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|Introduction My first contact with industrial milling was during the time I worked in the electricity generating industry in the United Kingdom. In visits to power stations to investigate either deposits in the boiler furnaces or polluting deposits settling around the stacks. I had to check the performance of the vertical coal pulverizers, since poor pulverization aggravated both problems. Naturally, then, when I came to the USA in 1957 to take a PhD in fuel technology at Penn State, I was put to work to review the science of coal pulverization. After this reviewing, I was completely confused. On one hand, there was a well-developed understanding of stress-strain equations, and a rap- idly developing knowledge of how stressed, brittle solids fractured, based on the Griffith crack theory. On the other hand, reading in the grinding literature gave me: • Kick's Law, which was clearly not correct in the light of modern fracture theory; • Rittinger's Law, which was also clearly not correct; • Bond's Third Law of Comminution, which was claimed to have something to do with the Griffith crack theory, but where the connection between the two was made by intuitive pseudo- scientific reasoning I could not accept; • the choice of mill motor power for the most common type of coal mill, the Raymond pulverizer, was calculated from the fan power required to move air through the mill. Although I could accept the empirical connection between the two, it made no sense from the point of view of fracture energy. Even today, most books or review chapters on size reduction start from these laws. incorrect statements abound in the literature, such as “the Hardgrove Index is based on Rittinger's Law," which it is not, "The Bond theory states that work input is proportional to new crack tip length produced in particle breakage," which is not true, etc. My own test work showed that these "laws" did not fit the data for grinding of coal. At about this time, Epstein (1 948) and Broadbent and Callcott (1 956), following the original work by R.L. Brown (1941) at the British Coal Utilization Research Association, proposed describing breakage as a series of fracture stages. I took their concepts and developed the basic differential equation for a batch grinding process continuous in time, analogous to a batch chemical reactor. Robin Gardner then joined the project and did his PhD on treating batch grinding in the same way as a batch chemical reactor. He found that the basic equation had already been partially derived by Sedlatschek and Bass (1 953) in Germany. We confirmed experimentally the validity of the equations for describing batch grinding (1 962) and formulated the equation describing steady-state continuous grinding in a fully-mixed mill. At about the time this work was published, Gaudin and Meloy (1962) and Filippov (1961) independently published essentially the same equations, but without experimental proof of the validity of the concepts. I will give a brief overview of what these beginnings had led to in the design of mills for size and power, and show some of the results of this more detailed understanding of grinding processes. Concepts of Fracture Mills such as tumbling ball, rod, pebble and autogenous mills and vertical mills such as the Raymond, and E-type apply compressive stress to lumps or particles relatively slowly. Compressive stress applied to a particle of an elastic brittle solid imparts overall strain energy to the solid and produces local regions of tensile stress, (Fig. 1) (Berenbaum and Brodie, 1959). Irwin (1949) showed from solution of the stress-strain solutions that a small hole in a region of tensile stress reduces stress concentration at the hole, that is, the tensile stress at the tip of a crack or flaw in a solid is much higher than the general tensile stress in the region. The longer the crack, the higher the stress concentration. Griffith (1920) hypothesized that when the regional tensile stress is large enough, then the chemical bonds at a preexisting crack tip are stretched to breaking point, as illustrated in Fig. 2. When the bonds break, the crack becomes longer, the tensile stress concentration increases, the situation is unstable and a crack opens up (propagates) a surface of tensile stress, creating its own tensile stress at the leading edge. Stored strain energy is converted to the kinetic energy of the moving stress field, which is analogous to sound propagation through the solid, so the crack tip accelerates to velocities approaching those of sound. The moving crack will pass through regions that were previously under regional compressive stress. The equations for "ideal" and "Griffith" strengths are where a is the intermolecular distance, y is Young's modulus, g is the energy|