74 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



interference pattern was quite absent, while it was clear on the other. This 

 seemed to be particularly the case whenever the component ray did not quite 

 retrace its path, i.e., when the paths through the column were separated; but 

 I have been unable to find a reason for the peculiar result. 



40. Equations. In the earlier papers I showed that the coordinate of a 

 movable opaque mirror N c , varying with the position of the center of the ellip- 

 ses in the spectrum, in case of the displacement micrometer, could be written 



where e is the thickness of the plate of the grating, or other plane parallel 

 glass body interposed in one of the component beams, R the angle of refraction 

 (the corresponding angle of incidence is / for all colors) for the color X and the 

 index of refraction n. If, in addition to the plate of the grating, the column 

 of glass of length E is interposed at normal incidence, R = o, but having the 

 same ju for the same X, 



For an air-column of length E replacing the glass column for the same color 



Hence, 

 (4) 



where the centers of ellipses are brought to the same spectrum line, both for 

 the glass- and for the air-column. Hence, if we write approximately, for 

 brevity, 



(5) 



(6) 



In other words, to measure the index of refraction /x for a given color X, the 

 correction 2EB/\* must be added to the corresponding value of A7V the 

 shift of micrometer, or 



, . AM: - 2EB/P 



(7) M-i- - - 



Again, if for the same column the displacement of the micrometer 5N C = N C 

 N' c , corresponding to different lines of the spectrum, is in question, since 



(8) W.- { (E+* co.J90.-iO- 



the reduced equation becomes 

 (9) 



