248 
DR. T. R. MERTON AND PROF. J. W. NICHOLSON ON 
accurate method of determining the breadths, which is of much greater value than 
any method of direct measurement. For the measurement of such small distances 
cannot achieve a high degree of accuracy, even with the aid of a construction on the 
plate, giving a geometrical magnification. 
According to the conditions of discharge, the bounding curves on the plate are 
either straight lines or parabolas, and in both cases the breadths at the base can be 
determined as follows :—-The dots on the photographs produced with the screen are at 
the rate of 100 to the inch—-in order of magnitude—-in two perpendicular direc¬ 
tions. They are so close that the area of any blackened region is very accurately 
proportional to the number of contained dots. Under a magnifying lens, these dots 
can be counted visually without difficulty, and the breadth of the line is proportional 
to the number of dots divided by the height. The preceding formulas for the 
absolute contained energy could therefore be put into the form :— 
- (Number of dots) (photo. intensity)/(height) (log J0 photo, intensity)" 
where n = ^ for the ordinary discharges, and n — 1 for the condensed discharge. 
Even in the case of parabolas, the area is a definite numerical fraction of that of the 
containing rectangle. 
The photographic intensity measures and the dot counts need not be done 
simultaneously on plates of the same magnification—the degree of magnification is not 
relevant to the formula—-as is readily perceived, though, of course, the enlargements 
should be made from the same negatives. 
The breadth of a line, of course, requires correction by the dispersion factor (\ — A 0 ) 2 , 
where A 0 = 2257'5 in these experiments, regarded as uniform across the line, and 
must be multiplied for each line by this factor. The effect of enlargement does not 
enter directly at this point into the question of integrating the whole energies in the 
lines, for it acts equally on all the lines. The energy is proportional to I c which must 
be eliminated by comparison with the carbon arc. 
We may, for purposes of clearness, summarise the results of this section and of the 
preceding sections in the following terms :— 
In the quantitative analysis of a spectrum line by comparison with the carbon arc. 
regarded as giving black-body radiation, there are two important magnitudes to be 
considered :—(l) the maximum energy-density at the centre of the line, I, such that 
the energy distribution in the line at its centre is I A dX for a small range dX of its 
width, and (2) the whole energy-content of the line, or the energy thrown into this 
wave-length when the gas is emitting its series spectrum. In the case of the carbon 
arc emitting a continuous spectrum, we only have energy-density to consider, and it 
can furnish a standard of comparison for both (l) and (2). The absolute relative 
intensities of the carbon arc for any wave-lengths can he calculated theoretically, 
and are exhibited in a previous table in the preceding section. Their photographic 
