Logarithms at Merchiston

Some inventions arrive in a flash of vision, and the world remembers the night they came. Others are made by a slow private arithmetic in an upper room, sheet after sheet, year upon year, until one afternoon a man wraps a parcel and pays a boy sixpence to carry it down a hill. The century that follows is altered, and the room where the work was done keeps no record of itself beyond a brass plate.

THE LAIRD IN THE TURRET

John Napier, eighth Laird of Merchiston, was sixty-four in the spring of 1614. He had been born in 1550 to Sir Archibald Napier and Janet Bothwell, sent to St Andrews at thirteen, married twice, fathered ten children, and inherited the small stone tower three quarters of a mile south of the Edinburgh High Street. He was a Lothian Protestant of fixed convictions. He had spent ten years on a hostile commentary upon the Book of Revelation, in which he calculated the year of the world's end from the trumpets and the vials. He had patented a hydraulic screw for the draining of coal pits. He had drafted four conceptual war-machines against the threat of Spanish invasion, including a burning-mirror and a chariot with a movable axle of muskets. He kept a black rooster which followed him in the yard, and the cook and the steward and the parish of St Cuthbert's were agreed, in their kirk-session way, that the bird was his familiar and the laird himself a magician. He had also, since 1594, been calculating a table.

THE AFTERNOON OF THE FIRST OF APRIL

It is a quarter past four on the first of April 1614. The light off the Pentlands comes in long and flat through the south-west turret window. Below the tower lies the Burgh Loch, and beyond it the city wall and the smoke of the High Street chimneys, and beyond that the grey line of the Forth. The chamber is small: a writing-desk with a sloped board, a coal brazier banked low, the laird's black scholar's robe over a fine linen shirt with a ruff. His secretary Thomas Aitkin sits in the corner with the third clean copy of the manuscript, the chapter-headings ruled in red ink. The manuscript is in four books of Latin, ninety folio sheets, and a separate quire containing the table. The table runs from one to ten million in stepped values, each value paired with its logarithm. It is the work of twenty years of pen-and-ink arithmetic in this room, checked at intervals by his cousin John Craigie of Edinburgh. Andrew Hart, printer at the foot of the High Street, has set the cases for the first quire and is waiting upon the table.

THE SECOND ABOVE THE BURGH LOCH

He stands at the desk with the parcel half wrapped, and he weighs, as a man weighs anything in his sixty-fourth year, what he is about to send down the hill. The table is what no other man in Christendom has at present. The book without the table is a treatise upon ratios; the book with the table is the next century of navigation, of astronomy, of the surveying of entails. He has lived sixty-four years in a small kingdom on the rim of Europe, and he has the habit of small kingdoms, which is to give the work away plainly without keeping back the method. Briggs in London will read it before the year is out. The Edinburgh advocates will use it within twenty years upon their feu charters. The English navy within five, the Spanish within fifteen, the Dutch already are halfway there in their own fashion. The parish thinks he is a magician because the parish has not been told what he has been doing in this room, and the parish will not be told for another two hundred years; the parish will only ever be told that the rooster was a tame rooster and the table was arithmetic, and the parish, he supposes with a dry private satisfaction that does not reach his face, may decide for itself which is the more interesting story. In his Latin preface he has already written, in the plain voice he uses for plain things, that nihil est mathematicis molestius, magisque calculatoribus iniucundum, quam multiplicationes, nothing is more troublesome to mathematicians, nor more grievous to calculators, than multiplications; and that he has laboured to ease it. He sets down the pen. He calls Aitkin over.

THE PARCEL ON THE STAIR

He puts the third copy on the desk for Aitkin to wrap in oiled linen and tie with cord. 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 within the next half hour, since the light will fail by six. Aitkin goes down the turret stair. The laird stands at the window and watches the small figure cross the yard and pass the kitchen, where the cook is at that moment defending the black rooster against the steward, who has decided again that the bird must be drowned. He watches Aitkin take the path north towards the Burgh Loch and the Cowgate Port. He sits ten minutes. He returns to the desk, opens a clean folio, and begins the second book, the Constructio, the constructive account of how the table was made, which he will not finish, and which his son Robert will publish in 1619, two years after the laird is in the ground.

THE LETTER FROM GRESHAM COLLEGE

The book came off Andrew Hart's press in July 1614 under the title Mirifici Logarithmorum Canonis Descriptio, the description of the wonderful canon of logarithms. A copy reached Henry Briggs, professor of geometry at Gresham College in London, in the autumn. Briggs read it through in his rooms above Bishopsgate. He wrote to a friend, by the tradition his contemporary recorded, that he had never seen a book which pleased me better, or made me more wonder. He set out for Edinburgh in the summer of 1615, a four-day ride. He was shown up to the turret by Aitkin, and, by the tradition preserved by the historian William Lilly, the two men sat looking at each other across the table for a full quarter of an hour before either spoke, because Briggs could not believe the book had been written by a living man, and Napier had the courtesy not to break the silence first. They worked together for the following two summers, and reformulated the system in base ten, which is the common logarithm that ran out into the dockyards and the observatories and the surveyors' chambers of the next three centuries.

THE RETURN

Napier died at Merchiston on the fourth of April 1617, sixty-seven years old, three years after the parcel went down the hill. He was buried in the kirk of St Cuthbert's at the west end of the High Street. Briggs published the base-ten tables in 1624. Kepler, who had received Napier's book in Linz in 1619, used the logarithms to finish the Rudolphine Tables and the third planetary law. Galileo, writing his Dialogo in 1632, set the canon down as the greatest invention of the last hundred years. The Royal Navy carried logarithm tables to sea from the 1670s until the pocket calculator displaced them in the 1970s; three hundred years of dead reckoning and longitude work and ballistics rest on the quire that Thomas Aitkin carried in oiled linen to Andrew Hart's shop. The black rooster died of natural causes in the same year the book appeared, and was buried, by the tradition of the household, under the kitchen wall.

Some lives close in a single decisive hour on a battlefield, with all Europe watching. Others close slowly, in a turret, in the late light of an ordinary April afternoon, with no one watching but a secretary and a rooster in the yard below. Merchiston Tower stands today inside the campus of Edinburgh Napier University on Colinton Road. The south-west turret is a small panelled room at the corner of the modern building, and on its door is a brass plate, in English: Logarithms were calculated in this room.