REVERSED AND NON-REVERSED SPECTRA. 



93 



Thus the relations are quite complicated, but if Di = Dz, or the gratings 

 have the same constant, rays of all wave-lengths should, after double diffrac- 

 tion, issue normally to the grating G', and the arrangement is therefore 

 achromatic. If DI is not quite the same as D%, but nearly so, an adjustment 

 of a would probably meet the case approximately. If the original incidence is 

 at an angle i\, DI sin i\ would have to be subtracted from the first member, 

 but the diffractions would now differ on the two sides of the apparatus. 



The relations of the rotations of the striations of D\ and D 2 light to 

 the fore-and-aft motion is next to be considered. It will be convenient to 

 make use of figure 68 for this pur- 

 pose, the notation being the same 

 as in figure 69. The two rays, i 

 and 2 (Di and D 2 ), have both 

 been introduced, and the position 

 of G' is such that the DI rays 

 intersect in its face and are dif- 

 fracted into TV In such a case 

 the combined pencil is divergent, 

 DI rays will undergo an earlier ^ 

 intersection, and consequently be 

 separately diffracted into TI and 

 T'i. Hence DI and D 2 are differently circumstanced in relation to the fore- 

 and-aft motion, and the rotation produced will thus be advanced in one 

 case, as compared with the other, for the reason discussed in Chapter III, 

 paragraph 26. It is also clear that the difference of phase in the two rotations 

 mil be greater, as the total path of rays between G and G' is greater, so that 

 the large distances used in the present experiments (nearly 3 meters) account 

 for the astonishing sensitiveness of the phase of rotation to the wave-length 

 difference. In fact, D- 2 will be in the same phase as DI, if the grating is moved 

 forward from G' to g', figure 68, since in both cases the rays intersect in the 

 normal. Hence if R is the total path GmNG', and if the angle of dispersion 

 between DI and D* is d6, 62 the angle of diffraction at G', and h the displace- 

 ment from G' to g', D the grating space, 



69 



or 



and the resolving power 



h\ 

 ''DR 



d\ h 



Dh 



X R cos 62 R]/ D 2 ] 

 In the given adjustment, roughly, 



whence 



h = ' 



0.34 



== 



