330 TRANSACTIONS OF SECTION B. 
beam undergoes reflection at the surface of a crystal plate. The interpretation 
of the novel results indicates that the homogeneous crystal structure acts upon 
the X-ray beam much as a solid diffraction grating might be expected to do, and 
that each deflected transmitted ray is a reflection from one set of parallel planes 
of atoms in the crystal. 
The experimental and theoretical study of the X-ray effects has been prose- 
cuted with brilliant success by W. H. and W. L. Bragg, the result being that a 
method is now available which makes it possible to determine, with very great 
probability, the actual arrangement of the constituent atoms in crystal structure. 
Sufficient time has not yet elapsed for the thorough exploitation of this new 
and fruitful field of research, but many data are available already for com- 
parison with the conclusions drawn from the consideration of the equilibria 
possible in crystal structures; it is found that the two methods do not at once lead 
to identical conclusions. Thus, in accordance with the first method, the structure 
of the diamond would be indicated as some slight modification of the cubic 
closest-packed assemblage of equal spheres, the modification consisting in the 
main of a grouping of sets of atoms which leads to the partial cubic symmetry 
which the diamond apparently exhibits; one particular mode of grouping which 
leads to the required result consists in supposing the carbon atoms formed into 
sets of four, tetrahedrally arranged, two oppositely orientated sets of such tetra- 
hedral groups being distinguished. If each of these tetrahedral groups be 
replaced by a single point situated at the group-centre, the structure which the 
Bragg experiments indicate for the diamond is obtained. 
The simple geometrical relationship which thus exists between the two sug- 
gested structures for diamond raises a suspicion that the particular form in which 
the assumption of equilibrium is stated requires qualification : that possibly the 
domain of the carbon atom when packed with others, as in the diamond, does 
not become converted into a rhombic dodecahedron, but into a polyhedron roughly 
tetrahedral in shape. 
Leaving this particular point for the moment and turning again to Table T., 
it is seen that the binary compounds, like the elements, also tend to crystallise in 
the cubic or hexagonal systems; the axial ratios of the hexagonal binary com- 
pounds approximate very closely to the value, a: c=1:1-°6330, calculated for the 
closest-packed, hexagonal assemblage of equal spheres. The values of c/a for 
all the known cases are : BeO—1:6365, ZnO —1-:6077, ZnS—1:6350, CdS—1-6218, 
and AgI—1-6392. 
Assemblages representing the crystal structures of the cubic and hexagonal 
binary compounds may be derived from the two closest-packed assemblages of 
similar spheres already described, by homogeneously replacing one half of the 
spheres by different ones of the same size. The degrees of symmetry presented 
by these arrangements are not so high as those of the unsubstituted assemblages ; 
this is in accordance with the fact that the crystals themselves have not the full 
symmetry of the holohedral cubic or hexagonal system. Thus, on warming a 
hexagonal crystal of silver iodide, one end of the principal axis e¢ becomes 
positively, and the other negatively, electrified. The axis c is thus a polar axis, 
having different properties at its two ends; this axis will be found to be polar in 
the model. Again, when hexagonal silver iodide is heated to 145°, it changes 
its crystalline form and becomes cubic; this so-called polymorphous change can 
be imitated in the hexagonal model by slightly shifting each pair of layers of 
spheres in the assemblage. 
A very close agreement thus exists between the properties of the assemblages 
deduced and the observed properties of those binary compounds which crystallise 
in the cubic or hexagonal systems. The remaining 12 per cent. or so are not, in 
general, pseudo-cubic or pseudo-hexagonal, and it is noteworthy that they com- 
prise those binary compounds in which the two component elements have not the 
same lowest valency; amongst them are the substances of the compositions, 
PbO, FeAs, HgO, AsS, and CuO. 
On comparing the structures of the binary crystalline compounds indicated by 
the foregoing method of consideration with those deduced by the Braggs, dis- 
crepancies are again obvious; again, however, the former assemblage is converted 
into the latter by replacing groups of spheres by their group-centres. The rela- 
tion thus rendered apparent is once more a suggestion that the type of equilibrium 
