DISTRIBUTION OF INTENSITY IN BROADENED SPECTRUM LINES. 
471 
of parabolas whose vertices are not at C, which therefore exhibits a sharp peak. In 
fact, the original dotted parabola really consists of arcs of two parabolas which 
happen to he coincident when q — 0, and the analysis always applies only to one side 
of the axis, as was emphasised earlier. 
The interaction of two laws of energy distribution in a line, one being the simple 
exponential law, could therefore explain the peaked appearance at the vertices of the 
photographs, but it is incapable of explaining the nature of the curvature if the 
other law is that of probability. It is evident on inspection of corresponding points 
why one curve is flatter than the other, although the parabolas are equal. 
On the supposition that H a is not complex in these experiments (a supposition 
which is ultimately disproved), it is a matter of practical importance to isolate the 
simple exponential law which may be superposed on any other, and although the 
curves appear, in their continuous parts, to follow a law of the form y n oc x, we must 
assume, in view of their peaked nature, that the best representation in terms of one 
component will be 
y n +$y = fa, 
where $ and (3 are constants, n being less than unity. The curves, when of continuous 
curvature, are obviously so nearly straight lines—as, for example, in the upper part 
of the curves for H a —that the simple exponential law is evidently the predominant 
feature, and much analysis is thereby saved. For, as a first approximation, y = 6oc/$, 
and the second approximation is easily found to be 
fa /3”x n 
y ~ 8 S n+1 ' 
