PROF. J. W. NICHOLSON AND DR. T. R. MERTON ON THE 
466 
(V.) Theoretical Discussion. 
We may now consider the mathematical interpretation and analysis of' the curves 
obtained. 
1. A critical intensity of illumination I c must exist, such that any intensity smaller 
than I c , falling on the plate under the conditions of, and for the time occupied by 
the exposure, does not produce an effect which can be perceived by the eye. More 
generally, it would be equally convenient for many purposes to define I c as the intensity 
which will produce any specified amount of blackening on the plate, and in the 
method adopted the amount of blackening specified will represent a dot which is just 
visible on the enlarged photograph. For, as will appear later, the loci of all the points 
of equal blackening on the plate, due to one component, form similar curves, which 
only differ in regard to the values of the constants contained in their equations. In 
determining the general nature of the curve given by any line—and therefore the law 
of energy distribution in the original image of the slit without incidence on the wedge 
—this more general conception of I c is sufficient. 
It has been pointed out that the type of broadening of a spectrum line from a gas 
at low pressure and excited by uncondensed discharges is in accord with discussions 
based on the theory of probability, following the law 
I = I 0 e-^, 
where I 0 is the intensity at the “ centre ” of the line—only the case of symmetrical 
broadening is at present contemplated—and I the intensity at a distance x from the 
“ centre,” measured on the wave-length scale, and k a constant. 
The assumption has usually been made hitherto that the broadening associated 
with the condensed discharge also followed the probability law, although the actual 
amount of broadening is of another order of magnitude under suitable conditions. In 
fact any other supposition raises difficulties in the physical interpretation according 
to any suggestions yet put forward. It has never been implied that the effect may 
not be complex, and due to the joint action of several causes. The broadened line 
might therefore be formed by the superposition of several probability curves—one 
arising from each cause—and the resultant intensity law might then cease to be of 
the usual type, although that type pertained to each of its components. Cases of 
unsymmetrical broadening can also come into the scope of such a view. 
Perhaps the most fundamental result which emerges from a preliminary inspection of 
the plates is the necessity of abandoning this view. The plates contain photographic 
records of the intensity curves—showing variation of intensity with wave-length— 
across certain lines, and although the traces on the plates are not the actual intensity 
curves, which may be derived from them by a simple formula, yet abrupt changes of 
curvature in the intensity curves must be accompanied by similar changes on the 
plates. In other words, the number of separate components, whatever their origin, 
