Gunpowder and Geometry Read online

  This was fun rather than savage criticism, but the characters were the ancestors of those in Blake’s later personal mythology, in which the imposition of mathematical laws on the world was the act of a malevolent demiurge and his human aides: Urizen wielding his golden compasses. Ultimately this was a view of mathematics and its relationship to the world that Hutton would find himself pushing against for much of the second half of his career, as he pressed his own belief that mathematics was both a useful and a humane part of intellectual culture, a necessary foundation for the sciences and a vital element of any education worthy of the name.

  As for practical action against Banks, Hutton and his friends toyed with reopening the debate by demanding sight of the will that created the foreign secretaryship in the first place. The threat alarmed some of those close to Banks, but in the end the plan was abandoned. There was some rumour of an attempt to unseat Banks at an annual election. But again nothing, in the event, was done.

  A core ambition was the production of a journal that would announce to the world the seriousness of the new group, thumb its nose at the Royal Society, and of course provide an alternative vehicle of publication for those Fellows who were now unwilling to publish in the Philosophical Transactions, involving as it did the scrutiny of a committee led by Banks.

  Banks’s friend Charles Blagden – now secretary of the Royal Society – was keeping an eye on the Friday Club and its plans. He quizzed Maskelyne, who provided what seems to have been equivocal or contradictory information. In October 1785 Blagden reported that Hutton was busying himself about London soliciting and collecting material for the ‘secession transactions’, of which he – who else? – would be the editor. There was even a report in one of the newspapers: the ‘dissatisfied members’ who had seceded from the Royal Society intended ‘to publish their philosophical writings in half-yearly volumes, somewhat in the manner of the present philosophical transactions; by which means the public will still be favoured with the labours of those truly philosophical and scientific geniuses’. Hutton kept a copy of the clipping and probably endorsed what it had said, if indeed it was not he who had briefed the press himself.

  It all sounded awfully promising, but it came to nothing. Not one issue of the promised secession transactions ever appeared in print, and there is today no evidence even of what papers or promises of papers Hutton succeeded in collecting for it: if indeed he collected any. The mathematical club meeting on Fridays, meanwhile, carried on until at least 1802, with Hutton, Horsley, Maskelyne, and others including astronomer William Herschel and mathematicians William Frend and Francis Maseres meeting fortnightly during the London season for dinner and conversation. But we hear no more of its ambitions to rival the Royal Society or to produce a journal of its own, and it seems quite clear that it morphed quietly into an unpretentious dining club involving a fairly small circle of friends.

  The group that had threatened in all seriousness to supplant the Royal Society and its journal had fizzled out quickly and unimpressively. One factor was that small incremental advances in mathematics and its applications already had perfectly good forums in the philomath journals, including The Ladies’ Diary, edited by Hutton, and The Gentleman’s Diary, edited by a man whom Hutton had recommended for the post. The launch of another publication carrying broadly similar material and edited once again by Hutton could hardly have impressed the world and may have failed to impress the London publishers. The Ladies’ Diary, indeed, was burgeoning at this time, and it’s perhaps no coincidence that during the same few years that the ‘secession transactions’ missed fire Hutton launched – at his own expense – a Diary Companion, ‘being a supplement to the Ladies’ Diary’.

  The Companion was like a Ladies’ Diary without the diary – without the almanac that took up the first twenty-four pages. For the rest, the contents were of almost exactly the same kind: riddles, rebuses and ‘charades’ in verse, mathematical problems and their solutions in prose. The Companion carried both supplementary solutions to problems from the main Diary, and a separate series of problems and solutions of its own. Perhaps the only notable difference was that, in the somewhat more intimate space of the Companion, Hutton did not keep up the pretence of editorial anonymity that still reigned in the Diary proper – and he and his contributors were perhaps even less restrained about praising and promoting Hutton’s books at every opportunity. Even the elusive Margaret Ord made a couple of appearances as author of verses in the Companion.

  The Companion ran until 1806. It sold well; Hutton was left with just a handful of copies of each issue on his hands, and it seems to have satisfied readers. A few wrote in with their suggestions for its management, which on the whole seem to have amounted to more mathematics and more solutions to each problem. From an initial thirty-two pages it grew to forty-eight.

  If Hutton’s own impulse to edit a new periodical was absorbed by the Diary Companion, at least to some degree, there was still the question of where actual scientific papers from his pen could go. By 1785 he had amassed nine, and the backlog had attained such a size that he took the perhaps obvious course of simply issuing the whole lot as a volume. Tracts, Mathematical and Philosophical appeared in 1786, at a time when he still had some thought of making a regular series of ‘secession transactions’: the title page was that of a standalone single volume, but within the print shop the book was referred to as ‘vol. 1’ of Hutton’s Tracts. Indeed, as late as 1795 Hutton still occasionally referred to it as ‘my 1st vol. of Tracts’, although no second volume would appear.

  If a one-off volume was a poor substitute for the ongoing ‘transactions’ that had been half-promised, it at least contained both mathematics and science of a character that could easily have appeared in the Philosophical Transactions. Readers understood that this was matter that would, indeed, have gone to that venue had it not been for the Dissensions.

  And the Tracts dealt with very much the same range of subjects as Hutton’s papers in the Philosophical Transactions over the previous decade, giving the clearest indication of the course in which his thoughts were running at this time. There was a new proof of Newton’s binomial theorem, the algebraic result that tells you what you get when you raise x + y to a power (any power, even a fraction or a negative number). There were geometrical pieces, including one that concerned obscure new properties of the sphere motivated by questions about perspective: what fraction of the inside of a hemispherical bowl can your eye see from a given point? And a lovely geometrical conjuring trick: divide a circle into several parts that all have the same area and all the same circumference. Finally Hutton gave a new, longer version of his material about ballistics, which he had continued to work on throughout the early 1780s.

  It was a fine new mathematical miscellany, and proved to those who cared that Charles Hutton was not dead, crushed or consigned to oblivion. It provided the opportunity for those loyal to Hutton and the kind of British science he stood for to make personal statements of that fact in print; there were kind words in a couple of the book-review journals about the quality of the achievement the Tracts represented: full of ‘ingenious and useful discoveries’; written with ‘perspicuity and elegance’.

  As always seemed to be the case with Charles Hutton, there was more. No sooner had the Tracts appeared than he was firing off a couple of papers to the Royal Society of Edinburgh. One dealt with experiments on the expansion of freezing water reported to him from Quebec by his old friend Edward Williams, now a major in the Royal Artillery (where there was plenty of freezing water, and you could make an iron shell burst by filling it with water and leaving it outside all night). Another reported Hutton’s own ongoing work on the resistance of the air, a topic that would increasingly exercise him over the next decade. More privately, Hutton was exchanging manuscripts with friends on topics including the motion of comets and the vibration of strings. He occasionally carried out an observation at the Royal Observatory, under the presumably watchful eye of his loyal friend the Astro
nomer Royal. He was reading furiously as ever in British and foreign mathematical works. At the same time he was developing his interest in the history of mathematics: several of the Tracts touched at more than token length on the history of the problems they attacked, and this, too, would become one of Hutton’s obsessions into the 1790s.

  That historical interest came together with the continuing need to rebuild his career and his public persona in another curious habit Hutton acquired around this time: that of discovering that he was related to other minor (or sometimes major) celebrities. It was something he talked about rather than wrote down, but by the time of his death it could be stated in print as an uncontroversial fact that he was the cousin of the nonconformist leader James Hutton, although the latter’s biographers were unaware of the fact and it has so far defied confirmation from the genealogical records. At some stage he and the popular novelist Catherine Hutton also decided that they were ‘cousins’, though in this case there was an air of acknowledged fiction about the matter. One biographer was confused enough to invent a specific relationship (daughter of mother’s sister), but it was eventually acknowledged in print that the two families were not really connected.

  Most spectacularly, Hutton started putting it about that he was related to the ultimus heroum of British science, Sir Isaac Newton. Newton never married and had as far as anyone knows no children, so the closest relationship available was to be descended from Newton’s mother. By 1805 the story had acquired such currency that Lord Stanhope left Hutton in his will the famous Vanderbank portrait of Newton, as being the most fit person to have it. A descendant eventually passed it on to the Royal Society, where it more properly belonged, but the tale continued to circulate in the form that ‘cousin’ James Hutton’s grandmother was the sister of Newton’s mother. (There is, to be fair, evidence that James Hutton really was a descendant of Hannah Ayscough.) Fully elaborated, the tale had the Hutton family hailing originally from Westmorland, with one branch then moving to Lincolnshire (where the Newtons lived) and another to Northumberland. Entirely beyond proof or disproof today, the story is a testimony more than anything to Hutton’s assiduity in persuading people that he belonged in the world of metropolitan science to which he still – and since the Dissensions more urgently than ever – aspired.

  A more solid piece of personal reconstruction came in 1785. In May that year Hutton’s wife Isabella died in Jesmond near Newcastle. She was buried in the Dissenters’ burial ground in Percy Street: very close to Hutton’s birthplace, as it happened. The mails being what they were, it’s probable Hutton was unaware of her death until the funeral was over; certainly he did not attend or visit the north at this time.

  He lost no time in regularising his relationship with Margaret Ord. She became Margaret Hutton just two months later, in what was evidently quite a private ceremony at the Fleet Street church of St Dunstan in the West. It was the parish church for the set of rooms Hutton rented at Clement’s Inn, and both parties gave Clement’s Inn as their place of residence. There must have been a degree of connivance on the part of the celebrant, Joseph Williamson, who presumably knew perfectly well that neither party really lived in his parish.

  Charles and Margaret’s daughter Charlotte was sent to school at a convent in France around this time, together with her (half-)sister Eleanor. Hutton was keen on French culture (‘it is but justice’, he wrote in the Tables, ‘to remark the extraordinary spirit and elegance with which the learned men and the artisans of the French nation undertake and execute works of merit’). And evidently he was keen for his children to acquire a high degree of social polish: another aspect of his rebuilding and self-reinvention during this period. But just what prompted what was surely a rather odd decision for an English Protestant is one of Charles Hutton’s mysteries.

  The 1780s were a period of reconstruction not just for Hutton personally, but also for the country and the institution for which he worked. Victorious in most of the American battles, Britain had nevertheless lost the war, and with it the thirteen east coast colonies which now formed the United States of America. George III received John Adams as Minister Plenipotentiary in June 1785:

  I was the last to consent to the separation; but the separation having been made and having become inevitable, I have always said, as I say now, that I would be the first to meet the friendship of the United States as an independent power.

  Britain was demoralised, humiliated, and the war had been costly in monetary terms. Servicing public debt was costing around two-thirds of public revenue, and cutbacks were inevitable.

  After the Treaty of Versailles in 1783 the British Army was sharply reduced in size. The Royal Artillery, too, was cut by more than half, from over five thousand men to just two thousand. But twelve companies were still stationed at Woolwich, and the cadet company was left untouched. After years of frantic need for officers there were, suddenly, no commissions in sight: for four years no cadets were made lieutenants. Public exams restarted and there was a sense of normality returning, at least as far as the teaching was concerned.

  The cadets were now arranged in three ‘academies’ within the Academy – a ‘second’ was added to the old upper and lower academies – and each of those into four classes. Judging who had achieved what and who deserved to be moved up or down took a good deal of effort: written class lists and certificates from the staff; examinations to progress from one academy to another. Such a degree of fuss and documentation was unknown in normal schools. Hutton’s role and judgement remained crucial, and mathematics – algebra and geometry – remained prominent in the teaching, the tests and the examinations.

  It was in some ways much the same as before the war: the same routine of calling out boys singly or in small groups to talk them through their work while the rest got on with exercises. The same round of definitions, rules and worked examples, pulled from book after book; selecting and arranging and editing the material into something uniform enough to make sense. Hutton wasn’t one to stick rigidly to a printed source, even if it was such a revered text as Euclid’s. When the students complained about parts of the theory of ratios in the Elements, he dropped or modified it.

  He got on with the cadets, by all accounts. Howard Douglas, who joined in 1790 aged thirteen, was a quick favourite of Hutton’s: head of his mathematics class and so proficient that Hutton used him as a sort of assistant, telling boys in difficulty with the material to ‘go to Douglas’. He always remembered Hutton with gratitude and affection. Another commentator noted Hutton’s ‘goodness and simplicity’ towards both his colleagues and the cadets in his charge; one of the junior masters under Hutton later wrote that

  As a preceptor, Dr. Hutton was characterised by mildness, kindness, promptness in discovering the difficulties which his pupils experienced, patience in labouring to remove those difficulties, unwearied perseverance, and a never-failing love of the act of communicating knowledge by oral instruction. His patience, indeed, was perfectly invincible. No dullness of apprehension, no forgetfulness in the pupil, ever induced him to yield to irascible emotions, to forfeit his astonishing power of self-control.

  … during the last twenty-five years, I have had the most favourable opportunities of acquainting myself with the best modes of giving instruction in the University of Cambridge, and in other institutions, both public and private; and during much of that time, I have been extensively engaged in the same profession; but I do not hesitate to say that I have neither seen, nor have the least conception of, any oral instruction, the excellencies of which bear any comparison with those of Dr. Hutton.

  The immediate post-war period saw one final piece of rebuilding from Hutton. He had always complained of the unhealthiness of the Woolwich site. Miasmic in the summer, it could be bitterly cold in the winter, the wind off the river blowing chill down the long open spaces between the buildings. He claimed in print that the air at Woolwich had shortened the lives of two of his predecessors.

  In May 1787 Hutton’s complaints abo
ut his health came to a head, and he applied for leave to move further away from the Academy than the house in the arsenal he had inhabited so far. He was convinced that the location was responsible for his persistent lung complaints, though early inhalation of quantities of coal dust probably played a role as well. He represented that his health was in danger from this and perhaps from overwork.

  He was granted house-rent and he moved up to Shooter’s Hill. The air and the exercise of climbing the hill (twenty minutes or so, done briskly) did him good. There were a few other officers’ houses there: possibly a certain amount of society for his family. If the Royal Artillery sometimes pounded away on the common below, it was equally often Hutton’s own experiments doing the pounding, so he could scarcely complain.

  Neither could it escape him that the common itself was ripe for development. From 1774 building plots there had been sold off, a plot having been enclosed a year before for the new Royal Artillery barracks. Meanwhile a Barrack Tavern was added to Shooter’s Hill, and one of the large houses became a small factory. When ten acres of freehold on the common came up for sale, Hutton had little hesitation in bidding, and after delays which in the end stretched on for several years, he succeeded in buying.

  He cleared the existing low cottages and in 1790 began to build. He had designed and built a house in Newcastle already, and he was an authority in print on at least the surveying, quantity surveying and accounting side of house building. It’s probable that the designs were his own, and certain that he oversaw the work closely. Even the bricks and slates were manufactured locally, from the clay of the common. Hutton interested himself in the process, and was said to have hit on certain improvements and even to be setting up in business as a brick manufacturer, though that came to nothing.