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XXXIV. The Theory of X-Ray Reflexion. By C. G. 

 Darwin, M.A*, Lecturer in Mathematical Physics in the 



University of Manchester *« 



1. r¥lHE formula developed by Prof. Lauef in connexion 

 JL with the interference of X rays in crystals are 

 competent to show the positions in which the interference 

 maxima occur, but do not give the intensities at the maxima. 

 For it is readily calculated that it is impossible experi- 

 mentally to get a crystal so small that the spherical waves 

 coming from a source at any manageable distance can be 

 regarded as plane. If, following Bragg J, we regard the 

 phenomenon as due to reflexion in a set of parallel planes of 

 atoms, the extreme shortness of the waves makes the Fresnel 

 zones in these planes very small (in Friedrich and Knipping's§ 

 experiments they would be about 2xl0 -7 sq. cm.), and this 

 vitiates the application of Laue's formula for the intensity. 

 In a later paper Laue || has made use of the Fresnel diffrac- 

 tion principles to account for the shapes of the spots on the 

 interference photographs, but a complete theory must regard 

 the whole problem as one of spherical waves. 



In working out such a theory there is great advantage in 

 taking as model that experimental arrangement which has 

 in fact proved most fruitful, reflexion from the planes 

 parallel to an external face of a crystal. This gets rid, both 

 for theory and experiment, of a great deal of rather com- 

 plicated geometry, w T hich is useful in investigating the 

 structure of crystals, but has nothing to do with the nature 

 of the reflexion. 



2. Assumptions. 



We shall assume simply that X-ray phenomena are a 

 branch of optics. The optical theories of diffraction, and 

 also of dispersion, etc*, work out correctly on principles 

 depending on a simple vibration theory, although some of 

 the phenomena of light can only be reconciled with this 

 theory with difficulty. Thus the photoelectric effect depends 

 on Planckian considerations which seem contradictory to the 

 wave theory. In the same way we shall suppose that X rays 

 obey the ordinary laws of the electromagnetic theory, in 



* Communicated bv Sir Ernest Rutherford, F.E.S. 



t M. Laue, Kon. Bay. Ah. 1912, p. 303. 



t W. L. Bragg, Proc. Cainb. Phil. Soc. vol. xtii. i. p. 43. 



§ Wi Friedrich & P. Knipping, Kon. Bay. Ak. 1912, p. 311. 



|i M. Laue, AnnaL d. Phys. Bd. xli, p. 1003 (1913). ' 



