The Scottish mathematician John Napier (1550-1617) discovered logarithms and effectively introduced the modern notation of decimal fractions.

John Napier, or Neper, the son of Sir Archibald Napier, was born at Merchiston Castle near Edinburgh. At the age of 13 he entered the University of St. Andrews. He might also have studied at universities in the Low Countries, France, and Italy. What is known with certainty is that by 1571 Napier was back home and the next year married Elizabeth Stirling. His life at the newly built castle at Gartnes left him with ample time for such varied interests as mathematics, agriculture, and religious politics.

A Calvinist resolved to keep Catholicism out of Scotland at any price, Napier rallied against the conspiracy known as the Spanish Blanks with a book, A Plaine Discovery of the Whole Revelation of St. John (1594). To make the resistance more effective, he devised four new weapons: two kinds of burning mirrors, a piece of artillery, and a battle vehicle covered with metal plates having small holes for emission of offensive firepower and moved and directed by men inside.

Since the danger of the Catholic, or rather, Spanish, take-over soon evaporated, Napier resumed his other avocations. In agriculture he advocated the use of manure and common salt for the improvement of the soil. In mathematics his efforts were not only epoch-making but also met with immediate and universal approval. His method of calculating with logarithms was published in Mirifici logarithmorum canonis descriptio (1614). During the next 16 years more than 20 accounts, excerpts, and translations of its contents were printed, a clear evidence of the extent to which the new invention reduced the labors of trigonometrical calculations present in navigational and astronomical work. Napier's Mirifici logarithmorum canonis constructio (1620), on the art of computing logarithms, was published posthumously.

Napier sent a copy of his 1614 work to Henry Briggs, professor at Gresham College. While Briggs was explaining it to his students, the idea occurred to him that Napier's logarithms could be made easier to handle if the logarithm of 1 was set at 0. Briggs's proposal met with Napier's full approval, but Napier left it to Briggs to prepare a new logarithmic table based on that proposition; it is known as the table of common logarithms and was first published in 1624.

For over two decades Napier worked on a problem the solution of which was of crucial importance for physical science. The device, known as Napier's bones or rods, evidences the creativity of his mind in practical mathematics. With that device one could perform multiplication and division by mechanical means, and thus it was a distant forerunner of slide rules and analog computers. Its details were disclosed in a two-volume work, Rabdologiae; seu Numerationes per Virgulas libri duo (1617), published the year he died.

Further Reading

• The most important modern source of information on Napier's life, writings, and activities is the work edited by Cargill G. Knott, Napier Tercentenary Memorial Volume (1915). E. W. Hobson, John Napier (1914), is a biography of his life and achievements. For broad background see Charles Singer, A Short History of Science to the Nineteenth Century (1941).