58 THE INTERFEROMETRY OF 



itself is beyond the present purposes ; but it appears that the colored fringes 

 will not appear until the corresponding DI and D 2 lines are shared by the 

 whole of the two continuous spectra. 



The final question at issue is the bearing of the present Fresnel phenome- 

 non on the reversed spectra. If in figure 40, 5 and s' represent the traces of 

 two reversed spectra in the principal focal plane, superposed throughout their 

 extent (i.e., in longitudinal coincidence), the rays aia'-JB, through the line of 

 symmetry a, a', are at once in a condition to interfere with a given difference 

 of phase; but so are all the symmetrically placed pairs of colors, c, c' , b, b', of 

 the two spectra (the distances cc' , bb', being arbitrary), provided the corre- 

 sponding rays meet. As they do not meet in the principal focus, they can 

 interfere only outside of this b and b' at B, c and c' at C, etc. Similar con- 

 ditions must hold at B' and C' within the principal focal plane. The linear 

 interference is thus successively transferred to different pairs of wave-lengths. 

 The phenomena of this paper can not, therefore, be detected in case of reversed 

 spectra, because in the principal focal plane different wave-lengths are every- 

 where superposed, except at the narrow strip aa', which experiment shows to 

 be about one- third of the width of the sodium doublet, in apparent size. 

 Beyond the principal focus the corresponding conditions in turn hold for the 

 rays at B, C, etc., B', C', etc. Hence there can not be any Fresnellian inter- 

 ferences (paragraph 22), for there are not two virtual slits, but only a single 

 one, as it were, and the interferences are laid off in depth along the normal 

 C'C. The phenomenon may, in fact, be detected along this normal for 2 or 

 3 meters. 



25. Rotation of colored fringes. Non=reversed spectra. When the slit is 

 oblique, it effectively reproduces the wide slit, locally, and therefore does not 

 destroy the colored fringes. At every elevation in the field the slit is neces- 

 sarily linear, though not vertical. In figure 41, let the heavy lines, H, denote 

 the colored fringes for a fine vertical slit and white light, showing nearly the 

 same distance apart, throughout. Let the light lines, L, denote the fringes 

 for a wide vertical slit and homogeneous light, X. These fringes are due to 

 the successively increased or decreased obliquity of the rays in the horizontal 

 plane. Now let acb be the image of the oblique slit in homogeneous light. It 

 is thus merely an oblique strip, cut from the area of light lines or striations, 

 as it were, and consists of an alternation of black and bright dot-like vertical 

 elements in correspondence with the original striated field. We may suppose 

 ab to have rotated around c, so that the vertical through c is its position on 

 the colored field (white light and fine vertical slit). 



A color, X' (near the one X) , corresponding to the field of the lines L in case 

 of a wide slit and homogeneous light X', will supply nearly the same grid, so 

 far as the distance apart of fringes is concerned. But the grid is displaced 

 laterally, in consequence of the different angle of diffraction, 6. This is shown 

 by the dotted lines D in figure 41, the effect being as if the slit had been dis- 

 placed laterally. If the wide slit for homogeneous light X' is now narrowed and 



