EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 83 



The adjustment adopted is shown in diagram in fig. 45^, where L is the lens 

 about 6 inches in diameter, with its focus at F, about half a meter or more 

 from the lens. G is the circular grating, s the distant screen, several meters 

 off. On the plane G the diameter of the concentric annulus is 2y; on the plane 

 5 the diameter is 2X, where R\ is the distance apart of the planes measured 

 along the white rays, which are elements of a hollow cone with its apex at 

 F. If E is the center of the ring 2X and R the normal to G, the rays ^'2 are 

 diffracted to E, and with R\ determine the angles 6 and i. We may then 

 write in succession, for first order of spectra, if the grating space is D, 



(1) sin *-f- sin = 



(2) smi=(x- 



If the dispersion y is small compared with the distance R and the incidence 

 i of small obliquity, 



(3) R\ = R 2 

 whence 



(4) x/R' = l/D 



Thus the result is independent of the diameter of the annulus 27, if R" is 

 small, and the grating may therefore be placed at the focus F. 

 The equation may be more correctly written 



(s) *= 



y being always small compared with x. If R is the normal distance between 

 screen and grating, the full expression would be inconveniently 



*__ iy/x __ , y/x \ 

 ~ 



Vi 



\ " r ' / 



or if y = o, with G at F, 



Dx i 



In table 12 a series of such measurements is recorded, in which X is computed 

 from D, x, y, R. Only the outer lines of the circular grating G, fig. 450, were 

 used, the center being rendered opaque by a concentric disk of cardboard S'. 

 The grating was then moved into the divergent cone of white light limited 

 by the circular hole in the screen S", until the desired color appeared on the 

 distant white screen at the center of the white ring. The diameter ?x of the 

 latter is then the only variable. Later an annulus cut in an opaque screen 

 S", fig. 456, was also used. In such a case, the position S" determines x, while 

 the position of the grating is of no consequence. The wave-lengths so obtained 

 are as a rule larger than the normal values expected, a result due in part to 

 errors in the judgment of color and in part to the approximate equation used. 

 It is not worth while to enter further into the reason for this, the chief point 

 being that with the use of an annular source all the colors may be made to 



