150 PROCEEDINGS OF THE AMERICAN ACADEMY 



and using the same coating through all the experiments ; so that such 

 error as may have been introduced only entered in its differences. 



The superposition upon the spectrum of the reflection from the 

 back of the prism causes a considerable error. This was cut off by a 

 screen of card-board. 



There is another source of error, pointed out to me by Dr. Hastings, 

 which fortunately was sufficiently small to be neglected here, but 

 which may prove to be of considerable magnitude in differently 

 arranged or in more delicate experiments. 



If the prism be, as is usually the case, and as was the case in these 

 experiments, one having equal angles, the part of the ray interiorly 

 reflected from the second surface upon which the light strikes will be 

 reflected again from the back and from the first side of the prism, and 

 when it comes out of the prism will form an undispersed image super- 

 imposed upon the spectrum. 



If the two angles at the back of the prism be denoted by y3 and y, 

 we have as follows : 



Deviation after first interior reflection = = tt — 2 i 

 " " second " " = 0, = tc — 2 i, 



" " third « " =6 u — - ir — 2i ll 



Total deviation = A = 2(9 = 37r — 2 2* 



Suppose i = s- — /3 -\- 6, 



then %, = 2 /3 — | — 0, 



and i u = y — 2 + \ + 6 



A = 2tt — 2 (/? — y ) — 2 6. 



Suppose ft = y, and = 0, then A = 2 ir, that is, an image of the 

 slit is formed on the screen at a point where the ray has minimum 

 deviation. 



For a ray of different refrangibility 



= f- { /3 = y} ±e > 



and 



A = 2 77 qp 2 6. 



Hence an image formed by two refractions and three internal reflec- 

 tions is undispersed. 



