On the interpretation of the indications of atomic structure presented by crystals when interposed in the path of X-rays

W. L. Bragg states in his exposition of the method of investigating the structure of crystals by means of X-rays, that a slight symmetrical distortion of the arrangement of the atoms, which would reduce the crystal symmetry, would not affect any of the results that he had just been describing. Advancing considerably beyond this conclusion, it is proposed to show that a large amount of a certain kind of deformation of an atomic system arranged according to either of the three space-lattices possessing cubic symmetry, considerable enough to profoundly alter the nature of the arrangement, can take place with out any appreciable evidence of this deformation being presented by the X-ray results. The argument consists of the proofs of the following propositions:—Proposition 1.—Each of the three space-lattices which posses cubic symmetry can, by a simple modification, be converted into a regular point-system having this symmetry, but the system of trigonal axes of which, unlike that of the space-lattice, is of non-intersecting kind. The method employed to effect this modification is to so select one-fourth of the trigonal axes of the space-lattice concerned that no two of the selected axes intersect, and then to destroy the remaining three-fourths by symmetrically shifting each point of the space-lattice to the same extent in the appropriate direction along the selected trigonal axis on which it lies, and consequently away from the three other trigonal axes which passed through it. In the cases of the cubic space-lattice and the cube-centred space-lattice, the shifts, can take place in both directions on an axis or in one only. The effect of axes continues to be a trigonal axis of the system of points is that each of the selected axes continues to be a trigonal axis of the system of points, while each of the remaining three-fourths of the trigonal axes ceases to be so. The system of points resulting has cubic symmetry, but in nearly all the cases this is of a lower class than that of the space-lattice from which it is derived.