78 THE INTERFEROMETRY OF 



the first equation being more practical. N, therefore, is the differences in 

 distances of the extremities I, I' of the normal n at the point of impact / 

 from the mirrors N and M respectively; x" is the air-distance apart of the 

 two mirrors (after rotation). 



To find the change of wave-length per fringe, d\/dn may be deduced. 



d\ \* 



(4) 2 dn = N^, 



This equation has a maximum when 



and this is the coordinate N e for centers of ellipses on any given spectrum 

 line X. N = N C in equation (2) gives 



c 



cos R d\ 



In general fi=A+B/\*', = is adequate for experimental work. Thus 



uX X 



if Z? = 4.6Xio~ n , e=i cm., R = o, then w c = 88o, or 880 sodium wave-lengths 

 are expended in the path-difference at the elliptic center. 



If n' fringes pass at a given color X for a displacement AAT of the mirror M 



If n' fringes lie between two given colors X and X' for the same position N 

 of the micrometer mirror M 



/Li' COS R' U.COS R\ /I A 



(8) n' = , e (t -- L-_J_ 2 ^___J 



or if 5 is the differential symbol 



cos R i 



2Nd- 

 X X 



The question next of interest is the change of the angle of altitude of the 

 ray per fringes transversely to the spectrum. Light is homogeneous, AT there- 

 fore constant. Let a be the angle of altitude of an oblique ray in the hori- 

 zontal plane L, figure 53, impinging at I. If i' and R' are the corresponding 

 angles of incidence and refraction, then i', i, a make up the sides of a spherical 

 triangle, right-angled at the angle opposite i'. Hence 



(9) cos i' = cos i cos a, and ft cos R' = vV i +cos 2 i cos 2 a 



With this introduction of R' for R, equation (2) is again applicable, since 

 nothing has been changed in N, e, f.t, X, or i. Hence 



(10) n\ = 2N 2evV 1+ cos2 * cos2 a 



