PHENOMENA RELATING TO THE SPECTRA OP HYDROGEN AND HELIUM. 249 
effect as affected by the wedge can be thrown on the same plate with a series spectrum 
under the same conditions. 
In order to determine from this plate the relative maxima of energy-density, or the 
relative central intensities of the lines in the series spectrum, as in (l), we apply the 
formula 
(photo, intensity of line) (absolute intensity of arc)/(photo. intensity of arc) 
for each wave-length. The dispersion factor enters into the absolute intensity of the 
arc, but into neither of the other quantities concerned. The relative central 
intensities are proportional to the results thus calculated. 
But in order to determine the relative energy-contents of the lines, as in (2), we 
must use the formula, where n = T or 1, 
(breadth of line) (photo, intensity of line) (absolute intensity of arc) 
(photo, intensity of arc) (log of photo, intensity of line)" 
which is the formula already deduced in this section, with the variable I c removed by 
substitution of absolute intensity divided by photographic intensity in the arc, to 
which it is proportional. The dispersion ratio automatically cancels from the 
formula in this second case, as in fact it should in the present method whenever two 
magnitudes at the same wave-length, which involve a consideration of a range dx in 
the neighbourhood of this wave-length, are to be compared. 
«■" (VII.) The Helium Spectrum under Different Conditions. 
One of the most interesting applications of the preceding theory does not involve 
the carbon arc, and consists of the examination of the relative behaviour of Helium 
lines under different conditions of excitation. In this case, we are not concerned with 
the intensity of one line in a spectrum relatively to the others, but with the changes 
of intensity of one line under different conditions relatively to those in other lines 
under the same conditions. Some interesting results in this connection have been 
obtained, and it is perhaps convenient to give some account of them before proceeding 
to the comparative intensities along the whole spectrum at any one time. The 
dispersion does not enter into the question in this case, when the lines are produced 
in the same manner on the same plate, and the ratio of the central intensities of any 
line from the two sources is the ratio of the photographic intensities which it shows, 
the photographic intensity being again log ]0 1 
m 
, where h k is the height of the 
line, D a the density of the wedge at the particular wave-length, and H the height of 
the wedge on the enlarged photograph. 
In the following table are exhibited the results and intermediate steps in one 
important case—the ordinary Helium spectrum and the spectrum as given by the bulb. 
In each case, H was equal to 34'0 mm. 
