In this article, I will extend the falling ball method to measure the viscosity of liquids regardless of the degree of their viscosity. For this, I will show that one can obtain a measurement of the terminal velocity of a falling spherical ball in a viscous liquid by solving numerically the equation of motion which describes the dynamics of the ball from the beginning to the end of the fall. The present numerical approach is proposed here particularly for measuring the viscosity of weakly viscous liquids using the falling ball viscometer. (Contains 2 figures and 1 table.)