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This thesis contains a description of the technique used to measure the optical linear polarisation of the Orion Nebula and the nebula, M43, and the results obtained from these measurements. This work was undertaken while the author was a member of the Durham University Astronomy Group. The first chapter is an outline of the differing states of polarisation and the method used to describe these states via the Stokes Parameters. A short review of the mechanisms producing linear polarisation of the optical radiation from astronomical objects is included. Chapter 2 describes briefly the mechanisms producing plane polarisation and dust scattering and also contains a description of Rayleigh and Mie Scattering. Chapter 3 contains a brief account of the design and operation of the Durham University nebular polarimeter used to detect and measure optical linear polarisation, along with a short description of the electronographic camera used as a recording device. Also, the technique for the reduction of the data, from its initial electronograph to the final extraction of the Stokes parameters for over 8550 points in the Orion Nebula is described. The next chapter contains an account of gaseous nebulae, particularly the Orion Nebula, where a review of the present properties of this object and some general remarks on M43 are made. In Chapter 5 of this thesis, the technique employed to measure the optical linear polarisation of these nebulae, together with a final map of the polarisation for each of them, and a comparison of the results obtained by the present method for the Orion Nebula with those measurements of Hall (1974) and Pallister et al (1977) are described which confirm the success of the present technique. In the following chapter, some interpretation of the results and the geometry of the Orion Nebula and M43 are described. Also a simple model of the Orion Nebula as a spherically symmetric dust cloud with 0(^1)ori at the centre is presented. A comparison between his model considering the constant dust density case, and the polarisation measurements, is made in this chapter and some possible causes of the disagreement between this model and observational results are presented. In conclusion, the success of the technique is confirmed for the production of high resolution, accurate polarimetric measurements.

This thesis comprises two separate but related topics in the study of optical polarization of galaxies. In part I we investigate interstellar polarization within 2 kpc of the sun and attempt to quantify the local structure of the galactic magnetic field. In part II we report the results of polarization measurements of the peculiar galaxy M82, obtained using a new polarimeter and digital reduction techniques, and discuss models of the origin of the polarization. Measurements of the linear polarization of starlight have been collated into a catalogue containing the Stokes' parameters in galactic coordinates for those stars for which reliable distances could be determined. The catalogue is presented in the form of vector maps on the sky in several distance intervals. Assuming a magnetic alignment hypothesis we have investigated the direction and form of the galactic magnetic field through e-vector plots and from the periodicity of the Stokes' parameters Q(ɭ) and U(ɭ) with galactic longitude. The results show the existence of a longitudinal field directed towards ɭ = 45º ± 10º within 500 pc, and beyond this there is much confusion with a possible change in direction, associated with the bifurcation of the spiral arm, to ɭ = 74º ± 10º, There is no evidence for a field directed towards ɭ = 90º, It is clear however that a simple longitudinal model of the field is rather naive. The U(ɭ) plots show strong evidence for an inclination of the field by 15º to the plane and this is not associated with a helical structure. The possible significance of this conclusion to the origin of the field is discussed. Incremental polarization maps have been produced but show little correlation with the spiral structure of the galaxy. There is strong evidence for irregularities in the field. The polarization appears to saturate in all directions at about 1 kpc from the sun. We interpret this as an observational selection effect. The major part of this work is directed towards studying the importance of irregularities in the field structure. Autocorrelation techniques have been used and unlike previous authors we can find no coherence in this component on scales greater than 50 pc. In the second part of the thesis we describe an imaging polarimeter constructed for use with a McMullan electronographic camera and designed to operate at an f/15 focus. This is the first polarimeter to use electronographic detection and the principles, construction and method of operation are described. The instrument is intended for observations of galaxies and other nebulae to diameters of up to 8 minutes of arc and has been successfully used to observe the irregular galaxy M82 in the B-band. The results of these observations are reported in this thesis. The polarimeter enables the simultaneous measurement of the linear polarization at more than 1500 locations in a 40 mm field of view to be made. This information is obtained in a series of eight exposures, which enables the effect of cathode sensitivity variations to be removed. The method is independent of variations in background sky brightness and polarization, and in atmospheric transparency. A review of the existing designs of polarimeter, their advantages and disadvantages and the possible sources of systematic errors are discussed. The optical system is also suitable for use with two-dimensional digital detectors but so far none have been used with the instrument. In order to take full advantage of the vast amount of information contained on each electronograph an entirely new digital analysis technique has been developed. Attempts have been made to locate features such as stars, grid overlaps, scratches and dirt blobs automatically using a random search technique. This proved unsatisfactory, and possible explanations and refinement in the approach outlined. A simple contour method is shown to be a satisfactory means of carrying out the feature extraction with manual assistance. A Highly accurate image registration method capable of producing a picture to picture registration better than 2µ is developed and the method takes into account small scale flaws, saturation effects, cathode sensitivity variations and differing exposure times. The technique is vastly superior to conventional methods of plate analysis and future refinements are discussed. The performance of the instrument in the laboratory and at the telescope is reported, the existence of severe instrumental effects established, and corrections derived and applied to the polarization data. Their eradication from the instrument is described and results of calibration measurements of standard stars with the improved optics presented, showing the instrument is capable of reaching a precision of ±0.5% in p and ± 3º in ɵ. The results of polarization measurements of M82 are presented and compared with previous observations. These results have a spatial resolution of between 5 and 8 times that of previous observations, are 20 times as numerous and have comparable accuracy (± 2.5% in p and ± 4º in ɵ). These results represent the first complete mapping of the linear polarization in an extragalactic system at optical wavelengths. A review of the existing observational material on M82 is presented and the relevance of the current observations established. The predictions of simple scattering models for producing the observed polarization are compared with the observations and show moderate agreement. The active region of the galaxy is located and the evolutionary status and energetics of M82 are discussed. The current problems in our understanding of the galaxy and suggestions for future work are detailed.