namely, (i.e. the deflection experienced by the extra rays) corresponds to the following velocities:
| βm = 0,516; β = 0,47; β = 0,588; |
= 10,18 mm = 0,971 cm = 0,954 cm |
For rays that are passing through rectilinearly, i.e. the normal rays, mm, and eventually for faster rays, the deflection is 0,954 cm. You see, that the deflection of these rays lies in the vicinity of the normal rays, so that (at most) a small widening can occur by that. The distance of the condenser plates is ½ mm, this at most gives a width of up to ¾ mm; actually, the curve is not wider. This clearly proves, that the extra rays play no role.
Wien: I would like to ask the reader, if he maybe has evidence, why the experiment of Kaufmann has led to results which are different from his ones.
Bucherer: I don't want to start a criticism of Kaufmann's experiments, without expressly confirming, that I highly esteem the pioneering work of Kaufmann. When I now pass to a criticism of Kaufmann's experiments, then I want to allude at first to the difficulty in the measurement of such a small curve.
The velocities, which come into account, are 0,8 to 0,56 of the speed of light. I haven't taken into account the lower values of the deflection, since the percentage errors are too high at this place. In the area, which come into question for Kaufmann, the curve is already very small as well. I precisely looked at the curve and discovered an asymmetry of 5 perc. at one portion, which is as much as the difference of the theories in this range of velocity. I alerted Kaufmann to this fact, so he has measured again and has actually found the deviation of 5 perc. Another point is as follows: I have measured the resistance of the condenser; Kaufmann assumes it to be infinitely great.
When the resistance of the condenser doesn't vanish, then an error is inserted by that, which I estimate to 1 perc. in Kaufmann's experiment. I myself have found the following relations (a drawing is following, in which condenser, resistances, and the battery are indicated schematically). When the switched resistance doesn't vanish against that of the condenser, then the potential difference of the battery is evidently not relevant. This error alone amounts to 0,06 perc. at my experiments. (Numbers are given again.) You see, already there you get noticeable resistances. At Kaufmann's experiments, the resistances already amounted several megohm. Also the voltage measurements of Kaufmann are invalid in my view. Another error is possibly that one: At such exact measurements as they come in question here, the plate may not be so compressed, that the pressure occurs in the middle, but the pressure may only exerted upon the quartz plates, otherwise the pales will be easily bend. When one studies interference phenomena, one sees that when it is pressed from the middle, surely a dozen rings are leaving. Then, the difficulty of the magnetic field has to be mentioned. Kaufmann uses a permanent magnet of 145 Gauss; he had an armature, which was removed and then the magnetism possibly changes with time. Also at this place, a source of error possibly enters.
Bestelmeyer: I don't believe, that the question concerning the sources of error mentioned by me, can be decided here. Thus I only want to say, that I'm not convinced that the mentioned sources of error actually play no role here. Here, it is about very precise measurements. When one considers the smaller dimensions of the apparatus, then the curves approximately show the same sharpness, as in my experiments. For the faster rays, the velocity function according to Lorentz's theory, is ca. 1,24, according to Abraham it is 1,19. The larger velocities correspond the smaller values of deflection. The smaller velocities correspond to the larger deflections. Even at great velocities, the difference between the theory of Lorentz and that of Abraham only amounts to a few tenths of a millimeter at the measurement; I believe, that the measurements can possibly be imprecise by that amount. Though I don't want to definitely assert this here, without a more detailed examination of the numbers.
Bucherer: I'm responding to this: Here, the values of are of such kind, that one can assume without further ado, that the extra rays have no effect. Take an optical analogue. Imagine, that the condenser plates are sooty, then the extra rays will only come to deflection in small number through the condenser (drawing). They cannot exert an influence, this is totally excluded. Here, this influence
