The authors calculate the phonon-assisted hopping conductivity for a system of localised electronic states, using a current-current correlation function. A Green function equation-of-motion method has been applied. In doing the calculation they have established the general approximation one must make to the equations of motion and the model, in order to reproduce the random resistance network, regardless of whether one uses a position-position, a current-position, or a current-current correlation function. It is found that diagonal elements of position and electron-phonon interaction play equivalent roles and that it is insufficient to make an approximation neglecting all but diagonal position elements.