A Ballistic Paradox

Extract

In the first war, not only did computers not exist, but the labour of calculating trajectories by a step by step process was regarded as quite prohibitive, and approximate formulae were the only resource. In the end these proved surprisingly accurate. The methods inevitably worked on approximations valid in the first instance for small values of a parameter, ø, say. But it was found possible to find formulae correct to the fourth or fifth order of ø, and as a result there emerged the principle that “In Ballistics 25° can be a ‘small’ angle”; results for 25° could be correct to 0·1%.