In the X-ray scattering curve of chain-molecules in solution, essentially four regions may be distinguished as is shown by a more detailed mathematical discussion:1. The scattering at the smallest angles, showing an approximately Gaussean course, whose ordinate, when extrapolated to zero angle, is proportional to the square of the mol. weight. It is due to the diffraction effect of the whole coiled chain-molecule. This is followed by a region of @-values where the scattering falls off as 1/19?. It is due to parts of the chain molecule which themselves already occur in all possible orientations.After a transition region (which is also accounted for by the theory) there follows a scattering which is proportional to 1/19. It is to be considered as the scattering of mostly straight parts of the molecule. 4.The scattering at large angles, caused by smaller parts ot the molecule (monomer group and single atoms), which at the same time indicates the periodicity ( = length of structural unit in the direction of the chain axis) by a step, at an angle corresponding to Bragg's law. Its sharpness, too. is a measure for the coiling of the molecule.It can be shown that the abscissa of the intersecting point of the 1/82 and 1/19 branches, when extrapolated to the transition region, is connected in a characteristic way with the statistical chain element or the "length of persistance", which represent two different measures for the stiffness of the chain molecule.Measurements with polyvinyl bromide lead to a length of persistance of 11 _+ 1 A. which agrees satisfactorily with the value of 13 A for polyvinyl chloride as derived from the birefringence of flow. At large angles two weak steps were found, one of which corresponds to the monomer length of 2.56 A.Measurements on solutions of cellulose nitrate gave a curve -1/9without any steeper ascent up to the smallest angles, corresponding to 300 A. W e have, therefore, to conclude that the chain-element of cellulose 2.3.

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