A static equilibrium mathematical model of the lead,flotation circuit at The Zinc Corporation Limited is developed to permit the feasibility of applying computer control techniques to be studied. The model is based on the relationship between the cumulative recovery of a mineral species R from n flotation cells or assemblies in a unit given asR = M(1-(1 - p))where M is the maximum possible: recovery and p is the probability of flotation for the particular mineral.The verification of this relationship by data from pilot plant cell-to-cell and plant open flow flotation units shows that these systems behave as if the probability p is constant for each cell or assembly of anyone unit. It is also concluded from this study that mineral recovery is independent of the head assay. Two consequences of this probability relationship, are demonstrated.1. The total recovery from an open flow unit is enhanced by increasing the number of flotation assemblies but maintaining a constant flotation time and total air addition.2. The rougher and scavenger capacity required to recover a bulk lead-zinc concentrate is approximately half that used for selective flotation.The static equilibrium model is derived by solving a series, of mass balance equations which incorporate the recovery-probability relationship for each type of flotation unit. It is used to calculate the complete metallurgy of the circuit for any arrangement of cells knowing only the plant feed assays and the probabilities of flotation for the three mineral types, galena, marmatite, and gangue for rougher, scavenger, and cleaner flotation. The high degree of prediction obtained is demonstrated by comparison with plant results.Pulp flowrate is the principal variable affecting the accuracy of the present model. Work is in progress to establish this effect and permit the derivation of a dynamic model. Even so, the static model is valuable in its present form for the analysis and design of circuits, and optimisation studies using computer services have been conducted.