Of the five assumptions underlying Stokes’s Law, the first, third, and fourth were altogether satisfied in Dr. Arnold’s experiment. The second assumption he found sufficiently realized in the case of the very smallest drops which he used, but not in the larger ones. The question, however, of the effect of the walls of the vessel upon the motion of drops through the liquid contained in the vessel had been previously [Pg 97] studied with great ability by Ladenburg,[49] who, in working with an exceedingly viscous oil, namely Venice turpentine, obtained a formula by which the effects of the wall on the motion might be eliminated. If the medium is contained in a cylinder of circular cross-section of radius and of length , then, according to Ladenburg, the simple Stokes formula should be modified to read Arnold found that this formula held accurately in all of his experiments in which the walls had any influence on the motion. Thus he worked under conditions under which all of the first four assumptions underlying Stokes’s Law were taken care of. This made it possible for him to show that the law held rigorously when the fifth assumption was realized, and also to find by experiment the limits within which this last assumption might be considered as valid. Stokes had already found from theoretical considerations[50] that the law would not hold unless the radius of the sphere were small in comparison with , in which is the density of the medium, its viscosity, and the velocity of the sphere. This radius is called the critical radius. But it was not known how near it was possible to approach to the critical radius. Arnold’s experiments showed that the inertia of the medium has no appreciable effect upon the rate of motion of a sphere so long as the radius of that sphere is [Pg 98] less than .6 of the critical radius. Application of this result to the motion of our oil drops established the fact that even the very fastest drops which we ever observed fell so slowly that not even a minute error could arise because of the inertia of the medium. This meant that the fifth condition necessary to the application of Stokes’s Law was fulfilled. Furthermore, our drops were so small that the second condition was also fulfilled, as was shown by the work of both Ladenburg and Arnold. The third condition was proved in the last chapter to be satisfied in our experiments. Since, therefore, Arnold’s work had shown very accurately that Stokes’s Law does hold when all of the five conditions are fulfilled, the problem of finding a formula for replacing Stokes’s Law in the case of our oil-drop experiments resolved itself into finding in just what way the failure of assumptions 1 and 4 affected the motion of these drops. IV. CORRECTION OF STOKES’S LAW FOR INHOMOGENEITIES IN THE MEDIUM