Helen Maria Bayly, my fourth great aunt, was the second youngest of the sixteen children of Henry O’Neale Bayley (1757–1826) and Anne Penelope Bayley nee Grueber (1762–1837). Helen married a famous mathematician and astronomer. Was this an unhappy union with a man who neglected his wife in a too-zealous pursuit of his career, or was it zany, zestful, and zingy?

Helen Bayly married William Rowan Hamilton (1805–1865) on 9 April 1833 at Ballinaclough, Ireland. The marriage was announced in the Belfast Newsletter of 16 April 1833:

At Ballinaclough Church on Easter Tuesday, William Rowan Hamilton Esq. Royal Astronomer of Ireland to Helen Maria, daughter of the late Rev. Henry Bayly, Rector of Nenagh.

They had three children:

  • William Edwin Hamilton 1834–1902
  • Archibald Henry Hamilton 1835–1914
  • Helen Eliza Amelia Hamilton 1840–1870
Dunsink Observatory was established in 1783. On the right is the main building. On the left is the dome housing the 12″ Grubb refractor. William Rowan Hamilton was a director of the observatory and lived here with his family from 1827 to 1865. Photograph retrieved from geograph.ie.

William Rowan Hamilton’s biographer, Robert Perceval Graves, wrote in the 1880s of the Bayly family: “The lady whom Hamilton married in the year 1833 was a daughter of the Rev. Henry Bayly, Rector of Nenagh, in the county of Tipperary, a member of the family whose head is settled at Debsborough in that county : she was in this way connected with Lord Dunalley and with Dean Head, Dean of Killaloe, who were neighbours in the country, took an interest in the marriage, and were subsequently Hamilton’s acquaintances and correspondents. Miss Bayly’s mother, whose maiden name was Grueber, and who by her letters appears to have possessed a bright mind and amiable disposition, was at this time a widow and resided at Bayly Farm, near Nenagh. She (Anne Grueber) had many children, two of whom were married to brothers, Mr. William and Mr. Henry Rathborne, whose country-houses, Scripplestown and Dunsinea, were in immediate neighbourhood to the Observatory. With the elder of these sisters, Mrs. William Rathborne of Scripplestown, Helen Bayly was often a guest.”

There seems to be considerable disagreement among biographers of William Hamilton about the success or otherwise of his marriage.

In their “Math and mathematicians: the history of math discoveries around the world” Lawrence Baker and Leonard Bruno, portray it as a dismal failure:

[Having had two marriage proposals rejected, in 1833] “Hamilton married Helen Marie Bayly, a country preacher’s daughter. Although they had three children together, his wife proved not only to be chronically ill but extremely pious, shy, and timid. Since she was also unable to run a household, Hamilton’s married life was both difficult and unhappy.”

Retrieved through archive.org (requires free registration)

On the other hand, Anne van Weerden, a Dutch researcher, disagrees strongly with the description of Hamilton by various biographers as “an unhappily married alcoholic”. She notes that his own account of the discovery of the quaternions [an extension of the complex numbers], “…which he made when he was walking with his wife, breathes such a peaceful atmosphere that it became the inducement to investigate how an alleged unhappy marriage could lead to such a circumstance.” In her “A Victorian Marriage : Sir William Rowan Hamilton” (Weerden, Anne . A Victorian Marriage: Sir William Rowan Hamilton. 2017. Internet Archive BookReader.), she argues that “…he did have a good marriage, and that according to current standards he was by no means an alcoholic.”

Images of Sir William Rowan Hamilton and his wife Helen, Lady Hamilton retrieved from http://www.annevanweerden.nl/HamiltonPhotoPage.html

Anne van Weerden was surprised by part of a letter Hamilton wrote to his son Archibald on the 5th of August 1865 while “the hand which penned it was at the time tremulous with approaching death.” The letter triggered her research and she argues that the dark view on this marriage as having been an unhappy one, or even a burden for Hamilton, does not seem to fit in with Hamilton’s recollection of how he found the quaternions:

But on the 16th day of the same month – which happened to be a Monday, and a Council day of the Royal Irish Academy – I was walking in to attend and preside, and your mother was walking with me, along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an undercurrent of thought was going on in my mind, which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth, the herald (as I foresaw, immediately) of many long years to come of definitely directed thought and work, by myself if spared, and at all events on the part of others, if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse – unphilosophical as it may have been – to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula with the symbols, i, j, k; namely, i² = j² = k² = ijk = −1 , which contains the Solution of the Problem, but of course, as an inscription, has long since mouldered away. A more durable notice remains, however, on the Council Books of the Academy for that day (October 16th, 1843), which records the fact, that I then asked for and obtained leave to read a Paper on Quaternions, at the First General Meeting of the Session: which reading took place accordingly, on Monday the 13th of the November following.

Broome Bridge (also known as Broom Bridge and called Brougham Bridge by Hamilton, perhaps in jest) on the Royal Canal in 2007. Renowned as the location where, in 1843, the Irish mathematician, physicist and astronomer William Rowan Hamilton came up with an important mathematical equation.  He was walking from the observatory to
Dublin, because he had to preside the monthly meeting. Apparently, his wife had joined him when he was walking along the canal, he had not noticed where she came from. He scratched the formula on the stone work, perhaps to celebrate it. Photograph retrieved from georgraph.ie.
The plaque on Broome Bridge commemorating William Rowan Hamilton’s discovery. The the fundamental formula for quaternion multiplication reads i² = j² = k² = ijk = −1 .
Dunsink Observatory is about 10 kilometers north-west of Dublin City centre.
There is an annual Hamilton Walk on 16 October from the Observatory to Broome Bridge to commemorate the discovery of the non-commutative algebraic system known as quaternions.

Having read Anne van Weerden’s essay and her other writings I am convinced by her arguments that William Rowan Hamilton was happily married to his wife Helen. William Rowan Hamilton’s zeal for his work was not interrupted by his wife. She ran her household around him and did not interrupt him with demands to come to dinner. Perhaps this was the foundation of their zero-problem marriage. Each had their zone; one zigged, the other zagged.

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