Gunpowder and Geometry. Benjamin Wardhaugh

(which paid for the Academy) or by the teachers who had to deliver it. And there was a more detailed question about how responsibility for the practical parts of mathematics – surveying and so on – should be divided between the Professor of Fortification and Artillery (Pollock) on the one hand and the Professor of Mathematics (Hutton) on the other. In both respects, sane compromises took some time to arrive at, and Pollock made himself increasingly ridiculous. Early in 1774 the inspector wished the more advanced boys to be shown how to take an angle of elevation with a theodolite or quadrant, and asked Pollock either to do it or to lend the instruments to Hutton. He refused ‘in a very haughty and imperious manner’ and added ‘that the Academy is not a fit place to mention those things’. He took to refusing to allow the inspector into his classroom, standing on a technicality in his written instructions.

      Hutton as Professor of Mathematics also shared a curricular boundary with the Master of Classics, Writing and Arithmetic: William Green, another difficult character. For three days a week, while Hutton and Pollock were teaching the older boys, Green taught elementary mathematics and writing – and possibly some Latin – to the younger and less able. He received a smaller salary than Hutton and Pollock and taught in theory twice as many hours as they did, so he had some reason for ill feeling. And his duties were subject to repeated redefinitions during the 1770s, the teaching of classics being in part suspended at some periods and the teaching of writing theoretically unnecessary since illiterates were not supposed to be admitted as cadets. Harassed and dissatisfied, Green became irregular in his attendance, and eventually his permission to live away from Woolwich was withdrawn. His performance affected Hutton directly, since if Pollock taught the boys badly they would graduate to the upper academy, Hutton’s domain, inadequately prepared.

      In this somewhat chaotic situation, Hutton could have thrown in his lot with the masters: done minimal work, obstructed the inspector and governor in their duty, and hoped to get away with it for as long as he could; although by the early 1770s it was tolerably obvious that dismissal was on the horizon for the erring Pollock. Or he could take the other path.

      It wasn’t a hard choice, and indeed it wasn’t a hard task. In a way the situation was a gift to him. Merely by turning up regularly (and he was a punctual man) and actually delivering the nine hours of instruction he was being paid for each week, Hutton necessarily outperformed Pollock and Green – incidentally making them look worse than they did already. They resented it, but they could hardly stop him. The inspector was won over quickly, and Hutton was rewarded with a growing degree of power and influence that went beyond anything in the written instructions. There began the first of a very long series of organisational changes at the Royal Military Academy that reflected Hutton’s priorities and agenda.

      Early in 1774 an entrance exam was instituted in consultation with the inspector and masters. Pupils should be ‘well grounded in the first four rules of Arithmetic, with a competent knowledge of the Rule of Three’, as well as some Latin grammar. It’s hard not to see Hutton’s hand in a change that would ensure the boys he had to teach weren’t utterly incompetent in his own subject. In theory the curriculum stood still, but there is no doubt Hutton was adjusting it to suit his notions, and by 1775 his Mensuration was a set text.

      And, crucially, by the late 1770s it was at Hutton’s word alone that boys graduated from the lower to the upper academy. For the boys, graduation was a desirable thing in itself: a move from learning basic arithmetic and basic military drill to being taught advanced material by the two professors, introduced to the properly military subjects of artillery and fortification, and allowed to wear the full uniform and sword of the cadet company. Furthermore, promotion within the Royal Artillery and the Engineers’ corps – like the Navy but unlike the Army – was entirely by seniority, which meant that the date of passing one’s exams relative to the other cadets was highly significant, setting to some extent the course of an entire future career. With Hutton’s judgement now vital to the progress of cadets through the Academy, he became in some ways a very important man indeed.

      Meanwhile, in 1777, Professor Pollock was pensioned off with an almost insulting fifty pounds per year. He tried to make one final fuss, but the Board of Ordnance wisely refused to be drawn into any argument about the matter.

      Soon afterwards William Green brought to a head his resistance to what he evidently felt was an alliance of management and Hutton. He disputed Hutton’s academic judgement and demanded that a Mr Mudge, and certain other boys, be moved to the upper academy despite Hutton having failed them. He stated that they were more worthy than some who had been moved up, that they had solved several questions in algebra that members of the upper academy were unable to understand. He spoke of ‘much injustice’ and named several cadets.

      This was a key moment for Hutton at the Academy; if Green’s complaint had been upheld Hutton would have looked absurd and his position would have been scarcely tenable. Perhaps not surprisingly, a board consisting of the governor, the inspector and the new Professor of Fortification and Artillery found ‘that Professor Hutton has done justice’.

      After this vindication there was no doubting that Hutton was the de facto academic head of the Academy. In time the Professor of Mathematics ceased to be called ‘second master’ and became the first. There is no further report of questions about his academic judgement, or of challenges to his right to pass cadets from one class or academy to another. The notion that the teaching of mathematics and mathematical competence were at the heart of the Royal Military Academy had triumphed. Green, perhaps surprisingly, was brought round to accept Hutton, and the two worked together with no more outbursts until the older man retired in 1799.

      Pollock’s departure, replaced by a congenial Frenchman named Landmann, might have marked the commencement of a period of calm for Hutton’s work at Woolwich. But the mid-1770s saw rather more than just a few schoolmasterish tensions come to a head. In December 1773 the Bostonians dumped ten thousand pounds’ worth of tea into their harbour. By April 1775 there was fighting in Massachusetts, and by 1778 the conflict was a global one; France became involved that year and Spain the next, making India, the West Indies and Central America into theatres of war. Hutton and his colleagues, suddenly, were training and approving young men for active, urgent deployment around the world, and their work took on a new character as a projection of British power across the globe.

      Sixteen companies of the Royal Artillery participated in the American War of Independence. When Spain besieged Gibraltar in 1779 it created a particularly acute need; the siege was by its nature an artillerymen’s affair and five companies of the regiment were there from start to end. The Royal Artillery would receive a special message from the King when it was all over.

      In consequence, the war created a sudden need for more graduates from the Royal Military Academy. And in a pattern that would be repeated in later conflicts, the institution coped poorly. Almost at once the shortage of suitable candidates became a matter of official comment, and the Academy came under intense pressure to increase its throughput of young men at almost any cost.

      Public examinations were discontinued, replaced by private examinations in front of the governor, the inspector and the two professors. Boys were examined who had never been formally admitted to the Academy or the cadet company. The intention was naturally to pass as many as possible, but by 1780 it was being remarked that cadets were being hurried through the upper academy too fast and were graduating little qualified to hold commissions. Reports from one examination coyly stated that the cadets understood ‘a little Algebra, and a little Geometry’. But the expertise needed to handle ordnance effectively or even safely could not be created out of nothing just because need pressed. Permission was given for some notionally qualified second lieutenants to stay on at Woolwich for a further year in order to complete their studies.

      Even in these conditions, when cadets were being pushed into and out of the upper academy with the minimum of ceremony or even propriety, the Master-General took time to note that new boys in the upper were on probation to Hutton. They were ‘neither to have their full uniform nor the allowance of one shilling a-day pocket-money until admitted by the Professor of Mathematics’. He was expected ‘to turn them back into the Lower School’ if they displayed