748 BELL SYSTEM TECHNICAL JOURNAL 



intensity is everywhere zero. Spectroscopists broaden this linear 

 pattern in practice by using as source of light not a point, but a 

 luminous line — an incandescent filament, for instance, or a slit backed 

 by a flame — made parallel to the slits or rulings of the grating. Then 

 the diffraction-pattern is spread into a band. If the light is mono- 

 chromatic, one sees in the focal plane, at the positions of the principal 

 maxima, not a sequence of brilliant points as the foregoing theory 

 implies, but a sequence of brilliant lines — the lines of the spectrum. 



Instead of these lines one will obtain circles, if one uses a point-source 

 of light and a mosaic of gratings all lying side by side in a single plane 

 and oriented every way. Each piece of the mosaic forms its own 

 linear diffraction-pattern, perpendicular to the direction of its own 

 rulings; and if the pieces are numerous enough, all of these are fused 

 into a single circular pattern, each of the principal maxima standing 

 forth as a brilliant ring. I am not sure whether this has been done 

 with plane optical gratings; but the analogous method with X-rays 

 and crystals is the familiar procedure known by the names of Debye 

 and Scherrer and Hull, or as the "powder method." Being a case 

 of diffraction in three dimensions, it is not entirely like my imaginary 

 case of a mosaic of plane gratings. The resemblance however extends 

 so far, that from the broadness of the rings one may infer the size of 

 the tiny crystals which make up the three-dimensional mosaic, the 

 "powder"; for the smaller these are, the fewer rows of atoms each 

 contains, and the wider their diffraction-maxima must be. But it 

 requires very fine grinding indeed, or the dispersion of the crystals as 

 a colloid in solution, to make them so small that the broadening of the 

 rings is noticeable. 



What would be observed, if individual slits or apertures or atoms 

 were dispersed completely at random over the plane or throughout 

 space? If there were many apertures all alike and all similarly 

 oriented, but with no regularity whatever in arrangement, the 

 diffraction-pattern would be the same as that of any singly, though 

 more intense. The water-droplets in misty air act thus in forming 

 haloes. If atoms were truly spherical and could be crowded together 

 into a dense mass without any regularity, the diffraction-pattern of the 

 mass would be that of the individual atom, and would disclose the 

 radial distribution of its scattering-power — whether that be negative 

 electricity, or something else. Even if atoms are not spherical, one 

 might expect to learn in this way the average distribution of scattering- 

 substance over all the orientations. Experiments have been con- 

 ducted for this purpose; but it is difficult to find a piece of matter in 

 which the arrangement of the atoms is entirely irregular, that is, a 



