A wide range of concentration (1.0 x 104 to 6.0 x 10-2 g/rnl) of cellulose acetate in acetone is considered and dissymetry of all these concentrations is measured at different angles from 450 to 900 at intervals of SO degree. These dissymetries are measured by using two wave lengths ( 436 nm. and 546 nm. ) of incident light. An equation is derived for the dependence of dissymetry upon angle of measurement, considering the system as coil-like molecules. Making use of this equation and Zimm plot method, the radii of gyration of these solutions are measured. It is concluded that one gets the same results by both the methods. It is further concluded that the radius of gyration increases as the concentration decreases.