I9II.] WITH REFLECTING GRATING. 137 



ing X, the corresponding coefficients would be i\d(n -{- N)/d$, and 

 these are much more in error, here and in the preceding cases. If 

 from d9/dn, e is ehminated in terms of {n -\- N ) the equation is 



dd \ ' I 

 (i6) 



dn D{n + N^cosi' 



so that for a given vahie of i, 6, jVq, they decrease in size with n. 

 If ;/=o they reach the hmiting size 



dd \ 



dn DN^ cos / ' 



If the crack N ^JJ should be made infinitely small, they would be 

 infinitely large. To pass through infinity, A'^ must be negative, 

 which has no meaning for i > ^ or would place one eft'ective edge of 

 the crack 5" behind the other. These inferences agree with the 

 observations as above detailed. If, however, i <^ 0, a. negative value 

 of Nq restores equation (i6) for //:^o to equation (17), as was 

 actually observed (Figs. 2 and 3). 



Finally equation (14) might be used for observation in the incre- 

 mented form 



. „ D cos i 

 (17) A{de/de) = ^^^Ae; 



but I did not succeed with it. One loses track of the run of a 

 fringe w^ith de. 



II. Colored Slit Images and Disc Colors of Coronas. — In the 

 above experiment the fringes were but a few minutes apart. It is 

 obvious, however, that if A''^ is sufficiently small the fringes will grow 

 with decreasing 11, in angular magnitude, until there are but a few 

 black bands in the spectrum. Under these circumstances the unde- 

 viated image of the superimposed slits must appear colored, particu- 

 larly so if an effect equivalent to A^^, is present throughout the 

 grating. This phenomenon of colored slits is apparently of interest 

 in its bearing on the theory of coronas, where there is also an inter- 

 ference phenomenon superimposed upon a diffraction phenomenon, 

 as is evidenced by the brilliant disc colors. For instance suppose 



