CONTEMPORARY ADVANCES IN PHYSICS 417 



sum-of-squares (hx^ + h-r + /zs"), their rings coincide. They appear 

 as dark circles on a photographic film so placed as to coincide with 

 such a sphere or such a plane, exposed and subsequently developed. 

 Each of these circles consists of the diffraction-spots with the appro- 

 priate indices cast by the various crystals. If the crystals are few, 

 one sees the individual spots (the ring looks ragged and spotty, like a 

 star-cluster); if they are few and small the spots are hazy; if instead 

 of being turned at random they favor certain orientations, the circles 

 are not evenly dark all the way round. But these are matters for 

 later studv. 



Fig. 19 — "Powder method" diffraction-rings obtained with X-rays and a nickel- 

 iron alloy. Like the alloys used in Figs. 17, 18, the crystals of this are built on a 

 cubic lattice but with a differently-shaped atom-group, whence the changed ap- 

 pearance. (R.|[M. Bozorth.) 



If we measure the radii of the first few rings and calculate from 

 them the values of (1 — cos $) for the corresponding cones (a simple 

 matter of geometry) we should find that these stand to one another 

 as 1 : 2 : 3 : 4 • • — provided, that is, that the lattice is cubic and 

 the incident waves are nearly monochromatic. This is verified by 

 experience for X-rays and electron-waves. The first ring consists of 

 spots having the indices (1, 0, 0) or (0, 1, 0) or (0, 0, 1); the indices 

 for the second ring are (1, 1, 0) or (0, 1, 1) or (1, 0, 1), while those 

 for the third are (1, 1, 1). The reader can easily guess the indices 



