in Spectrum-analysis, and Distortion of the Spectrum. 365 



the prism are there refracted, and a portion of them pass down 

 another telescope, and are brought to the vertical wire of its eye- 

 piece. By moving either the telescope by which the rays are 

 viewed, or the position of the prism, all the different lines of 

 the spectrum can be seen in succession. In the first case the 

 changes in the refrangibility of the rays and the requisite angular 

 motion of the telescope are nearly proportional ; in the second 

 case, in which the prism is moved, it will be found that the 

 angular changes in the position of the prism are by no means 

 proportional to the changes in the indices of refraction of the 

 rays corresponding to those positions. 



The following investigation arose from a suggestion I made in 

 the summer to Mr. Becker, that the readings on the graduated 

 arc should be either the refractive indices of the lines corre- 

 sponding, or should, give the principal lines of the solar spectrum. 

 Mr. Becker then requested me to examine how the scale might 

 be so graduated. 



1. Let ABC be a prism whose 

 angle is a ; D E a ray from the slit 

 of the first telescope; <£, </>', i/r', i|r 

 the angles of incidence and refrac- \£r 



tion at the first and second surfaces 

 of the prism; fi E the index of re- // x 



fraction for the line E ; D the devia- 

 tion for the line whose index is p,. A. £ — — " — X B 

 Then 



sin <£>=/£ sin <£' (1) 



sini|r=:yu,sini/r' (2) 



</>' + t-« ( 3 ) 



D = (£ + "</r-a ...... (4) 



Let the angle between the telescopes, or the deviation, be fixed 

 by the condition that the line X shall have a minimum deviation. 

 Then 



and 



D = 2sin -1 (/i X sin-j — «. 



The direction of DE being fixed, an angular change in the 

 position of the prism is equivalent to a change in <£. It is 

 required therefore to investigate a relation between p and <f> 

 when the total deviation is fixed. 



