CONTEMPORARY ADVANCES IN PHYSICS 405 



up of planes of atom-groups laid parallel to one another at equal 

 intervals. Suppose the space above and below the plane of Fig. 5 

 to be thus stratified; select, from the stratum just above or just below 

 that figured on the page, an atom-group close to A, preferably the 

 closest. Call it D; let a" stand for the distance from A to D, 0" 

 for the angle between the direction in which the primary waves 

 advance and the direction AD, d" for the angle between the direction 

 from A towards Q and that from A to D. When the scattered waves 

 from all jour groups ABCD reinforce one another best at Q, all these 

 three equations are valid simultaneously: 



a (cos d — cos (j)) = wX, (3) 



a'(cos d' - cos 0') = n'\, (4) 



o"(cos 6" - cos 4)") = n"\, (5) 



n" standing for a third integer, which may or may not be the same 

 as either of the other two. In all directions for which d, d', 6" conform 

 with equations (3), (4), and (5), there will be maximum amplification 

 of the scattering-pattern of any atom-group by its triad of neighbors. 



Now in thus adding a third equation to the previous one and two, 

 we have made the conditions so severe that save in exceptional cases 

 they are quite unfulfillable. Equations (3) and (4) confined the 

 amplification-effects for which we seek to the points of intersection 

 of a few rings belonging to two families, oblique to one another upon 

 the wall of the bulb. Equation (5) supplies a third family of rings 

 oblique to both, having for its poles the points where the diameter 

 parallel to AD reaches the wall of the bulb. Agreement of phase 

 between the waves scattered from A and B and C and D, optimum 

 amplification, can occur only if and where a ring of the third family 

 cuts rings of the first and the second just where these happen to cut 

 one another. And when the set of four atom-groups ABCD is repeated 

 over and over again in an extensive crystal lattice, these points of 

 optimum amplification are the only points where the amplification 

 is great enough to enhance the diffraction-pattern into visibility. 

 Visible luminous spots will appear on the coating of the wall of the 

 bulb, only if three rings one from each family happen to intersect at 

 the same point — only by coincidence, in the popular sense of the word. 



To bring about such a coincidence, there are four practicable ways. 



(I) If the incident beam is monochromatic, or comprises a narrowly 

 limited range of wave-lengths, we can rotate the crystal — presenting 

 it to the beam under varying aspects, and so in effect varying the 



