PHENOMENA RELATING TO THE SPECTRA OF HYDROGEN AND HELIUM. 267 
difficulty of securing uniform illumination, such a calculation would be of no value. 
If measurements of the pattern to a high order of accuracy are required, it must in the 
first place be made “ normal in a manner subsequently explained. The variation in 
distance apart of the maxima is, in fact, in the present experiments, very small, as 
will appear from the measurements, and a high degree of accuracy could have been 
obtained by neglecting it. 
The most important linear magnitude in the pattern, when it is obtained for two 
spectrum lines close together, whose separation is to be deduced, is, of course, the 
difference of wave-length corresponding to the distance between successive orders. 
Variations in D can be allowed for by making the pattern normal, and we may treat 
I) as constant in the present theoretical investigation. Its value is 
D = 2 fxd cos r, 
or, for grazing incidence, for which sin r — lj/x, 
D = 2 fid cos sin -1 = 2d (/jl 2 — l) l, \ 
\ JJ., 
Between successive maxima, 7 tD/a increases by i r, and, therefore, if A'—A. is the wave¬ 
length separation corresponding to the distance between these maxima on the 
photograph, 
7rD 7 tD x / x 
- t = 7 r, or A — A = AA L). 
XX' 
To a first approximation, A' — A = A 2 /D. We may denote this quantity by e, and 
e = A 2 /2 d U 2 -1)V 
The accurate value is e = X 2 /(D—A), but its use would never be required. For 
a given plate, e may be tabulated in a form suitable for interpolation. We have in 
this manner calibrated the plate used in these experiments. The plate was supplied 
by Messrs. Hilger, and its indices of refraction for the yellow sodium line and for the 
lines H a , H^, H y were known with great precision. With the old notation, C, D, F, G, 
for these lines, the values were :— 
Mc = U50746, md = F50990, Mp = 1*51560, mg = F52025, 
and the thickness of the plate was d = 4‘439 mm. 
The corresponding calculated values of e are :— 
e c = 0-43010, e D = 0-34615, e F = 0-23376, e G = 018533, 
and they fit the interpolation formula 
e A = 0-1853 + 0-8786 (A-4341) + 04)001 (A-4341) 2 
