Page:Über die Konstitution des Elektrons.djvu/5

 ==General theory of the curve.==

Let $$\epsilon$$ be the charge of the electron in electromagnetic measure, $$\mu$$ its mass at velocity $$q$$, $$\mu_0$$ its mass when the velocity is very small. Furthermore, let $$z$$ and $$q$$ the magnetic and electric deflections; eventually let $$E$$ and $$M$$ be the "electric" and "magnetic field integral" reduced to proportionality with the deflectabilities; i.e. two quantities equal to the mean field strength with a factor each dependent on one of the dimensions of the apparatus. At last let $$\beta=q/c$$, where $$c$$ is the speed of light. It is

$\mu=\mu_0 \cdot\phi(\beta),\,$

where $$\phi(\beta)$$ is a function of velocity, whose form is different depending on the basic assumption concerning the constitution of the electron. Then it is:

If one sets for abbreviation:

thus one can write:

Thus a auxiliary table is calculated, which gives the $$v$$-values corresponding to a most tight row of $$u$$-values, then (when the constants $$A$$ and $$B$$ are known) the corresponding $$y'$$ by equation (7.) can be compared to every $$z'$$. It is easily achieved to find approximate values for both "curve constants" $$A$$ and $$B$$, and then to calculate the improvements still to be made, by the method of least squares.

The curve constants determined in this way, can be compared with those values partly given from the dimensions of the apparatus