Radio-frequency corona breakdown of the air surrounding a transmitting aerial operating under conditions of reduced pressure occurs for a comparatively low radiated power. In this paper the theory of diffusion-controlled breakdown is discussed and used to deduce the critical field strength for breakdown at the tip of a prolate spheroidal unipole aerial. Two independent methods are used to determine the electric field strength at the tip of the unipole. In one of these the voltage on the coaxial transmission line feeding the unipole is measured at a distance of three-quarters of a wavelength from the base of the unipole. In this way the current entering the base of the unipole can be found, and hence the electric field at the tip can be calculated. The other method makes use of a small microphone actuated by the attractive force of the electric field. When this method is used, the radio-frequency oscillator is square-wave modulated. The two methods give satisfactory agreement. In the breakdown experiments two unipoles of different base diameter were used. For each of these experimental values of the critical field strengths for onset of corona are compared with the values deduced from the diffusion theory of breakdown.