The Intensity of Reflexion of X-JRays by Rock-Salt. 323 



angle, although this depends on the state of perfection of 

 the face as explained above. A direct comparison showed 

 that when a narrow beam of X-rays falls on the face (100) 

 set so as to reflect it, the intensity of the reflected beam is 

 about one twenty-fifth of the incident beam.] 



Theoretical Formula for the Intensity of Reflexion. 



13. Formulae for the intensity of reflexion have been 

 deduced by Darwin and Compton (loc. cit.). The formula 

 given by Compton is directly applicable, for he calculates 

 the total amount of energy reflected when the crystal is 

 turned at a uniform rate through the reflectino- - anode. 

 That given by Darwin may be extended to this case, and is 

 in agreement with Compton's formula. 



These formulse are based on the amount of radiation 

 scattered by a free electron when set in oscillation by rays 

 of given intensity. It has been shown by J. J. Thomson * 

 that the amount of energy S radiated per second by a single 

 electron is given by 



S >Stt e" 



where P is the energy of the incident radiation falling on 

 1 sq. cm. per second, e and m are the charge and mass of 

 the electron respectively, and c is the velocity of light. 

 This expression is confirmed by Barkla's work f on the 

 total amount of radiation scattered by elements of low 

 atomic weight, from which he deduced that the number 

 of electrons in the atoms of these elements is approximately 

 equal to one-half the atomic weight. If the incident radia- 

 tion is plane polarized, the relation between the amplitude of 

 the electric vector of the incident radiation, and that of the 

 radiation scattered in any direction perpendicular to the 

 direction of the electric vector, is given by 



a;_^_ i 



A ->g» 2 'E' 



where R is the distance from the electron. To simplify 

 matters, we will consider that the radiation reflected from 

 the crystal face is plane polarized in such a manner that the 

 electric vector is perpendicular to the plane of incidence, 

 and allow for the "polarization factor" at a later stage ol 

 the calculation. 



* J. J. Thomson, ' Conduction of Electricity through Gases,' p. 321. 

 t C. G. Barkla, Phil. Mag. vii. p. 543 (1004), and xxi. p. (US (1911), 



