In this paper the author intends to treat with the motion of a falling body through viscous fluids by solving equations of motion of particle, in which the drag force plays a very important role. The first case, which corresponds to the Stokes' relationship, is that the resistance is proportional to the velocity. The second one is that the resistance involves the so-called inertia term and corresponds to the Oseen's formula which yields good results somewhat beyond that of Stokes.
In the result of analysis, the author concluded and proposed two things. First, at the measurement of fluid viscosity through the use of the falling spheres method the necessary data for the calculation of the final velocity are only two, that is, the fall distance from the rest and the time taken by falling, because the time until reaching the finai velocity is practically negligible. The second is that the use of the Oseen's expression, in place of the Stokes' formula, can extend to some degree the region in which the falling spheres method has been applicable.