420 BELL SYSTEM TECHNICAL JOURNAL 



If therefore a diffraction-spot {hi, h2, hs) can with any reason be 

 attributed to a reflection of part of the incident energy from mirrors 

 traversing the crystal, then these mirrors must be so tilted that 

 their normal is pointed in the direction defined by equation (13). 



This equation being attained, we are prepared to discern the physical 

 meanings of the integers h. 



One of their meanings is evident. They state the "order" of the 

 diffraction-spot, in the sense in which that word is used in describing 

 the spectra cast by optical gratings. An ordinary ruled grating 

 supplied with light of a single wave-length forms, it may be, six or 

 seven or even more different "lines" on the focal plane of the lens 

 installed in front of it. These correspond to diffraction-spots on the 

 surface of our imaginary bulb. Take any one of these lines, say the 

 wth. The paths of the light from the source via consecutive rulings of 

 the grating to this nth. line differ by precisely n wave-lengths; the 

 contributions of any two adjacent rulings to the wave-motion at this 

 line differ in phase by n complete cycles. It is named the line, or 

 the image, or the diffraction-maximum of the nth order. There may 

 be lines of positive, of negative and of zero order; the line of zero 

 order is commonly called the "direct image" of the source. 



Now in the same sense a diffraction-spot with the indices hi, ho, hz, 

 cast by a crystal, is of three orders simultaneously; these indices are 

 its orders with respect to the three principal directions of the crystal 

 lattice. Referring to our quartet of atom-groups ABCD: the paths 

 of the waves from the source via A and B to the diffraction-spot 

 differ by hi wave-lengths, those via A and C differ by ho and those 

 via A and D by h^ wave-lengths. The (000) spot is in the prolongation 

 of the incident stream, and is called the "direct image." 



This is one important meaning of the indices h. Happily there is 

 another which is much more picturesque — happily indeed, for other- 

 wise it is likely that the art of crystal analysis would have developed 

 more slowly than it has, while the art of X-ray spectroscopy might 

 not even have begun for years. It does not always happen, perhaps 

 indeed it rarely happens, that the earliest formulation of a theory is 

 the one best adapted to make it widely understood and useful. 

 Someone other than the founder meditates upon the idea, and tries to 

 re-express it to himself, and hits upon a novel way of stating it — 

 a new aspect to it, possibly, or perhaps nothing more than a new 

 distribution of the emphasis, laying the greatest stress upon some 

 feature which to his forerunner seemed minor. Then suddenly the 

 theory appeals to the world of physicists in general. Experimenters 

 see what can be done with it, how it can easily be tested and how it 



