Walter Kaufmann

“ When one specifies in an absolute way, then it is much harder to reach agreement, because an error of 1% in the determination of , already gives an error of 10 or 20% for . Therefore it is necessary, to compare the relative values with each other. For the time being, an absolute measurement was carried out by me only for the first, older experiments of the previous year. There, one gets deviations of up to 7% for the value of . If one calculates (after correction of this deviation) from that the value of , then one gets the value , while was found for cathode rays. ”

“ The results accessible to observation are thus the same with respect to both authors; however, while Lorentz only shows that his hypotheses lead to the desired result without excluding that the same can also be achieved in another way, it is shown by Einstein, that when the desired result, namely the principle of relative motion, is placed at the top of the whole of physics, then the kinematics of the rigid body must necessarily be changed in the way stated, and that the equations of electrodynamics [18] must assume the form stated by Lorentz. ”

“ Thus a auxiliary table is calculated, which gives the -values corresponding to a most tight row of -values, then (when the constants and are known) the corresponding by equation (7.) can be compared to every . It is easily achieved to find approximate values for both "curve constants" and , and then to calculate the improvements still to be made, by the method of least squares.
The curve constants determined in this way, can be compared with those values partly given from the dimensions of the apparatus alone, and partly from the connection with the value found with respect to cathode rays. ”

“ To this geometric fundamental assumption, he still added the physical one, that all molecular forces are changing the same way with velocity as the electrostatic forces, and that the "masses" of mechanics are changing the same way as the electromagnetic mass of the electron. ”

“ If is the velocity of the moving system, the speed of light, and if , then all dimensions parallel to the direction of motion shall be contracted in the ratio , the dimensions normal to the direction of motion shall remain unchanged. ”

“ Since the same ratio of axis also applies to Lorentz's electron, one can derive the equations given by Bucherer for mass, energy, and momentum of the electron, without further ado from the ones of Lorentz, when one introduces, instead of the invariable transverse diameter of the electron that occurs as a parameter in the equations of Lorentz, a transverse diameter depending on the velocity, so to be measured that the volume of the ellipsoid is equal to the original sphere. ”

“ Furthermore, let and the magnetic and electric deflections; eventually let and be the "electric" and "magnetic field integral" reduced to proportionality with the deflectabilities; i.e. two quantities equal to the mean field strength with a factor each dependent on one of the dimensions of the apparatus. At last let , where is the speed of light. It is
where is a function of velocity, whose form is different depending on the basic assumption concerning the constitution of the electron. ”

“ Curves II and III are recorded with a voltage of 2000 volt, and at curve IV the voltage was increased to ca. 5000 volt by the rotating switch as described l.c. The agreement with theory is so good, as it can be expected by the precision of observation, since the mean error of the individual values only amounts 1 to 1,4% with respect to all four curves. ”

“ In the calculation of the field for a rapidly moving electron, Abraham made the kinematic fundamental assumption, that the field of the electron is infinitely extended into the exterior, however, into the interior it is extended up to the surface of a sphere of constant radius . ”

“ The average error of the single curve points amounts:
A final decision is only possible by comparison of the curve constants with the apparatus constants and the value of the cathode ray from .
There, the third of equations (8.) and (12.) gives, as it can easily be seen, the average between the values calculated from the first and second ones, which only deviate from each other as far as equation (9.) is not precisely satisfied. ”

“ Although it is immediately clear due to the unambiguity of the reasoning of Lorentz and Einstein, that Bucherer's electron cannot strictly remove the influences of the absolute velocity, it is still probable from the outset, that at least effects of second order are at least partially removed. ”

“ If one consequently considers this fundamental assumption as disproved, then the attempt to establish the whole of physics (including electrodynamics and optics) upon the principle of relative motion, has to be denoted as failed for the time being. ”

“ The -rays or radium show, as it is known, qualitatively the same properties as cathode rays; they are magnetically [7] and electrically [8] deflectable, and they carry an electric charge with them.
In quantitative respects, they are different from the cathode rays even under crude observation, in so far as they have a much higher penetration capability as the other ones. ”

“ I want to ask after the shortcomings of the photographic plate: can we recognize them by the fact, that the errors always occur at the same place and the same magnitude?
Kaufmann: These errors are almost always present, however, they are not systematic, i.e., they do not belong to the curve, since they occur upon the single plates at quite different places and they are different with respect to magnitude and sense.
↑ Verhdl. D. Naturf. u. Ärzte Hamburg 1901. II. 1. 45. Gött. Nachr. 1901. H. 2. ↑ Phil. Mag (5) 44. 340, 1897. ↑ Gött. Nachr. 1902. H. 1. ”

“ This quantity actually cannot be defined by us at all, since the result of the now described calculation is, that there is no means to define this velocity even by a thought experiment. We cannot even give the amount of the deformation change belonging to the observable change of relative velocity , as long as we don't know the absolute velocity . For example, if the original length of a body is , it thus becomes deformed by into
and by into
The length change corresponding to an observable increas of velocity, is thus not only a function of , but also of . ”