unable to do so. It is instructive therefore to consider the results in
connexion with the power of the atoms and molecules of the differ-
ent elements to acquire a negative charge obtained by the study of
the positive rays. These show that, while the atoms of hydrogen,
carbon, oxygen, fluorine or chlorine readily acquire a negative
charge, those of helium, nitrogen, neon, and argon do not ; and again
that, while it is very exceptional for a molecule whether of a com-
pound or an elementary gas to acquire a negative charge, the mole-
cule of oxygen is able to do so. We see that this result is in accord-
ance with the behaviour of the carrier of the negative charge in an
ionized gas. Since the atoms in the positive rays show so much
greater affinity for the electrons than the molecules, it follows that
if the agent producing ionization were to dissociate some of the
molecules of the gas into neutral atoms (and to do this would require
the expenditure of much less energy than to ionize the gas), these
atoms would be much more effective traps for the electrons than the
undissociated molecules. Loeb has shown that even in oxygen an
electron collides on the average with about 50,000 molecules of oxy-
gen before it is captured; thus if the oxygen atom could capture an
electron at the first encounter, if only one molecule in 50,000 were
dissociated into atoms, the effect of the atoms would be as efficacious
as that of the molecules in capturing the electrons. When this
dissociation takes place the abnormal velocity of the negative ion
will only occur in gases like nitrogen and the inert gases whose
atoms cannot receive an electron.
Recombination of the Ions. Even when the ions are not re- moved from a gas by sending a current of electricity through it, their number will not increase indefinitely with the time of expo- sure of the gas to the ionizing agent. This is due to the recombina- tion which takes place between the positive and negative ions; these ions as they move about in the gas sometimes come into collision with each other, and by forming electrically neutral systems cease to act as ions. The gas will reach a steady state with regard to ionization when the number of ions which disap- pear in one second as the result of the collisions is equal to the number produced in the same time by the ionizing agent.
If there are n ions of either kind per cub. cm., the number of colli- sions between the positive and negative ions in one second in a cub. cm. of the gas will be proportional to n 2 ; hence the number of ions of either sign which are lost by recombination in one second will be represented by a 2 when a is called the coefficient of recombina- tion. If the ionizing agent produces q ions per cub. cm. per second, then
dn
- -*-*
The solution of this equation, if we reckon I from the instant the ionizing agent begins to act, so that n=o when / = o, and where
We see that, when the gas reaches a steady state, n = X = , and that the gas will not approximate to this state until t is large compared with i/Ca, i.e. to jttoa where no is the value of n in the steady state. Thus when the ionization is very weak it may take a considerable time for the gas to reach a steady state.
When the ionizing agent is removed, the ions do not disappear at once, but decay at the rate given by the equation
dn -fi-3-an:
The solution of this, where t is the time which has elapsed since the removal of the ionizing agents, and no the number of ions when
n =na/
Thus the number of ions will be reduced to one-half their initial value after a time i/ano. We may therefore take I /an as the measure of the life of an ion when there are n ions per cub. centi- metre. The values of a/e, where e is the charge on an ion, have been measured by various experimenters, and for different methods of ionization the results are given in the following table :
Values of a/e for various gases at atmospheric pressure and ordi- nary temperature.
Town-
send
Mc- Clung
Lan- gevin
Thir- kill
Hen- dren
Ret- schin-
sky
Rume- lin
Gas
Ront- gen
rays
Ront- gen
rays
Ront- gen
rays
Ront- gen
rays
a rays
a rays
a rays /3 rays
Air CO 2 H 2
3420 3520 3020
338o 3490 2940
3200 3400
35o 35o
3300
4200
4240 5820
2
338o
SO 2 N 2 O CO
3000 2960 1780
The results as ascribed to Thirkill were obtained by extrapolation from experiment made at lower pressures. Since e, in electrostatic measure, is 4-8Xio 10 , the value of a for air is about l-6Xio", so that, when there are n positive and n negative ions per cub. cm., the number of ions which recombine per second is
i-6Xio-% 2 .
This shows very markedly the influence of the electric charge in increasing the number of collisions between the particles, for the number of collisions in a second between 2n, uncharged molecules in a cub. cm. of air is only
which is only about 1/4,000 of the number of recombinations between the same number of ions.
It is a very remarkable fact, and one which has not yet received a satisfactory explanation, that the values of a for gases of such different molecular weights as H 2 , O 2 , CO 2 , SO 2 should be so nearly equal, while the value of a. for CO is only about one-half of that for the other gases.
For pressures less than one atmosphere Thirkill has shown that a diminishes as the pressure p diminishes, and that the relation between a and p is a linear one. Langevin showed that a for air attained a maximum value at a pressure about two atmospheres, and that at higher pressures it diminished somewhat rapidly as the pressure increased.
When the density is constant the value of a diminishes as the temperature increases. The connexion between o and the abso- lute temperature T seems to be expressed with fair accuracy by the equation
a = cT-".
According to Erikson, n is equal to 2-3, 2-4.2, 2-35 for hydrogen, air and COz respectively, while Phillips' experiments gave n = 2.
Large Ions. The ions we have been considering are those produced in dust-free gases by Rontgen or cathode rays. In some cases, however, ions with very much lower mobilities are to be found in gases. Thus Langevin found in air from the top of the Eiffel Tower two types of ions, one consisting of ions of the kind we have been considering, with a mobility of about 1-5 cm/sec., the other of ions with a mobility of 1/3,000 cm/sec. Ions with mobilities of the same order as this second type may be pro- duced by bubbling air through water, by passing air over phos- phorus, or by drawing air from the neighbourhood of flames. They are probably charged particles of dust of various kinds, held in suspension in gas which is exposed to some kind of ionizing agent which gives a supply of ions of the first type; these settle on the particles of dust and form the slow ions. The number of these slow ions when the gas is in a steady state will only depend on the number of dust particles in the gas, and will not be affected by the strength of the ionizing agent. This follows from the principle that in the steady state the number of dust particles which acquire a positive charge must equal the number which lose such a charge. A positively electrified dust particle might lose its charge by meeting and coalescing with a negative smaU ion or by coalescing with a negatively electrified dust particle. These dust particles are, however, so sluggish in their movements that, unless the dust particles are enormously more numerous than the small ions, we may neglect the second source of loss in comparison with the first.
Thus if U is the number of uncharged dust particles in a cub. cm. of the gas, P and N the number of those with positive and negative charges respectively, and p, n the number of positive and negative small ions, the number of dust particles which acquire per second a positive charge will be a\Jp and the number losing such a charge by coalescing with a negative ion /3Prc, where o and are constants; hence for equilibrium
a\Jp = ffPn.
Similarly by considering the negatively charged particles we get
o'Un= 0'Np.
Hence we see that the proportion between the charged and uncharged particles of dust depends only upon the ratio of p to n, and not upon the absolute magnitude of either of these quantities. Thus, though it would take much longer to reach the steady state with a feeble source of ionization than with a, strong one, when that state was reached there would be as much dust electrified in one case as in the other. De Broglie estimates that in this state about one-tenth of the particles would be electrified.
Relation between the Potential Difference and the Current through an Ionized Gas. We shall take the case of two infinite parallel metal plates maintained at different potentials and immersed in an ionized gas; the line at right angles to these plates we shall take as the axis of x, it being evidently parallel to the direction of the electric force X. Let i, 2 be respectively the number of positive and negative
