Napier's Bones

Napier's "bones" were composed of a set of four sided rods on which were inscribed the multiplication tables. Each face of a rod was the multiplication table for a specific digit, each engraved in a square with a top-right to bottom-left diagonal separating the units digit of the result (in the right-hand triangle) and the carry digit as shown to the left for the 6-times table. The device, named "Rabdologia" by Napier, got the name "bones" since several original versions were inscribed on rods of ivory, and looked like bones.

To complete a multiplication project, the user would pick out a set of rods corresponding to the digits in one of the multipliers, and arrange them on a board (see the board on the left of the figure above) alongside each other so the row of uppermost squares "spelled out" the number. The left side of the board had permanently attached a special rod inscribed simply with the digits 1 through 9. Each row across the selected rods then represents the elements of the multipication table for the digit on the leftmost rod and the top digit on the rods. By adding on the diagonal, the result can be determined. In most cases the diagonal addition is simple, but in some cases it is necessary to have an additional carry to the next column. To mulitply two multi-digit numbers, it is necessary (a) to select the corresponding rods, and then (b) read off the multiplication for individual digits in the other multipler, writing down the results as in completing a multiplication by hand.

The emulation below demonstrates how the rods are selcted and how a row is selected to determine the multiplication of one number by one digit. To operate the emulation, seclect the rods to be used by clicking on the digits across the top of the rods to display the chosen digit. As you do this you will see each rod displayed below. Then select the multiplier digit from the display on the left. The result will then be shown on the right. Check that by "adding on the diagonal" the result shown on the right is correct.

NOTE: Napier did not provide a rod corresponding to the zero (0) multiplier; this emulation provides this rod for completeness but leaves the table elements blank. Similarly the original bones did not show carry when its value was zero (0)!

Last updated 2001/08/08