REVERSED AND NON-REVERSED SPECTRA. 125 



two respective extremities of the normal to the half-silver, at the point where 

 the incident ray impinges on it, the equation may be more completely written 



(i) n\ = 2efj. cos R 2N 



if a is temporarily disregarded. N is independent of color X, but otherwise 

 represents the difference of air-paths of the two interfering rays. From this 

 equation 



(a) d\ = _ X 2 _ 



dn " 2*0* cos R- (X/cos K) (dn/d\) )-2N 

 so that the center of ellipses is at X in the spectrum when 



(3) N=N c = e( fJ .cosR--- 



\ cos R 



Furthermore, 



d\ X 



(4) 



dN N-N C 



2e dfj, d/j, 



and n = - - depends essentially on 



cos R d\ d\ 



On the other hand, in case of homogeneous light of wave-length X, 



( s di = _ X = X 



dn 2/j, cos R. (de/di) 26 tan R cos i n\(de/e)/di2e tan R cos i 



where de/di may be either positive or negative. 

 Centers occur when 



de e tan R cos i de 



(6) = - -=- or =etanR 



di /x cos R dR 



Thus di/dn is never independent of X and the centers of equation (6) are, as a 

 rule, quite different from those of equation (3). If the angle a is admitted, 

 equation (6) takes the form 



de 



(7) =e tanK (i 2 a/sin 2R) 



The occurrence of the residual fringes for the same adjustment of the 

 micrometer as the centered spectrum fringes is thus incidental. To obtain 

 the latter the two superimposed spectra of a fine slit must coincide horizontally 

 and vertically throughout their extent i.e., the two linear white slit images 

 must coincide. If now the slit is indefinitely widened, there are two vertical 

 lines in the superposed broad white images which are completely in coinci- 

 dence. In case of ordinary plate-glass the remainder of the images will not 

 be mutually in coincidence or generally there can not be coincidence in every 

 color. The residual or achromatic fringes are found at and near the line of 

 coincidence in question. Hence if either opaque mirror is slightly rotated 

 on a vertical axis the residual fringes pass from edge to edge of the broad 

 white slit images, 5 and 5', figure 85, of slightly unequal width. Thus if the 

 mean breadth is S and the difference of breadth AS = 5' S, the very small 



