80 THE INTERFEROMETRY OF 



single white image of the slit ; but the grating G reproduces the spectrum and 

 enlarges it, in which case, however, not absolute position but the direction 

 of rays is the determining factor. 



40. Continued. Reversed spectra, etc. The equation underlying the 

 greater number of experiments in the work with reversed spectra is of the form 



(17) wX = 20cos 5/2 



where 5 is the double angle of incidence at either opaque mirror and e is the 

 effective distance apart of the two mirrors i.e., the distance between the 

 faces when one is rotated 180 about the axis of symmetry into parallelism 

 with the other. In the present case, therefore, e corresponds to N in 39. 

 The angle 5 = 2 0i, where 2 and 61 are the angles of refraction of the col- 

 lecting and the dispersing grating, respectively, so that sin 6 = \/D if D is 

 the grating space. If the silvered right-angled reflecting prism is used for 

 alining the separated pencils, 5 = 90 61. 

 From the above equation the change of X per fringe is 

 d\ X 2 



/-Q\ _ _ _ _ 



dn ~ e(2 cos 5/2 +\(dd/d\) sin 5/2) 

 cos = tan 9 



( } = __ _ 



dn e(z cos 5/2+sin 5/2 (tan 2 tan 0i)) 



This is a maximum if e = o, as the quantity in the parenthesis can not vanish 

 for very acute angles, such as and 5 must be. 



If 5 = o, or Di = D t , d\/dn= -X 2 /2<?. 



Similarly, since e is now the micrometer variable or coordinate, and n 

 constant, 



dX _ 2X _ 



de 0(2+tan 5/2 (tan 2 tan 0i)) 



from which the similar conclusions may be drawn with regard to the motion 

 of a given fringe. There is a maximum for e = o. The equation, it will be 

 seen, is quite cumbersome, so that further treatment is inexpedient. Never- 

 theless equation (20), if and 5 are expressed in terms of X, should admit 

 of integration, at least approximately. 



The equation n\ = 2e cos (90 0)/2 for reflecting prisms needs special 

 treatment, since 90 is not derived from 0. The coefficients after reduction 

 become 



d\ -X 2 \AZ?()+X) 



dn ~~ 

 and 



d\ 2 X(>+X) 



(22) ==- --with the aid of (23). 



de e(2D-\-\) C 2.D+X 



In both cases there is a maximum for e = o. 



