246 
DR. T. R. MERTON AND PROF. J. W. NICHOLSON ON 
regions of wave-length, and does not require expression as an energy density per unit 
length. The effect of unequal dispersion in any narrow region is negligible. If, 
however, the line were very broad, dispersion would become important within its 
extent, as in the case of II a under the conditions of excitation employed in the work 
described in the preceding communication.* 
When the wave-length scale is used, it is only necessary to multiply the 
theoretical ratio in the second column by ~ /(—') , which can be read directly. 
ax I \ day 3888 
(VI.) The Energy in an Emission Line. 
In the case of emission lines, the intensities to which we have referred hitherto 
in this communication have been “ central intensities,” or the maxima of energy 
density in the lines. The central intensity determines the height of the line when it 
is photographed through the wedge, and “photographic intensity” has signified 
photographic central intensity. But every line, however narrow, has a definite 
breadth within which dispersion, for lines so narrow as those dealt with in the present 
experiments, may be regarded as uniform. If all lines were equally sharp, it is 
evident that this central intensity would be a satisfactory measure of the actual 
energy-content of the line, but the condition of equal and extreme sharpness cannot 
be assumed to occur, except under certain specified circumstances. 
If \ c is the intensity just visible photographically, the height of the line, originally 
of intensity I A at its centre, on the plate after enlargement is, with the previous 
notation, h K , where 
f = log ,.,- 1 
4 - n 
Tfi/qA 
H / 
= 10 11 
and I A /I C is the quantity defined already as the photographic intensity, representing 
actually the photographic central intensity. The critical intensity I,, affecting the 
plate is a function of X, so that the use of the carbon arc is necessary as a standard 
of comparison, but in an individual line, I c may be treated as constant, together 
with I) A . 
Taking account of both sides of the line, the whole energy in it is proportional to 
10 11 d\ 
where the upper limit is effectively infinite, and the lower one is the wave-length of 
the central component. The law of energy distribution in the line determines the 
dependence of h K on the wave-length. There are two important cases :— 
(l) The law of the simple exponential, found in the former paper* to be applicable 
in the case of the condensed discharge ; and 
* Loc. cit. 
