The work described in this thesis was carried out at the Institut Laue Langevin, Grenoble, France as a member of the group searching for the electric dipole moment (EDM) of the neutron. The first chapter is an introduction to ultra-cold neutrons (UCN) and their use in the search for an EDM. In chapter two a description is given of the data acquisition procedure and the data analysis method as well as a discussion of the various sources of spurious EDM signals. The data taken by the author yielded the result I-fe/e = ( -3.7 ± 5.4 )xl0-25 cm, which together' with all the other data previously and subsequently collected on PN5 gives I-fe/e = ( -3.7 ± 5.4 )xlO- 25 cm. The third chapter contains some calculations, based on a simple model of the polarizer's properties, of the time dependence of the polarized UCN density in the apparatus during a data ~cquisition cycle. It. also includes the results of the experiments made in an attempt to determine experimentally the model's parameters. The other two chapters are concerned with the problem of transferring efficiently UCN from the 0.6 K volume of the 4He superthermal source to thf! 300 K EDM apparatus without allowing the heat transfer by radiation to overload the source's refrigerator. The possibility of using metal coated polypropylene windows to achieve this aim is investigated in the fourth chapter. In chapter five the infra-red transmission of the stainless steel neutron guides is estimated by calculation and then determined experimentally with a view to using lengths of cold guides to attenuate the radiation heat transfer from the apparatus to the source.