current in the stage when it does not depend upon the electromo-
tive force is said to be saturated. The reason for this saturation
is that the passage of a current of electricity through the gas in-
volves the removal of a number of ions proportional to the quanti-
ty of electricity passing through the gas. Thus the gas is losing
ions at a rate proportional to the current; it cannot go on losing
more ions than are produced, so that the current cannot increase
beyond a critical value which is proportional to the rate of pro-
duction of ions. This sometimes produces a state of things which
seems anomalous to those accustomed to look at conduction of
electricity exclusively from the point of Ohm's law. For example,
when gases are exposed to Rontgen rays, the number of ions
produced per second is proportional to the volume of the gas, so
that, if two parallel plates are immersed in such a gas and a cur-
rent sent from one to the other, when the distance between the
plates is increased the number of ions available for carrying the
current and therefore the saturation current will be increased
also. Thus apparent " resistance " will diminish as the length of
the gaseous conductor is increased.
The Nature of the Ions. The question arises, what is the na- ture of the particles which carry the charges of electricity? Are they the atoms or molecules of the gas, or, for the negative charges, electrons? Information on these points is afforded by measuring the velocity of the ions under given electric forces.
It follows from the kinetic theory of gases that the velocity V of an ion due to an electric force X is given by the equation :
V = X^ (i)
m v
Here X is the mean free path of the ion through the surrounding molecules, v the average velocity of the ion due to its thermal agi- tation, this velocity depending only on the mass of the ion and the temperature of the gas, and m is the mass of the ion and e the elec- tric charge carried by it. If we calculate by this formula the velocity of an ion in hydrogen, assuming that the mass of the ion and its free path are the same as those for a molecule of hydrogen, we find that it would be 26 cm/sec, for an electric force of a volt per cm. ; the value found by experiment is 6-7 cm/sec, for the positive and 7-9 cm/sec, for the negative ion. The assumption that both X and m are the same for the ion as for the molecule is therefore wrong. It is clear that if, as we have every reason to believe, the normal hydrogen molecule is made up of positively and negatively electri- fied parts, the ion in virtue of its charge, even if its mass is the same as that of the hydrogen molecule, will exert a greater force upon a neighbouring molecule than would an uncharged molecule, and this increase in the force implies a diminution in the free path, and therefore by equation (i) a diminution in V. That a part of the dis- crepancy between the results given by the equation and those found by experiment is due to this cause cannot be questioned; the point which is still doubtful is whether the attraction due to the charge on the ion may not cause some of the hydrogen molecules to cling to it, forming a cluster of molecules with a greater mass and smaller free path than a single molecule. It would follow from the general principles of thermodynamics that, if the work required to separate a neutral molecule of hydrogen from a positive charge in its near neighbourhood were comparable with the average energy of trans- lation of the molecules at the temperature of the gas, some such clusters would be formed, and that, if the work of separation were large compared with the energy of agitation, practically all the ions would consist of such clusters. This work would be greater for molecules which, like those of ammonia, or the vapours of water and alcohol, have a finite electrical moment, than for those which, like the molecules of hydrogen, oxygen and nitrogen, have no such moment, so that it is quite possible that, though there may be no clustering with these very permanent gases, there may be some when gases of the other type are present. This differentiation seems borne out by experiment, for no clear indications of clustering seem to have been found for the permanent gases. Since clustering is analo- gous to chemical combination, we should expect the mobilities, if they depended upon clusters, to have very large temperature coeffi- cients. The mobilities of some of the permanent gases at constant density have been measured by Erikson over a considerable range of temperature, and though there is a considerable temperature effect it is not nearly so large as we should expect if it depended on chem- ical combination. Again, since clustering is a process of condensa- tion, it would be favoured by an increase in pressure ; thus a decrease in pressure would be accompanied by a simplification of the ion, ana would increase its mean free path beyond the natural increase due to the diminution in the number of molecules with which the ion comes into collision. If there were no change in the character of the ion with the pressure, the mobility would vary inversely as the pressure; if the character of the ion changes, the mobility at low pressures will be greater than that given by this law. Now experi- ments show that for the positive ion the mobility is, very accurately,
inversely proportional to the pressure over a wide range of pres- sures; this again is inconsistent with the existence of clusters. On the other hand, it is found that the addition of small quantities of gases which, like the vapours of water and alcohol, have a finite electrical moment produce a marked diminution in the mobility; this effect is more pronounced for the negative than for the positive ion, but as Zeleny has shown it exists for both ions. -This effect is readily explained by supposing the water molecules to cluster round the ion. It would seem in accordance with the evidence to conclude that, though there is no evidence of clustering for the permanent gases, it does occur when certain easily condensible gases are present.
The behaviour of negative ions is in many respects quite different from that of the positive ones. In the first place the mobility of the negative ions is for the permanent gases greater than that of the positive; thus, for example, in dry hydrogen the velocities of the negative and positive ions, when the electric force is one volt per cm., are 7-95 and 6-7 respectively, and for air 1-87 and 1-36. The difference is less for moist gases than for dry, while for complex vapours which have comparatively small mobilities Wellisch found that there was very little difference between the mobilities of the positive and negative ions.
For the permanent gases the ratio of the mobilities of the nega- tive and positive ions varies but little with the pressure, until the pressure is reduced below that represented by about 10 cm. of mer- cury. For lower pressures than this, the mobility of the negative ion increases, as Langevin showed, more rapidly than that of the positive; at the pressure of a mm. or so the mobility of the negative ion in air may be three or four times that of the positive.
An even more interesting result was discovered by Franck and Hertz, who, when they experimented with very carefully purified nitrogen or argon, found that the mobility of the negative ion was more than 100 times that of the positive. The mobilities in these gases are extremely sensitive to traces of oxygen, and a fraction of I % of oxygen added to the pure gas will reduce the mobility of the negative ion to less than one-tenth of its maximum value. The enormous mobility of the negative ion in nitrogen and argon as compared with that of the positive shows that in them the negative electricity must be carried by electrons and not by atoms or mole- cules, while the effect of introducing traces of oxygen shows that these electrons readily attach themselves to the molecules of oxygen though they are unable to adhere to molecules of nitrogen or argon. The same effect has also been observed in helium and hydrogen.
These properties of the negative ion are of great importance in connexion with the mechanism of ionization in gases and the struc- ture of atoms and molecules. In the first place, they furnish strong evidence in support of the view that the first stage in the ionization of a gas is the ejection of an electron from the molecule of the gas rather than the separation of the molecule into atoms of which some are charged with positive and others with negative electricity. On this view the negative ion begins its career as an electron and not as an atom, while the positive ion from the beginning is of molecu- lar dimensions. As an electron has much greater mobility than a molecule the mobility of the negative ion will at first be much greater than that of the positive. In some gases, such as oxygen, the electron soon gets attached to a molecule, and its mass and mobility become comparable with those of the positive one. The mobility we measure is the average mobility of the negative ion during its life; part of the time its mobility, being that of an elec- tron, is very much larger than that of the positive ion, while in the other part the two mobilities will be much the same. The excess of mobility of the negative over the positive ion will depend upon the fraction of its life which the negative ion spends as a free elec- tron a fraction which would tend to increase as the pressure of the gas diminished.
To calculate the mobility of an electron as compared with that of a molecule, we must make some assumption as to the effect of the charge on the mean free path of an electron. We saw that there were some grounds for supposing that, in the case of the positive ions, the mean free path was determined rather by the charge of the ion than by the dimensions of the molecule carrying the charge. Since the magnitude of the charge on the electron is the same as that on the positive ion, we might expect, if this were the case, that the mean free path of an electron would be much the same as that of an ion, so that in equation (i) it would be the factor mv which would differentiate the mobility of the ion from that of the electron. If the electron is in thermal equilibrium with the surrounding gas, mv* will be the same for the ion and the electron, and thus the mobil- ity will be inversely proportional to the square root of the mass; as the mass of the hydrogen molecule is 3-6 Xio 3 times that of the electron, the mobility of the electron in hydrogen should be 60 times that of the positive ion; in nitrogen the mobility of the electron would be about 220 times that of the positive ion. If the positive ion were a cluster of molecules instead of a single molecule, the mobil- ity of the electron as compared with that of the positive electron would be much larger than the preceding figures would indicate.
The difference between the behaviour of the electron in nitrogen or argon and in oxygen is of great importance in connexion with the structure of the atom and molecule, for it indicates that, while a molecule of oxygen can accommodate another electron in addition to those already present, the molecules of nitrogen and argon are
