A new theory of dielectric relaxation is developed, which relates the relaxation time of a polar solute in a non-polar solvent to "mutual viscosity" of the polar non-polar combination. The theory is based on Andrade's theory of viscosity and the "mutual viscosity" which appears when this theory is extended to the case of a mixture, can be calculated from the relation [equation] where 7a, 7b 7 are the viscosities of the pure components, A and B, and the mixture respectively, there are intermolecular distances and the f's are mole fractions. This mixture law is tested against experimental results for seven pairs of substances, and is found to represent the variation of viscosity with concentration well, the mean error being 2%, and the maximum error 9%. The relation between the relaxation time and mutual viscosity is [equation] where the I's are moments of inertia, the m's are molecular masses, and is independent of concentration and does not differ much from unity. This relation is tested against existing results, and further measurements made to supply the deficiencies in these, and is found to be in closer agreement with experiment than the Debye relation, both for pure polar liquids and for polar molecules in solution.