where To is the period for 4. Let T, be the time from r=minimum to r=maximum and back again. by a well-known result to the first order in 1/c2 : We have where a is defined by equation (15) of the text. Thus to the first order in a Tr S" ~" / (1 — B2) dt = (1 — a/2n2) ["√(1—p2)dt. . (vi.) (1—a/2n2) Now we see from (7 a) and (12) of the text that so that where (viii.) J, = √ dr / √(A + 2B/r+C/r2) · and the negative sign is introduced on account of the negative nature of the integrand. Jr may now be evaluated by the usual method of contour integration in the complex plane. We have to find the residues of the integrand at r=0 and r=∞. At r=0 it behaves as which is regular. So that putting r=1/s, we have =-2πi × B/A√A, where it is observed that the sense of rotation at r∞ is negative. Also since (-1/A) is seen from (ix.) to govern the sign of the integrand at r∞ it follows (see figure) that (-1/A) must be negative and imaginary, and therefore ✔A must be taken as the negative (imaginary) root of A. On substituting for A and B in (ix.) from (8) of the text we have Jr = -2πieEmo [2m。W] −3/2 [1+W/4m。c2 + ..], which yields to the first order on substituting for W from (25), J‚ = −(n1+n}31⁄23[1 − &{}+341(n,/n)}/2 (n1+n)2]/(2πeЕm), and from (vi.), (vii.), and (x.) we have √(1—82) dt = T。[1—afg(n)], where To has the same meaning as in the text and f2(n) = {}+341(n1/n)+(1+n1/n)3}/2 (n1+n)2 (x.) = [1+5n1/2n+n12/2n2] / (n,+n)2 from (26 a). This is the result quoted in the text. LVI. Electrical Discharges in Geissler Tubes with Hot Cathodes. By W. H. MCCURDY, M.A., 1851 Exhibition Scholar, Princeton University". IN N a recent number of the Physical Review,' Duffendack + reported results obtained from work on low-voltage arcs, stimulated by the emission from a hot cathode, in diatomic gases. As his work dealt only with the arc characteristics, it was thought possible that additional light might be thrown on the process of ionization by a study of the discharge in Geissler tubes, if a hot filament were used as cathode to stimulate the discharge. This eliminated the uncertainty as to the source of the electrons which produced the ionization in the tube, and, at the same time, overcame the very high cathode fall of potential encountered in cold electrode tubes. With an apparatus provided with a hot cathode and a movable anode, it should be possible to study the successive stages in * Communicated by Professor K. T. Compton. + Phys. Rev. vol. xx. No. 6, p. 665. the type of discharge as the type changes from the characteristic arc type at short distances to the characteristic Geissler tube type at greater distances. This may aid in identifying the causes of various features of the Geissler tube discharge. The work here recorded was divided into three parts, which will be treated separately : : (1) Relation between current through the tube and potential applied to the tube; also observations on the appearance of the discharge under various conditions. (2) Relations existing between the filament temperature pressure of the gas, and the least voltage (V) necessary to maintain the discharge in hydrogen. (3) Similar observations in mercury vapour. The apparatus used is shown in fig. 1, as are also the electrical connexions. The filament (F) was a tungsten spiral of only a few turns, which served to concentrate the heat at the centre, thus making it possible to obtain a reasonably high electron emission without a large potential drop across the filament. This potential fall was never more than 3-75 volts; thus, assuming that the discharge was maintained to the centre of the filament, which seemed probable as it was the part of greatest electron emission, the correction was never more than 18 volt. Further, as the voltage across the tube was applied between the negative terminal of the filament and the anode, the correction due to potential drop was approximately balanced by that due to the initial velocities of emission of electrons from the filament. Consequently the voltages given in the following data are the actual voltmeter (Vm) readings. The anode (A) was either a nickel or an aluminium disk with a piece of soft iron (I) attached to it, by means of which it was possible to place the anode at any desired position. The potential was supplied by a battery of accumulators and regulated by a rheostat (R2), the current being measured by the milli-microammeter (A2). Two tubes of hard glass were used, one of diameter 4.0 cm. and the other 2.8 cm. Both were thoroughly baked out, and the filaments glowed until no appreciable amount of gas was given off. The hydrogen used was obtained by the electrolysis of dilute sulphuric acid, dried and purified by phosphorus pentoxide and coconut charcoal in liquid air. The charcoal was so placed as to serve both as a purifying agent and as a reservoir to replace the hydrogen "cleaned up" by the discharge. The discharge was sustained before any readings were taken until the pressure, as measured on the McLeod gauge, no longer decreased. PART I. Relation between current through the tube and potential applied to the tube; also observations on the appearance of the discharge under various conditions. The filament current was adjusted to the amount which gave the lowest value to the potential necessary to maintain the discharge at the distance between electrodes being used; then, with this current constant, the potential across the tube was gradually increased up to values of from 80 to 100 volts, and the current through the tube noted at suitable intervals. The potential was then decreased and current readings taken at intervals as when it was being increased. The whole process was then repeated at different distances and pressures. The relation between the current and voltage for two typical cases is shown in fig. 2. Curve I. shows the relation that was found to hold with the 4.0-cm. tube and at pressures about 0.4 mm. at distances less than about 1.2 cm. At lower pressures this sort of a relation would be found to hold at slightly greater distances. Under conditions given there was only one discontinuous change in the current, after which it gradually increased towards a maximum value. It will also be noted that the discharge was maintained at lower voltages than those necessary to start it, which has been explained by Duffendack* as due to the fact that the potential distribution is more favourable for maintaining the discharge if there is a region of positive space charge surrounding the cathode. Curve II. represents the type of relation that existed *Loc. cit. at distances greater than 12 cm. Here there were two distinctly marked discontinuities as the potential was increased, and sometimes, though not always, two as it was decreased. It will further be noticed from the figure that, for a portion of the region of voltage between the two discontinuities, the current remained constant as the voltage was increased. In some cases it was found to decrease with an increase in voltage. An explanation for this has not yet been found. The two breaks in current at the greater distances were found to be associated with the appearance or disappearance of two distinct types of discharge, which were termed types A and B. This phenomenon was also found by MacLennan* in his work on low-voltage arcs in cadmium. Type A showed very feeble luminosity, and the current associated with it was much smaller than that which was found with type B. The striations which, in the discharge in cold electrode tubes, form the positive column, extended well in toward the cathode. An increase in potential caused them to approach the cathode at a constant distance of separation, new striations appearing at the anode as the first ones disappeared at the cathode. Type B showed strong luminosity, and the current was much larger. The appearance of the discharge was the same as that in the cold electrode tubes, with a well-defined dark space but rather diffuse negative glow. In this case the striations approached the anode at a constant distance of Proc. Phys. Soc., Dec. 1918. |