I think this came from a crystal set made in Japan during the mid-20th century. It has a ball on the end of the ferrite rod like the crystal sets that were shaped like a rocket and this ball was at the rocket’s nose. The coil measures 38 to 380 microhenrys depending on the position of the ferrite core. This slides in and out to tune the crystal set, and the capacitor is a fixed value, not variable. In order to tune the AM broadcast band of 530 to 1605 kHz, about a 3 to 1 frequency range, the coil (or tuning capacitor) has to vary over about a 10 to 1 range, hence 38 to 380 uH. I used the Electrodoc, an app for smart phones, resonance tool to calculate the capacitor needed to give the full tuning range. It came to 260 picofarads. The two standard values that give 260 pF when connected in series are 470 and 560 pF. In order to make this crystal set complete, it needs a germanium diode, a piezoelectric crystal earphone and a few dozen yards or meters of antenna wire and a back yard where the wire can be hung from a tree.
