Absorption on the Resolving Poiver of Prism Trains. 371 



Bb (or /3) and w, the apparent " width," the following values 

 (from Table I. and fig. 1) : — 



For Bb = 000 w = m m =2'00a , 

 Bb = *575 w =2 , 04a > 



Bb = 1*386 iv = mii))i = 2'16ct 0j 

 B&=2'197 w =3'66« , 



Bb = 2'77 w = m 2 m 2 — 4:'8aQ, 

 B/> = 4*61 ii' = 7n 3 m^^7'6oc , 

 B6 = 7-83 w; ^13-5« - 



The apparent width of the line for the last value of Bb is 

 therefore nearly seven times as great as the theoretical width, 

 2a , for zero absorption. This large increase in w, together 

 with the accompanying reduction in the practical resolving- 

 power, R^, is quite sufficient to explain the apparent haziness 

 and lack of definition frequently observed in certain portions 

 of a spectrum formed by prisms with strong selective 

 absorption. 



The effect of absorption on the form and distribution in 

 intensity in the spectral image, and hence on the resolving- 

 power of the prism-train, may be entirely eliminated by 

 mechanical diaphragming of the prism aperture. By referring 

 to equation (7) we see that the form of the expression for F 

 is the same as would be obtained if the illumination were 

 uniform over the wave-front, and the latter were limited by 

 an aperture whose length (along the x axis) is b, as before, 

 but whose width at any point is the ordinate to the exponential 

 curve 



y = ae~ Bx (25) 



If, therefore, we limit the aperture of the prism-train by a 

 diaphragm whose width is y~ Y , the illumination remaining 

 .the same as in (7), we obtain for the distribution in intensity 

 in the image of the spectral line 



2 _zV 





pa" 2tt£ -] -2 



'-! v J 



. + b 



\ * e -Bx e Bx cos % x ( { x 1 



,7TfA 



• 9 9 r- /"* o \ «- — i •> • o til Sill" 



i V f ( 2 2tt£ 1 - i -arb- \f 



(fj 



