Wide-ranging Polynomial Approximations to Wilson’s and Hill’s Equations

A close approximation to Wilson’s equation has been obtained that is applicable for exhaustion levels between 30 and 99.9 % at an accuracy of up to four significant figures. A similar approximation to Hill’s equation was also obtained, which is shown to be highly accurate. The approximation to Wilson’s equation has been used to calculate the diffusion coefficient of C.I. Disperse Violet 1 in alkali-corroded polyester fibres. The effects of removing the surface fibre layer by alkali hydrolysis on the physical characteristics of a polyester fibre and on the diffusion coefficient of the disperse dye in the fibre are discussed