[dawes] dispersion BY INTERFERENCE METHOD 291 



,, Dcos a T sin (a — b) 



Hence na= — : ^— 



X X sin b 



Since a, b, are small and sin a = ii sin b the value of w^ approximates 

 to 



or „.=„„-^_|P+r(l--l)} (3) 



Hence X«.=Z3- F^- 1) - (^J 1 Jd+T (^I - ^) | 



expresses the relation between y and the wave-length for any selected 

 value of Ua 



and X„„=Z,-nM-l)-(}^y |{z>+r(l- 1)} 



the relation between x and y. 



(3) shows that n^ diminishes as a increases at any selected wave- 

 length so that, as regards the partial variation of n with y, n is a 

 maximum when y is zero, the central point of the fringe system is, 

 therefore, a maximum for variations in both X and y. The locus of 

 the fringe of any order w is a closed curve and the fringe system forms 

 a family of curves enclosing the central point. The photographs 

 show only a few complete curves, but if the spectrum were sufficiently 

 widened the complete system might be shown. 



Calibration of Spectrograph 



8. The arrangement may be readily adapted to calibrate the 

 spectrograph, forming, in fact, a modification of the well-known method 

 of Edser and Butler. If the plate G is removed the spectrograph slit 

 will be illuminated by light in which successive constituents are 

 interference maxima and minima. The number of wave-lengths in 

 the difference of path becomes simply D/\. The spectrum will show 

 a series of fringes of orders n-\-l, n-^2, . . . from X toward the 

 violet end and w— 1, w — 2, . . . toward the red end. The wave- 

 length at each such fringe is, therefore, obtained by dividing D by 

 the number of the corresponding order. 



Plate 9 shows a spectragram used for calibration. For it D is 

 .03770 cm. and n for the Di line 639. 3. The total number of fringes 

 measurable on the negative is 319 so that this negative yields a very 

 close calibration. From the comparator readings a large scale 



