270 



PEOF. W. H. BEAGG ON X-EAYS AND CEYSTAL STEUCTUEE. 



As will be seen presently, we are examining the circumstances when this is zero, and 

 we are at liberty to conclude that when this is zero there is no reflection at all, which 

 is all that we require. 



The amplitude of the wave at P, as made up of reflections from all the strata within 

 one period, x = to x = d, is 



I" 



Jo 



o . 



! Sin 2-7T -r Sill rf> ZTT . 



dj 



7 



ax. 



Thus 



Remembering that 2 sin $/A = n/d, we see that this vanishes unless n = 1. 

 a harmonic medium can reflect at one angle only, not at a series of angles. 



If we know the nature of the periodic variation of the density of the medium 

 we can analyse it by FOURIER'S method into a series of harmonic terms. The 

 medium may be looked on as compounded of a series of harmonic media, each of 

 which will give the medium the power of reflecting at one angle. The series of 

 spectra which we obtain for any given set of crystal planes may be considered as 

 indicating the existence of separate harmonic terms. We may even conceive the 

 possibility of discovering from their relative intensities the actual distribution of the 

 scattering centres, electrons and nucleus, in the atom ; but it would be premature to 

 expect too much until all other causes of the variations of intensity have been 

 allowed for, such as the effects of temperature, and the like. 



There is no harm, however, in ignoring these considerations for the present, in order 

 that we may examine the working of the principle. We believe these disturbing 

 causes to have no great effect. 



Let us imagine then that the periodic variation of density has been analyzed into a 

 series of harmonic terms. The coefficient of any term will be proportional to the 

 intensity of the reflection to which it corresponds. This may be justified in the 

 following way. 



Suppose the density of the medium to be represented by the ordinates of the 

 harmonic curve in fig. 18 ; we may look on all the matter represented by the 

 area below the dotted line as inoperative. It is only the part represented by the 



Fig. 18. 



Fig. 19. 



corrugations above that are effective. The number of effective centres is proportional 

 to the area above the dotted line. If we compare the effect with that of a deeper 

 corrugation as in fig. 19, where the amplitude has been increased, the number of 



