Gunpowder and Geometry Read online

  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.

  5

  Odd-Job Man

  Woolwich: the Royal Military Academy. Charles Hutton’s study. 13 January 1779. He’s in a gloomy mood.

  ‘I am here almost as recluse as a hermit,’ he writes to a northern acquaintance, ‘being almost single in my studies & manner of thinking in this place, my nearest neighbour in these respects being the Astron. Royal at Greenwich with whom I have the honour to be on very good terms.’

  As recluse as a hermit? What about his family?

  Hutton’s wife and children did not accompany him to Woolwich. His relationship with Isabella had broken down some time after the birth of their fourth child in 1769, and she never left the North-East.

  Hutton and his family were always coy about this, and most of his obituarists and early biographers did all they could to avoid telling the story; so it’s hard to say just what really happened. One Newcastle historian was indiscreet, though, and related in the 1820s that Hutton was initially accompanied to Woolwich by a different woman: an officer’s widow named Maxwell. Apparently he soon found himself obliged to dismiss this lady on account of her extravagant habits. That sounds slightly fanciful, and it was written many years after the fact by a writer whose sources of information are far from clear. It is certain, though, that within a few years Hutton was living with another woman. At least some of his friends knew Margaret Ord as ‘Mrs Hutton’ – although his first wife was undoubtedly still living – and in 1778 she bore him a daughter, Charlotte Matilda.

  Who was Margaret Ord? Born around 1752, she was in her twenties during Hutton’s first decade in Woolwich: eighteen years younger than Isabella. It would be interesting to know something about her background: how she compared with the first Mrs Hutton in terms of social rank, for instance. Unfortunately for the curious historian, Ord was not an uncommon name. There were Ords
in the Royal Artillery and a prominent family of the same name in Newcastle; the latter, indeed, were part owners of the Long Benton colliery where Hutton, once, had worked. There were three Fellows of the Royal Society named Ord around this time. Margaret could have been related to any of them; the fact is that we know nothing of her origins, nothing of where and how she and Charles Hutton met.

  Isabella remained in Newcastle and took to styling herself a widow, but by March 1776 Hutton’s son Harry was in Woolwich as a cadet at the Royal Military Academy. He graduated about a year later and went into the Royal Artillery. Hutton’s other children initially stayed with their mother, but by the early 1780s they too had moved to Woolwich. Just what had passed between them, their father and their mother we will never know.

  Not quite a hermit, then: by the end of his first decade at Woolwich Hutton headed a household consisting of himself, Margaret, and his four daughters ranging from twenty-one-year-old Isabella down to six-year-old Charlotte.

  But still, Woolwich was not London, and it could indeed feel isolated. You can walk to Woolwich from the City of London, but it takes half a day. You can shorten the time by riding, or take a boat; to row from the Tower of London down to Woolwich took a couple of hours. In time, Hutton took to renting a set of rooms in the city, at one of the Inns of Court, and spent a couple of days there every fortnight, judging that that made the best use of his time.

  Much of Hutton’s time was in fact his own, since his teaching filled only three afternoons each week. He took every opportunity he could find to fill that time by doing extra work and making new professional connections. He was, and would always remain, a superb networker.

  Nevil Maskelyne.

  A couple of miles up the river, at Greenwich, lay the Royal Observatory. This was the domain of the Astronomer Royal, Nevil Maskelyne, who was a member of the committee that examined the candidates for the Woolwich job and selected Hutton. And as Hutton put it in his letter of 1779, Maskelyne was his closest scientific neighbour. As early as September 1773 Hutton was corresponding with Maskelyne’s assistant Reuben Burrow, lending books back and forth, and soon Hutton was on good terms with the Astronomer Royal himself. They would remain close until Maskelyne’s death; an obituarist reckoned Hutton among Maskelyne’s ‘most intimate friends’.

  Honest and popular, Maskelyne was a key member of the London scientific world. By the mid-1780s Hutton was sending him drafts of his papers to look at, and on occasion detailed comments from Maskelyne found their way into the published versions of Hutton’s books. Hutton acknowledged Maskelyne’s ‘generous advice and assistance’ with a dedication to him in 1785.

  One of the projects in which he involved Hutton arose from his role on the Board of Longitude. The board existed to assess – and potentially to reward – schemes for finding the longitude at sea, a problem whose unsolved state was leading to losses of life for Britain and for every nation engaged in more than coastal seafaring. Maskelyne had a scheme of his own for finding the longitude: to use the moon’s predictable motion across the background of stars – or relative to the sun – as a sort of clock. Starting in 1767, with the blessing of the Board of Longitude, he oversaw the printing of tables of the moon’s position in the sky up to several years in advance, under the title of The Nautical Almanac and Astronomical Ephemeris. If you observed the moon’s position and compared it with the table of predictions, you could deduce exactly what time it was. Knowing the exact time, an accurate look at the apparent position of the sun or the stars would tell you where you were.

  The annual books of tables cost two shillings and sixpence; you also needed an instrument for observing the moon – a ‘Hadley’s quadrant’ costing eight pounds or so – and a two-shilling book of extra tables. The calculations could be reduced to a feasible, if laborious, recipe that took about half an hour. The Nautical Almanac was distributed at ports around Britain, Europe and America, and during the final third of the eighteenth century ‘lunars’, so called, became an accepted method of finding your position at sea, and much the cheapest. An alternative way to determine the exact time and hence your position was to carry a really good clock; but a clock accurate and reliable enough – like the chronometers built and promoted by John Harrison – cost dozens of guineas, and unlike books of lunar tables they broke if you dropped them. Maskelyne took some criticism for his suspicion of the chronometer method, but frankly he was right; for most sailors it was still an inaccessible and impractical answer to the ‘longitude problem’.

  An issue of the Nautical Almanac contained the moon’s position for every three hours, night and day, of the whole year. Making the tables in the first place was laborious, and far beyond the power of one person, even if Maskelyne had had nothing else to do (he did) and had been paid to work on the Nautical Almanac (he was not). Instead he outsourced the work on the cottage-industry model, to a network of human ‘computers’ around the country. Maskelyne’s computers were teachers, surveyors, minor mathematical authors: much the same kind of people who contributed to philomath journals like The Ladies’ Diary. Indeed, they were sometimes recruited directly from the ranks of the Diary’s problem-solvers.

  They worked not with the equations and geometry that described lunar theory, but rather from a set of computational instructions prepared by Maskelyne. Calculating a single lunar position typically involved looking up about a dozen figures in printed tables and carrying out a similar or larger number of seven- or eight-figure arithmetical operations, all done in base 60. It was demanding, meticulous work.

  The computers were (mostly) good at what they did, but errors had the potential to lead to large losses of life, and a good deal of careful checking was needed to make sure no disastrous mistakes found their way into the printed tables. So a ‘comparer’ kept an eye on things, standing between Maskelyne and the computers. And here Hutton got involved. It was unglamorous work involving liaison with the computers as well as with Maskelyne. And it was a deeply picky process. The computers worked in pairs, without communicating with each other; one found the moon’s position for every midnight and one its position for every noon. The comparer merged the tables and checked that the moon’s predicted motion contained none of the implausible jumps that would signal a mistake in someone’s calculations. If there was a problem, the comparer redid the calculations himself until everything was right and he had a full month’s table of lunar positions for both noon and midnight.

  Then he selected some stars that lay close to the moon’s path, and sent the complete, correct table back to the computers so they could both, independently, compute tables of the moon’s predicted distances from those stars through the month. When the comparer received this information, he checked that the tables drawn up by the two computers were identical and, once again, sorted out any discrepancies by repeating the work himself if necessary.

  He also prepared various other pages of the Nautical Almanac such as the initial explanation of symbols and a chart showing the positions of Jupiter’s satellites. And finally, when the almanac was being printed, he corrected the proof sheets: yet more checking of long tables of numbers that were supposed to be identical.

  On and off during 1777–9 Hutton did all this, covering the comparing work for a total of twelve months’ worth of Nautical Almanacs; he also performed some extra tasks such as checking the predictions for eclipses of Jupiter’s moons that were printed in one almanac. He was paid (a total of about seventy-five pounds), but the money was far from being the point. ‘Comparer’ was a position of significant trust, and Maskelyne did not give it to just anyone. Hutton was very possibly doing Maskelyne a favour by filling in for months when no other comparer had been found or was available. And by doing so, and doing it well, he significantly increased his credit in the network around the Astronomer Royal. He was establishing himself as part of Maskelyne’s mathematical/astronomical circle, and confirming his valuable relationship with the Astronomer Royal.

  There was more. His work for Maskel
yne gave Hutton the opportunity to make contact with the Board of Longitude itself, and to do more work for it on an occasional basis. Through 1779 he corrected proofs of mathematical publications for the board – at a guinea a sheet – and for one book he was paid to translate a preface from Latin into English. In 1781–2 he provided lunar computations apparently outside the normal cycle of work on the Nautical Almanac, for which he was paid ten pounds ten shillings ‘for my Trouble’. And by 1780 he was writing to the Board to present a work of his own: a book of mathematical tables.

  Mathematical tables had long been one of Hutton’s interests. His very first book, the School-master’s Guide, had ended with a little table of the first twelve powers of each of the nine digits, and the 1770 Mensuration similarly closed with a thirty-page table of the areas of segments of a circle. During the 1760s and 1770s he had found himself repeatedly making computations involving roots and reciprocals of numbers,

  and as it seemed probable that this might be the case with me for many years longer, I formed the resolution of preserving all such roots and reciprocals as I should occasionally produce in my calculations, that I might have them always ready on any future occasion; which I did by entering them always in a little book, ruled for the purpose, till I have at last collected to the number of 1000.

  He published the resulting table in the 1775 Miscellanea Mathematica.

  His next venture of the kind was similar, but larger: a standalone table of the products and powers of numbers: products up to 1000 times 100; powers up to 10010. It could well have been collected together over a period of years like the table of roots and reciprocals, and when it was complete it enabled the rapid looking-up of over a hundred thousand different products or powers.