John Napier (1555-1617)

Discoveries

John Napier is most famous for inventing a method of calculation using logarithms. He also devised:

• Other rules for calculating
• Several portable calculating devices
• Some very successful weapons of war.

Logarithms

Invented in 1614, Napier's logarithms allowed people to do more calculations in one hour than they could previously have done in a day.

Logarithms turn complicated multiplication and division problems into addition and subtraction. They are laid out in logarithmic tables, popularly known as 'log tables'.

Variations on Napier's logarithmic tables were used everywhere until the 1970s, when electronic calculators were invented.

Logarithms depend on ratios between numbers. By substituting different 'artificial' numbers for the numbers you are working with, you make calculations on 'artificial numbers'. You then convert the resulting total to the actual answer.

Fellow mathematicians applauded Napier's work on logarithms, 'Mirifici logarithmorum canonis descriptio' (1614), almost immediately. Professor Henry Briggs was so excited about it that he made the book 'his Bosom and Darling Companion by Night and by Day'.

Briggs and others revised and expanded the work, but its principles remained the same.

Napier's rules of circular parts

Napier drew up rules for calculations involving spherical triangles which are still valid today.

These are now known as 'Napier's rules of circular parts'.

A spherical triangle is the shape enclosed if you join up three points on the surface of a sphere.

Portable calculating devices – Napier's bones

In his book 'Rabdologia' John Napier describes a set of rods which came to be called 'Napier's bones'.

Without this early 'calculator', the discoveries of others would have been delayed by years of long and complex calculations.

To multiply numbers, you had to choose the appropriate rods, lay them next to each other, read the relevant numbers and do a simple addition to find the answer.

See our Useful links page for more information about 'Napier's bones'.

Portable calculating devices – Promptuary

The promptuary could be said to be the world's first calculating machine. Napier invented it for larger calculations.

A more complicated version of 'Napier's bones', the promptuary was a box of 100 or more strips of a firm material.

Each strip was divided into squares, and each square halved into triangles. Some strips had triangular peepholes so you could read the result when strips were overlaid.

Portable calculating devices – Chessboard calculator

Napier's chessboard calculator was significant in that it used a binary method of entering data.

Each square on a chessboard had an assigned value. To represent the numbers needed for the calculation, you placed counters, similar to those used in 'draughts', on the relevant squares.

Binary entry in this context meant that a square was either empty or contained a counter.

The chessboard calculator could be used for multiplication and division, and finding the square root of binary numbers.

See our Useful links page for more information about Napier's chessboard calcuator

Napier's weaponry

Invasion by Spain was a serious threat to England and Scotland in the 16th century.

Napier designed several weapons for use against the Spanish Armada.

These included:

• A burning mirror which could to destroy enemy ships
• A canon alleged to have destroyed a herd of cattle in one go.

Back to top