REVERSED AND NON-REVERSED SPECTRA. 



117 



is in a measure not unexpected, because the amount of displacement, caet. 

 far. (i.e., the mobility and size of ellipses), increases in marked degree as the 

 plate compensator is thinner. But apart from this Ah is in some way, yet 

 to be stated, associated with the obliquity of rays in a vertical plane. 



In case of the rotating compensator, vertical and lateral displacement of 

 centers of ellipses go together. It is therefore next in order to determine the 

 ratio of vertical and lateral displacement. 



The equation deduced in 8, which follows easily from figure 77, may be 

 put in the form (for a single passage of light through the plate) 



n\ = 2e(sm*i/2 p sin 2 r/2) 

 or into the approximate form for small angles 



From the former equation 



or approximately, again, 



di 



dn e(sin i cos i tan r) 



_di 

 dn 



Hence, if Ai corresponds to x fringes, 



. di \n 



Ai=x~ = x ~TT~ ~ 

 dn e^(|J: i) 



roughly 



Again, for the corresponding normal displacement AN of the micrometer at 

 the opaque mirror, 



x\ = 2 AN cos 6 

 Hence 



ei(u. i)Ai 2 AN cos 6 

 x=^- = - 



The data given in table 3 1 were found from successive positions of the plate 

 = 0.705 cm., while the center of ellipses moved as in figure 78, at the D line. 



TABLE 31. 



In view of the small values of AN and Ai and the estimated /* and 0, the 

 two sets of values of x are no more divergent than would be expected. The 



