REVERSED AND NON-REVERSED SPECTRA. 63 



Chapter II. In other words, when e, the virtual distance apart, is zero, since 

 ncce/\, the fringes are infinitely large horizontally. The collimator, how- 

 ever, furnishes a pencil of rays which are parallel in a horizontal sectional 

 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 horizontally, this is not the case vertically; i.e., from top to 

 bottom of the spectrum the path-difference still regularly varies. The adjust- 

 ment around an axis through 0, G'OG", normal to the rulings, is still out- 

 standing. It does not seem worth while to enter the subject further because 

 much of the rotational phenomenon will depend upon whether the axes used 

 are, in fact, truly vertical or parallel to the slit. In my apparatus this was 

 not quite guaranteed, and the quantitative results obtained may therefore be 

 due to mixed causes. Also, a rotation around an axis normal to always 

 requires an adjustment for superposition of the longitudinal axes of the spectra, 

 and this introduces path-difference. 



Finally, the case of figure 21, Chapter II, or the rotation around an axis 

 parallel to IT in the present figure 43, is to be considered. This has already 

 been given in terms of colored fringes (white light), but it occurs here for 

 homogeneous light, in which case the above explanation is not applicable. 

 Seen in the principal focal plane with telescope and wide slit, the non-reversed 

 spectra would require careful adjustment of longitudinal and transverse axes ; 

 otherwise they vanish. Nothing will rotate them. 



Figure 43 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 N 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 corresponding 

 to any virtual distance apart, e = b <p, of the halves of the grating G'G", 

 have been installed, the rays as a whole may still be rotated at pleasure 

 around a horizontal axis. In this way a change in the number of fringes inter- 

 sected by a vertical line through the spectrum is produced. The number of 

 intersections will clearly depend on the obliquity of the rays (axes of vertical 

 pencils) , and will be a minimum when the center of the field of view corre- 

 sponds to an axis of rays normal to the grating G'G". In other words, the 

 vertical maximum in figure 22 occurs under conditions of complete symmetry 

 of rays in the vertical plane. If, therefore, e or the virtual distance apart 

 of the half gratings, G"0 and OG', is also zero, the field will show the same 

 illumination throughout. 



In conclusion, therefore, to completely represent the behavior of fringes, it 

 will be sufficient and necessary to consider that either grating, G'G" for 

 instance, is capable of rotation, not only around a vertical axis through 0, 

 but also through a horizontal axis through parallel to the grating. The 

 last case has been directly tested above, Chapter II, 16. But a rotation 



