in Case of N on- reversed and of Reversed Spectra. 65 



viously, if parallelograms are to be obtained in figure 1, b'=b", 

 appreciably. This is the case in experiment. Hence if we 

 evaluate the height in the triangle ego' for each angle, it fol- 

 lows that 



/ tan y' 



sin x — 



V(H/l>'- 1) + tany 



If B = b', x = 90° for all values of y' ; i. e., the fringes remain 

 vertical. If B is equal to 2b', x' = y\ the fringes and slit are 

 symmetrically equiangular with the longitudinal axis of the 

 spectrum. This is nearly the case in figure 1 and frequently 

 occurs in experiment. If b' differs from b", the fringes would 

 not be straight. This also occurs, particularly when the thick- 

 ness e of the air film is very small. 



2. Treatment of reversed spectra. — To obtain an insight into 

 the cause of the interferometer fringes as obtained with 

 reversed spectra and two gratings, it is convenient to represent 

 both gratings, figure 2, GG and G" G' as transmitting, and 

 suppose both diffracted beams, ID' and ID" , subsequently 

 combined in view of the principal plane, PP, of an objective 

 or a lens. It is clear that this simplified device can apply only 

 for homogeneous light. In the case of white light, the opaque 

 mirrors, M and JY, of the interferometer (1. c.) return a diver- 

 gent colored beam or spectrum, so that only for a single color 

 can the second incidence be the same as the first. Again, if 

 the constants of the two gratings are different, it is the function 

 of these mirrors to change the incidence at the second grat- 

 ing, correspondingly, so that for homogeneous light the rays 

 issue in parallel. Finally, no reference to the lateral displace- 

 ments, OG" and OG', of rays need be made because (as shown 

 in the next paragraph) this is eliminated by the theory of dif- 

 fraction. 



The motion of the opaque mirrors M and N (above), on a 

 micrometer merely shortens the air path GG' or GG" in its 

 own direction and consequently the same fringe reappears for 

 a displacement of half a wave length, as in all interferometers. 



The case of a single grating, moreover, is given if the planes 

 of the grating GG and G'G" and their lines are rigorously 

 parallel, the planes OG' and G" being coplanar. To repre- 

 sent the interferences of the two independent gratings and with 

 homogeneous light for the case of oblique incidence, it is 

 necessary to suppose the grating G'G" cut in two halves at 0, 

 parallel to the rulings, and to displace the parts OG' or OG" 

 separately, normally to themselves as at Ofi". The figure 



Am. Jour. Sci.— Fourth Series, Vol. XLII, No. 247. — July, 1916. 

 5 



