386 SCIENCE PROGRESS 



interference maximum. Therefore, by going along a distance 



i • 3 



-OA parallel to the X axis and up a distance - OC parallel to 



the Z axis, an atom D is reached, the wavelet from which is 

 in phase with that from O, since 



-h, -^h 3 = 



2 2 3 



The wavelet from E is also in phase with that from O, since 



-h 2 -ih 3 = 



2 2 2 3 



and therefore when a pulse falls on these atoms the pulses from 

 the atoms O, D, E are all in phase in the direction of the 

 interference maximum ; that is to say, this is the direction in 

 which the pulse would be reflected from a plane O, D, E. 



The advantage of this way of looking at the formation of the 

 spots is that it enables one to follow what happens when the 

 crystal is not placed symmetrically. If the crystal be tilted so 

 that the incident radiation does not pass along an axis of 

 symmetry, the spots of the pattern will all be displaced and 

 they will move as if they were reflections in planes fixed in the 

 crystal and tilting with it. This is shown very well by two 

 photographs which Laue published in his paper. The first shows 

 the effect obtained when a trigonal axis of symmetry of the 

 zinc blende was parallel to the incident beam (see fig. 2a); the rays 

 now making equal angles with the three cubic axes, a pattern of 

 threefold symmetry is the result ; the spots of this pattern are 

 reflections in planes of the crystal, some of the planes being the 

 same as those which give the spots in the pattern of fourfold 

 symmetry. In the second photograph, the crystal was tilted 

 though 3 from its normal position about an axis perpendicular 

 to one of the cube axes. The pattern is distorted exactly as it 

 would be if the spots were reflections ; it is also interesting 

 to notice that certain spots are very much changed in intensity. 

 If the angle of incidence of a pulse in a set of planes be altered, 

 the value of 2 d cos 6 alters accordingly and so the wave- 

 length of the reflected train may vary from a value characteristic 

 of intense spots to one characteristic of weak ones and vice versa. 

 It was found before, in the case of the square pattern, that 

 intense spots corresponded to a wave length 'o6a and this is 

 true of the two photographs considered here. One spot in 



