The design and construction of an astronomical polarimeter is described and an evaluation made of its performance. Extensive observations of cataclysmic variables with emphasis on the AM Her and DQ Her classes are then presented. The polarimeter permitted simultaneous linear and circular polarisation measurements, or, by rearranging the order of the retarders in the beam, linear polarisation measurements alone, or circular polarisation measurements alone, with enhanced efficiency. Extensive sets of observations using the polarimeter were obtained for six of the ten AM Her variables. A comparison was made between the competing models for the cyclotron emission, showing that those which take into account the temperature structure of the accretion region provide the best results.