A useful predictive model is developed for the partition function when fine coal is cleaned on a spiral concentrator. The calculation of the partition function for the spiral is complicated because the behaviour of any particle is strongly influenced by its size as well as its density. In addition two distinct regimes of behaviour are identified depending on whether the particle is in suspension in the flowing water or in the sliding bed on the floor of the spiral trough. Although the (density) cut point is a strong function of the position of the splitter at the foot of the spiral, the range of cut points that can be achieved is limited. This is the chief limitation of the spiral as a device for the production of clean coal. Also the density cut-point was found to be a strong function of particle size with a distinct minimum that varied with the splitter position.