Gunpowder and Geometry: The Life of Charles Hutton, Pit Boy, Mathematician and Scientific Rebel

By his early teens Hutton was living with his family in the village of Heaton, and attending school half a mile away at Jesmond. His teacher, Jonathan Ivison, was a would-be clergyman: a university graduate marking time while he waited for his first benefice.

Ivison represented another link to a wider world for Charles Hutton. He was no spectacular example of worldly success, but he illustrated the very different kind of life that could be reached through education. And his teaching provided direct access to parts of that education. He taught Hutton some Latin and some mathematics, and Hutton discovered talents for both. These were whole new worlds to explore: ancient literature or the heady abstractions of algebra and geometry could easily occupy a person for a lifetime. Meanwhile Hutton’s ability at accounting drew some attention, and presumably provided evidence to his family that keeping him in school remained a reasonable choice. And he was also learning practical geometry and surveying: food for the mind, but skills that could one day be of use in the world of the collieries, too.

His continued success at school reportedly made Hutton a favourite with those who taught him. He seems to have become quite close to Ivison. Ambitious, always keen to be at the top of everything in hand, he was envied by other students.

But time was running out. Hutton couldn’t remain the hope of his family for ever, and unless an unexpected opportunity opened up the only route his family or his world could offer him was a career in the coal pits, perhaps working up to overman or viewer if he was very lucky. At fourteen he passed the age when schooling for boys of his class ended and work or apprenticeship began; and it wasn’t clear what was going to happen next.

Indeed, it’s not clear what did happen next. Jonathan Ivison gained his benefice in the autumn of 1751, when Hutton was fourteen, and after hasty ordination he was licensed as curate at Whitburn, near the coast in County Durham, a couple of days later. Whitburn was nine miles from the schoolroom at Jesmond – a dozen by road – and commuting between the two was scarcely feasible. Schools were transient things, and there was no particular reason this one would stay open once its single teacher was gone.

Yet Ivison’s new salary was just twenty-five pounds a year: barely enough to live on. He badly needed more money. One report says Hutton acted as Ivison’s assistant. It’s possible he acted as his substitute, keeping the school open while Ivison performed his parish duties half a day away. There was nothing awfully unusual about the head of the class helping to teach the younger children, and nobody ever denied that Hutton was the head of this and every other class he ever entered.

Whatever the truth of the matter, Hutton was spared a return to the pits for a few more years. There’s no hint in any of our sources that he ever did the kind of work to which teenagers normally graduated in the mines: ‘putting’, that is, dragging or pushing the heavy wicker baskets full of coal from the face to the shaft.

But his reprieve was not to last indefinitely. The next firm fact we have about him is a pay bill from the Long Benton colliery for September 1755, when he was eighteen. He was working as a coal hewer in the ‘Rose’ Pit, under his stepfather Francis Frame as overman.

Put one leg through a loop in the rope, and hold it hard for the breathless minutes of descent: three hundred feet down. At the shaft bottom the darkness is total, outside the reach of a few brief candles. Long, dreary galleries lead off in every direction, and it’s oppressively warm. Walls of coal; wet under foot. Fossils in the roof to remind you of the weight of rock, the inexorable crushing force ever-present above your head. Constant noise: rushing water and the distant thud of the engines; corves of coal being dragged past by teams of exhausted, shattered boys. Grimy, weary men everywhere, bustling in the gloom.

Strip to the ‘buff’: short breeches, low shoes, cotton skull-cap (or even less). Take your wedge, hammer and five-pound pick. Kneel, sit, stoop to get at the coalface. Or just lie down. Coal seams could be as little as two foot six high, and Hutton was a tall young man. Channels of sweat in the coal dust on your face.

First, make vertical cuts from the top of the seam to the bottom, dividing the coalface into what the men called ‘juds’. Then, undercut the juds one by one: skilled and, by some accounts, athletic work. Next hammer in wedges at the top of the jud, and bring down the coal section by section. It could take an hour or two, and then, of course, you did it again. And again, all day. A hewer could bring down four tons or more in a shift. Putters bundled it away in the wicker baskets, and up it went to the daylight.

At the coalface.

It was hard, it was dirty, it was dangerous. But coal hewers were actually the elite of the pit; indeed, it’s surprising Hutton was allowed to do the work as young as eighteen, and without working his way up through gruelling years at the back, and then the front, of a corf of coal. Francis Frame perhaps used his own position in the pit to make it happen. Hewers were relatively well paid: quite possibly better paid than manual workers in other fields like agriculture. And they worked shorter hours than the trapper boys and the putters: seven or eight hours of the day, starting in the very early morning.

The stars are twinkling in the sky,

As to the pit I go;

I think not of the sheen on high,

But of the gloom below.

Not rest or peace, but toil and strife,

Do there the soul enthral;

And turn the precious cup of life

Into a cup of gall.

That was Joseph Skipsey, the ‘Pitman Poet’, in the 1860s: but the words could have applied to Hutton, or to many and many another.

Charles Hutton had known, briefly, the life of a country schoolteacher, and had felt the stirrings of a talent for both languages and mathematics. A world wider than the pit had come into view more than once during his short life, in the person of John Wesley and in that of Jonathan Ivison: university graduates both, and holders in their different ways of promises about what life could be.

In a pamphlet for children, printed in Newcastle, Wesley wrote that you shouldn’t ever wish for more than you have. Men are fallen, grace is a gift, and if we had what we deserve we’d all be in hell. But however docile Hutton was, and however resigned to the will of Providence, it’s hard to imagine he didn’t wish.

I think Charles Hutton’s return to the coal pit must have represented desperation – perhaps exasperation – on the part of his family. The hope that if he stayed in school he might somehow make a better or a different life for himself was showing no clear sign of paying off, so far as we know. Children younger than him were earning their keep; the favoured youngest son had been indulged for many years, but he would not be indulged for ever. One source says he was ‘taken from school’, and there is almost the sense of a violent abduction away from his natural element to the now quite alien world of the pits.

The pit, and its cup of gall, could have been the rest of his life: for a time there must have been no reason to imagine anything else was going to happen. Two things made a difference.

One was that Hutton was bad at hewing coal. The pay bills show him bringing down less coal than his fellows, and as a result he was employed less – much less – than they were. In old age Hutton would say his injured arm was to blame for his poor performance at the coalface. Maybe it was, though we never hear that the lame arm affected him later in his life. Maybe it was simply that his schooling and his comparative lack of experience down the mines had left him without the strength, the endurance and the skills the work needed.

The other thing was that Hutton was using his time away from work to exploit his connections, to invent a way out of colliery life and make something quite different for himself. Who knows just what hustling Charles Hutton did during the months he worked down the pit, in the winter of 1755–6. But it came to the point that he knew he had it in his power to escape, and some sort of scene appears to have taken place at the colliery. He was ‘laid idle’ one day, whether for some fault or simply because a more able man was available, and he made a fuss about it. He told the overman that he’d soon be out of his power, that he was going to go to a more respectable life. It must have been quite a row; men who were there remembered the scene seventy years later.

But Hutton was speaking the truth, however ungraciously. Jonathan Ivison had been the curate at Whitburn for four years now, and if his Jesmond schoolroom had been limping along meanwhile, it was time to pass it on for good to someone who lived near by. Ivison knew the man for the job. Presumably he squared it with the owner of the building where the school was held. And presumably he squared it with Francis Frame. For he wanted Charles Hutton to take over.

At the age of eighteen, Hutton was legally a minor and too young, in theory, to set up on his own in any trade or profession. (He was also, perhaps crucially, too young to have signed any sort of binding contract at the colliery.) But it’s hard to imagine his parents having much hesitation about an offer that would get the useless hewer away from the coalface, where he was little more than an obstacle in the way of fitter, stronger men, and would secure him – if he pulled it off – an income and even a career. One day in March 1756 Charles Hutton clung to the rope and ascended to day for the last time.

2

Teacher of Mathematics

Autumn 1758. High Heaton, near Newcastle. Silence (or almost). Boys seated at rows of desks. Slate pencils squeaking; quills scratching on paper. Another harvest is in the fields, and the coalface is as hellish as ever. But Charles Hutton is above ground now, in what was once Jonathan Ivison’s schoolroom.

The young schoolmaster is seated at the front, where he can see all the boys. One at a time comes forward, shows his work, is praised or blamed. Can he spell the words set the class; has he written his fair copy fairly enough? Can he read the passage assigned? Has he worked the sum correctly and by the right method? Does he know his catechism answers? He is given a new exercise to do or a new instruction or definition to copy down in his book; sent back to his desk.

Over the course of the day and the week the work cycles through reading, writing, arithmetic, divinity. The boys spell from a textbook: probably the same one, by Ann Fisher, that Hutton learned from himself. They read from the Bible, learn to count or do their sums from another book. Start again on Monday.

It would be intriguing to know how Charles Hutton spoke to his students. Firmly or gently? Leading or prodding? What was he really like as a teacher? We shall never know.

A master and his pupils.

But the books he wrote, later on, record something of the quality of thought that went into Charles Hutton’s work in the classroom; they hint at a man who had his material impeccably organised, who always had something new to show the student, a new trick, a new bit of complexity to stretch the growing mind. The Georgian classroom involved lots of one-on-one teaching, most of the children working quietly while the teacher spoke with each in turn at his desk. It demanded huge agility of mind from the teacher, as each student to be seen was at a different place and needed a different sort of help.

It’s easy to imagine that a teacher with a less than perfect grasp of the material, or who relied too heavily on a printed textbook, would end up with most of the students spending most of the time on repetitious exercises they only partly understood, and would quickly find he had lost the weaker ones. But for the exceptionally wide-awake teacher the system provided a maximum of flexibility and opportunity. It depended on having the material very clear in your mind, and above all minutely graded into separate steps. Hutton seems to have excelled at this. He would make a few enemies during his long life, and pick up criticism, some of it deserved. But no one ever denied he was a superb teacher.

He was talented, he was full of energy and he worked hard. The school at High Heaton ran both days and evenings, teaching local boys and adult miners, some of them Hutton’s former mates from the pits. Local children flocked to him as students, to such a degree that the schoolroom proved too small. So Hutton obtained the use of a room in nearby Stote Hall, and there he and his scholars trooped daily for their lessons.

It’s demolished now, the former mansion of Sir Robert Stotte; only the gateposts and gatehouse survive. But photos show an imposing house. It looked over the small valley of Jesmond Dene and you can still retrace Hutton’s walk of a quarter of an hour or so from one village to the other. First a very gentle rise through what was then open farmland; then down the hill and across a steepish valley of never-farmed woodland. Sloping paths and views away through the trees. It was already a walk into a very different world from that of the colliery, and infinitely removed from the coalface in the Rose Pit.

And yet for many, schoolteaching was a despised profession, a mark of failure for a man of education. ‘School’, indeed, is a grand term for what was no more than a room provided by someone’s goodwill and in which Hutton collected pennies for teaching young children to read and write, to add up and remember a few Bible stories. Chemist and religious controversialist Joseph Priestley was typical: ‘Like most other young men of a liberal education, I had conceived a great aversion to the business of a schoolmaster, and had often said that I would have recourse to anything else for a maintenance in preference to it.’ Elementary teaching in particular was widely seen as work for old women, widows, or the humblest members of society. Nor did it bring any very great material rewards for its long, demanding hours: pay only slightly above that of a labourer; no such thing as promotion; no such thing as a pension.

There was no teacher training. Giftless graduates stumbled into teaching and stumbled through it; impecunious clergymen practised it with a savage resentment that they took out physically on the children in their charge (it was the boast of Dr Parr of Harrow that he never flogged a boy twice in the same lesson). A typical contemporary observation is contemptuous of what went on in small ragged schools like Hutton’s:

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.