368 SCIENCE PROGRESS 



worked out independently and almost simultaneously in 

 Germany (Debye and Scherrer, Physik. Zeitsch., xvii, 191 6) 

 and in America (A. W. Hull, Phys. Rev., 9, 84, 1917)- 



The general principles governing the regular scattering or 

 reflection of X-rays by crystals could not be more lucidly 

 explained than in the account given by the original investi- 

 gators (W. H. and W. L. Bragg, X-Rays and Crystal 

 Structure). Many of the results obtained by these earlier 

 methods were necessary, and are assumed in the interpretation 

 of the powder photographs, e.g. the measurement of wave-length 

 and the examination of the characteristic spectra of the metals. 



When a parallel, homogeneous beam of X-rays penetrates 

 a crystal, the latter acts as a three-dimensional grating. The 

 regularly distributed scattering points lie in planes regularly 

 spaced throughout the mass, the spacing being greater or less 

 according as more or less points are included in each plane. 

 Each may be considered to act as a mirror reflecting a small 

 fraction of the incident rays. A strong maximum of such 

 reflected energy occurs when the contributions from all the 

 similar planes (the number of such co-operating planes is of the 

 order of several milUons) are in phase, which only occurs when 



n\ = 2dsm6 ( i ) 



where w is a small integer, the " order " of the reflections, \ the 

 wave-length, d the spacing of the planes, and 6 the angle of 

 incidence. 



If a crystal be rotated about an axis in the plane, a fine 

 beam will be reflected as a series of beams, in a plane perpen- 

 dicular to the axis, corresponding to w = i, 2, 3, etc., the higher 

 orders being progressively fainter and necessarily ceasing when 

 n\ > 2d. If other axes are taken, the reflections will all lie 

 on cones whose axis is the undeviated beam and semi-vertical 

 angle 26 given by equation (i). Thus, if a crystal be given 

 every possible orientation, there will be reflected a system of 

 cones corresponding to all possible planes and orders for which 

 equation (i) can hold. This is practically attained in a fine 

 crystalline powder in random distribution, with rotation and 

 stirring if necessary, as with a coarse, lamellated or fibrous 

 powder. 



Though an infinite number of planes can be drawn in a 

 crystal, the number capable of reflecting is strictly limited 



and includes only those in which d> -. Hence the number of 



lines, among which the greater part of the scattered energy must 

 be divided, is finite and each has equal reflecting opportunity. 

 In diamond with the tungsten Ka, A. =0-2 12 A, this number 

 is 100, while the iron doublet, \ = 1-93, can be reflected by 



