802 Mr. 0. G. Darwin on the Reflexion of 



problem led to a formula for the intensity of reflexion. The 

 experimental arrangements to which the calculations were 

 adapted were those in vogue at that time — that is, with 

 crystal fixed during each observation. This was the 

 arrangement used in the experiments of H. Gr. J, Moseley 

 with the present writer *, and it was to them that the 

 theoretical calculations were applied. In the course of 

 those experiments a single, but a fairly good, measure was 

 made of the absolute intensity of the reflexion of " white 

 X-rays " and also the curve of reflexion against angle was 

 found. By means of a quadrature it was therefore possible 

 to measure the effect of a single atom, and the result was of 

 the right order for the number of electrons anticipated. 

 Yet it was apparent that the theory was defective, for it 

 was calculated that the diffraction pattern of the reflexion 

 could at most be a few seconds across^ and that even if all 

 the available radiation in this breadth were reflected the 

 total would still be far short of the observed amount. 



Now, if the reflexion was perfect over any region, it could 

 not be legitimate to treat of the atoms as all scattering in- 

 dependently. In D. ii. therefore the mutual influence of the 

 successive planes was included. It was found that over a 

 breadth of a few seconds the reflexion was perfect, and that 

 in this region the ordinary absorption of the rays by the 

 crystal was swamped by a far more powerful special extinc- 

 tion. These principles led to a modified reflexion formula, 

 but one which could explain the magnitude of the reflexion 

 no better than the old. A way was found out of the 

 difficulty by supposing the crystal to be a conglomerate of: 

 small blocks of perfect crystal all orientated approximately 

 in the same direction, for such a conglomerate would reflect 

 the radiation at many of its blocks, internal as well as 

 external, and this would much increase the total amount 

 reflected. No attempt was made to treat the problem at 

 all fully, but a general line of argument suggested that the 

 effect would be approximately to reinstate the formula of 

 D.i. without the objections that had before attached to it. 



All the calculations of these papers were based on experi- 

 ments in which the crystal was fixed. A. H. Compton t 

 carried out a somewhat similar process quite independently, 

 but based it on the experimental arrangement which has, in 

 fact, proved more convenient in the study of monochromatic 



* Moseley and Darwin, Phil. Mag. vol. xxvi. p. 1024 (1913). 

 t Compton, " The Intensity of X-Ray Reflexion," etc., Phys. Rev. 

 vol. ix. p. 29 (1917). 



