in Case of Non-reversed and of Reversed Spectra. 71 



direction, by the same amount. If then the grating G' is 

 rotated around an axis at G', perpendicular to the diagram, 

 fig. 3, over a small angle, <£, the result (apart from the super- 

 posed rotational effect) is equivalent to a displacement of the 

 mirrors M l and N i in opposite directions, producing a virtual 

 distance apart e and the corresponding interference fringes. 

 In other words, the rotational effects may be explained here in 

 the same way, as in the preceding paragraph. 



The angle 2dd within which the interference rays lie, per 

 fringe, is subtended by Se and is very small, scarcely T?I Vo °^ 

 the D X D„ distance of sodium light. Hence all pencils consist 

 of practically parallel rays. 



Another result is the angular size of fringes : i. e., if. e m and X 



d6„ X 



dn e sin 8/2' 



Thus they become infinitely large when e passes through zero. 

 The angular size is independent of the distance between the 

 gratings. It ought, therefore, to be easy to obtain large inter- 

 ference fringes, which is not the case. The reason lies in this, 

 that the two opaque mirrors are not quite symmetrical, so that 

 in fig. 3, on rotation of M 1 180° on GG', the trace of M x 

 crosses N l at an angle (wedge effect). YldQ/dn = 3"7 X 10" 4 , 

 the distance apart of the sodium lines, and Z> 2 =173 X 10 -6 cm., 

 e = 1*8 cm., i. e., path lengths on the two sides would differ 

 by about 2 centimeters. 



4. Nonsymmetrical positions. Fore and aft motion. — It 

 remains to account for the marked effect produced on displac- 

 ing the grating G' , in a direction nearly normal to itself. If 

 the displacement is symmetrical, or even if the grating and 

 mirrors are reciprocally non-symmetrical, the former at an 

 angle <fi to the transverse line of symmetry gg' ', figure 5, no 

 effect results from the displacement of G' . The virtual images 

 G m and G n are parallel and the different rays therefore also 

 parallel. 



If, however, this compensation does not occur, if the grating 

 G', the mirrors N 1 and 31 l make angles <j>, <r/2, t/2, respec- 

 tively, with the transverse line of symmetry gg', the fore and 

 aft motion of G' is more effective as a — cj> (a angle between 

 the mirrors) is greater. The diffracted rays are then no longer 

 parallel, but make angles of incidence at the second grating, 

 9„' for the N l side and 2 for the M 1 side, and of diffraction 

 i and i', respectively, as shown in figure at T a and T m . The 

 following relations between the angles are apparent 



a- = 0/ + e.; - $ t = 8 ] + 2 + <£ 



