1283 



take a suiniiiation of similar expressions for the different wave- 

 lengths, so rliat instead of iah we may write 



Slab • 



The sign of summation S refers to tlie different wavelengths. The 

 distribution of infensitj' is now a line system with a limited number 

 of lines, one light line in the middle and on both sides light and 

 dark ones. At some distance Siab = 0, because there where for one 

 wavelength cos [ff\i — tpb) '«^s a positive value, there will be a 

 wavelength which is hardly different from it (and therefore makes 

 the same impression in our eye) for which this expression has a 

 negative value. 



With natural* light we thus have the superposition of a uniform 

 field and of narrow line-systems crossing each other near the 

 centre. 



From this we may conclude: i/' the classic theory can explain 

 the phenomena investigated by v. Laue, tke.-ie line systems are the 

 fibres observed by him. But whether the theory can furnish the 

 explanation remains for the present more oi' less dubious. 



This is evident from the following considerations. In each elementary 

 line-system a, b the intensity varies between ^- 2 and -j- 2, while 

 ix) the uniform field it has the much highei' value it,. If there are 

 e. g. 10000 grains, the superposition of one line system on the 

 uniform field will give fluctuations from 10002 to 9998, which it is 

 of course impossible to observe. 



One single line-system is thus undetectable. But the lines connecting- 

 each pair of apertures and therefore also the line-systems perpendicular 

 to those lines have all possible directions determined by probability. 

 Lines visible on the background n can be formed when accidentally 

 a number of line-systems has so nearly the same direction that at 

 a distance from the centre which is not too great, the maxima 

 (-}- 2) of one system coincide with those of another system. The 

 question whether the classic theory can explain the phenomenon 

 may thus be formulated as follows: 



I. Is such an accidental accumulation of different line-systems 

 in a definite direction to be expected often enough, according to the 

 theory of probability ? 



The theoretical treatment of this question will he left aside here. 



Only the following may be remarked : In reality many line-systems 

 will fall out. We do not work namely with a light-point, but with 

 a source of certain dimensions (aperture in the screen). Each point 

 of this source gives its own diffraction image and all these images 

 are shifted with respect to each other. In this way the finest line- 



