Results of Crystal Analysis. 83 



§ 7. Calculation of Intensities and Determination of 

 the Parameters. 



When the rays are reflected from a face with equivalent 

 and equidistant planes the intensity distribution is said to 

 be normal, and according to Bragg it is characterized by a 

 gradual diminution of intensities with increasing order. 



The exact law for this variation is not known. Bragg * 

 finds that the intensities corrected for the temperature 

 effect as derived from the formula of Debye f are approxi- 

 mately inversely proportional to the square of the order 

 number (n). The cause of this variation is yet unknown. 



In spite of the fact that the rate of variation will vary 

 from one case to another, it will generally not be difficult to 

 see from the observed intensities whether the spectrum is 

 normal or not. The criterion is not so much the rapidity 

 with which the intensity falls with increasing order, but 

 much more a typical regular form of the intensity curve. 



The problem of finding the distribution of intensities in 

 the case that not all the reflexion planes of the face are 

 identical, has been treated by W. H. and W. L. Bragg. The 

 calculation is based on the assumption that the amplitude 

 reflected from a certain point-plane is proportional to the 

 mass associated with unit area of the plane. 



In view of the theory of secondary radiation given by 

 Sir J. J. Thomson % , it would be more natural to suppose 

 the amplitude proportional to the number of electrons per 

 unit area, and introducing the atom-model of Rutherford 

 and Bohr we should put the reflecting power of an atom 

 proportional to the atomic number. 



As the atomic number for most elements is approximately 

 proportional to the atomic weight, it will make very little 

 difference whether we use atomic weights or atomic numbers ; 

 but as it must be the number of electrons and not the gravi- 

 tational mass which is concerned, we shall introduce the 

 atomic numbers in our calculations. 



Let unit area of the reflecting plane be composed of v x 

 atoms of atomic number N l5 v 2 atoms of atomic number N 2 , 

 &c, then the number of electrons per unit area (jjl) will be 



fJ/ =v 1 $ l + * 2 N 2 + (9) 



* W. H. Bragg & W.L.Bragg, ' X-Eays and Crystal Structure/ 

 p. 193. 



f P. Debve, Verh. d. D. Phijs. Ges. xv. 1913 ; Ann. d. Phys. 1914, 

 p. 49. 



% Sir J. J. Thomson, 'Conduction of Electricity through Gases,' 

 p. 321. 



G2 



