Weber and Kohlrausch:
In 1857 Wilhelm Weber and Rudolf Kohlrausch were the first to show that the ratio of electrostatic to electromagnetic units produced a speed matching the then known value for the speed of light. It was already known, from dimensional arguments, that the ratio was a speed. Weber and Kohlrausch built what were for the time ingenious devices and their measurements found a speed close to the then known speed of light. The race to deduce light propagation from the laws of electricity and magnetism was on, to culminate in Maxwell's Electricity and Magnetism treatise in 1873.
" Maxwell knew that his equations had to produce wave-like solutions because in 1856, W. Weber and F. Kohlrausch had measured the ratio of electrostatic to electromagnetic units, a quantity known from dimensional analysis to be a velocity, and had found it equal to the velocity of light. In the experiment, a Leyden jar of known charge capacity had had its potential determined by an electrometer, thereby establishing its charge in electrostatic units; it was then discharged through a ballistic galvanometer calibrated in magnetic units. "
(source: Louis Brown in physicstoday)
The exact meaning of "the ratio of esu to emu" units is somewhat lost on today's public (and probably on most physicists). It seems worthwhile to clarify this concept and re-create the Weber-Kohlrausch experiment.
After Maxwell published his theory of electromagnetism (1873)
it became possible to calculate the speed of light indirectly from the
magnetic permeability and electric permitivity of free space.
This was first done by Weber and Kohlrausch in 1857.
In 1907 Rosa and Dorsey obtained 299,788 km/s in this way.
It was the most accurate value at that time.
A new determination of the Ratio of the Electromagnetic to the Electrostatic Unit of Electricity, Bulletin of the Bureau of Standards, August, 1907.