76 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 

 If in equation (13) we convert d\ into dd 



dl d& dO 

 "dedN~dN L 



whence 



( X\ de - * e 



dN = ^ D cosd cos R ^ 



/tan 2 fl/JjLA 3 

 \ \dl) 



we may compare this deviation with the corresponding case when X and n do 

 not vary, but R and N do; i.e., the case of motion along the direction of 

 any given spectrum line. This is a comparison of the vertical and horizontal 

 axes of the ellipses. 



42. Equations. Sensitiveness in terms of order. The quantity d\/dn, 

 where n is the order of the fringe of color X, has subsidiary interest. 

 Since 



__ _ _ _ 

 dn ~ a e (cos R X sec R dn/dX) N 



generally, and the condition of centers of ellipses is dX/dn = j , the coordinate 

 of a center is 



./Ve ; o i ft ^uz> jv i^ 



V cos R 



If we combine this with the general equation 



N = en cos RnX/2 



using w,; as the order corresponding to centers of the wave-length X, and apart 

 from signs, 



e ~ cosR dl 

 In case of the above blue column, for example, 



^=25.4 cm.; B = 4-6Xio- u ; fl = o; ^ = 5X10^; 



4X25.4X4.6X10-" 

 "<= T^XT^ =37,4oo 



half wave-lengths of path difference in the glass, not including the addi- 

 tional number in the grating. 



It is interesting to return to the original equation 



dn 2 Nc-N 



where N c = e (cos R X sec Rdn/d\) and d\ D cos dd, since sin sin 6 = 

 \/D. 



