the limits .0013 cm. per sec. and .47 cm. per sec. Complete records of a few of these observations are given in Tables IX, X, XI, and XII.

[The reader may consult these tables in the original article, but they are here necessarily omitted for lack of space.]

The readings shown in these tables are merely samples of the sort of observations which we took on between 100 and 200 drops between December, 1909, and May, 1910. The sort of consistency which we attained after we had learned how to control the evaporation of the drops and after we had eliminated dust from the air may be seen from Table XIII which contains the final results of

our observations upon all of the drops except three which were studied throughout a period of 47 consecutive days. The three drops which have been excluded all yielded values of e, from 2 to 4 per cent too low to fall upon a smooth ev, curve like that shown in figure 2 which is the graph of the results contained in Table XIII. It is probable that these three drops corresponded not to single drops, but to two drops stuck together. Since we have never in all our study observed a drop which gave a value of e, appreciably above the curve of figure 2, the hypothesis of binary drops to account for an occasional low value of e, is at least natural. Before we eliminated dust we found many drops showing these low values of e1, but after we had eliminated it we found not more than one drop in

ten which was irregular. The drop shown in Table I is perhaps the best illustration of the case under consideration which we have observed. It yields a value of e, which is 4 per cent too low to fall on the curve of figure 2. This is as large a departure from this curve as we have thus far obtained.

The simple form of Stokes's law, which has been used in obtaining the values of e, involves the assumption that there is no slip at the bounding surface between the medium and the drop, or that the coefficient of external friction between oil and air is infinite. From the standpoint of the kinetic theory this surface slip, though in general very small, is, strictly speaking, never zero, and to take it. into account a term must be introduced into the equation of motion which is proportional to the ratio between the mean free path of the

gas molecule and the radius of the drop. Since it is conceivable, however, that there is some other cause for slip than that assigned by the kinetic theory, it will be well to make this discussion as independent as possible of all theoretical considerations.

From whatever point of view, then, the phenomenon of external slip be regarded, it is clear that the very existence of any surface effect of this sort between the medium and the drop must tend to produce an actual velocity higher than that computed from the simple form of Stokes's law, i. e., it must tend to produce departures from Stokes's law of the kind actually shown in the experiments herewith recorded. Furthermore, it will be evident from the analysis underlying Stokes's law that any surface effect whatever between oil and air which might modify the velocity given by Stokes's law must be more and more effective in so modifying it the more the radius of the drop is diminished, and that when the radius is taken sufficiently large the term which represents this surface effect must become negligible. We could then write a corrected form of Stokes's law, which would take into account any kind of surface phenomenon which might alter the speed, in the general form

in which is a constant of the medium and a the radius of the drop. If we were in complete ignorance of the form of the function f we could express it in terms of the undetermined constants, A, B, C, etc., thus

and so long as the departures from the simple form of Stokes's law were small, we could neglect the second order terms in l/a and have therefore

Using this form of equation to combine with (1) and denoting now by e the absolute value of the elementary charge and by e,, as heretofore, the value of the charge obtained from the use of (4), there results at once

1 See O. E. Meyer, Kinetische Theorie der Gase, p. 211, for the correction of Poiseuille's law for slip, and Cunningham, Proc. Roy. Soc., 83, p. 57, 1910, for the corresponding correction of Stokes's law.

Al

α

[The author then determines the value of the correcting term and confirms his result by reference to independent work of other observers. For these discussions the reader should consult the original article.]

Taking the value of A as 0.817 the value of e was determined from (9), and the values of e1, a, and I obtained as explained above.

FIG. 3.

The next to the last column of Table XIV gives the results of this computation of e for all of the observations recorded in Table XIII

Six months after the original work on this table was done the laboratory obtained a very reliable Weston laboratory standard voltmeter which made it possible to obtain a more perfect calibration curve of the Kelvin and White electrostatic instrument than had been made at first. With the aid of this new calibration curve every value of e, in the above table was recomputed, with the result that the final value of e was reduced 0.06 per cent. Furthermore, in the computation of the above table the m of equation (1) was through oversight treated as the real mass instead of as the apparent mass. This necessitates a further reduction of e amounting to 0.14 per cent, so that the most reliable value obtainable from the work thus far done is e=4.891×10-10.

except the first four and the last four. These are omitted not because their introduction would change the final value of e, which as a mat