This dissertation describes the measurement of angular diameters of compact radio sources by the technique of interplanetary scintillation. The design, construction and testing of a four acre radio aerial functioning at a frequency of 81.5 MHz is described, and its operation during a survey of the sky between declinations -07° and +46° and right ascensions ten hours and sixteen hours. The calibration of the apparatus is explained and the method of analysis of the output from the receiving equipment. The theory of interplanetary scintillation has been adapted to this frequency and extended, especially for the case of radio sources at large solar elongations. More stringent limits have been set on the rate of change with distance from the sun of the size of the irregularities in the interplanetary medium. Some nine hundred radio sources have been studied in the survey, and one hundred and ninety-four have been found to contain structure of angular dimension less than one second of arc. Limits have been put on all the others. Fifty per cent of sources in the 3C catalogue have been found to show interplanetary scintillations. Angular diameters of eighty-five sources have been measured: these measured values are in good agreement with other existing measurements, and values are now available for a large number of sources in the 4C catalogue in the area covered by the survey. The radio source 3C 273 has been found to contain two small diameter components, and the more compact of these to be surprisingly strong. A more rigorous test of the correlation between spectral index of and the presence or absence of fine structure in a source has been carried out. A correlation between an enhancement of scintillation and a reduction in cosmic ray index has been noted. A description of the discovery of pulsed radio sources is given.