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out) and they contain four variables (X, /Si, /So, /Ss) so that diffraction- 

 spots can appear only for special sets of values of these four, to be 

 obtained by solving the equations. In the original method of Laue, 

 a wide range of values of X is constantly provided, and the screen 

 extends over a wide range of values of jSi, ^2, ^s', consequently the 

 chance of observing spots is good. In the method of Davisson and 



68 V. 



Fig. 15 — Gradual appearance and disappearance of a diffraction beam as the 

 mean wave-length of the primary waves passes through one of the values compatible 

 with equations (6). (Davisson and Germer.) 



Germer the different values of X are realized in succession and a mov- 

 able Faraday chamber searches out the peaks — a process much more 

 long-drawn-out, but whenever one finds a peak one knows the wave- 

 length to which it is due. With the other two methods the value of 

 X is prescribed, and consequently two at least of the direction-cosines 

 a must be variable ; therefore the crystal with its implanted coordinate- 

 frame must be revolved, or else a multitude of crystals oriented every 

 way must be placed in the path of the incident beam. 



In the foregoing passage it seems as if I had taken for granted 

 that the integers hi, ho, hs have fixed unchangeable values. As a 

 matter of fact they may be any three integers at all. Strictly speaking, 

 there is a different quintet of equations for every conceivable triad 

 of integral values of the "indices" h. One might infer that in Laue's 

 experiment the screen would be found completely covered with spots 

 due to all the different triplets. However it turns out that only the 

 spots for which all the integers are small stand out strongly enough 

 to be seen. Meanings for these integers must now be found; but 

 before findmg them I will deduce two more equations out of the 

 quintet. 



Squaring and adding the left-hand members of equations (6a, 6b, 6c), 

 doing the same with the right-hand members, equating the sums and 



