508 H. A. Bumstead — Lorentz-FitzGerald Hypothesis. 



and calculation based upon this hypothesis. The small magni- 

 tude of the departures from the Newtonian law, of which more 

 or less rough estimates have been given above, render it prob- 

 able that there would be no serious lack of agreement. This 

 probability is strengthened by a calculation published some 

 years ago by Lorentz.* 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 0*000005. He did not, it is true, take into account the effects 

 of variable mass, which had not at that time become prom- 

 inent even in electrical theory. The introduction of electro- 

 magnetic 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.] 



* Amsterdam Proc. II, p. 571, 1900. 



