When we assume the foregoing equation of Stokes and combine it with equation (5) on p. 55, an equation whose exact validity was proved experimentally in the last chapter, we obtain, after substitution of the purely geometrical relation , the following expression for the charge carried by a drop loaded with electrons which we will assume to have been counted by the method described: According to this equation the elementary charge should be obtained by substituting in this the greatest common divisor of all the observed series of values of () or (). Thus, if we call this ( we have But when this equation was tested out upon different drops, although it yielded perfectly concordant results so long as the different drops [Pg 92] all fell with about the same speed, when drops of different speeds, and, therefore, of different sizes, were used, the values of obtained were consistently larger the smaller the velocity under gravity. For example, ex for one drop for which per second came out , while for another of almost the same speed, namely, , it came out 5.482; but for two drops whose speeds were five times as large, namely, .0536 and .0553, came out 5.143 and 5.145, respectively. This could mean nothing save that Stokes’s Law did not hold for drops of the order of magnitude here used, something like cm. (see Section IV below), and it was surmised that the reason for its failure lay in the fact that the drops were so small that they could no longer be thought of as moving through the air as they would through a continuous homogeneous medium, which was the situation contemplated in the deduction of Stokes’s Law. This law ought to begin to fail as soon as the inhomogeneities in the medium—i.e., the distances between the molecules—began to be at all comparable with the dimensions of the drop. Furthermore, it is easy to see that as soon as the holes in the medium begin to be comparable with the size of the drop, the latter must begin to increase its speed, for it may then be thought of as beginning to reach the stage in which it can fall freely through the holes in the medium. This would mean that the observed speed of fall would be more and more in excess of that given by Stokes’s Law the smaller the drop became. But the apparent value of the electronic charge, namely, is seen from equation (13) to vary directly with the speed ( imparted by a given force. [Pg 93] Hence should come out larger and larger the smaller the radius of the drop, that is, the smaller its velocity under gravity. Now, this was exactly the behavior shown consistently by all the oil drops studied. Hence it looked as though we had discovered, not merely the failure of Stokes’s Law, but also the line of approach by means of which it might be corrected. In order to be certain of our ground, however, we were obliged to initiate a whole series of new and somewhat elaborate experiments.