\Vhen the directions of successive steps of a path in space are correlated, the position of the endpoint of a path of given length will show correlation with the orientation at this endpoint. The present paper deals with the limiting case in which the length of the steps approaches zero. Using the method introduced by K r a m e r s 6) in the theory of Brownian nmvement, a differential equation is set up for the distribution of positions and orientations. It is shown that the result is in conformity with that derived by D a n i e 1 s s) who used a different method and eliminated the orientation from the very beginning.
The Laplace transform of the intensity of the light scattered in a given direction is derived, and it is shown that the asymptotic result for very long chains is identical with that derived by previous authors for Gaussian chains, while that for very short chains is the same as the result for stiff rods.
Formulae are also derived for the intensity of the light scattered by optically anisotropic chains, where the correlation between position and orientation is a decisive factor. The relation between the intensity of the light and the angle of scattering is shown to depend on the optical anisotropy of the chains, except at the limit of very long chains, as was to be expected.
Attention is drawn to the fact that the model should be applicable also to certain problems concerned with the scattering of nuclear particles.
1. Introduction.
The statistics of polymer chains was based by K u h n and others 1) on the random flight concept: the chain is replaced by a number of links, called statistical chain elements,