94 REVERSED AND NON-REVERSED SPECTRA. 



As the resolving power is, roughly, h/R, and if h = 0.003 cm. is still appreciable, 



3Xio 2 



i.e., lines i/ioo of the distance apart of the sodium lines should be rotationally 

 separated. 



Again, the displacement, fore and aft, between like rotational phases of 

 DI and Di should be about 3 mm., and this agrees fairly well with the order 

 of values found. 



The case of the transmitting grating (fig. 59) is thus also elucidated, though 

 it is not clear to me why the duplication of fringes is so efficiently concealed 

 in the nodular forms observed. The reason for the minimum of size, for the 

 symmetrical position i = o, and the two maxima for oblique positions of the 

 grating (2 =20 about), suggests an explanation similar to that given in 

 Chapter II. In other words, in the oblique position the short path-length 

 is compensated by the increased thickness resulting from the greater obliquity 

 of grating, whereas the long path-rays traverse the plate of the grating more 

 nearly normally. In this way the path-difference is reduced as compared 

 with the symmetrical position, and the fringes are therefore larger. The 

 oblique grating acts as a compensator in both of the component beams, and the 

 fringes may be visible, even if in the original position (fig. 59) they are all but 

 invisible. If, however, the apparatus (fig. 57) is used with a plate-glass com- 

 pensator symmetrical at c, there are no maxima or minima for any obliquity. 

 Hence the tentative explanation for the case of figure 59 is not warranted. 



The fore-and-aft motion of the plate grating (fig. 59) produces no effect, 

 since the rays are reflected back so as to retrace their paths. They are also 

 reflected between parallel mirrors A r , m and n, M. Thus the path-difference 

 is not modified. The result is merely a decrease of the distance M, N, and a 

 corresponding increase of m, n, and vice versa. 



The marked effects produced by rotating the transmitting grating around a 

 normal axis, finally, follow the explanations given for the rotation of fringes 

 of non-reversed spectra in Chapter III, paragraphs 25 and 26. 



In conclusion, an interesting application of the apparatus (fig. 56) or the 

 other similar types may be suggested. By half -silvering the mirrors and pro- 

 viding a similar opaque set beyond them, there should be no difficulty (in 

 the case of homogeneous light) of bringing the interferences due to crossed rays, 

 c, and to parallel rays, a'b', into the field of the telescope together. Strictly 

 homogeneous light (mercury arc) would be needed to obviate the duplication 

 of the sodium arc. In such a case, therefore, the parallel fringes could be used 

 after the manner of a vernier on the crossed fringes, with a view to a repetition 

 of the experiment of Michelson and Morley, if this experiment had not been 

 so thoroughly carried out by the original investigators. However, the plan 

 would be to rotate the apparatus, as a whole, so that the two crossed rays 

 would be alternately in and at right angles to the earth's motion, whereas the 

 two parallel rays would preserve the same relation to that motion. Naturally, 

 the parallel and crossed paths would in such a case have to be lengthened by 

 multiple reflections. 



