TABLE VIII

Sign of Drop Sec. Sec.

63.050 }

63.186 41.728} 8

63.332 41.590}

- 63.328

62.728 25.740}

62.926 25.798 11

62.900 25.510

63.214 25.806} }

Mean = 62.976 }

63.538 22.694} 12}

63.244 22.830}

63.114 25.870}

63.242 25.876 11

+ 63.362 25.484}

63.136 10.830}

63.226 10.682

63.764 10.756 22

63.280 10.778

63.530 10.672

63.268 10.646} }

Mean = 63.325 }

63.642 }

63.020 71.664} 6

62.820 71.248}

63.514 52.668}

+ 63.312 52.800 7

63.776 52.496

63.300 52.860}

63.156 71.708 6

63.126

Mean = 63.407 }

63.228 42.006} }

63.294 41.920 8

63.184 42.108}

63.260 53.210}

63.478 52.922 7

- 63.074 53.034

63.306 53.438}

63.414 12.888}

63.450 12.812 19

63.446 12.748

63.556 12.824}

Mean = 63.335 }

Duration of experiment 1 hr. 40 min. Mean = 6.697

Initial volts = 1723.5 Mean = 6.700

Final volts = 1702.1

Pressure = 53.48 cm.

Since this is about the limit of the experimental error (the probable error by least squares is 1 part in 1,500), we may with certainty conclude that there are no differences of more than this amount between the values of the positive and negative electrons. This is the best evidence I am aware of for the exact neutrality of the ordinary molecules of gases. Such neutrality, if it is actually exact, would seem to preclude the possibility of explaining gravitation as a result of electrostatic forces of any kind. The electromagnetic effect of moving charges might, however, still be called upon for this purpose.

VI. RESISTANCE OF MEDIUM TO MOTION OF DROP THROUGH IT THE SAME WHEN DROP IS CHARGED AS WHEN UNCHARGED

A second and equally important conclusion can be drawn from Table VIII. It will be seen from the column headed “” that during the whole of the time corresponding to the observations in the third group from the top the drop carried either 6 or 7 electrons, while, during the last half of the time corresponding to the observations in the second group from the top, it carried three times as many, namely, 22 electrons. Yet the mean times of fall under gravity in the two groups agree to within about one part in one thousand. The time of fall corresponding to the heavier charge happens in this case to be the smaller of the two. We may conclude, therefore, that in these experiments the resistance which the medium offers to the motion of a body through it is not sensibly increased when the body becomes electrically charged. This demonstrates experimentally the exact validity for this work of the assumption made on p. 70 that the velocity of the drop is strictly proportional to the force acting upon it, whether it is charged or uncharged.

The result is at first somewhat surprising since, according to Sutherland’s theory of the small ion, the small mobility or diffusivity of charged molecules, as compared with uncharged, is due to the additional resistance which the medium offers to the motion through it of a charged molecule. This additional resistance is due to the fact that the charge on a molecule drags into collision with it more molecules than would otherwise hit it. But with oil drops of the sizes here used () the total number of molecular collisions against the surface of the drop is so huge that even though the small number of charges on it might produce a few more collisions, their number would be negligible in comparison with the total number. At any rate the experiment demonstrates conclusively that the charges on our oil drops do not influence the resistance of the medium to the motion of the drop. This conclusion might also have been drawn from the data contained in Table VI. The evidence for its absolute correctness has been made more convincing still by a comparison of drops which carried but 1 charge and those which carried as many as 68 unit charges. Further, I have observed the rate of fall under gravity of droplets which were completely discharged, and in every case that I have ever tried I have found this rate precisely the same, within the limits of error of the time measurements, as when it carried 8 or 10 unit charges.

VII. DROPS ACT LIKE RIGID SPHERES

It was of very great importance for the work, an account of which will be given in the next chapter to determine whether the drops ever suffer—either because of their motion through a resisting medium, or because of the electrical field in which they are placed—any appreciable distortion from the spherical form which a freely suspended liquid drop must assume. The complete experimental answer to this query is contained in the agreement of the means at the bottom of the last and the third from the last columns in Table VI and in similar agreements shown in many other tables, which may be found in the original articles.[42] Since is in this experiment large compared to , the value of the greatest common divisor at the bottom of the last column of Table VI is determined almost wholly by the rate of fall of the particle under gravity when there is no field at all between the plates, while the velocity at the bottom of the third from the last column is a difference between two velocities in a strong electrical field. If, therefore, the drop were distorted by the electrical field, so that it exposed a larger surface to the resistance of the medium than when it had the spherical form, the velocity due to a given force, that is, the velocity given at the bottom of the third from the last column, would be less than that found at the bottom of the last column, which corresponds to motions when the drop certainly was spherical.

Furthermore, if the drops were distorted by their motion through the medium, then this distortion would be greater for high speeds than for low, and consequently the numbers in the third from the last column would be consistently larger for high speeds than for low. No such variation of these numbers with speed is apparent either in Table VI or in other similar tables.

We have then in the exactness and invariableness of the multiple relations shown by successive differences in speed and the successive sums of the speeds in the third from the last and the last columns of Table VI complete experimental proof that in this work the droplets act under all circumstances like undeformed spheres. It is of interest that Professor Hadamard,[43] of the University of Paris, and Professor Lunn,[44] of the University of Chicago, have both shown from theoretical considerations that this would be the case with oil drops as minute as those with which these experiments deal, so that the conclusion may now be considered as very firmly established both by the experimentalist and the theorist.