Abstract
A simple procedure for calculating the expected maximum resistance value in a length L of a one-dimensional random chain is used to calculate the d.c. conductivity of systems of length L, and forms the basis of calculations of the low-frequency a.c. conductivity. The high-frequency a.c. conductivity is given in a pair approximation. A smooth transition to the low-frequency calculations is obtained. Both spatially random and variable-range hopping (VRH) systems are treated.