She was a popularizer of astronomy and wrote textbooks. The Royal Academy in Britain awarded her an honorary membership (women were not permitted to hold membership in those days). Mary translated the difficult work by mathematician/astronomer Laplace - Mécanique Céleste - into English, an effort for which her English contemporaries owed her much. It was used as a college textbook for nearly a century. Laplace himself said that she was the only woman to understand his work. She was mainly self-taught. She produced an amazing series of papers, presented on her behalf to the Royal Society by her husband. After her death Oxford University named one of its colleges after her. She had the incredible gift of synthesizing the works of others into comprehensible language. She wrote a book called The connexion of the physical sciences in which she discusses the possibility of an undiscovered planet being responsible for the irregularities in Uranus's orbit. This led directly to John Couch Adams research and subsequent discovery of the planet Neptune. Ogilvie's book Women in Science has a very nice article about her as does the web site at Agnes Scott College.
"In 1834 mathematician and author Mary Somerville published On the Connexion of the Physical Sciences, a work that was instrumental in the making of modern physics as a discipline. Contemporaries praised the book’s clear and lucid survey of astronomy, experimental physics, and chemistry, and it became a classic of Victorian scientific writing. But Connexion also posed key questions for a rapidly expanding and largely male-dominated world at a moment of intense intellectual ferment. Could women excel at science? Were the scientific writings of a woman inherently different from those of a man? “Notwithstanding all the dreams of theorists,” wrote Cambridge philosopher William Whewell in his review of Connexion, “there is a sex in minds”—in other words, Whewell felt that Somerville’s sex would always set her writings apart from those of her male contemporaries."
In October 2017 she appeared on the new 10 pound note of the Royal Bank of Scotland. See Physics Today article
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