X-RAYS AND CRYSTALS 



385 



one plane go to build up a reflected wave front and therefore, 

 as the incident pulse traverses the crystal, a train of reflected 

 waves — one from each plane — is formed, the pulses in the train 

 following each other at intervals of 2 d cos 6, where d is the 

 distance between successive planes and 6 the angle of incidence. 

 These reflected pulses may be analysed by Fourier's theorem 



into trains of waves of wave lengths X, -, -, -, where \=2 d cos 9. 



2 3 4 



Now though the pulses in^the beam have been supposed to be 

 quite irregular, they possess some quality which is expressed 

 by saying that they have an average " breadth " of something 

 like io -9 cm. If in the reflected train pulses follow each other 



Fig. 4. 



at intervals much smaller than this they will interfere and cut 

 each other out ; if, on the other hand, they follow each other at 

 long intervals, the trains will contain little energy per unit 

 length. Thus out of all the possible ways of dividing the crystal 

 into planes, a certain group will be selected, these being planes 

 for which the value 2 d cos 6 lies within a range of wave 

 lengths of the order of the average " breadth " of the pulses. 



This way of looking at the interference must be analytically 

 exactly the same as that used by Laue. The numbers h x , h 2 , h 3 

 in his analysis correspond to parameters defining one of these 

 methods of dividing the crystal into planes. For instance, a 

 spot in the photograph corresponds to the values 3, 1, 1 of 

 hi, h 2 , h 3 . This means that (see fig. 4) the wavelet from the 

 atom at O is three wave lengths behind that from the atom at A, 

 one wave length ahead of that from C, in the direction of the 



