Napier's bones

Napier's bones are an abacus invented by John Napier for calculation of products and quotients of numbers. Also called Rabdology (from Greek ραβδoς , rod and λóγoς , word). Napier published his invention of the rods in a work printed in Edinburgh, Scotland, at the end of 1617 entitled Rabdologiæ. 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 extract square roots. Note that Napier's bones are not the same as logarithms, with which Napier's name is also associated.

Related Topics:
Abacus - John Napier - Calculation - Edinburgh - Scotland - 1617 - Square root - Logarithm

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The abacus consists of a board with a rim; the user places Napier's rods in the rim to conduct multiplication or division. The board's left edge is divided into 9 squares, holding the numbers 1 to 9 . The Napier's rods consist of 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.

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A rod's surface comprises 9 squares, and each square, except for the top one, comprises two halves divided by a diagonal line. The first square of each rod holds a single-digit, and the other squares hold this number's double, triple, quadruple and so on until the last square contains nine times the number in the top square. The digits of each product are written one to each side of the diagonal; numbers less than 10 occupy the lower triangle, with a zero in the top half.

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A set consists of 9 rods corresponding to digits 1 to 9. The figure additionally shows the rod 0; although for obvious reasons it is not necessary for calculations.

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