REVERSED AND NON-REVERSED SPECTRA. 79 



To determine the change of altitude per fringe, 



da X-y/V i + cos 2 i cos" a 



(n) ~T = ~ 9 . . 



an e cos 2 1 sin 2 a 



and this is a maximum when a = o; i.e., in the plane of figure 53. In this 

 case equation (2) is reproduced from (10), so that a double maximum occurs 



for a = o and 



X d{i\ 



The other practical datum is the shift of a given fringe per centimeter of 

 displacement of the mirrors. Here n and e are constant while N, X, ^, R vary, 

 so that 



(12) - 2 



dN~ 26 



cos Rd\ 



26 df-l 



This is a maximum when n = n e = - =4^5/X 3 , or when N = N e - In 



cos R d\ 



other words, there is a minimum displacement relative to wave-length shift 

 of fringe at the centers of ellipses. 



Equation (10) is thus inclusive. If i = o, which is nearly the case, experi- 

 mentally, in my work and no restriction on the apparatus, and since a is 

 always very small, equations (10), (u), (12), etc., may be simplified. 

 Hence approximately (i = o) 

 (13) n\ = 2N- 



da X 



(u) J- = ' 



an 2ea 



(15) 2- 



dn 

 (16) 



dN ~ n+2e.d{i/d\ 



where n is the order of the fringe at X for N, e, <w, a. Again, n c 2e.d[i/d\. 

 Equation (13) admits of an interpretation in terms of the approximately 

 elliptic locus found for constant n. The equation may be written, if [J. is 

 treated as a mean constant, 



= 



e 2 



Here e (a/(.i) and X may be regarded as the coordinates of a curve described on 

 the face of the plate of glass toward the observer, so that the equation is an ellipse 

 referred to an eccentric axis of ordinates. The axes of this ellipse are ze[i/n 

 horizontally and e vertically. Of course, the telescope converges all this to a 



