Reflected- Diffracted and Diffracted- Re fleeted Rays. 47 



When the air space is small, coarse and fine fringes (fluted 

 fringes) are simultaneously in focus, one of which may be 

 used as a coarse adjustment on the other. Finally, the 

 sensitiveness per fringe to be obtained is easily a length of 

 one half wave-length in the fine fringes and one wave-length 

 in the coarse fringes, though the latter may also be increased 

 almost to the limit of the former. 



2. Observations. 



The following observations were made merely to corroborate 

 the equations used. The general character of the results 

 will become clear on consulting the following abbreviated 

 table chosen at random from many similar data. An Ives 

 replica grating with 15,000 lines to the inch (film between 

 plates of glass *46 cm. thick) was mounted as usual on a 

 spectrometer admitting of an angular measurement within 

 one minute of arc. Parallel light fell on the grating, fig. 1 , 

 gg, under different angles of incidence, i, and the spectrum 

 lines were observed by reflexion (after reflexion from gg and 

 the rear f&ceff) at an angle of diffraction &' in air, both in 

 the first and second order of spectra, and so far as possible 

 on both sides of the directly reflected beam. In view of the 

 front plate, the angle i corresponds to an angle of refraction 

 r within the glass, and the angle 6' similarly to an angle of 

 diffraction 6, respectively. Hence r>6 2 or & 1 <r denotes the 

 sides of the ordinary ray on which observation is made. As 

 a rule these were as nearly as possible in the region of the 

 D line passing toward E. Finally, SO denotes the angle 

 between two consecutive dark fringes, observed and computed 

 as specified. Similarly Be will be reserved for changes of 

 thickness e of the glass and oV for changes of the air space 

 in case of an auxiliary mirror M. 



For i = 0° the number of groups of lines was a single set 

 in each order, but only the end of the spectrum could be 

 seen. Measurements refer (about) to the C line. For z = 45° 

 several groups were too close together, or too faint for 

 measurement, and the same is true for i = 22°'5. An estimate 

 of divergence is all that could be attempted on the given 

 spectrometer. The case 6 1 > r was usually not available, but 

 for i = 22°*5 two sets were found in the first order, one being 

 the normal set. The fringes in all cases decrease in size from 

 red to violet, but less rapidly than wave-length (§ 7). 



Whether they are convergent or divergent for a given set 

 of fringes, as for instance for the strong set, depends on the 

 position of the grating. Thus the divergent rays become 

 convergent when the grating is rotated 180° about its normal. 



