Question on antennas for 1930s radios

[dtvmcdonald]

That radio is a predecessor of the AA5, just with a transformer. A 34 ohm
antenna coil (for broadcast band) means it is high impedance input,
300-1000 ohms. Short wires are expected.

If a short wire inside does not work you need a loop antenna. Without modifying
the radio there is no choice but using a tuned loop, with its own
tuning cap that you tune in sync with the radio. Its easy to make one
like I did, to try out. Get a 360 to 450 pF tuning cap and a cardboard box
15 inches square. Wind 14 turns of wire on it, spaced to fill 2 inches.
(a 15 inch square loop.) Twist taps one, two, and three turns from one end.
Hook the boom of that end to the tuning cap and radio grounds, and the other
loop end to the tuning cap. Try each of the three taps to the radio antenna
connection to see what works best. If you like the results you can
build a nice looking loop. Mine works well with all the radios I have,
from one like that to old A-K coffin TRFs to various boatanchors (which have
100 ohm inputs).

There is no substitute for a tuned loop without a modified radio!

For SW a 10 foot wire will work well, or rather,
would if there were any signal ... this winter the bands are dead, dead, dead.