THE AID OF THE ACHROMATIC FRINGES. 81 



The center of fringes is very definite throughout and the measurement nearly 

 as easy as with plates. 



If a lens of 15 or more diopters is placed in the solution (ellipses centered 

 in the green or yellow ray), the fringes become very indistinct, because of the 

 different divergence of the rays of the two slit-images. In this case it is inter- 

 esting to let both beams pass through the lens, when the two slit-images will 

 usually be short spectra, direct or reversed, according to the manner in which 

 the beams pass the lens. In the latter case one obtains the interferences of 

 reversed spectra at the line of color coincidence of the two spectra. If the 

 phenomenon is enlarged by the spectro-telescope, an oval area of very sharp 

 fringes may be obtained and the area passed from end to end of the spectrum 

 by rotating the mirror m on a vertical axis. If the ellipses are centered, hori- 

 zontal arrow-like figures are usual, much resembling a shark's head with the 

 mouth strangely outlined in black. 



61. Equations and data. An example of data obtained when the Billet 

 compensator was used for interpolation may now be given. In the earlier 

 paper (I.e.) it is shown that as a rule the equation 



(i) e(n-n l + 2(B-B')/\*)=n\ 



adequately represents the experiment. Here n, B, //, B', are the indices of 

 refraction and dispersion constants 



of the glass and solution, respectively; e the thickness of plate; X the wave- 

 length of light ; and n the number of X-f ringes which pass a given fixed point 

 in the telescope. We may write 



(2) n\ 



\= 



if Arc is the displacement of the wedge of the compensator corresponding to 

 n wave-lengths. The factor C refers to the displacement of wedge per fringe, 

 to be found experimentally. Hence 



, 2(B-B'} 

 (3) M = / --- - - 



If the medium M', B' is air, the equation becomes practically (fjf = i , B' = o) 



Using this for the wedge of the compensator, if 8e is the displacement of wedge 



for 100 fringes, 



CAx 



~ M -I + 25/X' 



In an experiment 100 yellow fringes (io 6 X = 6o cm.) corresponded to 22.65 

 scale-parts of the wedge micrometer-screw, so that 



C=io 2 X6Xio- 5 /26.65 

 6 



