function u03c0 u03b8 is far more general than such an ensemble of infinitely thin rods would imply for many types of particles measured the generated u03c0 u03b8 will not comply with the stricture of eq 2 except at the very smallest of angles these are the angles always least accessible for the measurements required to generate the mean square radius r g 2 by deriving the analytical function u03c0 u03b8 from the scattering data collected from mals measurement the inventive method is able to produce a mean square radius that will permit the recovery of particle structural features even for particles that lie well beyond the restrictions of eq 2 the least squares fit of the collected data to the function f m u03be produces the values of the coefficients c i i 0 1 m and thereby u03c0 u03b8 from the functional form thus derived the mean square radius is calculated from eq 11 i e however since u03c0 u03b8 f m u03be c 0 we have the immediate result as is well known a weighted least squares fit also may be made by the suitable weighting of the squared difference terms of each datum i u03b8 i by its normalized reciprocal standard deviation where the standard deviation of i u03b8 i is u03c3 the details of this weighted least squares fit may be found elsewhere for the present disclosure we consider only the.