An investigation on the breakage characteristics of closely sized orc samples at different levels of input energy was carried out to determine an appearance function for possible use in ball mill modelling. A consistent pattern of breakage behaviour was observed and the resultant size distributions could be described by a one-parameter, ('t'), family of curves. For each particle size range tested, this parameter 't' has an exponential relationship with input energy below an upper energy limit. A tentative linear relationship between the input energy at a constant value of 't' and the work-index leads to reconstruction of 'I' - input-energy curves from the work-index values. To normalise the efrect of particle size and input energy, multidimensional cubic spline regression was performed on thc entire range of data. The results indicated that the parameter 't' can be determined, reasonably accurately, as a function of Ln (input energy, kWh/tonne) and Ln (particle size, mm) for input energies between 0.5 and 8.0 kWh/tonne.