474 
PROF. J. W. NICHOLSON AND DR. T. R. MERTON ON THE 
very accurate agreement. When the axis was thus verified, measurements of the 
breadth between the two extreme dots visible laterally were taken at various levels 
on the height of the curve. It is not thought necessary to give these measurements 
in detail, and perhaps one example will suffice. The measured distance between the 
extreme dots at the lower end of the photograph, where it is broadest, is 59'0 mm. 
as stated already, and the violet and red portions have breadths 30'5 and 28'5, 
measuring on either side of the axis. This difference is 2'0 mm. against the theoretical 
value 1'97. This agreement, typical of the agreement throughout, is a convincing 
proof that the broadened H a is, in its energy distribution, absolutely symmetrical 
about its centre, and that the apparent asymmetry—only evident to the eye on the 
magnified photographs—is entirely due to the fact that the prismatic spectrum is not 
normal. 
This is the second fundamental result of the work—that the broadening of Ii a under 
the condensed discharge is cm absolutely symmetrical one. 
To a high order of approximation, inequality of dispersion lengthens the breadth of 
the violet and shortens that of the red to an equal extent, so that their sum is the 
breadth of the curve with a dispersion uniformly equal to that at A6563. To draw 
a graph of the symmetrical curve for uniform dispersion, therefore, we merely require 
to measure the total breadth of the photograph for various heights, and plotting half 
total breadth against height, we obtain one side of the curve for uniform dispersion. 
Now the total height, from base to apex, of the H a curve in question, is 192 mm., and 
the excess of breadth of the violet over the red end, even at the base, is only 2 mm. 
in a total breadth of 59 mm. The alteration in shape caused by this correction is 
therefore very slight, and can produce no appreciable tendency to a parabolic form on 
either side. The previous conclusion as to the absence of a probability law remains, 
therefore, unaffected. «. 
(VII.) The Complex Structure of II„ when Excited by Condensed Discharges. 
The symmetry of H a being established, the two alternatives still remain. H a may 
be a single component symmetrically broadened—to disprove this supposition is our 
immediate object—or a set of symmetrically-arranged but close components, each 
broadened in a symmetrical manner. The theory of this second case has not yet been 
given, and in assuming that it is a possible interpretation of the photographs, we are 
anticipating the theory given later. Confining attention for the present to the first 
alternative, and recalling that any law must, for physical reasons in the case of' 
emission, be of some exponential type, and from the appearance of the curves, mainly 
a linear exponential, we have the formula, for magnification m, 
V = 
fix 
T 
fi n x n 
<k +l 
m 
1 -n 
