Gunpowder and Geometry Read online

  It was a piece of work that sat very neatly on the boundary between the worlds of the technician or assistant and that of the original natural philosopher: facing both ways, or rather displaying two faces of its author. Once again, Hutton presented himself as someone who relished calculation for its own sake, and who loved details; the paper described minuscule corrections for the effect of temperature on the surveyors’ measuring rods and for the fact that by the end of the work they had worn to a shorter length than they started; it described rubbing out certain lines on the plan in order to leave other information clear. The work was in a clear sense firmly under Maskelyne’s protection, and Hutton had been directly paid by the Royal Society to do it. But at the same time, he also presented himself as a natural philosopher in his own right: someone who was thoroughly in control of the large picture, the overall scheme that made the individual calculations mean something. Someone who could turn a book of numbers into important information about the earth and the planets. Against the background of the Royal Military Academy and its wartime chaos, Hutton had flown in thought to every planet that orbited the sun, deducing their densities and laying the foundation for deductions about their structure. He had travelled to the interior of the earth and seen in his mind’s eye the metals that lay there. And he had not only felt the force of universal gravitation but determined its strength in absolute terms: the first to do so in the century since Newton’s discovery.

  And still this was not all. Hutton wished to do more to establish a reputation as a working experimentalist, and he was never a man to rest on his laurels. During summer 1775 he devised a programme of experiments in ballistics that he would carry out at Woolwich, ably assisted by the men and cadets of the Royal Artillery. They took place under the auspices of the Woolwich Military Society, set up in 1772 to promote military science and experiment. Hutton was the society’s secretary for a time. Military oversight came from Thomas Blomefield, captain-lieutenant in the Royal Artillery and aide-de-camp to the Master-General of the Ordnance; but it was Hutton who both determined the direction of the ballistics experiments and, usually, oversaw them from day to day.

  He was far from being the first in the field; there was a long history of trying to describe the flight of projectiles using mathematics. But it was only in the last thirty years or so that experimenters had found ways to look empirically at what happened when a ball came out of a gun. How could you possibly measure such rapid motion?

  Hutton’s ballistic pendulum.

  The clever answer had been found by Benjamin Robins, a mid-century mathematical practitioner and engineer who missed out on a job at Woolwich in his day. You fire your gun at a large pendulum, and you measure how far the pendulum swings as a result of being hit. Knowing the weight of the ball, the weight of the pendulum and something about the behaviour of pendulums, you can work out the ball’s speed. Robins used the so-called ballistic pendulum to revolutionise the study of artillery – his device has been called ‘as much a scientific milestone as Galileo’s telescope or Watt’s steam engine’. ‘There can have been few cases in history of one man changing the state of knowledge of any branch of science by so great a step.’ But he only built fairly small pendulums and used them to study musketry; the subject badly needed work on a larger scale.

  So Hutton built himself a really big ballistic pendulum.

  It was about fifteen feet high, and the bob used in the first series of experiments weighed 328 pounds. A brass cannon was procured, and supplies of powder and shot. Over the summer of 1775 and the following two summers, teams of gunners under Hutton’s direction fired balls at the pendulum, varying the size of the powder charge in order to find how it affected the speed of the shot. The explosive properties of gunpowder were in some respects not well understood. Should the ball fit the cannon exactly, or should there be a gap: ‘windage’, so called? Too tight a fit and artillery pieces would be liable to explode. Too much of a gap and some of the explosive force would be lost. Too much powder and it wouldn’t all burn (unburnt powder frequently blew out of the mouth of Hutton’s cannon, scattering the area and even the bystanders).

  It was once again laborious, meticulous work, but of a very different kind from the meticulous calculation that had so far been the foundation of Hutton’s success. In addition to the regular drill of loading and firing a cannon, it was necessary to size and weigh each ball before firing; after firing, to check and record the pendulum’s recoil; and, if there was a hole in the pendulum, to plug it and adjust the weight of the pendulum in the subsequent calculations. Pendulums regularly had to be repaired, rehung and reweighed and their centres of gravity redetermined. Different sizes of charge had to be made up and kept ready for use; thermometer readings were taken on each day of work. At first, the team managed only about four shots per hour.

  If it hadn’t the briskness of a pitched battle, it had at least a hint of the dangers. The pendulum was understandably apt to fall to pieces under bombardment, and Hutton’s notes regularly report that shot passed through it, pieces fell off it, its metal bands burst. One ill-advised attempt to strengthen the pendulum with lead resulted in a cannon ball breaking to pieces when it struck, firing splinters of metal in all directions. In later series of experiments, when the shots were being fired from longer distances, an alarming proportion of them missed the pendulum altogether, burying themselves in the earthwork behind it. Hutton perhaps brought to such efforts some recollection of the physically tough environment of his youth, and the men and cadets of the Royal Artillery were of course no strangers to flying metal. Hutton was lucky no one was ever hurt; there’s no record that any of those involved in the experiments had any kind of cover.

  It was hard to get it all right. Gunpowder varied in quality; gunners rammed it with varying degrees of vigour. The measuring tape attached to the pendulum flapped around in the wind and became tangled. Even when all the equipment behaved properly, all Hutton could do was record the displacement of the pendulum for later calculation; working out the actual velocities of the balls was not something to be done on the spot. Only later, in his study, did Hutton find out just how fast the balls had been moving or how their speed varied from one shot to the next.

  By the end of three summers, experimenting as and when opportunity offered, Hutton had fired several dozen rounds of ammunition into giant pendulums, and he was in a position to write up what he had found so far. His conclusions were several. A cannonball’s speed varied as the inverse square root of its weight: quadruple the weight and, other things being equal, the ball would go half as fast. The speed also varied as the square root of the charge: quadruple the charge and the ball would go twice as fast. He noticed that decreasing the windage greatly increased the ball’s speed, and recommended strongly that this be pursued in practice.

  There was a first account of all this for the Military Society and Lord Townshend, the new Master-General of the Ordnance. Hutton struggled with this piece of writing, his first attempt at the role of natural philosopher, and Margaret read over his drafts and improved his prose in places. The work had been a good deal of trouble and had cost the Board of Ordnance sixty-odd pounds, and Hutton was determined that it should seem to be of good value and the work be authorised to continue. He wanted to study air resistance, how shots’ range depended on their speed, and how different kinds of gunpowder affected matters.

  Townshend did approve, and Hutton went on to write up the work for presentation to the Royal Society. It was by far his most ambitious paper yet, intended to establish his reputation as not just a backroom calculator but a front-rank natural philosopher.

  The paper was read to the Royal Society on 8 January 1778 and printed in the Philosophical Transactions later that year. As with some of Hutton’s other performances, the author’s name concealed the work of quite a number of other people in procuring equipment, building and repairing pendulums, firing cannon and recording data. Margaret’s revisions of the text received no credit; neither did the accura
te drawings, probably done by one of the more talented Woolwich cadets, that accompanied the paper in print.

  The military importance of the work spoke for itself, but Hutton stressed in his paper that his results mattered not just for the accurate firing of cannon but for all ‘those parts of natural philosophy which are dependent on the effects of fired gunpowder’; for the study of explosions planned and unplanned, of the composition of the air, of the behaviour of gases. And the Royal Society was collectively convinced. By July the Society’s Council had voted to award Hutton the Copley Medal for his paper on ballistics.

  Hutton’s toil had paid off. The Copley was the Society’s only medal for intellectual distinction: not just the highest but almost the only scientific honour in England at this time. The ceremony of its presentation took place on the Society’s most solemn day of the year, the anniversary of its foundation on St Andrew’s Day in 1662. In his speech, the president of the Royal Society, John Pringle, mentioned that the Society made the award ‘with the more cordial affection, as by your other ingenious and valuable communications they are assured, not only of your talents, but of your zeal, for promoting the interests and honour of their Institution’.

  For a few months Hutton was quite the golden boy at the Royal Society. Samuel Horsley was stepping down as secretary of the Society in the same year, and Hutton was given to understand the job was his if he wanted it (he did). While writing his speech Pringle got to know him and found him a congenial man; he invited Hutton to the prestigious and exclusive ‘Club of the Royal Philosophers’. Hutton described the scene with relish:

  there was a select number of gentlemen who constituted themselves into a certain club, that, after the usual weekly meeting of the Royal Society, retired to Slaughter’s Coffeehouse, at the top of St. Martin’s Lane, to eat a few oysters, and hold familiar discourse together on the subjects that had occurred at the Society’s meeting, and on any other current scientific matters.

  This was Charles Hutton’s apogee. A few transcendently busy years, and a great deal of networking, had transformed him from provincial mathematics teacher to the darling of the Royal Society; brought him out of the shadowy world of backroom calculation to the sunlight of public admiration. From the secretaryship of the Royal Society he could perhaps dream of a further step to vice-president or – who knew? – even the presidency itself.

  6

  Foreign Secretary

  8 January 1784. Somerset House, on the Strand in London. A meeting of the Royal Society. A big panelled room that echoes when you talk; nearly 170 men seated in rows. The scene dominated by the president’s chair, his table, his ceremonial mace.

  For all the finery – the wigs, the lace, the gilt – it’s no genteel scene. Samuel Horsley, bishop and mathematician, is making a speech, or trying to. He’s been on his feet for some time, and he’s getting hoarse from shouting. People are clattering their sticks, shouting him down, clamouring for him to come to the point. Noise, confusion. The president isn’t in control, isn’t trying to be in control.

  Horsley, goaded beyond civility, cries at last that he and his friends ‘can at least SECEDE … the President will be left, with his train of feeble Amateurs, and’ – pointing to the mace – ‘that Toy upon the table, the GHOST of that Society in which Philosophy once reigned and Newton presided as her minister.’

  In the uproar that follows Nevil Maskelyne, Astronomer Royal, jumps to his feet and roars, ‘Yes, sir: for where the Learning is, there will the Real Royal Society be.’

  At the meeting in 1778, at which Hutton was presented with the Copley Medal of the Royal Society, and a lengthy speech made in his praise and honour, his success in that particular world also showed the first, small signs of unravelling. There was an upset about the secretaryship of the Society that Hutton had been promised; a second candidate had declared himself, campaigned vigorously, and on a vote the role went to him. This was Paul Henry Maty, a clergyman who had recently developed career-ending scruples (had discovered he didn’t believe in the Holy Trinity, to be exact). Hutton and his friends resented what had happened, and felt Maty had lobbied harder than was decent. But there was no denying that his need for employment was great. Hutton was consoled with election as an ordinary member of Council and promised he could have the next secretaryship that fell vacant; and after a little dithering he was also given Maty’s previous position as foreign secretary to the Society.

  Though foreign secretary may sound similar to secretary, it was not. The two ordinary secretaries read out the papers at the weekly meetings, and were highly visible and influential. The foreign secretary occupied a backroom position of exactly the kind Hutton wished to leave behind. The written instructions saw the role as comprising two parts. First, the foreign correspondence proper: answering letters to the Society from overseas; letting foreign members know that they had become foreign members; acknowledging their gifts, usually of books. In practice the gifts were much the most frequent occurrence. A Council decision of about a decade earlier specified that thanks should be returned using a pre-printed form, to minimise any impression that judgements of merit were being passed on the books. Not, then, a position of much responsibility or intellectual stimulation.

  The second, rather more interesting, part of the foreign secretary’s role was to translate foreign papers – usually from French or Latin – for the Society, so that they could be read at a meeting and, if desired, printed in the Philosophical Transactions. Practice varied somewhat; for papers in modern languages the Transactions carried both the original and an English translation, while for Latin papers the original was printed and the translation merely kept on file for those who wished to admit they couldn’t read Latin and consult it.

  Hutton read French – and Italian – fairly confidently, and he had already carried out paid translation work from Latin for the Board of Longitude. He was sure he could acquit himself well in the role, and so he did. If the translating was bulkier than the correspondence, it was by no means onerous. Latin papers in the Transactions during the three years Hutton was in the role numbered five; French four, Italian two and Swedish one. Presumably he called on outside help for the Swedish.

  More varied and perhaps more interesting were his duties as a member of the Society’s Council. It met every month for most of the year, and Hutton attended diligently. Council made decisions about the day-to-day running of the Society, as well as selecting from the papers submitted by Fellows those to be read at meetings and printed in the Philosophical Transactions. Occasionally papers were referred specifically to Hutton for judgement. Council also oversaw the running of the Royal Observatory and carried out an annual visit to that institution, in which Hutton took part.

  From a distance it certainly looked as if all was well, despite the upset about the secretaryship, and as if Hutton was now firmly embedded in the most elite scientific circle Georgian Britain had to offer: busy, influential, prestigious. To add to his prestige, in the summer of 1779 two of Hutton’s friends, joint professors of mathematics at Edinburgh, arranged for him to receive an honorary doctorate from that university; Professor Hutton was now (also) Doctor Hutton.

  Sir Joseph Banks.

  Yet all was not well. At the same meeting at which Hutton had missed out on becoming secretary of the Royal Society, his new friend and supporter Sir John Pringle stepped down as president. He was replaced by Joseph Banks, a man with rather different interests and priorities. Over the next couple of years he would become Hutton’s decided enemy.

  Had there been a tiff? a slight? a disagreement? (Just a few years before, Banks had signed Hutton’s nomination for fellowship.) The mores of the time hindered close scrutiny of the affront, if such there had been. Certainly the cold official minutes of the Council show Hutton behaving neither unusually nor offensively towards the president. Some of the best-informed of contemporaries denied that there had been any specific incident at all, and that appears to be correct.

  On one level, though, t
here was certainly a clash of personalities. Joseph Banks had great qualities, but he liked his subordinates docile, and that Charles Hutton was not. It was his habit to express his views ‘with freedom and firmness’ at Council, and he may simply have succeeded in irritating the new president beyond endurance. Banks would later describe Hutton as ‘a forward young man’; perhaps he was too forward for Banks’s liking, and turned out to be someone Banks could not work with.

  There were several other factors. One was lingering doubts about Hutton’s presentability. He retained a northern accent, and would do so to the end of his life, and – although he did nothing to advertise his pit-boy origins – some could detect from his manner that his gentlemanly status was quite new. One journalist made a joke of the claim that Charles Hutton the Newcastle schoolteacher, author of the School-master’s Guide, the Mensuration and the Principles of Bridges, ‘could not possibly’ be the same man as Professor Hutton, Fellow of the Royal Society and lately awarded the Copley Medal. A crueller later critic, also writing anonymously, found it difficult to imagine how a man of Hutton’s background could ever have functioned as foreign secretary of the Royal Society without constantly giving offence.

  Hutton was moreover strongly identified with mathematics; and mathematics was something of a cross for the Royal Society to bear. Its weekly meetings consisted of the two secretaries reading out papers sent in by Fellows: a sort of literary re-creation of experimental or observational work done far away. When the subject was the birds and beasts of Botany Bay, rocks and fossils in northern Britain, or even spectacular new experiments on hydrogen gas (or gunpowder), it worked very well.