and calculation based upon this hypothesis. The small magnitude of the departures from the Newtonian law, of which more or less rough estimates have been given above, render it probable that there would be no serious lack of agreement. This probability is strengthened by a calculation published some years ago by Lorentz.[1] In this he found the secular variations of the elements of the orbit of Mercury due to the substitution of electro-dynamic forces for the strictly Newtonian force. The variations in the angular elements amounted to only a few seconds of arc in a century and the change in the eccentricity to He did not, it is true, take into account the effects of variable mass, which had not at that time become prominent even in electrical theory. The introduction of electromagnetic mass will, in general, tend to diminish the effects of the sun's motion and to exaggerate the effects of the motion of the earth relative to the sun. But from a comparison of the theoretical accelerations in the two cases, it does not appear that the variations could be increased enough to produce a sensible discrepancy.
[Note added in Proof, Oct. 12. Since the above was written, two papers have come to my knowledge which bear upon this question. A. Wilkens (Phys. Zeitschr., vii, p. 846, 1906) has introduced electromagnetic mass in the ordinary Newtonian equations and has calculated the resulting secular variations in the elements of Mercury, Venus, the Earth, Mars, and Encke's comet. In all cases the variations are within the limits of accuracy of the observations. F. Wacker (Ibid., p. 300) considers the case when both force and mass are electromagnetic and, upon applying his equations to Mercury, finds for the motion of its perihelion a value less than one-fifth of that which is at present unaccounted for. The changes in the scales of length and time which would be introduced by the principle of relativity could affect these results very little; so that it seems quite certain that our present observational knowledge of gravitation is not sufficiently exact either to exclude the general application of the principle or to supply evidence in its favor.]
