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XCVII. The Intensity of Reflexion of X Rays by Crystals. 

 By W. H. Bragg, M.A., F.R.S., Cavendish Professor 

 of Physics in the University of Leeds*. 



WHEN a pencil of homogeneous X rays is incident 

 upon a crystal face it is reflected when, and only 

 when, the angle 6 between the pencil and the face satisfies 

 the equation 



n\ = 2d sin f, 



where X is the wave-length of the rays, n is an integer, and 

 d is the distance between any plane and the nearest which 

 is similar and similarly placed. In the simplest kind of 

 arrangement, all the planes are similar and equally spaced, 

 and d is then the distance between two neighbouring planes. 

 If A, and d are given, if, that is to say, a certain X-ray 

 pencil falls on a certain crystal face, several values of 6 may 

 be found to satisfy the equation, corresponding to consecutive 

 values of the integer. The reflexions occurring at the angles 



. , X . ,2\ . ,3\ 

 sln 23' sm 22' Sm ~2d' •••• 



may be called the reflexions or spectra of the first, second, 

 third order, and so on. 



When the planes are equal and equally spaced the inten- 

 sities of the reflexions decrease rapidly and continuously as 

 n increases ; reflexions of an order higher than the fifth or 

 perhaps the sixth have not been observed. 



When the arrangement of planes is more complicated this 

 regular diminution in intensity may be greatly modified. 

 Complication may arise in either or both of two ways. The 

 planes may be unequally spaced, or they may be dissimilar. 

 An example of the former effect is to be found in the 

 reflexion from the cleavage face (1 1 1) of the diamond. In 

 this case the planes are arranged at distances apart which 

 are alternately as 1 to 3 %. In consequence the second order 

 reflexion disappears entirely (loc. cit.). The intensity of the 

 third and fifth are normal in comparison with the first, but 

 the fourth is twice as strong as it should be. 



An example of the effect of want of similarity in the planes 

 may be illustrated by reference to the (111) planes of rock- 

 salt §. In this case the spacing is uniform but the planes 



* Communicated bv the Author. 



t W. L. Bragg, Proc. Oamb. Phil. Soc. xvii. p. 43. 



X W. H. Bragg and W. L. Bragg', Proc. Roy. Soc. lxxxix. p. 277. 



§ W. L. Bragg, Proc. Roy. Soc. lxxxix. p. 274. 



