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John Napier

John Napier of Merchiston (1550 – 4 April 1617) – also signed as Neper, Nepair – named Marvellous Merchiston, was a Scottish mathematician, physicist, astronomer & astrologer, and also the 8th Laird of Merchistoun. He was the son of Sir Archibald Napier of Merchiston. John Napier is most renowned as the discoverer of the logarithm, although the actual founder of logarithms was Michael Stifel who invented an early form of logarithm tables independently of and decades before John Napier. Napier is the inventor of the so-called "Napier's bones". Napier also made common the use of the decimal point in arithmetic and mathematics. Napier's birthplace, the Merchiston Tower in Edinburgh, Scotland, is now part of facilities of Edinburgh Napier University. After he died primarily of the disease of gout, Napier's remains were buried in St Cuthbert's Church, Edinburgh.

Mirifice Logarithmorum Canonis Descriptio

Early life

Napier's father was Sir Archibald Napier of Merchiston Castle, and his mother was Janet Bothwell, the daughter of a member of the Estates of Parliament, and a sister of the clergyman Adam Bothwell, who became the Bishop of Orkney. Archibald Napier was only 16 years old when John Napier was born.

As was the common practice for members of the nobility at that time, John Napier did not enter schools until he was 13. He did not stay in school very long, however. It is believed that he dropped out of school in Scotland and perhaps traveled in mainland Europe to better continue his studies. Little is known about those years, where, when, or with whom he might have studied, although his uncle Adam Bothwell had written a letter to his father on December 5, 1560, saying "I pray you, sir, to send John to the schools either to France or Flanders, for he can learn no good at home", and it is believed that this advice was followed.

In 1571, Napier turned 21 years old, and he also returned to Scotland. In 1572, he married Elizabeth Stirling, the daughter of James Stirling, the 4th Laird of Keir and of Cadder. Napier then bought a castle at Gartness in 1574. The two Napiers had two children before Elizabeth died in 1579. John Napier later married Agnes Chisholm, with whom he had ten more children. Upon the death of his father in 1608, Napier and his family moved into Merchiston Castle in Edinburgh, where he resided the remainder of his life.

Advances in mathematics

His work, Mirifici Logarithmorum Canonis Descriptio (1614) contained fifty-seven pages of explanatory matter and ninety pages of tables of numbers related to natural logarithms. The book also has an excellent discussion of theorems in Spherical Trigonometry, usually known as Napier's Rules of Circular Parts. Modern English translations of both Napier's books on logarithms, their description and the method of their construction can be found on the web, as well as a discussion of Napier's Bones(see below)and Promptuary (another early calculating device) link title His invention of logarithms was quickly taken up at Gresham College, and the leading English mathematician Henry Briggs arranged to visit Napier in 1615. Among the matters they discussed was a re-scaling of Napier's logarithms, in which the presence of the mathematical constant e (more accurately, the integer part of e times a large power of 10) was a practical difficulty. Napier delegated to Briggs the computation of a revised table. The computational advance available via logarithms, the converse of powered numbers or exponential notation, was such that it made calculations by hand much quicker.[1] The way was opened to later scientific advances, in astronomy, dynamics, physics; and also in astrology.

Napier made further contributions. He improved Simon Stevin's decimal notation. Arab lattice multiplication, used by Fibonacci, was made more convenient by his introduction of Napier's bones, a multiplication tool using a set of numbered rods. He may have worked largely in isolation, but he had contact with Tycho Brahe who corresponded with his friend John Craig. Craig certainly announced the discovery of logarithms to Brahe in the 1590s (the name itself came later); there is a story from Anthony à Wood, perhaps not well substantiated, that Napier had a hint from Craig that Longomontanus, a follower of Brahe, was working in a similar direction.[2]


Napier had a strong interest in the Book of Revelation, from his student days at St Salvator's College, St Andrews. Under the influence of the sermons of Christopher Goodman, he developed a strongly anti-papal reading.[1] He further used the Book of Revelation for chronography, to predict the Apocalypse, in A Plaine Discovery of the Whole Revelation of St. John, which he regarded as his most important work. Napier believed that the end of the world would occur in 1688 or 1700.

In his dedication of the Plaine Discovery to James VI, dated 29 Jan. 1593–4, Napier urged the king to see "that justice be done against the enemies of God's church," and counselled him "to reform the universal enormities of his country, and first to begin at his own house, family, and court." The volume includes nine pages of English verse by himself. It met with success at home and abroad. In 1600 Michiel Panneel produced a Dutch translation, and this reached a second edition in 1607. In 1602 the work appeared at La Rochelle in a French version, by Georges Thomson, revised by Napier, and that also went through several editions (1603, 1605, and 1607). A new edition of the English original was called for in 1611, when it was revised and corrected by the author, and enlarged by the addition of A Resolution of certain Doubts proponed by well-affected brethren; this appeared simultaneously at Edinburgh and London. The author stated that he still intended to publish a Latin edition, but it never appeared. A German translation, by Leo de Dromna, of the first part of Napier's work appeared at Gera in 1611, and of the whole by Wolfgang Meyer at Frankfurt-am-Main, in 1615.[1]

Astrology and the occult
John Napier

In addition to his mathematical and religious interests, Napier was commonly believed to be a magician, and is thought to have dabbled in alchemy and necromancy. It was said that he would travel about with a black spider in a small box, and that his black rooster was his familiar spirit.[3][4]

Napier used this rooster to find out which of his servants had been stealing from his home. He would shut the suspects one at a time in a room with the bird, telling them to stroke it. The rooster would then tell Napier which of them was guilty. Actually, what would happen is that he would secretly coat the rooster with soot. Servants who were innocent would have no qualms about stroking it but the guilty one would only pretend he had, and when Napier examined their hands, the one with the clean hands was guilty.[5]

Another occasion which may have contributed to his reputation as a sorcerer involved a neighbour whose pigeons were found to be eating Napier's grain. Napier warned him that from now on he intended to keep any pigeons found on his property. The next day, it is said, Napier was witnessed surrounded by unusually passive pigeons which he was scooping up and putting in a sack. The previous night he had soaked some peas in brandy, and then sown them. Come morning, the pigeons had gobbled them up, rendering themselves incapable of flight.[6]

A contract still exists for a treasure hunt, made between John Napier and one Robert Logan of Restalrig. Napier was to search Fast Castle for treasure allegedly hidden there, wherein it is stated that Napier should

" his utmost diligence to search and seek out, and by all craft and ingine to find out the same, or make it sure that no such thing has been there."[1]


An alternative unit to the decibel used in electrical engineering, the neper, is named after John Napier, as is Edinburgh Napier University in Edinburgh, Scotland.

The crater Neper on the Moon is named after him.[7]

List of works

* (1593) A Plaine Discovery of the Whole Revelation of St. John.
* (1614) Mirifici logarithmorum canonis descriptio (a translation into English by Edward Wright was published in 1616).
* (1617) Rabdologiæ seu Numerationis per Virgulas libri duo (published posthumously).
* (1619) Mirifici logarithmorum canonis constructio (written before the Descriptio, but published posthumously by his son Robert)
* (1839) De arte logistica

See also

* List of universities named after people
* Scientific revolution


1. ^ a b c d s:Napier, John (DNB00)
2. ^ s:Craig, John (d. 1620)
3. ^ Scotsman article about John Napier
4. ^ Scotsman article specifically about Napier's interest in the occult
5. ^ John Napier and the Devil
6. ^ A Biography of John Napier
7. ^ Neper Gazetteer of Planetary Nomenclature – USGS Astrogeology


* O'Connor, John J.; Robertson, Edmund F., "John Napier", MacTutor History of Mathematics archive, University of St Andrews, .
* Diploudis, Alexandros. Undusting Napier's Bones. Heriot-Watt University, 1997.
* "John Napier." Math & Mathematicians: The History of Math Discoveries around the World. 2 vols. U*X*L, 1999.
* John Napier. The History of Computing Project.
* John Napier—Short biography and translation of work on logarithms
* Johnston, Ian. Scots genius who paved way for Newton's discoveries. The Scotsman, May 14, 2005.
* Intro to Spherical Trig. Includes discussion of The Napier circle and Napier's rules
* EEBO (Early English Books Online) has electronic copies of some of his work, in facsimilies of editions of Napier's time (subscription or Athens login required).
* [1]
* [2]


Mathematics Encyclopedia

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