Abstract The fluctuating electric microfileld in a plasma in thermal equilibrium can be divided into two components. One has the character of rare sharp peaks, due to the occasional close approach of single ions or electrons to the observation point, while the other, the background, results from the simultaneous action of a large number of more distant charges. This longrange component may be imagined as arising from the random superposition of intercrossing longitudinal plasma waves, with all, wave-lengths down to a small multiple of the Debye length. Their spectral energy distribution is obtained by counting the modes of oscillation by Jeans’s method, combining this with the dispersion law given by Bohm & Gross, and giving each rnode an energy kT. The cut-off near the Debye length is estimated by various considerations, which lead, to the conclusion that the spectrum extends approximately over one octave above the critical or ‘plasma frequency’. The argument is supported by showing that there is a thermodynamical upper limit to the energy of the plasma waves. The scattering of electrons in a plasma by long-range effects is calculated from their momentum and energy exchange with the random plasma, waves. It is found to be much smaller than the scattering due to close encounters, which proves conclusively that the phenomena first observed in low-pressure arc discharges by Langmuir, and which appear to suggest a very strong electron-electron interaction, cannot be accounted for by the dynamics of equilibrium or steady-state plasmas. This suggests very forcibly that these arc plasmas are the seat of strong, partially organized, self excited oscillations, to which the considerations of the present paper do not apply.