472 
PROF. J. W. NICHOLSON AND DR. T. R. MERTON ON THE 
The relation of these constants S and ft to the constants of the energy distribution 
of the original spectral line may be found as follows :—If the law of intensity 
distribution is 
I = l l>e - kx "- qx , 
around the maximum at x = 0, and if H and 2D are the height and breadth of the 
photograph, 
py tan a + kx n + qx — Z D" -f gD — pH tan a 
with reference to the old axes. Taking the new axes at the vertex, 
Thus 
and also 
ky n + qy — px tan a. 
S — q/k, ft = p tail a\k 
BH = D re + Dd 
where 2D is the photographic breadth of the original spectral line. 
The actual photographs on which measurements have been made were previously 
magnified in definite ratios. For a magnification m, the equation of the upper portion 
of such a photograph as those of H a would become 
ft' l X n 
It is necessary to determine whether a unique value of n exists through the 
photographs of one particular line, permitting the equations of the contours to take 
this form, in order to decide whether the line has one or more components. H a is a 
suitable medium for this determination, and a succeeding section takes up this 
question. 
(VI.) The Effect of Dispersion. 
When the photographs are magnified on a large scale they all appear unsym- 
metrically broadened towards the violet. This is the effect to be expected from the 
fact that the spectrum produced by the prism is not normal, and it is necessary, before 
a detailed analysis of the photographs can be made, to calculate the asymmetry due 
to this cause and to compare it with the actual effect observed. A complete account 
of this problem is given below in connection with the best magnified photograph 
obtained for H a . The dispersion on the original plate, before magnification, was 
known to be given very accurately by the formula 
X — A 0 + kjJ{n-\-nft) 
o 
where A 0 = 2257'5, C = 11 (3,802'9, A is in A.U., and n + n 0 is in millimetres of the scale. 
T1 re scale reading for the centre of the pattern of Ida, A = 6563, is, therefore, on the 
original plate 
n + n 0 = 116,802-9/(6563-2257-5) = 2713 mm. 
