In the expression for the viscosity of polymer solutions η=η0+[η]C+K[η]2C2+···, the Huggins constant K is calculated for hard spheres and for interpenetrable spheres of uniform segment density. For hard spheres K = 0.6909, and for soft spheres where K is larger, the dependence of K on the segment—segment interaction constant is given. Difficulties in the basic theory caused by the long range of hydrodynamic perturbations are resolved. The theory is approximate, in that the velocity field arising from Sphere 1 is assumed to vary slowly in the vicinity of 2, but within this approximation all orders of ``reflections'' are correctly summed.