endurance, give further insights.
The question, whether and why the influence of Earth's motion upon the electric and optical phenomena cannot be detected at Earth's surface, is for the time being by no means decided. H. A. Lorentz himself surely was hardly of the opinion, to definitely solve them by stating the system of hypotheses H, I, K, L. He probably wanted to show only, that the absence of a noticeable influence doesn't necessarily speak against the general fundamental hypotheses A, B, C, D of electron theory, but that these hypotheses can be combined with the other ones without contradiction, so that the influence of Earth's motion vanishes with respect to all observable phenomena.
If the dynamics based on hypotheses A to G should further be proven in the field of cathode and Becquerel rays, yet a birefringence of dispersing bodies of order (following from these hypotheses together with H, I) due to Earth's motion cannot be demonstrated, then there still remain several possibilities.
In the light of our incomplete knowledge concerning the molecular forces, it is near at hand to abandon or modify hypothesis H. Because it was by no means achieved for the time being, to electrically interpret the molecular forces of resting bodies in a satisfying way.
Also the nature of the assumed quasi-elastic forces, which shall pull the electrons into their equilibrium positions, is unknown to us. Its interpretation on the basis of electromagnetism would give the electromagnetic theory of spectral lines. Unfortunately, we don't posses such a theory; therefore we are far from completely understanding the optical properties of resting bodies on the basis of electron theory. Hypothesis I thus completely hangs in the air, it is very much capable of being changed.
In the course of assessing the probability of the various hypotheses, one has to care that ideas concerning the nature of the molecular forces and the quasi-elastic forces are far less clarified, and are far less accessible to experimental verification, than the ideas concerning the constitution of the free negative electrons. Thus one won't be willing to abandon a theory, which correctly describes the behavior of free negative electrons, but which doesn't agree in a satisfactory manner with an optics that is based on hypotheses H, I. One will rather try to modify hypotheses H, I, so that an agreement with the totality of observations is achieved.
In the ninth paragraph of my work concerning the dynamics of the electron[1] I have stated the formulas for energy- and momentum radiation, emitted by a rapidly moving and simultaneously accelerated electron. Recently I have supplemented the extensive derivation of this formulas[2] and discussed their meaning for the theory of a moving illuminating point. In this investigations, as I have explicitly emphasized several times, the electron is considered as point charge which is permitted in the calculation of radiation under certain circumstances. The results of this investigations are therefore independent from any hypothesis concerning the constitution of the electron; they are exclusively based on the fundamental hypotheses A to D of electron theory. The development of Lorentz's model and every other in agreement with it, must thus lead to exactly the same results with respect to radiation, unless reasoning errors occur, for example violations of Doppler's principle or erroneous applications of Pointing's theorem.
Thus it is to be wished urgently, that the authors writing in the field of electron theory, follow the example of H. A. Lorentz by giving account of their hypotheses (underlying their investigations) in a clear and unequivocal manner, instead of attempting to belatedly present their explanations as "free of hypotheses". A deviation in the end results of such theories that are "free of hypotheses", could occasionally be derived from a lack of care of the concerned author. Authors, who doesn't provide a clear representation of their fundamental hypotheses and a thorough development of the consequences derived from them, cannot demand to be noticed by serious consideration.
Edinburgh July 28, 1904.
(Received July 30, 1904)
