DISTRIBUTION OF INTENSITY IN BROADENED SPECTRUM LINES. 
469 
a single component, or a set of close components, broadened by the condensed 
discharge, is not a probability law. Whatever it may be, it must be far removed 
from this, for the curvature of every curve on the j)lates is diametrically opposite to 
the requirements of the law. We are therefore not dealing with a case in which 
the law ceases to be a good approximation, but with something fundamentally 
different. It is evident that broadening due to a condensed discharge has no relation 
to the ordinary phenomena, and that the uses made of these phenomena, for example, 
by Buisson and Fabry, are definitely inapplicable if the conditions of excitation 
are those of a condensed discharge. This definite conclusion serves to remove several 
anomalies which have arisen in connection with the application of interference 
methods to spectral lines, but which need not be classified in detail here. 
In view of this failure of the ordinary superposed probability curves towards an 
explanation of the laws of intensity found in these experiments, it is necessary, before 
proceeding to a detailed examination of the plates, to give the general theory of the 
experiment, which from a mathematical point of view is simple. With the notation 
selected above, let I 0 be the intensity on the axis of a spectral line, and let the law 
of variation from the axis be f(x). Then the intensity at a distance x along the 
wave-length scale is l 0 f(x)/f( 0 ). For example, in the preceding case f (x) — e~ k ~ x " 
andy(o) = 1. A depth >7 of wedge reduces this to I 0 f (x) e~ pri /f ( 0 ). 
If H is the height and 2D the breadth of the resulting image on the plate, 
I c = Io/(D)//*(0) = I 0 e -pHtan “ 
and 
f{x)ff{ D) = e py tan 
Using a function \fs(:x ) instead, where — as being more convenient 
for calculations, equally general, and more suited to the physical necessity for an 
exponential type of law 
'A(D) — A (O) = pH tan a = \js {x) — \fs ( 0 )+py tan a. 
Referring the curve to new axes at its vertex, as in the case already discussed, 
transferring the origin through a distance H, reversing the axis of y, and finally, 
interchanging the axes of x and y, we obtain 
i/r (y) = px tan a, 
and the law of intensity denoted by \fs can be found if the equation of the curve on 
the plate is determined. For example, if the photograph has the equation 
y"/x = constant. 
3 s 2 
