40 THE INTERFEROMETRY OF 



If E is expressed in terms of D and D', and B in terms of S and 5', and 

 the first equation is used, then 



5 sin x D' 



from which, in the fourth equation, 



E \/D*+D' 2 +2DD'cos<p 



sin (p sin 



Similarly, 



E' 



sn ip sin <p 



Again, the angle y' is given from 



sin y' D 



or on reduction 



. D sin <p 

 tan y' = -=-, 



, 



D D COB <f> 



If D = D', or 5 = 5', then 



sin (<p/2) cos (<>/2) 



. sin <p 



tan y = -r -. -r^ = cos (<p/2)/sm (<p/2). or tan y tan p/2 = i 

 sin (<p/2) 



Thus if <p = o, tan y'= co t y' = 90, or the fringes are horizontal and 5 = aS. 

 If 7' is nearly zero 



changing very rapidly with <p. 



If one grating of a pair, with identical grating spaces D, is moved parallel 

 to itself, in front of the other, the effect to an eye at a finite distance is to 

 make the grating spaces D virtually unequal ; or 



cos 



j 



2 COS (<f>/2) 



so that for an acute angle <p, the fringe breadth is increased. Thus B Q is a 

 minimum in case of coincident gratings. 



The analogy is thus curiously as follows: The fringes just treated rotate 

 with the rotation of either grating in its own plane and pass through a mini- 

 mum size with fore-and-aft motion; whereas in the above results the optical 

 grating showed a passage through a maximum of size with the rotation of 

 either grating in its own plane and a rotation of fringes with fore-and-aft 

 motion of the grating. 



Returning from this digression to figure 26, if the grating G' is not quite 

 symmetrical, but makes a small angle <p with the symmetrical position as at 

 g', the fore-and-aft motion will change the condition of path-excess on the 

 right (position g' 2) M path larger) to the condition of path-excess on the left 



