His love for astronomy meant that he had to do tedious calculations with large numbers. This motivated him to search for a simpler way. After twenty years of research, he discovered logarithms. They were first described in 1614. Logarithms are basically the opposite of exponentials. The intervals on a scale will get closer to each other the higher the value, rather than farther apart. Examples include the Richter Scale or the decibel scale. He invented a mechanical tool for using logarithms to calculate called "Napier's Bones". His active mind led him to create weapons of war, including mirrors to burn distant ships, area-effect artillery, and primitive tanks.

Napier's Bones were used to aid mathematical calculations. They consisted of sticks made of ivory or similar materials, which were divided into sections that were marked with digits.

Edmund Gunter (1581-1626), Professor Astronomy at Gresham College in London, was responsible for the evolution of Napier's Bones to something more ruler-like. He is also the inventor of scientific devices such as the "Gunter Chain", which can be used in surveying and 100 links that are 66ft long (side note: one chain, 22yrds in length), the "Gunter Quadrant", which is used to determine the hour of each day, www.trustytimenoob.com and the "Gunter Rule", which is arithmic ruler with dividers for calculations. Variants of Gunter Rule were used on ships throughout the 19th century.

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William Oughtred was a Church of England Rector and Fellow of Kings College Cambridge. He was also a teacher of mathematics, and was contemporaneous with Edmund Gunter. He simply took two Gunter Rules and placed them side-by-side, eliminating the need to use dividers. He also invented the circular slide rule, but was involved in a dispute about priority with one his students. His mathematics and the instruments that accompanied them are described in his book The Circles of Proportions and the Horizontal Instrument (1632). Oughtred also created a new type of sundial,roger dubuis replica which is still named after him.