REVERSED AND NON-REVERSED SPECTRA. 51 



of displacement. It was found to be, between appearance and evanescence 

 of fringes, 



0.119, e tc., cm. 



thus scarcely larger than a millimeter, whereas in the case where a grating 

 (D = 352Xio~ 6 cm.) was used in place of P the range of displacement was of 

 the order of 5 mm. 



If the spectra be regarded with a prism grating, they become relatively 

 long and short, respectively; but the phenomenon is none the less strong, 

 although it is apt to lie outside of the two sodium doublets and not midway 

 between them, as with the telescope. It seeks out the line of coincident 

 wave-lengths. Now, inasmuch as the refraction from M is normal and the 

 rays virtually retrace their paths both in the case of the prism and the grating 

 (in the original adjustment) , it seems at first difficult to avoid the conclusion 

 that wave-trains are more uniform in proportion as they have been more 

 highly dispersed. The only misgiving would be the fact that the phenomenon 

 with prism appears and vanishes in hair-lines, whereas with gratings it goes 

 out rather abruptly. Otherwise one would regard white light as consisting of 

 irregular pulses incapable of prolonged interference, whereas the dispersed 

 wave consists of wave-trains in each color, which throughout a considerable 

 number of wave-lengths are plane polarized. True, if there is sliding, the 

 sections of the two light -pencils, the points of which are capable of interfering 

 in pairs, increase in area proportionately to the dispersion. 



Suppose that for low dispersion the fringes may be regarded as extremely 

 eccentric, virtually linear ellipses, the lateral distance between which very 

 rapidly diminishes, so that, since Be = 0.12, but 



I 0.12 



=2000 



can be seen by the given telescope. These lines would move behind the strip 

 carrying interference fringes as Mis displaced. If now the dispersion were much 



d0 



increased, say from = 2 X 760 for the prism to 2 X 2880 for the grating, the 



d\ 



ellipses would be much less eccentric as a whole and their lines would have 

 grown coarser, so that many more would be visible by the given optical 

 system. As the dispersion is increased 2880/760 = 3.8 times, the range of 

 displacement should increase similarly to 0.12X3.8 = 4.6 cm. The plane 

 ruled grating (D = 3 52X10^ cm.) in question was now again mounted in 

 place of P and under good illumination the range 0.48 cm. was found experi- 

 mentally. This agrees very well with the estimated value. Moreover, on 

 close inspection it is discernible that the linear phenomenon really consists 

 of extremely eccentric ellipses, which in case of the best adjustments manifest 

 the very sharp arrow-like forms. It also enters and vanishes in multilinear 

 form, though the lines are not hair-lines. Thus the assertion that increased 

 uniformity of wave-train accounts for the long range of displacement and 



