rusk inJohn Ruskin (1819 – 1900)
Rocks in Unrest


Phoebe Sarah Marks  was born on 28 April 1854, in Hampshire, England. She was the third child of a Polish-Jewish watchmaker named Levi Marks, an immigrant from Tsarist Poland; and Alice Theresa Moss, a seamstress. Her father died in 1861, leaving Sarah’s mother with seven children and an eighth expected. Sarah took up some of the responsibility for caring for the younger children.
At the age of nine, Sarah was invited by her aunts, who ran a school in London, to live with her cousins and be educated with them.
In her teens she adopted the name “Hertha” after the heroine of a poem by Algernon Charles Swinburne that criticized organised religion.

By age 16, she was working as a governess, but  George Eliot supported Ayrton’s application to Girton College, Cambridge.
Eliot was writing her novel Daniel Deronda at the time. One of the novel’s characters, Mirah, was said to be based on Ayrton.
During her time at Cambridge, Ayrton constructed a sphygmomanometer, led the choral society, founded the Girton fire brigade, and, together with Charlotte Scott, formed a mathematical club. In 1880, Ayrton passed the Mathematical Tripos, but Cambridge did not grant her an academic degree because, at the time, Cambridge gave only certificates and not full degrees to women.

Upon her return to London, Ayrton earned money by teaching and embroidery, ran a club for working girls, and cared for her invalid sister.
She was also active in devising and solving mathematical problems, many of which were published in “Mathematical Questions and Their Solutions” from the Educational Times.
In 1884 Ayrton patented a line-divider, an engineering drawing instrument for dividing a line into any number of equal parts and for enlarging and reducing figures. Its primary use was likely for artists for enlarging and diminishing, but it was also useful to architects and engineers. From then until her death, Hertha registered 26 patents.

That year Ayrton began attending evening classes on electricity at Finsbury Technical College, delivered by Professor William Edward Ayrton, a pioneer in electrical engineering and physics, and a fellow of the Royal Society.
In 1899, she was the first woman ever to read her own paper before the Institution of Electrical Engineers. Her paper was entitled “The Hissing of the Electric Arc”. Shortly thereafter, Ayrton was elected the first female member; the next woman to be admitted to the IEE was in 1958.
She petitioned to present a paper before the Royal Society but was not allowed because of her sex, and “The Mechanism of the Electric Arc” was read by John Perry in her stead in 1901.
Ayrton was also the first woman to win a prize from the Society, the Hughes Medal, awarded to her in 1906 in honour of her research on the motion of ripples in sand and water and her work on the electric arc.

By the late nineteenth century, Ayrton’s work in the field of electrical engineering was recognised more widely. At the International Congress of Women held in London in 1899, she presided over the physical science section, and she spoke at the International Electrical Congress in Paris in 1900. Her success there led the British Association for the Advancement of Science to allow women to serve on general and sectional committees.

Ayrton’s interest in vortices in water and air inspired the Ayrton fan, used in the trenches in the First World War to dispel poison gas.
She helped found the International Federation of University Women in 1919 and the National Union of Scientific Workers in 1920.

Two years after her death in 1923, Ayrton’s lifelong friend Ottilie Hancock endowed the Hertha Ayrton Research Fellowship at Girton College, which continues today.



Stag Beetle

durer stag beetle g
What beauty is, I know not, 
though it adheres to many things.
—Albrecht Dürer

Variations on an Ascending Scale

herschelFriedrich Wilhelm Herschel (1738 – 1822) was born in the Electorate of Hanover, part of the Holy Roman Empire, to Isaac Herschel and Anna Ilse Moritzen. The family were Lutheran Christians, probably descended on his father’s side from converted Moravian Jews. His father was an oboist in the Hanover Military Band. In 1755 the Hanoverian Guards regiment, in whose band Wilhelm and his brother Jakob were engaged as oboists, was ordered to England. At the time the crowns of Great Britain and Hanover were united under King George II. As the threat of war with France loomed, the Hanoverian Guards were recalled from England to defend Hanover. After they were defeated at the Battle of Hastenbeck, Herschel’s father Isaak sent his two sons to seek refuge in England. Although his older brother Jakob had received his dismissal from the Guards, Wilhelm was accused of desertion (for which he was pardoned by George III). Wilhelm, nineteen years old, was a quick student of the English language. In addition to the oboe, he played the violin and harpsichord, and composed music. After terms as first violin and soloist in one orchestra, and first organist at a church, he was appointed director of the orchestra at Bath, with his sister often appearing as soprano soloist, and three of his brothers as musicians.  His compositions include 24 symphonies and many concertos. Six of his symphonies have been recorded in the 21st century, by the London Mozart Players.
Herschel’s music led him to an interest in mathematics and lenses. He started building his own reflecting telescopes and would spend up to 16 hours a day grinding and polishing the mirrors they used. He began to look at the planets and the stars in 1773, and on 1 March 1774 began an astronomical journal by noting his observations of Saturn’s rings and the Great Orion Nebula. From the back garden of his house in New King Street, Bath, Herschel began a systematic search among “every star in the Heavens.” His theoretical and observational work provided the foundation for modern binary star astronomy. In 1783 he gave Caroline a telescope, and she began to make astronomical discoveries in her own right, particularly of comets. She discovered or observed eight comets, eleven nebulae and, at her brother’s suggestion, updated and corrected Flamsteed’s work detailing the position of stars which was published as the British Catalogue of Stars. She was honoured by the Royal Astronomical Society for this work. From studying the proper motion of stars, Herschel was the first to realise that the solar system is moving through space, and determine the approximate direction of that movement. Studying the structure of the Milky Way he concluded that it was in the shape of a disk. He also coined the word “asteroid”, meaning star-like to describe the appearance of small moons. As part of his attempts to determine whether there were a link between solar activity and the terrestrial climate, he collected records of the price of wheat, as direct meteorological measurements were not available. He theorised that the price of wheat would be linked to the harvest and hence to the weather over the year. In 1800, Herschel was testing filters for the sun so he could observe sun spots. He found infrared radiation in sunlight by passing the light through a prism and holding a thermometer just beyond the red end of the visible spectrum. This thermometer was meant to be a control to measure the ambient air temperature in the room, but after it showed a higher temperature at that end, he ultimately concluded that there must be an invisible form of light. Herschel also used a microscope to establish that coral was not a plant, as many believed at the time, since it lacked the cell walls characteristic of plants Despite his important scientific discoveries, Herschel was not averse to wild speculation. In particular, he believed every planet was inhabited.
Chamber Symphony in F Major: II. Adagio e cantabile


Tractatus de Conclusionibus Astrolabii Bred and mylk for childeren

Lyte Lowys my sone, I aperceyve wel by certeyne evydences thyn abilite to lerne sciences touching nombres and proporciouns; and as wel considre I thy besy praier in special to lerne the tretys of the Astrelabie. Than for as moche as a philosofre saith, “he wrappith him in his frend, that condescendith to the rightfulle praiers of his frend,” therfore have I yeven the a suffisant Astrolabie as for oure orizonte, compowned after the latitude of Oxenforde; upon which, by mediacioun of this litel tretys, I purpose to teche the a certein nombre of conclusions aperteynyng to the same instrument.

A Treatise on the Astrolabe

Little Lewis my son, I perceive well by certain evidences thine ability to learn sciences touching numbers and proportions; and as well consider I thy constant prayer in special to learn the treatise of the Astrolabe. Than for as much as a philosopher saith, “He wrappth him in his friend, that condescendth to the rightful prayers of his friend”, therefore have I given thee a suffisant Astrolabe as for our horizons, compounded after the latitude of Oxford; upon which, by means of this little treatise, I purpose to teach thee a certain number of conclusions pertaining to the same instrument.
Geoffrey Chaucer (c. 1343 – 25 October 1400)
[“the firste fyndere of our fair langage,”  Thomas Occleve (c. 1368–1426)
“lodesterre … off our language,”  John Lydgate of Bury (c. 1370 – c. 1451)]

Vanishing Point

uccello,_studio_di_cavalierePaolo Uccello (1397 – 1475), born Paolo di Dono, painter and mathematician