366 Prof. F. L. 0. Wadsworth on the Effect of 



From (18), (19), and (20) we then obtain at once 



1 + -0063(^2) 



which is similar in general form to the expression for the 

 purity of the spectrum with slits of finite width *; 



To find the value of r for which R,3 is a maximum we have 



d „ l-0063(^£,) 2 _, 



dr 



I 



R. = _ v an ' = 0, . . (22) 



or for R j 3=max 





"-= is - 59 l-S« (23) 



and for the corresponding maximum value of R^ 



R /3 (max.)=6-29|.J = i^, . . . (24) 



that is, the maximum practical resolving-power that can be 

 attained with a prism spectroscope is one-half what we could 

 attain with the same spectroscope if there were no absorption. 

 For the flint glass 0*102 which we have been considering, 

 the value of the ratio 



dn 



dX 



for wave-length X=3900 is about 4250. The value of /3 for 

 the same region is, as we have seen, about "37. Hence for 

 this glass we have 



R /3 (max.)= 72000, 



for r m 2T144000. 



The relation between r and R/3, as given by (21), is 

 tabulated in Table II. and plotted in Curve 1 of fig. 3 

 (PI. VIII.). It will be seen that the increase in R/3 is very 

 small (less than 7 per cent, of the maximum) between the 

 points r= 100000 and r m = 144000; and it would therefore 

 in general be inadvisable to go beyond the first point, if we 

 proposed to work in the neighbourhood of the H and K 

 lines with a prism spectroscope of dense flint glass. The 

 theoretical resolving-power of the Bruce instrument for this 



region is about 153000, i -=- (ti — t 2 ) f , and is therefore 

 * See Phil. Mag. vol. xliii. pp. 333-339. 



