[Phlogiston]

Well, you are not "dense" unless I am too.

The turns ratio on the same iron, laminated crore is going to determine the impedance ratio. It does not guarantee that the resistance in ohms is going to be the same ratio. Resistance measurements are just a good way to guess. If resistance is way off or open or shorted, the trans is broken.

In some of these radios the first trans is for voltage gain ( the tubes themselves were only good for a gain of 9 - 15 unlike later tubes that could have gain in the hundreds or thousands. The second trans can be center tapped for radios that have push pull outputs (2 tubes). The gain for these can be as little as 0 or in this case 1.5 - 2 per side. The transformer's first job is to provide the phase shift required to run tubes in the config. - one going + at the same rate as the other side is going - ). A lot of gain in this stage can drive the output into distortion, but they  - generally - do provide some voltage gain. These push - pull trans age generally a bit larger than the 2 that you have.

Russ

P.S. the "core" of thes early AK trans is usually a bunch of iron wires twisted into a "core". Kind of messy, but it works. Also, yours is not push-pull (center tapped secondary), but a lot of these trans were made for that service.