Plasma emission (i.e. emission at about the plasma frequency and twice this frequency) is treated taking into account the effects of the magnetic field on the electron plasma waves, on the conversion processes, and on the escaping radiation. The expected degrees of polarization of the fundamental and second harmonic are calculated in the weak field limit. The results are used to estimate the magnetic field strength B at the 80 MHz level from the observed polarization of type III bursts; the result B < 0·04 G is smaller than previous estimates. The possible importance of electron· cyclotron waves in an application to type I bursts is noted.