A fine set of Napier’s Bones, to the design of William Leybourn

English, circa 1680

96 x 65 x 20mm; boxwood; case with 34 separate rods

The first modern digital calculating instrument. An early set of Napier’s calculating rods in boxwood, contained in the original case. The variant form designed by William Leybourn and popularized by him in 1667 – far more powerful computationally, but also far rarer than the standard square-section design.

The box contains a tabulat with one numbered side, and a total of 34 separate rods in five compartments. The first compartment with an enlarged space for the table of squares and cubes (which is present). Between five and eight rods per group (0/9, 1/8, 2/7, 3/6, 4/5). Potential space for 41 rods, but it is unknown how many were supplied, and we can find no obviously complete sets in this form.

This is an improved form of ‘Napier’s Bones’, the calculating device invented by John Napier of Merchiston (1550–1617). This design is attributed to William Leybourn (1626-1716) who described them in his 1667 book The Art of Numbring by Speaking-Rods (the subtitle of which gives us the name ‘Napier’s Bones’). Napier’s original design included ten rods, with four sides each. Leybourn converted the rods into slips, inscribed on two sides only, but with a large number crammed into the tiny space of the box. This more than tripled the number of useable rods, meaning that larger numbers (or more decimal places) could be calculated, and, perhaps more importantly, numbers wouldn’t ‘run out’ (for example in a calculation including 55,555, which is not possible in the original form).

The basic principle of Napier’s Bones is to lay out a multiplication table such that it can be rearranged; in this way products can be read across any table the user wishes to set up, with the two factors forming the first column (always 1–9, as this is fixed on the tabulat) and the first row.

This form is notoriously scarce: we can locate examples only at the Science Museum, London, and the Whipple Museum, Cambridge. All examples are believed to have been made shortly after they were described in print.