Greenock

Greenock, a town of 42,000 people, lies on the south side of the Clyde estuary, we might say on the corner where it opens out to the sea. Initially a small fishing town, Greenock grew rapidly in the 18th and 19th centuries through shipbuilding and merchant shipping. It was the birthplace of the engineer James Watt whose surname is commemorated in the SI unit of power.

It is no surprise to learn of small observatories in Greenock, chronometers, a time gun (like the one o'clock gun still fired ceremonially every day in Edinburgh); the apparatus of Astronomy as applied to navigation. Nevertheless just one article in all of the Astronomy bibliographic database ADS refers to "Greenock" in the title. It was published in Monthly Notices of the Royal Astronomical Society in 1874 by J W L Glaisher and goes by the title, Account of a MS. table of twelve-figure logarithms of numbers from 1 to 120,000, calculated by the late Mr. John Thomson, of Greenock, and recently presented to the Royal Astronomical Society by his sister, Miss Catherine Thomson; severe but accurate. After some very brief biography of Mr Thomson, deceased since 1855, the article gives a detailed discussion of the tables of logarithms he had compiled and assesses their accuracy and value in comparison with other known tables.

Logarithms are, amongst other things, an aid to rapid computation. To multiply two numbers together we look up their logarithms, add them together, then consult the tables again to find out the number whose logarithm we now have. Addition is easier and faster than multiplication so logarithms were an invaluable tool for complicated arithmetic in the centuries before electronic calculators and computers. Few people would ever have needed logarithms precise to twelve decimal places but some sorts of astronomer might on occasion have been among them.

If I want to know the logarithm of a number to some number of decimal places I only need a computer and appropriate software. In the era of the internet this software doesn't even need to be installed on my own computer. For example, Wolfram Alphaa very quickly and easily tells me - or you - that the logarithm of 3, to 12 decimal places, is 0.477121254720 (to base 10, as were Thomson's). The same number will be given in John Thomson's tables but it is the result of many minutes' calculation, by hand with pencil and paper. No electronic calculating machines - indeed, no mains electricity or electric light! - for him. He worked as a clerk, and later as an accountant, and the completion of these tables must have been a spare-time activity for many years, incredibly tedious for my tastes but requiring continual, fastidious attention (I used Mathematica on my laptop to calculate a table of the logs of the first 120,000 whole numbers, to 12 decimal places, in less than a minute). Other tables existed which he could have consulted, at least as starting points, but it seems clear that he calculated everything from scratch himself, either having no access to these other documents or simply preferring to rely solely on his own efforts. There are very few discrepancies between his tables and the others. Glaiser comments that, 'It is not uncommon for persons with a taste for mathematics to devote their leisure to the formation of logarithmic tables, though most likely there is no case in which so extensive a table as Mr Thomson's has ever thus been produced.' It was judged valuable for confirming or correcting the other, existing tables.

Mr Thomson was born in Strachur in 1782, the second of eleven children of Dougal Thomson, a farmer, and his wife Margaret. At the age of 12 he was sent to Greenock for continued schooling - for a farming family to do this suggests he had already shown significant academic talent. He was taught by Colin Lamont (1764 - 1851), a man renowned for promoting the use of Astronomy in navigation, 'from whom he imbibed a taste for mathematical studies'. He started working in Greenock as a clerk and spent the rest of his life there. He never married and was buried in an unmarked grave. The sister, Catherine, who gifted his tables to the Royal Astronomical Society was 20 years younger than him. We have the sense she didn't really know him very well. Glaisher says, 'The work undertaken by Mr Thomson, and the manner in which he has performed it, testify more clearly than could anything else to his steady and methodical habits.'

I'm struck by the singular person glimpsed in this story: a farmer's son, labouring in professional roles in a town very different from the circumstances of his youth. Nights spent under candles or oil lamp on steady, fastidious, anonymous effort; years devoted to the construction of his remarkable tables, all to some unknown private end. A Milton of computation, mute and inglorious until after his death. Was there a courtship that came to nought? Did he sing in the church choir? Was he insular, uncommunicative, or quiet but charming? His tables are still retained in the RAS Library but their numerical purity won't touch on such questions.

Greenock is out of sight downhill from this picture, looking roughly west from a rough wee road south of Port Glasgow.