Using Napier’s Bones to Multiply

The seventeenth century saw the beginning of the development of instruments to aid calculation, making the process gradually more and more automatic. One of the forefathers of calculating machines were Napier’s bones (also known as Neper’s rods). Neper was the Latin name used for John Napier, 8th Laird of Merchistoun (1550 – 1617).

Napier’s bones are described in the book Rabdologiae seu Numerationis per virgulas libri duo, published in 1617.

In the Preface to the book, Napier declares that the purpose of his work was to eliminate the difficulty and length of time involved in making calculations, turning many against the study of mathematics. The same was true of the invention of logarithms, for which Napier is chiefly remembered.

To multiply using Napier’s bones ten different “bones” or rods are used, numbered across the top from 0 to 9, and a further rod we shall call “ruler”, marked by an ×. Each rod is divided into nine squares bearing numbers. Apart from the ruler, the squares are divided by a diagonal making two triangles. The diagonal goes from the bottom left to the top right.

The video tutorial below will demonstrate how to multiply a single digit number with one of multiple digits. The idea can be extended to multiply larger numbers as well using the “galley” method.