be drawn out of the cathode without the necessity for the bom- bardment by positive ions. It is interesting in this connexion to notice that Skinner has shown that the anode " fall of potential " occurs quite abruptly, as far as can be tested by experiment; this, again, if the fall took place in molecular distances might be sufficient to drag positive ions out of the anode itself. By using a cathode heated to incandescence, and therefore emitting a plenti- ful supply of electrons, we can reduce the cathode fall of poten- tial to a small fraction of its normal value; we cannot, however, with a luminous discharge get rid of the anode fall; thus in the arc discharge the anode fall of potential is greater than the cathode fall. Matthies has shown that, in chlorine, bromine and iodine, the anode fall of potential may rise to hundreds of volts, that in air or hydrogen being only about 18 volts. Reichenheim and Gehrke utilized this fact to get positive ions of sodium and potassium projected with great velocity. They made the anode of a mixture of the halogen salts of these metals and graphite, and worked at a very low pressure; under the action of the dis- charge the halogens were liberated from the anode, and the large anode fall they produced was sufficient to project sodium and potassium ions from the anode with great velocity; this stream of positive ions constitutes what is known as " anode rays."
The electric force in the positive column is a linear function of the pressure; it depends slightly on the diameter of the tube through which the discharge is passing; it also depends on the current through the tube; in most cases, though not invariably, an increase of current produces a decrease in the electric force. The condition determining the electric force in the positive column is that it should give to an electron during its free path the amount of energy that will enable the electrons to produce by collisions as many ions per second as are lost during the same time by recombination.
Striated Discharge. The form of discharge when the positive column is striated is so beautiful and remarkable that it has attracted a great deal of attention. To get this type of discharge the current and pressure must be within certain limits. The striations are 'developed more readily in mixtures of gases than in a pure gas; in fact some physicists have advanced the view that they could not be obtained in an absolutely pure gas. There is no doubt, however, about their occurrence in gases in which great attention has been paid to purification. Nerbeck could not get them in pure nitrogen or pure helium, though they were conspicuous as soon as a trace of impurity was admitted. Nitro- gen and helium are gases in which, when pure, the carrier of negative electricity is always an electron; in these gases the elec- tron does not join on to a molecule and become a negative ion. Spottiswoode found that, in some cases when the positive column snowed no signs of striation when observed in the usual way, striations moving rapidly down the tube could be seen when the discharge was observed after reflection in a rapidly rotating mirror. Aston and Kikuchi, who have studied this effect in neon and helium, are of opinion that the striations are moving in these gases with the velocity of sound; it must be remembered, however, that the velocity of sound in many gases is of the same order as the velocity of a positive ion under the electric forces in the positive column, so that this result does not necessarily prove that the moving striations are analogous to sound waves.
The distance between the striations increases as the pressure diminishes (in hydrogen the distance is inversely proportional to the square root of the pressure) ; it depends upon the size of the tube: the striations are nearer together in narrow tubes than they are in wide. The distance between the striations also depends upon the current. When several gases are in the tube, spectroscopic observation of the bright parts of the different striations shows that we may have one set of striations corre- sponding to one gas, another to another and so on. Thus Crookes observed in a tube containing hydrogen three sets of striations, one set red, another blue and a third grey; the spectroscope showed that the first was due to hydrogen, the second to mercury vapour and the third to hydrocarbons. The striations are often curved with their concavities turned to the anode.
To get a general idea of the causes which might give rise to strati-
fication, let us consider a case where the current is carried entirely by electrons, the positive ions being regarded as immovable in com- parison with the electrons. Let us imagine a stream of electrons coming from the negative glow; the electric force in this region is exceedingly small, so that these electrons will have very little energy and will be unable to ionize the gas ; the electrification in this part of the tube will be that due to the electrons and thus will be nega- tive, so that the electric force will increase as we approach the anode; as the electric force increases the energy of the electron increases, and the electron will acquire enough energy to enable it to ionize the gas and produce positive ions and electrons; the increase in the number of ions will check the rate of increase in the electric force. The connexion between the ionization and this rate of increase is in the case we are considering represented by a very simple equa- tion. For if n and m represent respectively the number of nega- tive and positive ions per unit volume, X the electric force, and x the distance from the cathode
dX
(2 4 ).
If the current i is carried, as we have supposed, by the electrons, neu = i, where M is the velocity of the electron, and if we neglect the current carried by the positive ions, then when things have reached a steady state the number of positive ions produced in any region per second must equal the number which disappear owing to re- combination. Hence, if q is the rate of ionization, a the coefficient of recombination, q = amn or m = Hence we see that (24) is equivalent to
dX 47Tt A-jrqeu
Tx = -^ ^ ' ' ' (2 5 } '
Thus as long as q vanishes, dX/dx is positive, but as soon as q becomes finite the rate of increase will be retarded ; as X increases q increases, and when e-qu- = a.i?, dX/dx will vanish; but though X reaches its greatest value at this point, the values of u and q, which depend on the energy acquired by the electron, will continue to increase beyond it. For the energy acquired by an electron depends on fXdx, taken over a distance measured by the free path of the electron ; at low pressures this may be a centimetre or more, and the place where fXdx is a maximum will be beyond that where X is a maximum by a length of this order. Thus after X has reached its maximum u and q will increase and dX/dx will become negative, so that X will diminish; the diminution in X will ultimately produce a diminution in fXdx and also in u and q; the rate of decrease will slow down; X will attain a minimum, and begin to increase again when similar changes will be repeated. Thus the curve which repre- sents the relation between X and x will resemble fig. 14, giving alter-
FIG. 14
nate maxima and minima for the value of x. Thus/Xdx, the energy acquired by an electron, will vary periodically along the path of the discharge. There are two values of this energy which are of special importance in connexion with discharge through gases, one the ionizing potential we have already referred to, the other, sometimes called the " radiation potential," is the energy which the electron must possess to make the gas luminous. The radiation potential is less than the ionizing potential, and electrons with energy between these potentials will make the gas luminous but will not ionize it. Thus the molecules of the gas will give out light but will not be charged. When the energy of the gas exceeds the ionizing potential the luminous molecules are or have been charged. If the variations in the energy along the line of discharge are large enough to make it sink below the radiation potential, then along the discharge we shall have: (i) places where the energy is below the radiation potential, these will be dark; (2) places where the potential is between the radiation potential and the ionizing potential, the molecules here will be luminous and uncharged and will, therefore, not move under the electric field; (3) places where the molecules are luminous and charged, these molecules will move down the tube towards the cathode with the velocity which the positive ion acquires under the electric field. This velocity, when the pressure is low and the field several volts a centimetre, as it is in the positive column, may be many thousand centimetres per second. Place (i) corresponds to the dark parts of the striations, (2) to the stationary luminous parts, while (3) is the origin of the striations moving down the tube observed by Wulner, Spottiswoode, Aston and Kifcuchi.
Cathode Rays. In 1859 Pliicker observed on the glass of a highly exhausted tube in the neighbourhood of the cathode a
