Page:Die elektromagnetische Masse des Elektrons.djvu/3

derived from the directly measured $(y,z)$-curve by simple transformation.

Thus the task emerges, to determine constant $k_{1}$ by means of the method of least squares, so that the ratio of the left side of 8) is as constant as possible; ${\overline {k_{2}}}$ is the average of all $k_{2}$ found, thus

9)	$\Sigma \delta ^{2}=\Sigma (k_{2}-{\overline {k_{2}}})^{2},$

must be brought to a minimum. Due to the complicated form of $\psi \left(k_{1}{\tfrac {\zeta }{\eta }}\right)$, this can only happen by trying; after some routine one soon will find suitable values of $k_{1}$, namely up to a precision of ½%.

At the end, I report some results of measurement:

Table I is related to my older observations, in which a calculation-error that unfortunately happened at that time and about which I was alerted by E. Gehrcke, was removed. Table II, III, and IV contain the new observations of considerable greater precision,^[1] that were recently made by me with kind support of Mr. and Mrs. Curie, who gave a small quantity of there extremely valuable, pure radium-chloride at may disposal. The enormous activity of this preparation allowed the application of very small granules as radiation source, and a correspondingly fine diaphragm, so that the curves became considerable finer than before, and even the mere voltage of the high voltage battery (ca. 2000 volt) was sufficient, to cause a sufficient separation of the two arms. 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.

If the absolute value of $H$ is known, one can also determine $\epsilon /\mu _{0}$ by equation 7. I haven't measured $H$ in the new experiments, while in the old measurements (tab. I) it was $H=299$, from which it is given

10)	$\epsilon /\mu _{0}=1,84\cdot 10^{7}.\,$

in good agreement with the value found for cathode rays:

11)	$\epsilon /\mu =1,865\cdot 10^{7}.\,$

If one calculates (for the experiments in tab. I) the constants $k_{1}$ and $k_{2}$ from the apparatus dimensions, one finds for $k_{1}$ a value deviating by ca. 7,2%^[2], i.e., one doesn't obtain the speed of light for the velocity of the fastest rays, but $2,785\cdot 10^{10}$.

It is very probable, that this differences will vanish with sufficient refinement of the measurement. Experiments in this direction are under way.

Summarizing, it can be said already now, that the observation allow of the following conclusions:

The mass of the electrons forming the Becquerel rays, depends on the velocity; the dependence is precisely representable by Abraham's formula. Consequently, the mass of the electrons is purely electromagnetic in nature.

The value calculated for small velocities, agrees with the value found for cathode rays within the margin of observational errors.

(Self-lecture of the reader.)

Discusson.

Meyer (Königsberg): May I ask, how is the function $\psi (\beta )$ calculated, theoretically or by measurements?

Kaufmann: Perhaps it is better, when we carry out the discussion after the lecture of Abraham.

Abraham (Göttingen): The theoretical derivation will just be given by me; but we can speak about, to what extent the form of function $\psi (\beta )$ (as required by the theory) is confirmed by the observations.

Kaufmann: The comparison with the theory is in the first place made on the basis of the deflections measured on the plate, by determining the two constants depending on the apparatus dimensions and field strengths, not by absolute measurement, but empirically according to the method of least squares.

When one specifies in an absolute way, then it is much harder to reach agreement, because an error of 1% in the determination of $\beta$, already gives an error of 10 or 20% for $\psi (\beta )$. 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 $k_{1}$. If one calculates (after correction of this deviation) from that the value of $\epsilon /\mu _{0}$, then one gets the value $1\cdot 84\cdot 10^{7}$, while $1\cdot 865\cdot 10^{7}$ was found for cathode rays.

1. The plates will be shown here.
2. W. Kaufmann, Gött. Nachr. 1902. H. 5.