Variometer tuning went out of fashion in the 1930s when it was realized variable capacitor tuning was far easier to implement. The top surface looks plastic and the insulation on the wires is PVC so these are clearly replicas.
They have nothing to do with regeneration, that came later when vacuum tubes became available to give enough gain for it to be possible, this was just for main tuning in crystal sets.
I have an original 'BBC' variometer tuned crystal set here - and it still works - but you need great patience to find a good spot to land the cats whisker on the Galena crystal (that's a diode to anyone under the age of 90!) to get a usable signal.
Brian.