Gunpowder and Geometry Page 3

  Poor Reuben Dixon has the noisiest School

  Of ragged Lads, who ever bow’d to Rule;

  Low in his Price – the Men who heave our Coals

  And clean our Causeways, send him Boys in Shoals.

  Indeed, teaching unruly boys just a few years younger than himself demanded more natural authority than Charles Hutton yet possessed. He would be remembered ominously as having ‘kept up the most rigid order’ as a teacher, and sometimes having carried ‘his severity too far’. One student from these early days recalled that he ‘assumed a degree of importance’ in the classroom: pomposity might have been a blunter word. For a while he affected a large academic gown and, to complete the effect, a scarlet cap. Even his best friends were embarrassed. He turned up to a parish election in this finery, and ‘his friends, who would have supported him in the state of a Caterpillar, were so disgusted when they saw him transformed into a Butterfly, that they did not support him and he lost his election’.

  Hutton was very young, and the phase passed. The excellence of his teaching continued. He quickly determined that the schoolroom at Stote’s Hall would not be the end of his journey. With the ferocious energy and the self-discipline that would attract comment again and again, he set himself to improve still further. He read all he could: not chapbooks of romantic stories now, but the hardest and the newest mathematical books he could lay hands on. Newton’s works and the works of his contemporaries and disciples: Christiaan Huygens, Roger Cotes. Descartes and his followers. Textbooks of gauging and surveying, and the works of Hutton’s own contemporaries in Britain and beyond.

  On top of his teaching and his reading, he went down the hill to Newcastle in the evenings and attended classes given by a Mr Hugh James, who specialised in mathematics. It was a conspicuously demanding regime, and his mother feared for his health. But Hutton could see where his future lay, and he had determined to pursue it as hard as he could, whatever the cost.

  In fact it was his mother that died, in March 1760. She was buried near her first husband in St Andrew’s, Newcastle, on the seventeenth of that month.

  Hutton was twenty-two. We don’t know just how relations stood between him and his mother when she died, or even whether he had already moved out of the family home. We do know that less than three weeks later he returned to St Andrew’s to be married. His bride, Isabella, was four years his senior; she had trained as a dressmaker. The marriage licence gives her maiden name as Hutton, so she may have been a relative. The scarcely decent haste hints at a family drama now lost from view: a match on which the enamoured couple were keener than were their families, perhaps. Soon there was a son, Henry, known to his parents as Harry.

  They moved into rooms in Newcastle itself, just off the Flesh Market: central, bustling, but rich in shrieks and stink. And just a week after his marriage Hutton advertised a new school in the Newcastle papers.

  TO BE OPENED

  On Monday, April 14th, 1760, at the Head of the Flesh Market, down the Entry formerly known by the name of the Salutation Entry, Newcastle, A Writing and Mathematical School, where persons may be fully and expeditiously qualified for business, and where such as intend to go through a regular course of Arts and Sciences, may be compleatly grounded therein at large.

  He promised to teach writing, arithmetic and shorthand, as well as a long list of mathematical subjects: accounts, algebra, geometry, mensuration, trigonometry, conic sections, mechanics, statics, hydrostatics, calculus. Any youths not satisfied by these would also be shown their applications to practical life: navigation, surveying, gunnery, dial-making, measuring, geography, astronomy.

  The tree of mathematical knowledge.

  It all seems premature, precocious, absurdly risky. Hutton was just four years out of the coal pits; he was quite unknown, his fees were twice those asked by his rivals and his list of subjects promised an impossible range of expertise, including any number of practical subjects in which the twenty-two-year-old had no practical experience. He was aiming very high, hoping to become a different class of teacher: a specialist in mathematical training, no longer bound to the drudgery of teaching the very young to read and write. Friends advised him to promise less, and ask for less money. He didn’t listen, and the result was a struggle, the high prices keeping some away during years when Hutton’s family was growing.

  But there was real demand for this sort of thing: specialist mathematics teaching for boys up to fourteen or even older. In a period when a quarter of the country was unable to read, northern parents had a reputation for being keen to educate their children, for sending able, well-educated boys to London to work in counting houses and trade. Trade was increasing during the eighteenth century, and the demand for those boys multiplied; they became bookkeepers, accountants, land stewards, surveyors, navigators (think of James Cook, who would sail round the world on a Whitby coal-ship; while he was still in the coal trade he learned all the mathematics he could at Newcastle schools between voyages). Schools proliferated, and Newcastle became England’s best-educated city after London: four charity schools and the prestigious Trinity House School were founded in the first half of the century, and its well-regarded grammar school flourished. A few landowners maintained schoolmasters for the benefit of their employees, and it wasn’t unknown for the employees themselves to club together to fund a school, as they did at the Newcastle ironworks. Hutton had picked a growing market.

  Teaching mathematics at this level meant teaching to add, subtract, multiply and divide, to find square roots and cube roots (Hutton had his own special method for this). It meant fractions both natural and decimal: how to read and write them and how to do arithmetic with them. It meant handling England’s enormously complicated systems of units: grains, scruples and drams for drugs; yards, poles and furlongs for length; firkins, kilderkins and barrels for beer; and many, many more. It meant converting between currencies, which brought similar difficulties: how many Flemish guilders will I buy with one hundred and seventy-three pounds, fourteen shillings and twopence, if one pound is worth thirty-five stuivers three and a half penning?

  Above all, it meant reasoning with proportions: or rather, for the less able who were the majority, applying a series of rote-learned rules that would tell you the right answer in certain situations to do with linked ratios. If eight yards of cloth cost twenty-four shillings, what will ninety-six yards cost? In how many days will eight men finish a piece of work that five could do in twenty-four days? In a school career a child might do hundreds, if not thousands of these problems.

  It was dry stuff; but Hutton made it work, and over time the numbers at his school grew. By 1764 he moved downhill to the more fashionable, though somewhat unfortunately named ‘Back-Row’, where he, his school and his family shared premises with a dancing master named Stewart. Hutton got involved with selling tickets for the man’s public balls. Stewart’s prices (half a guinea at entrance and a guinea a quarter for six days’ teaching each week) would have limited his students to the well-to-do, but still the presence of a dance school in the house can only have been disruptive, both to Hutton’s own teaching and to his domestic life.

  We have few glimpses of that life. In one of his books Hutton, searching for a memorable image, remarked that a triangular prism ‘is something like a hat box’. Indeed it is: but hats in hat boxes were not a picture that would have sprung to Hutton’s mind a few years before. An admirer remarked much later that Hutton ‘was soon conscious of his great abilities, and claimed that rank in society to which they entitled him’. That was a polite gloss on the fact that material success gave him the means to act, dress, and for all practical purposes be middle-class. He was now indisputably the butterfly, not the caterpillar.

  Still, he could not altogether avoid criticism. Some remembered ‘a very modest, shy man’ at this period; but we also hear of him knocking a boy down in the street while he was surveying Newcastle. In this or another incident someone taxed him with being only a pit boy, and Hutton retorted that
if he – the critic – had been a pit boy he would be there still. Memories of the cap and gown lingered; two different witnesses, seventy years later, independently recalled the red cap.

  There were three more children: Isabella, Camilla and Eleanor (known to her family as Ellen). They were baptised in the nonconformist chapel at Hanover Square.

  At the time of writing Hanover Square is a demolition site tucked away near the line of the old town walls. Trains rattle past over the nearby viaduct, and it’s hard to get a sense of what was once Newcastle’s only open square. The chapel there was established in 1727; from 1767 it had a school, and by 1810, after some modification, it was large enough to hold an organ and six hundred people. Its congregation included prominent local poets, newspaper proprietors and politicians.

  Hutton had remained a zealous Methodist for some time after his childhood conversion: one report says he wrote sermons and preached them, though if this is true they have – sadly – not survived. His connection with Hanover Square may mean he had now left behind a movement which at this date still aimed to reform the Church of England from within, not from without.

  In fact the Hanover Square chapel would later acquire a reputation for Unitarianism, and Hutton’s presence there likely signals that he and his wife had come to be interested in more radical kinds of Protestant nonconformity, mixing in circles which questioned even such traditionally core doctrines as the Trinity, the atonement, and the divinity of Jesus. His private commitments are nowhere recorded, but a wider circle of Unitarians and those with radical sympathies – religious and political – would shape Hutton’s professional development long after he left Newcastle.

  This could have had serious practical consequences. Probate courts, marriage, schools and universities all potentially discriminated against non-Anglicans, and the ill-named Toleration Act of 1688 specifically excluded deniers of the Trinity (as well as Catholics) from its provisions. Meanwhile the Blasphemy Act of 1698 threatened them with up to three years’ imprisonment and loss of civil rights. Enforcement was patchy, but the risk of penalties was real, as was that of the loss of friends. Hutton’s clerical benefactor Ivison is conspicuous by his absence from Hutton’s life after his move to Newcastle.

  Work continued, and at a remarkable pace. Materially, Hutton was certainly prospering. His trajectory culminated for the moment with a final move to Westgate Street, one of Newcastle’s wealthier residential spots. He met the recurring problem of inadequate premises by acquiring a plot of land and building his own house and school. It was quite the elegant Georgian pile, with cellars and other conveniences. The Huttons could now avail themselves of all that the prosperous, growing city had to offer.

  The old town walls (they had started to come down in 1763) enclosed an area of less than 200 acres, but those acres held the north of England’s capital and a good proportion of the northern counties’ population. There were tall elegant buildings and wide open spaces by the several churches. By the early 1770s the town had three hundred street lamps and a well-organised night watch. If the lower town tended to be smoky from house fires, and if the riverside was dominated by busy warehouses and the bustle of shipping on the Tyne (not to mention a growing concentration of poor tenements near the Black Gate), there were open fields just a little further up the hill, some under conversion into elegant pleasure gardens.

  Newcastle in 1745.

  The town offered the full range of mid-Georgian amenities. Subscription concerts, both at the assembly rooms and outdoors in the summer. Visits from famous musicians en route from London to Edinburgh, who would often stop and give a performance or two to offset the costs of travel. Charles Avison, Newcastle’s own resident composer and concert promoter, a man who enjoyed national fame. A literary club; theatres. Scientific lectures: Newcastle was the first provincial town to have them, with both local talents and the nationally famous visiting on tour. A popular press: for most of the century there were two weekly papers. Newcastle had local histories and local poets and balladeers. There were shops, inns, clubs, societies; fashion, food, wine.

  Ultimately it all rested on coal; you could hardly forget that, if you lived anywhere near either the river or the coalfields, and Charles Hutton was never likely to forget it either. The sale of coal was so lucrative, contemporaries reckoned, that despite all the goods it imported Newcastle made a net gain every year, and had more money per head than anywhere else in the kingdom.

  Mathematically, too, Newcastle and its environs were a rich world. There was William Emerson, a nationally famous mathematician who lived in nearby Hurworth. His studied eccentricity of manner and dress (home-made linen, big floppy hats and shapeless old jackets) earned him a local reputation as a wizard. Hutton corresponded with him and they became acquainted, though unsociable Emerson and ambitious Hutton did not really hit it off. There was John Fryer, who assisted Hutton with his surveying work; he was also Hutton’s teaching assistant at Westgate Street.

  The school had its own separate entrance. Advertisements, briefer and more sober now, stated that there ‘Youth are qualified for the Army, Navy, Counting-house’; they could also be ‘compleatly instructed in the Theory and Practice of Land Surveying, with the use of the necessary Instruments’. Newcastle Grammar School took to sending its students to Hutton for specialist mathematics teaching. Not an altogether unusual arrangement – everyone knew that private academies did mathematics and science better than the grammar schools – but a gratifying endorsement of Hutton and his work.

  His new-found middle-class status also meant that Hutton could work as a private tutor to the local gentry. As one biographer put it, Hutton’s ‘manners, as well as his talents’, now ‘rendered him acceptable’ in this role. Robert Shaftoe was one such patron, his home at Benwell Hall one of the more impressive local mansions (the Bobby Shaftoe of the popular song was a relative). Hutton’s tuition of his children impressed Shaftoe so much that he took to attending the lessons himself, revising the mathematics he had perhaps learnt at college. And he gave the young man the run of his impressive library. Newcastle had at least a couple of subscription libraries, and no shortage of booksellers, but access to a large, private book collection was a boon for Hutton, who remorselessly continued to improve himself. Over the years he added a reading knowledge of French, Italian and German to his early-acquired Latin. By 1772 he had read enough on geography to offer public lectures in the subject (to ‘gentlemen and ladies’) at half a guinea for the course. How many takers he found is not recorded.

  Indeed, Hutton’s school was becoming something of a centre for learning. During the Christmas vacation of 1766–7 Hutton taught mathematics to other schoolteachers there, and at about the same time external lecturers began to use it as a venue. Caleb Rotherham covered geography, astronomy and other scientific subjects; likewise the popular James Ferguson. Ferguson was a house guest, and gave private performances to Hutton’s friends and family in the evenings, though Hutton was shocked when he discovered how little geometry the man knew. Hutton’s school was in a way a forerunner for the Literary and Philosophical Society that would be founded in Newcastle thirty years later, its first paid lecturer the same Caleb Rotherham.

  His arrangement with Newcastle Grammar School brought Hutton himself two of his most celebrated pupils, and certainly his most colourful. John Scott was the son of a coal merchant; Bessie Surtees a wealthy banker’s daughter. Both went to Hutton for their mathematics lessons, but it was presumably not under his eye that their youthful romance blossomed. Scott went up to Cambridge in 1772, but the calls of love proved stronger and in November he came back and eloped (ladder, first-floor window) with Bessie. The scandal – or the romantic adventure, depending on your perspective – ran and ran through the nineteenth century, and Bessie Surtees merchandise is still to be had in her Newcastle home town.

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  Author

  A country clergyman, anywhere in England, any time in the eighteenth century. At his desk, in his study. April
. Open windows; sunlit air. An open manuscript of mathematical work. Solutions to puzzles from magazines, copied fair.

  He copies this year’s set of solutions fairer still, adds a couple of suggestions for problems the magazine could ask this year. Mends his pen and adds a covering letter. Dear Sir. I enclose my mite for this year’s Diary, hoping you will find it worthy of notice. Your humble servant. Dusts the sheets, folds, seals.

  A scene repeated many times – many hundreds of times – across Britain every year of the Georgian period. A few months later, in about October, the annual magazines went on sale: The Ladies’ Diary, The Gentleman’s Diary, The Mathematical Repository, and more. Some readers had the thrill of seeing their names, their mathematical work in print – a few won small prizes. Others looked in vain for their names, their work in the magazine, and concluded, humiliated, that their solutions had been wrong.

  If Hutton had done no more than succeed as a provincial schoolteacher, his story would be a striking but not a very unusual one. The majority of mathematics teachers in Georgian Britain, indeed, were working-class lads who had made good: self-made men who had themselves attended private academies or bettered themselves by private reading. There were schools right across the United Kingdom that bore witness to their success in attracting students, providing them with high-level instruction and sending them out to work in the burgeoning literate and numerate trades.

  Hutton was not satisfied with this. He wanted the wider recognition and the promise of greater rewards that publication would bring. And he approached publication through that remarkable Georgian institution, the mathematical periodical.