Q:

Did Sommerfeld derive or measure the fine structure constant the first time he introduced it?

I used Wikipedia to try to figure this out but I am not clear on the explanation.  As for Newton's Law of Gravitation does not give the value for the Gravitational constant but it was measured by Cavendish.
I am wondering how the derivation was put together to arrive at the fine structure constant given that the units all cancel out or perhaps Sommerfeld calculated it's value.

A:

Computed (as $\alpha=e^2/\hbar c$) in equation (12a), p. 51 of: Zur Quantentheorie der Spektrallinien, Ann. Physik (4) 51 (1916) 1–94.
(Earlier he had used $\alpha = (e^2/2\hbar c)^2$ in equation (16), p. 469 of Die Feinstruktur der Wasserstoff- und der Wasserstoff-ähnlichen Linien, Münch. Ber. 1915 (1916) 459–500. For discussion see e.g. M. Eckert (ed.) Die Bohr-Sommerfeldsche Atomtheorie, Springer (2013).)

