424 BELL SYSTEM TECHNICAL JOURNAL 



swer is given by a standard formula: the three direction-cosines are: 



7i = 



72 - , _ ," — ; (14) 



The common factor a has vanished, as it should. 



Compare these expressions with those in equation (13). One sees 

 instantly that the strata {Hi, H2, H3) are so oriented that these 

 strata could serve as mirrors to reflect the primary beam towards the 

 diffraction-spot of which the indices are h = Hi, hi = H2, h = Hz; 

 or towards the spots of which the indices are (nHi, nHi, nHs), where n 

 stands for any integer. Or: the diffraction-spot {hi, hi, hs) may be con- 

 ceived as due to a reflection of part of the wave-motion in the incident 

 stream, by the atom-layers of which the symbol is nJC, W2/C, W3/C; 

 C standing for the greatest common divisor of hi h^ h^. 



This is part of the principle which Bragg deduced from Laue's 

 theory, but not the whole of it. 



I have shown in an earlier article of this series * (and the reader can 

 easily work out) that when a beam of plane waves falls successively 

 on two plane parallel surfaces which reflect a part and transmit a 

 part of it, the two reflected beams are in phase with one another 

 and the resultant is maximum, when the following relation prevails 

 between the wave-length X of the light, the distance d between the 

 mirrors, and the angle 6 of incidence and of reflection: 



n\ = 2dcosd, w = 0, 1, 2, 3 •••• (15) 



When instead of a pair there is an endless or a very long sequence 



of mirrors spaced at equal intervals, the result is much the same as 



when a pair of atoms is supplemented by a very long row. The angles 



defined by equation (15) are now not merely the angles of maximum 



reflection ; they are the only angles where reflection is at all appreciable. 



If a pile of parallel semi-transparent mirrors is to reflect to any notable 



extent, their thicknesses and the wave-length and the angle of incidence 



of the light must be very carefully adjusted according to equation (15) 



with some integer value for 11. 



* Number 15 (October, 1928), p. 24. The formula there given contains an index 

 of refraction which I here equate to unity, and an additive constant which vanishes 

 if the phase-change at reflection is the same at each of the reflecting surfaces, which 

 is here the case. 



