REVERSED AND NON-REVERSED SPECTRA. 



77 



bined ray, the telescope is always the more convenient instrument, since its 

 use is not restricted to definite distances from the system. 



It has been shown that as a whole the above phenomena correspond very 

 closely to the behavior of the ellipses encountered in displacement interferom- 

 etry. Thus the cases of non-reversed spectra, of inverted spectra, etc., if we dis- 

 regard certain exceptional accompaniments for the moment, can be at once so 

 classified. The shift of ellipses behind a narrow slit in an opaque screen and ob- 

 served in front of it, for instance, would exhibit all the rotational occurrences. 



39. Displacement interferometry. Equations. It is thus desirable to ad- 

 duce the equations of displacement interferometry in a somewhat different 

 way, but in the main as taken from my earlier reports. In figure 53, G is a 

 thick plate of glass on which the blade- 

 shaped pencil of white light L from a 

 collimator impinges at an angle i. M 

 and N are the opaque mirrors of a 

 Michelson device. G' is a plate grating 

 by which the white beam R (feeble 

 spectrum) is resolved, P the principal 

 plane of the objective of the telescope, 

 rv the image seen through the ocular. 

 The plate disperses the white light L 

 into the spectrum rv, as shown in the 

 figure. The direct reflection at R' is 

 not used. For convenience in discus- 

 sion the mirror N and its component 

 ray may be rotated 180 around the 

 trace of the grating G as an axis, into 

 the position N f , where IN becomes x-\- 

 x'-\-p+x", intercepted between normals. If perpendiculars be let fall from 

 I to AT or N' and I' to M, their difference of length is 



\ / ' 



N is an important coordinate used throughout, below, since it is indepen- 

 dent of color (X and ju). In (i) i is the angle of incidence, R of refraction 

 of the plate of thickness e and index of refraction /z. 



If we draw the wave-front w, the path-length of the red ray through glass to 

 M, for instance, is en/cos R+p. The path of the ray through air (only) to 

 mirror M is 



x-\-x'+p-\-x" = e cos i-\-e sin i tan R+p+x" 



If sin i=p sin R be introduced, the path-difference thus becomes, after re- 

 duction, 



(2) n\ = 2N 2e/j. cos R 

 or 



(3) X = 2e ( n - cos (i-R) } /cos R 



