Page:Über die Konstitution des Elektrons (1906).djvu/47

of the curve equally well. However, from the values for $\beta$ one can easily see, that Lorentz's theory requires totally different velocities, than the one of Bucherer or Abraham. For these two theories, the velocities are nearly identical, and what is even more remarkable: The function $\Phi (\beta )$ numerically agrees, as one can easily convince himself, with both of them (within the velocity interval given here) with a deviation of at most 2%.

The decision thus only depends on equations (19) and (22) or (20) and (23).

The values of the field integrals, calculated in the appendix p. 543ff, are:

$E=315\cdot 10^{10}$ Electromagn. Units (with 2500 volt P.D.)

$M=557,1$

Thus

$E/Mc=0,1884.\,$

On the other hand, the calculation by means of the curve constants (under consideration of the corrections due to the error of the $z$-scale mentioned on p. 513):

					Difference in perc.
I.	nach	Abraham:	AB	= 0,1817	-3,5
II.	"	Lorentz:	C	= 0,1689	-10,4
III.	"	Bucherer:	AB	= 0,1831	-2,8

The values for $\epsilon /\mu _{0}$ are

a) For cathode rays:[1]				1,878 · 107.
b) For β-rays:					Difference in perc.
according to	Abraham	1,858	1,788	1,823	2,9
"	Lorentz	1,751	1,569	-11,6
"	Bucherer	1,833	1,780	1,808	3,7

Eventually one can also make a comparison of the different theories, by determining the constants A and B, or C and D themselves, from equations (16) be means of the measured values of M and E and the

1. Corrected by the value 1,865 · 10⁷ found by S. Simon (Ann. d. Phys. 69. p. 589. 1899), for ∞-small velocities. See appendix p. 548.