Absorption of Light by the Goldberg Wedge. Ill 



If i/i and y a are the distances on the plate corresponding 

 to t \\ and x 2 on the wedge, then 



(.'/i-i/2)/0''i-.'- 2 )=M i , (2) 



where M A is the magnification produced by the optical 

 system of the spectroscope at wave-length X. 

 " Whence from (1) and (2) 



„log 10 Ii/I, (3) 



Kyi—yz) 



The magnification is obtained by placing an opaque object 

 of known length across the jaws of the spectroscope and 

 comparing the length, at different wave-lengths, of the image 

 obtained on the plate. If, now, y 1 and y 2 can be determined 

 from the plate, A A can be calculated. Now, y x and y 3 are 

 simply the distances from an arbitrary point, such as the 

 image of the end of the slit, along any one line to any two 

 points of equal density (intermediate between zero and 

 maximum density), and can readily be measured in the 

 following way. Fig. 2 (PL XVII.) is a positive printed from 

 one of the original spectrographs. It will be noticed that 

 the change from black to white along any one line is very 

 gradual. The steepness of this change will, of course, 

 depend on the gradation of the wedge and the kind of plate 

 used. The distances y x and y 2 will be approximately as 

 indicated in fig. 2. If a succession of transparencies of 

 this spectrograph are now made, the change from black to 

 white will be made sharper with each reproduction. 



Fig. 3 (PL XVII.) shows the " second" positive obtained 

 from the same original spectrograph by three reproductions. 

 The change from black to white is now practically a sharp 

 line, and coincides with the point of half maximum density ,, 

 or any other density intermediate between the maximum 

 and zero. The distances y i and y 2 can now be measured 

 directly by means of the travelling microscope. In fig. 3 

 it will be noticed that towards the end of longer wave- 

 lengths some of the lines (e. g. E, K, and M) are suf- 

 ficiently intense to cause blackening over the whole length 

 of the slit. These, of course, cannot be used for making 

 measurements, but on each photograph wave-lengths can be 

 selected at which the intensity is such that y 1 and y 2 are 

 both of suitable length, with the ends well clear of the end 

 of the slit. For example, lines A, B, 0, D, F, Gr, H, and L 

 were used in this case. The wave-lengths of the various 

 lines can always be ascertained at once by reference to a 

 standard spectrograph. 



The value of (t/i—yz) at any given wave-length for a given 

 Phil. Mag. S. 6. Vol. 40. No. 240. Dec. 1920. 3 E 



