of different Forms of the Spectroscope. 



41 



the logarithm of this distance, or to log N x BC sin J a, or in 

 prisms admitting the same amount of light (that is, in which ED 



is the same) to lo£ BD x N 



sin 



COS I 



1 



', since BC 



BD 



cosz 



; but the dis- 



persion is proportional to N ^- ; hence in spectroscopes dis- 

 persing equally, and composed of prisms of the same material, 

 the loss by absorption ivill be the same in all-, so that, as far 

 as the absorption is concerned, it makes no difference whether 

 a spectroscope is composed of a large number of very acute- 

 angled prisms, or of a less number in which the angle is more 

 obtuse. 



Thus we avoid the difficulty which seemed at first sight in- 

 surmountable, since the actual amount of light absorbed varies 

 not only with the material, but with the refrangibility of the 

 rays, and according to laws not yet discovered. 



The following Tables give the deviation, dispersion, and 

 amount of light escaping reflection, of spectroscopes composed 

 of from one to ten prisms of indices of refraction 1*5, 1*6, 

 and 1*7. 



Table I. applies to prisms of 45°, Table II. to those of 60° 

 (these being the forms in general use), and Table III. where the 

 angle is such that the reflected light would be totally polarized 

 (a being 67° 22', 64°, and 60° 56' in the three cases respectively). 

 This form of prism appears to present great advantages for large 

 spectroscopes, since at most but one-half of the light can be 

 reflected, while one prism disperses as much as two of 45°. 



Table 1.-45° Prisms. 





n. 



1 sur- 



1 



2 



3 



4 



5 



10 





face. 



prism. 



prisms. 



prisms. 



prisms. 



prisms. 



prisms. 



Deviation f 



. a \ 



'-* -I 



1-5 

 1-6 

 17 



12° 32' 

 15° 15' 



18° 5' 



25° 4' 

 30° 30' 

 36° 10' 



50° 8' 

 61° 0' 



72° 20' 



75° 12' 



91° 30' 



108° 30' 



100° 16' 

 122° 0' 

 144° 40' 



125° 20' 

 152° 30' 



180° 50' 



250° 40' 

 305° 0' 

 361° 40' 



Dispersion r 

 . a 

 Sm 2 1 



1-5 

 1-6 

 17 



•467 

 •484 

 •504 



•935 



•968 

 1-008 



1-870 

 1-936 

 2-016 



2-804 

 2-904 

 3-023 



3-739 



3-872 

 4 031 



4674 

 4-840 

 5-039 



9-348 



9-680 



10078 



cos i '" - 

 Transmitted f 



+ (1-B')'»] I 



1-5 

 1-6 

 17 



•957 

 •943 

 •926 



•916 



•892 

 •859 



•841 

 799 

 745 



774 

 719 

 •653 



724 



•651 

 •578 



•661 

 •592 

 •516 



•461 

 •391 

 •324 



