Rabdology

This first English translation of Napier's Rabdologia provides a clear and readable introduction to a group of physical calculating devices, which, long overshadowed by Napier's logarithms, have their own intrinsic interest and charm. "The tasks which fill'd beginners with dismayThis little book has banish'd clear away." John Napier had already discovered and published an epoch­making treatise on logarithms when in 1617 he turned to "rabdology" or rod-reckoning as yet another means by which to confront the problem of simplifying the huge calculations involved in multiplication, division, and the extraction of roots. This first English translation of Napier's Rabdologia provides a clear and readable introduction to a group of physical calculating devices, which, long overshadowed by Napier's logarithms, have their own intrinsic interest and charm. Book I describes the first device, a set of rods known as "Napier's Bones," which were inscribed with numbers forming multiplication tables and used in conjunction with pencil and paper. Book 11 presents a series of simple calculations that readers can solve by using the rods, and a series of tables of ratios useful for division. Napier then describes the second mechanical device for calculation, a forerunner of the modern calculator that he named promptuary or "place where things are stored ready for use." The third device, similar to a chessboard, allowed calculations to be performed by moving counters around the squares. Observing that the numbers had to be represented in what would now be called binary form, Napier provides instructions for changing from ordinary to binary numbers and back again, a method that worked equally well for multiplication and division and that had a particularly elegant symmetry when applied to the extraction of square roots.