CONTEMPORARY ADVANCES IN PHYSICS 



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Start then as heretofore from a solitary atom-group A, and add to 

 it two others B and C (Fig. 5). They must not all three be collinear; 

 as a rule it is best that B and C should be the two groups nearest A } 

 As before P stands for the source of the primary waves, Q for the 

 point (on the wall of our imaginary bulb) where the scattered waves 

 are to be measured. The question is: under what condition do the 

 scattered waves from A and B and C all three reinforce one another 

 best at (2? under what condition do the waves from all three groups 

 arrive at Q in identical phase? 



9 



Q 



9 



9 



9 



9 



9 



9 



9 



9 



Fig. 5 — Illustrating diffraction by a plane of atom-groups in regular array. 



Evidently we have only to restate the condition that the waves 

 from A and B arrive in identical phase, and supplement it with one 

 exactly like it for the waves from A and C. We have only to repeat 

 equation (3), and beside it write another like it in which a is replaced 

 by a', the distance from ^ to C; by <^', the angle between the 

 direction of the primary waves PA and that from A to C\ and 6 by 6' , 

 the angle between the direction of the scattered waves AQ and that 

 from A to C. When the waves from all three atom-groups reinforce 

 one another, both equations prevail : 



a(cos d — cos 0) = wX, 

 a'(cos 6' — cos <!>') = n'\. 



(3) 

 (4) 



^ The choice of groups to serve as B and C is purely a question of expediency. 

 The same results are reached whichever two we choose, so long as they are not 

 collinear with A ; but the results when reached are in a form which depends upon 

 the choice, and is most convenient when AB and AC are parallel to the crystallo- 

 graphic axes in the plane. 



