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 Iog 10 f ^j where I and I t 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 D x 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 



i i /DA\ 



log* (-^) 



where h x and H were the heights of the line, and of the wedge, on the enlarged 

 photograph. If h is the height of the wedge on the original plate, and m is the 



magnification, 



H = mil. 



Let D A //t = d K , 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 



by 



lo gl 



-> 



m 



The height of the line on the enlargement is h x and on the original plate before 

 magnification, is // x /m. 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 cZ A 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. 



