[ 39 ] 



VIII. On the comparative Efficiency of different Forms of the 

 Spectroscope. By Edward C. Pickering*. 



IT is the object of the present paper to furnish a means of 

 comparing with accuracy spectroscope prisms of different 

 forms, and to determine what must be their refracting angle to 

 produce the greatest dispersion with the least loss of light. We 

 have then to consider the dispersion, the loss by reflection, and 

 that by absorption. 



1. Dispersion. — 'The dis- 

 persion of any part of the 

 spectrum is proportional to 

 the angular interval between 

 two rays of nearly equal re- 

 frangibility as the two parts 

 of a double line. 



Let a be the refracting- 

 angle of the prism ABC, 

 n the index of refraction of 

 the less refrangible ray. For minimum deviation, 



IV 



7'= - smz = ft sin^. 



(1) 



If dn be the difference of the indices of refraction of the two 

 rays, di will be their angular divergence. Differentiating (1), 



sin - | 



% dn == - tan i dn, 



cos i n 



(2) 



in which -tani serves as a measure of the dispersion under dif- 

 ferent angles of incidence. It differs essentially (when the angle 

 of incidence is large), from the deviation, which is commonly, but 

 incorrectly, assumed as the measure. 



Comparative Dispersion and Deviation of a Ray entering a me- 

 dium in which 71= 1*5. 



Angle of inci- 1 



dence i J 



Dispersion 1 



- tan i ... [ 



0° 



•0 



15° 



•179 



30° 

 •385 



45° 

 •667 



56° 19' 

 1000 



60° 

 1-1565 



75° 

 2-488 



80° 

 3-781 



85° 

 7-620 



90° 



GO 



Deviation i—r... 

 Deviation re-1 



: 



5° 4' 



10° 32' 



16° 53' 



22° 38' 



24° 44' 



34° 55' 



38° 58' 



43° 23' 



48° 11' 



duced to same 1 

 unitasdisper- f 

 sion J 



■0 



•231 



•465 



•746 



1-000 



1-093 



1-543 



1-720 



1-917 



2-121 





* From the American Journal of Science and Arts, vol. xlv. (May 1868). 

 Communicated by the Author. 



