REVERSED AND NON-REVERSED SPECTRA. 



67 



symmetrical, so that in figure 47, on rotation of MI 18 on GG' , the trace of 

 Mi crosses Ni at an angle. If dd/dn = $.'jX'io- 4 , the distance apart of the 

 sodium lines, and DZ = 1 73 X lo" 6 cm., 



e=i.S cm., about 



i.e., path-lengths on the two sides should differ by about 2 centimeters, if the 

 mirrors were quite symmetrical. 



28. Non=symmetrical positions. Fore=and=aft motion. It remains to 

 account for the marked effect produced on displacing the grating G' in a direc- 

 tion nearly normal to it- 

 self. If the displacement 

 is symmetrical, or even if 

 the grating and mirrors -.^ 



are reciprocally non-sym- 

 metrical (i.e., the former fl- 

 at an angle <p to the trans- 

 verse line of symmetry 

 gg' , the latter inclosing 

 an angle a, fig. 49), no 

 effect results from the 

 displacement of G', if the 

 mirrors MI and NI are 

 so placed that the vir- 

 tual images G m and G n 

 are parallel and the dif- 

 fracted rays, therefore, 

 also parallel. In such a 

 case G m and G n are dis- 

 placed by the same amount, normally, their distance apart is constant, and 

 the intercepts of rays equal. 



If, however, this compensation does not occur; if the grating G', the mirrors 

 NI and Mi make angles <p,ff/2, r/2, respectively (za= r <r), with the trans- 

 verse line of symmetry gg' , the fore-and-aft motion of G' is more effective as 

 the angle a <p is greater. The diffracted rays are then no longer parallel, 

 but make angles of incidence at the second grating, 0' 2 for the N\ side and 

 2 for the Mi side, and of diffraction i' and i, respectively, as shown in figure 

 49, at r n and T m . The following relations between the angles are apparent: 



49 



If at the first grating 0i= 0'i and a is the angle between the mirrors, 



2<X= T ff= 62 0'2 



The images are at an angle /3, where 



