Absorption on the Resolving Power of Prism Trains. 357 

 If we retain i as a variable function, 



*'=<K^)> (3) 



but consider the second and third assumptions as correct, we 

 obtain similarly 



(4) 





In the case of the prism spectroscope the aperture of the 

 prism-train is generally rectangular, and if all parts of the beam 

 of light falling on the first prism-face are of uniform intensity, 

 the diminution in the amplitude of vibration due to the 

 absorption of the glass of the train will be uniform along any 

 line parallel to the refracting edge of the prisms. Along 

 any line at right angles to this the change will be expressed by 

 the law 



i=i e-l^ (5) 



where i and i are the amplitudes of vibration of the ray after 

 traversing thicknesses of / and / centimetres of glass, and /3 

 is the coefficient of absorption. 



If we choose the two lines just defined as the axes of y 

 and x respectively we have for ${xy) in (3) 



<$>(osy) = i Q e~~ B * (6) 



since the length of path, l — l , through any given point in 

 the prism-train is directly proportional to x, the distance of 

 that point from the central ray. 



The functin oe~ Bx is independent of y, and, for a rectangular 

 aperture, the limits of integration for y in both terms of (4) 

 are constant. Hence we obtain at once for the distribution 

 in intensity along the axis of £ in the focal plane 



T 2 v^tH r . ^ 7 T , >;x 2 rf + ^ v 27r S , 1 



For convenience put 



= ^kc 2 -hS*] (7) 



^-k. 



Phil. Maa. S. (i. Vol. 5. No. 27. March 1903. 



