PHENOMENA RELATING TO THE SPECTRA OF HYDROGEN AND HELIUM. 24.1 
f(\)Bdx/(x+x 0 ) 2 within a distance dx centimetres, the apparent intensity at the 
point x being Bf{\)l(x + x^) 2 . It is this law of intensity distribution on which the 
law of action of the wedge is actually superposed. ‘ The expression is equivalent to 
/(x)(\-x 0 )VB 
being the energy within a distance dx centimetres. After magnification in, this is 
spread over m dx centimetres, but as the magnification is the same for all regions of 
the spectrum, the intensity ratio on the plate for two wave-lengths \ x and X 2 is 
/(X 1 )(X 1 -X 0 ) 3 //(X 2 )(X a -X 0 ) a 
where both m and B disappear. The true relative intensities of the carbon arc at \ x 
and X 2 affecting the plate are, therefore, obtained by multiplying the entries in the 
preceding table for X = Xj and X = X 2 , T = 3750° C. absolute, respectively by 
(Xi — X 0 ) 2 and (X 2 —X 0 ) 2 . 
The actual approximate law of dispersion for the plate used in the case of the 
carbon arc was 
X = 2257'5-t 
116802-9 
x - 
• Xq 
so that X 0 = 2257"5. But for X close to X 0 , a better approximation is obtained by 
direct comparison of a prepared wave-length scale, which fits the lines, with an 
ordinary millimetre scale. 
Again taking X3888 as the standard of reference, the following table has been 
constructed for the absolute relative intensities in the arc with which the individual 
lines in the Helium spectrum must be compared :— 
Table of Absolute Relative Intensities (Energy Densities) of Carbon Arc on the 
Plate. 
X. 
Ratio to X3888 
(Wien’s law). » 
Ratio corrected 
for dispersion. 
X. 
Ratio to A3888 
(Wien’s law). 
Ratio corrected 
for dispersion. 
7065 
4 
347 
28-98 
4472 
1-810 
3-02 
6678 
4 
200 
28-00 
4438 
1-761 
2-73 
5876 
3 
623 
16-10 
4388 
1-688 
2-56 
5047 
2 
639 
7-04 
4144 
1-339 
1-73 
5015 
2 
595 
6-92 
4121 
1 • 308 
1-61 
4922 
2 
464 
6-08 
4026 
1-178 
1-31 
4713 
2 
148 
4-475 
3965 
1 ■ 098 
1-17 
It is evident that no correction for dispersion is required in the case of individual 
lines in a series spectrum, the preceding investigation being only necessary in the 
case of continuous spectra. For the energy in the line spectrum is confined to narrow 
2 M 
YOL CCXVII.—A. 
