Absorption on the Resolving Power of Prism Trains, 365 



particularly it* a denser glass than 0'102 is used. Prism 

 spectroscopes have been constructed having an aperture of 

 from 2*2 cms. to 2'b cms., and prism-trains of from 10 to 

 13 dense flint prisms'*. These prism-trains have been 

 constructed of very dense flint-glass whose coefficients of 

 absorption are probably considerably higher than those for 

 0*102, which is unusually white and transparent. Assume 

 the coefficients to be only 33 per cent. (1/3) larger. Then, 

 since the ratio B6-=-/3 is roughly only one-half as large for 

 the Bruce instrument as for the Young and Grubb instru- 

 ments, we have for the latter : 

 In the visible spectrum 



feri'OO ff = 1-025 a . 



In the photographic region 



\=4300 B6~ 3-7 a= 1-35 * 

 \=3900 B/Q20-0 (7=11-0 a . 



In this last case the resolving-power of the spectroscope is 

 reduced more than 90 per cent, by absorption in the neigh- 

 bourhood of the H and K lines. 



It is evident from these results that it is useless to increase 

 the theoretical resolving-power r of our prism spectroscopes 

 beyond a certain point. For every value of /3 there will be 

 a certain limiting value of « , and hence of r, for which the 

 practical resolving-power of the instrument as affected by 

 absorption (which we will call R/3) will be a maximum. To 

 find this value we must transform equations (18) and (19) so 

 that all variables are expressed in terms of r and R^. 



From the well-known relation 





m A. 



ceo AX, 



we have obviously 







Efyj _ «o 





r ~ <x 



We have also the relation 



m 



sin <f>/2 r d\ f 

 Vl-^sin 2 </)/2 = 2' dn 



(20) 



* Young, ' Nature,' vol. iii. p. 110 ; Grubb, Monthly Notices R. A. S. 

 vol. xxxi. pp. 36-38. 



t See Astrophysical Journal, vol. i. p. 55 (189r>). 



