The current-field characteristic of a 1D, variable-range hopping system is calculated for the first time by solving nonlinear electron conservation equations. A previous linearised calculation is shown to violate total electron number conservation. The condition is imposed in the nonlinear calculation together with appropriate modifications of the contact boundary conditions. For weak fields these changes have no effect on the results but for large fields there are large changes in the calculated values of the current. The standard deviation of the fluctuations of log J produced by varying the chemical potential mu is shown to decrease with increasing field. Previous calculations of the variation of (log J)_mu with the number of sites, N, are extended to N=10⁴. Fluctuations of (log J)_mu with increasing N are found, approximately 0.5, about a systematic decrease towards what appears to be an asymptotic limit.