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 Maskelyne 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.
The eighteenth century was a period of heroic manual calculation (as the Nautical Almanac illustrated), and well-judged, accurate printed tables were of real use to those involved in such work. Hutton rightly saw that the genre offered a route to bring himself once more to public notice. The Board of Longitude accepted his project and agreed to grant him two hundred pounds to see it through the press: nearly as much as his annual salary at Woolwich. Five hundred copies were printed, and as well as being sold they were adopted as a standard part of the Nautical Almanac computers’ equipment.
The table of powers showed once again that Hutton loved rapid, accurate calculation and was extraordinarily good at it. The preface displayed a virtuosic facility at getting the tables to do more than they at first sight seemed capable of: using a table of squares to compute square roots, using interpolation or repeated calculation to multiply numbers larger than those allowed for in the tables. One reviewer dryly remarked that ‘but little trouble will be saved’ by using the tables in such complex cases, but that wasn’t entirely the point: as before, Hutton was telling the reader something important about who he was and what kind of mind he had.
There was more (with Charles Hutton there was always more). One of the natural goals for a mathematician interested in tables was to work on tables of logarithms. Judiciously deployed, logarithms speeded many types of calculation, and tables of them to six or eight or even more decimal places had been in print since early in the seventeenth century. Computing them was laborious, and getting them right in detail – and printed correctly in detail – was famously hard; the standard work, Sherwin’s Tables, was notorious for its inaccuracy by the time of the 1771 fifth edition. Hutton himself had compiled a list of several thousand errors in that book, and he reckoned the time was right to begin again from scratch.
He conceived a project to print new, freshly calculated logarithm tables to seven places, together with supplementary smaller tables, enabling the user to find the logarithm or antilogarithm of any number to twenty or to sixty-one places. Through the early 1780s he worked on these: they represented thousands of hours of work on top of everything else he was doing. Calculate, recalculate. Check the calculation. Transcribe into a fair copy. Check the transcription. Quiet, endless scratch of the quill against a background of ordnance testing, cadets drilling (or rioting) and military bands practising. You wonder how he found the discipline, the energy, or even just the time.
In fact, he didn’t, or not all of it. The manuscript of his logarithm tables survives, and it clearly shows he got his family to help him. The rough work and the fair copies are in at least two different hands: Margaret’s almost certainly, and quite possibly those of one or more of his older children. A biography that appeared later during Hutton’s lifetime, indeed, acknowledged that the labour and calculation for the product tables was ‘chiefly owing to the industry’ of Margaret, who assisted him with other, unspecified laborious calculations too.
It wasn’t an unusual arrangement for women to work as unpaid assistants in support of their husbands’ work. Acknowledgement was rare, so we don’t know exactly how common it was. Margaret’s hand also possibly appears making comments and revisions in some of Hutton’s scientific manuscripts from the 1780s. His daughter Isabella would later become Hutton’s main amanuensis; when old age made his own handwriting wobbly she wrote nearly all his letters for him. The youngest, Charlotte, was not as yet old enough to be involved, but her turn would come.
So, rather than heroic solitary labour on the tables – or perhaps on anything else – we should imagine a sort of bustling family workshop, in which drafts were passed from hand to hand and might receive work from two or three different people. The name of Charles Hutton alone appeared on the title pages. But others played a role, as he occasionally acknowledged, and without them he would almost certainly have been unable to complete the volume of work he did.
The point perhaps deserves pressing slightly. Within the philomath world,