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      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

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