Fig. 4
To find an exact expression for this correction we may proceed as follows: The average distance which a gas molecule goes between two collisions with its neighbors, a quantity well known and measured with some approach to precision in physics and called “the mean free path” of a gas molecule, is obviously a measure of the size of the holes in a gaseous medium. When Stokes’s Law begins to fail as the size of the drops diminish, it must be because the medium ceases to be homogeneous, as looked at from the standpoint of the drop, and this means simply that the radius of the drop has begun to be comparable with the mean size of the holes—a quantity which we have decided to take as measured by the mean free path
. The increase in the speed of fall over that given by Stokes’s Law, when this point is reached, must then be some function of
. In other words, the correct expression for the speed
of a drop falling through a gas, instead of being
