Skip to main content

Napier's Bones

Napier's Bones

Although John Napier is mainly remembered for the invention of logarithms , he considered mathematical studies as a hobby. Born in the mid-1500s into a wealthy Scottish family, Napier was able to pursue all manner of subjects from religion to politics to agriculture during his life.

In 1617, shortly before his death, Napier developed a mechanical method for performing multiplication and division. This method, known as "Napier's bones," was based upon manipulation of rods with printed digits. The rods were made of bone, ivory, wood, or metal. Napier's bones became a very popular device for calculating in England and western Europe, because most people lacked these mathematical skills.

The set is composed of ten bones, nine of which display the multiples of a given number between one and nine. For example the "two" rod contains 02, 04 18: multiples of two. The tenth bone, known as the index, displays the numerals 1 through 9. To multiply 6 by 58, the index bone is placed beside the 5 and 8 bones. The value for 6 5 from the 58 is read from the sixth location on the five bone, i.e. 30, and it is placed in the hundreds column. Then 6 8 is read from the sixth location on the 8 bone, i.e. 48, and this is placed in the tens column. The columns are added together, resulting in 348.

This method of adding and subtracting applied to logarithmic values resulted in the development of the slide rule. As late as the 1960s, English children used Napier's bones to learn multiplication.

see also Abacus; Analog Computing; Slide Rule.

Bertha Kugelman Morimoto

Internet Resources

"Undusting Napier's Bones." Department of Computing and Electrical Engineering web site. Heriot-Watt University, Edinburgh. <http://www.cee.hw.ac.uk/~greg/calculators/napier/>

"John Napier and Napier's Bones." Maxfield and Montrose Interactive web site. <http://www.maxmon.com/1600ad.htm>

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"Napier's Bones." Computer Sciences. . Encyclopedia.com. 14 Nov. 2018 <https://www.encyclopedia.com>.

"Napier's Bones." Computer Sciences. . Encyclopedia.com. (November 14, 2018). https://www.encyclopedia.com/computing/news-wires-white-papers-and-books/napiers-bones

"Napier's Bones." Computer Sciences. . Retrieved November 14, 2018 from Encyclopedia.com: https://www.encyclopedia.com/computing/news-wires-white-papers-and-books/napiers-bones

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.