Where does the $6.24 \times 10^{18}$ number come from? How was it historically derived?

I know that $1$ C $=$ $1$ A s but that just pushes the question down another step, and another and another, at some point where do these numbers actually originate and bubble up from?

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    $\begingroup$ Would this be better on HSM? $\endgroup$ – Aaron Stevens Sep 12 '19 at 23:12
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    $\begingroup$ Possible duplicate of Definition of Ampere $\endgroup$ – jacob1729 Sep 12 '19 at 23:15
  • $\begingroup$ Well, apart from the historic conventions, the number stems from the value of the (low energy) electromagnetic coupling constant. It is one of the dimensionless parameters that we simply measure and can't predict using the current best framework of particle physics which is known as the standard model. $\endgroup$ – Dvij Mankad Sep 12 '19 at 23:34
  • $\begingroup$ I believe that the coulomb (actually a small fraction of it) was originally defined as the charge supported by a typical ball of sulfur, at the time Coulomb made his experiments. But I may be wrong. $\endgroup$ – Cham Sep 12 '19 at 23:59

As you said, the coulomb is an ampere-second. The ampere was historically defined to make the magnetic force per unit length between two parallel one-amp currents with a “nice” separation have a “nice” value. As Wikipedia explains (with my bolding for emphasis),

“The ampere was originally defined as one tenth of the unit of electric current in the centimetre–gram–second system of units. That unit, now known as the abampere, was defined as the amount of current that generates a force of two dynes per centimetre of length between two wires one centimetre apart. The size of the unit was chosen so that the units derived from it in the MKSA system would be conveniently sized.”

  • $\begingroup$ So the modern Ampere is a tenth of the Abampere, why was Abampere not appropriate for usage? I don't understand what "The size of the unit was chosen so that the units derived from it in the MKSA system would be conveniently sized." is referring to specifically, I presume Ampere? Why was two dynes chosen? $\endgroup$ – user51819 Sep 12 '19 at 23:20
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    $\begingroup$ That’s the history, not the modern definition. Modern SI units are not defined in terms of other unit systems. $\endgroup$ – G. Smith Sep 12 '19 at 23:23
  • $\begingroup$ An answer to this question has an explanation for the factor of 2. I can’t vouch for it. $\endgroup$ – G. Smith Sep 12 '19 at 23:29
  • $\begingroup$ There is no physics in unit systems. They are completely arbitrary human conventions. $\endgroup$ – G. Smith Sep 12 '19 at 23:31
  • $\begingroup$ I understand they are arbitrary but I like knowing where the numbers come from, otherwise it just looks like a random number I could pull out of a hat, it helps to know why certain numbers were chosen for whatever convenient reasons in whatever contexts in whatever time period $\endgroup$ – user51819 Sep 12 '19 at 23:32

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