PHENOMENA RELATING TO THE SPECTRA OF HYDROGEN AND HELIUM. 247 
(2) The probability law, valid for the ordinary discharge. If we take first the 
simple exponential, then before incidence on the wedge, if I is the intensity of the 
central component at A = A,, 
I x /I - e-* (x - Xl) , 
and after incidence, the trace on the final plate is a straight line on either side of the 
central component of height h Xr The height at wave-length A is 
a-aA 
b ! 
from the equation to the straight line, where B is the half breadth on the photograph. 
Substituting this value in the integral, the total energy becomes 
21,10 (D A/ H) I d\ . lO-W K ~ x ' )lbh = -4^ H 
io ( W H 5 
DA, loge 10 
and is therefore proportional to 
(breadth) (photo, intensity)/log 10 (photo, intensity), 
where the breadth of the line on the base of the wedge photograph is implied, and 
the photographic -intensity is that of the central component. It is not difficult to 
prove in a similar manner that when the law of distribution in a line of the original 
light is that of probability, the whole energy in a line is proportional to the quantity 
(breadth) (photo, intensity)/\/Tog (photo, intensity) 
with the same definitions of breadth and intensity as determined from the wedge 
photograph. It is therefore necessary, in obtaining absolute measures of contained 
energy, for comparison along a given spectrum series, to consider the circumstances 
of production of the lines ; but these two cases include those which have at present 
been explicitly recognised, and the effective one can at once be seen by inspection of 
the photographs. 
The dispersion used in the present experiments has, in most cases, not been 
sufficient to overcome the effects of irradiation, which must be reduced to a relatively 
small magnitude in order to determine the true breadth of a line, which is small, at 
the base of the wedge photograph. The quantitative information contained in this 
portion of the paper is, therefore, limited to the maximum intensities of the lines, 
which provide a basis at present sufficient to elucidate the main phenomena, and 
from which the absolute ratio of the energy contents can be determined at any 
subsequent time by measurements of the relative breadths of the lines concerned, with 
a high dispersion, and without the necessity of repeating the present measurements. 
Bqt it is important to notice that the use of the ruled “ process ” screen supplies a very 
g M % 
