The Scattering of X-Rays by Monatomic Liquids

Since the former method of treatment has the advantage of simplicity and the latter that of mathematical exactness, we shall describe them both briefly and show that they lead to the same results. 

We shall now imagine the origin of a co-ordinate system fixed in some special atom and consider a lattice point at any distance r from it. The scattering, which is calculated for this lattice point on the basis of the above theory, is then a measure of the distortion of the lattice at this point, and at the same time is also a measure of the mobility possessed by an atom r units away from the initial atom. 

To invest this method of consideration with formulas, we proceed from the above mentioned central atom and establish progressively in every direction in space, the distances of the surrounding atoms. In this way we obtain statistics of the inter-atomic distances within the liquid, the quantitative determination of which is the object of the investigation. 

It is convenient to imagine a thin spherical shell described around the initial atom, the radius of which is allowed to increase gradually so as to include, during the expansion, the atoms present in concentric spherical shells. The radii of these shells are then plotted as abscissae and the values W for the density of distribution of the atoms in the shells as ordinate. If we establish, for example, that a shell of radius r contains exactly n atoms, the density of the atoms in the shell is 

If we apply the calculation to the lattice of hexagonal close spherical packing, we obtain the diagram shown in Fig. 57. On moving out from 

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