Functions for Specific Geometric Shapes Sphere, Ellipsoid, Random Coil and Thin Rod

Interference Functions for Specific Geometric Shapes. Sphere, Ellipsoid, Random Coil and Thin Rod. 

Applied to spheres equation (56) gives (Rayleigh, 1914, Debye, 1947). 

The corresponding problem for an assembly of randomly oriented ellipsoids is somewhat more difficult and no simple closed expression has been found for P( ). For discussions see Guinier (1939) and Roess and Shull (1947). The first three terms of the solution have been derived 

Since this manuscript was written Debye (personal communication) 

This equation holds for all values of ft from rods (ft = 00) to discs (/ = - ). 

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