A diffusional driving force, called the radial force, which is responsible for the increase with time of the scalar separation between a fixed point and a particle undergoing three-dimensional Brownian motion, is derived using Boltzmann's equation. The radial force is used to derive several results from the classical theory of Brownian motion, namely Einstein's <x2> = 2Dt equation and the expression for the one-dimensional harmonic oscillator. The radial force concept is then extended to establish a thermodynamic criterion for the occurrence of a melting transition in a liquid whose particles attract one another by means of centrally symmetric forces. The theory, when applied to the alkali halide and alkaline-earth oxide molten salts, accurately predicts the observed melting temperatures. The definition of the dielectric constant used in the ionic salt fusion theory also provides a basis for understanding molten salt surface tensions. Finally, the radial force is used to demonstrate that an ideal rubber network is not prone to collapse into a state having zero volume.