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



Equation (26) is suitable for use in computations for low 

 temperatures. The expanded form for ^(0) analogous to 

 (24) is suitable for use with high temperatures and is more 

 immediately intelligible than (26). This form is 



x(o )= wn W J/M^ 



x fa (*-*)* 2(d-*y-d (d-*)*y 

 and the corresponding form of the second virial coefficient is 



»=1 n ! 



x {(^? 2(d-a) H (d-a)*1 



XCII. The Reflexion of X-Raijs from Imperfect Crystals. 

 By C. Gr. Dak win, Fellow and Lecturer of Christ's College^ 

 Cambridge *. 



1. Introduction. 



PTVHE recent work of Bragg, James, and Bosanquet |, on 

 X the reflexion of X-rays from rock-salt crystals is of 

 extreme importance in that it promises more directly than 

 any other method to supply information about the actual 

 positions which the electrons occupy in the atom. The 

 method consists in a study of the intensity with which the 

 various faces of the crystal reflect a given wave-length, and 

 is based on the theoretical formulae given by the present 

 writer %. These formulae showed that such experiments 

 should determine a certain quantity, which is, roughly 

 speaking, the amplitude of the wave scattered by all the 

 electrons in a single atom in the direction of the reflected 

 beam. A study of the various faces of a crystal gives this 

 amplitude as a function of the angle of scattering, and from 

 that the positions of the electrons can be inferred — with this 

 second half of the problem I shall not be here concerned. 

 But the deduction of the amplitude from the experiments 

 encountered certain peculiar difficulties ; for the absorption 



* Communicated by the Author. 



f Bragg, James, and Bosanquet, Phil. Mag. vol. xli. p. 309, and 

 vol. xlii.p. 1(1921). 



\ Darwin, Phil. Mag. vol. xxvii. p. 315 and p. 675 (1914). 



