DISTRIBUTION OF INTENSITY IN BROADENED SPECTRUM LINES. 
475 
n being less than unity, and $ large and positive. The first condition, as regards n, is 
necessary to secure the curvature in the right direction. Now this could also be 
secured mathematically if n were greater than unity, and S negative, hut this case is 
a physical absurdity, for it signifies a law of intensity in the original light of 
the form 
I = 
where a and b are real constants, and n > 1. The intensity would then begin by 
decreasing from the centre, and finally increasing without limit. This is contrary to 
experience and also to physical possibility. But it is unfortunately the case to which 
we are led when an attempt is made to apply the formula to the curve for H tt . The 
following numerical example from one photograph makes this clear, and indicates at 
the same time that small changes in the measurements would not reverse the 
conclusion. 
/3/S at the vertex may be obtained with accuracy as the initial slope, and is found 
to be 0'0573, by a construction involving the result as a ratio of two large distances. 
The following points are on the curve, and distances are expressed in millimetres. 
x = 162'5 | x — 192‘Ofi 
y= 16T j y= 29'5 J 
and applying the formula we find, 
n - 5’97, S/m"- 1 = -CT870. 
The mixed law, 
I = I 0 e- qx ~ kx \ 
can therefore give no interpretation of the curves, and a more general conclusion is 
possible. For the result may be extended in the same way to a law compounded of 
three, when further measurements are made. It is not thought necessary to reproduce 
the calculations to this effect. The conclusion, therefore, appears inevitable that the 
details of the shape, and even the general form, of the curve H a , are not compatible 
with the view that H a contains only one component broadened, perhaps by various 
agencies, simultaneously by any physically possible exponential laws, the total 
argument of the exponential being additive in the complete law. We are compelled 
to seek an explanation of the curve in terms of several components whose individual 
curves are superposed, and are led directly to the Stark effect as the foundation of the 
whole phenomenon. Several qualitative reasons have already been advanced in favour 
of this hypothesis, and it now appears further that a quantitative study of the curves 
necessitates the same hypothesis. For if several components are to be admitted, only 
the Stark effect seems capable of providing them, and the fact that they must be 
symmetrical in H a enhances this conclusion. The components are conspicuous in H/3 
3 T 
VOL. CCXVI.-A. 
