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Napier's Bones

Date: 01/20/97 at 11:14:12
From: Crystal
Subject: Napier's Bones

How do I solve the problem 364 x 27 on the bone rods?  Can you explain 
how to figure this out? 


Date: 01/20/97 at 12:28:49
From: Doctor Ken
Subject: Re: Napier's Bones

Hi there -

Here's some information I found by searching the math-history mailing 
list on our site.  You can search the Math Forum site too by going to:    

and using the keyword Napier:

On Mon, 12 Feb 1996, Emmanuel CE Middle wrote:

Hello! Our names are Mark Atkins and Richard Pinel aged 12 of Emmanuel 
C of E aided school and we are wondering if anyone knows anything 
about John Napier or his "bones". 

John Napier was Baron Napier of Merchistoun, Scotland, and lived in 
Merchistoun Castle.  The thing he's really famous for is his discovery 
of logarithms: his book on them was published in 1609.

Napier's "bones" are a collection of little sticks, each one bearing 
the multiples of some particular digit: for instance the "8-bone" 
would look like:

               |0 /|
               |1 /|
               |2 /|
               |3 /|
               |.. |

(actually those slanting lines should be diagonals of the squares they 
are in).

These were used in multiplying:  to multiply by 8314 for instance, 
you'd put an 8-bone, a 3-bone, a 1-bone and a 4-bone side-by-side, and 
then you'd find it easy to read of the first 9 multiples of 8314.  
[The digits above the slanting lines "carry over" to the preceding

I suggest you make a set of such "bones" out of paper, place them 
side-by-side like this, and see how easy they make these 
multiplications.  If you have any difficulty in following this, please 
write again.

It's probably much better to try to make them yourself and work out 
how to use them, rather than to just read about them in a book.

John Conway


You can also check out the previous answer in Dr. Math's archives 
about just how the bones work:   

As a cautionary note, you may find that different people have 
different ideas of what exactly Napier's Bones are.  Some people use 
the term as a funny name for a slide rule, and others mean the actual 
objects that John Napier used to do multiplication, which were the 
forerunners of the slide rule. So if you see conflicting information 
out there, that may be where it came from.

-Doctor Ken,  The Math Forum
 Check out our web site!   
Associated Topics:
Elementary Multiplication
Elementary Number Sense/About Numbers
Middle School Number Sense/About Numbers

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