Discharge at Very Low Pressure.

(J. E. Lilienfeld. Zur Hochvacuumentladung. Ann. d. Phys. 61, pp. 221—263, 1920).

The impetus for a number of the author’s works on this question1 was the circumstance that the voltage at the edges of the tube necessary for obtaining a definite current increases as the pressure rises, once a certain limit of rarefaction of the gas has been passed. Lilienfeld explains this by insufficient ionization in the residual gas and by the consequent appearance of a space charge due to the presence of electrons. With further ionization of the pressure, there finally comes a moment when all the phenomena accompanying the discharge no longer depend on the density of the gas. In this case an increase in the potential difference is observed when the current is increased, and the relation between these quantities—i.e. the characteristic—can in the general case be expressed by the formula \(i = av^n + b\), where, for not especially small values of \(i\) and \(v\), the constant \(b\) may be neglected. Especially characteristic are the exponents 2 and \(3/2\). With proportionality of the current to the square, equality of the potentials along the axis of the discharge is not ob—

...the volumetric charge is observed, and thus, with the sign of very small elasticity of the gas in the tube, the author considers the relation \(i=ax^2\), in contrast to other investigators, as well as to the data of technique, which indicate, as a necessary and sufficient sign of a strong discharge, the presence of the exponent \(n=3/2\).

The paper under review has as its aim to verify the above-cited results of the author’s earlier works; moreover, for measuring the difference of potentials along the axis of the tube he uses, instead of probe electrodes or a movable anode, either two fixed anodes in two cylindrical elbows of the same diameter but of different length, or, finally, one fixed and one removable anode in one and the same cylindrical elbow. The cathode in tubes of these three types is a tantalum incandescent lamp placed in the widened part of the tube. Since the character of the phenomena investigated depends on the current density and on the presence or absence of a volumetric charge, the potential difference was measured only in the cylindrical part of the tubes; moreover, particular care had to be taken at the places where the narrow parts of the tubes pass into the wide ones, where all phenomena are considerably complicated and it is very difficult to establish any regularity.

By measuring the voltage at the necks of the tube for various distances of the anode from the cathode and subtracting the obtained figures, the potential drop along the axis of the cylindrical part of the tube was determined, and at the same time the phenomena occurring directly at the electrodes (cathode and anode drop) were eliminated.

A series of similar observations, carried out within the limits of 1060–8980 Volt and 3.3–21.7 Mil. amp., gave a rectilinear fall of potential. As regards the characteristic curve, the relation between the current strength and the potential difference confirmed the formula \(i=av^n+b\), where for \(n\) the following values were obtained: 1.51; 1.72; 1.73; 1.86; 2.00. The deviation from the “law of squares” is the smaller, the stronger the rarefaction and the longer the cylindrical part of the tube. This deviation probably arises from the imperfection of the tube construction. The exponent \(n=3/2\) can, in the author’s opinion, characterize a strong discharge only in particular cases, when the paths of the electrons go from the cathode either radially or in parallel.2 This is confirmed by the construction of the characteristic of a special kind of valve tube, for which, with a strong discharge, the author obtained for \(n\) the values 1.66; 1.46; 1.57; 1.55. Another characteristic sign of a strong gas discharge in cylindrical tubes, corresponding to a rectilinear fall of potential—the absence of a volumetric charge—leads to the conclusion that we have electrical conductivity analogous to that in metals. Consequently, in addition to the transfer of electric charges between the electrodes, there must be observed an unimpeded motion, the free energy of which in any section of the tube is liberated in the form of heat. Into each volume between two cross-sections of the tube perpendicular to the axis there enters, from one side, the same amount of energy of motion of charges as leaves from the other, notwithstanding the considerable fall of potential. In such a case the heating of the anode should not depend either on the length of the discharge axis or on the voltage at the necks, i.e. on the distance of the anode from the cathode. The correctness of this conclusion the author proves by measuring the temperature of the anode. Within the limits of experimental error, in two cylindrical elbows of equal length, with the same current strength, the temperatures of the anode...

were found to be identical. In conclusion, we shall present a new experiment with a special Röntgen tube, in which, instead of the anticathode, on a quartz support there is placed a quartz plate, which can be heated to any temperature by a discharge between an emitting lamp and glow cathodes. Despite the high degree of rarefaction in the tube, the insulator evidently is not charged to a potential that could impede further bombardment by electrons. Consequently, the absence of charge on quartz and glass in an evacuated tube cannot yet serve as proof that there is some conductivity that might be ascribed to insufficient rarefaction, as Langmuir asserts ³).

A. Trapeznikov.

1. J. E. Lilienfeld. Ann. d. Phys. 32, p. 673, 1910; 43, pp. 24, 26, 1914; Phys. Zeitschr. 9, p. 193, 1908.
   Lilienfeld u. Rosenthal. Fortschr. a. d. Geb. d. Röntgenstr. 18, 4, p. 256, 1912.
   Lilienfeld. Phys. Rev. 3, p. 364, 1914; Phys. Zeitschr. 15, p. 744, 1914; Fortschr. a. d. Geb. d. Röntgenstr. 23, p. 383, 1915; Ber. d. Säch. Ges. d. Wiss. 66, p. 76, 1914; Leipzig. Sächs. Ges. d. Wiss. 69, p. 45, 1917. ↩

2. Langmuir Phys. Rev. (2) 2 p. 450, 1913; Phys. Zeitschr. 15 p. 348, 1914; Gehrshausen Ann. d. Phys. 51, s. 705; 847; 1916. ↩