In the preceding investigation we have supposed that the electric field between the plates was uniform; if it were not uniform we could get discharges produced by very much smaller differences of potential than are necessary in a uniform field. For to maintain the discharge it is not necessary that the positive ions should act as ionizers all along their path; it is sufficient that they should do so in the neighbourhood of cathode. Thus if we have a strong field close to the cathode we might still get the discharge though the rest of the field were comparatively weak. Such a distribution of electric force requires, however, a great accumulation of charged ions near the cathode; until these ions accumulate the field will be uniform. If the uniform field existing in the gas before the discharge begins were strong enough to make the corpuscles produce ions by collision, but not strong enough to make the positive ions act as ionizers, there would be some accumulation of ions, and the amount of this accumulation would depend upon the number of free corpuscles originally present in the gas, and upon the strength of the electric field. If the accumulation were sufficient to make the field near the cathode so strong that the positive ions could produce fresh ions either by collision with the cathode or with the gas, the discharge would pass though the gas; if not, there will be no continuous discharge. As the amount of the accumulation depends on the number of corpuscles present in the gas, we can understand how it is that after a spark has passed, leaving for a time a supply of corpuscles behind it, it is easier to get a discharge to pass through the gas than it was before.

Fig. 15.

The inequality of the electric field in the gas when a continuous discharge is passing through it is very obvious when the pressure of the gas is low. In this case the discharge presents a highly differentiated appearance of which a type is represented in fig. 15. Starting from the cathode we have a thin velvety luminous glow in contact with the surface; this glow is often called the “first cathode layer.” Next this we have a comparatively dark space whose thickness increases as the pressure diminishes; this is called the “Crookes’s dark space,” or the “second cathode layer.” Next this we have a luminous position called the “negative glow” or the “third cathode layer.” The boundary between the second and third layers is often very sharply defined. Next to the third layer we have another dark space called the “Faraday dark space.” Next to this and reaching up to the anode is another region of luminosity, called the “positive column,” sometimes (as in fig. 15, a) continuous, sometimes (as in fig. 15, b) broken up into light or dark patches called “striations.” The dimensions of the Faraday dark space and the positive column vary greatly with the current passing through the gas and with its pressure; sometimes one or other of them is absent. These differences in appearances are accompanied by great difference in the strength of the electric field. The magnitude of the electric force at different parts of the discharge is represented in fig. 16, where the ordinates represent the electric force at different parts of the tube, the cathode being on the right. We see that the electric force is very large indeed between the negative glow and the cathode, much larger than in any other part of the tube. It is not constant in this region, but increases as we approach the cathode. The force reaches a minimum either in the negative glow itself or in the part of the Faraday dark space just outside, after which it increases towards the positive column. In the case of a uniform positive column the electric force along it is constant until we get quite close to the anode, when a sudden change, called the “anode fall,” takes place in the potential.

Fig. 16.

The difference of potential between the cathode and the negative glow is called the “cathode potential fall” and is found to be constant for wide variations in the pressure of the gas and the current passing through. It increases, however, considerably when the current through the gas exceeds a certain critical value, depending among other things on the size of the cathode. This cathode fall of potential is shown by experiment to be very approximately equal to the minimum potential difference. The following table contains a comparison of the measurements of the cathode fall of potentials in various gases made by Warburg (Wied. Ann., 1887, 31, p. 545, and 1890, 40, p. 1), Capstick (Proc. Roy. Society, 1898, 63, p. 356), and Strutt (Phil. Trans., 1900, 193, p. 377), and the measurements by Strutt of the smallest difference of potential which will maintain a spark through these gases.

Gas. Cathode fall in Volts.Least potential
difference required
to maintain a Spark.
Platinum Electrodes. Aluminium
Electrodes.
Warburg. Capstick. Strutt.Warburg. Strutt.
Air 340-350 .. .. .. 341
H2 about 300 298 .. 168 302-308
O2 .. 369 .. .. ..
N2 230 if free 232 .. 207 251
from oxygen
Hg vapour 340 .. .. .. ..
Helium .. .. 226 .. 261-326
H2O .. 469 .. .. ..
NH3 .. 582 .. .. ..

Thus in the cases in which the measurements could be made with the greatest accuracy the agreement between the cathode fall and the minimum potential difference is very close. The cathode fall depends on the material of which the terminals are made, as is shown by the following table due to Mey (Verh. deutsch. physik. Gesell., 1903, 5, p. 72).

Gas. Electrode.
Pt Hg AgCu Fe ZnAl Mg NaNa-K K
O2 369 .. .. .. .. .. .. .. .. .. ..
H2 300 .. 295 280 230 213 190 168 185 169 172
N2 232 226 .. .. .. .. .. 207 178 125 170
He 226 .. .. .. .. .. .. .. 80 78.5  69
Argon 167 .. .. .. .. .. 100 .. .. .. ..

The dependence of the minimum potential required to produce a spark upon the metal of which the cathode is made has not been clearly established, some observers being unable to detect any difference between the potential required to spark between electrodes of aluminium and those of brass, while others thought they had detected such a difference. It is only with sparks not much longer than the critical spark length that we could hope to detect this difference. When the current through the gas exceeds a certain critical value depending among other things on the size of the cathode, the cathode fall of potential increases rapidly and at the same time the thickness of the dark spaces diminishes. We may regard the part of the discharge between the cathode and the negative glow as a discharge taking place under minimum potential difference through a distance equal to the critical spark length. An inspection of fig. 16 will show that we cannot regard the electric field as constant even for this small distance; it thus becomes a matter of interest to know what would be the effect on the minimum potential difference required to produce a spark if there were sufficient ions present to produce variations in the electric field analogous to those represented in fig. 16. If the electric force at a distance x from the cathode were proportional to ε-px we should have a state of things much resembling the distribution of electric force near the cathode. If we apply to this distribution the methods used above for the case when the force was uniform, we shall find that the minimum potential is less and the critical spark length greater than when the electric force is uniform.

Potential Difference required to produce a Spark of given Length.—We may regard the region between the cathode and the negative glow as a place for the production of corpuscles, these corpuscles finding their way from this region through the negative glow. The parts of this glow towards the anode we may regard as a cathode, from which, as from a hot lime cathode, corpuscles are emitted. Let us now consider what will happen to these corpuscles shot out from the negative glow with a velocity depending on the cathode fall of potential and independent of the pressure. These corpuscles will collide with the molecules of the gas, and unless there is an external electric field to maintain their velocity they will soon come to rest and accumulate in front of the negative glow. The electric force exerted by this cloud of corpuscles will diminish the strength of the electric field in the region between the cathode and the negative glow, and thus tend to stop the discharge. To keep up the discharge we must have a sufficiently strong electric field between the negative glow and the anode to remove the corpuscles from this region as fast as they are sent into it from the cathode. If, however, there is no production of ions in the region between the negative glow and the anode, all the ions in this region will have come from near the cathode and will be negatively charged; this negative electrification will diminish the electric force on the cathode side of it and thus tend to stop the discharge. This back electric field could, however, be prevented by a little ionization in the region between the anode and glow, for this would afford a supply of positive ions, and thus afford an opportunity for the gas in this region to have in it as many positive as negative ions; in this case it would not give rise to any back electromotive force. The ionization which produces these positive ions may, if the field is intense, be due to the collisions of corpuscles, or it may be due to radiation analogous to ultra-violet, or soft Röntgen rays, which have been shown by experiment to accompany the discharge. Thus in the most simple conditions for discharge we should have sufficient ionization to keep up the supply of positive ions, and an electric field strong enough to keep the velocity of the negative corpuscle equal to the value it has when it emerges from the negative glow. Thus the force must be such as to give a constant velocity to the corpuscle, and since the force required to move an ion with a given velocity is proportional to the pressure, this force will be proportional to the pressure of the gas. Let us call this force ap; then if l is the distance of the anode from the negative glow the potential difference between these points will be alp. The potential difference between the negative glow and the cathode is constant and equals c; hence if V is the potential difference between the anode and cathode, then V = c + alp, a relation which expresses the connexion between the potential difference and spark length for spark lengths greater than the critical distance. It is to be remembered that the result we have obtained applies only to such a case as that indicated above, where the electric force is constant along the positive column. Experiments with the discharge through gases at low pressure show the discharge may take other forms. Thus the positive column may be striated when the force along it is no longer uniform, or the positive column may be absent; the discharge may be changed from one of these forms to another by altering the current. The relation between the potential and the distance between the electrodes varies greatly, as we might expect, with the current passing through the gas.