PHENOMENA RELATING TO THE SPECTRA OF HYDROGEN AND HELIUM. 2711 
normal contours take removes the necessity for giving a detailed investigation of the 
effect of this procedure. It is evident that, as could be proved otherwise, it 
introduces no appreciable change in the distances between axes of parabolas. 
(XVI.) Isolation of Components of a Line. 
The photograph for H a is found to consist of two parabolas—-slightly distorted—as 
in the figure (fig. 6), where the normal parabolas are 
shown, intersecting at P. The axes are a x and a 2 and <r 
is their separation on the photograph whose contour is 
APBC. Near P, of course, since intensities are additive, 
the parabolic forms are lost, and points close to P should 
not be selected for measurement. Calculation shows 
that this region round P is, in fact, nearly negligible, 
but we do not exhibit the calculation, for it is somewhat 
tedious. The equation for the parabolic form above P 
can be found with accuracy as in the last section for 
the distorted or normal curve. It is convenient to use ^ c 
the latter. We can then calculate the half breadth x 
of the normal curve at Q, and thence the apparent one x' by the formula 
x 
x — 
ax 
2 ~d} 
The whole breadth QB of the contour may be measured, and thence the apparent 
BN in the figure, equal to x". This can be reduced to the normal value x (say), 
which is o r + X, where <r is the separation and X the co-ordinate of B relative to the 
axis of its own parabola. By finding X and the heights for various points, <r may be 
deduced and thence SX. There is, however, a simpler method of procedure. The 
axis of the upper parabola, when made normal in the longitudinal direction, is the 
locus of the central points of the various breadths, and can be drawn on the curve. 
Since Bayleigh’s theory has been shown by a direct method to be applicable to 
these experiments, we may at once assume that k 2 in the law of intensity is the same 
for both components of IT a . The equations of the separate parabolas, with reference 
to the axis of y just constructed, should therefore be 
kf = f — y + ftg, 
ki^—rr)' — h 2 —y + ft£, 
where /q and h 2 are their heights, and ft is the rate of change of height of the 
maxima per millimetre. For the same height y, if £ and are two abscissae, 
<T ) 2 } — h 1 —h 2 +ft(£i—£'i) 
