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Despite the family's fortunate economic standing, Mary's education was, as was characteristic of much of the education of young girls of her time, quite "scant and haphazard" (Osen 97). She found her only year of full-time schooling, during which she attended a boarding school for girls in Musselburgh, rather miserable and unhappy (Osen 97). Mary studied her first simple arithmetic at the age of thirteen, when her mother took a small flat for the winter months in Edinburgh and she was enrolled briefly in a writing school there. Also at about this time, she, quite by accident, began her study of algebra, as she happened upon some mysterious symbols in the puzzles of a women's fashion magazine and was able to persuade her brother's tutor to purchase some elementary literature on the subject for her (Perl 87).
In 1804, at the age of twenty four, Mary married her cousin, Captain Samuel Greig. Greig was a member of the Russian Navy and had little interest in the math and science that his wife so dearly loved. Although he held intellectual women in rather low esteem, he interfered little with her work. The couple had two sons, Woronzow (1805-1865) and William George (1806-1814), but Samuel did not live to see much of the lives of his children, for he died in 1807 after only three years of marriage (Grinstein and Campbell 209).
The death of her husband, although difficult and tragic, did, however, afford Mary an opportunity quite rare to women of her time. She found that widowhood and a comfortable inheritance had left her both emotionally and financially independent. No longer controlled by either her parents or husband, Mary was free to study according to her personal convictions. She mastered J. Ferguson's Astronomy and became a student of Issac Newton's Principia, despite the fact that many of her family and friends disapproved (Grinstein and Campbell 209). Her circle of friends in the scientifc community was limited, but she corresponded frequently with Scotsman William Wallace, who, at the time, was mathematics master at a military college. It was upon his advice that Mary obtained a small library of works to provide her with a sound background in mathematics.
She remarried in 1812 to another cousin, Dr. William Somerville, who was a surgeon in the British Navy. Dr. Somerville was very supportive of his wife's intellectual endeavors, despite the fact that some of his family wished that Mary would "give up her foolish manner of like and make a respectable and useful wife" (Osen 104). The couple had four children together.
Mary Fairfax Somerville's scientific investigations began in the summer of 1825, when she carried out experiments on magnetism. In 1826 she presented her paper entitled "The Magnetic Properties of the Violet Rays of the Solar Spectrum" to the Royal Society. The paper attracted favorable notice and, aside from the astronomical observations of Caroline Herschel, was the first paper by a woman to be read to the Royal Society and published in its Philosophical Transactions (Grinstein and Campbell 213). Although the theory presented in her paper would eventually be refuted by the investigations of others, it distinguished her as a skilled scientific writer respected among her colleagues.
In 1827 Lord Brougham, on behalf of the Society for the Diffusion of Useful Knowledge, began correspondence with Mary through her husband, as social convention dictated, to persuade her to write a popularized rendition of Laplace's Mecanique celeste and Newton's Principia (Osen 106). He hoped that she could reach a larger audience by communicating the concepts clearly through simple illustrations and experiments that most people could understand. Unsure of her qualifications, Mary undertook the project in secrecy, assured that, if she should fail, the manuscript would be destroyed and only those immediately involved would ever need to know (Osen 107). The Mechanism of the Heavens was a great success, probably the most famous of her mathematical writings. In recognition, a portrait bust of her was commisioned by her admirers in the Royal Society and placed in their great hall, now in the headquarters of the society in London (Grinstein and Campbell 211).
While in Europe for eleven months in 1832-1833, she largely completed her second book, which was published in 1834. With The Connection of the Physical Sciences, which was an account of physical phenomena and the connections among the physical sciences, came new scientific distinctions. She and Caroline Herschel were elected in 1835 to the Royal Astronomical Society, the first women to receive such an honor. She was given a pension of 200 pounds per year form the King of England and received honorary memberships from various other distinguished scientific organizations, including eleven Italian scientific societies between 1840 and 1857 (Grinstein and Campbell 212).
In 1848, at the age of sixty eight, Mary Fairfax Somerville published yet another book. Physical Geography, a work for which she was preached against in York Cathedral, proved to be her most successful yet and was widely used in schools and universities for the next fifty years (Grinstein and Campbell 214).
With the deaths of her second husband, only remaining son, and valued friend Sir John Herschel, Mary Fairfax Somerville wrote in 1871, "Few of my early friends now remain--I am nearly left alone" (Perl 92). She lived to complete two more works before her death in Naples in 1872. Her last scientific book, Molecular and Microscopic Science, which was published in 1869 when Mary was eighty-nine, was a summary of the most recent discoveries in chemisty and physics. In that same year she completed her autobiography, of which parts were published by her daughter Martha after her death (Grinstein and Campbell 214). Although deaf and frail in her later years, she retained her mental faculties and even continued to, in her words, "read books on the higher algebra for four or five hours in the morning, and even to solve problems" until her peaceful death at the age of ninety two (Perl 92).