The electrical conductivity of discontinuous metal films in weak fields is discussed. All the structural and electrophysical characteristics of the films (the electric field distribution, the island shape, the size distribution of islands and interisland spacings, the field dependence of the conductivity and the influence of temperature on the film resistivity) are investigated using a special chamber in a transmission electron microscope with a device for electron interference. The results obtained allow us to evaluate critically the current theories and to show the important role of the charge effect in the conductivity of discontinuous films in a weak field.