We present the results of experimental studies of hadron showers in a copper:quartz-fiber calorimeter, based on the detection of Cherenkov light. These studies show that there are very significant differences between the signals from protons and pions at the same energies. In the energy range between 200 and 375 GeV, where these studies were performed, the calorimeter's response to protons was typically 10% smaller than the response to pions. On the other hand, the energy resolution was about 25% better for protons. In addition, the protons had a Gaussian line shape, whereas the pion response curve was asymmetric. These differences can be understood from the requirements of baryon number conservation in the shower development. They are expected to be present in any non-compensating calorimeter, to a degree determined by the e/h value. (C) 1998 Elsevier Science B.V. All rights reserved.