View from the Pennines: Euler Goes Ballistic

It is easy to construct theories about why something happens, and even to start to believe them. My early visits to the Pennine reservoirs convinced me that an interesting nineteenth century phenomenon must have been the shift from the church to engineering as a destination of choice for impoverished yet well-born younger sons. This theory was based on two observations. The obsessive levels of detail in small bridges crossing isolated catchments (conduits) and linking one windswept piece of moorland to another equally windswept and equally bereft of human occupancy; and the obvious training in classical mythology which led water engineers to construct vertical cylindrical outlet towers which, when operating, were surely intended to mimic the whirlpools of Charybdis. What middle-class-ocentric tosh! The younger sons probably went to the colonies where they could live appropriately on the backs of others without troubling their brains, and the water engineers were a peripatetic band of experts, who learned their trade through apprenticeship and may well have started as stone-masons or mill-wrights (see [5] but don't believe everything you read!). So, don't accept anything just because it sounds nice { in theory, theory works in practice, but in practice, practice can be a lot more complicated (to paraphrase a quote I cannot place). Galileo was responsible for another nice theoretical idea which is still current: the parabolic projectile trajectory. This is so neat that it is taught at both school and undergraduate level as a triumph of the Newtonian revolution, giving practical advice on how to aim a cannon or catch a cricket ball through a magical mathematical formula. What starry-eyed tosh! Galileo's intuition may have come from celestial observations where wind resistance is not an issue, but whether ring cannon or hitting cricket balls this air resistance and its e ects cannot be ignored. However, the beauty and simplicity of the mathematics has meant that even though an experienced bombardier would have known how inaccurate they were, tables for cannon ranges based