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  Tried out with the students in its manuscript form, the course of mathematics found some favour, and Hutton approached the management of the Academy to fund its publication. He managed to persuade them that this key textbook by a key member of staff should be quite handsomely supported, and the Board of Ordnance undertook to pay a hundred guineas for the first three hundred copies, and seven shillings per copy for as many more as were needed. In the event the sums were increased, Hutton finding he had underestimated the cost of printing the books.

  The first copies issued from the press in 1798, and Hutton’s Course of Mathematics became a staple of life at the Royal Military Academy. Every cadet had to buy a cheap copy; every graduating lieutenant was given a bound copy as a present. It was fairly clear from the start that the book would outlast Hutton at the Academy; in fact it remained in use for decades across three continents. It was a fine monument to Hutton’s style of teaching and to all he had achieved at Woolwich.

  But there were undoubtedly flaws. Despite the rearrangement and rewriting the Course remained in large stretches merely a compendium of what Hutton had written elsewhere, and not all the changes, compressions and adaptations to the military point of view were improvements. If complexity was trimmed, say from the long series of theorems on conic sections, so were long and vital series of example problems, and in places such as the arithmetic the substitution of problems dealing with specifically military matters felt forced (‘Suppose 471 men are formed into ranks of 3 deep, what is the number in each rank?’). Volume 2 in particular felt like a mere miscellany of different topics: trigonometry and mensuration; conics; dynamics; hydrostatics and hydraulics; fluxions and their mathematical applications. And there was an unevenness of tone between different parts of the book, betraying their origins in textbooks written for rather different constituencies at different times in Hutton’s life.

  It received mixed reviews. Too hard, said some; too compressed, others. Much was good but perhaps too little was new or was properly (re)considered. One reviewer was ‘not perfectly pleased’ with the order of subjects and thought some difficulties ‘not sufficiently softened for beginners’; another judged it a mere selection from other works. Cadets at the sister college at Addiscombe found the Course as indigestible as their dinners:

  How shall I name the o’erbaked ribs of beef,

  The stringy veal, and greasy legs of mutton,

  Whose very sight oppress the soul with grief?

  (Almost as great as brought on by a Hutton.)

  The Dictionary and the Course were large projects, the Dictionary a hugely laborious one. But they had exhausted neither Hutton’s energy nor his desire to place mathematics before the reading public on the largest possible scale. His research for the Dictionary had made him more aware than ever of the volume of interesting mathematics and writing about mathematics in circulation on the European continent, and one name prominent in both popularisation and mathematical history was that of Jean-Étienne Montucla. He had published a history of attempts to square the circle in 1754 and a comprehensive history of mathematics in 1758; Hutton greatly admired both works, and there is some evidence he may have corresponded with Montucla about revisions to the latter. And in 1778, with a second edition in 1790–1, Montucla produced a new version of an old favourite, the ‘Mathematical Recreations’ of one Jacques Ozanam. First published in 1694, this was a compendium of games, puzzles, riddles, tricks and mathematical popularisation. The book had been translated into English early in the eighteenth century, but Montucla’s new French version was massively expanded and updated, and Hutton saw a chance to put a great deal of well-written mathematical exposition in front of an English audience without having to compile it from scratch himself. The four volumes of ‘Montucla’s Recreations’ duly appeared, under the title Recreations in Mathematics and Natural Philosophy, in English translation in 1803.

  It was a jolly compilation, ranging across arithmetic, geometry, and many kinds of applied mathematics including astronomy, navigation and music. There were counting games and card tricks, optical illusions and instructions for making fireworks. How to draw a circle without compasses; how to construct a magic square; how to build a water clock; how to build a microscope.

  The title page and preface stated that the book was – compared with its French parent – much augmented, enlarged and improved with ‘notes, remarks and dissertations’. But the careful reader would search many chapters in vain for any such items. There were a few obvious changes such as a table of English rather than French weights and measures, or a list of eclipses visible from London instead of Paris. There was an occasional simplification to the prose, by the removal of a metaphor, say. Now and again there was a mistake of Montucla’s to correct, a facetious footnote to omit or an algebraic demonstration to add. Sometimes changes were marked ‘editor’ but more often they were not. Mostly, though, it was a very straightforward translation. Footnotes remained footnotes; remarks remained remarks. There was very little in the hundreds of pages of ‘Hutton’s Recreations’ that was not in Montucla’s.

  It was, indeed, never quite declared in the prefatory matter that Hutton was the translator, though it was everywhere implied. If there were added a few sections about some of his favourite hobby-horses – the specific gravity of various substances, steam engines, hot air balloons – there were also at least a few places in the Recreations which it is hard to believe Hutton worked on: notably a remark about the impossibility of determining the masses of the planets which stands in flat contradiction to his own published determination of those masses. The translation itself occasionally reads like the work of a man less than fully conversant with mathematical terminology (‘squarrable’; ‘cube foot’) and the references to recent – particularly British – work, that Hutton would easily have been able to add, are altogether absent.

  Did Hutton translate the Recreations? Or did he do no more than lend his name, cast an eye over, perhaps add a few notes here and there about subjects that interested him, to a volume translated by one or more invisible assistants? Was this, as the harshest critic said of the Dictionary, merely a project cooked up in collusion between the booksellers and a big name? It’s hard to say. Hutton probably didn’t do all the translating work, but just how big or small his contribution was we are unlikely ever to know.

  In a similar vein, it was and is sometimes said that Hutton translated a second work on popular mathematics during this period: Select Amusements in Philosophy and Mathematics; proper for agreeably exercising the minds of youth, by one M.L. Despiau. In fact he merely provided an endorsement for the English version. But the title page was set out in a way that made it ambiguous just how much was ‘by Professor Hutton’, and some were evidently fooled. Hutton’s was becoming a name about which mathematical publications accreted, whether relevantly or not.

  Reviewers on the whole liked the Recreations project. The British Critic found the book not merely entertaining but useful, and gave it ‘warm commendation’:

  It is no small proof of a genuine regard for philosophy, when men, whose peculiar privilege it is to move in the most exalted sphere of science, will condescend to smooth the rugged path to eminence, and strew with flowers the wearisome way to the Temple of Knowledge.

  The Monthly Review concurred, reckoning the book ‘well adapted to lie on the table or chairs of our parlours’, since science would not lose its dignity by losing its formality. Both reviewers approved the project of popularisation in general and thought this a fine specimen of the genre. The British Critic was similarly enthusiastic, singling out various sections for praise and quotation: ‘The whole work indeed reflects much credit upon a man, who has already deserved so well of the scientific world,’ though he excepted the chemical section which he thought poor. He thought it would make a useful form of recreation in schools.

  A dissenting voice came from The Imperial Review: alas we don’t know whose voice it was. The reviewer implied that the Recreations contained much
matter that was ‘insipid and puerile’ and that Hutton had done far too little to the book in passing it through his hands, making only trifling additions and alterations: indulging in negligence rather than adding the thorough updates and pointers to recent literature one would have expected. The reviewer, like others, suspected the work might have been Hutton’s in name only.

  Almost incredibly, Hutton had in hand yet another project, and one on an even more heroic scale.

  The Philosophical Transactions of the Royal Society now ran to nearly a hundred volumes, and even such a devoted and assiduous book collector as Charles Hutton could not get hold of them all; some were scarcely to be had for money. He knew from personal experience what a chore it therefore was to chase a subject through multiple volumes that might have to be consulted in different libraries. There had been printed compilations, ‘abridgements of the Transactions’ before, but none – at least in English – for some decades. An attempt was announced in 1802, but flopped and was quickly abandoned. The publishing firm of C. and R. Baldwin jumped into the gap, and in March 1803 announced in a short prospectus that they were going to do the thing properly. They had engaged a team of three: Charles Hutton of Woolwich, George Shaw of the British Museum and Richard Pearson of Bloomsbury Square. Under their care there would appear, in weekly numbers from June that year, a new abridgement that would serve the function of a complete set of the Transactions for those who didn’t have them and couldn’t obtain them, containing in full the most interesting articles and in brief the moderately interesting ones, while leaving out a few of the wholly superseded or uninteresting. The whole would be in English (except where ‘from the peculiarly delicate nature of the subject, there would have been a manifest impropriety in giving them in English’) and enriched by notes and biographies. By 1806 eight volumes had appeared and in 1809 the Abridgement went on sale complete, in eighteen volumes totalling something like fourteen thousand pages.

  The project had much in common with the 1775 Miscellany that brought together lightly edited reprints of The Ladies’ Diary from the previous seventy years. It was widely reported that the Abridgement was under Hutton’s principal care, and it would be repeatedly stated in print that he was paid the fantastic sum of six thousand pounds for his trouble. If that colossal figure is anything like the truth it can only have been envisaged that he would use it to employ assistants to do much of the work: translating, editing and annotating. We hardly need to imagine Hutton, in his late sixties, actually penning the eighteen volumes or any significant fraction of them. Nevertheless, there were places that bore his distinctive mark. Annotations on papers of personal interest to him – such as certain items to do with the density of the earth – were occasionally voluminous, and neither did he hesitate to do some discreet rewriting of his own paper on that particular subject.

  One of the most notable achievements of the Abridgement was as a subject classification of the matter that had appeared over the 136 years of the Philosophical Transactions. From volume 3 (following criticism, in fact, of volumes 1 and 2) a very full classification was adopted in the contents list, and it featured mathematics and ‘mechanical philosophy’ (much of which was applied mathematics) as the first two of its eight main headings. This was, as well as anything else, a substantial assertion about the place of mathematics in the intellectual world and in the work of the Royal Society. (A 1787–91 Paris abridgement of the Transactions, in fourteen volumes arranged by subject, did not have a volume devoted specifically to mathematics.) Under pure mathematics alone there were nearly three hundred articles (a quick look at the contents pages would have revealed that the number fell off markedly during the period of Joseph Banks’s presidency).

  This was, of course, a bold, even a cheeky project as well as a huge one. Just before Baldwin’s announcement, Hutton wrote to Banks ‘signifying his intention to undertake the care of arranging and printing a new abridgement of the Philos: Transactions, and trusting that the President and Council would please to countenance this undertaking’. Council noted the matter and gave it no further discussion, but by 1809 permission had nevertheless been received to dedicate the work to ‘the Right Honourable the President, the Vice Presidents, the Council and the rest of the Fellows of the Royal Society of London’. It’s possible that the abandonment of a planned supplementary volume containing a history of the Society and additional biographies of Fellows – which would surely have been an occasion for some Banks-bashing – was connected with this permission. If the project gave anyone the impression of an improvement in relations it was a deceptive one, unfortunately. But whatever Banks really thought, Hutton had succeeded in putting his own mark on how a large fraction of readers for the foreseeable future would view the Royal Society and its activities.

  There were criticisms from The Monthly Review, which was becoming quite consistently hostile to Hutton and his work. There the reviewer thought a full republication of the Transactions would have been better, or failing that perhaps reduction into the form of a compendium or encyclopedia; he found the selection bewildering and even capricious. But the Abridgement was well received by most, its balance and even-handedness coming in for particular praise. The British Critic called it a work ‘even of national importance’, possessing ‘spirit, taste, and judgment’ and, judging from the early volumes, shaping up to be ‘a national honour’. The Literary Journal praised its accurate, ‘perspicuous and unaffected style’. One of Hutton’s friends, Thomas Leybourn, said the early volumes ‘have fully justified the public expectation, a circumstance which will not appear remarkable when it is recollected that the execution of the work is confided to men of the highest eminence in the departments of Science they have engaged to superintend’. There was even a favourable notice in France. Of Hutton’s large-scale projects from the second half of his career the Abridgement was arguably the most successful, and most unambiguously achieved his oft-stated goal of public utility.

  During the long decade from the appearance of the Dictionary to that of the Abridgement, Hutton’s activity and his public persona were focused no longer on practical experiment, hands-on surveying and the other dirty business of practical mathematics, but on text, and text in huge quantities. Whatever the role of assistants, his work on Dictionary and Course, Recreations and Abridgement must have taken up a substantial portion of his time, against a background of personal disaster and the chaos of war at the Royal Military Academy.

  It was possible to be very sharply critical, to say that Hutton had spent a decade and more on scissors-and-paste work. But that was to miss the point. The compilations and translations he had produced were not about intellectual innovation or conceptual novelty. Rather, he had carefully, deliberately, made himself the leading voice speaking for mathematics in English. And he had given the English-speaking world a series of massive monuments to its mathematical culture: monuments whose endurance was never in serious doubt.

  More than that, these works were finely crafted tools. Citations of ‘Hutton’s Dictionary’, ‘Hutton’s Recreations’ and the rest would become ubiquitous in discussions of scientific and mathematical subjects, in writing about mathematics and its place in culture and education. It’s not too much to say that Hutton, by providing them, changed the way English speakers spoke and thought about mathematics. His view of what mathematics was, of what it included and excluded, and where and how it was relevant, became the norm, and he did more than anyone else to make mathematics an accepted part of British culture, an accepted strand of British science.

  Yes, much of the work on these books could have been done by any competent translator, editor, compiler: and some of it probably was. But Hutton knew what he was about. In the face of hostility to mathematics from parts of the scientific and the literary worlds, through these massive works he both consolidated his own reputation beyond doubt, and gave unique, permanently valuable service to the mathematical culture he knew and loved.

  10

  Securing a Legacy
/>   Mount Schiehallion, in Scotland: June 1801. Two thousand feet and more above sea level; long views over the Grampians away from the ridge. Steep, rugged, ‘a very beautiful conoidal shape’. Charles Hutton’s friend John Playfair, mathematician and geologist, treads the high ground. Retreads the ground, indeed, that Maskelyne and Burrow trod back in the 1770s.

  All that remain from 1774 are the ruins of the two observatories, and two cairns on top of the mountain. The long chain of surveying stations, meticulously positioned and measured, is gone without trace.

  Playfair nevertheless tries to follow the lines of the original survey, using theodolite, sextant and compass to determine the lines of the different strata. The strata, nearly vertical, break out through the surface, and Playfair, hammer in hand, collects specimens of each, notes their positions. Quartz, lustrous as enamel. Schist and limestone; porphyry and greenstein. Hutton’s paper from the 1778 Transactions is seldom out of his hand.

  The Course, for all its imperfections, was the culmination of Hutton’s work on the wide-ranging mathematics syllabus at Woolwich. After it was done, wartime conditions left him little opportunity to develop his teaching further; he was becoming more and more a manager of other men’s work and of a complex system of academies and classes, with their attendant tests and documentation.

  The Academy at last moved to new buildings on Woolwich Common in 1806 in order to relieve what had become intolerable overcrowding on the riverside site. Not all the cadets could be accommodated even then; only the senior academy of 128 went to the new buildings. The remainder, now numbering 180, were split between the old Woolwich Arsenal site and the Royal Military College at Great Marlow. But the new buildings were a great improvement; each of the four classes now had its own separate housing and classroom. There were a library, a lecture room and two model rooms; a fencing room and two racquet courts; assembly areas and gardens.