John Napier and Napier's Bones

by Jenny Mitchell
In the early seventeenth century, calculators and computers weren’t available, of course, so how did people calculate long multiplication problems? Well, one way would be to use a device called “Napier’s Bones”, or “Rabdology”, invented by John Napier.

Napier (1550-1617) was a Scottish mathematician, physicist, and astronomer. A list of his works would include A Plaine Discovery of the Whole Revelation of St. John, Mirifici logarithmorum canonis description, Rhabdologia, and Mirifici logarithmorum canonis construction. Best known for inventing “logarithms” and Napier’s Bones, he also popularized the use of the decimal point.

How does Napier’s Bones work? To answer this, let’s take a sample problem: 4 x 4528. To use Napier’s Bones, first arrange the “bones”, or columns according to the number you are multiplying by, the multiplicand (4528). Next, delete all of the columns except for 4, 5, 2, 8, and the “multiplier column” (the column in red). Find the row that corresponds with the multiplier (4). Now, take the bottom right number in the right-most cell of the row corresponding with the multiplier. This is the smallest digit in your answer; the right-most digit. Write it down. Subsequently, add the two numbers in the parallelogram (shown in the red circle) adjacent to the cell you previously dealt with, and write the sum to the left of the first digit in your answer. If the sum is greater than nine, write down only the ones digit, and carry the tens digit, i.e. add it to the sum of the next parallelogram (working from right to left). Continue adding the parallelograms until you have reached the end of the row. The final digit in you answer is simply the upper number in the left-most cell. The correct answer is 18112. At this time you have successfully found the answer to a complex multiplication problem without using a calculator or a computer, only by using an ancient method; Napier’s Bones.

Now that you understand how to use Napier’s Bones, abandon your calculator, shut down your computer, and have done with tedious modern methods of pencil and paper multiplication. Let Napier’s Bones do the work for you!

Images courtesy www.mathworld.wolfram.com

page revision: 2, last edited: 17 Feb 2009 22:33