Absorption on the Resolving Power of Prism Trains. 373 



For the same case considered before for which Bb is 6' 59, 

 we have 



T 3 



Fin all)', for the ratio between the intensities with and 

 without a diaphragm we have from (30) and (32), 



I 2 e Bb + e- B6 -2 



which gives us for the Bruce instrument in the H region 



(33) 



e t c ~: — a 



:uce instrument in the H regions 

 ^| IT '0001 (33 a) 



The curve bounding the edges of the diaphragm for any 

 given case is given by the equation [see (25) and (29)], 



+jMT , sin ?/ 2 -(x-L) 



y=±e ^i-^ 2 sin2(p/2 v 2 \ . ( , (34) 



For the above case 



R • sin»/2 = 



v / l-« 2 sin 2 </)/2 

 b =5-1. 



If with these values of b and B we make d — b and compute 

 y for different values of &, we shall find the form of the 

 required diaphragm to be that shown in fig. 4 (PL VIII.). 

 The widths at the two ends are 0'008 cm, and 5'1 cms. respec- 

 tively, with the wide end toward the base of the prism. 



When so placed this diaphragm will entirely eliminate the 

 effect of the variable absorption, but only, as indicated by 

 (33) and (33 a), at a very large sacrifice of intensity of 

 illumination. This device can therefore be used only when 

 we have abundance of light. In other cases the only means 

 we have of reducing the effect of absorption for any given 

 material is to decrease the resolving-power of the prism- train 

 either by reducing the aperture or the number of prisms. 

 or both. 



General Conclusion. 



The results of the preceding investigation show that in the 

 case of prismatic spectroscopes we are confined to certain 

 resolving-powers. We are limited in one direction by the 

 physical properties of the glass now at our disposal, in another 

 by the difficulty, we might almost say impracticability, of ob- 

 taining blocks of crystalline minerals of larger than a certain 

 size, and in a third by lack of sufficient illumination. 



Phil. Mag. S. 6. Vol. 5. No. 27. March 1903. 2 C 



