As gold prices soar, Americans rush to sell or melt down their jewelry—even family heirlooms from the 1800s

At the biggest jewelry center in the United States, Alberto Hernandez fired up his machine on a recent day and waited until it glowed bright orange inside before shoveling in an assortment of rings, earrings and necklaces weighing about as much as a bar of soap: just under 100 grams, or 3.2 troy…