DISTRIBUTION OF INTENSITY IN BROADENED SPECTRUM LINES. 
473 
We shall suppose provisionally that the law of energy distribution round the central 
component of the original line is the same on both sides, so that with equality of 
dispersion, the final pattern would be symmetrical. Let 6563 +a be the limiting 
wave-lengths which can just be seen on this pattern at the thin end of the wedge. 
Then the corresponding scale readings at the ends of the pattern are 
n + n 0 = C/(6563 — A 0 + a), 
or 
27'13 + Ca (6563-A u )- 2 + Ca 2 (6563 —A 0 )- 3 . 
The length of the red end of the pattern is aC (6563 —A 0 )~ 2 —a 2 C (6563 — A 0 )~ 3 and of the 
violet end, aC (6563 — A u )~ 2 + a 2 C (6563 —A 0 ) -3 , neglecting higher powers. The difference 
is 2a 2 C (6563 — A 0 ) -3 and the total length 2aC (6563 —A 0 )~ 2 . If this total length is d , 
the difference becomes ad/(6 563—A 0 ) or (6563 —A 0 ) d 2 / 2 C. By calculation, this becomes 
d 2 / 54*26 in the present case, where d is in millimetres. 
This calculation is valid not only for the extreme thin end of the wedge, but for any 
thickness of wedge, for both the wave-lengths, 6563±a, have the same original 
intensity, and therefore disappear on the photograph at equal heights, corresponding 
to equal thicknesses of wedge traversed. We may now apply this result to one of 
the photographs of H a (Plate 2 ).* 
This plate lias been reproduced by the half-tone process, which reproduces the 
dotted effect used in determining the boundary of the curve. The vertex of the 
curve* is well defined, and the axis must be parallel to the original slit, and can be 
determined precisely. The magnification in this case was x 33, and the breadth of 
the curve at its base is 59 '0 mm. The breadth of the original plate was therefore 
59/33 = 17879 mm. Thus, 
d = 1*7879 mm. = v+'r 
where v and r are the breadths of the violet and red ends. 
Also 
v — v = d 2 / 54*26 = 0*0589 mm. 
The difference on the photograph magnified 33 times is 0*0589 x 33 or 1*97 mm., but 
where, on this photograph, d — 14 mm. say, the difference is 1*97/16 or 0*12 mm. 
and could hardly be observed. Even the magnified curves must therefore look very 
symmetrical at some distance from the apex, and this is actually the case. An 
important corollary from this result is that the upper part of the curve can be used 
to give a geometrical construction for the determination of the axis of the curve. 
This method has been applied to H a , to check the supposed position of its axis, with 
* In the reproduction (Plate 2) the whole of the paper is dotted, and the outline cannot therefore be 
traced exactly. In the original photographs used for measurement, the only dots visible are those which 
build up the magnified image, thus enabling the boundary to be precisely determined, 
