Homogeneous tissue-equivalent ionization chambers containing a methane-based gas mixture are widely used to determine the absorbed dose of neutrons employed in radiobiology and radiotherapy. Conversion of the measured ionization charge to the absorbed dose requires knowledge of $W_{{\rm n}}$ , the mean energy expended to form an ion pair in the gas by the initial spectra of secondary charged particles produced by the neutrons. This report discusses the computed charged particle spectra in the gas and the relative kermas contributed by the various types of charged particles. These spectra are combined with an evaluation of the available experimental data on W for the secondary particles to compute $W_{{\rm n}}$ as a function of neutron energy. Over the energy range of 0.1 to 20 MeV, $W_{{\rm n}}$ was found to vary from 32.8 to 31.0 eV, respectively, including sharp changes in $W_{{\rm n}}$ due to large resonances in the ener...