316 Mr. C. G. Darwin on the 



spite of the well-known fact that their absorption occurs by 

 means of the emission of high-speed electrons. But a some- 

 what less satisfactory assumption must also be made. The 

 observed exponential absorption of homogeneous rays is 

 probably a statistical effect, but it is here assumed that the 

 amplitude of a wave passing through matter diminishes 

 exponentially with an absorption coefficient half that ob- 

 served for the intensity. This assumption brings out the 

 correct form for the absorption, and is to a certain extent 

 justified by one of the experiments of Mr. Moseley with the 

 present writer*. It was found that the intensity of reflexion 

 from a crystal was cut down by exactly the same amount by 

 a given piece of aluminium, whether it was placed so as to 

 intercept the whole radiation before reflexion, or the selected 

 radiation after reflexion. This experiment proves that the 

 absorption of a heterogeneous beam can be calculated by 

 Fourier analysis. 



It should be said at once that part of the quantitative 

 discussion in the present paper is inadequate and can only 

 be regarded as a first approximation, but several points of 

 interest have emerged. It is hoped to treat of a more 

 complete theory in a future paper. 



3. The Structure of a Reflected Line, 



The first point we shall consider is employed in Moseley'sf 

 method ior discovering the characteristic X-ray spectra of 

 the elements. A crystal reflects waves of given length A 

 only at the angles given by the equation n\ = 2a sin 6, where 

 n is an integer, a the distance between successive planes in 

 which the atoms of the crystal are arranged, and is the 

 ''• glancing 3i angle between the incident beam and the 

 crystal face. If homogeneous radiation coming from a fine 

 source falls on a crystal it is only reflected in the neigh- 

 bourhood of a certain line on the crystal, this line being such 

 that the incident beam there makes the proper angle with 

 the crystal face. The reflected beam falls on a photographic 

 plate and produces a fine line on it. Our present object is 

 to discuss the structure of this line, which is of course not 

 infinitely narrow. This can be done without calculation. 

 First consider the effect of the outermost plane of the 

 crystal on radiation coming from a point source. Each atom 

 scatters a certain amount of radiation into a small spherical 

 wave. These scattered wavelets reconstruct themselves into 



* Moseley & Darwin, Phil. Mag-, vol. xxvi. p. 210 (1913;. 

 t Moseley, Phil. Mag. vol. xxvi". p. 1024 (1913). 



