CONTEMPORARY ADVANCES IN PHYSICS 399 



brighter than they were before. Interference between the waves 

 scattered from the various atom-groups has exalted the brightness of 

 certain points on the wall of the bulb, to the detriment of all the rest; 

 it has amplified the diffraction-pattern of the single group in certain 

 directions, and destroyed it in the others. The spots due to the atoms 

 of a single plane have been observed with electron-waves, but never 

 with X-rays (Figure 6). 



Add finally a great number of such planes, thus building the three- 

 dimensional crystal. Now except for certain wave-lengths the spots 

 vanish altogether. For those exceptional waves, however, they are 

 intensified into visibility. One group of atoms by itself would have 

 produced a complete diffraction-pattern — at least we suppose that it 

 would — but never one intense enough to be perceived. But when it 

 is joined with an enormous number of its peers in a lattice, they all 

 conspire to enhance not indeed the entire pattern, but the intensities 

 at certain of its points. The physicist, if he varies the direction in 

 which the rays fall upon the crystal or the wave-length of the rays or 

 both, can observe a great number of these intensities which the crystal 

 has so obligingly amplified for him; and out of them he can reconstruct 

 the entire diffraction-pattern of the individual atom, which but for 

 this amplification would have been forever out of his reach. ^ 



I must not leave the impression that the diffraction-pattern of the 

 atom-group is amplified equally in all the directions in which the 

 lattice amplifies it at all. Amplification depends on direction. If 

 the observer sees two spots produced by diffraction-beams inclined 

 say at 45° and at 60° to the primary beam, he is not to infer that the 

 ratio of their brightnesses is the ratio of the intensities of the waves 

 scattered at 45° and at 60° by the individual group. A correction- 

 factor must be employed to translate one ratio into the other. Later 

 on we will consider this factor. Meantime, not forgetting it but not 

 yet taking it into account, we will calculate the directions m which 

 amplification occurs. 



We start as before from the solitary atom-group. In Fig. 4 this 

 is depicted as a two-dimensional figure, irregular and utterly without 

 symmetry. It ought to be conceived as a three-dimensional, perfectly 

 unsymmetrical mass. This depiction is meant to imply that if a 

 stream of waves strikes the atom-group on any side, the intensity 

 of the waves scattered in any direction — what aDove I called the 

 diffraction-pattern of the group — is or may be a thoroughly unsym- 



' If the atoms or atom-groups of a substance would orient themselves all alike 

 without at the same time spacing themselves at regular intervals, and without being 

 too much crowded together, the entire pattern would be amplified instead of certain 

 spots only. 



