CONTEMPORARY ADVANCES IN PHYSICS 423 



Now try the plane containing the atom-groups BCGH. Its inter- 

 cepts on the X and y axes are both equal to a, but it is parallel to the 

 z-axis, a fact which is described by giving its z-intercept as infinity. 

 The reciprocals of its intercepts then are 1/a, 1/a, 0; we multiply by a 

 and obtain (1 1 0) as the symbol for all the strata parallel to the 

 one containing the atom-groups BCGH. The reader can easily identify 

 members of the (0 1 0) and (0 1) families, and ascertain how many 

 new families of planes he can get by reversing the signs of some or all of 

 the indices. There are six altogether; one sometimes sees facets with 

 these indices, beveling off the edges of natural cube-shaped crystals. 



Next consider the plane containing CFHE. It is parallel to the 

 3'z-plane and distant from it by a, so that its intercepts are a, ^ , =o , 

 and its symbol is (1 0). One sees immediately that (10 0) and 

 (0 1 0) and (0 1) are the symbols for the three families of planes 

 which comprise these which we have taken for our coordinate-planes. 

 When a substance with a cubic lattice forms crystals which are cubes, 

 their facets belong to these families. 



What could a symbol such as (2 1 0) imply? It would stand for 

 a family of planes, one of which would have for its intercepts the 

 values a/2, a/1, a/0 or |a, a, °o. This plane would be parallel to the 

 z-axis and would traverse the atom-groups B and G, and would slant 

 across the cell in such a way as to pass through the wall A CDH midway 

 between its vertical edges. Continuing it and the lattice in imagi- 

 nation, one sees that at the far angle of the next cell it would traverse 

 another pair of atom-groups, and at the far angle of every second 

 cell thereafter it would do the like. It is therefore a fairly "important" 

 stratum, though not so populous as those of which the indices are 

 zeros and ones exclusively. It might form facets, and would be likely 

 to give a noticeable diffraction-spot. But in general as the indices 

 mount up, the importance of the plane declines. 



It is evident that if any set of indices is multiplied by any constant, 

 the new set thus obtained corresponds to the same family of planes. 

 To choose one set definitely for each family, we may agree to adopt 

 the triad of integers having no common divisor. Thus all three of the 

 symbols (963), (642) and (321) refer to the same family of planes; 

 we always choose the last one. 



Given these the so-called " Millerian " indices of a family of planes, 

 what are the direction-cosines of their common normal? 



Denote the three indices by Hi, H2, H3. The question is: what 

 are the direction-cosines 7172T3 of the normal to a plane, of which 

 the intercepts on the coordinate axes are a/Hi, a/H-i, a/Hs? The an- 



