ESSAY-REVIEWS 



89 



that, since each atom of the crystal emits spherical diffraction 

 pulses, the latter must resolve themselves into a reflected wave. 

 This reflection is quite independent of any polished surface, 

 but is an interior effect depending on the existence in the 

 crystal of parallel and definitely spaced planes of atoms. A 

 crystal may in imagination be bisected by any number of planes 

 in every conceivable direction, but certain of these, namely 

 those, in general, parallel with the natural faces of the crystal, 

 will be crowded with atoms to a much greater extent than 

 planes taken at random. Fig. 1 shows a beam of X-rays of 

 wave-length X falling at angle 6 on a natural face of a crystal, 

 which consists of parallel planes, /, p r , etc., spaced apart a 

 definite distance d. The reflected waves from the lower planes 

 add themselves on to and augment those from the upper plane 



P 

 P 

 P 

 P 



u 



p 

 p 



Fig. 1. 



only when the length of their path, from the line A, A', A" } A'", 

 say, to C, is some whole number of wave-lengths longer than 

 that reflected from the surface. Otherwise they are in different 

 phases, interfere and cut each other out. In short, the path of 

 the ray from each plane must be the length of the line N D, 

 which is 2<afsin0 longer than that from the one above it, and 

 therefore 2^sin# must be some integral multiple of X, the wave- 

 length. According as this multiple is 1, 2, 3, and so on, we 

 have reflections of the first, second, and third order, much as 

 in the diffraction grating. 



A crystal imagined to be slowly rotating from an initial 

 position in which a beam of X-rays, of definite wave-length, 

 just grazes its face, will reflect X-rays intermittently as its face 

 makes the angles U 0.,, 3 , etc., with the beam. The sines of 

 these angles, or the angles themselves approximately if, as is 



