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# How Mathematical Logarithms Aided the Royal Navy

Mathematical logarithms and history might seem unrelated to one another, but this summer Turner Trapp ’15 is conducting interdisciplinary research into the role mathematical developments have in history. In his Emerson Foundation project, “The Discovery of Logarithms, Their Application to Ballistics, and Their Role in the Royal Navy’s Rise to Dominance in the Age of Sail,” he is working with Professor of History Kevin Grant to examine how the development of logarithms relates to England’s rise to naval dominance.

A high school pre-calculus teacher sparked Trapp’s interest in the topic when he mentioned that the English conquered the Spanish Armada because of logarithms. In his research, Trapp later found that the first publication of the method of logarithms in 1614 came after the English victory over the Spanish in 1588. However, the concept sparked an enduring interest in the importance of logarithms to the English Royal Navy. Trapp was particularly intrigued because not much research has been done on the topic before. While there is plenty of work on the scientific revolution and the naval history of the time, not many historians have investigated the relationship between the two movements.

Scottish mathematician John Napier introduced logarithms as a way to simplify calculations. With the use of logarithm tables and tools such as the slide rule, people who were not high level mathematicians could make complex calculations. Trapp explained, “The point of logarithms is to bring a higher level of math to the common man and in turn advance society.” Scientists, engineers, and navigators began using logarithms to advance their work. Eventually gunners in the English navy applied logarithms to simplify their calculations and improve their aim and effectiveness. They used the calculations to determine the ideal cannonball size, shells, and amount of powder for each shot.

However, Trapp has found that the standard implementation of logarithms by the English Navy’s gunners was slow. Private investors with smaller ships were the first to take advantage of the new methods. Trapp has developed a number of theories about why logarithms were not immediately widely applicable within the Royal Navy. First, at the time, the navy used fleet tactics that did not prioritize aiming. Smaller private ships, on the other hand, commonly used pursuit-based tactics that relied more on aim. Perhaps the most significant barrier, though, was education. Many gunners were unable to read or understand math well, which made using the gunners’ manuals a challenge.

If Trapp has the opportunity to continue his research, he is hoping to look more into the gradual standardization of education within the navy, which would eventually enable the gunners to take advantage of logarithms. The advancement of naval education also relates to a broader theme of higher math and technology being spread to more people within Britain. Trapp will begin to explore this in his Emerson paper, which will summarize his very original research on how logarithms connect the military and scientific revolutions in England.

Trapp is a graduate of John Burroughs School in St. Louis, Missouri.

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