There are numerous experimental results in the diffraction of x-rays in liquids that seek explanation by an adequate theory. They may be enumerated at least in part as follows: (1) small scattering intensity near zero diffraction angle, (2) a principal maximum in the intensity-diffraction-angle curve corresponding to distance of molecular separation, (3) the position of this chief maximum as independent of the length of the molecule which forms a straight chain, (4) the variation of the position of a second diffraction peak with carbon content in the case of a normal hydrocrabon or a derivative of a hydrocarbon in a manner that makes the variation of the corresponding "planar" distance (computed by Bragg's Law) with carbon content in the straight chain, a linear one, (5) the similarity of the foregoing variation in solid and liquid saturated normal fatty acids, (6) the agreement of the molecular separation computed by Bragg's Law and other experiments upon the cross-sectional area of straight chain molecules, (7) the alteration in computed separation by attached branches, (8) the presence of three peaks apparently corresponding to three dimensions of a branched chain molecule, (9) the agreement among the computed cross-sectional areas of the three straight carbon chains, normal paraffins, saturated nomal fatty acids and normal alcohols.

The theories of Raman and Ramanathan and of Zernike and Prins give a fairly good account of the first two phenomena just mentioned. But the conception of molecular non-crystalline groupings in the liquid makes possible the use of the crystal powder theory as an idealized one for liquids. It is found that, used as an approximation, this theory explains all the above phenomena.

The Ehrenfest formula, intended by its author for gases but which has been used to obtain the mean molecular separation in liquids, and which varies from Bragg's Law by about 19 percent, cannot be so applied to liquids.

• Received 1 June 1918

DOI:https://doi.org/10.1103/PhysRev.32.558