OF ARTS AND SCIENCES. 275 



sandths of a niilliniotre to inilliinetivs, and l.y ^ gives the followin.r 



an '^ 



values for tlio dispersion of a GO'' flint jjlass prism. For B, 98 ; for E, 

 242 ; and for G, i>0'^. The correspondii)<r values for a 00° prism filled 

 with bisulphide of carbon are : for B, 140 ; for E, 404 ; and for C, 1 1 ;i;i. 

 Comparing these numbers with those given above for difn-action 

 gratings, we see the superiority of the hitter as regards dispersion, 

 especially at the red end of the spectrum. 



These advantages are, however, in a measure counterbalanced by 

 the greater loss of light. It is shown elsewhere (Am. Jour. Sci. 

 xlv.) that in a spectroscope containing ten 60° prisms the loss of light 

 by reflection would equal 50.9 per cent; so that the transmitted ray 

 would have an intensity of 49.1, the incident ray being taken as 100. 

 This would be further reduced by the loss from absorption, but the 

 amount would vary with the material, the wave length, and the length 

 of path, or size of prisms. Estimating this loss as one half, still leaves 

 the intensity of the whole of the spectrum as 25 per cent of the 

 original beam passing through the slit. In a diffraction spectrum the 

 light is much less; allowing one half for the light lost in the central 

 white image, evidently if we have five spectra on each side, the average 

 amount of light in each cannot exceed five per cent. And even tlfis 

 must be diminished by the loss due to reflection and absorption in the 

 case of glass gratings, and to imperfect reflection in the case of 

 speculum metal or silvered glass. 



The discussion of the effect of the collimator *ind observing telescope 

 on the dispersion involves another consideration ; namely, the size of 

 the image of the slit. To render this clearer, suppose we are observing 

 the sodium spectrum, when a small amount of the metal is present.* We 

 shall then obtain two sharply defined images of the slit separated by an 

 interval dei)endent on the dispersion. These images may overlap, and 

 will vary in width as the slit is open or shut, but their distances apart 

 will not alter. Call w the true width of the slit, W that of its image 

 as seen througli the telescope, and referred to the distance of distinct 



* If much sodium is present, the lines widen and become hazy, and with a 

 large dispersion both appear again double, owing to tlie absorption of the outer 

 layer of sodium vapor. Tliis effect is readily obtained by putting a lump of 

 borax in the flame, wlien at first it gives a bright blaze and shows the four 

 lines ; presently, however, the light becomes feeble, and the usual double line 

 IS alone seen. If now an image of the flame is projected on the slit, the spec- 

 trum of any part of it may be studied, and it will then be found that the central 

 portion only gives the four lines, the edges giving the usual double line. 



