Here is a US Model 1882 headless shell extractor. Excellent condition. Poyer and Riesch "The .45-70 Springfield" explains it on pages 202 and 203. You have the M1882 extractor. Unscrew the small 'drift' that is screwed into one end. Now take the 'extractor' (large part) and insert it into the muzzle. The end that you took the small drift off of goes first. (Those things that look like threads on one end are actually called grasping grooves). Now take the 'drift' that you unscrewed from the extractor and screw it onto the cleaning rod/bayonet. This is then inserted into the muzzle and down into the front face of the extractor. Inserting the drift causes the front fingers of the extractor to expand and grasp the sides of the cartridge. You can now tap the broken cartridge case out of the chamber.