Gunpowder and Geometry Page 18
Cavendish’s was a beautiful experiment; he was, indeed, one of the most talented British natural philosophers of his generation. It used a torsion balance: a horizontal rod with weights at the ends, suspended by a fine thread and capable therefore of rotating horizontally. The force needed to rotate it was tiny, but could be measured, and the idea of Cavendish’s experiment was simply to use the gravitational attraction of a ball of lead to attract the rod, to make it turn slightly away from its position of rest. Knowing the characteristics of the system (in particular, the period with which the rod oscillated once displaced) you could work out accurately the force the lead ball had exerted, and thus the strength of gravity. And hence by comparing the much larger force exerted by the earth on rod, lead and everything else, you could deduce the mass (or the density) of the earth.
As an experiment it had the advantage of real simplicity, and there was no need to go to a damp mountain for half a year to do it. It was a delicate experiment, but Cavendish obtained what he thought were reliable results and published them in the Philosophical Transactions in 1798. They flatly contradicted Hutton’s value for the density of the earth; Cavendish made it about five and a half times that of water; Hutton more like four and a half.
Hutton never accepted Cavendish’s result, and he became alarmed that in discussions of the subject the Schiehallion experiment, which he considered superior, was tending to be sidelined. It also annoyed him that when the Schiehallion work was discussed there was a tendency to call it Maskelyne’s experiment, his own name being omitted. Writing to Cavendish didn’t help, but Hutton managed to interest John Playfair, Professor of Mathematics at Edinburgh, in revisiting – literally – the Schiehallion experiment by doing a lithological survey of the site. This would result in more accurate estimates of the distribution of mass within the mountain: where was the schist, where the quartz.
In 1778 he had assumed the hill had the density of ‘common stone’ and found on that basis that the density of the earth was 4.5 times that of water, though he had urged a repetition of the experiment and two years later published a paper aimed at improving future experiments by finding the best place to put the observation stations, where the attraction of a wedge-shaped hill would be greatest. He had also pointed out that to get a really good result would require examining the interior of the hill by boring holes in it (‘after the manner that is practised in boring holes to the coal mines from the surface of the ground’). In the 1808 Abridgement he then modified his 1778 paper, pushing the density of the earth up to nearly five times that of water by assuming the mountain was a little more dense than originally thought.
Meanwhile in 1801 Playfair carried out, and in 1811 he published, the lithological survey Hutton had pressed him to do. He was able to raise Hutton’s original estimate of the earth’s density to the range 4.56–4.87 times that of water, depending on assumptions about the rock strata below the surface, but Hutton now seems to have lost confidence in these reworkings. In an 1812 reprint of his 1778 paper he suggested that a calculation based on an assumed distribution of rocks within the hill would be ‘a mere useless labour’ because of how much was unknown about that distribution, and he stuck with the value of ‘nearly 5’ times the density of water that he had put in the Abridgement. In the 1815 second edition of the Dictionary he did the same.
This new flurry of activity around the Schiehallion work succeeded in increasing the visibility of Hutton’s contribution, reviewers of the works concerned hurrying to note that the calculations he had done in 1778 had been ‘greater than can easily be imagined’: they were ‘more laborious, and, at the same time, called for more ingenuity than has, we believe, been brought into action in any computation undertaken by a single person since the preparation of logarithmic tables’. But Hutton’s sensitivity on the point was itself becoming a matter of comment, and a full recalculation based on Playfair’s new survey of the site had not yet been done. There, for a while, the matter rested.
Amid all this attention to his own old texts Hutton might seem to have given up producing new work. Yet he did have new scientific papers on his desk, and the old problem remained of where to publish them.
Over the years some projects were simply abandoned. His furious rate of work gives an impression of tremendous efficiency, with nothing wasted and nothing thrown away. But the reality was different, and by the time of his retirement Hutton’s study was littered with the remnants of work that he had not seen through to completion or publication. A project to construct trigonometric tables in radians rather than degrees, for instance: back in 1784 Hutton had solicited helpers to work on the calculations, and he was at one stage giving some thought to how to organise the several assistants who were ‘closely engaged’ in the work. The project stayed warm for a few years, but it never appeared in print and by now it was clear that it never would. Likewise, Hutton had obtained the papers of the Royal Society’s librarian John Robertson after his death and, from these, put together a substantial amount of information about mathematical instruments, including historical notes and lists of old works on the subject. He copied the texts out on the backs of cut-up sheets of calculations, but he never got around to publishing them. Again, he made lengthy selections and abridgements from the works of Archimedes and Pappus ‘to exhibit the elegance and force of the ancient Geometry’. And again, no publication ensued.
Some pieces, though, were ready for publication and were languishing simply for want of a suitable venue, or perhaps for want of the time to liaise with a publisher and organise the text into the right size and shape. There was a book-length translation from the sixteenth-century Italian mathematician Niccolò Tartaglia, on the solution of cubic equations; made around 1790, this had been used as source material for Hutton’s history of algebra in the Dictionary, but the translation itself had not yet seen print. There were a few new results about infinite series, including methods for finding the lengths and angles of a triangle from incomplete information, without the use of tables. And there were a few new explorations of geometry, including some on cross-sections of the spheroids, conoids and hyperboloids that had long featured in his Mensuration and other works.
Furthermore, Hutton had continued to pursue his historical work, amassing new material on the history of algebra: new details about British and European mathematicians, but also a mass of information concerning Indian and Arabic algebra, based on recent publications in the Asiatic Researches and elsewhere. He had seen specimens of Indian algebraic works both in Persian and English translations, sent by Edward Strachey of the East India Company to a mutual acquaintance; Hutton also copied out a series of relevant papers on the subject by his one-time rival Reuben Burrow.
The treatise on bridges, too, had generated new matter Hutton wanted to publish; in 1801 he had authorised a reprint of the original text, but he wished both to respond to the early critics of that text and give some new proofs. Again he had exercised his historical interest, compiling a history of iron bridges over the twenty-odd years of their existence. There was an urgency to this particular project, since the technology of iron bridges was still poorly understood; some of the specimens of which Hutton had obtained descriptions he reckoned to be in danger of falling, while a few had already fallen. Where the force went in such a rigid structure, and how it was different from a construction made of separate stones, were subjects on which Hutton felt he had valuable observations and theories to contribute. A compilation of descriptions and drawings might at least do something to help avoid engineers repeating the same mistakes.
Most obviously of all, there was the final account of the work on ballistics, unpublished (at least in English) since the last experiments in 1791. It was large enough to be a book by itself, with page after page of detailed descriptions of the experiments and lengthy derivations from them of formulae and rules. Hutton had also prepared a separate final discussion of practical problems in gunnery, considered in the light of his new results. Quite probably some of this mate
rial had circulated at Woolwich, but a wider public had no idea it existed.
As he had done in the 1780s, Hutton eventually adopted the obvious solution of publishing a collection of these papers – though by no means all – in a volume of his own. Or rather three volumes: there were so many of them. He again called the work Tracts, and there was perhaps a vague sense that this was a continuation of the long-abandoned project for a periodical to rival the Philosophical Transactions.
But it was more than that. For Hutton the new Tracts had something of the character of a final legacy: a compendium of all the original research he had ever done. He stated in the preface that it would probably be his last original work. As well as the new matter, chief among it the ballistics work, he reprinted all of his papers from the Philosophical Transactions of the 1770s and 1780s, the history of algebra from the Dictionary, the history of logarithms from the introduction to his Tables, and even a few of what he judged his more interesting pieces from the 1775 Miscellanea Mathematica. It was an opportunity to reinvent some of that material, and by judicious editing to form it all together into a whole. It was also an opportunity to modify some of his judgements and in at least a few cases to downgrade the credit he gave to others. Finally, Hutton the schoolmaster could not resist including in this research publication a concluding series of exercises and worked questions about the material.
It was all compiled and ready by July 1812 (some new matter on the history of algebra was added at the last minute, disturbing one tract’s structure); the result was a miscellany of thirty-eight ‘Tracts’ that defied summary. A fat set of three books – 1,300 pages in all – that were laborious in the extreme to print and to proofread, with Greek and Arabic notation in places, as well as mathematical symbols. Hutton called in a favour from the oriental librarian at the East India Company, who supplied some pieces of Sanskrit type and an explanation of the accompanying notation.
The books were a true monument to Hutton: to his work, his achievements, and the style of mathematics he valued. Reviewers, on the whole, were kind, and there were some long and prominent notices as readers laboured to pick out which parts were the most interesting and the most significant. Playfair in the Edinburgh Review took the opportunity for a little adulation. For him Hutton was one of those who ‘have the most contributed to the diffusion of mathematical knowledge in this island’ in the last half century. ‘A popular as well as a profound author’, Hutton was fully deserving of his celebrity and his success.
11
Controversies Old and New
8 May 1814. Off Spithead, in the ship known as the horrible old Leopard. Charles Blacker Vignoles – Hutton’s grandson – is writing to his fiancée, and in a reflective mood.
Till within the last year I lived with my Grandfather, a Man celebrated in the literary world: a Philosopher, a Mathematician of the first rank in the present age: one to whom the scientific world is indebted, and who by his own natural Genius and Talents raised himself to what he now is – under the eye of such a Man and associating with the literary friends who frequented his house …
So many brilliant flashes of natural and genuine wit; so many quaint and original Ideas upon classical and literary Subjects, as met my Ear in the Attic Meetings, which I once had the honor of attending – They were held at the House of Mr Pxxxxn of Burners Street: His Daughter Ellen a young Lady of the most surprising Genius and Talents, was the chief attraction: she was far from being handsome: a petite brunette with plain features: but a pair of fine black eyes, uncommon good humour, a flow of animal spirits and an extraordinary share of ready talk & repartee attracted all her Fathers literary friends[.] Among these was the celebrated sculptor Fxxxxxn, and his Family. This extraordinary Man is deformed, and what is very singular his Sister, (and I believe his only one) is also a sharer in that apparent misfortune, which is the Ridicule of Fools and Children.
Charles Hutton around his retirement.
F was the soul of the meetings. A naval man brought home a curious piece of wood which after discussion was formed into a small chest and called facetiously Η ΘΕΚΕ ΑΤΤΙΚΕ, the attic chest. Contributions to the chest were sent in anonymously, chosen and read every second Tuesday from nov to 17 jul.
Yes, Charles Hutton was admired, revered, loved. In retirement his round of friends and colleagues was happy, even brilliant – as Vignoles recalled – and his own household was distinguished, charming and popular.
But others weren’t so sure, and during the years of his retirement he was dogged by a series of controversies and old scores. It’s rare to attain a position of Hutton’s eminence without making a few enemies, leaving a few disgruntled former colleagues such as Reuben Burrow along the way. In a similar incident, William Saint, a former teaching assistant at the Royal Military Academy, launched in 1810 a slashing attack on that institution and its educational standards. He wrote to William Mudge, by now the governor of the Academy – several times – and when he received no satisfactory response he printed his letters as a book. The state of studies was, for him, ‘miserable and abject’ and cadets were graduating ludicrously ignorant.
Evidently some of his ire arose from his own bad experiences as a teacher. He had resented both the dominance of Hutton’s Course and a series of orders that required him to stick to it in his teaching. After making a certain amount of fuss he had received a verbal order stating that he was at liberty to instruct as he pleased; but that a knowledge of the Course would still be required at examinations.
While never actually naming Hutton as the author of the Academy’s (alleged) troubles, he insinuated that he had presided over a total ossification of the syllabus, with the students doing little more than copy out sections of the printed Course and cram them without understanding. Mudge as governor was also at fault, of course, for his ‘disgraceful management’ of the institution under his care. The sister establishment, the Royal Military College at Great Marlow, incidentally, taught nothing but ‘idleness and depravity’.
Saint was one of those people who by their vehemence tend to obscure matters. It’s hard to tell whether there was any truth in his charges, and if so, where it lay. It’s possible that a too exclusive reliance on Hutton’s Course had arisen, that uniformity of teaching was being secured at the expense, at least in some cases, of students’ understanding what they learned. A profusion of new orders about the teaching of mathematics at the Academy in the few years after Hutton’s retirement in 1807 suggest that others than Saint thought something was amiss. And there seems some ground for his additional charge that with nearly two hundred cadets now at Woolwich, the Academy was again seriously understaffed. But that the college was rotten to the core seems unlikely, and Saint’s evidence suggests instead that little had changed since the mid-eighteenth century: some of the cadets didn’t understand all the material they trotted out in their examinations, some were idle (indulging in games, in ‘loose and filthy conversation, in making obscene drawings upon their slates and books, in caricaturing the masters’) and a few cheated.
Saint’s attack may have wounded Hutton personally, but it produced no other consequences; the drastic reforms he wished for did not take place, and Hutton’s Course remained the foundation of the syllabus at Woolwich and Marlow as well as at a number of other military schools. That the governor of the Royal Military Academy shortly afterwards asked Hutton to prepare the new third volume of the Course was a clear mark of his confidence in Hutton and his book. William Saint’s subsequent career is obscure.
Saint’s opposition to Charles Hutton, like Burrow’s before it, had something of farce about it, but from a different direction there came a far more serious and damaging threat. As early as 1802 it had become apparent that the mathematical reviewer for the widely read Monthly Review was waging a one-man war against Charles Hutton and the kind of mathematics he stood for. A distinctly mixed review of the Dictionary (‘not remarkable for the accuracy of his definitions’) had appeared in 1798, and in March 1802 came a
frankly rude one-page notice of the new edition of Hutton’s Principles of Bridges. The reviewer alluded to the ‘unsubstantial systems which the pride of calculation is continually erecting’, to the ‘triflings’ of ‘speculative men’. He implicitly accused Hutton of plagiarising fellow northerner William Emerson, and he stated that the book did not answer the purpose for which it had been (re)published. The piece was anonymous, as nearly all reviews were, but it was no secret that the main, virtually the only reviewer of mathematical books for the Monthly was Robert Woodhouse: a Fellow of Caius College, Cambridge and a most able mathematician (he had been senior wrangler – highest-placed in the examinations – in 1795).
Woodhouse’s insults were strong stuff, and Hutton wrote in some wrath to the editor of the Monthly, asking that his (enclosed) rebuttal be printed. The editor consulted Woodhouse and decided to stand by him, declining to print Hutton’s piece. Woodhouse seems to have pointed out that some of his criticism did not make it unambiguously clear whether he meant to attack ‘speculative men’ in general or Hutton in particular, and that he had not explicitly accused Hutton of plagiarism. Flimsy, as Hutton pointed out: no reader of the offending article could possibly have doubted what Woodhouse meant. Hutton was sensitive at this stage in his career to the issue of damage to his reputation (‘some consideration is due from you in such a case for the feelings of an author so outraged’) and the two closely, rapidly written sides of his reply breathed indignation. Finally he asked for the return of his rebuttal so that he could print it elsewhere; it eventually appeared in The Monthly Magazine as a short essay on the ‘abuse of reviews’, while in a sort of compromise Hutton was allowed to insert a shorter piece in The Monthly Review, to which Woodhouse again replied. Hutton also asked the editor not to have his future books noticed in The Monthly Review, but this was ignored, and Woodhouse was allowed to write lukewarm reviews of the Recreations in 1804 and of the Abridgement (‘in some places we discern something like caprice’) in 1805.