CONTEMPORARY ADVANCES IN PHYSICS 421 



can be applied after the tests are passed; and progress for a time is 

 furiously fast. Something much like this befell the theory of the 

 diffraction of waves by crystals. The form in which I have thus far 

 developed it (except while describing the powder method) is the one in 

 which it was clothed by the brilliant inspiration of Laue. However 

 it was W. L. Bragg who made the theory well known and widely 

 used all the world over, by singling out and featuring the fact that 

 each diffraction-beam is due to its own special set of atom-strata in the 

 crystal, which reflect it as light is reflected by a pile of parallel mirrors. 



The integers h are then no other than the indices, by which the 

 crystallographers denote these strata. For, to the student of crystal- 

 lography, the strata are very real — as much so as the rows of atom- 

 groups, by referring to which I developed the theory of the diffraction- 

 spots in Laue's way. We started with the individual group and went 

 on to the row, and then constructed the plane by laying rows down 

 side by side ; but we might have started with planes, and defined the 

 rows of atom-groups as the lines or edges where two planes intersect, 

 and located individual atom-groups at corners where three planes 

 meet. This is the historical way; for the planes are the prominent 

 feature of any well-developed crystal. The smooth flat facets which 

 are the boundaries of every well-formed crystal are parallel to im- 

 portant strata, they are themselves examples of important strata. 

 In studying a crystal otherwise than by diffraction, the first step is 

 to measure the directions (relative, of course) of all the available 

 facets. Before the invention of analysis by diffraction, this was 

 often the last step also; but if the crystals available have grown up 

 really well, it is a very long step. Having taken it, the crystallographer 

 proceeds to visualize the crystal as a region of space which is inter- 

 sected and partitioned by flocks of planes, long sequences of evenly- 

 spaced planes parallel to the facets; and he locates the atom-groups 

 at their intersections. How then shall we harmonize these inferences 

 of his with the implications of the diffraction pattern? 



A good way to unify the two procedures is to explain the notation 

 by which the crystal planes are named. In doing this, I shall often 

 speak of planes "containing atom-groups," meaning in the strict sense 

 planes containing lattice-points around which atom-groups are placed. 



Return to the cubic lattice and to the basic set of four atom-groups 

 ABCD, so chosen that the lines AB, AC, AD are three edges of the 

 fundamental or "unit" cube. Complete the cube by adding four 

 more atom-groups EFGH. We will pick out the planes which 

 contain three or four of these eight groups. They will be the most 

 populous with atom-groups of all the planes traversing the cube or 



