Copyright

William Collins

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This eBook first published in Great Britain by William Collins in 2019

Copyright © Benjamin Wardhaugh 2019

Cover illustrations: engraved illustrations of Artillery Carriages © bauhaus1000/Getty Images; engraving of Charles Hutton © Pictorial Press Ltd/Alamy Stock Photo.

Benjamin Wardhaugh asserts the moral right to be identified as the author of this work

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Source ISBN: 9780008299958

Ebook Edition © February 2019 ISBN: 9780008299972

Version: 2019-01-11

Dedication

In memory of Jackie Stedall

Contents

Cover

Title Page

Copyright

Dedication

1 Out of the Pit

2 Teacher of Mathematics

3 Author

4 Professor

5 Odd-Job Man

6 Foreign Secretary

7 Reconstruction

8 A Military Man

9 Utility and Fame

10 Securing a Legacy

11 Controversies Old and New

12 Peace

Epilogue

Notes

Select Bibliography

Image Credits

Index

Acknowledgements

About the Author

About the Publisher

1
Out of the Pit

August 1755. Newcastle, on the north bank of the Tyne. In the fields, men and women are getting the harvest in. Sunlight, or rain. Scudding clouds and backbreaking labour.

Three hundred feet underground, young Charles Hutton is at the coalface. Cramped, choked with dust, wielding a five-pound pick by candlelight. Eighteen years old, he has been down the pits on and off for more than a decade, and now it looks like a life sentence. No unusual story, although Charles is a clever lad – gifted at maths and languages – and for a time he hoped for a different life.

Many hoped. Charles Hutton, astonishingly, would actually live the life he dreamed of. Twenty years later you would have found him in Slaughter’s coffee house in London, eating oysters with the president of the Royal Society. By the time he died, in 1823, he was a fellow of scientific academies in four countries, while the Lord Chancellor of England counted himself fortunate to have known him. Hard work, talent, and no small share of luck would take Charles Hutton out of the pit to international fame, wealth, admiration and happiness. The pit boy turned professor would become one of the most revered British scientists of his day.

This book is his incredible story.

Newcastle upon Tyne occupies a fine site for a town: a long south-facing slope, down towards the river. The Great North Road runs through it: 90 miles north to Edinburgh, 250 south to London. And the river joins the town to the world. As the old song goes,

Tyne river, running rough or smooth,

Brings bread to me and mine;

Of all the rivers north or south

There’s none like coaly Tyne.

By the time coaly Tyne passes under the bridge at Newcastle it has seen the Pennines and the wild country of Northumbria: land fought over by the Romans and the Picts, the English and the Scots. If the water had once been dyed with their blood, by now it was dyed with coal.

The town was spacious and populous. Only three English towns were bigger; but still Newcastle was no sprawl early in the eighteenth century. Just five main streets within the old town walls, and open country beyond them to east and west.

We know next to nothing about Charles Hutton’s parents, Eleanor and Henry. It’s probable they moved to prosperous, growing Newcastle from elsewhere: possibly from Westmorland, on the other side of the Pennines.

Eleanor and Henry seem not to have prospered in any tremendous way in Newcastle, though neither were they at the bottom of the heap. Henry was a ‘viewer’ in the collieries: something less, that is, than a land steward or estate agent, and something more than a manual labourer. Viewers were literate, numerate men who kept the colliery’s records and compared notes with their colleagues at neighbouring mines. They measured and calculated rates of production, kept an eye on how fast the pit was filling with water and how well the pumps were coping. They allocated labour, planned, inspected. Some stayed up at night to catch coal thieves.

Viewers were expected to be down the pits daily, but also to see the estate agent daily. They faced two very different worlds: the wealthy owners and the men who hewed the black diamonds out of the rock beneath their feet. They had responsibility and power; some abused it, keeping owners ignorant about the mine work. Many used their position to command high fees. The coal industry was expanding, and new shafts and new mines depended on the advice of experienced colliery viewers. High-end viewers had their own assistants and apprentices: minor deities in their own field.

One source says Henry Hutton was a land steward for Lord Ravenscroft, a step further up still. We don’t know if it was true, and it may just be a garbled reflection of the fact that he oversaw a mine or mines on that nobleman’s land in Northumberland. Either way, he was a man who had a good deal more than the very minimum.

By 1737 Eleanor and Henry lived with their children – three or four boys, perhaps more – in a thatched cottage on the northern edge of Newcastle. Nineteenth-century historians would be rather sniffy about this ‘low’ dwelling (low, probably, both literally and metaphorically); but compared with the cottages of the miners themselves it was luxury. Thatch, indeed, was a luxury, as was the ability to live more than a stone’s throw from the pit mouth.

Just as Henry Hutton worked at – was – the interface between landowner and manual workers, his house stood on the edge in more than one sense. Sidegate, their street, was one of the first to burst out of the still intact medieval town walls, and while open land surrounded it on both sides, a stroll down the hill took you back to the bustle of Newcastle. Away to the north it led across the Great Northern coalfield, engine of England’s prosperity.

The ‘low’ cottage of Hutton’s birth.

Charles, Henry’s youngest son, came into the world on 14 August 1737. A fortnight or so later his parents took that stroll downhill to the parish church of St Andrew’s, just inside the town wall – stubby tower, Norman interior, bright new set of bells – and he was baptised.

For a few years, all was well. There were games with other children in the street; there were fights. Ladies liked little Charles; they thought him uncommonly docile and good-natured.

The Huttons sent some, perhaps all, of their children to school. On the walk from their cottage to St Andrew’s they passed Gallowgate (actual hangings were a rarity by Hutton’s time: one every few years, if that). And on the corner of Gallowgate a house stuck out awkwardly into the street. In it an old Scots woman kept what the usage of the day optimistically called a school. That is, she took in a few of the local children and endeavoured to show them how to read, with the aid of a Bible. Charles Hutton remembered her as no great scholar; when she came to a word she couldn’t read, she would tell the children to skip it because ‘it was Latin’. But he did learn to read.

In the summer of Charles’s sixth year his father died. Swiftly his mother remarried; with several children to keep, the youngest of them five years old, there was perhaps little real choice. Their new father, Francis Frame, occupied a lower station than Henry Hutton. He was an ‘overman’ in one of the collieries: a labourer, but one who was also employed to superintend the others. Not necessarily literate, not necessarily numerate: there was a system of marks and tally sticks to avoid the need for that. His pay might have been half that of a viewer, and he basically worked underground. And he had to live near the pit. Shifts might start in the small hours, even at midnight, and you couldn’t be walking a mile or two in the dark just to get to the colliery. The family left the house in Newcastle, and moved north into the coalfield itself. And coal changed from a distant background, a what-my-dad-does, to an immediate daily reality for Charles Hutton.

Hundreds of thousands of tons of it went down the river each year, and the market was growing all the time. Over the course of the eighteenth century the industrial revolution and the steam engine would increase Britain’s hunger for coal to stupendous levels. As the coal trade grew it expanded away from the river, north and south; new collieries were opened and new wagon routes built to serve them. Landowners gambled huge sums on the chance of reaching a profitable seam, but they also told themselves – and believed – that they were doing a public service: providing jobs, providing coal.

The so-called Grand Alliance of colliery owners was sinking new pits on north Tyneside, where coal to last hundreds of years lay undug. The villages there – Jesmond, Heaton, Long Benton – would now be the Hutton family’s world. This was the true coal country. The landscape of the Great Northern coalfield was all pits and pit villages; the hills and the fields, the river and the tearing clouds formed little more than a scenic backdrop. Streams were everywhere, making steep little valleys and shaping where you could build, where you could walk. And where you could dig. The wet got into the pits, and a mine on north Tyneside could raise a dozen or more times as much water as it did coal. Horses plodded around horse-gins to wind the ropes that brought it all up, and unwind them again to send the men down.

The members of the Grand Alliance were technophiles, and they installed the new atmospheric engines designed by Thomas Newcomen – forerunners of the steam engine – at their pitheads to do some of the winding work. The machines were cheaper to run than horses, but they were loud, and they added to the noise, the smoke and the dust. It’s hard to get a sense of it today, now that the pits are closed and the collieries built over with smart modern houses. On a clear day you can see down from Long Benton, where the Huttons worked, to the spires of Newcastle’s churches, and beyond to the rolling country south of the river. There are still some open fields nearby – playing fields, now – and the long line of the old wagonway, down towards the river, remains as a peaceful footpath; birds sing in the hedges.

In the 1740s it was a very different place. The wagonway had wooden rails, and the Long Benton colliery and its neighbours ran an endless procession of horse-drawn wagons on them, taking the coal down to the staithes at the river’s edge. The spires of Newcastle may have been visible through the clouds of coal dust and smoke, but they represented a distant, unattainable world.

Nearly all collieries provided housing for the underground workers, and the Huttons presumably lived in such a dwelling. Long gone now, the miners’ cottages were packed in tightly, in rows as close to the pit mouth as could be managed. They were drab and uniform; two rooms was usual, with an extra chamber in the roof. Quite a few had gardens for vegetables, or even a pig or cow, or some hens. The tradition on the Great Northern coalfield – at least later – was for growing prize leeks.

The pit villages were isolated physically and socially. It was an unusual environment, supporting an unusual kind of work. The miners made a close-knit world, with massive revelry at weddings and christenings (and any other excuse): roaring bagpipes and roaring men; hilarious, vulgar, open-hearted.

Middle-class visitors typically found the miners and their families shocking, barbarous, uncivilised. Translated, that probably means miners’ pubs were noisy, their homes not absolutely spotless, and their knowledge of scripture of a slightly less than prizewinning standard. The miners’ world may have been rough and simple; squalid it was not.

They were proud of their appearance. Like sailors, you could tell the miners anywhere by their clothes: checked shirts, jackets and trousers with a red tie and grey knitted stockings. Long hair in a pigtail. And of course the pall of coal dust, almost impossible to wash out completely. Rings of it circled their eyes, and it made the cuts and abrasions of underground work heal into distinctive blue scars.

Charles Hutton would remember his stepfather Francis Frame as a kind man. But he was not Lord Ravenscroft’s land steward, nor anything like it, and there was no avoiding the fact that the family’s expectations had fallen. There had probably never been any question about what work the boys would go into, but if there had been hopes of climbing the ladder to become viewers and overmen they probably now hoped for nothing more than the status of plain coal hewers.

And by the age of six, or certainly by the age of eight, little Charles was old enough to start work. One report says he spent some time operating a trapdoor in the pits. For a miner’s lad this was typical entry-level work, done by the youngest boys. Different areas of the pit were isolated from each other by trapdoors, usually kept shut to make sure the air flowed where it was supposed to and reduce the risk of gas build-up and explosion. Each trap had a boy to pull the cord that opened it, and shut it again after men or coals had passed. Boring but crucial work; mines blew to smithereens if a trapper lad fell asleep on the job and let the bad air reach the candles. Solitude, silence and darkness worse than any prison. You learned not to fear the dark.

You learned much else, too; starting in the pits was not so much a training as total immersion in a culture. The all-male environment had its traditional ways: ancient facetiousness and long-lived jokes; bravado in the face of shared danger. Men died in the pits, often: candles in the gassy dark (there were no safety lamps as yet); shaft collapses; suffocation. Firedamp and chokedamp, the miners called the bad airs, and they were especially common in the northern pits. By the 1750s coal owners were asking the newspapers not to print reports of pit explosions; they were bad for morale, bad for trade.

So you learned the feel of the mines and the smell of the different airs, good and bad. You gained the true pitman’s instinctive sense of danger. You also learned to cling to the rope that pulled you up and let you down the shaft. Shafts could be a few hundred feet deep, and there were no cages to ride in. You just clung on, with your leg through a loop of rope. If your hands grew tired, you died. If the horses pulling the rope were startled and bolted, you died. Eventually that would happen to Francis Frame, in an accident at Long Benton colliery after Charles had left. Over the course of a life’s work in the pits your chance of dying in an accident was probably as high as one in two.

By the time the exploitation of children in the pits became the subject of official inquiry – in the 1840s – it had attained the proportions of a national disgrace. Boys were working twelve- or even eighteen-hour shifts that started at midnight; they were seeing the sun on only one day a week and they were getting rickets, bronchitis, emphysema. They were prostrated by exhaustion and they were not growing properly.

There’s no real reason to suppose conditions were better in the eighteenth century, but Charles Hutton was spared the very worst of it. There were schools in some of the local villages. Some pit villages had them, too, with practice varying seemingly from pit to pit: near-universal illiteracy at one; school provision built into the miners’ contracts at another. Hutton attended schools. He was bright, and neighbours were already saying the lad could go far, urging his parents to keep him at school. Kept in school he was: the hope of his family, even while his brothers went down the pits.

It must have made for some friction at home and in his village. The few pennies per day he would have earned on the trapdoors might not have been a real sacrifice for his family. But the fact that others were being prepared for a life in the coal mines and he wasn’t must have made for a difference, and not perhaps a pleasant one.

About this time Hutton injured his arm. The story he would tell many years later involved variously an accident or a quarrel with some children in the street. Nothing more than ordinary horseplay, perhaps, but by the time he confessed it to his parents the bone wouldn’t set properly, and it left him with a lasting weakness in his right elbow. Another reason to train his mind rather than his hands, at least for now.

A schoolteacher named Robson taught him to write, at a school a short step across the hill in the village of Delaval. Hutton may well have studied from a new, locally produced grammar book. Written and printed in Newcastle, Anne Fisher’s New Grammar promised to teach spelling, syntax, pronunciation and even etymology through its carefully graded series of exercises. Unlike other grammar teachers she kept it practical, and there was time set aside in her programme for taking dictation from a newspaper read aloud (the London Spectator was her preference) as well as spot-the-mistake games. Like every textbook author, she hooked her learners with aspirational promises. By the time you were done, she said, you’d be able to write as correctly as if for the press, engage in polite and useful conversation, and compose a properly styled letter to any person of quality. London and its cosmopolitan values were never far from her thoughts. Yet she had her other foot firmly in the North, and her correct pronunciation was a distinctly northern one. Say the following words, she advised, as though the o was a u: Compasses, Conjure, London.

As well as his schooling, young Hutton was indulged with pennies for books of stories, and – perhaps more precious – time in which to read them. He was fond of the so-called ‘border ballads’, the traditional songs of north Tyneside and the Scottish Borders: True Tom and his visit to Elfland, Tam Lin and his rescue from the fairies. By his early teens one of his lifelong habits was already in place: book collecting.

The routine of these years was disrupted more than once by events from outside the North-East. In September 1745, when Hutton was eight, the southward march of the Bonnie Prince and his army sparked panic in Newcastle. Some citizens hastily signed a pledge of loyalty to King George. Others spent their time walling up the town gates and mounting cannon to repel the Jacobite horde. Some fled from the northern villages to the dubious safety of the town. Others fled further south with all they could carry.

The events developed as farce rather than tragedy as far as Newcastle was concerned. Charles Stuart and his army came nowhere near; they took a western, not an eastern route down through England. The gates were unbricked, the cannon dismounted, and the King’s soldiers moved on. People came back to their homes and their work, some of them presumably feeling rather shamefaced.

One eyewitness to the ’45 in Newcastle was a visitor whose presence would ultimately wreak rather more upheaval, both for Newcastle and for Charles Hutton. John Wesley first visited the town in 1742. He was one of the middle-class commentators who was shocked by the drunkenness, cursing and Sabbath-breaking he found there, and he considered the field ripe for his mission.

He preached in the fields, and he preached in the churches, including the Huttons’ old parish church of St Andrews (where he found the congregation notably well-behaved). He visited some of the pit villages, and preached there too. Over time, Newcastle became John Wesley’s northern headquarters, the third point of a triangle whose base was London and Bristol, and he would visit again and again over the years.

The founder of Methodism was a small neat man in a gown and bands; he had been an Oxford tutor and he was good at calm, reasonable argument. But he had also been in the mission fields in North America, and he knew how to reach his hearers’ hearts, with an explosive combination of plain language and restrained rhetoric.

The results were extraordinary, with people crying out from a piercing sense of their sins or falling down in dread of the wrath of God. The dramatic personal changes, or some of them, lasted long after Wesley himself was gone. Charles Hutton was deeply impressed – he started to think of himself as a Methodist, and to call himself one.

It wasn’t about leaving the Church of England: that came much later for Wesley’s supporters. But it was about reinventing yourself and your relationship with God: about getting a new sense of what a life and a self could be. It was Christianity made both primitive and experimental, with doctrine founded on scripture, experienced and confirmed emotionally, and integrated into your personal habits, into who you were both internally and visibly.

Several of the anecdotes we have about Charles Hutton in his youth are concerned with his piety. He threw away his collection of profane stories. He built a cabin in the woods where he could pray on the way to school. He read devotional tracts. Time would eventually lower the temperature of Hutton’s enthusiasm, but he would remain a follower of Methodism – later shifting towards Unitarianism – until his thirties.

Some of the practical characteristics he gained at this time he would take to his grave, and they laid the foundation of much he achieved as an adult. ‘Never be unemployed for a moment,’ wrote Wesley; ‘never be triflingly employed.’ Charles Hutton would retain into old age a reputation for the good ordering of his time and his thoughts. Hard-working, self-disciplined, cheerful yet grave, and gifted at organising both ideas and people, he could have been a model for such works as Wesley’s Character of a Methodist. But perhaps the most important lesson Charles Hutton took from Wesley was that you could reinvent who you were, remake your mental world and your character. You could forge a destiny of your own choosing, both in the next world and – perhaps – in this.

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.

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.

3
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.

Now that they have disappeared, it’s hard even to imagine them, but in their heyday there were a dozen or so monthly or annual magazines whose purpose, or one of whose purposes, was to print mathematical problems and readers’ solutions to them. Construct a triangle given its base, one adjacent angle, and the line bisecting the opposite angle. Find a fraction with the property that, if you subtract its reciprocal, you get a square number. How many ways can you make fifteen from a pack of cards? This was not Sudoku, and it was not elementary arithmetic. The problems could be hard, using lots of algebra and geometry and sometimes even calculus. Since both problems and solutions were sent in by readers, an inevitable show-off effect meant that over time the problems tended to grow harder, the solutions more elaborate.

Despite the difficulty of the mathematics, the magazines sold plenty of copies: thousands, even tens of thousands. At any one time there were probably several hundred readers contributing their problems and solutions to them: it’s hard to say because, intriguingly, anonymity was the norm. Your name appeared in print only if you specifically said it was all right to print it. The writers were teachers, practitioners, gentlemen and women enthusiasts, schoolboys. They called themselves ‘philomaths’, and they loved mathematics for aesthetic and moral reasons as well as because it was, for many of them, a lifeline to a wider world of culture and ideas than they would ever reach otherwise: a world in which mathematical competence was everything. The austere language of mathematics was a very good place in which the shy, the modest and the provincial might both hide and shine, while allowing working-class and female mathematicians to contribute, perhaps anonymously, without being labelled. It enabled them to interact in a controlled way with people all across the country, to display what they were good at, improve their skills, lighten their countrified boredom.

Hutton approached this printed world under the tolerably transparent anagram of Mr Tonthu. Close to home, there was a mathematics column in the weekly Newcastle Courant, but he didn’t touch it. Instead, starting in December 1761, he sent in a string of able, elegant solutions to problems in Martin’s Magazine of the Sciences. (Benjamin Martin was a schoolmaster, lecturer, optician, seller of mathematical instruments, author, editor and tireless self-promoter: he issued his magazine monthly from 1754 to 1763.) He also appeared as the proposer of four questions of his own.

After two years Hutton/Tonthu became more ambitious: five of his solutions were printed in the much more prestigious Gentleman’s Diary, an annual compilation devoted to mathematical and other puzzles, and reputedly the home of the hardest of the philomaths’ problems. Hutton’s questions included equations to solve, geometrical constructions, and formulae for trigonometric expressions. Then he felt it was time for a fresh start under his own name, and the world heard no more of Mr Tonthu after 1763.

This time he aimed right at the centre of philomath culture: The Ladies’ Diary. Set up in the first decade of the century to contain charming little anagrams and easy mathematical problems in verse, the Diary had become under a series of editors the queen of the philomath journals, its four dozen pages containing – as well as an astronomical almanac for the year – problems as many and as hard as any of them. Some of the contributors were women, or pretended to be, but it had become primarily a place not to engage in genteel discussion of mathematics but to display high-level, up-to-date skills. Indeed, as an attempt to make mathematics a subject of polite public discourse it had by mid-century failed; like philomath culture as a whole it had become another instance of mathematics’ tendency to exclude and therefore to be anything but polite.

Visibility in this world was a prize worth having, and Hutton seized it. Over a decade from 1764 to 1773 he sent The Ladies’ Diary a total of fifty-seven correct solutions, of which twenty were printed in full. He answered the prize question correctly on five occasions: prizes were determined by lot and he won a total of twenty-eight free copies of the Diary for his pains. He also proposed four questions for solution by others, though two of them proved to be rather too hard and no correct solutions were received except his own. Still, if you were a British philomath in this period, you most certainly got to hear about Mr Charles Hutton of Newcastle.

Hutton would later write that an advantage of the mathematical correspondence promoted by The Ladies’ Diary and its sisters was that ‘considerable additions are made to the stock of mathematical learning in general, as well as to the particular knowledge of individuals’. Behind the scenes, he was finding other ways to add to his own stock of mathematical learning. Having already attended the schools of Hugh James in Newcastle and Mr Robson at Delaval, once in Newcastle he embarked on a systematic, historically motivated programme of mathematical reading, covering the Greeks, Romans, Spaniards, French and Germans as well as British mathematical writers.

During 1763 he distilled the fruit of his reading and his teaching experience – all six years of it – into a short textbook on arithmetic. The School-master’s Guide was published in Newcastle on 3 March 1764.

Its subject was just what Hutton had been teaching: elementary arithmetic, beginning with addition, subtraction, multiplication and division. The book continued with proportional reasoning in all its diversity and how to find square roots and cube roots. There was little more: one of the selling points of the book was its spare, uncluttered approach. Yet the careful control with which Hutton increased the complexity of his examples, and his penchant for introducing new tricks, rules or exceptions midway through what looked like routine series of examples, certainly kept things interesting. We gain a sense of what Hutton’s teaching was like in person: agile, thoughtful, tremendously well organised. Whatever exercise is being done, there’s always a slightly harder version of it just over the page.

Indeed, one of the reasons for the Guide’s success was the clarity with which it presented Hutton himself as a safe, sure, capable guide to the tricky territory of beginners’ arithmetic. Here was a man who loved calculation, who was almost preternaturally good at it. A man for whom common sense would unproblematically tell whether an answer was reasonable or not, for whom number sense was – as a matter of course – good enough to use obvious simplifications when the numbers in a calculation suggested them. For whom long division could be done largely in your head after a bit of practice: ‘when you are pretty ready in division, you may, even in the largest divisions, subtract each figure of the product as you produce it, and only write down the remainders.’

There were a few missteps in the Guide, indeed, when things were evidently clear to Hutton but he was unsuccessful in setting them out lucidly in words. Some of his attempts to give verbal equivalents of algebraic rules would have been scarcely comprehensible without the help of an able teacher. Some of his special tricks complicated more than they simplified: if a multiplier is itself a product, multiply by its factors separately. If it’s not a product, find a nearby number, multiply that, and then correct the answer by adding or subtracting.

But ultimately the aim of all his rules, tricks and practice examples was to impart to students something of his own feel for numbers, to help them develop a number sense and be able to select the right calculatory process even in an unfamiliar situation. And in that he appears to have succeeded.

Hutton moreover took pains to come across as a humane man, one who knew that children would get things wrong, that ‘calculations of the same accounts made at different times will sometimes differ’, that some pupils were simply not fitted for difficult calculation or found it off-putting. He drew on a wide range of personal knowledge to help the mathematics mean something to his students. Examples adopted almost every imaginable viewpoint: the workman who must get his quantities of material right; the factor who must manage multiple accounts dextrously; the substantial landowner who would redesign his bowling green or compute the value of his shipping interests discounted against time or loss.

Not surprisingly, it was the perspective of the merchant that returned again and again, and international trade was seldom far from view: 30 barrels of anchovies, 71 hundredweight of tobacco, 5 chests of sugar, 3 barrels of indigo. You can almost hear Hutton telling his students (and their parents): See how useful mathematics is, how rich it can make you, how much it can transform your life.

Writing a book was a much bigger step than sending in problems and solutions to magazines, and it demanded much more care. Blunders now would be costlier than wearing an embarrassing garment in a pit village. For the first edition Hutton paid for the printing himself, meaning that he alone bore the financial risk in case the book failed to sell. His patron Robert Shaftoe in fact contributed to the cost in return for the book’s dedication to him. The book was produced by a local print shop, with Hutton reputedly cutting his own type with a penknife when the shop didn’t have the fractions or algebraic characters the book needed.

The Guide was advertised in a number of newspapers, but of direct reaction there was practically none: no reviews, no comment in the press. It faced stiff competition. Even within Newcastle there were other mathematics textbooks being promoted, and other mathematical authors longer established and better known. The Banson dynasty, who dominated the city’s Free Writing School, had been publishing their own arithmetic books since 1709, most recently in 1760. Another northern author had an ‘easy introduction’ to mathematics out in 1763.

Despite that, the Guide found a market. We don’t know how many copies were printed, but a decent stock had sold out within a year or so, and Hutton managed to interest a London publisher in bringing out a second edition. This was good news, and ensured a much wider circulation for the book, this time at no financial risk to the author. His growing reputation was doing its work. By the time of the third edition, in 1771, the advert could say that the little book had ‘been found … useful in schools all over the kingdom’. The Guide, in fact, would run and run: it was still in print in the 1860s. The name of Charles Hutton was becoming harder and harder to avoid if you were interested in mathematics and its teaching.

Contacts in London made a huge difference. After the Guide Hutton devised a new, more ambitious publication project: a book on mensuration. This could have been a subject for another slim textbook on the model of The School-master’s Guide. But Hutton had something much grander in mind. Not a little book of practical rules but a veritable encyclopedia covering every aspect of geometry and its practical use. Hutton took to riding over to the village of Prudhoe at weekends to consult with the schoolmaster there, a Mr Young, who coached him in advanced geometry and mensuration and, it was said, worked over drafts of his new book with him.

Announced in the Newcastle papers in December 1767, Hutton’s Treatise on Mensuration appeared in twenty-eight instalments between March 1768 and November 1770. His publisher diligently promoted it in a range of national and local newspapers. Hutton undertook his own publicity campaign, writing personally to a long list of philomaths culled from The Ladies’ Diary and elsewhere. He obtained permission to dedicate the book to the Duke of Northumberland.

The results were spectacular. When the Mensuration appeared as a single collected volume at the end of 1770, the list of subscribers contained more than six hundred names. Probably amounting to more than half the active mathematicians and lovers of mathematics in the United Kingdom, from Penzance to Dundee, they included two dukes, one earl, and astronomers from Oxford University and the Royal Observatory. Both the English universities and most of the Scottish ones were represented, as were surveyors and instrument makers, schoolmasters and country curates, surgeons, excise officers and Fellows of the Royal Society.

This was self-publicity on a scale rare in Hutton’s century, or indeed in any. A good deal of money was involved – 600 subscriptions at fifteen shillings a book were not to be sneezed at – but the visibility had a value that could hardly be measured. It was rapidly becoming impossible to do mathematics, to like mathematics, to be aware of mathematics in Great Britain without knowing Charles Hutton’s name. Hutton was well advanced on the road from provincial schoolmaster with a taste for mathematical puzzles to national celebrity. He was aware of the change himself, of course. Throughout the 1760s he called himself ‘schoolmaster’ or ‘writing master’, but by the 1770s his title pages proclaimed him ‘author’; in 1772 he would switch to ‘mathematician’. And while Tonthu had been ‘of Newcastle’, Charles Hutton could call the town coldly ‘that part of the country in which I reside’, implying choice, impermanence, a lack of decisive ties to his provincial life.

What the subscribers to the Mensuration got for their money was a fat book which, despite a title that associated it with practical matters, was in fact a comprehensive treatment of theoretical as well as practical geometry – a substitute for Euclid’s Elements, indeed, as far as geometry was concerned. It began with definitions (‘A Line is a length conceived without breadth’), and it ran all the way up to the volumes of polyhedra and the areas contained under algebraically defined curves. Most of the book consisted of increasingly complex geometrical problems with rules for solving them: to find the area of a semicircle; to find the volume of a segment of a sphere; to find the surface area of a hyperboloid. Compared with the Guide, the emphasis was much less on carefully graded examples and much more on comprehensiveness, on a solid, gap-less treatment of a large body of material. It explained how to find the areas and the volumes of certain shapes and solids; how to construct certain curves and surfaces such as those arising from slicing a cone, or from rotating the conic sections that resulted (‘A conoid is a solid conceived to be generated from the revolution of the parabola or hyperbola about the transverse ax[is]’).

There was elegance and beauty here; there was also a tremendous display of learning. Hutton regularly succumbed to the temptation to exhibit his own cleverness at the expense of relevance or logical structure. Some of the more advanced, more difficult or more important solutions were backed up by proofs given in footnotes – and sometimes the footnotes were long, elaborate, even showy. Attached to a problem about right-angled triangles he indulged in not merely a demonstration but a ‘General Scholium’ (the term irresistibly recalls Isaac Newton’s use of it in his magnum opus, the Principia Mathematica) with ‘some new theorems concerning the relations of the sides and angles of triangles’. These derived from infinite series – never-ending algebraic formulae – for the sine of an angle. A problem aimed at finding the circumference of a circle from its diameter and vice versa occasioned a note which set out the history of infinite series for the circular ratio from the seventeenth century onwards. Finding the length of part of an ellipse became the occasion for another, typical burst of complexity, with the full apparatus of geometry, algebra and calculus deployed to provide five different ways of solving the problem. Passages like this give an impression of extraordinary authorial dexterity: partly because they seem slightly out of place, obtruding upon the reader’s notice.

So this book, like the Guide, carefully fashioned Hutton himself. As seen in the pages of the Mensuration, he was a technically dextrous, extremely well-read mathematician, who could quote thinkers of the calibre of Newton as easily as obscure practical manuals of gauging and surveying. He was entitled to expect a lot of his readers: introducing calculus without explanation, stating rules without proofs because they were ‘too evident’ to need it, demanding faultless skill in imagining three-dimensional shapes and their manipulations.

But this was also someone who knew all about mathematical practice. The final section of the book turned to the practical applications of geometry, and worked through lengthy rules and examples for surveying, gauging liquid volumes, and measuring roofs, windows and chimneys. Hutton went to some trouble to emphasise his experience as a surveyor; in fact his first, last and only published survey – a map of Newcastle – appeared in the same year, 1770. He suggested improvements to practice, dismissed some instruments and praised others, and casually remarked on the best way of operating in certain situations. He urged the use of decimal, not duodecimal arithmetic by measurers, and he lambasted sellers of timber for their sharp practices, at rather petulant length (Hutton must have had a bad experience on this score; he wrote a letter to one of the Newcastle papers about it too).

This practical section culminated with the imagined exercise of planning and building a house. With columns at the front door and over six hundred feet of plaster mouldings, maybe the imagined house, a smart, ambitious Georgian edifice, bore some resemblance to the real one Hutton had planned and built for himself on Westgate Street.

Not everyone was convinced by Hutton’s posturing. There were some poor reviews in the London papers, by anonymous authors whose objections centred on his pretensions to practical knowledge. By and large, though, the reaction seems to have been positive. And the Mensuration stood the test of time; it would run to four editions, remaining in print until 1812. As late as 1830 a supporter would call it the work of a ‘masterly hand’, still ‘by far the best treatise on mensuration’ published in any country. One reader in Shropshire broke forth in verse to express his admiration:

O Science! trade and commerce are thy end,

By thee we import, and by thee we vend;

By thee we build our houses, till our lands,

And weigh and measure with unerring hands.

What art or rules could never yet display,

Nor all the rules of Science till this day

Were able to disclose [by] genius’ force,

Thy true-born son hath traced to the Source.

Newcastle bridge in ruins.

Hutton’s daily round of work must have been frenetic during these years in Newcastle around 1770. To teaching and administering a school, together with a continuing programme of reading and self-improvement, were now added the demands of writing and seeing through the press a steady flow of publications. Mathematics is hard to proof-read, and a geometry book like the Mensuration also required hundreds of diagrams to be commissioned and checked. A young Newcastle engraver named Thomas Bewick, subsequently a celebrity himself for – particularly – his engravings of birds, did some of his first work on the Mensuration, and he remembered that Hutton frequently came into his work room to inspect what he was doing. Despite Hutton’s increasingly assertive public persona, he found him ‘grave or shy’ in this private setting.

Hutton remained capable of a misstep. Late in 1771 the bridge at Newcastle was partly destroyed by a flood, massively disrupting travel in the city and the area. While an inquiry was taking place and before a replacement had been decided on, Hutton rushed into print – it’s hard to see how he got the text through the press as fast as he did – with a 102-page book on the theory of bridge building. It was an able, even a learned work, full of geometrical diagrams and cutting-edge mathematical analysis using some very clever calculus; the voice was recognisably the same self-confident mathematician of the Mensuration. The chief problem tackled was to find what shape the upper curve of a bridge should be for a given lower curve – or vice versa – in order to ensure its theoretical equilibrium. Hutton found some neat results and expressed a decided preference for a curve of his own invention, related to the catenary (the shape of a hanging rope or chain).

All this was very well, but as the reviewers were quick to point out, few people could have been less qualified than Charles Hutton to lay down strictures about how a bridge should be built. He had no practical knowledge of structural engineering, and his mathematical analyses both contained elementary technical errors and displayed total ignorance even of the actual shapes of bridges. His formulae produced absurd results, demanding a bridge of infinite thickness in some cases. ‘We are at a loss to account for the author’s design in presenting this work to the public,’ concluded one. If that stung, and if Hutton regretted his rush into print, his reputation by this point could stand the damage.

Another large project was already in hand, too: a cheeky scheme to reprint The Ladies’ Diary itself. What better way to appeal to the philomaths of Britain? Hutton proposed a five-volume collection featuring every puzzle, problem, question and answer that had appeared in the Diary since its foundation in 1704.

It was a finely judged plan. Older copies of the original Diary were hard to come by – some issues extremely so – and as long as the price was right most of the hundreds of British philomaths could be relied on to purchase this collected edition of their favourite reading. Yet it would involve very little work: simply transcribing and very lightly rearranging the text from seventy slim pamphlets. Hutton even engaged an assistant to do the actual editing. (George Coughron’s was an interesting story in itself, but a tragically short one. Son of a farmer, good at mathematics, he won a national mathematics competition sponsored by the British Oracle and moved to Newcastle, where he fell in with Hutton, perhaps a little in awe of the older man – he was twenty to Hutton’s thirty-five. Their collaboration was not to continue past the Ladies’ Diary project, and Coughron fell victim to smallpox in 1774.)

Hutton added more extra matter to his Diarian Miscellany than might have been expected. It was issued in quarterly ‘parts’, and to each he appended a selection of new mathematical essays and correspondence. In true philomath style he also included a set of questions each time: readers’ answers to be printed in the following issue.

Hutton’s associates Coughron and Fryer themselves made contributions, as did a range of big names in the philomath world and a number of other people who were probably Hutton himself: ‘Nauticus’, ‘Geometricus’, ‘Astronomicus’ and ‘Analyticus’. He felt confident enough to admit to some errors in his Mensuration. But the problems column never really took off, perhaps because the market was already so crowded.

Nevertheless, Hutton found plenty of buyers for the Miscellany: it came out in slim ‘parts’ between July 1771 and July 1775. His publisher once again pushed the project hard, taking out advertising space in the national papers for every one of the thirteen separate parts.

So good was the idea that someone tried to copy it, and Hutton found himself with a rival. Samuel Clarke launched a Diarian Repository in 1774, printing just the mathematical items from The Ladies’ Diary and leaving out the other puzzles, and there was an undignified flurry of adverts and counter-adverts in the press. Hutton thought the work defective and took to calling it the ‘Repository of Errors’, but he was badly rattled by the incident, and matters were not helped when a couple of the numbers of his Miscellany were delayed at sea by bad weather; printing in Newcastle for distribution from London had its perils. But Hutton won the day. Clarke’s Repository abruptly ceased to appear, some months before reaching completion.

When Hutton’s Miscellany was printed complete in 1775, the collection made a handsome set of five neat volumes for which the publisher asked one pound nine shillings. The new matter took up an extra volume by itself, and was separately titled – a little pompously – Miscellanea Mathematica. Well indexed, the Miscellany became for some decades the standard reference for The Ladies’ Diary and its problems and contributors, and it incidentally contributed much to the Diary’s accessibility to modern historians.

Up to this time – the early 1770s – it’s not clear that Hutton’s relentless self-promotion in print had any very definite object. There were a number of relatively prestigious mathematical appointments available in Great Britain, including teaching jobs at institutions like the Royal Mathematical School at Christ’s Hospital, or the public lecturing posts at Gresham College in London. The chairs at Oxford and Cambridge were not realistically open to someone without a university degree, but a position in one of the ancient Scottish universities might have been possible with the right use of Hutton’s personal network. If he explored any of these possibilities, no trace of it has survived.

What happened in fact was a little more surprising.

Hutton was in London on Mensuration business when he heard from a friend – Edward Williams of the Royal Artillery – that an unusual job was open. John Lodge Cowley, professor of mathematics at the Royal Military Academy at Woolwich, had retired due to declining health. The job attracted two hundred pounds a year and a house at the Academy. Plenty of people wanted it, and quite probably some of them knew some mathematics. The official in charge – George, Viscount Townshend, Master-General of the Ordnance – reckoned it would be a good idea to fill the post with a man of ability rather than a well-connected nonentity. He had taken the rare step of announcing a public competition, giving it to be understood that ‘merit alone’ would decide the result. Advertisements had appeared in the newspapers.

Williams urged Hutton to present himself as a candidate. Back in Newcastle his supporter Robert Shaftoe did the same, and Hutton let himself be persuaded. In May 1773 he travelled back to London to take part in the supposedly impartial competition.

Merit alone? ‘Merit is useless,’ wrote Horace Walpole, ‘it is interest alone that can push a man forward. By dint of interest one of my coach-horses might become poet-laureate, and the other, physician to the household.’ There were increasingly meaningful public examinations at the British universities during the eighteenth century, and it was not absolutely unknown for public appointments to be made on a competitive basis. Expectations about public life and the right use of patronage were changing, after all, but they were changing slowly.

So the candidates for Townshend’s ‘impartial’ examination turned up armed with the usual array of recommendations from noblemen and politicians: testimonials, promises of favour or reminders of favours owed. Hutton would later claim that he himself competed ‘without any interest’. But in reality he too took his precautions. He obtained a recommendation from his acquaintance the Duke of Northumberland, to whom he had dedicated his Mensuration. Northumberland was a prominent Tory, a colliery owner and a Fellow of the Royal Society, and he controlled seven votes in Parliament. Through Robert Shaftoe, Hutton also obtained a recommendation from the Earl of Sandwich, a Whig (the party was in power at the time) who had been First Lord of the Admiralty; to Master-General Townshend his was probably a louder voice than Northumberland’s. Having covered both political bases, Hutton finally equipped himself with a letter from the prominent northern mathematician William Emerson, testifying to his intellectual abilities. Thus protected, he faced the examiners.

Theirs were names he knew, but none was even an acquaintance. Three, however, were men you had almost certainly heard of if you had any contact with the British scientific and mathematical scene. Nevil Maskelyne was the Astronomer Royal; Samuel Horsley a member of the Council of the Royal Society; John Landen a highly regarded mathematical author and Fellow of the Royal Society. The fourth examiner, representing the military side, was Henry Watson, a military engineer with experience from Havana to Bengal as well as a contributor to The Ladies’ Diary and a friend of and literary executor to its former editor.

They started by examining the candidates viva voce. It was a stiff competition. Other candidates included Benjamin Donne, Master of Mechanics to the King, and Hugh Brown, translator of major works on military mathematics. (There were at least six candidates in all, but Hutton’s telling of the tale seems to have grown over the years. The obituaries have him facing down a field of nearly a dozen.)

The questions ranged across the entire field of mathematics, its history, what the best books were on certain subjects, and how best to teach it. When the first day was over the examiners handed the candidates a set of deliberately abstruse written problems in mathematics and natural philosophy, telling them to come back at the end of the week with whatever answers they could manage.

A persistent rumour – it was still circulating in 1825, after Hutton was dead – said that Hutton, away from his books and his friends, struggled with the written questions, and visited the Duke of Northumberland in London in some despondency. The Duke, so the tale goes, got the examiners to provide a new, fairer set of written questions. Even if that is true, it must have been a tough week, wrestling with the problems all day for several days before finally writing up whatever answers one had been able to obtain and turning them in at the end of the week. And Hutton must have spent a tense weekend in his London lodgings waiting for the result.

It came on Monday. The examiners reckoned that most of the candidates were sufficiently well qualified to do the job and had given complete satisfaction as far as the written and verbal questions were concerned. But they felt compelled to single out Hutton for particular recommendation, on account of the exceptional strength of his performance. The Board of Ordnance ratified their decision on 25 May. And so patronage and merit worked together (as they sometimes did) and Charles Hutton became Professor Hutton, of the Royal Military Academy at Woolwich.

For Hutton it would be the biggest single change since he left the coal pits. And it all happened with furious speed. In less than a fortnight the school in Westgate Street was to let; in six weeks it was taken by John Fryer, Hutton’s former assistant. He advertised that he intended to keep up the teaching ‘in the same Manner as practised by Mr Hutton’, and had hopes of retaining Hutton’s students as his own.

And Hutton himself, after a brief visit to put his affairs in order, was gone from Newcastle. He would never visit the region again.

The coach journey – three days and two nights – had nearly shaken him to pieces on previous trips, so this time at least he made the journey to London in the different style offered by sea travel. It might take a couple of weeks, and he perhaps reflected that this was the same route that took so much of Newcastle’s other produce to the capital. Almost a million tons of coal sailed from Tyne to Thames annually, the ships crowding the two rivers. In June 1773, so did Charles Hutton.

4
Professor

Woolwich. South of the Thames, east of the City of London. The ‘Warren’. Rabbits were bred there in the Middle Ages, and by 1773 it’s an apt name once again. The teeming site is now Britain’s biggest munitions manufactory, its largest ordnance store.

Five hundred people working in a hundred acres. The closest thing in the Georgian world to a modern factory. Warehouses, workshops, laboratories, furnaces. A canal, a barracks, a parade ground. The Royal Artillery is quartered there; so is its cadet company. So is its band.

It’s loud; it’s dirty, dusty, smoky. The smells of gunpowder, its smoke and its ingredients hang heavy in the air: sulphur, saltpetre and charcoal. A harsh, confusing landscape, security-conscious and alienating to outsiders. Not so different from the collieries, perhaps.

There were two sides to the change in Charles Hutton’s status. He was no longer a member of that despised class the provincial schoolmaster, with a merely de facto high standing among British philomaths. His status was no longer based solely on his own furious efforts at self-promotion. He was no longer vulnerable to catastrophe the moment the fashion in Newcastle schools changed or a rival published a cheaper textbook. He was now a man who had received public recognition for his talents and his hard work, in the form of a teaching appointment in an institution of national significance.

On the other hand, Hutton had left a situation as absolute lord and master of a thriving business and had become an employee. He had changed from headmaster to ordinary teacher, and, what was more, he was becoming a civilian employee in a military establishment. He would have to work with a new set of colleagues and teach a new kind of pupil. He would have been less than human had he not experienced moments of doubt about what he was getting into during the summer of 1773.

First impressions were certainly discouraging, and in some ways Hutton retained mixed feelings about his new situation for years, as his letters show. The Royal Military Academy occupied a few rooms in the bustling military installation at Woolwich, downstream from the city of London and on the opposite side of the river. Docklands territory today, it was then barracks, ordnance factory, munitions depot and more. The dockyard went back to Henry VIII’s time, ordnance testing over a century. There was a laboratory for making gunpowder and a foundry for making ordnance and shot. By the mid-eighteenth century the ever-increasing collection of buildings and activities was straining the limits of possibility. Laboratory, arsenal stores and ordnance testing were much too close together, and from time to time there were fires or unplanned explosions. The latrines stank. There was too little water to go around. The four battalions of the Royal Artillery would move out of the site in 1777, but the Academy – despite sporadic complaints and a serious attempt to find a new site in the 1780s – would remain at the Warren until the next century. Contemporary guidebooks tried to talk the place up, with varying success:

The Royal Military Academy at Woolwich.

In the warren, or park, where trial is made of great guns and mortars, there are some thousand pieces of ordnance for ships and batteries; with a prodigious number of shot, shells, and grenadoes, heaped in large piles of various forms, and which have a very striking and pleasing appearance.

Even today, with the mounds of weaponry gone and the site sleepy, and with a good map in your hand, it takes an effort to find the building in which the Royal Military Academy held its schoolroom. The two imposing floors by Vanbrugh had windows east and west to let the light all the way through, with one big high-ceilinged room on the top floors. There were also a barracks for the cadets and dedicated houses for the two principal masters, of whom Hutton was now number two. His house needed ten pounds’ worth of repairs, hastily carried out during the summer he arrived.

The human landscape was not much more encouraging. Hutton’s family didn’t at first accompany him to Woolwich, and his new colleagues were a somewhat sorry crew. The Academy had existed for over fifty years, with a formal king’s warrant since 1741, but it was proving hard to get the setup right. Reform after reform had taken place. Initially it was meant as a sort of regimental university, providing lectures to anyone in the Royal Artillery who chose to attend: officers, NCOs, cadets, all those associated with the regiment. A series of mid-century reforms had given it a more manageable role as a sort of superior school for the Royal Artillery cadet corps. There was now an inspector-of-studies, with military rank, to look after the daily running of the Academy, to oversee the curriculum and make sure it was being delivered. Above him stood the Lieutenant-Governor, who reported to the Board of Ordnance and its Master-General. (The Ordnance, by the way, was not strictly speaking part of the Army: it was structured and governed separately, which goes some way to account for the uniqueness of its Academy.)

Some of the teaching staff had never accepted the changes to the style of the institution, or the inspector’s attempts to regulate what was taught and how it was taught; possibly they preferred the idea of themselves as university lecturers to that of schoolteachers. The chief master, Allen Pollock, had all but declared war on the management, doing everything he could to make the inspector’s task difficult. In principle he taught the prestigious subject of fortification and artillery. In practice he increasingly tended to teach absolutely nothing. He lived miles away from Woolwich without ever receiving permission to do so, and it was his habit to appear literally hours late for his lessons, then waste more time shuffling his books and his papers. For every adjustment to his teaching duties he demanded a direct written order.

There were also masters for French, dancing, fencing and ‘classics, writing and arithmetic’. The first two struggled to command the respect of the cadets – to put it delicately – while the last, a Reverend William Green, followed Pollock’s lead in calculated awkwardness.

Gentlemen Cadets.

Hutton would have learned at least some of this over the summer, while his new house was being repaired and he was finding his feet after the upheaval of his move from the North. When the boys arrived after the summer recess and the actual teaching began, it may have been something of a relief. The cadets, numbering about fifty, were a well-dressed body of young men with a rather splendid uniform: blue coats trimmed with scarlet and gold; lots of lace, hair neatly queued and powdered.

They may have looked genteel, but they ranged in age from twelve to about nineteen, and there were predictable problems with their behaviour. Some ingratiated themselves with the masters, sending home for hams, hares, pheasants and other little gifts that might smooth their passage through classes and exams. Others indulged a tendency to riot. Orders and letters from the governor remarked again and again on matters of discipline, expressing futile outrage and lamely prohibiting misdemeanours after they had taken place. Cadets must not ill-use the masters, must not treat them with disrespect or insult them. They must not disrespect their superior officers, nor use indecent or immoral expressions. They must not wilfully destroy fixtures, bedding, furniture, utensils or windows, nor must they force locks or open or spoil the desks of the teachers or other staff. They must not ‘nasty the walls or chimneys’. They must not leap or run over the desks, nor climb out over the walls at night.

As the crimes escalated, so did the punishments. (‘The first Cadet that is found swimming in the Thames shall be taken out naked and put in the Guard-room.’) We read in mid-century accounts of solitary confinements, bread-and-water diets, imprisonments in a dark room, degradations and a few exemplary expulsions. In the long run, things improved, but outbreaks of quite serious violence remained more frequent than anyone could have wished. The constant presence of a duty officer in the classrooms had little effect. There was continued noise, hallooing, shouting; there was window-smashing, and ‘pelting’ of the masters. A lieutenant lost the use of his middle finger. A cadet spent three years on the sick list after a prank whose details he permanently refused to specify but which he steadfastly described as a piece of ‘fun’.

Charles Hutton was suddenly a very long way from the genteel sons and daughters of middle-class Newcastle: the grammar school boys and girls taking advanced mathematics lessons; the private pupils paying a few guineas extra for dancing classes and a few more for the course of lectures on astronomy. Yet his orders required him to teach the cadets, and to teach them a demanding curriculum that ranged across pure and applied mathematics. Teach it he would. The theory classes were on Mondays, Wednesdays and Fridays. Professor Pollock – if he bothered to turn up – taught the boys his notions of fortification and artillery for three hours in the morning; in the afternoon Hutton took them for mathematics from three till six.

Facing about twenty-five of the older or cleverer boys, grouped at least notionally into four graded ‘classes’, he covered Euclid’s Elements of geometry, killing two birds by using algebraic explanations wherever possible. Trigonometry as applied to fortification and measuring, such as finding inaccessible heights and distances, and using logarithms for the calculations if needed. Conic sections (the shapes you get when you slice a cone using a plane). Mechanics with reference to moving heavy bodies (such as pieces of artillery): levers, pulleys, wheels, wedges and screws. The laws of motion with reference, naturally, to projectiles. Calculus – ‘fluxions’, in the Newtonian rather than the Continental style – and whatever uses could be found for it. Much of this would have been familiar stuff from his Newcastle classroom, but the style of teaching still made it an exhausting round.

As in any other Georgian classroom, the boys were mostly at their desks, called forward one at a time or in small groups. Each boy did some exercises, showed them to the teacher, copied them and the relevant section of the textbook out fair: and repeated that round for the whole three hours. For Hutton it might mean fifteen minutes with one cadet on calculus; fifteen minutes with another on Euclid. Then algebra, then logarithms, then something else. He also gave periodic lectures – virtually the only university-style lecturing still taking place at the Academy – on geography and the use of those favourite pieces of eighteenth-century teaching apparatus the terrestrial and celestial globes: two hours every other Wednesday.

When they weren’t in the theory classroom, meanwhile, the boys were instructed on the other days of the week in the practical arts of gunnery: loading and firing the artillery pieces, and pointing them in the right direction; exercises in hitting marks. Various other practical matters: transporting burdens by making pontoons, floats or bridges; mortars and their use; trenches and mines: how and where; the composition of gunpowder; the names of the parts of a gun. Casting and weights of artillery pieces and shot. Handling of stores.

As if that wasn’t enough, from 1778 a separate building was set up as a ‘military repository’. Here the boys were taught the finer points of handling the equipment: mounting and dismounting ordnance, crossing obstacles, and ‘overcoming by resourcefulness difficulties which did not arise in the ordinary routine’.

As far as dangerous fun for boys went, this was infinitely more attractive than the classroom work, and the cadets were after all in training for a severely practical life as officers in the artillery or in some case the Engineers’ corps. On graduation at about eighteen most of the boys were at once commissioned as second lieutenants in the Royal Artillery regiment.

This, then, was the real stuff of an artillery officer. Cannon up to ten feet long and weighing up to three tons; iron balls moving at the speed of sound. Howitzers; mortars for lobbing shells high overhead. Roundshot, grapeshot, case-shot; explosive shells. The relentless drill of firing: four men at work, and every action had to be right every time or disaster would follow. Loader puts the charge down the muzzle, in its paper cartridge. Ventsman blocks the vent with his thumb, and spongeman rams the charge home. Ventsman pricks the cartridge, primes it with quickmatch in a tube pushed down the vent. Loader puts the projectile in the muzzle, spongeman rams it up against the charge. Run the gun up, point it at its target: traverse, align, adjust the elevation. Firer touches the vent with his portfire. The blast of several pounds of gunpowder, and an iron ball travels a thousand yards. Check the recoil. Spongeman sponges the barrel clear. Repeat. Furious speeds were possible; with a light gun seven rounds a minute could be achieved in an emergency: nine seconds from one shot to the next.

In alternate years the summer saw a full-scale attack upon a polygonal front built at Woolwich for the purpose, done ‘with all the form and regularity that is used in a real siege’. Trenches, batteries, mines made by the besieged to blow up the batteries, mines made by the besiegers to make breaches in the walls. Fortunately there was a well-equipped hospital on the site.

With all this going on, it may be no wonder there was a problem getting the boys to attend to their theoretical studies. Some of them at least itched to get away from the mathematics and the theory, and there were still in Hutton’s day at least some officers of the regiment who thought the whole Academy a waste of space. General Belford wished it disbanded, and in the late 1770s wrote a stinging letter to the Master-General of the Ordnance suggesting that instead ‘a number of fine young fellows [be] appointed as Cadets to every Battalion’, where they might do practical work and see real action.

He may have had a point. The long series of reforms and adjustments had made the Royal Military Academy an institution whose details were not easy to defend. Admittedly some kinds of knowledge were best acquired in a school-like setting, but why should an artillery officer need to know algebra, geometry, trigonometry?

But the training was not so much about what you needed to know as about producing a particular kind of man with a particular kind of mind. The Academy, unique and exceptional in some ways, was nevertheless part of a much more general eighteenth-century trend in English education. Mathematics and the sciences enjoyed increasing prestige at the English universities, with Cambridge in particular stuffing its curriculum full of Euclid and Newton to the oft-remarked exclusion of almost anything else. Newtonian mathematics, together with the philosophy of John Locke and the rational theology of such as Samuel Clarke, ‘went hand in hand through our public schools and lectures’, said one contemporary. Cambridge University’s official calendar, too, boasted specifically of the ‘many excellent lectures in mathematics’ delivered in the colleges. John Locke himself had written that mathematics was ‘a way to settle in the Mind an habit of Reasoning closely and in train … In all sorts of Reasoning, every single Argument should be managed as a Mathematical Demonstration.’ It enlarged the mind, instilled intellectual humility, and taught the habit of clarity in one’s ideas.

It was a similar picture at the so-called Dissenting Academies. These were advanced schools or mini-universities for those whose non-Anglican commitments excluded them from Oxford and Cambridge. By mid-century there were dozens of them, and they enjoyed a fine reputation, often teaching curricula based on mathematics and natural philosophy as well as logic and theology, sometimes with the specific intention of disciplining the mind, teaching logical thought and a reliance on pure reason.

So the Royal Military Academy was doing nothing very odd by filling its curriculum with more mathematics than any practical consideration demanded. It was doing what its managers and staff conceived as its clear duty: training and moulding young men in desirable mental as well as physical habits. Just as the duties of a gentleman officer required a knowledge of dance and a smattering of French, they required an acquaintance with the results and, more importantly, the methods of Euclid and Newton. It was a situation that suited Charles Hutton; in any debate about whether it was worth teaching boys geometry, algebra and the rest, there was no doubt which side he would take. Over the years he would become ever more committed to the cause of promoting mathematics, its usefulness and its beneficial effects on the mind. Indeed, the status and the national importance of mathematics would exercise him for much of the rest of his life in one forum or another.

As a teacher, meanwhile, he seems to have succeeded in catching the attention of the boys, and in winning them over to take seriously what he had to impart. His manner was cheerful, friends reported, but deliberate in expression; he himself reckoned gravity a part of his character. His voice was clear and firm, with a slight northern accent that he would keep to the end of his days. His mind (in good Lockean style), they said, was ‘accustomed to communicate its feelings with a sort of mathematical precision’. Hutton was remembered by his former students with respect, affection, even veneration. One cherished a commemorative medal of Hutton’s august profile to the end of his life. It was never Professor Hutton who got pelted in the street.

If the boys were won round to Hutton fairly rapidly, the staff were a tougher task. Pollock was going from bad to worse. The teaching staff were civilians; so, unlike an officer of the regiment, he couldn’t be court-martialled for disobedience. Reprimand after reprimand had no effect on his attendance or his willingness to deliver the course as the inspector conceived it: just more elaborate, sometimes legalistic excuses. He disputed the rules about where he was supposed to live, and the system by which certain parts of his pay were worked out. He disputed what he was supposed to be teaching and where the boundary lay between Hutton’s subject area and his own.

There was indeed a long-running question as to whether the curriculum should be determined by the Board of Ordnance (which paid for the Academy) or by the teachers who had to deliver it. And there was a more detailed question about how responsibility for the practical parts of mathematics – surveying and so on – should be divided between the Professor of Fortification and Artillery (Pollock) on the one hand and the Professor of Mathematics (Hutton) on the other. In both respects, sane compromises took some time to arrive at, and Pollock made himself increasingly ridiculous. Early in 1774 the inspector wished the more advanced boys to be shown how to take an angle of elevation with a theodolite or quadrant, and asked Pollock either to do it or to lend the instruments to Hutton. He refused ‘in a very haughty and imperious manner’ and added ‘that the Academy is not a fit place to mention those things’. He took to refusing to allow the inspector into his classroom, standing on a technicality in his written instructions.

Hutton as Professor of Mathematics also shared a curricular boundary with the Master of Classics, Writing and Arithmetic: William Green, another difficult character. For three days a week, while Hutton and Pollock were teaching the older boys, Green taught elementary mathematics and writing – and possibly some Latin – to the younger and less able. He received a smaller salary than Hutton and Pollock and taught in theory twice as many hours as they did, so he had some reason for ill feeling. And his duties were subject to repeated redefinitions during the 1770s, the teaching of classics being in part suspended at some periods and the teaching of writing theoretically unnecessary since illiterates were not supposed to be admitted as cadets. Harassed and dissatisfied, Green became irregular in his attendance, and eventually his permission to live away from Woolwich was withdrawn. His performance affected Hutton directly, since if Pollock taught the boys badly they would graduate to the upper academy, Hutton’s domain, inadequately prepared.

In this somewhat chaotic situation, Hutton could have thrown in his lot with the masters: done minimal work, obstructed the inspector and governor in their duty, and hoped to get away with it for as long as he could; although by the early 1770s it was tolerably obvious that dismissal was on the horizon for the erring Pollock. Or he could take the other path.

It wasn’t a hard choice, and indeed it wasn’t a hard task. In a way the situation was a gift to him. Merely by turning up regularly (and he was a punctual man) and actually delivering the nine hours of instruction he was being paid for each week, Hutton necessarily outperformed Pollock and Green – incidentally making them look worse than they did already. They resented it, but they could hardly stop him. The inspector was won over quickly, and Hutton was rewarded with a growing degree of power and influence that went beyond anything in the written instructions. There began the first of a very long series of organisational changes at the Royal Military Academy that reflected Hutton’s priorities and agenda.

Early in 1774 an entrance exam was instituted in consultation with the inspector and masters. Pupils should be ‘well grounded in the first four rules of Arithmetic, with a competent knowledge of the Rule of Three’, as well as some Latin grammar. It’s hard not to see Hutton’s hand in a change that would ensure the boys he had to teach weren’t utterly incompetent in his own subject. In theory the curriculum stood still, but there is no doubt Hutton was adjusting it to suit his notions, and by 1775 his Mensuration was a set text.

And, crucially, by the late 1770s it was at Hutton’s word alone that boys graduated from the lower to the upper academy. For the boys, graduation was a desirable thing in itself: a move from learning basic arithmetic and basic military drill to being taught advanced material by the two professors, introduced to the properly military subjects of artillery and fortification, and allowed to wear the full uniform and sword of the cadet company. Furthermore, promotion within the Royal Artillery and the Engineers’ corps – like the Navy but unlike the Army – was entirely by seniority, which meant that the date of passing one’s exams relative to the other cadets was highly significant, setting to some extent the course of an entire future career. With Hutton’s judgement now vital to the progress of cadets through the Academy, he became in some ways a very important man indeed.

Meanwhile, in 1777, Professor Pollock was pensioned off with an almost insulting fifty pounds per year. He tried to make one final fuss, but the Board of Ordnance wisely refused to be drawn into any argument about the matter.

Soon afterwards William Green brought to a head his resistance to what he evidently felt was an alliance of management and Hutton. He disputed Hutton’s academic judgement and demanded that a Mr Mudge, and certain other boys, be moved to the upper academy despite Hutton having failed them. He stated that they were more worthy than some who had been moved up, that they had solved several questions in algebra that members of the upper academy were unable to understand. He spoke of ‘much injustice’ and named several cadets.

This was a key moment for Hutton at the Academy; if Green’s complaint had been upheld Hutton would have looked absurd and his position would have been scarcely tenable. Perhaps not surprisingly, a board consisting of the governor, the inspector and the new Professor of Fortification and Artillery found ‘that Professor Hutton has done justice’.

After this vindication there was no doubting that Hutton was the de facto academic head of the Academy. In time the Professor of Mathematics ceased to be called ‘second master’ and became the first. There is no further report of questions about his academic judgement, or of challenges to his right to pass cadets from one class or academy to another. The notion that the teaching of mathematics and mathematical competence were at the heart of the Royal Military Academy had triumphed. Green, perhaps surprisingly, was brought round to accept Hutton, and the two worked together with no more outbursts until the older man retired in 1799.

Pollock’s departure, replaced by a congenial Frenchman named Landmann, might have marked the commencement of a period of calm for Hutton’s work at Woolwich. But the mid-1770s saw rather more than just a few schoolmasterish tensions come to a head. In December 1773 the Bostonians dumped ten thousand pounds’ worth of tea into their harbour. By April 1775 there was fighting in Massachusetts, and by 1778 the conflict was a global one; France became involved that year and Spain the next, making India, the West Indies and Central America into theatres of war. Hutton and his colleagues, suddenly, were training and approving young men for active, urgent deployment around the world, and their work took on a new character as a projection of British power across the globe.

Sixteen companies of the Royal Artillery participated in the American War of Independence. When Spain besieged Gibraltar in 1779 it created a particularly acute need; the siege was by its nature an artillerymen’s affair and five companies of the regiment were there from start to end. The Royal Artillery would receive a special message from the King when it was all over.

In consequence, the war created a sudden need for more graduates from the Royal Military Academy. And in a pattern that would be repeated in later conflicts, the institution coped poorly. Almost at once the shortage of suitable candidates became a matter of official comment, and the Academy came under intense pressure to increase its throughput of young men at almost any cost.

Public examinations were discontinued, replaced by private examinations in front of the governor, the inspector and the two professors. Boys were examined who had never been formally admitted to the Academy or the cadet company. The intention was naturally to pass as many as possible, but by 1780 it was being remarked that cadets were being hurried through the upper academy too fast and were graduating little qualified to hold commissions. Reports from one examination coyly stated that the cadets understood ‘a little Algebra, and a little Geometry’. But the expertise needed to handle ordnance effectively or even safely could not be created out of nothing just because need pressed. Permission was given for some notionally qualified second lieutenants to stay on at Woolwich for a further year in order to complete their studies.

Even in these conditions, when cadets were being pushed into and out of the upper academy with the minimum of ceremony or even propriety, the Master-General took time to note that new boys in the upper were on probation to Hutton. They were ‘neither to have their full uniform nor the allowance of one shilling a-day pocket-money until admitted by the Professor of Mathematics’. He was expected ‘to turn them back into the Lower School’ if they displayed insufficient diligence.

To add to the disruption, Green was asked to help out by doing some teaching in the upper school, delivering quadratic equations and practical geometry to those who needed it. The lower-academy students he would normally have been teaching were presumably neglected as a result, compounding the problem of students entering the upper inadequately prepared. In 1782 an assistant mathematics master was belatedly added to the strength in a more robust attempt to fix the situation, though it remained the case that the quantity of mathematical instruction being delivered was large in relation to the number of mathematical staff. At the same time a pay rise was awarded based on the number of days the different members of staff actually taught: it had the striking effect of making Hutton and Landmann, the new Professor of Fortification, better paid than either the inspector or the governor.

Discipline wasn’t improved by the disruption, and it made things no easier that the firm-handed Inspector Pattison was promoted to major general and posted to America in 1777. During the war years certain cadets were degraded for being ‘in liquor’ and the corporals of the cadet company collectively turned bad, threatening boys who had the temerity to outperform them academically. Cadets had to be forbidden to read ‘books of entertainment and newspapers’ during lessons.

Then in 1780 a rumour went around the boys that you would get a commission sooner if, rather than waiting to graduate into the Artillery, you got yourself thrown out of the Academy and had your parents obtain a commission in an Army regiment by purchase or interest. Result: a spate of boys courting expulsion. France having recently entered the war, the French master was their target of choice. Cadets threw stones at him while he was trying to teach and continued to pelt him with dirt and stones on his way home. The size of the stones is not recorded, but the incident had the character of a serious assault, not a prank. Those in charge at the Academy acted with unexpected wisdom. They duly expelled the leaders of the assault, then pardoned them.

Another indirect consequence of the American war was that convicts could no longer be transported to the North American colonies. From 1776 they were held instead in hulks moored in the Thames off Woolwich: three ships holding nearly two thousand men. Escapes were not uncommon, adding to the woes of the Woolwich site; on occasion gun battles ensued on shore before the convicts were recaptured.

The physical situation in Woolwich remained demoralising, not to mention unhealthy. Although the Royal Artillery itself moved to new quarters on Woolwich Common soon after the outbreak of war, the Warren site was still crowded with the ordnance and munitions installations and the cadets and their Academy. Water came from a conduit house in the superbly named Cholick Lane; by the later part of the century there was too little of it to go around. One officer received permission to move house on account of the ‘Horrid Smells’ from the latrines.

To the chaotic situation at Woolwich was added for a while an air of national panic: in the summer of 1779 a Franco-Spanish fleet was at sea with the intention of invading Britain. That threat came to nothing, but panic was replaced in the longer term by national demoralisation. As poor strategic planning and steady underestimation of the American forces took their toll, it became increasingly clear that coercive military action was not going to solve a problem essentially political in its nature: that the seceding colonies would not be forced into submission, and that their independence was an accomplished fact. By 1780 Britain was isolated against America, France, Spain and the Netherlands, and the British public was losing its sense of why the conflict should be prolonged. The famous defeat at Yorktown in October 1781 was decisive for political as much as for strategic reasons.

When the Peace of Paris came in September 1783, Charles Hutton had been at the Royal Military Academy for ten years. It had been a draining period for the Academy and everyone connected with it, and although Hutton had established a strong position in the institution, it had cost him much in effort and exhaustion. Prone to lung disorders, he also developed chronic headaches, and he took to walking on the Academy’s roof where the air was fresher. From there you could see the shipping on the river, and, to the south, the open country of Shooter’s Hill and Woolwich Common. You could also see the City of London, and dream of all that it afforded.

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