434 On Inter ferometry ivith the Aid of a G ratine/. 



become movable ; for, inasmuch as there is complete 

 symmetry between the rays to be reflected from the mirrors 

 M and N, the stationary fringes become identical for both 

 plates of glass, from either of which they may be reflected 

 before or after diffraction. Hence the motion of either 

 opaque mirror changes the phase and moves the fringes, 

 which are now linear, vertical, and nearly equidistant. They 

 may also be regarded as confocal ellipses of infinite size, the 

 visible parts of their peripheries lying close together in 

 the field of view. They pass through infinity in this field 

 when the virtual path difference is zero. 



15. Continued. — The five equations given, when the first 

 group I' and II' is combined wiih the second group I, II, III, 

 lead to six other interferences, all of them of the movable 

 type and useful for interferometry. If for simplicity the 

 path difference is zero, they may be written, if y=y n —y n 

 and y , —y n —y\ l and y Q corresponds to the glass-path dif- 

 ference, N as usually referring to the displacement of the 

 opaque mirror, 



Eeflexion at 



IV, bottom, equation I-II', y' =e/j /cos ~R, N = g/* cos R. 



V, bottom, equation II-I', — y =e/i/cosR, N = gjucosR. 



VI, top, equation III-I', — y =c/i(cos 7 + sinR tan R), N = c/tcos0 l . 



VII, top and bottom, equation TI-II', ^/' = e/^sinRtan R, W=0. 



VIII. „ ,, III-ll', y' = efi(sec~R — cosGJ, N=e i u(cosR-co.s0 1 ). 



IX, bottom and top, equation 1-1', — y =e/xsmRtanR, N=0. 



Hence the fringes of the interference VII and IX are 

 identical throughout the spectrum, when the mirror N 

 moves. The remaining fringes are elliptic and eccentric, 

 because reflected from two faces of the thin wedge. 

 Nos. VII and IX are parallel lines which pass symmetrically 

 from negative to positive obliquity, or the reverse, respec- 

 tively, through horizontality, in opposed directions. 



The results of these equations have been computed for 

 light crown glass, but the treatment being less important 

 may be omitted here. 



My thanks are due to Professor Joseph S. Ames, of 

 Johns Hopkins University, for his kindness in lending me 

 the glass diffraction grating by which the above equations 

 were tested. I hope at some other opportunity to work with 

 a grating whose refraction is known throughout the spectrum 

 and also to endeavour to obtain the phenomenon as clearly 

 from film gratings (replicas), as has been possible for the 

 linear series in the preceding, paper (I. c). Thus far the 

 above phenomena as obtained from -film gratings are not 

 strong and sharp enough for measurements of precision. 



