1877.] 



Magnifying -power of the Half-prism. 



23 



Taking the case of a single half-prism with fixed collimator and spec- 

 troscope, we may increase the refracting angle (or the angle of refraction 

 for mean rays), and thns obtain much larger dispersion. In comparing 

 the three forms of prism (simple, direct-vision, and ordinary compound), 

 the irrationality was the most important consideration ; but this does not 

 here enter into the question. The direct-vision prism, however, has still 

 the advantage, as compared, with the compound prism, of giving a more 

 convenient form of spectroscope, whilst, as we can now use very deep 

 angles for the flint, the dispersion at the exterior surface of the crown 

 hardly affects the resulting dispersion. 



As compared with a simple half -prism of flint, there is the advantage 

 of being able to make if/ (or the angle of the flint) nearly twice as large, 

 with a corresponding increase in the purity ; for it will be remarked that 

 although the magnifying-power and dispersion may be increased almost 

 indefinitely, there is a limit to the purity given by making i//=the critical 

 angle ; and consequently there will be great advantage in a combination 

 of flint and crown surfaces which increases the critical angle without 

 materially diminishing the dispersive power. 



In illustration of this the following Table may be interesting. It is 

 calculated for a specimen of very dense flint glass (spec. grav. 5*0) of 

 remarkable purity, which Mr. Hilger has procured, and with which he 

 has made to my instructions several experimental direct- vision half- 

 prisms. The refractive indices of this glass for A and H are fx A = 1*7595 

 and //a =1-8411. 









D"=-D"'. 







P. 



m. 



n. 



A. 



o 



70 37 





16 37 



o / 



27 25 



o / 



98 2 





I 43 





54 



1-77 



44 2 



219 



10-3 



55 



72 47 



1-94 



17 47 



28 41 



46 28 



101 28 



243 



4 49 



11-7 



56 



75 10 



2-19 



19 10 



30 8 



49 18 



105 18 



2-89 



4 55 



14-2 



56i 



76 29 



2-36 



19 59 



30 57 



50 56 



107 26 



3-21 



5 1 



16-1 



57 



77 55 



2-61 



20 55 



31 49 



52 44 



109 44 



3-78 



5 7 



19-3 



57* 



79 33 



2-97 



22 3 



32 46 



54 49 



112 19 



4-56 



5 14 



23-8 



58 



81 27 



3-56 



23 27 



33 53 



57 20 



115 20 



5-50 



5 20 



29-4 



58* 



83 49 



4-84 



25 19 



35 13 



60 32 



119 2 



8-35 



5 26 



45-5 



59 



88 



14-76 



29 



37 20 



66 20 



125 20 



29-20 



5 32 



162-6 



