102 EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 



In case of the grating the sources of scattered light-waves are not only 

 identical as to phase, but these sources are at the same time equidistant. 

 Hence collectively they must determine a wave-front of somewhat inferior 

 intensity but otherwise identical with the wave-front of normally reflected 

 or diffracted light; i.e., the wave-fronts of regularly reflected and scattered 

 light are superposed. 



Moreover, if the grating is turned in azimuth even as much as 45 on either 

 side of the impinging beam (after which the many reflections and diffractions 

 seriously overlap) the blue and brown colorations are distinctly intensified. 

 This also is in accordance with anticipations, for the number of lines which 

 are comprehended within the lateral extent s of the narrow beam L as the 

 angle of incidence i is varied, increases as s sec i\ whereas the lateral extent 

 of the reflected beam is no larger than that of the impinging beam. Hence 

 there should be increased intensity of scattered light in the ratio of sec * 

 or increasing markedly with i from i for i = o , to oo for i = go . In other words, 

 the scattering lines of the grating are virtually more densely disseminated 

 when i increases. 



For the light reflected from the inside of the glass plate the evidence to be 

 obtained from color in case of the ruled grating is too vague to admit of definite 

 statements. I have not, therefore, attempted it. 



66. A further analogy to the reflection of X=rays. With regard to the 

 recent experiments (I.e.) on the reflection of X-rays from crystals, it may 

 further be interesting to recall my experiments (Phil. Mag., xxn, p. 121, 

 191 1) on the interferences produced by two identical but separate halves of a 

 reflecting grating, with the rulings parallel and originally in the same plane. 

 The interferences observed are brought out by moving one of the half gratings 

 micrometrically parallel to itself, to the front or to the rear of the other half, 

 and are here necessarily linear and parallel to the rulings. If i (angle of inci- 

 dence) = 6 (angle of diffraction) and d is the normal distance apart of the grat- 

 ings, the same equation n\ = zd cos 9 holds. In other words, two identical 

 spectra originating in parallel planes, at a distance apart commensurate with 

 the wave-length of light, are superimposed throughout their extent and pro- 

 duce interferences. I pointed out the bearing of this phenomenon on the 

 theory of the coronas of cloudy condensation (/. c. , p. 129), where the compound 

 diffraction spectra, due to successive, parallel, equidistant layers of fog- 

 particles (a sort of space lattice), are superimposed and interfere in a manner 

 evidenced by the disk colors of coronas. 



In the actual case of distribution, however, the fog-particles (as I also 

 pointed out) are too far apart to admit of the immediate application of the 

 direct theory in question. Some extension of this point of view must therefore 

 be forthcoming if the experiment with halved gratings one behind the other 

 is to be reconciled with the circumstances under which coronal phenomena 

 appear. 



