In a previous communication it has been shown that if a very long vacuum tube of moderate bore, filled with hydrogen at a pressure of ½mm., is operated by a direct or alternating high potential current, the secondary spectrum appears only at the ends of the tube in the vicinity of the electrode bulbs, the central portion showing the lines of the Balmer series, with a faint trace only of the secondary spectrum. By this method photographs of the series down to the twentieth member were obtained. In more recent work the series has been photographed to the eighteenth line in the third order spectrum of a 7-inch plane grating with a lens of 20-feet focus, and the wave-lengths determined to within a few thousandths of an Ångström. This work will be described elsewhere. Practically all of the very peculiar effects described in the paper referred to above have been explained, and in the pursuit of some of the more elusive phenomena, some extremely interesting properties of atomic hydrogen gas have come to light which will be described briefly in the present paper. The work developed out of a study of what I referred to in the earlier paper as “Infected Spots.” It was frequently observed that white spots sometimes appeared along the central portion of the tube, which normally is fiery-purple in colour, and almost invisible through a green colour filter. These spots showed the secondary spectrum of hydrogen, with the full intensity exhibited at the ends of the tube, some fifty times as intense as in adjacent portions of the tube which gave the nearly pure Balmer spectrum.
Strict Monotonicity and Unique Continuation for the Third-Order Spectrum of Biharmonic Operator
