482 
PROF. J. W. NICHOLSON AND DR. T. R. MERTON ON THE 
or if I Jq n = E, the measure of energy contained in a component determined by 
Stark’s tabular intensity, 
■p tan a 4^ = -fE 0 g 0 2 e~ r?o + 2 2 E ;i g n 2 cosh q n <r n . e 
(XX [ i 
-xq* 
E 0 g (J e xqa + 22 E n q n cosh <r n q n . e~ xq “ ^, 
whereas the initial slope is given by 
—p tan a dy/dx = g 0 . 
The difference, which reduces to 
(2 2 q n (g 0 —g n ) E„ cosh q n a n e gnX 'j j |E 0 g 0 e X5u + 2 2 E n g„ cosh <7 n q n . e I? *| , 
must be positive, which can only be the case in general if g 0 > g„. Thus when a line 
showing the Stark effect is broadened, the components become more diffuse in the 
order of their separations in general. Their energy is more spread out, and even if 
two components have the same tabular intensity in direct methods of resolution as 
tine lines, their heights on the photographs by the present method of the condensed 
discharge may be very different. For these heights are not determined by the 
energies- in the components, but by their central intensities, which are proportional 
to their rates of attenuation g. It is now possible to understand at once the reason 
for the absence of peaks in the curve for H a even when the energies of all the 
components may be strictly comparable with that of the central one. This increase 
of ‘‘spreading” of the components with their distance from the centre is to be 
expected from the fact that the change in frequency of the radiation from a specified 
particle depends on the degree of proximity of other charged particles, the distribution 
of which is subject to variations. If the arrangement of luminous and charged 
particles were not subject to some probability distribution, we should find sharp 
components as in Stark’s experiments. 
(IX.) Details of the Components of H a . 
The theoretical boundary of the curve for H a , on the basis of Stark’s results, has 
been plotted for various values of q attached to the different components, in order to 
discover the dependence of the curve upon these values. For values at all nearly 
equal, the curve consists of a series of sharp peaks of nearly equal height, separated 
by deep hollows ; and it is evident, therefore, that the decrease in the value of q as 
the components separate from the central one is rapid. I 11 these circumstances, the 
kink in the curve loses its peak-like character and becomes a mere protuberance. 
Moreover its shape for any component ceases to depend to any extent on any other 
component but the two adjacent, and more particularly the upper one. The 
