As is the case today, scientist of Napier's time frequently had to multiply and divide large numbers. Of course, at that time no calculators (or even slide rules) existed; a scientist had to make all calculation by hand. Such work was tedious and prone to errors. Napier invented logarithms as a system that would allow the relatively easy calculation of product and quotients, as well as powers and roots.
With this system, the product of two numbers was calculated by finding the logarithms of those numbers in a book of tables and adding the result. Napier spent twenty years creating the tables. This procedure represented a real shortcut; addition replaced multiplication, and addition is much simpler than multiplication when done by hand. This method of multiplying by adding was an especially useful application of what we know as the Multiplication-Become-Addition property, log (A . B) = log A + log B. Napier did not invented the notation of log (b) x; this notation was invented much later by Leonhard Euler. Napier did not use any notation in his writings on logarithms; he wrote everything out verbally.
Although Napier did not invent the decimal point, he is responsible for its widespread use. Napier's calculation system was very popular, and the logarithms in his tables were decimal numbers written with a decimal point.
A similar system was developed independently by Joost Burgi, a Swiss mathematician and watchmaker. Napier is generally credited with the invention of logarithms, because he published his work before Burgi.
As a member of Scottish aristocracy, Napier was an active participant in local and national affairs. He was also a very religious man and belonged to the Church of Scotland. These two interest led to an interesting story about Napier.
In sixteenth century Scotland, politics and religion were inexorably entwined. Mary, Queen of Scots, was a Roman Catholic, Elizabeth, Queen of England, was a Protestant, and both Church of Scotland and the Church of England were Protestant churches. Furthermore, Mary had a strong claim to the throne of England. Catholic faction wanted Scotland to form an alliance with France; Protestant faction wanted an alliance with England. After a series of power struggles, Mary was forced to abdicate her throne to her son who then became James VI, King of Scotland. Mary was eventually beheaded for plotting against the English throne.
It was well known that James VI wished to succeed Elizabeth to the English throne. It was suspected that he had enlisted the help of Philip II, King of Spain and Catholic, to attain this goal. It was also suspected that James VI was arranging an invasion of Scotland by Spain. John Napier was a member of the committee appointed by the Scottish church to express its concern to James.
Napier was not content with expressing his concern through the church. He wrote one of the earliest Scottish interpretation of scriptures, A Plaine Discovery of the Whole Revelation of Saint John, which was clearly calculated to influence contemporary events. In this work, Napier urged James VI to see that "justice be done against the enemies of God's Church." It also declared, "Let it be your Majesty's continual study to reform ... your country, and first to begin at your Majesty's owne house, familie, and court, and purge the same of all suspicion of Papits and Atheists and Newtrals."
This tract was widely read in Europe as well as in Scotland, and Napier earned a considerable reputation as a scholar and theologian. It has been suggested that the tract saved him from persecution as a warlock; Napier had previously been suspected of being in league with the devil.
Napier also invented several secret weapon for the defense of his faith and country against a feared Spanish invasion. These invention included two kind of burning mirrors desinged to set fire to enemy ships at a distance and an armored chariot that would allow its occupant to fire in all direction. Whether any of these devices were ever constructed is not known.
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