Interference Methods to Spectroscopic Measurements. 345 



determine the position of the brighter portion by gradually 

 increasing the difference in path from zero. If the fringes 

 are thereby displaced in the positive sense from the position 

 calculated from the mean wave-length, then the brighter edge 

 lies toward the violet. 



If the line is a double, the displacement relatively to the 

 position calculated from the brighter source is given by the 

 formula 



sm27r M 

 tan 2?™= 



r+ COSZ7TjT| 



in which n is the displacement in the fractions of a wave, Nis 

 the number of waves in the difference in path, M is the number 

 of waves between two successive minima of distinctness, and r 

 is the ratio of the intensities. 



The cases discussed in the preceding work are illustrated 

 by the figures in Plate VII., which give the function repre- 

 senting the distribution of light in a spectral line together 

 with its corresponding visibility-curve *. 



The equation for the visibility of the interference-fringes 

 has been somewhat arbitrarily assumed to be the ratio of the 

 sum to the difference of the intensities of the bright and dark 

 fringes ; that is, 



v={^ (1) 



i-l-r-i-2 

 If we assume that the visibility is the greatest value of 

 __dl 

 d<f> 



K^ + hf 



(2) 



and also that the intensity of the fringes may be represented 

 I=H+Kcos<k 



* The value of V as deduced, from the general formula is necessarily 

 positive ; so that there are no reversals of the fringes. There will be, 

 however, a change of phase, which is given by the formula 



In the case of asymmetrical function this change may behalf a period; 

 and it would not be incorrect to draw the corresponding parts of the 

 curve below the axis. 



