688 Mr. C. G. Darwin on the 



due to refraction remains, since the distortion of the crystal 

 does not influence the phase relations of the waves scattered 

 in the direction of the transmitted beam. The pattern 

 observed on a photographic plate will in general be very- 

 irregular, but when the plate and source are equidistant 

 from the crystal it should have the general character of a 

 band one side of which shades off exponentially. It is 

 readily calculated that the intensity in the band falls to a 

 fraction 1/e in a breadth sin <f> cos $//z. 



For convenience I repeat the reflexion formula?. 



The effect of monochromatic radiation measured in an 

 instrument at distance p from the image of the source with 

 a slit of length I and sufficient breadth is 



-rl A 1+ COS 2 2<£ XT9 f 2 - -^(2«7r)2,.^ , ti 



I- A 5 ^N 2 '— e aa - J\ 8 cosec 2$. .(13) 



pip, 



The intensity of reflexion of white radiation is 



Ai±^ W2 a e -^(£^\. . (14) 



p z 2 n n- \ p, J n 



The factor A will probably vary] from crystal to crystal 

 according to the amount of contortion, but we should not 

 expect it to depart widely from unity, its value in the earlier 

 paper. As we are now free from the argument about the 

 limitation of reflexion to a breadth of 5 /; , we may use the 

 experimental value of the efficiency to determine f 2 . When 

 A was unity it was found to be 26(e 2 /mC 2 ) 2 , and this is of the 

 order to be expected from atoms with about 10 electrons, of 

 which some, but not all, are concentrated close together. 



9. Scattering from a Single Atom. 



Since the first part of this paper was written two experi- 

 mental results have been published by W. L. Bragg f, which 

 have an important bearing on our subject. In the first place 

 he has shown that we must suppose that each atom scatters 

 a wave whose amplitude is proportional to its atomic weight. 

 Thus in fluorspar the two fluorine atoms give waves which 

 can destroy by interference the wave coining from one 

 calcium atom. Since ail experiments have shown that the 

 atomic weight is proportional to the number of electrons v 

 in the atom, we conclude that /' is closely proportional to v. 

 This result would hold if we could suppose that the majority 



* Loc. cit. p. 331. 



t W. L. Bragg, Proc. Roy. Soc. A. vol. lxxxix. p. 468 (1914). 



