Gunpowder and Geometry Read online

  Hutton would have learned at least some of this over the summer, while his new house was being repaired and he was finding his feet after the upheaval of his move from the North. When the boys arrived after the summer recess and the actual teaching began, it may have been something of a relief. The cadets, numbering about fifty, were a well-dressed body of young men with a rather splendid uniform: blue coats trimmed with scarlet and gold; lots of lace, hair neatly queued and powdered.

  They may have looked genteel, but they ranged in age from twelve to about nineteen, and there were predictable problems with their behaviour. Some ingratiated themselves with the masters, sending home for hams, hares, pheasants and other little gifts that might smooth their passage through classes and exams. Others indulged a tendency to riot. Orders and letters from the governor remarked again and again on matters of discipline, expressing futile outrage and lamely prohibiting misdemeanours after they had taken place. Cadets must not ill-use the masters, must not treat them with disrespect or insult them. They must not disrespect their superior officers, nor use indecent or immoral expressions. They must not wilfully destroy fixtures, bedding, furniture, utensils or windows, nor must they force locks or open or spoil the desks of the teachers or other staff. They must not ‘nasty the walls or chimneys’. They must not leap or run over the desks, nor climb out over the walls at night.

  As the crimes escalated, so did the punishments. (‘The first Cadet that is found swimming in the Thames shall be taken out naked and put in the Guard-room.’) We read in mid-century accounts of solitary confinements, bread-and-water diets, imprisonments in a dark room, degradations and a few exemplary expulsions. In the long run, things improved, but outbreaks of quite serious violence remained more frequent than anyone could have wished. The constant presence of a duty officer in the classrooms had little effect. There was continued noise, hallooing, shouting; there was window-smashing, and ‘pelting’ of the masters. A lieutenant lost the use of his middle finger. A cadet spent three years on the sick list after a prank whose details he permanently refused to specify but which he steadfastly described as a piece of ‘fun’.

  Charles Hutton was suddenly a very long way from the genteel sons and daughters of middle-class Newcastle: the grammar school boys and girls taking advanced mathematics lessons; the private pupils paying a few guineas extra for dancing classes and a few more for the course of lectures on astronomy. Yet his orders required him to teach the cadets, and to teach them a demanding curriculum that ranged across pure and applied mathematics. Teach it he would. The theory classes were on Mondays, Wednesdays and Fridays. Professor Pollock – if he bothered to turn up – taught the boys his notions of fortification and artillery for three hours in the morning; in the afternoon Hutton took them for mathematics from three till six.

  Facing about twenty-five of the older or cleverer boys, grouped at least notionally into four graded ‘classes’, he covered Euclid’s Elements of geometry, killing two birds by using algebraic explanations wherever possible. Trigonometry as applied to fortification and measuring, such as finding inaccessible heights and distances, and using logarithms for the calculations if needed. Conic sections (the shapes you get when you slice a cone using a plane). Mechanics with reference to moving heavy bodies (such as pieces of artillery): levers, pulleys, wheels, wedges and screws. The laws of motion with reference, naturally, to projectiles. Calculus – ‘fluxions’, in the Newtonian rather than the Continental style – and whatever uses could be found for it. Much of this would have been familiar stuff from his Newcastle classroom, but the style of teaching still made it an exhausting round.

  As in any other Georgian classroom, the boys were mostly at their desks, called forward one at a time or in small groups. Each boy did some exercises, showed them to the teacher, copied them and the relevant section of the textbook out fair: and repeated that round for the whole three hours. For Hutton it might mean fifteen minutes with one cadet on calculus; fifteen minutes with another on Euclid. Then algebra, then logarithms, then something else. He also gave periodic lectures – virtually the only university-style lecturing still taking place at the Academy – on geography and the use of those favourite pieces of eighteenth-century teaching apparatus the terrestrial and celestial globes: two hours every other Wednesday.

  When they weren’t in the theory classroom, meanwhile, the boys were instructed on the other days of the week in the practical arts of gunnery: loading and firing the artillery pieces, and pointing them in the right direction; exercises in hitting marks. Various other practical matters: transporting burdens by making pontoons, floats or bridges; mortars and their use; trenches and mines: how and where; the composition of gunpowder; the names of the parts of a gun. Casting and weights of artillery pieces and shot. Handling of stores.

  As if that wasn’t enough, from 1778 a separate building was set up as a ‘military repository’. Here the boys were taught the finer points of handling the equipment: mounting and dismounting ordnance, crossing obstacles, and ‘overcoming by resourcefulness difficulties which did not arise in the ordinary routine’.

  As far as dangerous fun for boys went, this was infinitely more attractive than the classroom work, and the cadets were after all in training for a severely practical life as officers in the artillery or in some case the Engineers’ corps. On graduation at about eighteen most of the boys were at once commissioned as second lieutenants in the Royal Artillery regiment.

  This, then, was the real stuff of an artillery officer. Cannon up to ten feet long and weighing up to three tons; iron balls moving at the speed of sound. Howitzers; mortars for lobbing shells high overhead. Roundshot, grapeshot, case-shot; explosive shells. The relentless drill of firing: four men at work, and every action had to be right every time or disaster would follow. Loader puts the charge down the muzzle, in its paper cartridge. Ventsman blocks the vent with his thumb, and spongeman rams the charge home. Ventsman pricks the cartridge, primes it with quickmatch in a tube pushed down the vent. Loader puts the projectile in the muzzle, spongeman rams it up against the charge. Run the gun up, point it at its target: traverse, align, adjust the elevation. Firer touches the vent with his portfire. The blast of several pounds of gunpowder, and an iron ball travels a thousand yards. Check the recoil. Spongeman sponges the barrel clear. Repeat. Furious speeds were possible; with a light gun seven rounds a minute could be achieved in an emergency: nine seconds from one shot to the next.

  In alternate years the summer saw a full-scale attack upon a polygonal front built at Woolwich for the purpose, done ‘with all the form and regularity that is used in a real siege’. Trenches, batteries, mines made by the besieged to blow up the batteries, mines made by the besiegers to make breaches in the walls. Fortunately there was a well-equipped hospital on the site.

  With all this going on, it may be no wonder there was a problem getting the boys to attend to their theoretical studies. Some of them at least itched to get away from the mathematics and the theory, and there were still in Hutton’s day at least some officers of the regiment who thought the whole Academy a waste of space. General Belford wished it disbanded, and in the late 1770s wrote a stinging letter to the Master-General of the Ordnance suggesting that instead ‘a number of fine young fellows [be] appointed as Cadets to every Battalion’, where they might do practical work and see real action.

  He may have had a point. The long series of reforms and adjustments had made the Royal Military Academy an institution whose details were not easy to defend. Admittedly some kinds of knowledge were best acquired in a school-like setting, but why should an artillery officer need to know algebra, geometry, trigonometry?

  But the training was not so much about what you needed to know as about producing a particular kind of man with a particular kind of mind. The Academy, unique and exceptional in some ways, was nevertheless part of a much more general eighteenth-century trend in English education. Mathematics and the sciences enjoyed increasing prestige at the English universities, with Ca
mbridge in particular stuffing its curriculum full of Euclid and Newton to the oft-remarked exclusion of almost anything else. Newtonian mathematics, together with the philosophy of John Locke and the rational theology of such as Samuel Clarke, ‘went hand in hand through our public schools and lectures’, said one contemporary. Cambridge University’s official calendar, too, boasted specifically of the ‘many excellent lectures in mathematics’ delivered in the colleges. John Locke himself had written that mathematics was ‘a way to settle in the Mind an habit of Reasoning closely and in train … In all sorts of Reasoning, every single Argument should be managed as a Mathematical Demonstration.’ It enlarged the mind, instilled intellectual humility, and taught the habit of clarity in one’s ideas.

  It was a similar picture at the so-called Dissenting Academies. These were advanced schools or mini-universities for those whose non-Anglican commitments excluded them from Oxford and Cambridge. By mid-century there were dozens of them, and they enjoyed a fine reputation, often teaching curricula based on mathematics and natural philosophy as well as logic and theology, sometimes with the specific intention of disciplining the mind, teaching logical thought and a reliance on pure reason.

  So the Royal Military Academy was doing nothing very odd by filling its curriculum with more mathematics than any practical consideration demanded. It was doing what its managers and staff conceived as its clear duty: training and moulding young men in desirable mental as well as physical habits. Just as the duties of a gentleman officer required a knowledge of dance and a smattering of French, they required an acquaintance with the results and, more importantly, the methods of Euclid and Newton. It was a situation that suited Charles Hutton; in any debate about whether it was worth teaching boys geometry, algebra and the rest, there was no doubt which side he would take. Over the years he would become ever more committed to the cause of promoting mathematics, its usefulness and its beneficial effects on the mind. Indeed, the status and the national importance of mathematics would exercise him for much of the rest of his life in one forum or another.

  As a teacher, meanwhile, he seems to have succeeded in catching the attention of the boys, and in winning them over to take seriously what he had to impart. His manner was cheerful, friends reported, but deliberate in expression; he himself reckoned gravity a part of his character. His voice was clear and firm, with a slight northern accent that he would keep to the end of his days. His mind (in good Lockean style), they said, was ‘accustomed to communicate its feelings with a sort of mathematical precision’. Hutton was remembered by his former students with respect, affection, even veneration. One cherished a commemorative medal of Hutton’s august profile to the end of his life. It was never Professor Hutton who got pelted in the street.

  If the boys were won round to Hutton fairly rapidly, the staff were a tougher task. Pollock was going from bad to worse. The teaching staff were civilians; so, unlike an officer of the regiment, he couldn’t be court-martialled for disobedience. Reprimand after reprimand had no effect on his attendance or his willingness to deliver the course as the inspector conceived it: just more elaborate, sometimes legalistic excuses. He disputed the rules about where he was supposed to live, and the system by which certain parts of his pay were worked out. He disputed what he was supposed to be teaching and where the boundary lay between Hutton’s subject area and his own.

  There was indeed a long-running question as to whether the curriculum should be determined by the Board of Ordnance (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 o
ther 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.