The falling ball viscometer has been widely used for measuring the viscosity of the Newtonian fluids because of its simple theory and low cost. The use of the falling ball viscometer for measuring the non-Newtonian viscosity has been of interest to rheologists for some years. The analysis of the experimental results in a falling ball viscometer rest on Stokes law which yields the terminal velocity for a sphere moving through an infinite medium of fluids. An attempt to use the falling ball viscometer to measure the non-Newtonian viscosity in the intermediate shear rate ranEe was sucessfully accomplished by combining the direct experimental obserbations with a simple analytical model for the average shear-stress and shear rate at, the surface of a sphere. In the experiments with highly viscoelastic polyacrylamide solutions the terminal velocity was observed to be dependent on the time interval between the dropping of successive balls. The time-dependent phenomenon was used to determine characteristic diffusion times of the concentrated solutions of polyacrylamide