Napier's bones

This article started off as a machine translation of an article from the Spanish Wikipedia. It needs lots of revision and editing before it is usable here. This is a work in progress. See Napier's bones/temp for a work-page.

Napier's bones are an abacus invented by John Napier for calculation of products and quotients of numbers. Also called Rabdologia (of Greek ραβδoς, rod and λγoς, word). Napier published his invention of the rods in a work printed in Edinburgh at the end of 1617 also entitled Rabdologia. Using the multiplication tables embedded in the rods, multiplication can be reduced to addition operations and division to subtractions. More advanced use of the rods can even be used to extract square roots.


The abacus consists of a board with a rim in which the Napier's rods will be placed to conduct the operations of multiplication or division. The board has its left edge divided into in 9 squares in which numbers 1 to 9 are written. The Napier's rods are strips of wood, metal or heavy cardboard. Napier's bones are three dimensional, square in cross section, with four different rods engraved on each one. A set of such bones might be enclosed in a convenient carrying case. The surface of the rod is divided into 9 squares, and each square, except for the top one, is divided into two halves by a diagonal line. In the first square of each rod a single-digit number is written, and the other squares are filled with double, triple, quadruple and so on until the last square contains nine times the number written in the top square. The digits of each product are written one to each side of the diagonal and in those cases in which they are less than 10, they are written in the lower square, writing a zero in the top square. A set consists of 9 rods corresponding to digits 1 to 9. In the figure the rod 0 has been represented; although for obvious reasons it is not necessary for calculations.

more to be copyedited: see Napier's bones/temp

Source: Hispano-American Encyclopedic Dictionary , Montaner i Simon (1887).\n

copyright 2004