In 1968, Finson and Probstein outlined a theory which could be used to analyse cometary dust tails. This theory is applied to a series of P/Halley images, obtained using the UK Schmidt Telescope. The theory is successful and shows that P/Halley underwent a series of major outbursts during early 1986. The duration of the outbursts is approximately 2 days. This value coincides with the 2.2day nuclear rotation period, estimated by other observers. The size of the dust grains varies from submicron to several hundred microns and their calculated orbital parameters indicate that a considerable fraction of the larger grains contibute to the Zodiacal Dust Cloud. A range of CCD and UK Schmidt images reveal dust features in the comae of comets P/Crommelin, P/Giacobini-Zinner and P/Halley. Intensity contours for many images exhibited a "swinging round" effect i.e. for each image there was a systematic change in the photometric axis from the central condensation outwards. This was attributed to radiation pressure effects. Astrometric images of P/Halley show sharp parabolic hoods. These hoods are discussed with reference to near-nuclear dust grain orbits. Preliminary results indicate that the rotation period of Hailey is at least a few days. Mie (1908), developed a method by which the general properties of scattering and emission by dust grains, can be used to model cometary thermal spectra. Such a method is applied to several P/Halley spectra, taken during April, 1986. The results indicate that the dust grains could be composed of both an absorbing (e.g. magnetite) and a dielectric (e.g. silicate) material. The interrelations between decaying comets and Earth-crossing asteroids are discussed. Optical and infrared observations indicate that comet P/Neujmin 1 may be a transitionary object. P/Arend-Rigaux however, is still very active, displaying a large dust coma, with anisotropic emission.

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