Page:Messungen an Becquerelstrahlen.djvu/6

is still to be noticed, that the small deviation of the value of ${\tfrac {\epsilon }{m_{0}}}$ is probably explained by the difficulty of current regulation, which is required at so small rays. A look upon the both last columns shows, that the decision turns out in favor of the Lorentz-Einstein theory.

Number of epxeriment	βm	H in Gauss	Zm in mm	${\frac {\epsilon }{m_{0}}}\times 10^{-7}$ according to Lorentz	${\frac {\epsilon }{m_{0}}}\times 10^{-7}$ according to Maxwell
10 u. 11 8 7 13 3	0,3178 0,3792 0,4286 0,5160 0,6879	104,54 115,76 127,35 127,54 127,54	16,37 14,45 13,5 10,18 6,23	1,695 1,706 1,706 1,704 1,705	1,676 1,678 1,670 1,648 1,578

It remains, to come back to the possibility of the inclusion of a certain correction at the values of deflection. My calculations are related to deflections, which the rays (being compensated within the condenser) experience in the pure magnetic field. However, besides those normal rays, also anomalous ones occur, namely rays that didn't experience a complete compensation of the acting forces withing the condenser, and therefore traverse the condenser in a curved path. They are making the radiographic curve somewhat less clear, and are possibly displacing somewhat the center-of-gravity line of the curve. I have calculated these extreme rays, and convinced myself that they didn't noticeably influence the results.

Finally I still want to shortly remark about the obvious constancy of the values of ${\tfrac {\epsilon }{m_{0}}}$; it is an advantage of the method used by me, that (as the calculation shows) small errors in the determination of the electric field strength are only slightly influencing this constancy, provided, that these slight errors are made evenly at all experiments. Thus when the value of ${\tfrac {\epsilon }{m_{0}}}=1,705\times 10^{7}$ contains a possible error, then the essential result of my experiment is not altered by that. This result is the confirmation of the relativity principle.

Supplement.

As a calculation shows, which was conducted only afterwards and which is based on a successful experiment, the action of the protection ring around the condenser is not without influence as I believed and also expressed at the beginning. Theoretically, this marginal action is just so, as if the radius of the condenser would be increased by a small amount – here 0,31 mm. If one applies this correction, than ${\tfrac {\epsilon }{m_{0}}}\times 10^{-7}$ becomes 1,730; 1,730; 1,729; 1,730 according to Lorentz for the experiments No. 8, 7, 13, 3 respectively.

(Received September 23, 1908.)

Discussion.

Bestelmeyer: I would like to ask the reader to provide the following dimensions. How large was the distance between the plates (reader: ¼ mm). How large was the diameter of the interior condenser (reader: 40 mm). How was the length of the path between the plates (4 cm) and outside of the plates? (4 cm), and how large was the deflection of the rays? (16 mm down to 6,23 mm). There, I would like to allude to a difficulty at the measurements. Electrons are moving rectilinear between the condenser plates, for which the electric and magnetic force is equal. However, besides the rays which are passing through rectilinearly in the condenser, also such ones are traversing which have a substantially greater and a substantially smaller velocity. For the dimensions that you have given now, those are (in my estimation) ca. ± 10 perc. which are passing through with different velocity, and when one determines now from the deflection of the value of $e/m$, then it is not sure as to whether it belongs to the rays of average velocity, or to the ones having a velocity which is 10 perc. higher or lower. Thus one must know the initial radiation distribution. If they are altogether of the same amount, then one can assume that the deflection also corresponds to the mean velocity.

Bucherer: I have taken pains to investigate this error strictly mathematically. For that purpose, I have solved a transcendental equation from that I measured the velocities and the radius of curvature. It is given, that these rays don't matter. This is different with Bestelmeyer's method. There, the slit is wider. When you look at the image, then you will see that the extra rays play no role at all. The image can only stem from the central rays, which are normally passing through, that is, which have no curvature. I want to write down here some numbers, which take this point into account;