Gunpowder and Geometry Read online

  Much had come out of the ballistics work that was quantitative, robust and useful: laws for muzzle speed in relation to shot size, powder charge and gun length; a law for the ranges of shot fired at 45 degrees of elevation; a law for air resistance in relation to size and speed for three different shapes of projectile. All of these had physical models attached that did at least something to explain or justify them, though they were not the most convincing or the most interesting aspect of the work. There were interesting side issues such as how long a cannon ball would take to attain a given height and how far it would go horizontally in a given time; or how high it would go if you fired it straight up. But putting it all together eluded him; the crown jewels of how air resistance operated on a projectile whose speed was changing, and how as a result the range of shot depended on the speed at which they were fired, escaped his grasp.

  Hutton had missed his aim, and his work on ballistics had not quite achieved the key results that would have made his scientific name for ever. It is very hard indeed to say how much his work contributed to military practice. Certainly he had found some definite results about the speed of balls and how far they would go in different circumstances; perhaps the most interesting and useful item was his calculations of the size of charge that would achieve the maximum velocity from a given gun. Certainly he taught all he had found out to the cadets under his charge. He summarised his results in exercises that he included in his textbooks, and in tables that could in principle have been of use to gunners. The work was much praised: ‘Military tactics have been much benefited by his important labours’, one obituarist would say, and some of the textbooks of gunnery of the next generation gave his work and his results a lot of space. There seems at least an indirect connection between Hutton’s demonstration that longer barrels added little to muzzle velocity and the enthusiastic introduction of short-nosed ‘carronades’ in this period; and in the fullness of time his opinion about reducing windage would become the accepted one.

  Perhaps more important, if less direct, was the impact of Hutton’s ethos of experimentation and military improvement on the cadets and staff with whom he was in contact. There passed under his teaching Henry Shrapnel and William Congreve, who would become the inventors of the shrapnel shell and the Congreve rocket. New types of rifle were tested at Woolwich; experimental work on the strength of timber was carried out. Chemical experiments took place in the Royal Laboratory, with outcomes for the quality and consistency of gunpowder and the methods by which it was tested, a subject to which Hutton himself had contributed with his new design for an eprouvette for the purpose. The whole arsenal site was a semi-public place that keen teachers and students visited to see experiments in progress; and indeed there were those who reckoned it an important site for the now-gathering reform of British science: dynamic, innovative and daring, and away from the eye of the Royal Society.

  By the time Hutton’s work on ballistics was finished war was once again threatening. An unhappy consequence was that it became impossible to publish the sensitive military information his work contained. Summaries appeared in his textbooks, but the masses of data and the full reports, drafted and redrafted, remained for years in manuscript form, circulated within Woolwich and the Board of Ordnance; they were not printed in full until the war was nearly over.

  Just ten years had been allowed to Britain and its armed forces before they were once again plunged into destructive war. The French invasion of the Netherlands, and the execution of the French king Louis XVI in early 1793, brought Britain into war against revolutionary France, and for most of the next twenty-two years Britain was at war with her neighbour in some combination of alliance with or against other continental nations and (from 1812) America. On the one hand the fear of invasion (scares in 1796 and again in 1803–5; two actual landings in 1797 and 1798) and a shared Francophobia made it a stirring, patriotic time that – some say – helped forge a nation. On the other, the spectacle of the French Revolution and of the military violence that followed were persistent sources of disorder both political and physical, and of deeply felt division and unease.

  By 1793, too, nine years of economy, reorganisation and reform under Pitt the Younger had brought the national debt under control but left the Army in no condition to fight. The armed forces and their administration were obliged to expand massively during the early years of the war, and a whole breed of career administrator sprang up to keep the system operating. A massive war, a massive war effort; one man in four of those of military age bore arms either as a regular or an auxiliary, through enlistment or balloting (the country stopped short of actual conscription). Professional families flooded the officer class; the business and trade classes the lower ranks. And in some campaigns 30 or even 40 per cent of those serving died. Britain lost perhaps 300,000 men in the Napoleonic wars.

  The experience of the Royal Artillery in the Napoleonic period is encapsulated in the award in 1833, after it was all over, of the motto ‘everywhere’ (ubique) to the regiment. Suddenly William Congreve was not just an experimenter and director of the repository; he was commander of the artillery in Flanders in 1793–4. The shrapnel shell and the Congreve rocket were no longer exciting toys but devastating new weapons. The boys who had carefully aimed shots into pendulums and over the Thames with Hutton fired ten thousand rounds in a day from their seventy-eight guns at Waterloo.

  Like the Army, the artillery regiment was expanded; this was a war that made huge use of artillery, the great opponent Napoleon being in origin an artillery officer of supreme tactical skill. A new horse artillery was created, followed by new battalions of regular artillery every few years, taking a strength of four battalions of artillery at the outbreak of the war up to ten in 1808; from four thousand men to twenty-seven. Much the same was true of the Royal Engineers, who served with extraordinary versatility in work ranging from sieges to river and road communications and river crossings, surveying and reconnaissance. The training provided by the Royal Military Academy to gunners and engineers was suddenly – once again – desperately important.

  And once again it was simply impossible to provide that training to enough cadets fast enough as the demand for officers grew. The number of cadets increased, reaching officially two hundred at the peak: most of them were at Woolwich, though from 1803 some were based at Great Marlow. There were complaints – once again – about overcrowding, about poor sanitation. Scarlet fever broke out. Hutton in 1795 wrote that the lecture rooms and barracks at Woolwich were ‘so small as to be insufficient for the purposes of the institution’; he also reckoned that the salaries of the staff were inadequate to their labours, a situation to which inflation after the American war had contributed, as had a ban on supplementing one’s income by taking private pupils. In 1797 the staff wrote jointly to the Board of Ordnance to ask rather desperately for a pay rise, citing wartime price inflation and their wish ‘to support ourselves and families with … credit and decency’; and quite surprisingly they got one.

  They were indeed teaching at a furious rate. A deal was signed that brought the cadets of the East India Company into the Woolwich system, swelling numbers in the regular classes. Furthermore, the Irish corps of artillery merged with the British in 1801 and came to Woolwich to acquire theoretical knowledge, attending the professors at their houses on a total of four days a week for three hours each day. ‘One guinea for each lesson to three pupils, or any less number, and seven shillings per lesson for every pupil more than three who may attend for instruction.’ Hutton also undertook to lecture on natural philosophy from May 1799, on top of his mathematics teaching.

  In 1803 the summer vacation was simply cancelled ‘in consequence of a most serious want of officers for the Royal Regiment of Artillery’; by the end of that year seventy-seven of the hundred cadets in the upper academy had received commissions. Formal exams were once again totally abandoned, and a sense arose anew among the boys that you were likely to be commissioned no matter what you did. ‘Disgraceful i
rregularities’ are heard of in the records, ‘unmilitary and riotous behaviour’. Cadets had to be forbidden to dine at the officers’ mess, following an incident in which ‘Mr. C— … was so drunk that he knew not what he did’. Other misdeeds ranged from insubordination and cheating to shooting a local woman with a fowling piece, and in December 1795 the Master-General of the Board of Ordnance remarked, appalled, that ‘this Institution being intended for Gentlemen only, the Regulations have not provided punishments for an offence, which it was supposed no gentleman could commit’.

  The curriculum was abridged in practice if not in theory, and eventually, in 1803, two new mathematical assistants were added to the staff to cope with the increased numbers, ‘it appearing to the Master-General that the Professors and Masters of the Royal Military Academy bear no proportion to the pupils under their instruction’. In 1806 three more assistants were added, and by then the system involved no fewer than six numbered academies, each subdivided into graded classes. It was becoming clear that the management of students’ progression from one class to another was not working properly: too complex, too burdensome. Hutton’s role in charge of at least the mathematical side of curriculum and organisation was the pedagogic equivalent of high command, and it stretched his skills. In the long run it would be said that he let things ossify under his rule, with the students merely cramming rather than being properly taught. But still the demand for officers pressed, and there was little he or anyone else could do.

  For all the chaos, it seems quite clear – as it probably was to most of those involved – that the teaching at the Royal Military Academy was of real utility to the war effort and the country. Until the Royal Military College was founded at Great Marlow there was no other major source of officers with technical training, and the training was far in advance of anything a regular Army officer could be expected to have. It was indeed a comprehensive scientific education, producing officers who knew their trade when commissioned and could function at once, without needing more experienced officers to help and guide them. Graduates of the Royal Military Academy successfully did work ranging across surveying and reconnaissance, liaison and engineering support, translation and the full range of ADC and staff-officer duties; made themselves invaluable in theatres of war from India to the Caribbean.

  The chaos of war was accompanied by changes to Hutton’s own household. By autumn 1790 his daughters Charlotte and Eleanor had come home from France (perhaps in some haste; we don’t know exactly when), rejoining the older girls Isabella and Camilla. Charlotte was a particularly welcome addition to the Cube House; she had become a young woman of charming temper and remarkable intellectual gifts. Early to rise, she helped to manage the house and the servants and was a ready conversationalist at Hutton’s often-visited table. Witty, cheerful, charming: but more, she alone of Hutton’s children showed signs of inheriting his talent for mathematics.

  Like her mother before her, Charlotte assisted Hutton with calculations. She made a new expanded table of square roots (to twelve places of decimals) for inclusion in one of the many re-editions of his works. She made drawings and maps for her father, and took over the arranging of his voluminous library. There is little doubt she was Hutton’s favourite, and in the midst of war the Cube House was for a while a lively and a happy place.

  One visitor had a more transformative effect than most. It had to happen sooner or later, and it was Camilla, it seems, who was the first of Hutton’s daughters to be seriously courted. Charles Henry Vignoles was the fourth child of an Army officer, and a junior officer himself. Quite how he became acquainted with the Hutton family we don’t know, but by October 1790 he was finding himself tongue-tied in the presence of his beloved’s father and resorted to a letter, in which he set out with perhaps excessive frankness his own personal financial situation: he was in debt to his friends for the price of his adjutancy. Without directly asking, he made Hutton’s consent to the match conditional upon Hutton’s settling the debt himself. With a possibly surprising magnanimity Hutton did consent, and the pair were married a week before Christmas.

  Soon after, Vignoles was posted to Ireland, and Hutton was informed by letter of the birth of his grandson Charles Blacker Vignoles in County Wexford in 1793. But then Vignoles’s regiment was ordered to the West Indies. The struggle with France for control of the Caribbean islands had made the region an important theatre of war; it was also a most notoriously unhealthy station, with a deserved reputation for yellow fever. Camilla nevertheless determined to accompany her husband, taking baby Charles with them. Hutton was not happy, and there seems to have been something of a row about the matter, but there was nothing he could do. The couple embarked at Cork in November, bound for a combined operation against the French islands of Martinique, St Louis and Guadeloupe, to be based in Barbados.

  Isabella and Camilla Hutton.

  9

  Utility and Fame

  The twenty-seventh of September 1794. The church of St Luke, Charlton: Charles Hutton’s parish church.

  Bitter wind; falling leaves. The long view north: past the Warren, across the river and over the levels. Tears dim the distance.

  A new-made grave; earth cast into it. We commit her body to the ground; earth to earth, ashes to ashes, dust to dust; in sure and certain hope of the resurrection to eternal life, through our Lord Jesus Christ.

  In his final decade at Woolwich Charles Hutton would know both triumph and, repeatedly, tragedy. By the 1790s, he was famous. Two brief biographies appeared in print. You could refer to ‘Dr Hutton’ and – as long as the context was mathematics – you would be understood. Newspapers and reviewers were calling him ‘distinguished’, ‘learned’, even ‘veteran’. The Ladies’ Diary in 1797 included an acrostic puzzle whose answer was ‘Hutton’, providing an opportunity for those who knew he was the editor – and a few who didn’t – to utter their homage:

  … a mathematic sage,

  To him what praise belongs!

  Whose works improve and grace the age

  And shine in Pindar’s songs.

  …

  Whose fame doth reach the arched skies,

  Whose works we all admire.

  …

  The work of his own hand,

  As long as learning is belov’d,

  Will unimpaired stand.

  There was a sense at least in this community that all his efforts to recover from the disaster of 1784 had borne fruit, and that his status was as high or nearly as high as it had been before. The Tracts, the long-running textbooks and the widely used tables had made his as close to a household name as a mathematician could get.

  A measure of his fame was a growing tendency to consult him on mathematical matters outside his areas of real expertise. On several occasions from the 1790s onwards engineers, architects and public bodies sought Hutton’s opinion about bridge-building projects: a stone bridge at Sunderland; two iron bridges in Wales at Conway and Bangor; repeated proposals for a new London bridge. Hutton was neither engineer nor architect and had never designed or built a bridge in his life, yet he evidently had enough of what would now be called name recognition for his opinions, impressionistic as they sometimes were, to be worth something. He had become the man non-specialists most readily thought of when they thought of mathematics.

  Hutton always said he had aimed not at fame for its own sake but at public utility, and as the years passed he protested more and more strongly that his only desire was to be of use to his country. There were those who believed him, but it is difficult not to detect, in some of his activities, at least the supplementary desire to build monuments to Charles Hutton. Nowhere is this more true than in the series of massive publication projects that would appear in the decade after 1795. After the 1787 Conics, in fact, Hutton never again published a book that consisted substantially of new material; every later project was based mainly on editing or reworking of one kind or another, although some large chunks of original research were, admittedly, included along
the way.

  Even before the Conics was done, on 20 May 1786 Hutton signed an agreement with Joseph Johnson, publisher, to write ‘a Mathematical & Philosophical Dictionary’. It was to be substantial – about eight hundred pages were anticipated – and Hutton was to be paid handsomely: around four hundred guineas depending on the exact length of the finished book (the sum was about twice his annual salary from Woolwich, although by this time that salary was noticeably low). Both parties apparently thought the book would be complete within four or five years, and Johnson would pay Hutton quarterly, twenty-five pounds each time: the balance to be made up after publication. Hutton undertook to supply drawings of the pictures and diagrams needed; Johnson agreed to supply Hutton with any and all books he needed to consult. On the whole it was a handsome and an optimistic document, indicating that both men thought a comprehensive dictionary of mathematics could be completed in a reasonable time and would sell well enough to be highly lucrative.

  Beyond that, it is not perfectly clear what Hutton intended to achieve with his mathematical dictionary. The agreement named the Encyclopaedia Britannica, recently published at Edinburgh, as a standard of reference as far as size was concerned, and though it was not explicitly laid down as a model, there was surely something of that intention. Hutton’s fondness for French culture and his admiration, expressed in print, for Diderot’s Encyclopédie suggests he was looking across the Channel for inspiration for his own project, but the word ‘Encyclopaedia’ was not directly applied to the mathematical dictionary at this stage. Hutton would eventually, in his preface to the published Dictionary, point to the existence of a number of dictionaries on various subjects recently published and the absence among them of one devoted to mathematics or natural and experimental philosophy; he would rate the Encyclopédie ‘stupendous’ but suggest that it, as well as the Britannica and Chambers’ Cyclopaedia, were alike deficient when it came to the details of particular sciences. A mathematical encyclopedia, then, rather than a mere dictionary, was perhaps in Hutton’s mind.