Gunpowder and Geometry

by Benjamin Wardhaugh

  On one level, all this looked like another merely personal attack. But, as Hutton said, there was no evident motivation for it, and he speculated that it was about the snobbery of Cambridge mathematicians (‘a general propensity … to affect to despise, & endeavour to disparage, whatever comes not from their own society’). In fact, he most likely knew perfectly well that it was about deeper issues: issues which would become increasingly visible over the next decade, and increasingly worrying to Charles Hutton.

  What it was about was the right way of doing mathematics, and the value of the distinctive British methods that had developed over the last fifty years or more. That was the mathematical culture to which Hutton had given his life: steady, amateurish, proceeding in the pages of The Ladies’ Diary and The Gentleman’s Diary to make small incremental additions to mathematical knowledge, in a framework laid down in large part by Isaac Newton back in the seventeenth century: celebratory of Euclidean geometry, which was a key part of British grammar school and university education, and reliant wherever possible on geometrical intuition, particularly in handling subjects like mechanics or astronomy.

  ‘A certain degree of mathematical science, and indeed no inconsiderable degree, is perhaps more widely diffused in England than in any other country in the world,’ wrote John Playfair in 1808, pointing to The Ladies’ Diary and the other philomath periodicals as evidence. As Hutton himself had put it in 1775, ‘By means of such problems, and little essays, considerable additions are made to the stock of mathematical learning in general, as well as to the particular knowledge of individuals.’ Such additions were not to be despised, and by its richness in them British mathematics was successful in its own terms. And it produced material such as Hutton’s ballistics and his Course that were successful as exports, taken seriously as research material or as pedagogy in Europe, America, and the British colonies in India. It produced mathematicians perfectly capable of working and teaching both at home and overseas, and it supported British engineers and engineering through a period of unprecedented change and innovation in the later eighteenth century. Moreover it produced men like Charles Hutton himself, taken seriously as author, colleague and correspondent by mathematicians across the world.

  France, and the European continent generally, had gone a different way. There, the learned academies supported a small number of elite mathematicians to carry out intensive research. They had no real counterpart in Britain: certainly not in the relaxed figures who held mathematical teaching posts or professorships in the British universities. Since the 1740s these well-funded, state-employed mathematicians at Paris, St Petersburg and elsewhere had been pursuing a special line of thought. Called analysis or infinitesimal analysis, its effect was to remake the calculus without the aid of geometrical or dynamical intuition. From the outside it initially looked like a highly abstract game with little point to it: playing on the edge of philosophical impossibility with the infinitely small and how it should rightly be studied. The sort of thing Fellows of the Paris Academy or favourites of the Tsar were free to indulge, but of little real interest to the working, practical mathematician.

  But by the end of the century the outcome was that on the European continent the study of force and motion – the phenomena that the calculus was ultimately about – had been placed on quite a new footing. And mathematicians there were increasingly doing things the British could not match in applied fields such as astronomy. Britons like Hutton kept an eye on all this; he had continental mathematics books in his personal library by the yard, and he subscribed to all the main continental scientific journals: as did others, and as did institutions like the Royal Society. His Dictionary was full of admiration for, and full of references to, new continental work; so were his Tracts. Other Britons followed him in this; some published translations of continental works, others tried actually using the new continental notation and conceptual language in their own writing. Hutton felt unable to go that far; perhaps constrained by his role and background as a teacher, and unwilling to create unnecessary difficulties for his readers.

  For a vocal minority among the coming generation of British mathematicians – and Robert Woodhouse was one of them – all this wasn’t enough. They cultivated a sense of crisis, of outrage, of national shame at what France was doing and Britain wasn’t. They wanted change, fast: thoroughgoing reform of research, publishing and teaching. When Laplace published his Traité de mécanique céleste in 1799, showing that France was now leading the way in the very areas of mathematical astronomy where the great Briton Newton had done so much, they reacted with something close to panic.

  During the last half century, [in] the mathematical sciences … scarcely any improvement has been made in them in England.

  A mathematical production, above the level of school-practitioners, finds little encouragement in this country; to enable a book to sell, it must be trifling; it must reduce all rules to mere mechanical operations; it must in fact be suited to the taste of solvers of problems, and not to investigators: – we have more of the former class, and fewer of the latter, than any empire in Europe.

  Even Hutton’s friend and admirer John Playfair, in a much-quoted review of Laplace, joined in the criticism of British mathematics. Despite the many good things he had to say about the thriving state of British mathematical culture, Playfair pointed out that there were only a handful of Englishmen who could read recent French mathematics with understanding, and he saw that as self-evidently a bad thing:

  A man may be perfectly acquainted with every thing on mathematical learning that has been written in this country, and may yet find himself stopped at the first page of the works of Euler or D’Alembert … from want of knowing the principles and the methods which they take for granted … If we come to works of still greater difficulty, such as the Mécanique Céleste, we will venture to say, that the number of those in this island, who can read that work with any tolerable facility is small indeed.

  Over the next few years some of the critics of British mathematics were to form the short-lived Analytical Society at Cambridge, to press for the reform of mathematical teaching there. They published a translation of Lacroix’s French calculus textbook and other material, and promoted the story that British mathematics was in crisis.

  On one level it was clear that much of their rhetoric was exaggerated and self-serving; and the sudden reforms they called for didn’t happen, were in no particular danger of happening. But at another level it was clear they had a point: that British mathematics was now being transformed – albeit slowly – by its contact with continental mathematics. That process acquired new momentum after the peace of 1815 made communication across the Channel a great deal easier. New research agendas arrived to stay; continental mathematics appeared in more and more English translations and summaries, and received more and more British responses, for instance in the pages of the Philosophical Transactions. And continental notation and concepts became increasingly visible even in native British mathematical publications.

  These were changes in which Hutton, in his seventies, was not likely to participate. He had done more than anyone living to define, shape and nurture the British mathematical culture that was now under attack. In the short term Hutton could try to limit the damage. He could write letters of protest to editors when his works were criticised, he could publish rebuttals and try to avoid sounding merely peevish when he did so. He could brief Olinthus Gregory to attack in his name – though Gregory himself was not wholly unsympathetic to continental-style mathematics. But Hutton could not, either by private remonstrance or public rebuttal, alter the fact that mathematics was changing, and that it now seemed he would live to see much of what he had achieved become out of date, even irrelevant.

  Of controversy, before and during his retirement, Hutton thus had more than enough from his colleagues. Unfortunately his family managed to provide a large dose too. Charles Blacker Vignoles, the young man plucked from Guadeloupe and welcomed into Hutton’s household i
n 1795, was now approaching his twenties. Hutton had provided for him, had overseen his education. There was a period at a school in Kent; there was probably private tuition from Hutton himself. Vignoles acquired a grounding in mathematics, classics and modern languages. For a long while he was a lively and much-liked member of the household. He showed talents for music and drawing; he wrote verse, plays and music; he sang and recited. His (step-)grandmother and his aunt Isabella doted on him, and in 1806 a cousin remarked that he seemed such a boy as might be expected to distinguish himself.

  But things were not altogether so happy. Vignoles perhaps tended to be somewhat too carefree and, as he grew a little older, ‘too fond of a dash, a show-off’, as he himself put it. He had the run of his grandfather’s library, but used it for pleasure rather than instruction and Hutton, pleased to see the boy reading at all, apparently neglected to regulate what he read. As an adult, Vignoles would recall working through logarithmic and other tables for Hutton’s published works; this must mean checking proof-sheets or perhaps doing recalculations and enlargements of matter for the later editions of Hutton’s Tables, or the tables in his Tracts or Course. Typical of the work members of Hutton’s household had been doing since the 1780s, but hardly the most stimulating activity for the young man.

  Hutton, for his part, was not entirely able to forget the expense or the disruption young Vignoles had brought with him. Several manuscripts show Hutton attempting to document the sums Vignoles had cost him, even to recover some of them from the government through a regulation providing recompense for items lost when officers died on active service. He wrote around distant acquaintances in pursuit of rumours about grants of land made to the Vignoles family in the Isle of Man, France, North America.

  Reading between the lines of Vignoles’s letters, Hutton also seems to have demanded too much of the boy, to have pinned on him too many of his hopes. Hutton’s own son had had a distinguished career in the Royal Artillery but had not made a splash intellectually. Two daughters were dead; one – Eleanor – was married, and we hear little or nothing of her and her children in Hutton’s letters, while faithful Isabella was Hutton’s devoted amanuensis and companion but – perhaps in part for that very reason – seems to have developed few independent intellectual interests. Charles Blacker Vignoles represented Hutton’s natural hope for a certain kind of intellectual legacy.

  The law, it was decided, would be his career; whether he had any say in the matter is not clear. He was placed under articles to a proctor in Doctor’s Commons: a sort of legal apprenticeship. With peace looming, this did indeed promise a more secure future than the perhaps more natural choice of the Army, where Vignoles had a family tradition and Hutton many personal connections. And the Inns of Court, home to generations of city lawyers, were just around the corner from Bedford Row. But Vignoles did not thrive. By the age of twenty he appears to have been quite desperate for escape of every kind. The situation had become an explosive one, and in the summer of 1813 it duly exploded.

  There was, Vignoles later hinted, an incident with a girl: or rather two girls. The details (naturally) are lost, but it seems that what he himself called his ‘extravagance and imprudence’ coupled with these ‘boyish inclinations’ to elicit a ‘thunderbolt’ from Charles Hutton. Vignoles, for his part, insisted on abandoning the law, breaking his articles and starting again in a military career.

  The outcome was that Vignoles left Bedford Row in about June 1813. He went to lodge with Hutton’s colleague Thomas Leybourn, mathematics master at the new Royal Military College at Sandhurst. He wasn’t a cadet; strictly speaking he still held a half-pay commission in his father’s regiment, awarded to him in infancy as a sort of compensation for his parents’ deaths. The intention was that through private tuition from Leybourn and some contact with the cadets Vignoles would acquire enough learning and demonstrate enough willingness to persuade some officer to admit him to serve in his regiment. The Leybourns were kind, the Huttons continued to provide financial support, and Vignoles had achieved the escape he seems to have craved. Hutton wasn’t altogether happy about the situation; in his seventies, he had become somewhat querulous about money, and he resented the sums he had already spent on Vignoles and the new waste involved in leaving his legal training.

  There followed a not unreasonable series of military adventures for Charles Blacker Vignoles. Commissioned in 1814, he was taken prisoner at the disastrous British attack on Bergen-op-Zoom and returned to England on parole. Having been exchanged and ordered to Quebec, he was shipwrecked (in the horrible old Leopard) at the mouth of the St Lawrence river. He was with the army of occupation in Paris after Waterloo; after repeated requests to be allowed to use his mathematical and drawing skills as a staff engineer – all refused – he was eventually made aide-de-camp to General Sir Thomas Brisbane at Valenciennes.

  The family watched with some consternation. Margaret was desperately worried for Vignoles, whom she thought of unhesitatingly as her grandson, and a cousin wrote with tears in his eyes of his hope of seeing him again. But as well as the obvious dangers there was on Vignoles’s part an equally obvious enjoyment of the new life. He left a manuscript tragedy behind him at Sandhurst, and an unfinished comedy; he wrote an eight-canto Sylphiad indebted to Alexander Pope and made quite a hit at regimental theatricals in Quebec, starring in no fewer than four female parts including Julia in The Rivals. Fond of ‘balls, routs, concerts, French and English plays’, he calls irresistibly to mind some of the more unsteady young men in Jane Austen (Henry Crawford, perhaps?).

  But. But. Like a thousand other lieutenants he was put on half pay in the reductions after Waterloo. The blow struck him personally in January 1816. His military career had lasted just two years, and he now despaired of its future. He had been a secretary to the Duke of Kent for a time, and both he and the commander in chief (Frederick, Duke of York) made vague promises to him. But they had many claims on their interest, and there simply wasn’t much work to go around compared with the glory days of sweeping Boney out of Spain and France. Vignoles chafed, he raged, he regretted, but there was little he, or anyone, could do.

  All might yet have ended in the reconciliation that most of the family wished for, but the years 1815–16 saw not comedy for Hutton but both family tragedy and further professional reversals.

  Henry’s son Charles Henry, born in 1800, moved to Woolwich in early 1814 to study at the military academy where his grandfather had taught for so long. Conceivably the example of cousin Charles Vignoles contributed something to the decision to pursue a military career at an unpromising moment. Briefly he appeared to be thriving there. In August he wrote home proudly of his passage from one class to the next and his hopes of soon being a corporal. He was studying under John Bonnycastle and Olinthus Gregory, old friends of his father and men who surely showed him some favour on that account.

  But then it all went wrong. From one month to the next he sickened of the life at the Royal Military Academy, took ‘quite a hatred to Woolwich, and the life of a soldier’. He sickened physically too. Consumption is spoken of in some documents, but precisely what the matter was is nowhere recorded. A bad cough, a loss of weight.

  In October he was moved to Bedford Row, his life despaired of. Hutton spared no expense on his comfort or his treatment. He called in two expensive doctors; they said that nothing could save the boy, but he nevertheless insisted they attend every day until the end.

  Charles Henry Hutton lingered for five months. He died on 13 February 1815. He was buried in the plot at Charlton where lay Charlotte, the aunt he had never known.

  Demoralised perhaps by the attacks from Saint, Woodhouse and others and exhausted by the vicissitudes of his family life, Hutton conceived the idea that his creative scientific work was over. Now seventy-seven, he planned to retire to a smaller house, perhaps in the country, for the remainder of his days. As a necessary corollary he set about disposing of his library. ‘I shall have little or no further use for it, and it would pr
event me from chusing another residence, and … it could be of no use to any of my family, after my death.’ (A rather devastating judgement, that, on the intellectual attainments of his children and grandchildren.)

  He had been accumulating books since the 1750s, and the mathematical section of his library was now generally acknowledged to be the best in Britain; it contained over three thousand volumes and included very rare early printed works on algebra and geometry, unique collections of editions of Euclid’s Elements of Geometry and of Newton’s Principia Mathematica among other treasures, and almost certainly the best private collection of continental mathematics books in the United Kingdom: more than 130 volumes from Clairaut, Euler, Lalande, Laplace and many more. He had collected manuscripts from friends and from the sale of their collections; had annotated some of his books and pasted letters from friends and colleagues into others.

  Hutton’s idea was to sell the collection complete to the British Museum, which had a fine library of its own. There were precedents; during his time on Council at the Royal Society, Hutton had seen the Society’s collection of artefacts transferred to the British Museum in an amicable and – at least in intention – a mutually beneficial arrangement.

  Letters came and went; it seemed the Museum had few mathematics books and the trustees would be happy to augment them by taking Hutton’s library. It was agreed to abide by a valuation determined by one representative from each party; the Museum appointed an officer to inventory the books, who reported favourably.

  But one of the trustees of the library, presently away from the capital in Lincolnshire, was Sir Joseph Banks. Fearing he might take offence if not informed of what was going forward, Hutton wrote to Banks, expressing the hope that he would approve of the proposal. No reply. But within a fortnight Banks was back in London, and the deal was off.