The interest in the Aurora Borealis and the problems associated with it, is evidenced by the extensive list of careful investigations that have been published upon this subject. Since the early work of Angstrom, we have the published records of over a hundred investigations on the spectrum, and many others on the origin or other phenomena characteristic of the aurora. Paulsen, Westman. Sykora, Vegard, and others have determined the wave-lengths of many of the lines of the general auroral spectrum, while, recently, Slipher, Rayleigh, and Babcock, have studied the light of the night sky. Babcock, using a Fabry and Perot interferometer, determined very accurately the wave-length of the auroral green line 5577. The precision of his measurements is in marked contrast to those obtained with low dispersion spectrographs. The laboratory experiments on the excitation of the auroral spectrum have not been less numerous than the spectroscopic investigations. The more recent work has been carried out by Stark. Rayleigh, and Vegard. After a careful examination of all the results obtained in these reports, we may only say that the exact nature of the cosmical rays, responsible for the aurora, remains a mystery.
One of the outstanding problems awaiting solution in the field of spectroscopy is the origin of certain unknown lines in the spectra of nebulæ. Another has to do with the origin of the famous green line, λ = 5577Å in the spectrum of the auroral light. As regards the solution of the first it has been suggested that the unknown nebular lines may be found to originate in the radiation emitted by helium in the molecular- state, provided the gas is stimulated to the emission of radiation under conditions of suitably low pressures and suitably low temperatures. It has also been suggested that the unknown nebular lines may originate in radiation from a gas consisting of molecules formed of atoms of hydrogen and of helium, provided this gas is subjected to suitable conditions of pressure, temperature, and excitation.
The paper describes experiments on the arc between metal electrodes in argon and other gases, in which the current was controlled by means of a kenotron. By varying the temperature of the cathode in the kenotron, it was found possible to obtain volt-ampere characteristics of the discharge for the transition from glow to arc or the reverse. It was also observed that in the arc stage, for at least smaller currents, the spectrum of the discharge is characteristic of the cathode material.
According to the Bohr Theory the hydrogen atom consists of an electron in circular or elliptical motion about a positively charged nucleus. The steady states are defined by discrete values of the angular momentum and, in the case of elliptical motion, the eccentricities of the ellipses are limited to certain definite values. Sommerfeld, by an extension of Bohr's theory involving quantising both angular and radial momentra, has established the formula γ = 2π 2 m E 2 e 2 / h 3 [ 1/(T' 1 + T' 2 ) 2 - 1/ (T 1 + T 2 ) 2 ] for the spectral series emitted by a system consisting of a nucleus with charge + E and an electron with charge - e . This is the familiar formula in which terms are included corresponding to elliptical as well as to circular motion for the revolving electron. By the theory of relativity it can be shown that the mass of an electron in the elliptical orbit is not the same as its mass in the circular orbit, but that it depends on the velocity v , thus m = m 0 (√1 - β 2 ) -1/2 , where β = v / c and m 0 is the mass of the slow-moving electron. From a mathematical standpoint for a slow-moving electron we may consider the path as an ellipse with slowly moving perihelion.
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