The quark charge asymmetry, summed over flavours, has been measured at centre of mass energies of 35 GeV and 44 GeV using the JADE detector sited on the electron-positron storage ring PETRA. The asymmetry is found to be consistent with the expectations of the standard model at both energies and enables a measurement of the product of the axial-vector coupling constant of the electron with the axial-vector coupling constants of the quarks, assuming the moduli of these latter to be flavour independent. This gives, with reasonable assumptions concerning the effects of B0B0−−− mixing,a e a q =−1.09±0.18±0.23 where the first error is statistical and the second systematic.