In this paper it is supposed that the effects produced by electric forces are intermittent and consist in the addition of finite increments of momentum occurring after finite intervals of time, and not, as is usually assumed, of a continuous flow of momentum. On the latter view, a body in the time δt receives an increment of momentum Fδt if F is the force; on the view discussed in this paper, it is a chance whether or not the body receives any increment; this chance is equal to δt/T, where T is a time, called the time interval of the force: it depends on the strength of the field and is equal to the average time between two increments. If I is the value of each increment of momentum, the expectation of increase of momentum in time δt is Iδt/T. Over intervals which are long compared with the time T the increase is the same as that under a continuous force equal to I/T, and for effects which are spread over such intervals the results of the intermittent theory agree with those of the usual theory. It seems possible, however, that in effects occurring in atoms or rays of light the times involved may be small enough to be comparable with T; in these cases the classical theory will no longer hold and an entirely different treatment is required. The paper discusses some of the effects which may be expected under these conditions : these include the spontaneous dissociation of electronic systems, the production of Röntgen rays. It follows, too, from the theory that there would be no radiation of energy from an electron describing a circular orbit; the theory, too, has an important application to the propagation of light; it shows that light cannot be propagated as divergent waves where the electric force falls off as the waves recede from the source; it requires that light should be corpuscular in character, i.e. must consist of units whose energy does not change as they travel through space.