274 PROCEEDINGS OF THE AMERICAN ACADEMY 



As an example, the grating that Angstrom employed in most of his 

 measurements contained about 133 lines to the millimetre; and, as he 

 commonly observed the fifth or sixth spectrum, his dispersion equalled 

 G65 or 798. The admirable gratings of Mr. Rutherford contain 6480, 

 8640, 12,960, and 17,280 lines to an inch, or 255, 340, 510, and 680 

 lines to a millimetre. Accordingly the fifth spectrum of the 8640 

 grating would have a dispersion of 1700. 



The case of refraction is a little more complex. As shown else- 

 where (Proc. Am. Ai-ad. vii. 478), when a beam of light, having an 

 index of refraction n, passes through a prism having an angle a, we 



shall have the relation —^= — , in which i\ and ,7-2 ai'e the 



dn cos i\ cos ?2 



angles of refraction after passing the first and second surfaces. For 



the position of minimum of deviation, r^ = r^ = ^ a, and in this case 



di\, 2 sin i a 2 • tc • i *.i nr\o 



— - =z — = - tang ^. It, as is commonly the case, a = 00 , 



dn COS I n 



dr^ . -r, , . . dr '^^' , , • 1 



^=secz. rJut this gives y' whue we want ,^ wlucn may be ob- 

 tained by multiplying by -^. The latter may be deduced from Cau- 



dA 



Ti C fl 



chy's formula, ?^ = ^ -[- _ -j- -. Differentiating this equation, ~^=. — 



A- \* dk 



__ _ — ,and multiplying by ^, gives -^ = ^ tang x \B^ -^j, 



or for a 60° prism — :L^ iB ■\- x-) sec ^. 



The substances most commonly used for spectroscope prisms are 

 flint glass and bisulphide of carbon. The indices of refraction of the 

 first of these varies very greatly with the composition, and that of the 

 second with the temperature. The lines B, E^ and G are selected as 

 sliowing the effects of the ends and central portion of the spectrum. 

 The indices for flint glass are those given by Fraunhofer for the 

 specimen No. 23, and equal 1.62775, 1.64202, and 1.66028. For the 

 bisulphide of carbon the temperature of 11°5 C. is employed, and the 

 indices 1.6207, 1.6465, and 1.6886. These values give for the flint 

 glass, 7i= .00789 and (7= .000307. The corresponding values for 

 the bisulphide are, i? = .00614 and C= ,001972, the wave lengths 

 being expressed in thousandths of a millimetre. F'rom these we may 



compute the three values of — for flint crlass to be .0568, .1381, and 



.2804; and for bisulphide of carbon, .0818, 12293, and .6073. And 

 finally multiplying tiiese values by 1000 to change the unit from thou- 



