John Napier

The life of John Napier

Timeline 1550Born at Merchiston Castle, near Edinburgh. His father, Archibald, is 16. 1563His mother dies. At 13, John enters the University of St Andrews. c. 1564Leaves St Andrews without a degree and goes to study on the Continent. 1571Returns to Scotland. 1572Marries Elizabeth Stirling. Goes to live at Gartness, where he builds a castle. 1593Publishes A Plaine Discovery of the Whole Revelation of Saint John, his most famous book in his lifetime. 1594Signs a contract to search for treasure hidden at Fast Castle. 1596Describes his “secret inventions” of war in a manuscript. 1608On his father’s death he becomes laird of Merchiston. 1614Publishes the Description of the Wonderful Canon of Logarithms. 1615Receives at Merchiston a visit from Henry Briggs, professor in London. 1617Publishes the Rabdologia, with his calculating rods. Dies on 4 April. 1619His son Robert publishes the Construction of the Wonderful Canon of Logarithms. The boy from Merchiston John Napier was born in 1550 in Merchiston Tower, a small stone castle a little over three kilometres from Edinburgh. His father, Sir Archibald Napier, was only 16. The family belonged to the Scottish nobility, and the name was spelled in many ways: Napier, Napeir, Nepair, and in Latin Neperus, from which comes the French form Neper.

October 15, 2026 Read

Multiplying by adding: the two progressions

Write the powers of 2 in a row and, below them, the exponents: $$\begin{array}{c|ccccccccccc} 2^n & 1 & 2 & 4 & 8 & 16 & 32 & 64 & 128 & 256 & 512 & 1024\\ \hline n & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \end{array}$$The top row is a geometric progression: each number is the previous one times 2. The bottom row is an arithmetic progression: each number is the previous one plus 1. Now try to multiply $16\times64$. Under 16 is 4; under 64, 6. Add them: $4+6=10$. Above 10 is 1024. And indeed

October 15, 2026 Read

Napier's two points: the definition of the logarithm

Napier did not have the exponent notation we use today. To define logarithms he used an image of motion, long before Newton and Leibniz created the calculus. The definition Imagine two points that start together. The first, $P$, moves along a segment $AB$ of length $10^7$, and its speed at each instant equals the distance still left to $B$: it starts fast and keeps slowing down, never arriving. The second, $Q$, moves along an endless line, always at $P$’s initial speed.

October 15, 2026 Read

Briggs and base-10 logarithms

These numbers were first invented by the most illustrious John Napier, Baron of Merchiston; they were then changed, following his own opinion, by Henry Briggs. — Title page of Henry Briggs's Arithmetica logarithmica (1624) Henry Briggs was professor of geometry at Gresham College in London and one of the greatest calculators in England. In March 1615 he wrote to a friend that Napier had set his “head and hands a work” with his new logarithms, and that he hoped to meet him that summer. He did. In the conversation at Merchiston the two agreed that the tables would be far more practical with two changes: the logarithm of 1 would be 0, and that of 10 would be 1.

October 15, 2026 Read

Napier's bones: multiplying with rods

Logarithms were meant for the great calculations of astronomy. For everyday sums Napier invented something else, published in 1617, the year of his death, in a little book called Rabdologia, from the Greek rhabdos, rod, and lógos, calculation: calculation with rods. The rods Each rod, or “bone”, because the most expensive ones were made of ivory, carries at the top a digit from 0 to 9 and, below it, its multiples from 1 to 9, in nine small squares cut by a diagonal. The tens go above the diagonal and the units below. The rod for 7, for example, shows $0/7$, $1/4$, $2/1$, $2/8$, $3/5$, $4/2$, $4/9$, $5/6$, $6/3$.

October 15, 2026 Read

The slide rule: logarithms that slide

A table of logarithms still requires looking numbers up, adding and looking up again. A few years after Napier, the English realised that the logarithms could be put on a ruler and the addition done with the hands. Gunter’s scale In 1620 the astronomer Edmund Gunter, Briggs’s colleague at Gresham College, drew a ruler on which each number $x$ stood at a distance proportional to $\log x$ from the mark for 1:

October 15, 2026 Read

The legacy of John Napier

By shortening the labours, the invention of logarithms doubled, so to speak, the life of the astronomer. — Saying attributed to Pierre-Simon Laplace Few inventions spread so quickly. In less than ten years logarithms were in use in England, Holland, Germany and Italy. For three and a half centuries they were humanity’s main calculating tool. Kepler The first great user was Johannes Kepler, who saw Napier’s tables in 1617 and was delighted. In 1619 he wrote a letter of thanks to the Scottish baron, not knowing he had been dead for two years, and dedicated his Ephemerides of 1620 to him. Kepler computed his own tables of logarithms and used them in the Rudolphine Tables of 1627, the most accurate tables of planetary positions of the time, which confirmed the elliptical orbits.

October 15, 2026 Read

Image credits

Historical images and photographs All come from Wikimedia Commons. We use the thumbnails provided by Commons, unedited. Portrait of John Napier, unknown artist, 1616, National Galleries of Scotland: source page · public domain. Title page of the Mirifici logarithmorum canonis descriptio, 1614: source page · public domain. A page of the 1614 tables: source page · public domain. Title page of Briggs’s Arithmetica logarithmica, 1624, photo by Phidus: source page · CC BY-SA 4.0. Napier’s bones in the Whipple Museum, photo by Marsupium: source page · public domain. Merchiston Tower, photo by Kim Traynor: source page · CC BY-SA 3.0. Slide rule, photo by Jacek Halicki: source page · CC BY-SA 4.0. Blog figures The map, the journey graph and the interactive figures (the two progressions, the two points, Briggs’s scale, the bones and the slide rule) are original and work in every language of the site. The map uses OpenStreetMap data.

October 15, 2026 Read