Data from ball mills of a wide range of sizes are analysed using detailed mathematical models and non-linear least squares fitting techniques. This analysis reveals that the relative power inefficiency of large ball mills is due to inefficient grinding of coarse (plus 4 mm) particles in these mills. A qualitative physical hypothesis is proposed to explain this behaviour. The results of the analysis can be used to scale up ball mill behaviour, using the mathematical models and techniques developed. A simpler ball mill scale-up procedure is also proposed, and its limitations stated. Laboratory experiments are being conducted to determine the average size distributions of single particles of different ores after breaKage. These experiments can distinguish between the different ores, and it is hoped to use their results to model and predict the grinding of different ores in ball Mills.