Clan Napier · 1614
Logarithms at Merchiston
In the spring of 1614, in the upper turret of Merchiston Tower south of Edinburgh, John Napier, eighth Laird of Merchiston, in his sixty-fourth year, in the twentieth year of work on the project, finished the manuscript of *Mirifici Logarithmorum Canonis Descriptio*, the description of the wonderful canon of logarithms, and sent it to the Edinburgh printer Andrew Hart for setting. The book came out in July of the same year. Henry Briggs, professor of mathematics at Gresham College, read it in London in November and crossed the Tweed in the summer of 1615 to come and see Napier at Merchiston. Within a generation the table of logarithms had taken navigation, astronomy and surveying off the arithmetic by hand, and was, by Galileo's observation in his 1632 *Dialogue*, *the greatest invention of the last hundred years*. Napier was a Lothian Protestant laird who had spent ten years on a hostile commentary on the Book of Revelation, who had patented a hydraulic screw for clearing coal pits, who had drafted four conceptual war-machines for the defence of Scotland against Spanish invasion, and whose neighbours in the Edinburgh suburbs had decided he was a wizard and his black rooster was his familiar. The most consequential mathematical work of seventeenth-century Britain came out of his turret in his late middle age.
It is a quarter past four on the afternoon of the first of April 1614, in the upper chamber of the south-west turret of Merchiston Tower, three quarters of a mile south of the Edinburgh High Street, in the long flat light off the Pentlands. He is sixty-four years old. He is John Napier, eighth Laird of Merchiston, born in 1550 to Sir Archibald Napier of Merchiston and his second wife Janet Bothwell, taught at St Andrews University from the age of thirteen, married twice, ten children. He is in a black scholar's robe over a fine linen shirt with a ruff. His secretary, Thomas Aitkin, is at the writing-desk in the corner with the third clean copy of the manuscript on a slope, in red ink for the chapter-headings.
The manuscript is Mirifici Logarithmorum Canonis Descriptio, four books in Latin, ninety folio sheets in his own first hand, with the table of logarithmic correspondences cut on a separate quire. The table runs from one to ten million in stepped values; each value is paired with a corresponding logarithm. The whole table is the work of nineteen years of arithmetic by hand, performed in this turret by him and at intervals by Aitkin, with the cross-checking by his cousin John Craigie of Edinburgh.
He thinks: I am two days behind the press. Hart has the cases set for the first quire and is waiting for the table.
He thinks: the table is what makes the book. The table is what no other man in Christendom has at present. The book without the table is a treatise on algebra. The book with the table is the next century of navigation.
He thinks: Briggs in London will read this in October. Briggs will write to me. Briggs will come to Edinburgh in the summer of next year.
He thinks: the Spanish navy will use this within fifteen years. The English navy will use it within five. The Edinburgh advocates and lairds will use it within twenty for surveying their entails. The book will be in continuous use in every counting-house and dockyard in Christendom in fifty years.
He thinks: the rooster on the kitchen roof is, by the report Margaret brought up at lunch, having to be defended by the cook against the steward who has decided again that the rooster is my familiar. The country has, as I expected, decided that I am a magician, because the country has not been told what I have been doing.
He thinks: the country will not be told what I have been doing for another two hundred years. The country will only ever be told that the rooster was a tame rooster, and the table was twenty years of arithmetic in this room. The country may decide which is the more interesting story.
He puts the third copy on the desk for Aitkin to wrap. He addresses the parcel to Andrew Hart, printer, at the foot of the High Street. He gives Aitkin sixpence and tells him to take it on foot in the next half hour. He sits at the window for ten minutes after Aitkin has left, looking down at the Burgh Loch and the city wall and the long view of the Forth. He is two months from beginning a second book on a constructive method for the table, which will not appear until after his death.
Mirifici Logarithmorum Canonis Descriptio was published at Edinburgh by Andrew Hart in July 1614. Henry Briggs of Gresham College in London read it in November and called it, in a letter to a friend, the most extraordinary book on a mathematical subject I have seen in my lifetime. Briggs travelled to Edinburgh in the summer of 1615 to see Napier in person; the meeting at Merchiston, by the tradition of the historians of mathematics, opened with Briggs sitting in silence for fifteen minutes looking at Napier across a table because he could not believe the book had been written by a man. Together over the next two years they reformulated the system in base ten (the present common logarithm), and that is the form that ran into navigation through the eighteenth and nineteenth centuries.
Napier died at Merchiston Tower on the fourth of April 1617, sixty-seven years old. He is buried in the church of St Cuthbert's at the west end of the Edinburgh High Street. The Tower is now incorporated into the Edinburgh Napier University main campus on Colinton Road. The turret is a tower-room at the corner of the building with a brass plate on the door, in English: Logarithms were calculated in this room. The tradition of the parish, that Napier had a black rooster which followed him about and which the household called the laird's familiar, is recorded in the kirk session minutes of St Cuthbert's of 1611 and is, by every careful account, true. The rooster died of natural causes in 1614.