Chapter 3

For the bibliography of electrolytic conduction seeElectrolysis. The books which deal more especially with the particular subject of the present article areDas Leitvermögen der Elektrolyte, by F. Kohlrausch and L. Holborn (Leipzig, 1898), andThe Theory of Solution and Electrolysis, by W. C. D. Whetham (Cambridge, 1902).

(W. C. D. W.)

III.Electric Conduction through Gases

A gas such as air when it is under normal conditions conducts electricity to a small but only to a very small extent, however small the electric force acting on the gas may be. The electrical conductivity of gases not exposed to special conditions is so small that it was only definitely established in the early years of the 20th century, although it had engaged the attention of physicists for more than a hundred years. It had been known for a long time that a body charged with electricity slowly lost its charge even when insulated with the greatest care, and though long ago some physicists believed that part of the leak of electricity took place through the air, the general view seems to have been that it was due to almost unavoidable defects in the insulation or to dust in the air, which after striking the charged body was repelled from it and went off with some of the charge. C. A. Coulomb, who made some very careful experiments which were published in 1785 (Mém. de l’Acad. des Sciences, 1785, p. 612), came to the conclusion that after allowing for the leakage along the threads which supported the charged body there was a balance over, which he attributed to leakage through the air. His view was that when the molecules of air come into contact with a charged body some of the electricity goes on to the molecules, which are then repelled from the body carrying their charge with them. We shall see later that this explanation is not tenable. C. Matteucci (Ann. chim. phys., 1850, 28, p. 390) in 1850 also came to the conclusion that the electricity from a charged body passes through the air; he was the first to provethat the rate at which electricity escapes is less when the pressure of the gas is low than when it is high. He found that the rate was the same whether the charged body was surrounded by air, carbonic acid or hydrogen. Subsequent investigations have shown that the rate in hydrogen is in general much less than in air. Thus in 1872 E. G. Warburg (Pogg. Ann., 1872, 145, p. 578) found that the leak through hydrogen was only about one-half of that through air: he confirmed Matteucci’s observations on the effect of pressure on the rate of leak, and also found that it was the same whether the gas was dry or damp. He was inclined to attribute the leak to dust in the air, a view which was strengthened by an experiment of J. W. Hittorf’s (Wied. Ann., 1879, 7, p. 595), in which a small carefully insulated electroscope, placed in a small vessel filled with carefully filtered gas, retained its charge for several days; we know now that this was due to the smallness of the vessel and not to the absence of dust, as it has been proved that the rate of leak in small vessels is less than in large ones.

Great light was thrown on this subject by some experiments on the rates of leak from charged bodies in closed vessels made almost simultaneously by H. Geitel (Phys. Zeit., 1900, 2, p. 116) and C. T. R. Wilson (Proc. Camb. Phil.Soc., 1900, 11, p. 32). These observers established that (1) the rate of escape of electricity in a closed vessel is much smaller than in the open, and the larger the vessel the greater is the rate of leak; and (2) the rate of leak does not increase in proportion to the differences of potential between the charged body and the walls of the vessel: the rate soon reaches a limit beyond which it does not increase, however much the potential difference may be increased, provided, of course, that this is not great enough to cause sparks to pass from the charged body. On the assumption that the maximum leak is proportional to the volume, Wilson’s experiments, which were made in vessels less than 1 litre in volume, showed that in dust-free air at atmospheric pressure the maximum quantity of electricity which can escape in one second from a charged body in a closed volume of V cubic centimetres is about 10-8V electrostatic units. E. Rutherford and S. T. Allan (Phys. Zeit., 1902, 3, p. 225), working in Montreal, obtained results in close agreement with this. Working between pressures of from 43 to 743 millimetres of mercury, Wilson showed that the maximum rate of leak is very approximately proportional to the pressure; it is thus exceedingly small when the pressure is low—a result illustrated in a striking way by an experiment of Sir W. Crookes (Proc. Roy. Soc., 1879, 28, p. 347) in which a pair of gold leaves retained an electric charge for several months in a very high vacuum. Subsequent experiments have shown that it is only in very small vessels that the rate of leak is proportional to the volume and to the pressure; in large vessels the rate of leak per unit volume is considerably smaller than in small ones. In small vessels the maximum rate of leak in different gases, is, with the exception of hydrogen, approximately proportional to the density of the gas. Wilson’s results on this point are shown in the following table (Proc. Roy. Soc., 1901, 60, p. 277):—

The rate of leak of electricity through gas contained in a closed vessel depends to some extent on the material of which the walls of the vessel are made; thus it is greater, other circumstances being the same, when the vessel is made of lead than when it is made of aluminium. It also varies, as Campbell and Wood (Phil. Mag.[6], 13, p. 265) have shown, with the time of the day, having a well-marked minimum at about 3 o’clock in the morning: it also varies from month to month. Rutherford (Phys. Rev., 1903, 16, p. 183), Cooke (Phil. Mag., 1903 [6], 6, p. 403) and M’Clennan and Burton (Phys. Rev., 1903, 16, p. 184) have shown that the leak in a closed vessel can be reduced by about 30% by surrounding the vessel with sheets of thick lead, but that the reduction is not increased beyond this amount, however thick the lead sheets may be. This result indicates that part of the leak is due to a very penetrating kind of radiation, which can get through the thin walls of the vessel but is stopped by the thick lead. A large part of the leak we are describing is due to the presence of radioactive substances such as radium and thorium in the earth’s crust and in the walls of the vessel, and to the gaseous radioactive emanations which diffuse from them into the atmosphere. This explains the very interesting effect discovered by J. Elster and H. Geitel (Phys. Zeit., 1901, 2, p. 560), that the rate of leak in caves and cellars when the air is stagnant and only renewed slowly is much greater than in the open air. In some cases the difference is very marked; thus they found that in the cave called the Baumannshöhle in the Harz mountains the electricity escaped at seven times the rate it did in the air outside. In caves and cellars the radioactive emanations from the walls can accumulate and are not blown away as in the open air.

The electrical conductivity of gases in the normal state is, as we have seen, exceedingly small, so small that the investigation of its properties is a matter of considerable difficulty; there are, however, many ways by which the electrical conductivity of a gas can be increased so greatly that the investigation becomes comparatively easy. Among such methods are raising the temperature of the gas above a certain point. Gases drawn from the neighbourhood of flames, electric arcs and sparks, or glowing pieces of metal or carbon are conductors, as are also gases through which Röntgen or cathode rays or rays of positive electricity are passing; the rays from the radioactive metals, radium, thorium, polonium and actinium, produce the same effect, as does also ultra-violet light of exceedingly short wave-length. The gas, after being made a conductor of electricity by any of these means, is found to possess certain properties; thus it retains its conductivity for some little time after the agent which made it a conductor has ceased to act, though the conductivity diminishes very rapidly and finally gets too small to be appreciable.

This and several other properties of conducting gas may readily be proved by the aid of the apparatus represented in fig. 5. V is a testing vessel in which an electroscope is placed. Two tubes A and C are fitted into the vessel, A being connected with a water pump, while the far end of C is in the region where the gas is exposed to the agent which makes it a conductor of electricity. Let us suppose that the gas is made conducting by Röntgen rays produced by a vacuum tube which is placed in a box, covered except for a window at B with lead so as to protect the electroscope from the direct action of the rays. If a slow current of air is drawn by the water pump through the testing vessel, the charge on the electroscope will gradually leak away. The leak, however, ceases when the current of air is stopped. This result shows that the gas retains its conductivity during the time taken by it to pass from one end to the other of the tube C.

The gas loses its conductivity when filtered through a plug of glass-wool, or when it is made to bubble through water. This can readily be proved by inserting in the tube C a plug of glass-wool or a water trap; then if by working the pump a little harder the same current of air is produced as before, it will be found that the electroscope will now retain its charge, showing that the conductivity can, as it were, be filtered out of the gas.The conductivity can also be removed from the gas by making the gas traverse a strong electric field. We can show this by replacing the tube C by a metal tube with an insulated wire passing down the axis of the tube. If there is no potential difference between the wire and the tube then the electroscope will leak when a current of air is drawn through the vessel, but the leak will stop if a considerable difference of potential is maintained between the wire and the tube: this shows that a strong electric field removes the conductivity from the gas.

The fact that the conductivity of the gas is removed by filtering shows that it is due to something mixed with the gas which is removed from it by filtration, and since the conductivity is also removed by an electric field, the cause of the conductivity must be charged with electricity so as to be driven to the sides of the tube by the electric force. Since the gas as a whole is not electrified either positively or negatively, there must be both negative and positive charges in the gas, the amount of electricity of one sign being equal to that of the other. We are thus led to the conclusion that the conductivity of the gas is due to electrified particles being mixed up with the gas, some of these particles having charges of positive electricity, others of negative. These electrified particles are calledions, and the process by which the gas is made a conductor is called the ionization of the gas. We shall show later that the charges and masses of the ions can be determined, and that the gaseous ions are not identical with those met with in the electrolysis of solutions.

One very characteristic property of conduction of electricity through a gas is the relation between the current through the gas and the electric force which gave rise to it. This relation is not in general that expressed by Ohm’s law, which always, as far as our present knowledge extends, expresses the relation for conduction through metals and electrolytes. With gases, on the other hand, it is only when the current is very small that Ohm’s law is true. If we represent graphically by means of a curve the relation between the current passing between two parallel metal plates separated by ionized gas and the difference of potential between the plates, the curve is of the character shown in fig. 6 when the ordinates represent the current and the abscissae the difference of potential between the plates. We see that when the potential difference is very small,i.e.close to the origin, the curve is approximately straight, but that soon the current increases much less rapidly than the potential difference, and that a stage is reached when no appreciable increase of current is produced when the potential difference is increased; when this stage is reached the current is constant, and this value of the current is called the “saturation” value. When the potential difference approaches the value at which sparks would pass through the gas, the current again increases with the potential difference; thus the curve representing the relation between the current and potential difference over very wide ranges of potential difference has the shape shown in fig. 7; curves of this kind have been obtained by von Schweidler (Wien. Ber., 1899, 108, p. 273), and J. E. S. Townsend (Phil. Mag., 1901 [6], 1, p. 198). We shall discuss later the causes of the rise in the current with large potential differences, when we consider ionization by collision.

The general features of the earlier part of the curve are readily explained on the ionization hypothesis. On this view the Röntgen rays or other ionizing agent acting on the gas between the plates, produces positive and negative ions at a definite rate. Let us suppose that q positive and q negative ions are by this means produced per second between the plates; these under the electric force will tend to move, the positive ones to the negative plate, the negative ones to the positive. Some of these ions will reach the plate, others before reaching the plate will get so near one of the opposite sign that the attraction between them will cause them to unite and form an electrically neutral system; when they do this they end their existence as ions. The current between the plates is proportional to the number of ions which reach the plates per second. Now it is evident that we cannot go on taking more ions out of the gas than are produced; thus we cannot, when the current is steady, have more than q positive ions driven to the negative plate per second, and the same number of negative ions to the positive. If each of the positive ions carries a charge of e units of positive electricity, and if there is an equal and opposite charge on each negative ion, then the maximum amount of electricity which can be given to the plates per second is qe, and this is equal to the saturation current. Thus if we measure the saturation current, we get a direct measure of the ionization, and this does not require us to know the value of any quantity except the constant charge on the ion. If we attempted to deduce the amount of ionization by measurements of the current before it was saturated, we should require to know in addition the velocity with which the ions move under a given electric force, the time that elapses between the liberation of an ion and its combination with one of the opposite sign, and the potential difference between the plates. Thus if we wish to measure the amount of ionization in a gas we should be careful to see that the current is saturated.

The difference between conduction through gases and through metals is shown in a striking way when we use potential differences large enough to produce the saturation current. Suppose we have got a potential difference between the plates more than sufficient to produce the saturation current, and let us increase the distance between the plates. If the gas were to act like a metallic conductor this would diminish the current, because the greater length would involve a greater resistance in the circuit. In the case we are considering the separation of the plates willincreasethe current, because now there is a larger volume of gas exposed to the rays; there are therefore more ions produced, and as the saturation current is proportional to the number of ions the saturation current is increased. If the potential difference between the plates were much less than that required to saturate the current, then increasing the distance would diminish the current; the gas for such potential differences obeys Ohm’s law and the behaviour of the gaseous resistance is therefore similar to that of a metallic one.

In order to produce the saturation current the electric field must be strong enough to drive each ion to the electrode before it has time to enter into combination with one of the opposite sign. Thus when the plates in the preceding example are far apart, it will take a larger potential difference to produce this current than when the plates are close together. The potential difference required to saturate the current will increase as the square of the distance between the plates, for if the ions are to be delivered in a given time to the plates their speed must be proportional to the distance between the plates. But the speed is proportional to the electric force acting on the ion; hence the electric force must be proportional to the distance between the plates, and as in a uniform field the potential difference is equal to the electric force multiplied by the distance between the plates, the potential difference will vary as the square of this distance.

The potential difference required to produce saturation will, other circumstances being the same, increase with the amount of ionization, for when the number of ions is large and they are crowded together, the time which will elapse before a positive one combines with a negative will be smaller than when the number of ions is small. The ions have therefore to be removed more quickly from the gas when the ionization is great than when it is small; thus they must move at a higher speed and must therefore be acted upon by a larger force.

When the ions are not removed from the gas, they will increase until the number of ions of one sign which combine with ions of the opposite sign in any time is equal to the number produced by the ionizing agent in that time. We can easily calculate the number of free ions at any time after the ionizing agent has commenced to act.

Let q be the number of ions (positive or negative) produced in one cubic centimetre of the gas per second by the ionizing agent, n1, n2, the number of free positive and negative ions respectively per cubic centimetre of the gas. The number of collisions between positive and negative ions per second in one cubic centimetre of the gas is proportional to n1n2. If a certain fraction of the collisions between the positive and negative ions result in the formation of an electrically neutral system, the number of ions which disappear per second on a cubic centimetre will be equal to αn1n2, where α is a quantity which is independent of n1, n2; hence if t is the time since the ionizing agent was applied to the gas, we havedn1/dt = q − αn1n2, dn2/dt = q − αn1n2.Thus n1− n2is constant, so if the gas is uncharged to begin with, n1will always equal n2. Putting n1= n2= n we havedn/dt = q − αn2(1),the solution of which is, since n = 0 when t = 0,n =k(ε2kαt− 1)(2),ε2kαt+ 1if k2= q/α. Now the number of ions when the gas has reached a steady state is got by putting t equal to infinity in the preceding equation, and is therefore given by the equationn0= k = √ (q/α).We see from equation (1) that the gas will not approximate to its steady state until 2kαt is large, that is until t is large compared with ½kα or with ½√ (qα). We may thus take ½√ (qα) as a measure of the time taken by the gas to reach a steady state when exposed to an ionizing agent; as this time varies inversely as √q we see that when the ionization is feeble it may take a very considerable time for the gas to reach a steady state. Thus in the case of our atmosphere where the production of ions is only at the rate of about 30 per cubic centimetre per second, and where, as we shall see, α is about 10-6, it would take some minutes for the ionization in the air to get into a steady state if the ionizing agent were suddenly applied.We may use equation (1) to determine the rate at which the ions disappear when the ionizing agent is removed. Putting q=0 in that equation we get dn/αt = -αn2.Hencen = n0/(1 + n0αt) (3),where n0is the number of ions when t = 0. Thus the number of ions falls to one-half its initial value in the time 1/n0α. The quantity α is called thecoefficient of recombination, and its value for different gases has been determined by Rutherford (Phil. Mag.1897 [5], 44, p. 422), Townsend (Phil. Trans., 1900, 193, p. 129), McClung (Phil. Mag., 1902 [6], 3, p. 283), Langevin (Ann. chim. phys.[7], 28, p. 289), Retschinsky (Ann. d. Phys., 1905, 17, p. 518), Hendred (Phys. Rev., 1905, 21, p. 314). The values of α/e, e being the charge on an ion in electrostatic measure as determined by these observers for different gases, is given in the following table:—Townsend.McClung.Langevin.Retschinsky.Hendred.Air34203380320041403500O23380CO2350034903400H230202940The gases in these experiments were carefully dried and free from dust; the apparent value of α is much increased when dust or small drops of water are present in the gas, for then the ions get caught by the dust particles, the mass of a particle is so great compared with that of an ion that they are practically immovable under the action of the electric field, and so the ions clinging to them escape detection when electrical methods are used. Taking e as 3.5×10-10, we see that α is about 1.2×10-6, so that the number of recombinations in unit time between n positive and n negative ions in unit volume is 1.2×10-6n2. The kinetic theory of gases shows that if we have n molecules of air per cubic centimetre, the number of collisions per second is 1.2×10-10n2at a temperature of 0° C. Thus we see that the number of recombinations between oppositely charged ions is enormously greater than the number of collisions between the same number of neutral molecules. We shall see that the difference in size between the ion and the molecule is not nearly sufficient to account for the difference between the collisions in the two cases; the difference is due to the force between the oppositely charged ions, which drags ions into collisions which but for this force would have missed each other.Several methods have been used to measure α. In one method air, exposed to some ionizing agent at one end of a long tube, is slowly sucked through the tube and the saturation current measured at different points along the tube. These currents are proportional to the values of n at the place of observation: if we know the distance of this place from the end of the tube when the gas was ionized and the velocity of the stream of gas, we can find t in equation (3), and knowing the value of n we can deduce the value of α from the equation1/n1− 1/n2= α(t1− t2),where n1, n2are the values of n at the times t1, t2respectively. In this method the tubes ought to be so wide that the loss of ions by diffusion to the sides of the tube is negligible. There are other methods which involve the knowledge of the speed with which the ions move under the action of known electric forces; we shall defer the consideration of these methods until we have discussed the question of these speeds.In measuring the value of α it should be remembered that the theory of the methods supposes that the ionization is uniform throughout the gas. If the total ionization throughout a gas remains constant, but instead of being uniformly distributed is concentrated in patches, it is evident that the ions will recombine more quickly in the second case than in the first, and that the value of α will be different in the two cases. This probably explains the large values of α obtained by Retschinsky, who ionized the gas by the α rays from radium, a method which produces very patchy ionization.Variation of α with the Pressure of the Gas.—All observers agree that there is little variation in α with the pressures for pressures of between 5 and 1 atmospheres; at lower pressures, however, the value of α seems to diminish with the pressure: thus Langevin (Ann. chim. phys., 1903, 28, p. 287) found that at a pressure of1⁄5of an atmosphere the value of α was about1⁄5of its value at atmospheric pressure.Variation of α with the Temperature.—Erikson (Phil. Mag., Aug. 1909) has shown that the value of α for air increases as the temperature diminishes, and that at the temperature of liquid air -180° C., it is more than twice as great as at +12° C.Since, as we have seen, the recombination is due to the coming together of the positive and negative ions under the influence of the electrical attraction between them, it follows that a large electric force sufficient to overcome this attraction would keep the ions apart and hence diminish the coefficient of recombination. Simple considerations, however, will show that it would require exceedingly strong electric fields to produce an appreciable effect. The value of α indicates that for two oppositely charged ions to unite they must come within a distance of about 1.5×10-6centimetres; at this distance the attraction between them is e2×1012/2.25, and if X is the external electric force, the force tending to pull them apart cannot be greater than Xe; if this is to be comparable with the attraction, X must be comparable with e×1012/2.25, or putting e = 4×10-10, with 1.8×102; this is 54,000 volts per centimetre, a force which could not be applied to gas at atmospheric pressure without producing a spark.Diffusion of the Ions.—The ionized gas acts like a mixture of gases, the ions corresponding to two different gases, the non-ionized gas to a third. If the concentration of the ions is not uniform, they will diffuse through the non-ionized gas in such a way as to produce a more uniform distribution. A very valuable series of determinations of the coefficient of diffusion of ions through various gases has been made by Townsend (Phil. Trans., 1900, A, 193, p. 129). The method used was to suck the ionized gas through narrow tubes; by measuring the loss of both the positive and negative ions after the gases had passed through a known length of tube, and allowing for the loss by recombination, the loss by diffusion and hence the coefficient of diffusion could be determined. The following tables give the values of the coefficients of diffusion D on the C.G.S. system of units as determined by Townsend:—Table I.—Coefficients of Diffusion (D) in Dry Gases.Gas.D for +ions.D for -ions.Mean Valueof D.Ratio of D for- to D for +ions.Air.028.043.03471.54O2.025.0396.03231.58CO2.023.026.02451.13H2.123.190.1561.54Table II.—Coefficients of Diffusion in Moist Gases.Gas.D for +ions.D for -ions.Mean Valueof D.Ratio of D for- to D for +ions.Air.032.037.03351.09O2.0288.0358.03231.24CO2.0245.0255.0251.04H2.128.142.1351.11It is interesting to compare with these coefficients the values of D when various gases diffuse through each other. D for hydrogen through air is .634, for oxygen through air .177, for the vapour ofisobutyl amide through air .042. We thus see that the velocity of diffusion of ions through air is much less than that of the simple gas, but that it is quite comparable with that of the vapours of some complex organic compounds.The preceding tables show that the negative ions diffuse more rapidly than the positive, especially in dry gases. The superior mobility of the negative ions was observed first by Zeleny (Phil. Mag., 1898 [5], 46, p. 120), who showed that the velocity of the negative ions under an electric force is greater than that of the positive. It will be noticed that the difference between the mobility of the negative and the positive ions is much more pronounced in dry gases than in moist. The difference in the rates of diffusion of the positive and negative ions is the reason why ionized gas, in which, to begin with, the positive and negative charges were of equal amounts, sometimes becomes electrified even although the gas is not acted upon by electric forces. Thus, for example, if such gas be blown through narrow tubes, it will be positively electrified when it comes out, for since the negative ions diffuse more rapidly than the positive, the gas in its passage through the tubes will lose by diffusion more negative than positive ions and hence will emerge positively electrified. Zeleny snowed that this effect does not occur when, as in carbonic acid gas, the positive and negative ions diffuse at the same rates. Townsend (loc. cit.) showed that the coefficient of diffusion of the ions is the same whether the ionization is produced by Röntgen rays, radioactive substances, ultra-violet light, or electric sparks. The ions produced by chemical reactions and in flames are much less mobile; thus, for example, Bloch (Ann. chim. phys., 1905 [8], 4, p. 25) found that for the ions produced by drawing air over phosphorus the value of α/e was between 1 and 6 instead of over 3000, the value when the air was ionized by Röntgen rays.

dn1/dt = q − αn1n2, dn2/dt = q − αn1n2.

Thus n1− n2is constant, so if the gas is uncharged to begin with, n1will always equal n2. Putting n1= n2= n we have

dn/dt = q − αn2(1),

the solution of which is, since n = 0 when t = 0,

if k2= q/α. Now the number of ions when the gas has reached a steady state is got by putting t equal to infinity in the preceding equation, and is therefore given by the equation

n0= k = √ (q/α).

We see from equation (1) that the gas will not approximate to its steady state until 2kαt is large, that is until t is large compared with ½kα or with ½√ (qα). We may thus take ½√ (qα) as a measure of the time taken by the gas to reach a steady state when exposed to an ionizing agent; as this time varies inversely as √q we see that when the ionization is feeble it may take a very considerable time for the gas to reach a steady state. Thus in the case of our atmosphere where the production of ions is only at the rate of about 30 per cubic centimetre per second, and where, as we shall see, α is about 10-6, it would take some minutes for the ionization in the air to get into a steady state if the ionizing agent were suddenly applied.

We may use equation (1) to determine the rate at which the ions disappear when the ionizing agent is removed. Putting q=0 in that equation we get dn/αt = -αn2.

Hence

n = n0/(1 + n0αt) (3),

where n0is the number of ions when t = 0. Thus the number of ions falls to one-half its initial value in the time 1/n0α. The quantity α is called thecoefficient of recombination, and its value for different gases has been determined by Rutherford (Phil. Mag.1897 [5], 44, p. 422), Townsend (Phil. Trans., 1900, 193, p. 129), McClung (Phil. Mag., 1902 [6], 3, p. 283), Langevin (Ann. chim. phys.[7], 28, p. 289), Retschinsky (Ann. d. Phys., 1905, 17, p. 518), Hendred (Phys. Rev., 1905, 21, p. 314). The values of α/e, e being the charge on an ion in electrostatic measure as determined by these observers for different gases, is given in the following table:—

The gases in these experiments were carefully dried and free from dust; the apparent value of α is much increased when dust or small drops of water are present in the gas, for then the ions get caught by the dust particles, the mass of a particle is so great compared with that of an ion that they are practically immovable under the action of the electric field, and so the ions clinging to them escape detection when electrical methods are used. Taking e as 3.5×10-10, we see that α is about 1.2×10-6, so that the number of recombinations in unit time between n positive and n negative ions in unit volume is 1.2×10-6n2. The kinetic theory of gases shows that if we have n molecules of air per cubic centimetre, the number of collisions per second is 1.2×10-10n2at a temperature of 0° C. Thus we see that the number of recombinations between oppositely charged ions is enormously greater than the number of collisions between the same number of neutral molecules. We shall see that the difference in size between the ion and the molecule is not nearly sufficient to account for the difference between the collisions in the two cases; the difference is due to the force between the oppositely charged ions, which drags ions into collisions which but for this force would have missed each other.

Several methods have been used to measure α. In one method air, exposed to some ionizing agent at one end of a long tube, is slowly sucked through the tube and the saturation current measured at different points along the tube. These currents are proportional to the values of n at the place of observation: if we know the distance of this place from the end of the tube when the gas was ionized and the velocity of the stream of gas, we can find t in equation (3), and knowing the value of n we can deduce the value of α from the equation

1/n1− 1/n2= α(t1− t2),

where n1, n2are the values of n at the times t1, t2respectively. In this method the tubes ought to be so wide that the loss of ions by diffusion to the sides of the tube is negligible. There are other methods which involve the knowledge of the speed with which the ions move under the action of known electric forces; we shall defer the consideration of these methods until we have discussed the question of these speeds.

In measuring the value of α it should be remembered that the theory of the methods supposes that the ionization is uniform throughout the gas. If the total ionization throughout a gas remains constant, but instead of being uniformly distributed is concentrated in patches, it is evident that the ions will recombine more quickly in the second case than in the first, and that the value of α will be different in the two cases. This probably explains the large values of α obtained by Retschinsky, who ionized the gas by the α rays from radium, a method which produces very patchy ionization.

Variation of α with the Pressure of the Gas.—All observers agree that there is little variation in α with the pressures for pressures of between 5 and 1 atmospheres; at lower pressures, however, the value of α seems to diminish with the pressure: thus Langevin (Ann. chim. phys., 1903, 28, p. 287) found that at a pressure of1⁄5of an atmosphere the value of α was about1⁄5of its value at atmospheric pressure.

Variation of α with the Temperature.—Erikson (Phil. Mag., Aug. 1909) has shown that the value of α for air increases as the temperature diminishes, and that at the temperature of liquid air -180° C., it is more than twice as great as at +12° C.

Since, as we have seen, the recombination is due to the coming together of the positive and negative ions under the influence of the electrical attraction between them, it follows that a large electric force sufficient to overcome this attraction would keep the ions apart and hence diminish the coefficient of recombination. Simple considerations, however, will show that it would require exceedingly strong electric fields to produce an appreciable effect. The value of α indicates that for two oppositely charged ions to unite they must come within a distance of about 1.5×10-6centimetres; at this distance the attraction between them is e2×1012/2.25, and if X is the external electric force, the force tending to pull them apart cannot be greater than Xe; if this is to be comparable with the attraction, X must be comparable with e×1012/2.25, or putting e = 4×10-10, with 1.8×102; this is 54,000 volts per centimetre, a force which could not be applied to gas at atmospheric pressure without producing a spark.

Diffusion of the Ions.—The ionized gas acts like a mixture of gases, the ions corresponding to two different gases, the non-ionized gas to a third. If the concentration of the ions is not uniform, they will diffuse through the non-ionized gas in such a way as to produce a more uniform distribution. A very valuable series of determinations of the coefficient of diffusion of ions through various gases has been made by Townsend (Phil. Trans., 1900, A, 193, p. 129). The method used was to suck the ionized gas through narrow tubes; by measuring the loss of both the positive and negative ions after the gases had passed through a known length of tube, and allowing for the loss by recombination, the loss by diffusion and hence the coefficient of diffusion could be determined. The following tables give the values of the coefficients of diffusion D on the C.G.S. system of units as determined by Townsend:—

Table I.—Coefficients of Diffusion (D) in Dry Gases.

Table II.—Coefficients of Diffusion in Moist Gases.

It is interesting to compare with these coefficients the values of D when various gases diffuse through each other. D for hydrogen through air is .634, for oxygen through air .177, for the vapour ofisobutyl amide through air .042. We thus see that the velocity of diffusion of ions through air is much less than that of the simple gas, but that it is quite comparable with that of the vapours of some complex organic compounds.

The preceding tables show that the negative ions diffuse more rapidly than the positive, especially in dry gases. The superior mobility of the negative ions was observed first by Zeleny (Phil. Mag., 1898 [5], 46, p. 120), who showed that the velocity of the negative ions under an electric force is greater than that of the positive. It will be noticed that the difference between the mobility of the negative and the positive ions is much more pronounced in dry gases than in moist. The difference in the rates of diffusion of the positive and negative ions is the reason why ionized gas, in which, to begin with, the positive and negative charges were of equal amounts, sometimes becomes electrified even although the gas is not acted upon by electric forces. Thus, for example, if such gas be blown through narrow tubes, it will be positively electrified when it comes out, for since the negative ions diffuse more rapidly than the positive, the gas in its passage through the tubes will lose by diffusion more negative than positive ions and hence will emerge positively electrified. Zeleny snowed that this effect does not occur when, as in carbonic acid gas, the positive and negative ions diffuse at the same rates. Townsend (loc. cit.) showed that the coefficient of diffusion of the ions is the same whether the ionization is produced by Röntgen rays, radioactive substances, ultra-violet light, or electric sparks. The ions produced by chemical reactions and in flames are much less mobile; thus, for example, Bloch (Ann. chim. phys., 1905 [8], 4, p. 25) found that for the ions produced by drawing air over phosphorus the value of α/e was between 1 and 6 instead of over 3000, the value when the air was ionized by Röntgen rays.

Velocity of Ions in an Electric Field.—The velocity of ions in an electric field, which is of fundamental importance in conduction, is very closely related to the coefficient of diffusion. Measurements of this velocity for ions produced by Röntgen rays have been made by Rutherford (Phil. Mag.[5], 44, p. 422), Zeleny (Phil. Mag.[5], 46, p. 120), Langevin (Ann. Chim. Phys., 1903, 28, p. 289), Phillips (Proc. Roy. Soc.78, A, p. 167), and Wellisch (Phil. Trans., 1909, 209, p. 249). The ions produced by radioactive substance have been investigated by Rutherford (Phil. Mag.[5], 47, p. 109) and by Franck and Pohl (Verh. deutsch. phys. Gesell., 1907, 9, p. 69), and the negative ions produced when ultra-violet light falls on a metal plate by Rutherford (Proc. Camb. Phil. Soc.9, p. 401). H. A. Wilson (Phil. Trans.192, p. 4O9), Marx (Ann. de Phys.11, p. 765), Moreau (Journ. de Phys.4, 11, p. 558;Ann. Chim. Phys.7, 30, p. 5) and Gold (Proc. Roy. Soc.79, p. 43) have investigated the velocities of ions produced by putting various salts into flames; McClelland (Phil. Mag.46, p. 29) the velocity of the ions in gases sucked from the neighbourhood of flames and arcs; Townsend (Proc. Camb. Phil. Soc.9, p. 345) and Bloch (loc. cit.) the velocity of ions produced by chemical reaction; and Chattock (Phil. Mag.[5], 48, p. 401) the velocity of the ions produced when electricity escapes from a sharp needle point into a gas.

Several methods have been employed to determine these velocities. The one most frequently employed is to find the electromotive intensity required to force an ion against the stream of gas moving with a known velocity parallel to the lines of electric force. Thus, of two perforated plane electrodes vertically over each other, suppose the lower to be positively, the upper negatively electrified, and suppose that the gas is streaming vertically downwards with the velocity V; then unless the upward velocity of the positive ion is greater than V, no positive electricity will reach the upper plate. If we increase the strength of the field between the plates, and hence the upward velocity of the positive ion, until the positive ions just begin to reach the upper plate, we know that with this strength of field the velocity of the positive ion is equal to V. By this method, which has been used by Rutherford, Zeleny and H. A. Wilson, the velocity of ions in fields of various strengths has been determined.

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