OF ARTS AND SCIENCES. 273 



X. — COMPARISON OF PRISMATIC AND DIFFRACTION 



SPECTRA. 



By Professor E. C. Pickering. 



Presented, June 9, 1875. 



The object of the present communication is to afford a means of 

 comparing the advantages of the two metliods commonly employed for 

 producing spectra, by diffraction gratings and by prisms. Two ques- 

 tions at once present themselves, the comparative length or dispersion, 

 and the comparative brightness of the spectra. In adopting a standard 

 of comjiarison, it is evidently necessary to select an absolute unit, 

 which shall be wholly independent of the instrument employed, and 

 defined entirely by the ordinary units of distance and direction. In 

 comparing the two kinds of spectra, since an observing telescope and 

 collimator are employed in both, it will be best first to compare the 

 effect of the prisms and gratings alone, and then see how far both are 

 affected by the telescopes. In the case of a diffraction grating, if i is 

 the angle of incidence, r the angle of reflection, D the distance between 

 the lines, ). the wave length, and n the order of the spectrum, these 

 four quantities must be connected by the relation nX = D (sin i -\- 

 sin r). The dispersion or angular deviation of two rays whose wave 

 length differs by dl is found by differentiating r with regard to )., 

 recollecting that ^ being constant, its differential equals zero. We 



thus obtain nd). = D cos rdr. or '- := — ^ If now the grating is 



dl D cos r 9 o 



placed at right angles to the observing telescope, as in.Meyerstein's 

 spectrometer, the dispersion takes the very simple form ^, or is inde- 

 pendent of the angle of incidence and of the wave length, and hence is 

 uniform throughout, and is simply proportional to the order of the 

 spectrum, and inversely as the distance between the lines. This 

 position has the further advantage that it gives a minimum of disper- 

 sion, and that consequently a slight error in setting is unimportant. 



If N is the number of lines per millimetre, or equals — , the dispersion 



assumes the still simpler form nN. This, then, forms the proper terra 

 of comparison for diffraction gratings, or the length of any minute 

 portion of the spectrum will be proportional to its order, and to the 

 number of lines j^er millimetre. 



VOL. XI. (n. s. hi.) 18 



