In recent years the spectra of Hydrogen and Helium have been perhaps more closely studied than those of any other element, owing partly to the importance of these substances in celestial bodies, and partly to the supposed simplicity of their atom which should render their spectra especially suited to theoretical investigation. Researches have been mainly directed to the study of the series relations in the spectra, and production of “enhanced” or “spark” lines under conditions of powerful excitation. The present investigation is devoted to a study of the spectra of Hydrogen and Helium, with special reference to the relative intensities of the lines under different conditions, a quantitative knowledge of which must necessarily be of importance in any discussion of the relation of spectra to the constitution of the atom. It has been the custom to record the intensities of spectrum lines on an arbitrary scale, ranging generally from 10 for the strongest lines to 1 or 0 for the weakest. The intensities have usually been assigned purely at the discretion of the observer, and without much regard to the conditions of observation, whether visual or photographic. In any case, the apparent intensities are affected by the optical system by means of which the spectrum is produced, and whereas in visual observations the sensitiveness of the eye to different wave-lengths should be taken into account, matters are even more complicated in the case of photographs of spectra, where the sensibility of the photographic plate varies very considerably with the wave-length in a manner which is not precisely defined, and which appears in fact to be to a great extent irregular. These remarks apply to the visible and ultra-violet regions of the spectrum. Measurements in the infra-red are usually carried out with the thermopile or bolometer, and in this case quantitative measurements of the intensities of lines are obtained. It is, however, the visible and the less refrangible part of the ultra-violet spectrum in which accurate measurements of intensity, on a precise and quantitative basis, are perhaps most urgently needed at the present time. For example, in the case of celestial spectra, the problem of the relative intensities of lines has become of considerable importance, and is probably, at present, the greatest obstacle in the direction of the further elucidation of the phenomena which occur in new stars. In these spectra, observations are of necessity limited to the visible and the less refrangible ultra-violet regions.