X-RAYS AND CRYSTALS 379 



ordinary line grating. In the latter case every wave length can 

 form an interference maximum, in other words, the grating can 

 give a continuous spectrum. In the former case two extra 

 conditions must be satisfied, only one more direction cosine is 

 available and now it is only certain wave lengths that can form 

 maxima at all. 



A similar effect may be got with a line grating and white 

 light. If half-silvered parallel plates are placed in front of the 

 grating of a spectroscope, thus introducing an extra condition 

 for interference, a continuous spectrum is no longer obtained 

 when white light is focussed at the collimator, but in its place is 

 seen a line spectrum representing a series of definite wave 

 lengths. If for the line grating a cross grating were substituted 

 and for the collimator slit a small hole at its centre, the analogy 

 would be still closer. 



If the photograph represent the most general pattern possible, 

 all values of h 1( h 2 , h 3 ought to correspond to spots. This is of 

 course impossible; consequently there must be some limit to the 

 values of h lt h 2 , h 3 and in a general way it may be said of the actual 

 photograph obtained that the larger these numbers are, the 

 fainter are the corresponding spots. But at any rate, it would 

 be expected that the spots in the photograph should correspond 

 to a list of numbers h 1( h 2 , h 3 complete over a certain range. This 

 is not so and some explanation must be put forward to explain 

 why certain spots fail to appear. 



The explanation which Laue suggests is this — that when a 

 spot corresponding to some simple set of numbers h x , h 2 , h 3 is 

 missing in the photograph, it is because there is absent from the 

 incident radiation that wave length which is the only one capable 

 of forming the spot in question. On the other hand, certain other 

 spots do actually appear, because the right wave lengths to form 

 them are available. In his paper, he shows that all the 

 prominent spots in the photograph can be explained as due to 

 five wave lengths which may be regarded as five broad lines in 

 the spectrum of the incident radiation. The lines must be broad 

 because the five definite wave lengths only satisfy the equation 

 approximately. This explanation is not very satisfactory. In 

 the first place it invokes the aid of five constants to explain the 

 pattern and in the second place these five wave lengths would 

 give many othenspots which, as a matter of fact, do not appear in 

 the photograph. 



