Theory of X- Ray Reflexion. 685 



In spite of their failure to account for the amount of re- 

 flexion, the formulae developed here are to be preferred to 

 the earlier ones, since they include an effect which has been 

 shown to have been unjustifiably disregarded in the fovmer 

 paper. The new formulae make the reflexion independent of 

 the absorption coefficient of the crystal. Now the work of 

 W. H. Bragg* has proved that absorption does play an 

 important part in the reflexion, and this suggests a way out 

 from the discrepancy. If a crystal is not perfect, so that 

 the planes are not everywhere absolutely parallel, it may 

 happen that some part of the beam which has not been ex- 

 tinguished by reflexion at the surface will find a piece of the 

 inside of the crystal at the proper angle, and so will give 

 rise to a second reflexion. Such an effect will obviously 

 involve the absorption coefficient of the rays in the crystal. 



8. Imperfect Crystal. 



The irregularity of a crystal is of necessity a rather in- 

 definite matter, which it would be perhaps difficult to discuss 

 with rigour. We shall only attempt to see the general type 

 of change to be expected. We will first study the effect of 

 supposing that the surface is irregular, without taking into 

 account the possibility of interior reflexions. Suppose that 

 the surface is divided up into a number of plates whose 

 normals all point in slightly different directions. It is clear 

 that in some cases there might be no reflexion or there might 

 be several. Now the rays reflected from two different plates 

 of the crystal will travel in slightly different directions, and 

 if a photographic plate is put in their path they will strike 

 it at different points. But if the distance of the photographic 

 plate from the crystal is the same as that of the source, they 

 will strike it at the same point ; for on account of the con- 

 stancy of the angle of reflexion, the locus of points which 

 can reflect rays from a given source to a given point is a 

 circle, and only when source and point are equidistant from 

 it does this circle touch the crystal. In this case only is 

 there any considerable area on the crystal which can all 

 reflect to the same point. Moreover, as we shall see later, a 

 very important fraction of the reflected radiation comes from 

 reflexions inside the crystal, and these will be focussed to 

 points only very slightly different from those coming from 

 the surface. The accuracy with which Moseleyt could 

 determine his X-ray spectra is probably partly due to this 



* W. H. Bragg, p roc . R ov . Soc. A. vol. lxxxix. p. 430 (1914). 

 t Moseley, Phil. Mag. vol", xxvi. p. 1024 (1913). 



Phil. Mag. S. 6. Vol. 21. No. 160, April 1914. 2 Z 



