The ${\ensuremath{\nu}}_{e}$ and ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ fluxes from decay of short-lived parents (presumed to be predominantly charmed particles) have been measured in a beam-dump experiment at Fermilab. Novel and important features of the experimental arrangement and procedures are presented and discussed in detail. Details of the analysis of the prompt flux and the backgrounds are presented together with a discussion of the systematic error. The energy and angular distributions of the prompt neutrino flux are presented, and the cross section for charm production is measured to be 57.2\ifmmode\pm\else\textpm\fi{}2.9\ifmmode\pm\else\textpm\fi{}8.5 \ensuremath{\mu}b/nucleon. The dependence of the cross section on atomic weight is measured to be ${\ensuremath{\sigma}}_{c}$\ensuremath{\propto}${A}^{0.75}$. The possibility that charm is produced by a mixture of central and diffractive processes is examined and discussed in the context of these results. The prompt fluxes of ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ and \ensuremath{\nu}${\ifmmode\bar\else\textasciimacron\fi{}}_{\ensuremath{\mu}}$ are roughly equal, as are the prompt fluxes of ${\ensuremath{\nu}}_{\ensuremath{\mu}}$ and ${\ensuremath{\nu}}_{e}$. Quasielastic neutrino interactions were identified and used to provide an independent measurement of the flux which corroborates the energy calibration of the detector. A search for additional sources of prompt neutrinos beyond charm is reported. Negative results were obtained for supersymmetric particles, heavy neutral leptons, and b quarks, subject to the assumption of specific characteristics of the particles and the production mechanisms.
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