Chapter III: Electric Conduction Through Gases (1)

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 (_Mem. 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 prove that 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):--

+---------+------------------------+-----------------+
| Gas. | Relative Rate of Leak. | _Rate of Leak._ |
| | | Sp. Gr. |
+---------+------------------------+-----------------+
| Air | 1.00 | 1 |
| H2 | .184 | 2.7 |
| CO2 | 1.69 | 1.10 |
| SO2 | 2.64 | 1.21 |
| CH3Cl | 4.7 | 1.09 |
| Ni(CO)4 | 5.1 | .867 |
+---------+------------------------+-----------------+

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 Baumannshohle 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 Rontgen 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 Rontgen 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 called _ions_, 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 Rontgen 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 will _increase_ the 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 [alpha]n1 n2, where
[alpha] 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 have

dn1/dt = q - [alpha]n1 n2, dn2/dt = q - [alpha]n1 n2.

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

dn/dt = q - [alpha]n^2 (1),

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

k([epsilon]^{2k[alpha]t} - 1)
n = ---------------------------- (2)
[epsilon]^{2k[alpha]t} + 1

if k^2 = q/[alpha]. 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 = [root](q/[alpha]).

We see from equation (1) that the gas will not approximate to its
steady state until 2k[alpha]t is large, that is until t is large
compared with 1/2k[alpha] or with 1/2[root](q[alpha]). We may thus
take 1/2[root](q[alpha]) 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 [root]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, [alpha] 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/[alpha]t = -[alpha]n^2.

Hence n = n0/(1 + n0[alpha]t) (3),

where n0 is the number of ions when t = 0. Thus the number of ions
falls to one-half its initial value in the time 1/n0[alpha]. The
quantity [alpha] is called the _coefficient 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
[alpha]/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. |
+-----+----------+----------+----------+------------+----------+
| Air | 3420 | 3380 | 3200 | 4140 | 3500 |
| O2 | 3380 | | | | |
| CO2 | 3500 | 3490 | 3400 | | |
| H2 | 3020 | 2940 | | | |
+-----+----------+----------+----------+------------+----------+

The gases in these experiments were carefully dried and free from
dust; the apparent value of [alpha] 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 X
10^-10, we see that [alpha] is about 1.2 X 10^-6, so that the number
of recombinations in unit time between n positive and n negative ions
in unit volume is 1.2 X 10^-6n^2. 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 X 10^-10n^2 at a temperature of 0 deg. 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 [alpha]. 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 [alpha] from the
equation

1/n1 - 1/n2 = [alpha](t1 - t2),

where n1, n2 are the values of n at the times t1, t2 respectively. 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 [alpha] 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 [alpha] will
be different in the two cases. This probably explains the large values
of [alpha] obtained by Retschinsky, who ionized the gas by the [alpha]
rays from radium, a method which produces very patchy ionization.

_Variation of [alpha] with the Pressure of the Gas._--All observers
agree that there is little variation in [alpha] with the pressures for
pressures of between 5 and 1 atmospheres; at lower pressures, however,
the value of [alpha] seems to diminish with the pressure: thus
Langevin (_Ann. chim. phys._, 1903, 28, p. 287) found that at a
pressure of 1/5 of an atmosphere the value of [alpha] was about 1/5 of
its value at atmospheric pressure.

_Variation of [alpha] with the Temperature._--Erikson (_Phil. Mag._,
Aug. 1909) has shown that the value of [alpha] for air increases as
the temperature diminishes, and that at the temperature of liquid air
-180 deg. C., it is more than twice as great as at +12 deg. 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
[alpha] indicates that for two oppositely charged ions to unite they
must come within a distance of about 1.5 X 10^-6 centimetres; at this
distance the attraction between them is e^2 X 10^12/2.25, 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 X 10^12/2.25, or putting e = 4
X 10^-10, with 1.8 X 10^2; 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 Value| Ratio of D for |
| | | | of D. | - to D for +ions.|
+-----+------------+------------+----------+------------------+
| Air | .028 | .043 | .0347 | 1.54 |
| O2 | .025 | .0396 | .0323 | 1.58 |
| CO2 | .023 | .026 | .0245 | 1.13 |
| H2 | .123 | .190 | .156 | 1.54 |
+-----+------------+------------+----------+------------------+

Table II.--Coefficients of Diffusion in Moist Gases.

+-----+------------+------------+----------+------------------+
|Gas. |D for +ions.|D for -ions.|Mean Value| Ratio of D for |
| | | | of D. | - to D for +ions.|
+-----+------------+------------+----------+------------------+
| Air | .032 | .037 | .0335 | 1.09 |
| O2 | .0288 | .0358 | .0323 | 1.24 |
| CO2 | .0245 | .0255 | .025 | 1.04 |
| H2 | .128 | .142 | .135 | 1.11 |
+-----+------------+------------+----------+------------------+

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 of isobutyl
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 Rontgen
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 [alpha]/e was between 1 and 6 instead of over 3000, the
value when the air was ionized by Rontgen 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 Rontgen 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.

The arrangement used by Zeleny is represented in fig. 8. P and Q are
square brass plates. They are bored through their centres, and to the
openings the tubes R and S are attached, the space between the plates
being covered in so as to form a closed box. K is a piece of wire
gauze completely covering the opening in Q; T is an insulated piece of
wire gauze nearly but not quite filling the opening in the plate P,
and connected with one pair of quadrants of an electrometer E. A plug
of glass wool G filters out the dust from a stream of gas which enters
the vessel by the tube D and leaves it by F; this plug also makes the
velocity of the flow of the gas uniform across the section of the
tube. The Rontgen rays to ionize the gas were produced by a bulb at
O, the bulb and coil being in a lead-covered box, with an aluminium
window through which the rays passed. Q is connected with one pole of
a battery of cells, P and the other pole of the battery are put to
earth. The changes in the potential of T are due to ions giving up
their charges to it. With a given velocity of air-blast the potential
of T was found not to change unless the difference of potential
between P and Q exceeded a critical value. The field corresponding to
this critical value thus made the ions move with the known velocity of
the blast.

Another method which has been employed by Rutherford and McClelland is
based on the action of an electric field in destroying the
conductivity of gas streaming through it. Suppose that BAB, DCD (fig.
9) are a system of parallel plates boxed in so that a stream of gas,
after flowing between BB, passes between DD without any loss of gas in
the interval. Suppose the plates DD are insulated, and connected with
one pair of quadrants of an electrometer, by charging up C to a
sufficiently high potential we can drive all the positive ions which
enter the system DCD against the plates D; this will cause a deflexion
of the electrometer, which in one second will be proportional to the
number of positive ions which have entered the system in that time. If
we charge A up to a high potential, B being put to earth, we shall
find that the deflexion of the electrometer connected with DD is less
than it was when A and B were at the same potential, because some of
the positive ions in their passage through BAB are driven against the
plates B. If u is the velocity along the lines of force in the uniform
electric field between A and B, and t the time it takes for the gas to
pass through BAB, then all the positive ions within a distance ut of
the plates B will be driven up against these plates, and thus if the
positive ions are equally distributed through the gas, the number of
positive ions which emerge from the system when the electric field is
on will bear to the number which emerge when the field is off the
ratio of 1 - ut/l to unity, where l is the distance between A and B.
This ratio is equal to the ratio of the deflexions in one second of
the electrometer attached to D, hence the observations of this
instrument give 1 - ut/l. If we know the velocity of the gas and the
length of the plates A and B, we can determine t, and since l can be
easily measured, we can find u, the velocity of the positive ion in a
field of given strength. By charging A and C negatively instead of
positively we can arrive at the velocity of the negative ion. In
practice it is more convenient to use cylindrical tubes with coaxial
wires instead of the systems of parallel plates, though in this case
the calculation of the velocity of the ions from the observations is a
little more complicated, inasmuch as the electric field is not uniform
between the tubes.

A method which gives very accurate results, though it is only
applicable in certain cases, is the one used by Rutherford to measure
the velocity of the negative ions produced close to a metal plate by
the incidence on the plate of ultra-violet light. The principle of the
method is as follows:--AB (fig. 10) is an insulated horizontal plate
of well-polished zinc, which can be moved vertically up and down by
means of a screw; it is connected with one pair of quadrants of an
electrometer, the other pair of quadrants being put to earth. CD is a
base-plate with a hole EF in it; this hole is covered with fine wire
gauze, through which ultra-violet light passes and falls on the plate
AB. The plate CD is connected with an alternating current dynamo,
which produces a simply-periodic potential difference between AB and
CD, the other pole being put to earth. Suppose that at any instant the
plate CD is at a higher potential than AB, then the negative ions from
AB will move towards CD, and will continue to do so as long as the
potential of CD is higher than that of AB. If, however, the potential
difference changes sign before the negative ions reach CD, these ions
will go back to AB. Thus AB will not lose any negative charge unless
the distance between the plates AB and CD is less than the distance
traversed by the negative ion during the time the potential of CD is
higher than that of AB. By altering the distance between the plates
until CD just begins to lose a negative charge, we find the velocity
of the negative ion under unit electromotive intensity. For suppose
the difference of potential between AB and CD is equal to a sin pt,
then if d is the distance between the plates, the electric intensity
is equal to a sin pt/d; if we suppose the velocity of the ion is
proportional to the electric intensity, and if u is the velocity for
unit electric intensity, the velocity of the negative ion will be ua
sin pt/d. Hence if x represent the distance of the ion from AB

dx ua
--- = --- sin pt
dT d

ua
x = ----(1 - cos pt), if x = 0 when t = 0.
pd

Thus the greatest distance the ion can get from the plate is equal to
2au/pd, and if the distance between the plates is gradually reduced to
this value, the plate AB will begin to lose a negative charge; hence
when this happens

d = 2au/pd, or u = pd^2/2a,

an equation by means of which we can find u.

In this form the method is not applicable when ions of both signs are
present. Franck and Pohl (_Verh. deutsch. physik. Gesell._ 1907, 9, p.
69) have by a slight modification removed this restriction. The
modification consists in confining the ionization to a layer of gas
below the gauze EF. If the velocity of the positive ions is to be
determined, these ions are forced through the gauze by applying to the
ionized gas a small constant electric force acting upwards; if
negative ions are required, the constant force is reversed. After
passing through the gauze the ions are acted upon by alternating
forces as in Rutherford's method.

Langevin (_Ann. chim. phys._, 1903, 28, p. 289) devised a method of
measuring the velocity of the ions which has been extensively used; it
has the advantage of not requiring the rate of ionization to remain
uniform. The general idea is as follows. Suppose that we expose the
gas between two parallel plates A, B to Rontgen rays or some other
ionizing agent, then stop the rays and apply a uniform electric field
to the region between the plates. If the force on the positive ion is
from A to B, the plate B will receive a positive charge of
electricity. After the electric force has acted for a time T reverse
it. B will now begin to receive negative electricity and will go on
doing so until the supply of negative ions is exhausted. Let us
consider how the quantity of positive electricity received by B will
vary with T. To fix our ideas, suppose the positive ions move more
slowly than the negative; let T2 and T1 be respectively the times
taken by the positive and negative ions to move under the electric
field through a distance equal to AB, the distance between the planes.
Then if T is greater than T2 all the ions will have been driven from
between the plates before the field is reversed, and therefore the
positive charge received by B will not depend upon T. Next let T be
less than T2 but greater than T1; then at the time when the field is
reversed all the negative ions will have been driven from between the
plates, so that the positive charge received by B will not be
neutralized by the arrival of fresh ions coming to it after the
reversal of the field. The number of positive ions driven against the
plate B will be proportional to T. Thus if we measure the value of the
positive charge on B for a series of values of T, each value being
less than the preceding, we shall find that until T reaches a certain
value the charge remains constant, but as soon as we reduce the time
below this value the charge diminishes. The value of T when the
diminution in the field begins is T2, the time taken for a positive
ion to cross from A to B under the electric field; thus from T2 we can
calculate the velocity of the positive ion in this field. If we still
further diminish T, we shall find that we reach a value when the
diminution of the positive charge on B with the time suddenly becomes
much more rapid; this change occurs when T falls below T1 the time
taken for the negative ions to go from one plate to the other, for now
when the field is reversed there are still some negative ions left
between the plates, and these will be driven against B and rob it of
some of the positive charge it had acquired before the field was
reversed. By observing the time when the increase in the rate of
diminution of the positive charge with the time suddenly sets in we
can determine T1, and hence the velocity of the negative ions.

The velocity of the ions produced by the discharge of electricity from
a fine point was determined by Chattock by an entirely different
method. In this case the electric field is so strong and the velocity
of the ion so great that the preceding methods are not applicable.
Suppose P represents a vertical needle discharging electricity into
air, consider the force acting on the ions included between two
horizontal planes A, B. If P is the density of the electrification,
and Z the vertical component of the electric intensity, F the
resultant force on the ions between A and B is vertical and equal to
_ _ _
/ / /
| | | Z[rho]dxdydz.
_/_/_/

Let us suppose that the velocity of the ion is proportional to the
electric intensity, so that if w is the vertical velocity of the ions,
which are supposed all to be of one sign, w = RZ.

Substituting this value of Z, the vertical force on the ions between A
and B is equal to
_ _ _
1 / / /
- | | | w[rho]dxdydz.
R _/_/_/

But [integral][integral]w[rho]dxdy = [iota], where [iota] is the
current streaming from the point. This current, which can be easily
measured by putting a galvanometer in series with the discharging
point, is independent of z, the vertical distance of a plane between A
and B below the charging point. Hence we have
_
[iota] / [iota]
F = ------ | dz = ------.z.
R _/ R

This force must be counterbalanced by the difference of gaseous
pressures over the planes A and B; hence if pB and pA denote
respectively the pressures over B and A, we have

[iota]
pB - pA = ------ z.
R

Hence by the measurement of these pressures we can determine R, and
hence the velocity with which an ion moves under a given electric
intensity.

There are other methods of determining the velocities of the ions, but
as these depend on the theory of the conduction of electricity through
a gas containing charged ions, we shall consider them in our
discussion of that theory.

By the use of these methods it has been shown that the velocities of
the ions in a given gas are the same whether the ionization is
produced by Rontgen rays, radioactive substances, ultra-violet light,
or by the discharge of electricity from points. When the ionization is
produced by chemical action the ions are very much less mobile, moving
in the same electric field with a velocity less than one-thousandth
part of the velocity of the first kind of ions. On the other hand, as
we shall see later, the velocity of the negative ions in flames is
enormously greater than that of even the first kind of ion under
similar electric fields and at the same pressure. But when these
negative ions get into the cold part of the flame, they move
sluggishly with velocities of the order of those possessed by the
second kind. The results of the various determinations of the
velocities of the ions are given in the following table. The
velocities are in centimetres per second under an electric force of
one volt per centimetre, the pressure of the gas being 1 atmosphere.
V+ denotes the velocity of the positive ion, V- that of the negative.
V is the mean velocity of the positive and negative ions.

_Velocities of Ions.--Ions produced by Rontgen Rays._

+----------------------+------+------+------+-----------------+
| Gas. | V+. | V-. | V. | Observer. |
+----------------------+------+------+------+-----------------+
| Air | .. | .. | 1.6 | Rutherford |
| Air (dry) | 1.36 | 1.87 | .. | Zeleny |
| " | 1.60 | 1.70 | .. | Langevin |
| " | 1.39 | 1.78 | .. | Phillips |
| " | 1.54 | 1.78 | .. | Wellisch |
| Air (moist) | 1.37 | 1.81 | .. | Zeleny |
| Oxygen (dry) | 1.36 | 1.80 | .. | " |
| Oxygen (moist) | 1.29 | 1.52 | .. | " |
| Carbonic acid (dry) | 0.76 | 0.81 | .. | " |
| " | 0.86 | 0.90 | .. | Langevin |
| " | 0.81 | 0.85 | .. | Wellisch |
| Carbonic acid (moist)| 0.82 | 0.75 | .. | Zeleny |
| Hydrogen (dry) | 6.70 | 7.95 | .. | " |
| Nitrogen | .. | .. | 1.6 | Rutherford |
| Sulphur dioxide | 0.44 | 0.41 | .. | Wellisch |
| Hydrochloric acid | .. | .. | 1.27 | Rutherford |
| Chlorine | .. | .. | 1.0 | " |
| Helium (dry) | 5.09 | 6.31 | .. | Franck and Pohl |
| Carbon monoxide | 1.10 | 1.14 | .. | Wellisch |
| Nitrous oxide | 0.82 | 0.90 | .. | " |
| Ammonia | 0.74 | 0.80 | .. | " |
| Aldehyde | 0.31 | 0.30 | .. | " |
| Ethyl alcohol | 0.34 | 0.27 | .. | " |
| Acetone | 0.31 | 0.29 | .. | " |
| Ethyl chloride | 0.33 | 0.31 | .. | " |
| Pentane | 0.36 | 0.35 | .. | " |
| Methyl acetate | 0.33 | 0.36 | .. | " |
| Ethyl formate | 0.30 | 0.31 | .. | " |
| Ethyl ether | 0.29 | 0.31 | .. | " |
| Ethyl acetate | 0.31 | 0.28 | .. | " |
| Methyl bromide | 0.29 | 0.28 | .. | " |
| Methyl iodide | 0.21 | 0.22 | .. | " |
| Carbon tetrachloride | 0.30 | 0.31 | .. | " |
| Ethyl iodide | 0.17 | 0.16 | .. | " |
+----------------------+------+------+------+-----------------+

_Ions produced by Ultra-Violet Light._

Air 1.4 Rutherford
Hydrogen 3.9 Rutherford
Carbonic acid 0.78 Rutherford

_Ions in Gases sucked from Flames._

Velocities varying from .04 to .23 McClelland

_Ions in Flames containing Salts._

Negative ions 12.9 cm./sec. Gold
+ions for salts of Li, Na,
K, Rb, Cs 62 H. A. Wilson
" 200 Marx
" 80 Moreau

_Ions liberated by Chemical Action._

Velocities of the order of 0.0005 cm./sec. Bloch

_Ions from Point Discharge._

+---------------+------+-------+------+----------+
| Hydrogen | 5.4 | 7.43 | 6.41 | Chattock |
| Carbonic acid | 0.83 | 0.925 | 0.88 | Chattock |
| Air | 1.32 | 1.80 | 1.55 | Chattock |
| Oxygen | 1.30 | 1.85 | 1.57 | Chattock |
+---------------+------+-------+------+----------+

It will be seen from this table that the greater mobility of the
negative ions is very much more marked in the case of the lighter and
simpler gases than in that of the heavier and more complicated ones;
with the vapours of organic substances there seems but little
difference between the mobilities of the positive and negative ions,
indeed in one or two cases the positive one seems slightly but very
slightly the more mobile of the two. In the case of the simple gases
the difference is much greater when the gases are dry than when they
are moist. It has been shown by direct experiment that the velocities
are directly proportional to the electric force.

_Variation of Velocities with Pressure._--Until the pressure gets low
the velocities of the ions, negative as well as positive, vary
inversely as the pressure. Langevin (loc. cit.) was the first to show
that at very low pressures the velocity of the negative ions increases
more rapidly as the pressure is diminished than this law indicates. If
the nature of the ion did not change with the pressure, the kinetic
theory of gases indicates that the velocity would vary inversely as
the pressure, so that Langevin's results indicate a change in the
nature of the negative ion when the pressure is diminished below a
certain value. Langevin's results are given in the following table,
where p represents the pressure measured in centimetres of mercury, V+
and V- the velocities of the positive and negative ions in air under
unit electrostatic force, i.e. 300 volts per centimetre:--