminates on a negative ion. Since the ionic charges are all equal, these tubes may be taken as unit tubes, which are no longer defined arbitrarily, but are based upon a constant of Nature.

281. The Voltameter.—These laws were used by Faraday to establish a method of measuring current by reference to an arbitrary standard. The method employs a vessel containing an electrolyte in which suitable electrodes are immersed, so arranged that the products of electrolysis, if gaseous, can be collected and measured, or, if solid, can be weighed. This arrangement is called a voltameter. If the current strength be desired, the current must be kept constant in the voltameter by suitable variation of the resistance in the circuit during the time in which electrolysis is going on.

Two forms of voltameter are in frequent use.

In the first form there is, on the whole, no chemical work done in the electrolytic process. The system consisting of two copper electrodes and cupric sulphate as the electrolyte is an example of such a voltameter. The weight of the copper deposited on the cathode measures the current.

The second form depends for its indications on the evolution of gas, the volume of which is measured. The water voltameter is a type, and is the form especially used. The gases evolved are either collected together, or the hydrogen alone is collected. The latter is preferable, because oxygen is more easily absorbed by water than hydrogen, and an error is thus introduced when the oxygen is measured.

282. Measure of the Counter Electromotive Force of Decomposition.— In the general formula developed in § 377 the quantity ${\displaystyle IA}$ represents the energy expended in the circuit which does not appear as heat developed in accordance with Joule's law. In the present case it is the energy expended during electrolysis in decomposing chemical compounds and in doing mechanical work. In many cases the mechanical work done is not appreciable; but when a liquid like water is decomposed into its constituent gases, work is done by the expansion of the gases from their volume as water to their volume as gases. In many cases some of this energy is also used in keeping the temperature of the electrolyte constant. These cases occur when the electromotive force developed varies with the temperature.

In case no such variation with the temperature occurs, we may calculate the electromotive force developed in terms of heat. Let ${\displaystyle e}$ represent the electro-chemical equivalent of one of the ions, and ${\displaystyle \theta }$ the heat evolved by the combination of a unit mass of this ion with an equivalent mass of the other ion, in which is included the heat equivalent of the mechanical work done if the state of aggregation change. Then ${\displaystyle I}$ will represent the number of electro-chemical equivalents evolved in unit time, and ${\displaystyle Ie\theta t}$ will represent the energy expended in the time ${\displaystyle t,}$ which appears as chemical separation and mechanical work. This is equal to ${\displaystyle IA;}$ whence ${\displaystyle A=e\theta t.}$ All these quantities are measured in absolute units. The quantity ${\displaystyle e\theta }$ represents the energy required to separate the quantity ${\displaystyle e}$ of the ion considered from the equivalent quantity of the other ion, and to bring both constituents to their normal condition. Now, ${\displaystyle {\frac {A}{t}}}$ represents the counter electromotive force set up in the circuit by electrolysis. Hence the electromotive force set up in the electrolytic process may be measured in terms of heat units.

It often is the case that the two ions which appear at the electrodes are not capable of direct recombination, as has been tacitly assumed in the definition of ${\displaystyle \theta .}$ A series of chemical exchanges is always possible, however, which will restore the ions as constituents of the electrolyte, and the total heat evolved for a unit mass of one ion during the process is the quantity ${\displaystyle \theta .}$

The theory here presented is abundantly verified by the experiments of Joule, Favre and Silbermann, Wright, and others. The extension of the theory to cases in which the electromotive force varies with the temperature was made by Helmholtz.

283. Positive and Negative Ions.—Experiment shows that certain of the bodies which act as ions usually appear at the cathode, and certain others at the anode. The former are called electro-positive elements; the latter, electro-negative elements. Faraday divided all the ions into these two classes, and thought that every compound capable of electrolysis was made up of one electro-positive and one electro-negative ion. But the distinction is not absolute. Some ions are electro-positive in one combination and electro-negative in another. Berzelius made an attempt to arrange the ions in a series, such that any one ion should be electro-positive to all those above it and electro-negative to all those below it. There is no reason to believe that such a rigorous arrangement of the ions can be made.

284. Grotthus's Theory of Electrolysis.— The foundation of all the present theories of electrolysis is found in the theory published by Grotthus in 1805. He considered the constituent ions of a molecule as oppositely electrified to an equal amount. When the current passes, owing to the electrical attractions of the electrodes, the molecules arrange themselves in lines with their similar ends in one direction, and then break up. The electro-negative ion of one molecule moves toward the positive electrode and meets the electro-positive ion of the neighboring molecule, with which it momentarily unites. At the ends of the line an electro-negative ion with its charge is freed at the anode, and an electro-positive ion with its charge is freed at the cathode. This process is repeated indefinitely so long as the current passes.

Faraday modified this view, in that he ascribed the arrangement of the molecules, and their disruption, to the stress in the medium which was the cardinal point in his electrical theories. Otherwise he held closely to Grotthus's theory. He showed that an electrical stress exists in the electrolyte by means of fine silk threads immersed in it. These arranged themselves along the lines of electrical stress.

Other phenomena, however, show that Grotthus's hypothesis can only be treated as a rough illustration of the main facts. Joule showed that during electrolysis there is a development of heat at the electrodes, in certain cases, which is not accounted for by the elementary theory above given. It must depend upon a more complicated process of electrolysis than the one we have described.

The results of researches on the so-called migration of the ions are also at variance with Grotthus's theory. If the electrolysis of a copper salt, in a cell with a copper anode at the bottom, be examined, it will be found that the solution becomes more concentrated about the anode and more dilute about the cathode. These changes can be detected by the color of the parts of the solution, and substantiated by chemical analysis. If this result be explained by Grotthus's theory, the explanation furnishes at the same time a numerical relation between the ions which have wandered to their respective regions in the electrolyte which is not in accord with experiment.

It is an objection against Grotthus's theory, and indeed against Thomson's method given in § 282 of connecting chemical affinity and electromotive force, that, on those theories, it would require an electromotive force in the circuit greater than ^, the counter electromotive force in the electrolytic cell, to set up a current, and that the current would begin suddenly, with a finite value, after this electromotive force is reached. On the contrary, experiments show that the smallest electromotive force will set up a current in an electrolyte and even maintain one constantly, though the current strength may be extremely small.

285. The Dissociation Theory of Electrolysis.—The foundations of a more satisfactory theory of electrolysis were laid by Clausius, who proceeded from the view with which he had become familiar by his study of the kinetic theory of gases, that the molecules of all bodies are in constant motion. He assumed that the collisions of the molecules of the electrolyte occasionally caused a separation of some of the molecules into their constituent ions, and that the province of the electromotive force in the electrolyte was to direct the motion of these ions toward their respective electrodes. A considerable extension of Clausius's theory has been made by Arrhenius and developed by Ostwald and others, in which the leading idea is, that the molecules of an electrolyte in solution are always separated to a greater or less extent into their constituent ions. In many cases, and always in very dilute solutions, the separation, according to this view, is complete. This theory is called the dissociation theory of electrolysis. The ions, however, are not in the condition of the constituent parts of a molecule which have been dissociated at a high temperature (§ 219), but possess certain peculiar electrical and chemical properties. It has been proposed to call their condition in solution ionization. This term certainly possesses advantages, but it has not yet come into common use, and we will therefore retain the term dissociation.

We have already seen that a current in an electrolyte may be considered as the transfer of charges on the moving ions. If the ions in solution be dissociated from each other, and if the effect of the electromotive force in the circuit be merely directive, it is plain that the quantity of current transferred will depend on the relative velocity with which the ions move past each other in the solution as well as on their number. Starting with this conception, we will show that the conductivity of an electrolyte is proportional to the sum of the velocities of its ions. The discovery of this fact by Kohlrausch laid the foundation for the dissociation theory.

Let us suppose a series of electrolytic cells, e'ach one of which is a cubical box with sides of unit length, and so arranged that a current passes in them between two opposite faces which serve as electrodes. The column of the electrolyte between the electrodes is then one centimetre long and has a cross-section of one square centimetre. Let the electrolytes used in these cells be prepared by dissolving in equal volumes of the same solvent masses of the substances to be decomposed which are proportional to the sums of the ionic weights of their constituent ions (§ 280). Equal volumes of these solutions will then contain the same number of univalent ions.

If a current be sent through the series of cells containing these solutions, the same number of univalent, ions will be liberated in each. The difference of potential between the terminals of the cells will be in general different for each of them. We have from Ohm's law the relation ${\displaystyle I=k(V_{1}-V_{2}),}$ where the current ${\displaystyle I}$ is the same for each cell and the difference of potential ${\displaystyle V_{1}-V_{2}}$ and the conductivity ${\displaystyle k}$ (§ 275) different for the different cells. Now consider a cross-section in one of the cells parallel with the electrodes; let ${\displaystyle u}$ and ${\displaystyle v}$ represent the velocities of the ions evolved in this cell. Let ${\displaystyle 2M}$ represent the number of univalent ions in the cell, and let ${\displaystyle c}$ represent the ionic charge. Now the relative velocity of the ions which pass through the cross-section taken in the cell is ${\displaystyle u+v;}$ the number of ions which pass through that cross-section in unit time in both directions is therefore ${\displaystyle M(u+v)}$ and the quantity of electricity carried through with them in both directions is ${\displaystyle cM(u+v).}$ But this quantity is equal to the current strength ${\displaystyle I,}$ and therefore ${\displaystyle cM(u+v)=k(V_{1}-V_{2});}$ or ${\displaystyle u+v={\frac {k(V_{1}-V_{2})}{cM}}\cdot }$ Now ${\displaystyle cM}$ is the quantity of current required to decompose the molecules in the cell, or the mass which is in solution in unit volume of the electrolyte; it may therefore be directly determined. Since equal volumes of the electrolytes contain the same number of univalent ions, this quantity of current is the same for all the cells, and since, with a known value of ${\displaystyle I,}$ we may determine the value of ${\displaystyle k}$ in each case by observations of ${\displaystyle V_{1}-V_{2},}$ the formula just obtained enables us to determine ${\displaystyle u+v.}$

This formula may be more conveniently used in another form. Let ${\displaystyle n}$ represent the weight of the hydrogen evolved by unit current in unit time, and ${\displaystyle m}$ the chemical equivalent of one of the products of electrolysis in the cell. Then ${\displaystyle mn}$ represents the weight of that product evolved by unit current in unit time, and ${\displaystyle {\frac {1}{mn}}}$ represents the current that will evolve unit weight in unit time. Now the electrolytes are prepared so that the weights of the constituents in the cells are given by ${\displaystyle Nm,}$ where ${\displaystyle N}$ is a number which is the same for all the cells. The current that will evolve these weights in the respective cells is therefore equal to ${\displaystyle {\frac {N}{m}},}$ and this current has been shown to be equal to ${\displaystyle cM.}$ Using this value of ${\displaystyle cM}$ in the equation for ${\displaystyle u+v,}$ we obtain ${\displaystyle u+v={\frac {nk(V_{1}-V_{2})}{N}}\cdot }$ In the experiments of Kohlrausch the difference of potential ${\displaystyle V_{1}-V_{2}}$ was the same for all the cells, and the value of ${\displaystyle {\frac {k}{N}}}$ determined for each cell. The values of ${\displaystyle u+v}$could then be calculated. The ratio ${\displaystyle {\frac {k}{N}}}$ is called the molecular conductivity.

Now in order to determine the values of ${\displaystyle u}$ and ${\displaystyle v,}$ we need them combined in another relation; this relation may be obtained from a study of the migration of the ions. For, consider a row of molecules in the electrolyte stretching between the electrodes, of which the ions are moving independently, the positive ions to the right with the velocity ${\displaystyle u,}$ and the negative ions to the left with the velocity ${\displaystyle v.}$ Let ${\displaystyle n}$ represent the number of ions of either sort in unit length of this line. At the end of the short time ${\displaystyle t}$ the relative displacement of the rows of ions will be ${\displaystyle (u+v)t,}$ and the number of ions freed at either end will be the same and equal to ${\displaystyle n(u+v)t.}$ Though the number of ions which are freed at either end is the same, the loss of molecules or of pairs of associated ions is different at the two ends. If a line be drawn perpendicularly across the line of molecules, the number of ions which pass to the right, and therefore the number of molecules lost on the left of this line is ${\displaystyle nut,}$ while the number of molecules lost on its right is ${\displaystyle nvt.}$ If, therefore, we measure the diminution of the substance decomposed at each electrode, the ratio of the values found will be the ratio of the velocities ${\displaystyle u}$ and ${\displaystyle v}$ of the constituent ions. The ratio of one of these losses or diminutions to the sum of them both, or the ratio of the velocity of the corresponding ion to the sum of the velocities of the two ions, is called the migration constant of the ion. The migration constants have been determined for many ions by Hittorf, Nernst, and others. By combining the ratios of the velocities thus found with the sums of the velocities found by Kohlrausch, the velocities may be separately determined. It is found that the velocity of any one ion is the same, whatever be the electrolyte of which it forms a part, provided the solution be sufficiently dilute. This result is a strong confirmation of the theory of the independent motion of the ions upon which the calculations are based.

In many cases, especially when the solution is not very dilute, the molecular conductivity is found to be less than that assigned by theory on the assumption that all the ions of the electrolyte are dissociated. This discrepancy is explained by Arrhenius by the assumption that in this case the dissociation is not complete; the ratio of the molecular conductivity found in such cases to the molecular conductivity at very great dilutions, in which case the dissociation is assumed to be complete, is taken as the measure of the dissociation in the solution. A similar theory of partial dissociation was assumed to account for the departures from the normal laws of osmotic pressure (§§ 94, 95), of the lowering of the freezing-point (§ 197), and of the lowering of vapor pressure (§ 204).

The agreement between the conclusions reached by these entirely independent methods with regard to the extent of dissociation is strong evideuce in favor of the hypothesis upon which the calculations are based. Starting with the same hypothesis, other relations have been theoretically discovered among the physical properties of solutions which have been confirmed by experiment. The dissociation theory of solution and of electrolysis is not yet fully established, but it furnishes by far the most satisfactory explanation of the nature and behavior of solutions.

286. Voltaic Cells.—From the discussion given in § 277 it is obvious that, if an arrangement be made, in a circuit, of substances capable of uniting chemically and such as would result from electrolysis, there will result an electromotive force in such a sense as to oppose the current which would eSect the electrolysis. If, then, the electrodes of an electrolytic cell in which this electromotive force exists be joined by a wire, a current will be set up through the wire in the opposite direction to the one which would continue the electrolysis, and the ions at the electrodes will recombine to form the electrolyte. There is thus formed an independent source of current, the voltaic cell. The electrode in connection with the electro-negative ion is called the positive pole, and that in connection with the electro-positive ion the negative pole.

Thus, if after the electrolysis of water in a voltameter, in which the gases are collected separately in tubes over platinum electrodes, the electrodes be joined by a wire, a current will be set up in it, and the gases will gradually, and at last totally, disappear, and the current will cease. The current which decomposes the water is conventionally said to flow through the liquid from the anode to the cathode, from the electrode above which oxygen is collected to the electrode above which hydrogen is collected. The current existing during the recombination of the gases flows through the liquid from the hydrogen electrode to the oxygen electrode, or outside the liquid from the positive to the negative pole. Such an arrangement as is here described was devised by Grove, and is called the Grove's gas battery.

A combination known as Smee's cell consists of a plate of zinc and one of platinum, immersed in dilute sulphuric acid. It is such a cell as would be formed by the complete electrolysis of a solution of zinc sulphate, if the zinc plate were made the cathode. When the zinc and platinum plates are joined by a wire, a current is set up from the platinum to the zinc outside the liquid, and the zinc combines with the acid to form zinc sulphate. The hydrogen thus liberated appears at the platinum plate, where, since the oxygen which was the electro-negative ion of the hypothetical electrolysis by which the cell was formed does not exist there ready to combine with it, it collects in bubbles and passes up through the liquid. The presence of this hydrogen at once lowers the current from the cell, for it sets up a counter electromotive force, and also diminishes the surface of the platinum plate in contact with the liquid, and thus increases the resistance of the cell. It may be partially removed by mechanical movements of the plate or by roughening its surface. The counter electromotive force is called the electromotive force of polarization. It occurs soon after the circuit is joined up in all cells in which only a single liquid is used, and very much diminishes the currents which are at first produced.

Advantage is taken of secondary chemical reactions to avoid this electromotive force of polarization. The best example, and a cell which is of great practical value for its cheapness, durability, and constancy, is the Daniell's cell. Two liquids are used—solutions of cupric sulphate and zinc sulphate. They are best separated from one another by a porous porcelain diaphragm. A plate of copper is immersed in the cupric sulphate, and a plate of zinc in the zinc sulphate. The copper is the positive pole, the zinc the negative pole. When the circuit is made, and the current passes, zinc is dissolved, the quantity of zinc sulphate increases and that of the cupric sulphate decreases, and copper is deposited on the copper plate. To prevent the destruction of the cell by the consumption of the cupric sulphate, crystals of the salt are placed in the solution. The electromotive force of this cell is evidently due to the loss of energy in the substitution of zinc for copper in the solution of cupric sulphate.

The secondary cell of Planté is an example of a cell made directly by electrolysis, as has been assumed in the preliminary discussion. The electrodes are both lead plates, and the electrolyte dilute sulphuric acid. When a current is passed through the cell, the oxygen evolved on the anode combines with the lead to form peroxide of lead, which coats the surface of the electrode. When the cell is inserted in a circuit, a current is set up, the peroxide is reduced to a lower oxide, and the metallic lead of the other plate is oxidized.

Cells of this sort, which have been constructed directly by coating lead plates with the proper oxides of lead, are called storage cells. They may be put in condition for use by sending a current through them in the proper direction. The sulphate of lead formed plays an important part in the operation of these cells.

The Latimer-Clarke standard cell is of great value as a standard of electromotive force. The positive pole consists of pure mercury, which is covered by a paste made by boiling mercurous sulphate in a saturated solution of zinc sulphate. The negative pole consists of pure zinc resting on the paste. Contact with the mercury is made by means of a platinum wire. As no gases are generated, this cell may be hermetically sealed against atmospheric influences. According to the measurements of Rayleigh, the electromotive force of this cell is very constantly 1,435 • 108 C. G. S. electromagnetic units at 15° Cent.

287. Theories of the Electromotive Force of the Voltaic Cell.—The plan followed in the preceding discussions has rendered it unnecessary for us to adopt any theory to explain the cause of the electromotive force of the voltaic cell. The different theories which have been advanced may be classed under one of two general theories, the contact theory and the chemical theory. On the contact theory, as advanced by Volta and supported by Thomson and others, the difference of potential which exists between two heterogeneous substances in contact is due to molecular interactions across the surface of contact, or, as it is commonly stated, is due merely to the contact. The chemical theory, as advocated by Faraday and Schönbein, holds that the difference of potential considered cannot arise unless chemical action or a tendency to chemical action exist at the surface of contact.

Numerous experiments have shown that the sum of all the differences of potential at the surfaces of contact of the various substances making up any voltaic cell is equal to the electromotive force of that cell. This is true even when the cell is formed solely of liquid elements. On the contact theory, this electromotive force is due merely to the several contacts, while the chemical actions of the cell begin only when the circuit is made, and supply the energy for the maintenance of the current. On the chemical theory the chemical action of the medium is concerned in the production of the difference of potential observed.

On either theory it is clear that the energy maintaining the current must have its origin in the chemical actions which go on in the voltaic cell.

288. The Electrical Double-sheet.—Suppose two plates of different materials, say one zinc and the other copper, joined by a wire and placed opposite each other like the plates of a condenser: as stated in the last section, a difference of potential then exists between them. The charge on one of them is given by ${\displaystyle {\frac {S(V_{1}-V_{2})}{4\pi d}}}$ (§ 259, (Eq. 92)). The difference of potential will remain the same, whatever be the distance between the plates, so that the charges on the plates and the distance between them vary inversely. When the faces of the two plates are in contact, that is, are separated by molecular distances, these charges become very great. Such an arrangement of equal and opposite charges, distributed over the surfaces of two bodies in contact and separated by a distance comparable with the distance between the molecules, was called by Helmholtz an electrical double-sheet. It evidently presents some analogies to the magnetic shell.

The charges making up the double-sheet cannot be detected by separating a plate of zinc from a plate of copper with which it has been in contact and examining the separate plates, because the separation cannot be effected so uniformly that no discharge takes place between the two bodies. If, however, those faces of the zinc and copper plates which are contiguous be insulated from each other by a thin layer of shellac and contact made between the plates by means of a metallic wire, so that a difference of potential is set up between them, on removal of the wire and separation of the plates they are found to possess charges of considerable magnitude.

We may explain in this way electrification by friction. We may assume that the two bodies rubbed together acquire different potentials by contact; the friction forces large areas of their surfaces into close proximity, and the charges upon those surfaces become very great; because the bodies ordinarily used for producing electrification by friction are nonconductors, the charges on their surfaces are not recombined as the bodies are separated, so that each body retains a large free charge.

A similar electrical double-sheet will exist on the surfaces of contact between a liquid and a metal. An arrangement by which the effects due to this double-sheet may be observed was invented by Lippmann. It consists of a vertical glass tube drawn out at its lower end in a capillary tube. The capillary tube dips into dilute sulphuric acid, which rests on mercury in the bottom of the vessel containing it. Mercury is poured into the vertical tube until its pressure is such that the capillary portion of the tube is nearly filled with it. When the mercury in the vessel is joined with the positive pole of a voltaic cell, and that in the tube with the negative pole, the meniscus in the capillary tube moves upward, in the sense in which it would move if its surface tension were increased.

This movement may be explained as follows: An electrical double-sheet will be formed on the curved surface of contact of the mercury and acid in the capillary tube, and the interaction of the parts of this double-sheet will give rise to an electrical pressure (§ 256), that diminishes the apparent surface tension in that surface. If a weak current be sent through the solution, the difference of potential between the liquid and mercury will be diminished or increased by the ionic charges transferred by the current, according as the current flows in one direction or the other. The apparent surface tension will be altered and the end of the mercury column will be displaced; the true surface tension of the surface will be efficient only when the mercury and solution are at the same potential, and this surface tension will be a maximum. The experiments of Helmholtz and A. König have shown that such a maximum exists in a way consistent with this view.

The arrangement described can manifestly be used to produce the effects just discussed only when the electromotive force introduced into the circuit is less than that required to cause active decomposition of the electrolyte.

Lippmann constructed an apparatus similar to the one described, with the addition of an arrangement by which pressure can be applied to force the end of the mercury column in the capillary tube back to the fixed position which it occupies when no electromotive force is introduced into the circuit. He found that when small electromotive forces were introduced, the pressures required to bring the end of the column back to the fixed position were proportional to the electromotive forces. He hence called this apparatus a capillary electrometer.

Lippmann also found that if the area of the surface of separation between the mercury and the liquid in the capillary tube were altered by increasing the pressure and driving the mercury down the tube, a current was set up in a galvanometer inserted in the circuit, in a sense opposite to that which would change the area of the meniscus back to its original amount.

The electrical double-sheet produced by contact of a liquid and a solid serves also to explain the phenomenon of electrical endosmose.

It is found that, if an electrolyte be divided into two portions by a porous diaphragm, there is a transfer of the electrolyte toward the cathode, so that it stands at a higher level on the side of the diaphragm nearer the cathode than on the other. This fact was discovered by Reuss in 1807, and has been investigated by Wiedemann and Quincke. They found that the amount of the electrolyte transferred is proportional to the current strength, and independent of the extent of surface or the thickness of the diaphragm. Quincke has also demonstrated a flow of the electrolyte toward the cathode in a narrow tube, without the intervention of a diaphragm. Those electrolytes which are the poorest conductors show the phenomenon the best. In a very few cases the motion is towards the anode. The material of which the tube is composed influences the direction of flow. It has also been shown that solid particles move in the electrolyte, usually towards the anode.

Helmholtz showed that these movements can be explained by taking into account the interaction between the ionic charges and the double-sheet, and the viscosity of the liquid.