The Collaborative International Dictionary
Napier's bones \Na"pi*er's bones`\, Napier's rods \Na"pi*er's rods`\ A set of rods, made of bone or other material, each divided into nine spaces, and containing the numbers of a column of the multiplication table; -- a contrivance of Baron Napier, the inventor of logarithms, for facilitating the operations of multiplication and division.
Wikipedia
Napier's bones is a manually-operated calculating device created by John Napier of Merchiston for calculation of products and quotients of numbers. The method was based on Arab mathematics and the lattice multiplication used by Matrakci Nasuh in the Umdet-ul Hisab and Fibonacci's work in his Liber Abaci. The technique was also called Rabdology. Napier published his version in 1617 in Rabdology., printed in Edinburgh, Scotland, dedicated to his patron Alexander Seton.
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.
The complete device usually includes a base board with a rim; the user places Napier's rods inside 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.
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, quintuple, 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.
A set consists of 10 rods corresponding to digits 0 to 9. The rod 0, although it may look unnecessary, is needed for multipliers or multiplicands having 0 in them.
Usage examples of "napier's bones".
He was enchanted, and he would have gone on for ever, if I had not mentioned Napier's bones, Gunter's scales - the applied mathematics of navigation - lunars - the necessary tables.
At last, running Water becomes the underlying unit of measurement, Planets hold their Courses, Constellations stately creep on, Napier's Bones click in the Surveyors' Tents, and quietly, calmly, ev'rything keeps coming back to Water, how it inhabits the Land, how it gets on with the Dragon beneath.
In his youth Jack had been wretchedly taught -mere rule of thumb at the best - and it was only quite late that the beauty of Pythagoras and Napier's Bones had been revealed to him, lighting a love of the mathematics that had burned steadily ever since.