Short Electromagnetic Waves by a Crystal. 47 
strength of a pulse reflected from a single plane will depend on 
the number of atoms in that plane which conspire in reflecting 
the beam. When two sets of planes are compared which produce 
trains of equal wave-iength it is to be expected that if in one set 
of planes twice as many atoms reflect the beam as in the other 
set, the corresponding spot will be more intense. In what follows 
I have assumed that it is reasonable to compare sets of planes in 
which the same number of atoms on a plane are traversed by unit 
cross-section of the incident beam, and it is for this reason that I 
have chosen the somewhat arbitrary parameters by which the 
planes will be defined. They lead to an easy comparison of the 
effective density of atoms in the planes. The effective density is 
the number of atoms per unit area when the plane with the atoms 
on it 1s projected on the zy axis, perpendicular to the incident light. 
Laue considers that the molecules of zinc-blende are arranged 
at the corners of cubes, this being the simplest of the cubical 
point systems. According to the theory of Pope and Barlow this 
is not the most probable arrangement. For an assemblage of 
spheres of equal volume to be in closest packing, in an arrange- 
ment exhibiting cubic symmetry, the atoms must be arranged 
in such a way that the element of the pattern is a cube with 
an atom at each corner and one at the centre of each cube 
face. With regard to the crystal of zinc-blende under considera- 
tion zine and sulphur being both divalent have equal valency 
volumes and their arrangement is probably of this kind. It will 
be assumed for the present that the zinc and sulphur atoms are 
identical as regards their power of emitting secondary waves. 
Take the origin of coordinates at the centre of any atom, the 
axes being parallel to the cubical axes of the crystal. The distance 
between successive atoms of the crystal along the axes is taken for 
convenience to be 2a. 
All atoms in the az plane will have coordinates 
pa o ga 
where p and q are integers and p+q iseven. See fig. 1 in text. 
The same holds for atoms in the yz plane. Therefore any 
reflecting plane may be defined by saying that it passes through 
the origin, and the centres of atoms 
pa o qa 
0 Ta sa 
For instance, the plane on which the triangle O.AB lies passes 
through the origin and 
a.0 3H 
G@. Oe 
