_142 
DE. T. E. MEETON AND PEOF. J. W. NICHOLSON ON 
the same plate, ensuring a valid basis for the comparison, and pass simultaneously 
through all the subsequent stages of the process. 
It has been found most convenient to deduce the photographic intensities in the follow¬ 
ing manner, the theory of which has been given in some detail in a previous paper,"^ 
though circumstances have slightly modified the method in the present instance. We 
define the “ density ” of the wedge at any point as—logjo^^) where Iq and Ii are re¬ 
spectively the intensities of the incident and transmitted rays. This density is 
proportional to the length measured from the thin end, and the density at the thick 
end was denoted by in the former paper, the suffix X relating to the particular 
wave-length in question. The photographic intensity of a line was proportional to 
the function 
where hj, and H were the heights of the line, and of the wedge, on the enlarged 
photograph. If Ji is the height of the wedge on the original plate, and m is the 
magnification, 
H = mh. 
Let Djh — dx, the change of density of the wedge per millimetre or its density 
gradient. Then the photographic intensity of a line of wave-length X is measured 
The height of the line on the enlargement is and on the original plate before 
magnification, is hxlm,. The magnification m can be found at once if the interval 
between any two lines, such as XX 6678 and 3888, is known both on the original plate 
and on the magnified photograph. 
A precise knowledge of the values of at various typical points in the region of 
the spectrum under investigation is required or, in. other words, the wedge must be 
calibrated. The wedge used in the present experiments was of somewhat more 
convenient dimensions than that employed in our previous investigation, and an 
improved method of calibrating it has been adopted. 
For this purpose, a vacuum tube containing Helium was excited to luminosity by 
means of the- induction coil with a mercury jet interrupter, and the capillary of the 
tube was brought to a focus of the slit of the spectrograph, with the wedge in 
position, by means of two convex lenses. The distance of the tube from the slit, and 
the positions of the lenses, were so adjusted that the distances between the capillary 
and the first lens, and between the second lens and the slit, were equal respectively 
* Loc. cit. 
