in Case of Non-reversed and of Reversed Spectra. \ 

 at G a by (3) 



cos0.,' 



resulting in the path difference AP, the difference between 

 these expressions. 



Since 6„ and 0/ are nearly the same, AP may be simplified. 

 One may notice in passing that in equation (1) and (3) the 

 negative sign of di/dd and the positive sign in cos [6 -t- i) 



belong; together 



Differentiating the functions (3) with respect to 6, putting 

 d6 = 6„ — 9„' — 2 (a — <£), and reducing the displacement he 

 per fringe, apart from sign, is 



X cos 5 (9 



8e = 



2{a—<t>)siu6 (4) 



Thus if 



\— 6 X 10- 6 cra., a — </> = 1° = -Q115, 0=20° 

 de = -0044 cm. 



The effectiveness of the fore and aft motion, according to 

 this equation, is evidence of a considerable angle of non- 

 symmetry, a — <fi. This is not improbable, as my apparatus 

 was an improvised construction, lacking mechanical refinement. 

 Further the wedge effect due to a would be superimposed on 

 the interferences and hence these could not be increased in 

 size above a certain maximum. This is also quite in accord 

 with observation. 



If a = $, /3 = 0, 6„ = #. 2 ' ; i. e., the virtual images G m and G n 

 and the diffracted rays are parallel and he = go . In other 

 words, the fore and aft motion has no effect. If a = 0, 

 /3 = 2(j> ; or if = 0, [3 = 2a. In either cases he is finite, and 

 fore and aft motion is effective. If the mirrors and grating 

 were rotated in counter direction so that <j> is negative, he will 

 depend on a + 0, and the fore and aft effect be correspondingly 

 marked. In general, moreover, the interference will not ap- 

 pear in the principal focus, but as a rule sufficiently near it for 

 adjustment. 



If he g is the actual displacement of the grating G' in the line 

 of symmetry, he e == &?/cos 0, so that the angle cf> enters equa- 

 tion (4) again, but only to a small extent. 



Brown University, 

 Providence, E. I. 



