in Case of Non-reversed and of Reversed Spectra. 67 



to tlie diagram is equivalent to the fore and aft motion of 

 G'G" when mirrors are used.* The rotation around OT in 

 the diagram and normal to the face of the grating, requires 

 .adjustment at the mirrors around a horizontal axis, to bring 

 the spectra again into coincidence. This is equivalent to rota- 

 tion around G" OG' . Both produce enlargement and rotation 

 of fringes as already explained. 



Let the grating G'G" be rotated over an angle <j) into the 

 position g'g" . Then it may be shown that only so long as cf> is 

 very small are the rays appreciably parallel on emerging ; but 

 this is usually the case, as (f> ~ is aimed at, and fringes are 

 thus seen in the principal focus. 



The next question at issue is the rotation of fringes with 

 fore and aft motion, or rotation around normal to the dia- 

 gram. When e, the virtual distance apart, is zero, since n ce e/\ 

 the fringes are infinitely large horizontally. The collimator, 

 however, furnishes a pencil of rays which are parallel in a hori- 

 zontal plane, only. They are not collimated or parallel in the 

 vertical plane (parallel to the length of the slit). Hence when 

 the fringes are reduced to a single one of infinite size horizon- 

 tally, this is not the case vertically, i. e. from top to bottom of 

 the spectrum the path difference still regularly varies. The 

 adjustment aroiind an axis through 0, G'OG", normal to the 

 rulings, is still outstanding. 



"Finally, the rotation around an axis parallel to IT in figure 

 2 is to be considered. This has already been given in terms of 

 colored fringes (white light), but it occurs here for homogene- 

 ous light, in which case the above explanation is not applica- 

 ble. Seen in the principal focal plane with telescope and wide 

 slit, the non-reversed spectra require careful adjustment of 

 longitudinal and tran verse axes ; otherwise they vanish. Noth- 

 ing w 7 ill rotate them. 



Figure 2 shows that if G'G" is rotated about IT, the 

 effect is merely to destroy the fringes, since the coincidence of 

 the longitudinal axes of the spectra is here destroyed. No 

 effect is produced so far as path difference is concerned. To 

 restore the fringes therefore, either of the opaque mirrors, M 

 or JV of the apparatus, must be rotated on a horizontal axis, 

 until the two spectra are again longitudinally superposed. It 

 is this motion that modifies the path difference of rays in a 

 vertical plane. In other words, when the fringes correspond- 

 ing to any virtual distance apart, e = bcp of the two halves of 

 the grating G'G", have been installed, the rays as a tv/iole may 

 still be rotated at pleasure, around a horizontal axis. In this 

 way a change in the number of fringes intersected by a vertical 

 line through the spectrum, is produced. The number of inter- 

 *This Journal, xli, p. 419, 1916. See fig. 12. 



