Neutron flux and energy spectrum measurements are of central importance in design considerations for detectors to be built at the SSC. An experiment (E-821) employing four liquid scintillation counters (BC-501A) and seven Bonner spheres was run at FNAL. The longitudinal neutron flux and energy spectrum, produced in high-energy hadronic showering occurring in iron, was measured. A pulse shape discrimination technique was used to discriminate neutrons from gamma rays. The hadronic showering was initiated by a beam of negative pions (25-150 GeV) incident on 1 to 15 interaction lengths of iron. The relative number of neutrons per incident pion, as obtained with the liquid scintillation counters, is presented in this thesis as a function of incident beam energy and interaction length. The technique of pulse shape discrimination is covered in detail.