PHENOMENA RELATING TO THE SPECTRA OF HYDROGEN AND HELIUM. 241 
Let I c be the intensity at which a line is just photographically visible. Then if its 
photographic intensity in the original light was I A , and if it is reduced to I c by the 
thickness corresponding to a length l K of wedge, we have the relation 
IJI K = 10— p dA tana 
or 
logjo (L/I e ) = p A Z A tana = p K lh K tan a/Ii = DA/H 
by the preceding relations, where D A is the density for this wave-length. Thus 
-1 
gives the photographic intensity of the original line, where D A is the density of the 
wedge, H the height of the wedge on the enlarged photographs, and h K the height of 
the line on the same photograph. The actual degree of enlargement adopted is 
immaterial, and so also, in the estimation of relative photographic intensities of 
different lines, is a knowledge of I c , the intensity just visible photographically. We 
may, therefore, define the photographic intensity of a wave-length X as 
where the notation signifies an anti-logarithm, or the photographic intensities may be 
arranged on any arbitrary scale in which the ratios of this quantity are preserved. 
The subsequent reduction of photographic to absolute intensities will be considered in 
a later section. 
(IV.) The Density of the Wedge as a Function of Wave-length. 
The density gradient of the wedge for different wave-lengths lias been determined 
as follows :—As a primary standard of density we adopted two Nicol prisms, one of 
« 
which could be rotated with respect to the other, the amount of rotation being read 
on a divided circle. These Nicol prisms were mounted in front of the slit of the 
spectrograph, the orientation of the fixed Nicol being such as to polarise the light in the 
same plane as the dispersing prism of the spectrograph. Light from a vacuum tube 
containing Helium passed through the two Nicol prisms and the neutral wedge, and 
an exposure was made for a definite time in the spectrograph, the movable Nicol 
being set in the same plane as the fixed Nicol. The gas in the vacuum tube was at 
a pressure estimated at about one millimetre of mercury, and was excited by means 
of an induction coil with a mercury break. For the comparatively short exposures 
which were involved, the light from this tube may be regarded as effectively constant. 
After the first exposure, a second^exposure was made on an adjacent portion of the 
same plate and for the same time, the movable Nicol being now turned through the 
