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A liquid hydrogen target was used to study the nuclear fragmentation of beams of relativistic heavy ions, Ne to Ni, over an energy range 400 to 900 MeV/nucleon. The experiments were carried out at the Lawrence Berkeley Laboratory Bevalac HISS facility, using the charge-velocityrigidity method to identify the charged fragments. Here we describe the general concept of the experiment and present total charge-changing cross sections obtained from 17 separate runs. These new measured cross sections display an energy dependence which follows semiempirical model predictions. The mass dependence of the cross sections behaves as predicted by optical models, but within the experimental energy range, the optical model parameters display a clear energy dependence. The isospin of the projectile nuclei also appears to be an important factor in the interaction process.PACS number(s): 25.75.+r, 24.10.Ht