Halley's Breslau Table
1693 · Life Table · Work 683 of 1,871
A quarto volume of a learned journal lying open on a sloping reading desk in the meeting room of a scientific society in London in 1693, the volume bound in brown calfskin with raised bands, the right-hand page a dense table of narrow paired columns seen at a flat angle and soft in focus as a grid of fine grey lines, on the desk beside it a bundle of folded letters with a broken red wax seal, a pair of brass dividers lying open, a slate and a stick of chalk, a man in a long dark coat and a full curled wig seen from behind leaning over the desk, one candle in a brass holder and grey daylight from a tall sash window, panelled walls.
- What it was used for
- Edmond Halley, clerk to the Royal Society, in 1693 computed from the Breslau parish registers a table giving, for each age, how many people are still alive. The data came from Caspar Neumann, a pastor in Breslau, who had recorded births and deaths with ages at death — according to a 2011 reassessment, apparently in order to dispel superstitions about climacteric years and about the influence of lunar phases on dying. By way of Leibniz in Hanover and the Royal Librarian Henri Justel the data reached London; Justel presented them to the Royal Society on 18 January 1693. Halley took the years 1687 to 1691, estimated the city at about 34,000 inhabitants, and used the table to price a life annuity: at 6 per cent, 13.44 years' purchase for a ten-year-old, 7.60 for a sixty-year-old.
- What was new
- What was new was not the mortality list but the table drawn from it, by both reassessments probably the first based on sound population data. With it Halley showed that a life annuity on a ten-year-old is worth something different from one on a sixty-year-old. Strictly speaking, though, his table is a population table and not a life table — so says the 2011 reassessment in the Journal of the Royal Statistical Society, which also shows that he rounded numbers, smoothed out outliers, and made errors in the annuity values at ages 5 and 15. The barb: the English Crown went on selling life annuities at seven years' purchase whatever the nominee's age. By Halley's own table the state was thereby selling too cheaply for every nominee under sixty, and it kept doing so after 1693.
What the sources leave open: Halley's paper in the Philosophical Transactions was not consulted in the original. All figures come from two reassessments (DePaul University; Journal of the Royal Statistical Society, 2011), which agree on the years 1687 to 1691 and on the population estimate. Both give the single price of seven years' purchase; that it stayed after 1693 appears only in the first, and the second puts the age limit for underpriced annuities at 65 rather than 60.