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We describe a simple deterministic model for the dispersion of particulate ash which has been ejected into the atmosphere by a volcanic eruption. In our model the atmosphere is divided into a series of horizontal layers within which the physical parameters involved are constant. This is an effective way to allow for the changing behaviour of the particulate ash and atmospheric flow with height whilst retaining simplicity. From our model we construct an analytical expression for the finaldoi:10.1017/s1446181108000047 fatcat:ier5gcfmj5aybcutdkgswtkz6u