Page:Über die Konstitution des Elektrons (1906).djvu/45

to the circumstances of my observations; the deviation of his equation for the electron's mass from that of Lorentz, is thus only apparent.

In cases I. and III., the following relations between the apparatus constants, the curve constants, and $\epsilon /\mu _{0}$ are given from equations (14) to (16):

(19)	$A\cdot B=E/Mc=\beta \cdot y'/z'.\,$

(20)	$\epsilon /\mu _{0}=c/AM=Bc^{2}/E=c{\sqrt {Bc/AME}}.$

In case II., a separation of the variables is possible and one obtains as the equations of the reduced curve:

(21)	$y'^{2}=C^{2}z'^{2}+D^{2}z'^{4}\,$

where

(22)	$C=E/Mc\,$

and

$\epsilon /\mu _{0}=cC/MD=c^{2}C^{2}/ED={\frac {cC}{D}}\cdot {\sqrt {cC/ME}}.$

Equations (19) and (22) allow us to compare $AB$ or $C$ with a quantity directly calculated from the experimental arrangement. They are thus a direct means of verification of the considered theory. Equations (20) and (23) also contain the cathode-ray-value $\epsilon /\mu _{0}$, about whose amount no complete agreement seems to exist. Here it is given by different ways, under consideration of either the electric or of the magnetic field integral alone. Both values deviate the more from one another, the less equations (19) and (22) are satisfied. For a comparison with the values observed with respect to cathode rays, it seems to be the best, to uniformly distribute the possible experimental errors upon the magnetic and electric field integral, and to take the geometric average from both values; this is the meaning of the third expressions for $\epsilon /\mu _{0}$ in equations (20) and (23).

The method of least squares gives the following value of the curve constants:

I.	According to	Abraham:	A	= 2,169 · 4/3	B	= 0,08355 ·3/4
II.	"	Lorentz:	C²	= 0,02839	D²	= 0,2672
III.	"	Bucherer:	A	= 2,9337	B	= 0,06234.