The aim of this research project was to assemble an apparatus to measure the electric quadrupole moments of gas molecules using the technique of electricfield- gradient-induced birefringence, or the Buckingham effect. Comprehensive research by various workers in the field has shown that this technique provides the only direct means of obtaining the quadrupole moment of a molecule. Theory has shown that the most accurate determination of the electric quadrupole moment is through a study of the temperature dependence of the effect. This not only allows for the quadrupole moment to be obtained but also enables the temperature-independent quadrupole hyperpolarisability term to be extracted. Both the quadrupole moment and the hyperpolarisabilty provide valuable information in a variety of applications, including intermolecular forces, electrostatic potentials and non-linear optical phenomena. This thesis fully describes the apparatus used in these measurements, including a description of the custom built oven that allowed for measurements to be performed over a temperature range spanning from 25"C up to 200"C. Results for the quadrupole moments and quadrupole hyperpolarisabilities of carbon dioxide, carbon monoxide, nitrous oxide and hydrogen are presented, together with a quadrupole moment for carbonyl sulphide from room-temperature measurements. Wherever possible, the results of this work are compared to previously published experimental and theoretical data. / Thesis (PhD) - University of KwaZulu-Natal, Pietermaritzburg, 2009.