149 



equal to d.sinQ, when <p is the glancing l ) angle which the incident 

 pencil makes with the planes V l or F 2 . The whole phase-difference 

 is therefore: 2d.sin(p and an interference-maximum will only 

 occur, if this difference be equal to A or to a multiple of it: 2A, 3A, 

 4A, etc. 



It is obvious from the equation: 



2d.sin(p = nh, 



that for constant d and for each definite value of A, the angle <J> 

 can only have definite values Q lt <J) 2 , < 3 , etc., the sines of which are 

 rational multiples of each other. Conversely: if V l is given in a 

 certain crystal, d is wholly determined by the internal specific crystal- 

 structure, and when homogeneous radiation of a known wave-length 

 A be used, we have only to measure Q lf <p z , etc., to find the distance 

 d between two consecutive layers parallel to V : . On the other hand 

 it must be clear that from all wave-lengths present in the incident 



radiation, only that which is equal to A, or , , etc., will be 



reflected under the angles mentioned, when the plane is in a fixed 

 position. The reflection at such a fixed set of net-planes under a 

 constant glancing angle <J) has, therefore, the effect of separating 



only special wave-lenghts A, and -, -, etc., out of the total number 



of wave-lengths present in the incident rays; it changes the incident 

 radiation, being in the case of uniform metallic anticathodes a 

 wave-motion of only a comparatively small number of wave-lengths, 

 into a "monochromatic" one of definite wave-length A or m A, corres- 

 ponding to a certain glancing angle <J), and, therefore, such a reflection 

 has a pronounced selective action. It may be remarked here that V l 

 need not be a limiting plane of the crystal; the so-called "reflection" 

 occurs within the crystal, and at the parallel, equidistant net-planes 

 present therein, which are situated in a relatively thin layer parallel 

 to the reflecting external surface of the crystal. 



When the original radiation falling on the crystal is itself mono- 

 chromatic, the effect is still more restricted. For only at a few charac- 

 teristic glancing angles <&, < 2 , < 3 , etc., can reflections then take 

 place, these all being determined by the equation: 2d,sin(p = nx. 



The crystal in this case must be held at exactly the characteristic 



*) The "glancing" angle is, therefore, the complement of the "incident" angle 

 between the incident ray and the perpendicular to the plane of reflection. 



