We have measured the mobility of , , and in methane over a wide range of the reduced field strength, E/N, from 15 to 520 Td with a drift-tube mass spectrometer. The mobility of the latter ion could be measured because of the presence of 200 ppm of water vapour in the gas, thus leading to the formation of by proton-transfer reactions between and with . A thorough measurement of the variation of the relative ionic fluxes of and with gas density, drift distance and E/N, allowed us to derive proton-transfer cross sections and rates for the above reactions, up to . The cross sections were found to decrease steadily with the mean energy of the ions, suggesting that a fraction of the field-induced energy could possibly be transferred collisionally into internal ionic energy.