340 Mr. A. A. Michelson on the Application of 



If a be sufficiently small, the variations of C and S with 3 

 may be neglected, and the maxima or minima occur when 



tanS= — p, 



or 



when 



I=P ± 4/C 2 +S 2 . 

 Hence 



C 2 + S 2 



V 2 = 



P 2 



In the following discussion of some of the more interesting 

 cases which have been solved, let A be the extreme difference 

 in wave-length of the radiations in question, and let A be the 

 smallest difference which can be " resolved " by a grating- 

 having as many lines, N, as there are waves in the difference 

 in path. 



Then if n= -r-, we have 



I. 4>{ x ) — constant. 



This case has already been treated, and the resulting visi- 

 bility-curve is 



sin irn 



V = 



irn 



ii. (\>{x)=yy-x\ 



This case has also been solved ; and if J x represent BessePs 

 function of order unity, the result is 



y = Ji(7m) 

 irn 



III. (f)(^)=COS7T-. 



T ' a 



The more general case cos mir — gives 



V= 



sin J(wi 



— %i)it 



a to 

 + sini(; 



m-\- "2il)it 



i( m - 



•2tt)7T 



+ 2n)7r 





9 sin %mir 



2 m7r 





