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I've done a little bit of research and it seems Millikan was able to measure the ratio between the charge of the electron and its mass. But how can one measure one of the two constants to get the value of the other?

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    $\begingroup$ No,Millikan was able to actually measure the charge on an electron.The charge to mass ratio constant was actually determined much before by cathode ray tube experiments. $\endgroup$ – Sandesh Kalantre Jan 29 '14 at 15:20
  • $\begingroup$ Can you make your comment an answer by providing sources and references ? $\endgroup$ – Gabriel Romon Jan 29 '14 at 15:27
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    $\begingroup$ Well even Wikipedia has an excellent article on them.I suggest you to take a look at them. $\endgroup$ – Sandesh Kalantre Jan 29 '14 at 15:36
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The mass-to-charge ratio $m/e$ of the electron was first measured by J.J. Thomson, the discoverer of the electron, using cathode rays in 1897:

It should not be surprising that one may measure this ratio even without isolating "individual electrons" because the electric force acting on a charge may be written as $$ F = ma = Ee, \quad a = E\cdot \frac em $$ So what was left was just to measure the mass or charge separately. Millikan and Fletcher did the relevant oil drop experiment in 1909.

The electric force $F=Ee$ acting on a single drop with charge $e$, a single extra (or deficit) electron, may be calculated when it is set equal to the drag force from hydrodynamics, $6\pi e\eta v_1$. The viscosity $\eta$ is the most difficult thing to know but otherwise all quantities are known so $e$ may be calculated.

If one knows the charge and the ratio, one may calculate the mass as $m = e/ (e/m)$.

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  • $\begingroup$ The viscosity can be measured by uncharged oil drops. As the viscosity term acts against gravity, it will reach a maximum velocity. From it and the radius and density of the oil-drop, you can calculate the viscosity. $\endgroup$ – abu_bua Jul 3 '18 at 16:26

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