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Physics, chemistry and astronomy are taught as separate subjects, with separate books and separate exams. Mary Somerville spent much of her life showing how they connect, and she did it after teaching herself almost everything she knew. This post tells her story from reliable sources, looks at what her most popular book was about, and works through a Kepler's-law calculation on the planets her book discussed.
How did Mary Somerville get an education?
According to the MacTutor biography from the University of St Andrews, she was born Mary Fairfax in Jedburgh, Scotland, on 26 December 1780, and grew up in Burntisland in Fife. Her brothers were educated; she was not. Her mother taught her to read, and a year at a boarding school in Musselburgh left her feeling, in her own words, "like a wild animal escaped out of a cage."
Back home she read every book she could find. An uncle encouraged her Latin. She overheard the painter Alexander Nasmyth tell another pupil that Euclid's Elements was the basis of perspective, and of astronomy too, and she began working through Euclid with help from her younger brother's tutor. Her parents worried the long nights of study would harm her health.
Her first husband had little interest in her studies, and after his death in 1807 she returned to Scotland. Somerville College, Oxford records that, with encouragement from John Playfair, professor of natural philosophy at Edinburgh, she solved problems set in a mathematical journal and won a silver medal in 1811. In 1812 she married William Somerville, who supported her work. They moved to London and met many of the leading scientists of the day, including Charles Babbage, and in Paris in 1817 she met Laplace.
What did she publish?
Her first paper, On the magnetizing power of the more refrangible solar rays, appeared in the Philosophical Transactions of the Royal Society in 1826. MacTutor notes that the paper attracted much interest, although its theory was later shown to be wrong.
In 1827 Lord Brougham asked her, on behalf of the Society for the Diffusion of Useful Knowledge, to translate Laplace's Mécanique Céleste. She went far beyond translation and explained the mathematics, which was unfamiliar to most English mathematicians at the time. The result, The Mechanism of the Heavens, appeared in 1831 and was too long for the society, so John Murray published it instead. Somerville College records that she was 51, and that two months after publication fellows of the Royal Society paid for a marble bust of her for their meeting room.
Her second book, On the Connexion of the Physical Sciences (1834), ran to nine editions and sold over 15,000 copies. Physical Geography followed in 1848 and was her most popular book.
Why did "connexion" matter?
Her book argued that the sciences share common principles. When the Quarterly Review reviewed it in 1834, the reviewer worried that science was splitting into narrow specialities and losing "all traces of unity". He noted that there was not even a single English word for people who studied the material world. Members of the British Association had felt the lack, he wrote, and "some ingenious gentleman proposed that, by analogy with artist, they might form scientist". At the time, the review adds, the suggestion was not generally palatable.
MacTutor quotes a passage from the 1842 edition about Uranus. Its tables were "already defective", she wrote, possibly because it "may be subject to disturbances from some unseen planet revolving about the sun beyond the present boundaries of our system." MacTutor says this discussion led the astronomer John Couch Adams to begin his own investigation, which became part of the story of how Neptune was found.
Worked example: Kepler's third law for Uranus and Neptune
For planets orbiting the Sun, T² = a³ when T is in years and a in astronomical units (AU). Data from NASA's planetary fact sheet:
Uranus. Orbital period 30,589 days. T = 30,589 / 365.25 = 83.75 years. Then a = T^(2/3) = 83.75^(2/3) ≈ 19.1 AU. The fact sheet gives a distance of 2,867.0 million km, and 2,867.0 / 149.6 ≈ 19.2 AU.
Neptune. Orbital period 59,800 days, so T ≈ 163.7 years and a ≈ 163.7^(2/3) ≈ 29.9 AU. The fact sheet's 4,515.0 million km gives 30.2 AU.
Both agree with the measured distances to within about 1 percent. Common mistakes: using days with AU without converting to years, raising T to the 3/2 power instead of 2/3, and applying T² = a³ to moons, which orbit a different central body. For the history behind the law, see our post on Kepler's laws of planetary motion, and for the planet whose orbit started it all, William Herschel and Uranus.
What happened later in her life?
MacTutor records that in 1835 she was elected to the Royal Astronomical Society at the same time as Caroline Herschel, and that she received a civil pension. The family moved to Italy, where she spent most of her later life. Somerville College notes that in 1868 she was the first person asked to sign John Stuart Mill's petition for women's suffrage, and that on the day before she died, in Naples on 29 November 1872, she was revising a paper on quaternions. The Oxford college was named after her in 1879.
What can a student take from Somerville's way of working?
Go to the source. She read Euclid, Newton and Laplace rather than summaries of them.
Explain to learn. Writing for readers who lacked the mathematics forced her to understand every step.
Look for links. Ask how a chapter in physics connects to one in chemistry or maths.
When you want to see how one idea links to others, the Fermi Concept Library covers every concept in physics, chemistry, biology and mathematics, each with its place in the map, so you can follow a connection across subjects.
Use the fact sheet's period for Saturn, 10,747 days, and check whether Kepler's third law gives its distance from the Sun.
