This thesis is an account of work carried out by the author at the Kelvin Laboratory, University of Glasgow, during the period between October 1978 and October 1979. The project involves the design study for a new, improved position sensitive detector system to be used at the focal plane of the magnetic spectrometer. The spectrometer forms part of the 160 MeV electron scattering facility at the Kelvin Laboratory. Although the detector was to be designed primarly for use in electron scattering experiments, it was felt that the use of a gas proportional counter as the main position sensing element might afford the instrument versatility, enabling it to be used in various light ion experiments. The first chapter of this thesis outlines, in general terms, the properties required of focal plane detectors, and expands on the advantages to be gained from using position sensitive proportional counters. The specific requirements for the detector in this study are outlined. Position sensitive proportional counters are becoming increasingly popular with nuclear spectroscopists, and a brief review of the progress made in the design of such instruments is included. The second chapter summarises the theory of operation of a position sensitive proportional counter. The important factors which affect the spatial resolution are considered, and where possible empirical or semi-empirical formulae are introduced in order to provide a means of estimating the relative contributions from various effects. Most of Chapters 1 and 2 are taken from the literature, although the application of noise theory to proportional counters operating in charge division mode has been studied, independently, by the author. Chapter 3 reports experimental work performed using simple, one-dimensional position sensitive proportional counters on the bench. Various aspects of the operation are investigated, the effects of varying detector parameters are observed and two methods used for signal processing are described. The experimental work of this chapter gave the author valuable experience in the operation of proportional counters, and provided important guidelines for the final design. Chapter 4 reports several tests conducted with proportional counters in the working environment of the spectrometer experimental area. The tests were performed to assess the sensitivity of gas detectors to the intense background radiation induced by the 160 MeV LINAC, and to measure the energy resolution attainable in an electron scattering experiment using a position sensitive proportional counter at the focal plane. Finally, Chapter 5 describes the detailed design of a focal plane array of resistive wire proportional counters which the author believes will provide adequate spatial sensitivity, so that the energy resolution measured at the focal plane will not be compromised by the resolving power of the detector.