PHENOMENA RELATING TO THE SPECTRA OF HYDROGEN AND HELIUM. 243 
assumed that the distribution of energy in this source is that of a black body at the 
temperature of the boiling point of carbon. Assumptions involved in the use of this 
standard, and their general validity, will be discussed in a succeeding section. 
The continuous radiation from the positive crater of the arc almost completely 
overpowers the band spectra which are superposed on it, except at certain regions in 
the spectrum where the intensities of the heads of bands cannot be neglected. But 
these regions, and points at which the lines due to impurities in the carbon are 
superposed, can easily be avoided in determining the photographic intensity curve of 
the arc. In Plate 2, a, is shown the photograph obtained of the spectrum of the 
positive crater of the carbon arc after the light had passed through the wedge. The 
Helium spectrum was superposed in order to provide lines of reference, and by 
measuring the height of the blackened area at a certain series of points, the 
photographic intensity curve of the positive crater has been determined. This curve 
refers, of course, only to the particular brand of plate employed, and must be 
re-determined for each batch of plates, or in the event of a particular batch being 
kept for a considerable time—for the sensibility curves of different batches may differ 
to some extent, and they are also subject to variation with time. 
Plate 2, B, shows the Helium spectrum photographed through the wedge in the 
same manner, and, by measuring the heights of the lines, their relative intensities 
can be determined in terms of the intensity—for the same wave-length—of the carbon 
arc, by comparison with the photographic intensity curve of the positive crater. If, 
therefore, we can assume the distribution of absolute intensity in the continuous 
spectrum of the positive crater—corrected, of course, for the dispersion—we have the 
necessary data for determining the relative intensities of spectrum lines in absolute 
terms. 
One of the main difficulties which at present somewhat restricts the accuracy 
which can be obtained by this method of comparison is our incomplete knowledge of 
the temperature of the crater. At the same time, very satisfactory results can be 
found from the existing data. The two temperatures usually quoted are T = 3700° C. 
absolute, found by Waidner and Burgess in 1904, and T = 3620° C. absolute, found 
by Harker in 1908, their mean being about 3650° C. absolute. These are black- . 
body temperatures of the positive crater. In connection with this question we have 
referred to Dr. J. A. Harker, F.PkS., of the National Physical Laboratory, who 
kindly informs us that the most probable temperature of the positive crater of the 
arc burning in air at atmospheric pressure should now be regarded as very close 
to 3750" C. absolute, or 100° C. higher than the mean. For purposes of comparison, 
we have, while accepting this estimate, computed according to both values in the 
following table. 
Planck’s formula for complete radiation is not necessary for the present values 
of wave-length and temperature, and Wien’s law may be used. A measure of 
the intensity for a given wave-length X is therefore \~ 5 e~ aX,T where a = 1‘445 cm. 
