PHENOMENA RELATING TO THE SPECTRA OF HYDROGEN AND HELIUM. 271 
then the equation to the parabola distorted by this effect should be 
-kx 2 = y-h JEzJL h' = DS, 
d 0 
for the height increases from the normal value at a rate (h'—h)/d 0 very closely for a 
unit increase in x, when x is positive. It decreases at the same rate when x is 
negative, or to the left, so that both sides of the distorted curve are included. As 
stated above, the correction is, in fact, not very important in the subsequent 
calculations, its inclusion affecting only the third significant figure in the final 
separation of the components deduced in the case of H a . In a calculation of 
separation, or distance between the axes of two overlapping parabolas, the effect along 
x is naturally the more significant. 
(XV.) The Law of Intensity Distribution in a Line Excited by the Ordinary 
Discharge. 
No direct proof of the validity of the usual law obtained for the intensity 
distribution around the maximum in a line broadened by the ordinary discharge—the 
law of probability I = I 0 exp ( — k\ 2 ) —-has been given hitherto, although the work of 
Lord Rayleigh* and Schonrock lias placed it on a secure theoretical basis, subject to 
certain well understood limitations in the conditions of excitement. It forms the 
basis of the calculations of atomic weights and emission temperatures of sources, made 
from the results of such experiments as those of Buisson and Fabry! , and on this 
ground it is desirable that it should be confirmed experimentally in at least one 
definite case, for it is not possible to foretell readily whether the theoretical conditions 
are satisfied in any practical case. Moreover, we showed in the previous paper that 
it breaks down completely in the condensed discharge, and that all the components 
into which the line is then split by the electrical resolution which takes place under 
these circumstances follow the exponential law I = I (J exp (— k\). From the present 
photographs, it is possible to give a direct proof of the applicability of the theory to 
the ordinary discharge in Hydrogen. For all that is necessary is to show that the 
individual contours of the components making up, say H a , are strictly parabolic. 
Inspection of the photographs indicates that both IL a and are double, and that 
each component is represented by a contour which appears very definitely parabolic— 
with, of course, the slight distortions dealt with in the preceding section. The 
parabolas overlap and represent lines of different intensities. We have not attempted 
to measure these intensities in the present experiments, but, as judged from the 
heights of the parabolas—one of these is calculated from the visible part of the contour 
—they are in at least rough accordance with Michelson’s! estimate of 10 to 7. The 
* ‘Phil. Mag.,’ XXIX., p. 274, 1915. 
f Loc. cit. 
2 p 2 
