Measuring the Earth with a pencil

Ted Nield reveals the “other” longitude story. From the 2008 BA Festival of Science, in Liverpool University.

Geoscientist Online 8 September 2008

From 1773 to 1815, Mary Edwards earned her living as a human computer - working to produce astronomical and navigational tables on which sailors and navigators of the period depended on - not only for their livelihood, but for their lives.

In the 18th Century the "Longitude Problem" was acute, as shipping was being lost and international trade hampered because of the difficultly of calculating longitude at sea. The problem was so bad that in 1714 the Government offered a prize of £20,000 for a practical solution to finding longitude at sea.

Harrison’s clocks

The story of how John Harrison's watch solved the problem, and how he had to battle so hard against the Board of Longitude to get his rightful prize money in the 1770s, has been popularised by Dava Sobel in her book Longitude.

Harrison's watch did indeed solve the problem of finding longitude at sea, but it was not a practical solution for the majority of 18th Century sailors. The watch was extremely expensive to produce; a copy made in 1769 cost £200. In the late 18th Century, only very wealthy ship owners, such as the East India Company, could afford to equip their ships with such technology. The price of marine chronometers did not become affordable until almost the turn of the 19th Century.

In contrast, Nevil Maskelyene, the famously irascible British Astronomer Royal, began to publish annually a collection of astronomical tables called the Nautical Almanac at the cost of only two shillings per annual volume. It is still published today. While the Nautical Almanac contained many of the standard astronomical tables available in many almanacs of the time, its novel feature was the lunar distance tables. These tables gave the distance between the moon and one of the fixed stars for every three hours of the day at Greenwich. The tables allowed sailors to observe this lunar distance from wherever they were in the world and look up from the tables what time it was at Greenwich for the same lunar distance. Finding local time was straightforward. Comparing local time with Greenwich time allowed navigators to find their longitude because a one-hour difference in time is equivalent to 15 degrees of longitude.

One of Maskelyne's longitude tables - from the 1799 Nautical Almanack.

Calculating

Annually calculating these tables was a long and tedious task. Each calculation could involve looking up 12 values in several books of mathematical tables (logarithms being the most common) and performing up to 14 mathematical operations in a prescribed sequence. All the numbers were in Sexagesimal notation - i.e. in degrees, minutes, seconds, and 60ths of seconds. The calculation had to be repeated for every day of each month of each year and sometimes for seven time points through the day. The work was slow, tedious and required great attention to detail - as a small error could cause a calculation to be out by up to 60 miles.

To undertake this work Nevil Maskelyne employed a network of human computers located across England to carry out the work. All communication between Maskelyne and his computers was by post and the work done up to five years ahead in order to allow explorers such as Captain Cook, to take copies of the Nautical Almanac with them for the duration of their voyage.

Mary Edwards was one of those human computers - the only woman to be so employed. Mary was married to a clergyman named John Edwards in Ludlow in Shropshire. Although John had a reasonable ecclesiastical living that included a house, he was passionate about improving the quality of telescope mirrors. To fund this very expensive hobby John took in pupils whom he prepared for entry to Cambridge University while Mary looked after the domestics. In 1773 official records show that to supplement his income further, John began to compute for the Nautical Almanac.

Fatal whiff

In 1784 John died from a fatal inhalation of arsenic fumes used in his telescope mirror experiments. He left Mary a widow with two young children, debts relating to goods purchased for his experiments and homeless as their house passed back to the church. Mary's solution to her problems was ask Maskelyne to pay off her husband's debts with the London tradesmen who had supplied her husband and to pick up his computing work for the Nautical Almanac.

“Having a woman take on such a role in the eighteenth century was highly unusual”, Dr Mary Croarken of the University of Warwick told the BA. “Living in Ludlow she could have been expected to be part of the extensive glove making cottage industry of the area but Mary was obviously different.”

It was not until 1811, after Maskelyne's death, when the new Astronomer Royal no longer allocated her sufficient work to make a living, that Mary revealed that from the start she had been the one doing the Nautical Almanac calculations, not her husband. The official records reveal that the transition of work from John to Mary Edwards was uninterrupted and it would suggest that Maskelyne knew all along that Mary was doing the work all along.

Mary Edwards was the only female computer of the Nautical Almanac. Croarken said: “How Mary acquired the level of mathematical education needed to undertake the work is still not known. Schools attended by girls at that time concentrated on the skills required to become socially accomplished or to run a household. It is possible that she learnt from her husband, an university educated clergyman or from a tutor engaged to teach her brother. Equally possible is that she was self taught from the growing number of mathematical text books published during the 18th Century. “

“Edwards is a very common name on the Welsh borders - and Mary and John no less common - and it has proved impossible to find Mary's maiden name to see if her family history might give us a clue. No matter how she developed the necessary skills, Mary was one of the most constant and most trusted computers of the Nautical Almanac doing the bulk of the work for many years. Overall she worked as a human computer for over 40 years until her death in 1815 when her daughter Eliza succeeded her. Eliza was not nearly so prolific a computer as her mother, and eventually retired in 1832 when the work was centralised in London. It was not until the 1930s that women once again were employed in this type of work - and by then calculating machines were very much a part of the process rather than pen, paper and ink.”