Self-taught Mary Fair­fax Somerville as­tounded the aca­demic world with her in­sights into astro­physics. ROBYN ARIANRHOD re­views a re­mark­able life.

Cosmos - - Life Science - 01 Mary Fair­fax Somerville: de­spite lit­tle for­mal ed­u­ca­tion, she was de­ter­mined to un­der­stand the nat­u­ral world.

WHEN THE ROYAL BANK of Scot­land (RBS) is­sues its new ten-pound note to­wards the end of 2017, the 19th cen­tury’s “Queen of Sci­ence” will surely in­spire new gen­er­a­tions in her home­land. But the le­gacy of self-taught math­e­ma­ti­cian Mary Fair­fax Somerville reaches way be­yond Scot­land: she was a bril­liant trans­la­tor of sci­ence for the pub­lic and a pas­sion­ate ad­vo­cate for women’s ed­u­ca­tion.

The RBS’S new poly­mer note shows Mary as a young wo­man; but she was 50 years old by the time she shot to fame in 1831, af­ter the pub­li­ca­tion of her cut­ting-edge Mech­a­nism of the Heav­ens. Aca­demics were as­tounded: it was said that no more than five men in Bri­tain were ca­pa­ble of writ­ing such a de­mand­ing book, based as it was on the work of lead­ing French math­e­ma­ti­cian Pierre-simon Laplace. It was a phe­nom­e­nal achieve­ment for a wo­man who taught her­self sci­ence and math­e­mat­ics at a time when most uni­ver­si­ties did not ad­mit fe­males. Mech­a­nism of the Heav­ens was not just a mo­men­tary cu­rios­ity; it was used as a text­book in Cam­bridge’s ad­vanced math­e­mat­i­cal as­tron­omy classes for the next cen­tury.

This lat­est ac­co­lade stems from RBS’S de­ci­sion to is­sue its first poly­mer ban­knotes. For the new ban­knote, Somerville was se­lected in an on­line com­pe­ti­tion. She gar­nered many votes from stu­dents at Somerville Col­lege. Ox­ford’s first women’s col­lege (it be­came co­ed­u­ca­tional in 1994) was named af­ter her in 1879, just a few years too late for her to en­joy the hon­our. She died in 1872, just shy of 92.

Mary Fair­fax (who later married physi­cian Wil­liam Somerville) was born in Jed­burgh, close to the bor­der with Eng­land, but raised in Burn­tis­land just across the pic­turesque Firth of Forth north of Ed­in­burgh. The old white­washed house where she grew up still stands, in what is now Somerville Square. A plaque above the door­way ac­knowl­edges its fa­mous for­mer res­i­dent but the house is rather run-down to­day. There is no sign of the spa­cious gar­den where Mary’s mother grew fruit and veg­eta­bles to feed the fam­ily – her fa­ther’s naval pay was poor, de­spite his even­tual rise to the po­si­tion of vice ad­mi­ral. But the com­mon where the fam­ily’s cow grazed still ex­ists, as does the nearby church they at­tended – and of course there is the beach, whose shore­line is de­picted in the de­sign of the new ban­knote. It is a sym­bolic choice. Ed­u­ca­tional wis­dom at the time held that be­cause women weren’t as strong as men, and had smaller brains, aca­demic study would dam­age girls’ health or even send them mad. Con­se­quently, while her broth­ers were sent to school, Mary was rel­e­gated to home du­ties; her only di­ver­sion was roam­ing the beach with the seabirds for com­pan­ions.

Not sur­pris­ingly, she grew up, as she later put it, a “wild crea­ture”. Even in her teens she was vir­tu­ally il­lit­er­ate and in­nu­mer­ate, de­spite “an ut­terly wretched” year at a board­ing school when she was 10. But Burn­tis­land’s rocks, birds, plants and stars in­spired a won­drous cu­rios­ity about the nat­u­ral world. She was de­ter­mined to un­der­stand the way na­ture worked.

As for math­e­mat­ics, her in­ter­est was kin­dled by tamer pur­suits. In the mid-1790s, when she was 15, an older girl showed her a women’s magazine con­tain­ing sewing pat­terns. Mary’s eye was taken not by the exquisite needle­work but by a col­lec­tion of x’s and y’s ar­ranged in strange, al­lur­ing pat­terns. It was a so­lu­tion to one of the magazine’s math­e­mat­i­cal puzzles, whose pop­u­lar­ity tes­ti­fied to the in­tel­lec­tual hunger among many women. Her friend knew only that “they call it al­ge­bra”; but those mag­i­cal sym­bols fired Mary with an in­domitable de­sire to speak this se­cret lan­guage.

It took her many years, and she did it mostly alone. When Bri­tain’s sci­en­tists and math­e­ma­ti­cians were fi­nally ex­posed to her eru­di­tion, they were stunned. Her in­tro­duc­tion to Lon­don’s sci­en­tific so­ci­ety had fol­lowed her 1812 marriage to Dr Somerville, who was sup­port­ive of his wife’s in­tel­lec­tual at­tain­ments. Through him she met lead­ing sci­en­tists on both sides of the Chan­nel, in­clud­ing Laplace. Some years later Lord Henry Brougham, co-founder of the lib­eral Ed­in­burgh Re­view, in­vited her to write on Laplace’s work. When she fin­ished her Mech­a­nism of the Heav­ens, how­ever, Brougham thought it too aca­demic for the self-

im­prove­ment book for tech­ni­cal pro­fes­sion­als he had en­vis­aged. Even­tu­ally the in­no­va­tive pub­lisher John Mur­ray took a chance on it, cat­a­pult­ing Mary to fame.

Un­der­stand­ing Laplace’s work re­quired knowl­edge of the user-friendly form of cal­cu­lus that Ger­man math­e­ma­ti­cian Got­tfried Leib­niz had de­vel­oped, and which is now uni­ver­sally taught in high schools. Bri­tish math­e­ma­ti­cians were still teach­ing Isaac New­ton’s more opaque sym­bol­ism but, be­cause she was self­taught, Mary had by­passed this and taught her­self Leib­niz’s “con­ti­nen­tal” cal­cu­lus, along with the Latin re­quired to read New­ton’s Prin­cipia and the French to read Laplace’s mon­u­men­tal fol­low-up work, Mé­canique

Céleste ( Ce­les­tial Me­chan­ics).

Laplace’s up­date of Prin­cipia had made him de­servedly fa­mous, but his celebrity hinged on his res­o­lu­tion of a co­nun­drum: was the so­lar sys­tem sta­ble?

The con­tro­versy had be­gun a cen­tury ear­lier. New­ton’s the­ory of grav­ity had sug­gested it was not. Early op­po­nents of New­ton’s the­ory, such as Leib­niz, had favoured the an­cient idea of “the ether”, un­seen cos­mic vor­tices car­ry­ing the plan­ets in their wake. It was also as­sumed that God had set these ethe­real whirlpools in per­pet­ual mo­tion to cre­ate a per­fectly sta­ble So­lar Sys­tem. The plan­e­tary mo­tions cer­tainly seemed sta­ble, but New­ton fol­lowed the log­i­cal con­se­quences of his grav­i­ta­tional the­ory. His fa­mous in­verse-square law gave rise to an el­lip­ti­cal or­bit tak­ing ac­count of the mu­tual grav­ity be­tween the Sun and a planet. But each planet’s or­bit would be dis­torted by the ad­di­tional grav­ity of nearby bod­ies, so New­ton pre­dicted that, far into the fu­ture, the ac­cu­mu­lated dis­tor­tions of all the or­bits would lead to chaos.

Laplace and Joseph-louis La­grange un­der­took the her­culean task of ap­ply­ing New­ton’s law of grav­ity to all the plan­ets, moons and other known bod­ies in the So­lar Sys­tem. They even­tu­ally found the re­sult­ing dis­tor­tions in the var­i­ous or­bits do in­crease and de­crease over the mil­len­nia, but within such nar­row lim­its the whole sys­tem re­mains sta­ble. (To­day chaos the­ory tells us the So­lar Sys­tem is in­her­ently un­sta­ble but mod­els sug­gest we’re un­likely to see any dis­as­trous plan­e­tary col­li­sions within the Sun’s life­time.)

The use of New­ton’s law alone to show the longterm sta­bil­ity of the So­lar Sys­tem was a great vic­tory for the the­ory of grav­ity, and gen­er­ated enor­mous ex­cite­ment among math­e­mat­i­cal physi­cists. Mary’s Mech­a­nism of the Heav­ens made that ex­cite­ment ac­ces­si­ble to a broader au­di­ence of physi­cists and univer­sity stu­dents, be­cause she ex­plained the math­e­mat­i­cal rea­son­ing un­der­ly­ing the rel­e­vant con­clu­sions in Laplace’s mon­u­men­tal Mé­canique Ce­leste. ( Mech­a­nism was an ex­pli­cated ac­count of the first two books of the five-vol­ume Mé­canique.)

Her next book, On the Con­nex­ion of the Phys­i­cal Sciences, was pub­lished in 1834. It was popular rather than aca­demic, and soon be­came a best­seller also trans­lated into Ital­ian and Ger­man. It cap­tured the spirit of the times – the sense that sci­en­tists were con­nect­ing the dots to re­veal a uni­fied cos­mic scheme. For in­stance, the con­nec­tion be­tween elec­tric­ity and mag­netism was big news. That these seem­ingly sep­a­rate phe­nom­ena were two sides of the same coin had only re­cently been demon­strated by Michael Fara­day: in 1831, 10 years af­ter Den­mark’s Hans Oer­sted dis­cov­ered elec­tric­ity can in­duce mag­netism, Fara­day found the con­verse, gen­er­at­ing elec­tric­ity sim­ply by mov­ing a mag­net through a coil of wire.

Con­nex­ion had ben­e­fited from Mary’s friend­ships with many of the lead­ing sci­en­tists of the day: as well as Laplace and Fara­day, she also knew Thomas Young, who pro­posed the wave the­ory of light, Charles Bab­bage, the com­puter pi­o­neer, and his col­lab­o­ra­tor Ada Lovelace (pro­filed in Cos­mos 60, p78) who she tu­tored and men­tored. Mary could not be­lieve such peo­ple took no­tice of her – she al­ways saw her­self as

She taught her­self Latin to read New­ton’s Prin­cipia and French to read Laplace’s mon­u­men­tal fol­low- up, Mé­canique Céleste.

a back­woods Scot­tish girl with no for­mal ed­u­ca­tion. Through this cir­cle she learned first-hand about the lat­est de­vel­op­ments in physics, although she was no stranger to sci­en­tific ex­per­i­men­ta­tion. In 1826 she had her first pa­per pub­lished in Philo­soph­i­cal Trans­ac­tions

of the Royal So­ci­ety. (She and Ger­man-born Bri­tish as­tronomer Caro­line Her­schel were the first women pub­lished in the prestigious jour­nal.)

Mary’s pa­per de­scribed her ex­per­i­ments on the pos­si­ble con­nec­tion be­tween mag­netism and light. No one knew then that light it­self was elec­tro­mag­netic but ex­per­i­menters were be­gin­ning to won­der if light and mag­netism could af­fect each other. Her con­clu­sions, though praised for their orig­i­nal­ity, were ul­ti­mately proven in­cor­rect – as is of­ten the way in sci­ence. The first de­fin­i­tive ev­i­dence of a con­nec­tion be­tween light and mag­netism was found by Fara­day 20 years later, in 1846. James Clerk Maxwell would com­plete the puzzle with his elec­tro­mag­netic the­ory of light in 1864 (see Cos­mos 66, p60).

In Con­nex­ion, she also con­jec­tured that ob­served dis­tor­tions in the or­bit of Uranus – dis­cov­ered by her friend Wil­liam Her­schel (Caro­line’s brother) – might be due to the ef­fects of a body as yet un­seen. Nep­tune was duly dis­cov­ered in 1846, as a re­sult of in­de­pen­dent cal­cu­la­tions us­ing New­ton’s the­ory by English­man John Couch Adams and French­man Ur­bain Le Ver­rier. Adams later said his search for the planet had been in­spired by the pas­sage in Mary’s book.

Per­haps there is no bet­ter tes­ta­ment to Somerville’s writ­ing than the opin­ion of one of the men she de­feated in RBS’S pub­lic poll: James Clerk Maxwell, the ul­ti­mate 19th-cen­tury uni­fier who the­o­rised the con­nec­tion be­tween elec­tric­ity, mag­netism and light. He said her sec­ond book put “into def­i­nite, in­tel­li­gi­ble and com­mu­ni­ca­ble form the guid­ing ideas that are al­ready work­ing in the minds of men of sci­ence … but which they can­not yet shape into a def­i­nite state­ment”.

Mary’s next book, Phys­i­cal Ge­og­ra­phy, pub­lished in 1848, was both suc­cess­ful and con­tro­ver­sial, be­cause it in­cluded dis­cus­sion of the new sci­ence of ge­ol­ogy. The use of rocks and fos­sils to un­der­stand the Earth’s his­tory put its age far be­yond the bi­b­li­cal es­ti­ma­tion of 6,000 years or so. Mary later re­called that this aroused more con­tro­versy than Dar­win’s the­ory of evo­lu­tion. Her fourth book, On Molec­u­lar and Mi­cro­scopic

Sciences, pub­lished in 1869, was by her own ac­count “a great mis­take”: by then 88 years old, she no longer moved in sci­en­tific cir­cles, and the book lacked the cut­ting edge fresh­ness of her ear­lier works.

Ev­ery­one seemed to love and ad­mire Mary Somerville. She was show­ered with hon­ours, in­clud­ing a gov­ern­ment pen­sion awarded to im­por­tant writ­ers and sci­en­tists. Even the Royal So­ci­ety, which did not ad­mit fe­male mem­bers at the time, erected her bust in its Great Hall, and the Royal Astro­nom­i­cal So­ci­ety made her an hon­orary mem­ber (along with Caro­line Her­schel, in 1835).

Af­ter her death, her story lay dor­mant for a cen­tury, un­til schol­ars went search­ing for his­tor­i­cal fe­male role mod­els to show girls that it was cul­ture, not bi­ol­ogy, that lim­ited women’s par­tic­i­pa­tion in sci­ence. Mary Somerville’s tri­umph against such great odds makes her story par­tic­u­larly res­o­nant.

At 91, while study­ing the new math­e­mat­i­cal topic of quater­nions, she re­vealed one of the se­crets of her suc­cess: when­ever she en­coun­tered a dif­fi­culty, she re­mained calm but de­ter­mined, be­cause “if I do not suc­ceed to­day, I will at­tack [the prob­lem] again on the mor­row.” She helped pi­o­neer the way for women in sci­ence, but her ap­proach to life re­mains time­less. ROBYN ARIANRHOD is a math­e­ma­ti­cian and au­thor. Her books in­clude Se­duced by Logic: Em­i­lie du Châtelet, Mary Somerville and the New­to­nian Rev­o­lu­tion. IMAGES 01 NYPL /Sci­ence Source / Getty Images

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