In quest of the specific charge of an electron

In the 1890th the knowledge about electrons was limited. Even the word electron was not very popular. But in this time some physicists (Herz, Perrin, Thomson, Kaufmann) worked hard on the point cathode rays. So the electron beam, produced by an experimental setup like the electron gun, was called in this time. They explored the cathode rays with different experiments. So Perrin showed that cathode rays are transporting electric charge.
J.J. Thomson tried to develop quantitative statements. He examined an experiment equal to the experiment, shown in this learning environment. He realized that the Lorentz force is equal to the centripetal force:$$F_{Lorentz}= F_{Zentripetal}$$ $$Q\cdot v_0 \cdot B = m\frac{{v_0}^2}{r}$$ Starting with this approach he seperated known and unknown values and so stand on one side only known, measurable or adjustable values:$${\frac {Q}{m} = \frac {v_0}{r\cdot B}}$$ In this way Thomson was able to determine the mass-to-charge ration. This ratio $\frac {Q}{m}$ is called the specific charge of a particle. In this manner and with the knowledge that cathode rays are electrons, we are able to determine the specific charge of an electron. The equation$$\frac{e}{m_e}=\frac{v_0}{r\cdot B}$$ yield the specific electron charge $\boldsymbol{\frac {e}{m_e}}$ .