| ELABORATE SET OF NAPIER'S BONES IN IVORY -- A MINIATURE DIGITAL
CALCULATING COMPENDIUM, English, late 17th century. The boxwood case, with
original lift-off lid, measures 3-3/4" x 2-1/8" x 5/8" (9.4 x 5.4 x 1.7
cm) overall, and contains a "tabulat" board in boxwood and ivory (able to
hold a 13-digit! number as multiplicand), 32 (of 39) 1-3/4" (44 mm) long
ivory bones, and a wider ivory slip for calculating squares and cubes of
numbers. Each "bone" gives the multiplication table for the integer on top
multiplied by 1, 2, ...9. Diagonal lines show how to carry the second digits.
All bones are original to the set, the same number punches being used on
all bones and on the tabulat. There are exactly five different designs of
these two-sided bones, bearing top integers of 0/9, 1/8, 2/7, 3/6, and 4/5.
Multiple bones (at least five) are present for each of the five types, and
thus for all ten integers, permitting multiplication of large numbers. A
few (7) duplicate bones are lacking. Number punches suggest that the case
was designed for 44 bones plus the square / cube slip, but in reality, the
maker could only fit eight bones into each of the five slots, and today,
after wood shrinkage, only seven per slot is comfortable. The set is in
excellent condition throughout. John Napier (1550 - 1617) first described
his calculating rods in 1617 in his Rabdologiae. The present variation of
Napier's bones, the provision of a large number of two-sided slips (rather
than a small number of four-sided rods) was advocated by Leybourn c. 1667
in his The Art of Numbring by Speaking-Rods: Vulgarly termed Nepeirs Bones
(and in his Cursus Mathematicus). Leybourn's intention was to speed up the
selection of bones in use (the four-sided ones being somewhat cumbersome).
He proposed sets with 25 or 30 two-sided bones. Surviving examples are most
rare -- we note one in the Whipple Museum of the History of Science (Bryden)
and one in the Science Museum (Baxandall and Pugh), neither of which is
in ivory. (7319) $13,500. |
 |
 |
"A description of these rods according to their best and
latest Contrivance: ...only whereas my Lord Nepair maketh them square, each
Rod to contain four sides, these are made flat, consisting each Rod but
of two sides.... one set of these Rods consisteth of five pieces, and therefore
hath but ten Faces or sides.... For the orderly keeping and ready finding
of these Rods, I have often (for my self and others) had a Box made of Walnut-tree
or Pear-tree, with five partitions in it, each partition to hold five or
six sets of these Rods, or more if more Rods were required...." (Leybourn,
1667) |