148 



and to avoid all calculations. It differs only from Von Laue's 

 method in form, not in essence, as several authors have shown. l ) 

 The principal idea of it is, that the phenomena observed can also 

 be described as if the radiation were reflected by the consecutive 

 parallel and equidistant molecular layers of the crystal under con- 

 sideration, the "reflected" vibrations interfering with each other 

 according to Huyghens' principle, because each particle becomes 

 in its turn the centre of a secondary wave-motion spread around 

 it spherically, when a pulse of the incident beams passes over it. 



Let us suppose, that the pencil of 

 parallel R on t gen-rays L^L t (jig. 125) 

 contains every possible wave-length over 

 a wide range, its spectrum, therefore, 

 being a continuous one. According to 

 our suppositions, each atom of a net- 

 plane V l struck by the primary radiation, 

 will become the centre of a new wavelet, 

 and these various diffracted wavelets 

 will touch a reflected wave-front per- 

 pendicular to the parallel beam L\L\ 

 which emerges from the crystal. The 

 same will be true for the atoms of the 

 consecutive net-planes F 2 , F 3 , etc. ; but 

 since the rays do not usually penetrate 

 more than e.g. one millimetre deep into 

 the substance, it is only a relatively thin 

 layer of crystalline substance that is 



engaged in the phenomenon considered, and in every case the 

 number of "reflecting" net-planes is a finite one. Only when 

 the reflected wave-trains are in the same phase, i. e. when they 

 interfere with phase-differences of A or a multiple of A, an 

 interference-maximum will occur. Now if bS be the plane per- 

 pendicular to the incident beam of radiation, and aS that perpendi- 

 cular to the "reflected" beam L\L' 2 , the difference in the path 

 travelled by a ray coming from V lt and by that coming from F 2 , 

 will obviously be bP + Pa. But bP Pa, is the projection of 

 the distance d between two consecutive net-planes F x and F 2 

 upon the direction of the incident an emergent beam, and therefore 



!) Cf.: T. Terada, Proceed. Tokyo math. phys. Soc., 7, 60, (1913); G. W. 

 Wullf, Phys. Zeils., 14, 217, (1913). 



Fig. 125. 



