This thesis is concerned with a project to apply the method of pressure modulation radiometry to measurements of the temperature and water vapour distributions in the atmosphere of Mars. The technique has already been used successfully to measure temperature (and occasionally composition) in the atmospheres of Earth and Venus. Two pressure modulators, containing carbon dioxide and water vapour respectively, are used in the Pressure Modulator Infrared Radiometer (PMIRR), on the payload of Mars Observer, scheduled for launch in September 1992. The composition of the Martian atmosphere is almost pure CO2, so the emission lines are unusually broad, so that the mean pressure in the CO2 modulator has to be much larger than for previous modulator...