268 
DR. T. R. MERTON AND PROF. J. W. NICHOLSON ON 
with great accuracy. By means of this formula, the plate can be calibrated for all 
wave-lengths, hut for the present purpose, only the values e = 0‘4301, CT23376 for 
H a and are required. 
Since the lines have a definite width, the theory outlined above is not strictly 
applicable in its entirety, but if the resolving power of the instrument is great in 
comparison with the observed (apparent) widths of the lines, it is well known that 
the maximum for any one wave-length is not altered except in magnitude, and that 
the plate gives reproductions of the lines in the successive orders with only a change 
in intensity—which is uniform along the narrow line—of each of the infinite number 
of components into which it can be resolved theoretically. Without the use of the 
plate, the wedge photograph should be parabolic for each line in the ordinary 
discharge as proved in a former paper*—according to the ordinary theory of 
broadening—and the combination of wedge and plate should, therefore, also give 
parabolic traces on the photograph under the condition that the lines are sufficiently 
narrow. This condition appears to be fulfilled in the case of the Hydrogen lines, 
and, in fact, it is proved later that the traces on the plate, when reduced to a normal 
pattern, are very accurately parabolic. 
Reduction of the Fringes to a Normal Standard. —-We have seen that in the case 
of a line broadened according to the probability law of intensity the fringes obtained 
from the wedge and plate should be a series of blackened patches with parabolic 
contours. Owing to the small variation of D, the path difference produced by two 
refractions in the plate, the parabolas are not uniform. They are not at equal 
intervals, and the distances between their axes must increase from the central 
member of the set of fringes. Their heights also vary continuously, and the 
appearance of the maximum heights of the individual fringes is as shown in the 
figure (fig. 5), where PA, QB, BO, SD, are four successive heights, and AB, BO 1 , CD 
are in descending order of magnitude. 
A theoretical consideration of the angle of refraction—nearly equal to sin -1 j > 
corresponding to each fringe, shows that the distance, say AB, between the n th and 
* Loc. cit. 
