Although John Bennett had a flair for mathematics at school, he did not take the scholarship he won to Oxford University. Instead, when World War I started, he joined the Royal Engineers at the age of 17. After the war he lived in Turkey and Greece for 15 years, where he worked as a diplomat and as an engineer on brown coal mining. Upon his return to England, he joined the British Coal Utilisation Research Association (BCURA), where he was appointed as its first director. BCURA was established in 1938, taking over current research on coal (McCaffrey 2003).
At the time, households or small industries that required graded or semigraded coal formed the main market for coal. Coal was broken from the seams by pick and shovel or blasting and prepared for market by screening into fractions. Fine coal burned poorly and this was a particular problem with the friable British coals. Hypotheses about maximizing the salable products were primitive at best. Even though the Rosin-Rammler equation was the first real clue about coal breakage, the exponential in the equation was difficult to handle, so for a time it went nowhere.
In 1936, Bennett, in collaboration with R. L. Brown (a mathematician from Oxford University), examined size analyses of run-of-mine coals from many British mines. These analyses were well fitted by a revised Rosin-Rammler equation: x = 100. exp(-(x/a)n), where a is the size at which (100/e) = 36.8% of particles are retained (Brown 1941). This equation, which became known as the Rosin-Rammler-Bennett (R-R-B) equation, opened the door to relating changes in parameters in an equation to changes in coal types and breakage conditions.
In 1956, Tom Callcott and Simon Broadbent took this idea further when they proposed a model in which a breakage function based on the R-R-B equation defined the coal type and the probabilities of breakage and discharge defined the breakage conditions. To simplify calculations, they wrote the model in matrix form, and it gave insight into how particles were broken into size fractions (Broadbent and Callcott 1956). This model proved to be suitable as a basic engineering model of size-reduction machines, and from it has come some of the comprehensive models of machines that are now so important in optimizing size-reduction processes.
Similar models were developed in the 1960s in other laboratories. The earlier models are discussed in Crushing and Grinding: A Bibliography (Bickle 1958).
Although the scientific techniques of observation, deduction, and experiment to improve size-reduction processes were in widespread use, there had been few if any case studies until the work of Oliver Evans. Born in Delaware in 1755, Evans became one of America’s great pioneering inventors. Delaware was a good place for him to spend his formative years because of its proximity to Pennsylvania and Virginia, where there was much intellectual and industrial activity associated with the growing population. His first invention in 1777 was a machine to produce teeth for wool-combing cards and came about because he disliked making them by hand (Lienhard 1988-1997). In 1781, he joined two of his brothers to buy a flour mill and soon discovered its deficiencies. Flour milling at the time involved taking batches of cereal grains through a series of processes and holding some of the products in piles for up to several hours before further processing. It was slow, cumbersome, labor-intensive, and rather unhygienic because stockpiles of partially processed flour attracted insects.
In 1782, Evans devised a system to change flour milling to a fast automatic process in which the stockpiles were eliminated. The flour mill he built on Red Clay Creek near Newport, Delaware, used a system of shafts, gears, and belts to drive the machinery in the plant from a water wheel, along with elevators, conveyors, and gravity pipes to move the partially processed flour from one machine to the next. Hoppers were used during sifting and for drying the grain. This system was very successful, and the book in which he described it passed through 14 editions (Evans 1785, 1805).
Yet flour milling does not seem to have been his main interest. Starting in 1784, he patented steam engines—notably a high-pressure engine—which were used in locomotives and factories. These engines made enormous contributions to America’s rapid industrial growth in the early 19th century. His book on steam engines, which contained a “description of a steam engine on new principles, rendering it much more powerful, more simple, less expensive, and requiring much less fuel than an engine on the old construction,” was a fine scientific treatise (Evans 1805).