240 
DB. T. B. MERTON AND PROF. J. W. NICHOLSON ON 
the region corresponding to the dense end. Thus the lengths of the lines on the 
plate correspond to their intensities, and it is necessary in the first place to obtain 
accurate measurements of the lengths of all the lines under consideration. This is 
accomplished most conveniently by preparing positives from the negatives and 
enlarging the positives on to bromide paper through a ruled “ process ” screen. This 
method provides an enlarged negative in which the lines are made up of minute dots, 
one hundredth of an inch apart, and the length of any line can be determined by 
pricking out the last visible dot, which is a perfectly definite and well-defined point, 
whereas in enlargements made without the “ process ” screen the determination of 
the “ end of the line ” is subject to a considerable amount of personal error. We 
believe that with the use of the “ process ” screen, personal error is almost entirely 
eliminated. We may now consider the method by which the lengths of the 
photographed lines may be used in the determination of an actual relative intensity 
scale. As a preliminary, a precise knowledge of the constants relating to the wedge 
must be obtained. 
(III.) Determination of the Photographic Intensities of Lines. 
The wedge employed was made of the so-called “neutral-glass” which shows no 
absorption of a selective character, but in which there is an increase of absorbing 
power with decreasing wave-length. If an incident intensity I 0 falls on such a wedge 
at any point, and if I is the intensity transmitted, the density at that point is 
defined as the value of — log 10 (I/I 0 ). The theory of the wedge is briefly as follows, 
and indicates the necessary account to be taken of the enlargement of the 
photographs, and the fact that the density so defined is the most convenient form of 
specification for future calculations. 
If p K is the “ coefficient of extinction ” of the glass for light of wave-length X, it is 
such that light of intensity I } , falling on a thickness y of glass, is reduced during 
transmission to I 2 , where 
I 2 = Ije-^A 
this law being equivalent to an exponential one. If a is the angle of the wedge, and 
x the distance from the thin end, y = x tan a and the complete length of wedge 
being l, the intensity ratio for the complete wedge is 
F/I, - e- p W an “ 
being the ratio of transmitted light at its ends, for the same incident intensity. 
The “ density ” is, therefore, — log 10 (L/F) or l tan a . y K and will be denoted by for 
this particular wave-length. 
If 4 is the visible length of a line before enlargement, the visible length after 
enlargement is h A or 4 H/4 where H is the length of the wedge after enlargement. 
For the magnification is equally A/4 and H /l. 
