Remarkable Phenomenon of Crystalline Reflexion, 257 



length is altered, say, by one twentieth part? Such a result 

 may arise from the interference of two streams under a 

 relative retardation of many periods ; hut in that case there 

 are necessarily a whole series of wave-lengths all equally 

 effective. Tbe prism should reveal a number of bright 

 bands and not merely a single band. The selection of a 

 particular wave-length reminds one rather of what takes 

 place in gratings ; and I was from the first inclined to attri- 

 bute the colours to a periodic structure, in which the twins 

 alternate a large number of times. Such a view explains 

 not only the high degree of selection, but also the copious- 

 ness of the reflexion. 



Partly with a view to this question, I have discussed in a 

 recent paper* the propagation of waves in an infinite lami- 

 nated medium (where, however, the properties are supposed to 

 vary continuously according to the harmonic law), and have 

 shown that, however slight the variation, reflexion is ultimately 

 total, provided the agreement be sufficiently close between 

 the wave-length of the structure and the half wave-length 

 of the vibration. The number of alternations of structure 

 necessary in order to secure a practically perfect reflexion 

 will evidently depend upon the other circumstances of the 

 case. If the variation be slight, so that a single re- 

 flexion is but feeble, a large number of alternations are 

 necessary for the full effect, and a correspondingly accurate 

 adjustment of wave-lengths is then required. If the variation 

 be greater, or act to better advantage, so that a single 

 reflexion is more powerful, there is no need to multiply so 

 greatly the number of alternations; and at the same time the 

 demand for precision of adjustment becomes less exacting. 

 The application of this principle to the case of an actual 

 crystal, supposed to include a given number of alternations, 

 presents no difficulty. At perpendicular incidence symmetry 

 requires (and observation verifies) that the reflexion vanish ; 

 hut, as the angle of incidence increases, a transition from one 

 twin to the other becomes more and more capable of causing 

 reflexion. Hence if the number of alternations be large, the 

 spectrum of the reflected light is at first limited to a narrow 

 band (whose width determines in fact the number of alterna- 

 tion-). As the angle of incidence increases, the reflexion at 

 the centre soon becomes sensibly total, and at the same time 



* " On the Maintenance of Vibrations by Forces of Double Frequency, 

 and on the Propagation of Wayea through a Medium endowed with a 

 Periodic Structure," Phil. Mag. Aug. ] 



Phil. May. B. 5. Vol. 26. No. 160. Sept. 1888. S 



